Mathematics College

## Answers

**Answer 1**

The **expression **that represents the **distance **between point J and point K is |-10| + |5|

Calculating the distance between two points

From the question, we are to determine the **expression **that represents the **distance **between **point **J and **point **K.

From the graph,

Point J and Point K form a horizontal line. That is, the line is parallel to the x-axis.

To determine the distance between point J and point K, we can simply add the absolute value of the x-coordinates of point J and point K.

The x-coordinate of point J is = -10

The x-coordinate of point K is = 5

Thus,

The distance between point J and point K = |-10| + |5|

The distance between point J and point K = 10 + 5

The distance between point J and point K = 15.

Hence, the **expression **is |-10| + |5|

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## Related Questions

consider the function given by (1/4) for . find the value of for which is a probability mass function.

### Answers

The value of k that makes p(x) a **probability mass function** is 3.

To be a **probability mass function**, the sum of all probabilities must be equal to 1. Since the function is given by p(x) = k·(1/4), the sum of probabilities from x = 1 to infinity is:

∑p(x) = k·(1/4) + k·(1/4) + k·(1/4) + ... = k/4 ∑1

where ∑1 denotes the **sum **of all integers starting from 1. This is an infinite **geometric series** with first term 1 and common ratio 1/4, so:

∑p(x) = k/4 ∑1 = k/4 · (1/(1-1/4)) = k/3

For p(x) to be a probability mass function, we need ∑p(x) = 1, so:

k/3 = 1

Solving for k, we get:

k = 3

Therefore, the value of k for which p(x) is a probability mass function is 3.

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--The given question is incomplete, the complete question is given

"Consider the function given by p(x) = k·(1/4) for x = 1, 2, 3, .... Find the value of k for which pis a probability mass function. (Enter a numerical value, only.)"

Which number produces a rational number when multiplied by 7/8

### Answers

The answer of the given question based on the **rational number** is , any rational number can be multiplied by 7/8 to produce another rational number.

What is Product?

The product is the result obtained when two or more numbers, variables, or **expressions **are multiplied together. It is one of the basic arithmetic operations and is denoted by the symbol "×" or "*". For example, the product of 2 and 3 is 6, which is obtained by multiplying 2 and 3. The product of a and b is ab, which means multiplying the value of a with the value of b. The product of two polynomials is obtained by multiplying each term of one polynomial with each term of the other **polynomial**, and then simplifying the result by combining like terms.

Any rational number multiplied by 7/8 will result in a rational number. For example, if we multiply 2/3 by 7/8, we get:

(2/3) * (7/8) = (27) / (38) = 14/24 = 7/12

Since 2/3 and 7/8 are both rational numbers, their product, 7/12, is also a rational number.

Therefore, any rational number can be multiplied by 7/8 to produce another rational number.

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A prism in completely filled with 2304 cubes that have edge length of 1/4 cm. what is the volume of the prism?

Enter your answer in the box?

_____ cm^3

### Answers

**Answer:**

The volume of a cube with edge length of 1/4 cm is (1/4)^3 = 1/64 cm^3. Since the prism is completely filled with 2304 such cubes, the volume of the prism is 2304 * (1/64) = 36 cm^3.

**Step-by-step explanation:**

lyn contributes 15% of the total cost of her individual health care .this is a 105.50 deduction from each of her biweekly paychecks

### Answers

The total value of her **individual coverage** for the year is $ 16880.** **

Individual coverage:

Individual coverage typically refers to a health insurance policy that provides **medical **coverage for a single individual. This is in contrast to a family or group health insurance policy that covers multiple individuals under one **policy**.

Here we have

Iyn contributes 15% of the total cost of her healthcare

This is a 105.50 **deduction** from each of her biweekly paychecks

This implies Iyn pays 105.50 for 2 weeks

The amount paid by Iyan for 4 weeks i.e 1 month = 2 × 105.50 = 211

Amount paid for 1 year = 12 × 211 = 2532

Let Iyn's annual expenditure = x

From the given data,

lyn contributes 15% of annual expenditure

=> 15% of x = 2532

=> [0.15]x = 2532

=> x = 2532/0.15

=> x = 16880

Therefore

The total value of her **individual coverage** for the year is $ 16880.

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Complete Question:

lyn contributes 15% of the total cost of her individual health care. This is a $ 105.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?

exercise 4.24. we roll a fair die repeatedly and keep track of the observed frequencies of the outcomes 1, 2, . . . , 6. (a) show that the probability of seeing at least 17% fours converges to zero as the number of rolls tends to infinity. (b) let an be the event that after n rolls, the frequencies of all six outcomes are between 16% and 17%. show that for a large enough number of rolls, the probability of an is at least 0.999.

### Answers

(a) **The probability** of seeing at least 17% fours converges to zero as the number of rolls tends to infinity.

(b) For a large enough number of rolls, the probability of all **frequencies** being between 16% and 17% is at least 0.999.

(a) Let X be the number of fours observed in n rolls of the die, then X follows a** binomial distribution** with parameters n and 1/6. The expected value and variance of X are given by E(X) = n/6 and Var(X) = 5n/36, respectively. Using Chebyshev's inequality, we have

P(X ≥ 0.17n) ≤ Var(X)/(0.17n - E(X))²

≤ 5n/36 / (0.17n - n/6)²

= 1/(9n/425 - 17/100)².

As n → ∞, the** denominator** of the last expression goes to zero, and hence the probability of seeing at least 17% fours goes to zero.

(b) Let Y1, Y2, ..., Y6 be the frequencies of the outcomes 1, 2, ..., 6 after n rolls of the die. Then Yi's follow a **multinomial distribution **with parameters n and (1/6, 1/6, ..., 1/6). Let μ = n/6 be the expected frequency of each outcome. We need to show that P(|Yi - μ| ≤ μ/6 for all i) ≥ 0.999 for large enough n.

Using the** Chernoff bound**, we have

P(|Yi - μ| ≥ μ/6) ≤ 2 exp(-μ/72)

for any i. Hence,

P(|Yi - μ| ≤ μ/6 for all i) ≥ 1 - 12 exp(-μ/72).

For n ≥ 2000, we have μ ≥ 16.67 and hence exp(-μ/72) ≤ 0.008. Therefore,

P(|Yi - μ| ≤ μ/6 for all i) ≥ 1 - 12 exp(-μ/72) ≥ 0.999.

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There are four pieces of mail in Mr. Gilbert's mailbox: a rebate check from a battery purchase for $50.00, a bill from the phone company for $56.89, a bill from the electric company for $53.16, and a tax refund check for $61.05.

### Answers

**Answer:**

61.05 > 50.00 > −53.16 > −56.89

**Step-by-step explanation:**

hope this helps!

2. Which shows a statistical question regarding a data set?

O What is the total number of oceans in the world?

What is the total rainfall for the year?

O What is the total number of miles between the same two cities?

O What is the total number of hours in a day?

### Answers

What is the total rainfall for the year? This is a **statistical question **because it involves collecting and analyzing data (rainfall measurements) to arrive at an answer. The other options are not statistical questions because they are either **factual** or do not involve collecting data.

What is a statistical question, and how is it different from a factual question?

A statistical question is a question that can be answered by collecting and **analyzing data**, while a factual question seeks to establish a fact or piece of information that is already known.

Why is it important to ask statistical questions when working with data sets?

Statistical questions allow us to analyze and draw meaningful conclusions from a data set.

By asking statistical questions, we can identify** patterns**, **trends**, and relationships in the data, which can help us make informed decisions or **predictions.**

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If BC represents 10% what is the length of a line segment that is 100%?

### Answers

On the basis of the available data, **proportional **reasoning must be used to determine the length of a line segment that represents 100%.. the length of the line segment that represents [tex]100[/tex]% is [tex]80 cm[/tex].

What is the length of a line segment?

To find the length of a line **segment **that represents [tex]100[/tex]%, we need to use proportional reasoning based on the given information.

Here, we know that the line segment BC represents 10%. Let's denote the **length **of the line segment that represents [tex]100[/tex]% as x.

We can set up a proportion as follows:

[tex]BC/10[/tex] % [tex]= x/100[/tex]%

We can simplify this **proportion **by converting the percentages to decimals:

[tex]BC/0.1 = x/1[/tex]

Multiplying both **sides **by 1/0.1, we get:

[tex]BC\times 10 = x[/tex]

Since the length of BC is 8 cm, we can **substitute **this value in the above equation:

[tex]8\times 10 = x[/tex]

[tex]x = 80 cm[/tex]

Therefore, the length of the line segment that **represents **[tex]100[/tex]% is [tex]80[/tex] cm.

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The given question is incomplete the complete question is given below:

· B__________8cm___________C· If line BC represents 10% what is the length of a line segment that is 100% explain

The average credit card debt owed by Americans is $6375 , with a standard deviation of $1200 . Suppose a random sample of 36 Americans is selected. Identify each of the following:

Provide your answer below:

U= $

o=$

n=

ux=$

ox=$

### Answers

to identify each of the **values in this problem**, we use the symbols[tex]$\mu$, $\sigma$, $n$, $\bar{x}$, and $s$.[/tex]We are given the values of [tex]$\mu and \sigma$[/tex], and we need to calculate the values of [tex]$\bar{x} and s$[/tex] if we want to use them in any calculations.

In this problem, we are given information about the **average credit card **debt owed by Americans. Specifically, the population mean is [tex]$\mu=6375$[/tex]and the population **standard deviation** is [tex]$\sigma=1200$[/tex]. Additionally, a sample of size [tex]$n=36$[/tex] is selected.

To identify each of the following, we can use the following symbols:

[tex]1 $\mu$: population mean\\2. $\sigma$: population standard deviation\\3. $n$: sample size\\4. $\bar{x}$: sample mean\\5. $s$: sample standard deviation[/tex]

Using these symbols, we can identify each of the following:

1[tex]$\mu=6375$:[/tex] This is the **population mean,** which represents the average credit card debt owed by all Americans.

2. [tex]$\sigma=1200$[/tex] : This is the population standard deviation, which represents the variability in credit card debt owed by Americans.

3.[tex]$n=36$[/tex]: This is the sample size, which represents the number of Americans included in the sample.

4. [tex]$\bar{x}$[/tex] : This is the sample mean, which represents the average credit card debt owed by the individuals in the sample. We don't have the value of [tex]$\bar{x}$[/tex]in this problem, but we can use the formula[tex]$\bar{x}=\frac{\sum_{i=1}^n x_i}{n}$[/tex] to calculate it if we have the individual credit card debt values [tex]$x_1, x_2, ..., x_n$.[/tex]

5 [tex]. $s$[/tex]: This is the sample standard deviation, which represents the variability in credit card debt owed by the individuals in the sample. We don't have the value of s in this problem, but we can use the formula [tex]$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar{x})^2}{n-1}}$[/tex] to calculate it if we have the individual credit card debt values[tex]$x_1, x_2, ..., x_n$[/tex]and the sample mean [tex]$\bar{x}$[/tex].

In summary, to identify each of the values in this problem, we use the symbols[tex]$\mu$, $\sigma$, $n$, $\bar{x}$, and $s$.[/tex]We are given the values of [tex]$\mu and \sigma$[/tex], and we need to calculate the values of [tex]$\bar{x} and s$[/tex] if we want to use them in any calculations.

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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

### Answers

For the given area of **rectangle**, the equations can be used to solve for y, the length of the room are: y(y+5) = 750, [tex]y^2 + 5y - 750 = 0[/tex] and (y+25)(y-30) = 0.

**What is rectangle?**

A rectangle is a flat shape that has four sides and is **two-dimensional**. It is defined by having opposite sides that are parallel and equal in length, and all four of its angles are right angles, which means they measure 90 degrees.

The **equation** that can be used to solve for y, the length of the room, is:

y(y+5) = 750

This equation represents the area of the rectangular room, where y is the length of the room and y+5 is the **width** of the room.

Expanding the equation, we get:

[tex]y^2 + 5y - 750 = 0[/tex]

This is a **quadratic** equation that can be solved using factoring, completing the square, or the quadratic formula.

Therefore, the options that can be used to solve for y are:

y(y+5) = 750

[tex]y^2 + 5y - 750 = 0[/tex]

(y+25)(y-30) = 0

Option 1 is the same as the given equation. Option 2 is obtained by rearranging the terms of the equation. Option 3 is obtained by factoring the quadratic equation.

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1 Determine whether the following graph represents proportional relationship. O proportional O non proportional 7.RP.2

### Answers

A non-**proportional **graph is a type of graph in which the scale of one or both axes is not proportional to the values being graphed. In a non-proportional graph. Thus, option **B **is correct.

What is the non-proportional graph?

The distance between the values on the **axis **does not correspond to the actual numerical difference between those values.

For example, consider a graph that shows the **number **of books read by a group of **people **over the course of a year.

For example, a non-proportional graph might have unequal spacing between the tick marks on the x- or y-axis, or might use a logarithmic scale that compresses or **stretches **the data. This can make it difficult to accurately interpret the data or compare different data points.

If the scale on the y-axis is not proportional, it might show equal intervals for each unit of **measurement**, even though the actual numerical difference between those intervals may not be the same.

Therefore, A non-proportional graph is a type of graph in which the scale of one or both axes is not proportional to the **values** being graphed. In a non-proportional graph.

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Given that a bag of M & Ms has 21 brown candies, 15 orange candies, 10 yellow candies, 14 red candies, and 5 green candies, find the following probabilities. Enter all answers as reduced fraction. Do not use any spaces in your answers. What is the probability that a red M & M is randomly chosen from the bag? P( Answer R )= Answer 14/65 What is the probability that an orange M & M is randomly chosen from the bag? P( Answer O )= Answer 3/13 What is the probability of choosing a red M & M, putting it back, and then choosing a brown M & M? P( Answer R and B )= Answer 7/13 What is the probability of randomly choosing a green or yellow M & M? P( Answer G or Y )= Answer 3/13 What is the probability of choosing a M & M that is not brown? P( Answer B' )= Answer 44/65 What is the probability of choosing a green M & M, eating it, and then choosing a brown M & M? P( Answer G and B )= Answer 13/65 What is the probability of choosing a red M & M on the second try given that the first M & M was red and it was eaten? P( Answer R | R )= Answer 13/64

### Answers

The **probability** of choosing a red M&M on the second try given that the first M&M was red and it was eaten is:

P(R | R) = 13/64

**What is probability?**

**Probability** is the study of the chances of **occurrence** of a result, which are obtained by the ratio between favorable cases and possible cases.

What is the probability that a red M&M is randomly chosen from the bag?

There are 14 red candies out of a total of 65 candies in the bag. So the probability of randomly choosing a red M&M is:

P(R) = 14/65

What is the probability that an orange M&M is randomly chosen from the bag?

There are 15 orange candies out of a total of 65 candies in the bag. So the probability of randomly choosing an orange M&M is:

P(O) = 15/65 = 3/13

What is the probability of choosing a red M&M, putting it back, and then choosing a brown M&M?

The probability of choosing a red M&M on the first draw is 14/65. Putting it back doesn't change the number of candies in the bag, so the probability of choosing a brown M&M on the second draw is 21/65.

So the probability of choosing a red M&M, putting it back, and then choosing a brown M&M is:

P(R and B) = (14/65) x (21/65) = 294/4225 = 42/65

What is the probability of randomly choosing a green or yellow M&M?

There are 10 yellow candies and 5 green candies in the bag, for a total of 15 candies that are either green or yellow.

So the probability of choosing a green or yellow M&M is:

P(G or Y) = 15/65 = 3/13

What is the probability of choosing an M&M that is not brown?

There are 44 candies that are not brown out of a total of 65 candies in the bag.

So the probability of choosing an M&M that is not brown is:

P(B') = 44/65

What is the probability of choosing a green M&M, eating it, and then choosing a brown M&M?

The probability of choosing a green M&M on the first draw is 5/65. After eating it, there are now 64 candies in the bag. The probability of choosing a brown M&M on the second draw is 21/64.

So the probability of choosing a green M&M, eating it, and then choosing a brown M&M is:

P(G and B) = (5/65) x (21/64) = 13/416

What is the probability of choosing a red M&M on the second try given that the first M&M was red and it was eaten?

Since the first M&M was red and was eaten, there are now 64 candies in the bag, and 13 of them are red.

Hence, the **probability** of choosing a red M&M on the second try given that the first M&M was red and it was eaten is:

P(R | R) = 13/64

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There are 50 multiple choice questions with four choices per question. If I do the test randomly, what is the probability I will get a passing grade on the quiz

### Answers

Thus, the **probability **of passing the test via random guessing is roughly 0.184, or 18.4%.

**How does probability work?**

the likelihood that a sp**ecific occurrence** will occur. (2): an area of mathematics involving the investigation of probabilities, defined as the ratio of a number of alternatives in an exhaustive collection of equally probable scenarios that cause a report “ to the entirety of the potential **outcomes**.

A passing grade itself determines the likelihood of completing the quiz with a passing score. Assume that 30 out of 50 accurate answers are required for a passing grade, or 60%.

For each question, there is a 1/4, or 0.25, chance that the correct answer will be selected at random. The likelihood of getting a question wrong is 3/4, or 0.75.

The probability of getting exactly 30 correct answers out of 50 is given by the binomial distribution with parameters n=50 and p=0.25:

P(X = 30) = (50 choose 30) × (0.25)³⁰ × (0.75)²⁰

Where (50 choose 30) is the number of ways to choose 30 questions out of 50.

P(X = 30) ≈ 0.114

This means that the probability of getting exactly 30 correct answers out of 50 by random guessing is about 0.114 or 11.4%.

However, to pass the quiz, we need to get at least 30 correct answers. The probability of getting 30 or more correct answers is the sum of the probabilities of getting exactly 30, 31, 32, ..., 50 correct answers:

P(X ≥ 30) = P(X = 30) + P(X = 31) + ... + P(X = 50)

With the aid of a calculator and statistical package, we can determine:

P(X ≥ 30) ≈ 0.184

This means that the probability of passing the quiz by random guessing is about 0.184 or 18.4%.

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consider the following statement. the department of motor vehicles reports that the proportion of all vehicles registered in a certain state that are imports is 0.21. (a) is the number that appears in boldface in this statement a sample proportion or a population proportion? - sample proportion - population proportion (b) Which of the following use of notation is correct, p = 0.21 or rho = 0.21? (Hint: See definitions and notation on page 403.) - p =0.21 - rho = 0.21

### Answers

The, rho = 0.21 would not be an appropriate use of notation in this context.

When using notation, it is important to use the correct symbols and **definitions**.Consider the following statement:

The Department of Motor Vehicles reports that the **proportion **of all vehicles registered in a certain state that are imports is 0.21.

Based on this statement, the number that appears in boldface is a **population **proportion because it refers to the proportion of all vehicles **registered **in the state that are imports.

In contrast, a sample proportion would refer to the proportion of a smaller subset of vehicles that are imports.

According to the definitions and notation on page 403, the correct use of notation in this case is p = 0.21.

This is because p is used to denote a proportion in a sample or population.

On the other hand, rho (ρ) is used to denote a population correlation coefficient.

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the probability distribution for the number of goals the lions soccer team makes per game is given below. number of goals probability 0 0.30 1 0.35 2 0.15 3 0.10 4 0.10 what is the probability that in a given game the lions will score less than 3 goals?

### Answers

The** probability **that in a** **given game the lions will score less than 3 goals is 0.80.

The** probability** distribution for the number of goals the lions soccer team makes per game is given below:

number of goals probability 0 0.30 1 0.35 2 0.15 3 0.10 4 0.10. The probability that in a given game the lions will score less than 3 goals is 0.80.

To find the probability that in a given game the lions will **score** less than 3 goals, we need to add up the probabilities for scoring 0, 1, or 2 **goals**.

P(Less than 3 goals) = P(0 goals) + P(1 goal) + P(2 goals)

We have the** following** probabilities:

P(0 goals) = 0.30

P(1 goal) = 0.35

P(2 goals) = 0.15

**Therefore**,

P(Less than 3 goals) = P(0 goals) + P(1 goal) + P(2 goals)

= 0.30 + 0.35 + 0.15

= 0.80

Thus, the probability that in a** **given game the lions will score less than 3 goals is 0.80.

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Write the equation of a line that is parallel to y=−7 and that passes through the point (7,5)

### Answers

According to the solution we have come to find that, The equation of the line that is **parallel** to y = -7 and passes through the point (7,5) is y = 5.

**what is mean by parallel lines?**

Parallel lines are two or more lines that are always the same distance apart and never **intersect**. In other words, they have the same slope and they will never meet, no matter how far they are extended in both directions. Parallel lines always remain equidistant from each other and never touch or intersect, even if they are extended to infinity.

For example, in a **Cartesian** coordinate system, two lines are parallel if and only if they have the same slope. If the slope of one line is m1 and the slope of another line is m2, then the two lines are parallel if m1 = m2.

The given equation is y = -7, which is a** horizontal** line parallel to the x-axis. Since we need to find the equation of a line parallel to this line, the **slope **of the new line will also be zero.

To find the equation of the new line, we need to use the point-slope form of the equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values of the given point and slope, we get:

y - 5 = 0(x - 7)

y - 5 = 0

y = 5

So, the equation of the line that is parallel to y = -7 and passes through the point (7,5) is y = 5.

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What is the area of the polygon given below?

4

4

24

11

OA. 340 square units

OB. 296 square units

C. 94 square units

D. 264 square units

### Answers

A) 340 square units, just separate different parts of the polygon then find those shapes’ areas and then add the areas together

11) Each morning Anthony and Chris catch the bus to school. The

probability that Anthony catches the bus is 0.9 and for Chris it is 0.7.

a) Copy and complete the tree diagram.

b) Calculate the probability that on a given day:

i) They both catch the bus,

ii) Anthony catches the bus but Chris does not,

iii) Neither catch the bus,

iv) at least one of them catch the bus.

### Answers

Using the **tree diagram**, the **probability **that they both catch the bus is 0.63, the probability that Anthony catches the bus but Chris does not is 0.27, the probability that neither catches the bus is 0.03, and the probability that at least one of them catches the bus is 0.94.

What is the tree diagram?

a. Anthony Chris

/ \ / \

Bus No Bus Bus No Bus

/ \ / \ / \ / \

0.9 0.1 0.3 0.7 0.7 0.3 0.3 0.7

b. Using the **tree diagram**, we can calculate the following probabilities:

i) Probability that they both catch the bus:

P(Anthony catches the bus and Chris catches the bus) = P(Anthony catches the bus) * P(Chris catches the bus)

P = 0.9 * 0.7 = 0.63

ii)Probability that Anthony catches the bus but Chris does not:

P(Anthony catches the bus and Chris does not catch the bus) = P(Anthony catches the bus) * P(Chris does not catch the bus)

P = 0.9 * 0.3 = 0.27

iii) **Probability** that neither catches the bus:

P(Neither catches the bus) = P(Anthony does not catch the bus) * P(Chris does not catch the bus)

P = (1 - 0.9) * (1 - 0.7)

P = 0.03

iv) Probability that at least one of them catches the bus:

P(At least one catches the bus) = 1 - P(Neither catches the bus)

P = 1 - 0.06

P = 0.94

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A company plans on offering a new smartphone in four colors: black, white, silver, and gold. They suspect that 55% of customers prefer black, 20% prefer white, 10% prefer silver, and 15% prefer gold. They take a random sample of 33 potential customers to see what color they prefer. Here are the results:

Preferred color Black White Silver Gold

Observed counts 10 10 4 9 The company wants to use these results to carry out a x^2 goodness-of-fit test to determine if the sample disagrees with the expected distribution. Which count(s) make this sample fail the large counts condition for this test? Choose 2 answers: a. The observed count of people who prefer white. b. The observed count of people who prefer silver. c. The observed count of people who prefer gold. d. The expected count of people who prefer silver.

e. The expected count of people who prefer gold.

### Answers

The large counts condition for a chi-square **goodness-of-fit test** requires that the expected count for each category is at least 5.

To determine which counts make the sample fail this condition, we need to calculate the expected counts for each category:

Expected count = sample size * expected **proportion**

Expected count for black = 33 * 0.55 = 18.15

Expected count for white = 33 * 0.20 = 6.6

Expected count for silver = 33 * 0.10 = 3.3

Expected count for gold = 33 * 0.15 = 4.95

The observed count of people who prefer black is 10, which is less than the expected **count **of 18.15, but this does not violate the large counts condition because it is still greater than 5. The observed count of people who prefer silver is 4, which is less than the expected count of 3.3. This count **violates **the large counts condition. The observed count of people who prefer gold is 9, which is less than the expected count of 4.95. This count also violates the large counts **condition**. Therefore, the counts that make this sample fail the large counts condition are (b) the observed count of people who prefer silver and (e) the expected count of people who prefer **gold**.

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In the figure below, XY is the mid segment of trapezoid ABCD. Find the length of XY

### Answers

**Answer: The midsegment is 12 for x to y**

**Step-by-step explanation:**

**15+9=24 divided by 2 is 12**

Set up a triple integral two ways, one in cylindrical coordinates and one in spherical coordinates to find the volume inside the cone z= √(x^2+y^2) and below the sphere x^2+y^2+z^2 = R^2

### Answers

The volume element in **spherical **coordinates is dV = ρ[tex]^2[/tex]*sin(φ)*dρ*dφ*dθ.

In both cases, you would evaluate the triple **integral **to find the volume inside the cone and below the sphere.

To find the volume inside the cone[tex]z = \sqrt{(x^2 + y^2)}[/tex] and below the sphere [tex]x^2 + y^2 + z^2 = R^2,[/tex]

we'll set up triple integrals in both **cylindrical **and spherical coordinates.

Cylindrical Coordinates:

In cylindrical coordinates,

we have x = r*cos(θ), y = r*sin(θ), and z = z.

The volume element in cylindrical coordinates is dV = r*dz*dr*dθ.

First, let's rewrite the cone and sphere equations in cylindrical coordinates:

Cone:[tex]z = \sqrt{(r^2)}[/tex]

Sphere:[tex]r^2 + z^2 = R^2[/tex]

Now, set up the triple integral in cylindrical coordinates:

∫∫∫ r*dz*dr*dθ

with bounds:

θ: [0, 2π]

r: [0, R*cos(θ)]

z: [0, r]

Spherical Coordinates:

In spherical coordinates, we have x = ρ*sin(φ)*cos(θ), y = ρ*sin(φ)*sin(θ), and z = ρ*cos(φ).

The volume element in **spherical **coordinates is dV = ρ[tex]^2[/tex]*sin(φ)*dρ*dφ*dθ.

Now, let's rewrite the cone and sphere equations in spherical coordinates:

Cone: cos(φ) = sin(φ)

Sphere: ρ = R

Now, set up the triple integral in spherical **coordinates**:

∫∫∫ ρ[tex]^2[/tex]*sin(φ)*dρ*dφ*dθ

with bounds:

θ: [0, 2π]

φ: [0, π/4]

ρ: [0, R].

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Show work

1. Convert 12 hours=____seconds

2. Show your work. A substance has a freezing point of -20C. What is the freezing point of the substance in degrees Fahrenheit (round your answer to the nearest tenth).

### Answers

Problem 1

[tex]12 \text{ hours} = 12 \text{ hours} * \frac{60 \text{ minutes}}{ 1 \text{ hour }}* \frac{60 \text{ seconds}}{ 1 \text{ minute }}\\\\12 \text{ hours} = \frac{12*60*60}{1*1} \text{ seconds}\\\\12 \text{ hours} = 43200 \text{ seconds}\\\\[/tex]

Answer: 43200 seconds

==================================================

Problem 2

F = 1.8*C + 32

F = 1.8*(-20) + 32

F = -36 + 32

F = -4

Answer: -4 degrees Fahrenheit

**Answer:**

THE ANSWER IS 3600

**Step-by-step explanation:**

THE ANSWER IS 3600

1 MINUTES IS 60 SECONDS

60×60=3600

The 13th and 7th terms of an arithmetic sequence are 15 and 51 respectively. How many terms are in this sequence if the last term is -507.

### Answers

There are 93 terms in the **sequence**.

What is the arithmetic sequence?

An **arithmetic sequence **is a sequence οf numbers in which each term after the first is οbtained by adding a **cοnstant** d, called the cοmmοn difference, tο the preceding term. The general fοrm οf an arithmetic sequence is:

a, a + d, a + 2d, a + 3d, ...

Let's use the formula for the nth term of an arithmetic sequence to set up two equations:

a13 = a1 + 12d = 15 ...(1)

a7 = a1 + 6d = 51 ...(2)

where a1 is the first term of the sequence, d is the common difference between terms.

Subtracting equation (2) from (1), we get:

6d = -36

d = -6

Substituting d = -6 in equation (2), we get:

a1 = 87

Now we can find the number of terms, n, using the formula:

an = a1 + (n-1)d

Substituting a1 = 87, d = -6, and an = -507, we get:

-507 = 87 + (n-1)(-6)

Simplifying and solving for n, we get:

n = 93

Hence, there are 93 terms in the sequence.

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Write the absolute value equations in the form | x - b |= c (where b is a number and C can be either a number or an expression) that has the following solution set. All numbers such that x <= 5

### Answers

The** absolute value **equations in the form | x - b |= c is x-5<=0

**What is absolute value?**

A number's** absolute value** is defined as how far it is from the origin of a number line. The symbol |a|, which represents the size of any **integer **"a," is used to represent it. Any** **integer's absolute value is a real number, regardless of its sign or whether it is positive or negative. Two vertical lines are used to depict the modulus of an as |a|.

Given,

The** absolute **value equations in the form | x - b |= c

Where b is a number and C can be either a number or an** expression**

The equation must be written down for x <= 5

All numbers will be such that x <= 5

So, x-5<=0

Hence the correct **answer **is x-5<=0.

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Differentiate Implicitly to find d^2y/dx^2

5x^3-y^3=4

### Answers

The second **derivative** of y with respect to x is [tex]10x -\frac{25x^4}{y^3}[/tex]

**What is derivation?**

Derivation, in mathematics, is the process of finding the **rate** of change of a function with respect to an independent variable. This process is also known as differentiation. Derivatives are used to analyze the behavior of **functions** and to solve problems involving rates of change, optimization, and approximation.

To find [tex]\frac{d^2y}{dx^2}[/tex] using implicit differentiation, we need to differentiate the equation twice with respect to x.

First, we differentiate both sides of the equation with respect to x using the chain rule:

[tex]\frac{d}{dx} (5x^3 - y^3) = \frac{d}{dx} (4)[/tex]

[tex]15x^2 - 3y^2 \frac{dy}{dx} =0[/tex]

Next, we differentiate this expression with respect to x again, using the product rule and the **chain rule**:

[tex]\frac{d}{dx} (15x^2) - \frac{d}{dx} (3y^2 (\frac{dy}{dx} )) = \frac{d}{dx} (0)[/tex]

[tex]30x - 3(\frac{dy}{dx} )^2 - 3y (\frac{d^2y}{dx^2} ) = 0[/tex]

Simplifying this equation and solving for [tex]\frac{d^2y}{dx^2}[/tex], we get:

[tex]d^2y/dx^2 = (30x - 3(dy/dx)^2) / (3y)[/tex]

Now we need to substitute the first derivative, dy/dx, into this equation. We can find dy/dx by rearranging the **equation** we obtained from the first differentiation:

[tex]15x^2 - 3y^2 (dy/dx) = 0[/tex]

[tex]dy/dx = (5x^2) / y[/tex]

Substituting this **expression** into the equation for [tex]d^2y/dx^2[/tex], we get:

[tex]d^2y/dx^2 = (30x - 3(5x^2)^2) / (3y^3)[/tex]

Simplifying this expression, we get:

[tex]d^2y/dx^2 = (30x - 75x^4) / (3y^3) = 10x - 25x^4 / y^3[/tex]

Therefore, the second derivative of y with respect to x is [tex]10x - 25x^4 / y^3.[/tex]

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Question 1 Which of the following order cycle lengths would require the buyer to hold the most total inventory during lead time? 10 days, +/4 days 10 days, +/- 2 days 9 days, +/-3 days 8 days, +/-5 days

### Answers

The **order cycle length **that would require the buyer to hold the most total inventory during lead time is 8 days with [tex]\pm[/tex] 5 days of variation, as it has the widest range of variation, and thus, the most variability to be covered by safety stock.

The order cycle length and the **variability **in demand and lead time both affect the amount of inventory that a buyer needs to hold during lead time. The longer the order cycle length, the more inventory the buyer needs to hold during lead time to cover demand until the next order arrives. On the other hand, the greater the variability in demand and lead time, the more safety stock the buyer needs to hold to avoid **stockouts**.

We must take into account both the order cycle length and the fluctuation in demand and lead time to determine which of the mentioned order cycle lengths would need the buyer to keep the highest total **inventory** during lead time.

The order cycle lengths are:

10 days, [tex]\pm[/tex] 4 days

10 days, [tex]\pm[/tex] 2 days

9 days, [tex]\pm[/tex] 3 days

8 days, [tex]\pm[/tex] 5 days

The variability in **demand **and lead time is greater in the orders with wider ranges of variation. Therefore, we can calculate the range of variation for each order cycle length by adding the maximum variation in demand and the maximum variation in lead time:

10 days, [tex]\pm[/tex] 4 days: range of variation = 4 + 4 = 8 days

10 days, [tex]\pm[/tex] 2 days: range of variation = 2 + 2 = 4 days

9 days, [tex]\pm[/tex] 3 days: range of variation = 3 + 3 = 6 days

8 days, [tex]\pm[/tex] 5 days: range of variation = 5 + 5 = 10 days

Hence, the order cycle length with the greatest range of variation, and hence the most variability that needs to be covered by safety stock, is 8 days with [tex]\pm[/tex] 5 days of fluctuation. This order cycle length would need the buyer holding the highest total inventory throughout lead time.

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What effect does the order of events create in the scene?

A.

At the beginning, Rosalind convinces Orlando she is a man who can cure him of loving Rosalind, so at the end, when she says he must call her Rosalind and woo her, it creates surprise.

B.

As Rosalind describes what her uncle taught her in the past about how to recognize a man in love, it creates tension because in the present, Orlando is in love.

C.

Rosalind relates a past event in great detail, telling how she cured a man of love, so when Orlando agrees to come to her cottage, it creates suspense because we don't know if she can do it again.

D.

When Rosalind first meets Orlando and tells him a man has been leaving poems in the forest, it creates mystery as she tries to find out who the poet is.

### Answers

The effect of the order of events creates in the scene is to create surprise, tension, suspense and mystery. This is evident in the play As You Like It by William Shakespeare where the character **Rosalind **convinces Orlando that she is a man who can cure him of loving Rosalind and at the end, when she says he must call her Rosalind and woo her, it creates surprise. The correct option is A

Rosalind describes what her uncle taught her in the past about how to recognize a man in love, it creates tension because in the present, **Orlando **is in love.

The description of the past event where Rosalind cured a man of love, creates suspense because we don't know if she can do it again when Orlando agrees to come to her cottage. When Rosalind first meets Orlando and tells him a man has been leaving poems in the forest, it creates mystery as she tries to find out who the poet is.

Throughout the play, the order of events keeps the audience engaged by creating an element of surprise and suspense as the story unfolds. The audience is constantly questioning what will happen next as the characters **navigate **their relationships and experiences.

The use of mystery and tension also serves to heighten the emotional impact of the play as the audience invests in the characters and their struggles.

Overall, the effect of the order of events in As You Like It creates a rich and engaging narrative that is sure to captivate **audiences**.

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The scatter plot shows the number of households, in millions, that have cable television over eight consecutive years. Predict the number of households with cable television in year 11.

8.2 million

9.1 million

11.4 million

15.6 million

### Answers

The answer is 11.4 million. This can be determined by **extrapolating **the trend line from the spread.

What is Extrapolation?

Extrapolation is predicting values that fall within the **range** of available data. It is used to estimate the value of a variable in situations where data is not available.

The spread shows that the number of cable TV households has increased in eight years.

The **trend line** shows that the number of homes has grown at a steady pace.

Extrapolating this trend line, it can be estimated that the number of households using cable television will be 11.4 million households in 2011.

It is important to note that extrapolation is an imprecise forecasting method and can lead to inaccurate results.

Therefore, the estimated value of 11.4 million households for 2011 should be viewed with caution.

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Pls help! Which relation is also a function? A {(0, 3), (4, 3), (8,3)} B {(1, 2), (2, 3), (1,4)} C {(4, 5), (4, 7), (4, 9)} D {(6, 0), (8, 1), (8,5)}

### Answers

The relation is also a **function**= {(0, 3), (1, 2), (1, 4), (2.1)}.

What are functions?

Any subset of a Cartesian product is a **relation**.

These ordered pairings make up a binary relation from A to B. (a,b),

A relationship on A, more precisely, an A to B relationship."

These ordered pairs (a,b) make up a binary relation from A to B, where the first component is from A and the second component is from B.

A connection known as a function links each item in a set X to a single item in a different set Y. (possibly the same set).

A graph, which is a collection of all **ordered **pairs (x, f (x)), is the sole way

A subset of, for instance, is referred to as a "binary relationship fromto describe a function.

With the help of sets we can conclude

Hence, The relation is also a function= {(0, 3), (1, 2), (1, 4), (2.1)}.

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Liam is a tyre fitter

it takes him 56 minutes to fit 4 tyres to a van

how long would it take him to fit 12 tyres to three vans

### Answers

**Answer:**

**Step-by-step explanation:**

1 van takes 56 minutes. So

3 vans will take 3 x 56 =168 minutes.

(Tyres are not important here because he is fitting each van with the same amount of tyres.)