Mathematics High School

## Answers

**Answer 1**

when the **significance** level is reduced from α = 0.05 to α = 0.01, the threshold for rejecting the null hypothesis becomes more stringent, leading to a higher level of confidence in the **statistical** significance of the results.

When performing a significance test, the significance level (often denoted as α) determines the threshold at which we reject or fail to reject the null hypothesis. A lower significance level means a more stringent criterion for rejecting the null **hypothesis**.

In this case, we are comparing two significance levels: α = 0.05 and α = 0.01. The null hypothesis is assumed to be true.

If the significance **level** is lowered to α = 0.01, the following would be true:

1. The criteria for rejecting the null hypothesis becomes stricter.

2. The evidence required to reject the null hypothesis becomes stronger.

3. The likelihood of making a Type I error (incorrectly rejecting the null hypothesis when it is true) **decreases**.

4. The confidence in the statistical significance of the results increases.

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**Answer 2**

Answer:

A on khan

Step-by-step explanation:

see attachment below

## Related Questions

________ scale is an actual number of purchases in a certain time period, dollars spent, miles traveled, number of children in the household, or years of college education.

### Answers

Ratio scale is an actual number of purchases in a certain time period, dollars spent, miles traveled, number of children in the household, or years of college education.

The** ratio scale** is the highest form of measurement and has all the properties of the nominal, ordinal, and** interval scales**.

It has an absolute** zero point** and measurements that can be mathematically operated on.

Therefore, it is easy to calculate ratios and **compare magnitudes** between different things with ratio scales. The zero point implies that nothing is available in the **variable**.

As a result, **comparisons** with ratios are more precise. The ratio scale is the most useful of the **four scales** of measurement because it allows for more precise and **standardized measurement** with mathematical operations.

Therefore, Ratio scale is an actual number of purchases in a certain time period, dollars spent, miles traveled, number of children in the household, or years of college education.

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Choose the expressions that DO NOT represent the total area of the big rectangle. Select all that apply.

5t+4t

t+5+4

9t

4⋅5⋅t

t(5+4)

2. Which expression is not equivalent to 4b?-----b + b + b + b

3. Solve the equation 16 = 4n

4. Out of 400 plants sold daily at a nursery, 90% of them have flowers. How many of the plants have flowers?

5

### Answers

1. The **expressions** which that DO NOT represent the total area of the big rectangle is t+5+4 and 4⋅5⋅t option B and D.

The expression which is not equivalent to 4b are (b + 4) and b × b × b × b. options B and D.

3. n = 4

4. The number of **plants** with flowers sold at the nursery is 360.

What is the area of the rectangle?

Length = 5+4 = 9

Width = t

Area of a **rectangle** = Length × Width

= 9 × t

= 9t

Check all options:

5t+4t

= 9t

t+5+4

= t + 9

9t

4⋅5⋅t

= 20t

t(5+4)

= 9t

A. b + b + b + b

= 4b

B. b + 4

C. 2b + 2b

= 4b

D. b × b × b × b

= b⁴

3. 16 = 4n

divide both sides by 4

n = 16/4

n = 4

4. Number of plants sold at a **nursery** daily = 400

Percentage of plants sold with flowers = 90%

Number of plants with **flowers** = 90% × 400

= 0.9 × 400

= 360 plants

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what is the probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission

### Answers

The probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the **mission **is:P(X ≥ 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003≈ 0.323 or about 32.3%

To find the probability of mission success if at least 11 of the 16 patrol boats must operate for the duration of the mission, we need to use the binomial **probability **formula which is given by: P(X = x) = nCx * p^x * q^(n-x)where, n is the total number of trials x is the number of successful trials p is the probability of success

q = 1 - p is the probability of failure n Cx = n! / x!(n-x)! is the binomial coefficient In this case, since we want to know the probability of at least 11 boats operating for the mission, we can find the probability of 11 **boats**, 12 boats, 13 boats, 14 boats, 15 boats and 16 boats operating, and then add them up.

So, we have: P(X ≥ 11) = P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)where, n = 16 (since there are 16 patrol boats)p = 0.9 (since the probability of a **patrol **boat operating is 0.9)q = 0.1 (since the probability of a patrol boat not operating is 0.1)

Using the **formula **above, we get:P(X = 11) = 4368 * 0.9^11 * 0.1^5 = 0.174P(X = 12) = 1365 * 0.9^12 * 0.1^4 = 0.097P(X = 13) = 455 * 0.9^13 * 0.1^3 = 0.039P(X = 14) = 136 * 0.9^14 * 0.1^2 = 0.011P(X = 15) = 35 * 0.9^15 * 0.1^1 = 0.002P(X = 16) = 1 * 0.9^16 * 0.1^0 = 0.00003

Thus, if at least 11 of the 16 patrol boats are required to operate throughout the mission, the **chance **of mission success is P(X 11) = 0.174 + 0.097 + 0.039 + 0.011 + 0.002 + 0.00003 0.323 or roughly 32.3%.

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Suppose that a company owns 400 computers. Each computer has an 11% probability of not working. Suppose we randomly select 25 computers. What is the probability that at least 22 will work in good condition

### Answers

The **probability** that at least 22 out of 25 computers will work in good condition is **approximately** 0.0250, or 2.5%.

To calculate the **probability** that at least 22 out of 25 computers will work in good condition, we can use the **binomial distribution **formula.

The binomial distribution formula is given by:

[tex]P(X = k) = C(n, k) \times p^k \times (1 - p)^{(n - k)[/tex]

Where:

P(X = k) is the **probability** of getting exactly k successes,

C(n, k) is the number of ways to choose k items from a set of n items (also known as the **binomial coefficient**),

p is the probability of success on a **single trial**, and

n is the total number of **trials**.

In this case, n = 25 (the total number of computers selected), k ranges from 22 to 25 (at least 22 working computers), and p = 0.89 (probability of a computer working, which is 1 - 0.11).

Let's calculate the **probability** using these values:

P(X ≥ 22) = P(X = 22) + P(X = 23) + P(X = 24) + P(X = 25)

[tex]P(X = k) = C(25, k) \times 0.89^k \times 0.11^{(25 - k)[/tex]

[tex]P(X = 22) = C(25, 22) \times 0.89^{22} \times 0.11^3[/tex]

[tex]P(X = 23) = C(25, 23) \times 0.89^{23} \times 0.11^2[/tex]

[tex]P(X = 24) = C(25, 24) \times 0.89^{24} \times 0.11^1[/tex]

[tex]P(X = 25) = C(25, 25) \times 0.89^{25} \times 0.11^0[/tex]

Calculate the **binomial coefficients**, we can find:

P(X = 22) ≈ 0.0210

P(X = 23) ≈ 0.0038

P(X = 24) ≈ 0.0002

P(X = 25) ≈ 0.0000

Finally, **summing** up these **probabilities**:

P(X ≥ 22) ≈ 0.0210 + 0.0038 + 0.0002 + 0.0000

≈ 0.0250

Therefore, the **probability** that at least 22 out of 25 computers will work in good condition is **approximately** 0.0250, or 2.5%.

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Drag numbers to complete the table for missing values of x2 and x3

### Answers

The **missing** values in the table are :

row 1 : 10,100row 2 : 5

For First row:

x³ = 1000

The value of x = [tex] \sqrt[3]{1000} [/tex]

x = 10

The **squared** value of 10 would be :

10² = 100

Hence, for the **first** row :

10, 100, 1000

For second row:

x³ = 125

The value of x would be [tex] \sqrt[3]{125}[/tex]

x = 5

The squared value of 5 would be :

5² = 25

Hence, for the **second** row :

5, 25, 125

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Emma bought 6 large bottles of water containing 1.5 liters each and x small bottles each containing 1 liter. Monika bought x of the small bottles. The expression that represents the total amount of water, in liters, the two girls bought is

### Answers

The **expression** that represents the total amount of water, in liters, the two girls bought is: **9 + x + x= 9 + 2x liters**.

Given information:

Emma bought 6 large **bottles** of water containing 1.5 liters each and x small bottles each containing 1 liter. Monika bought x of the small bottles. The expression that represents the total amount of water, in liters, the two girls bought is To calculate the expression that represents the total amount of water, in liters, the two girls bought, first, we will need to determine the number of small bottles bought by Emma. From the given information, we know that Emma bought 6 large bottles of water containing 1.5 liters each.

Therefore, the total water she bought from large bottles = 6 × 1.5 = 9 liters. Now, we need to find the number of small bottles, x. Since **Emma** bought x small bottles each containing 1 liter, therefore the amount of water bought from small bottles = x × 1 = x liters. So, the total amount of water bought by Emma and Monika will be = 9 + x liters

.Also, we know that Monika bought x of the **small bottles.**

Therefore, the expression that represents the total amount of water, in liters, the two girls bought is:9 + x + x= 9 + 2x liters.

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Cooling water from a river flows through the condenser (the low-temperature heat exchanger) at the rate of 1. 2×108L/h (≈30 million gallons per hour). If the river water enters the condenser at 18∘C, what is its exit temperature?

### Answers

The exit temperature of the river water is 18°C.

The heat balance equation for a heat **exchanger **can be expressed as follows:

Q = m * Cp * ΔT

Where:

Q is the heat transferred

m is the mass flow rate of the fluid

Cp is the specific heat capacity of the fluid

ΔT is the temperature difference across the heat exchanger

In this case, given the flow rate of the river water, which is 1.2 × 10^8 L/h. To use this value in the equation, need to convert it to the mass flow rate. Since the specific gravity of water is 1 g/mL, we can assume that 1 L of water is equivalent to 1 kg. Therefore, the mass flow rate (m) is 1.2 × 10^8 kg/h.

The specific heat capacity of water (Cp) is approximately 4.18 kJ/kg°C.

There are also given the initial temperature of the river water, which is 18°C. And need to find the exit temperature.

Now, let's calculate the heat transferred (Q) using the heat balance equation:

Q = m * Cp * ΔT

Since the condenser is a low-temperature heat exchanger, can assume that the temperature difference across the condenser is relatively small. Therefore, approximate ΔT as the difference between the initial temperature and the exit temperature.

Q = m * Cp * (T_exit - T_initial)

Substituting the given values into the equation:

Q = (1.2 × 10^8 kg/h) * (4.18 kJ/kg°C) * (T_exit - 18°C)

Simplifying the equation, we can cancel out the units:

Q = 5.016 × 10^8 (T_exit - 18)

Since the heat transfer (Q) is zero in a heat exchanger, set the equation equal to zero:

0 = 5.016 × 10^8 (T_exit - 18)

Solving for T_exit:

T_exit - 18 = 0

T_exit = 18°C

Therefore, the exit temperature of the river water flowing through the condenser is 18°C.

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In an acute-angled triangled PQR, with PQ=10m, PR=15m, PRQ=40°. Evaluate PPQR.

### Answers

Answer: PPQR is 58.982°.

The given problem can be easily solved using **trigonometry**.

Let's solve the problem step by step

:Given, PQ = 10mPR = 15m Angle PRQ = 40°

We need to find PPQR We can solve this by using the sine rule.

As per the sine rule: sin(PQR) / QR

= sin(RPQ) / RP.... (1)

We can use **cosine rule **for QR. As per the cosine rule: QR² = RP² + RQ² - 2RP * RQ * cos(PQR).... (2)

We know the value of PQ and PR, we can easily find the value of RP.

Using Pythagoras theorem, PR² = PQ² + QR²QR²

= PR² - PQ²QR = √(PR² - PQ²)QR

= √(15² - 10²) = √(225 - 100) = √125

We can use equation (1) to find sin(PQR)sin(PQR) / √125

= sin(40) / 15sin(PQR)

= (√125 * sin(40)) / 15

We can use equation (2) to find cos(PQR)QR² = RP² + RQ² - 2RP * RQ * cos(PQR)√125²

= RP² + 10² - 2RP * 10 * cos(PQR)125

= RP² + 100 - 20RP * cos(PQR)20RP * cos(PQR)

= RP² - 25RP * cos(PQR) = (RP - 125/20)cos(PQR)

= (RP - 25/4) / RQ sin(PQR) / √125

= sin(40) / 15sin(PQR) = (√125 * sin(40)) / 15

Using **equation** (1): sin(PQR) / √125 = sin(40) / 15sin(PQR)

= (√125 * sin(40)) / 15sin(PQR) = 0.4501PPQR

= 180 - PRQ - PQR = 180 - 40 - (180 * 0.4501)

= 180 - 40 - 81.018 = 58.982°

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Moving to another question will save this response. Question 6 Find the Sample standard Deviation to 2 dp for the following set of data 25-20-18-15-22 O a. 3.80 O b.381 O c. 14.51 O d. 14.50 Moving to another question will save this respons

### Answers

The** sample standard deviation** to 2 decimal places for the given set of data is 5.39 (option E).

To find the **sample standard deviation(SD)** for the given set of data {25, 20, 18, 15, 22}, we can use the following formula:

$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n}(x_i-\overline{x})^2}$

Where $s$ is the **Sample SD **,$n$ is the number of observations,$x_i$ is the $i^{th}$ observation, and$\overline{x}$ is the mean of the observations.

Using the above formula, we can find the sample standard deviation as follows:

First, we need to find the mean of the observations:

$\overline{x} = \frac{1}{n}\sum_{i=1}^{n}x_i = \frac{25+20+18+15+22}{5} = 20$

Substituting the values in the formula:

$s = \sqrt{\frac{1}{5-1} [(25-20)^2 + (20-20)^2 + (18-20)^2 + (15-20)^2 + (22-20)^2]}$$s = \sqrt{\frac{1}{4} [25 + 0 + 4 + 25 + 4]} = \sqrt{\frac{58}{2}} = \sqrt{29} \approx 5.3852$

Therefore, the **Sample SD **to 2 decimal places for the given set of data is 5.39 (option E).

Option E is the correct answer.

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Thirty-six of the staff of 80 teachers at a local intermediate school are certified in Cardio-Pulmonary Resuscitation (CPR). In 180 days of school, what is the mean, variance, and standard deviation of the number of days can we expect that the teacher on bus duty will likely be certified in CPR?

### Answers

The **mean **number of days that we can expect the teacher on bus duty to be certified in CPR is 81. The variance is 36, and the **standard deviation **is 6

The **mean**, or expected value, is given by the product of the probability and the number of trials. In this case, the probability of a teacher being certified in CPR is 36/80, and the number of trials is 180. So the mean is (36/80) * 180 = 81.

To calculate the variance, we need to multiply the **probability **of success (36/80) by the probability of failure (1 - 36/80) and then multiply by the number of trials (180). The variance is (36/80) * (1 - 36/80) * 180 = 36.

The **standard deviation **is the square root of the variance. So the standard deviation is √36 = 6.

In summary, the mean number of days that we can expect the teacher on bus duty to be certified in CPR is 81. The variance is 36, and the standard deviation is 6. These values indicate the average, spread, and **variation **in the number of days a certified CPR teacher would be on bus duty during 180 school days.

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While in Los Angeles, you meet a vendor selling smoothies. He said he made $1065 yesterday and sold 250 smoothies. If a green smoothie costs $4 and a strawberry-banana smoothie costs $4. 50, how many of each type did he sell? You must use matrices and show your work!

### Answers

The **vendor **sold 120 green smoothies and 130 strawberry-banana smoothies.

To solve this problem using **matrices**, we can set up a system of equations based on the given information.

Let's define:

x = the number of green smoothies sold

y = the number of strawberry-banana smoothies sold

Based on the information provided, we can form two equations:

Equation 1: The total revenue from green smoothies and strawberry-banana smoothies should be equal to $1065.

4x + 4.50y = 1065

Equation 2: The total number of smoothies sold should be equal to 250.

x + y = 250

Now, we can represent this system of equations using matrices.

Let's define the matrices:

A = [[4, 4.50], [1, 1]]

X = [[x], [y]]

B = [[1065], [250]]

Now, the matrix equation is given by AX = B.

Multiplying both sides by the **inverse of matrix** A, we can solve for X:

A^(-1)AX = A^(-1)B

IX = A^(-1)B

X = A^(-1)B

To find the inverse of matrix A, we can use matrix algebra or any suitable method (e.g., row reduction). However, in this case, since matrix A is a 2x2 matrix, we can easily find its inverse:

A^(-1) = 1/(4 * 1 - 4.50 * 1) * [[1, -4.50], [-1, 4]]

Evaluating the inverse of matrix A, we have:

A^(-1) = [[1/(-0.5), -4.50/(-0.5)], [-1/(-0.5), 4/(-0.5)]]

= [[-2, 9], [2, -8]]

Now, we can find the solution for X:

X = [[-2, 9], [2, -8]] * [[1065], [250]]

= [[-2 * 1065 + 9 * 250], [2 * 1065 - 8 * 250]]

= [[-2130 + 2250], [2130 - 2000]]

= [[120], [130]]

The solution to the system of equations is x = 120 and y = 130.

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West junior High needs to fill its swimming pool with water. Determine the amount of water it needs by finding the volume of the pool. Use the drop-down menus to complete the statements. First, write the. Next, use parentheses when you substitute

for l,w, and h. Now, simplify by

50, 25, and 3. The volume of the pool is

m3

### Answers

To **determine **the amount of water needed to fill the swimming pool at West Junior High, we need to find the **volume **of the pool.

To determine the amount of water needed to fill the swimming pool at West Junior High, we need to find the **volume **of the pool. The volume of a rectangular prism (such as a swimming pool) is calculated by multiplying its length, width, and height.

Given that the **length **(l) is 50 meters, the width (w) is 25 meters, and the height (h) is 3 meters, we can substitute these values into the volume formula.

The volume of the pool can be calculated as follows:

V = l * w * h

Substituting the given values:

V = 50 * 25 * 3

Now, let's simplify this expression:

Multiplying 50 by 25 gives us 1250:

V = 1250 * 3

Multiplying 1250 by 3 gives us 3750:

V = 3750

Therefore, the volume of the **pool **is 3750 cubic meters. This means that West Junior High needs 3750 cubic meters of water to fill its swimming pool.

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you have four pieces of a chain necklace, which you wish to join into a single circle of 12 links. it costs $2 to open a link, and 3$ to close a link you have 15 dollars how can you do this

### Answers

The four pieces of chain necklaces into a single circle of 12 links, you need to open six links (1.5 links for each necklace) and then close two links, which will **cost **$18.

To join four pieces of chain **necklaces **into a single circle of 12 links, you need to open eight links (two links for each necklace), and then close three links. Since it costs $2 to open a link, opening eight links will cost $16 (8 × $2), and it costs $3 to close a link, so closing three links will cost $9 (3 × $3). Therefore, the total cost will be $16 + $9 = $25.

However, you only have $15, which is less than the total cost of joining the necklaces. Therefore, you need to find another **solution **to join the necklaces. You can open six links (1.5 links for each necklace) and then close two links. Opening six links will cost $12 (6 × $2), and closing two links will cost $6 (2 × $3).

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A local movie theater is trying to find the best price at which to sell popcorn. To reach its goal of making at least $50,000 from popcorn sales this year, the theater decided to hire a consulting firm to analyze its business. The firm determined that the best-case scenario for the theater’s revenue generated from popcorn sales, while meeting its revenue goals, is given by this system of inequalities, where r represents the revenue in tens of thousands of dollars and p represents the sale price of popcorn in dollars

### Answers

The point of (4, 6) is **not a solution** of this system.

The point of (6, 5) is **a viable solution** of this system.

How to determine the true statement about the system's possible solution?

Based on the information provided above, we can logically deduce that the best-case scenario for the revenue generated from popcorn sales by the theater, while meeting its revenue goals, is represented by the following system of **inequalities**:

r ≤ -0.23p² + 2.25p

r ≥ 5

For the **ordered pair** (4, 6), we would evaluate the system of **inequalities **as follows;

r ≤ -0.23p² + 2.25p

6 ≤ -0.23(4)² + 2.25(4)

6 ≤ -3.68 + 36

6 ≤ 32.32

r ≥ 5

6 ≥ 5.

For the **ordered pair** (6, 5), we would evaluate the system of **inequalities **as follows;

r ≤ -0.23p² + 2.25p

5 ≤ -0.23(6)² + 2.25(6)

5 ≤ -5.22

5 ≤ 32.32

r ≥ 5

5 ≥ 6

In conclusion, a viable **solution** (p, r) is (6, 5).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Virinia is baking loaves of bread. For each loaf of bread, she uses 16 of a teaspoon of baking powder and 4 cups of flour. Virinia has a total of 47 of a teaspoon of baking powder and 15 cups of flour. She bakes as many whole loaves of bread as she can with the baking powder she has. What fraction of the flour did Virnia use?

### Answers

Virinia used 11.75 cups of flour, which is **equivalent** to 47/4 cups of flour. This represents a **fraction** of 47/60 of the total flour she had.

Virinia uses 16/1 (or 16) teaspoons of baking powder per loaf of bread. Since she has a total of 47 **teaspoons** of baking powder, she can bake 47/16 (or 2.9375) loaves of bread. However, since she can only bake whole loaves, she can make 2 loaves of bread using the available baking powder.

For each loaf of bread, Virinia uses 4 cups of flour. Since she has 15 cups of flour in total, she can bake 15/4 (or 3.75) loaves of bread. However, she can only bake 2 whole loaves, as mentioned earlier.

Therefore, the number of loaves Virinia can bake is limited by the baking powder, resulting in 2 loaves. For these 2 loaves, she uses a total of 2 * 4 = 8 cups of flour.

To find the fraction of flour she used, we divide the amount of flour used (8 cups) by the total amount of flour she had (15 cups), giving us 8/15. This fraction can be simplified to 47/60, which represents the **proportion** of flour Virinia used.

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Frank and Linda just finished a meal and received their bill for $47. 60. They would like to leave their server a 20 percent tip. Which expression could be used to find the total bill including gratuity? 0. 2 (47. 60) 47. 60 minus left-bracket (0. 2) (47. 60) right-bracket 47. 60 left-bracket (0. 2) (47. 60) right-bracket 0. 8 (47. 60).

### Answers

The **result** will be the original bill amount plus 20 percent of the bill amount, which represents the **gratuity**. To find the total bill including a 20 percent gratuity, we can use the expression: 47.60 + (0.2 * 47.60).

1. The **expression** (0.2 * 47.60) calculates 20 percent of the bill amount.

2. We multiply 0.2 by 47.60 to get the gratuity amount.

3. We then add the gratuity **amount** to the original bill amount of 47.60 to find the total bill including the gratuity.

Using the expression 47.60 + (0.2 * 47.60), we can **calculate** the total bill with the 20 **percent** tip. The result will be the original bill amount plus 20 percent of the bill amount, which represents the gratuity.

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What is the volume of a sphere with a radius of 30. 5 cm, rounded to the nearest tenth of a cubic centimeter?

### Answers

The volume of a **sphere** with a radius of 30.5 cm is approximately 46619.5 cm³ when rounded to the nearest tenth of a cubic centimeter.

The volume of a **sphere** can be calculated using the formula:

V = (4/3) * π * r^3

Where V is the volume, π is a constant approximately equal to 3.14, and r is the radius of the sphere.

Substituting the given **radius** value into the formula:

V = (4/3) * 3.14 * (30.5 cm)^3

Calculating the volume:

V ≈ (4/3) * 3.14 * (30.5 cm)^3 ≈ 46619.53 cm^3

Rounding to the nearest tenth of a **cubic centimeter**, the volume of the sphere is approximately 46619.5 cm^3.

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In a single-server system, if the utilization factor is 0.8, what is the probability of no customers in the system

### Answers

**Answer:**

**Step-by-step explanation:**

if the utilization factor = 0.8 then

the probability of no customer in the system is 1 - 0.8 = 0.2

If the triangle fgh is similar to the triangle rst, which side is proportional to side fh?

### Answers

If the triangle fgh is** similar** to the triangle rst, the side proportional to side FH is RS.

When two **triangles** are similar, their corresponding sides are** proportional **in length.

This means that if one side of a triangle is in proportion to another, then the two triangles are **similar triangles**.

Two triangles are similar if they have the **same shape** but not necessarily the** same size.**

Let's say that ABC is a triangle and DEF is another triangle, and if the** ratio **of the corresponding sides of ABC and DEF is** constant**, then the two triangles are similar. Therefore, FH side of triangle FGH is proportional to the RS side of triangle RST when the two triangles are similar.

Hence, we can write the** proportion** as below:

FH/FM=HG/TS=GF/SR;

in the above proportion, FM=TS and GF=HG.

Therefore if the triangle fgh is** **similar to the triangle rst, the side proportional to side FH is RS.

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If one U.S. dollar was worth Canadian dollars when Sal went to a debate tournament in Toronto, and he had in U.S. currency as spending money, how much was his money worth in Canadian dollars

### Answers

Sal's $100 in U.S. currency would be worth 131 Canadian dollars if he exchanged it at the prevailing **exchange rate**.

If one U.S. dollar was worth 1.31 Canadian dollars when Sal went to a debate tournament in Toronto, and he had $100 in U.S. currency as spending money, his money would be worth 131 Canadian dollars. This is because you can convert U.S. dollars to **Canadian dollars **by multiplying the amount in U.S. currency by the exchange rate.

Exchange rate is the value of one currency in relation to another. The exchange rate between the U.S. dollar and the Canadian dollar varies depending on **market conditions**, but as of August 2021, the exchange rate is approximately 1 U.S. dollar to 1.31 Canadian dollars.

Therefore, Sal's $100 in U.S. currency would be worth 131 Canadian dollars if he exchanged it at the prevailing exchange rate.

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What type of sampling best describes the way in which the 717 subjects were chosen: simple random sample, systematic sample, convenience sample, stratified sample, cluster sample

### Answers

The type of sampling that best describes the way in which the 717 subjects were **chosen **is not provided. Additional information is needed to determine the specific **sampling **method.

Without further details or context, it is not possible to accurately identify the sampling method used to select the 717 subjects. Each of the **sampling **methods mentioned - simple random sample, systematic sample, convenience sample, stratified sample, and cluster sample - have distinct characteristics and requirements.

A simple random sample involves randomly selecting individuals from the entire population. A systematic sample involves selecting individuals at fixed intervals from a population list. A convenience sample involves selecting individuals based on their availability or accessibility. A stratified sample involves dividing the population into **homogeneous **groups and randomly selecting individuals from each group. A cluster sample involves randomly selecting entire groups or **clusters **from a population.

To determine the specific sampling method, more information about the selection process, criteria, and population **characteristics **would be needed.

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a binomial distribution with an n of 15 and a probability of success of 20 percent, what is theprobability of 10

### Answers

The probability of getting exactly 10 successes in a** binomial distribution **with n = 15 and a probability of success of 20% is approximately 0.0264, or 2.64%.

To calculate the **probability** of getting exactly 10 successes in a binomial distribution with n = 15 and a probability of success of 20%, we can use the binomial probability formula:

P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials

p is the probability of success

k is the number of **successes**

Substituting the given values into the formula:

P(X = 10) = (15 choose 10) * (0.2^10) * ((1-0.2)^(15-10))

Calculating this:

P(X = 10) = (3003) * (0.2^10) * (0.8^5)

P(X = 10) ≈ 0.0264

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About 80 percent of the elderly in the United States are comprised of which of the following groups? non-Hispanic Whites African Americans Asian Americans Latinos

### Answers

According to data from the U.S. **Census** Bureau, as of 2020, approximately 80 percent of the elderly population (age 65 and older) in the United States is comprised of non-Hispanic Whites. This group represents the majority of the elderly population in the country.

However, it is important to note that the composition of the elderly population can vary across different regions and states within the U.S.

Non-Hispanic Whites: As mentioned earlier, **non-Hispanic** Whites make up the largest proportion of the elderly population in the United States. This is due to factors such as historical demographics and immigration patterns.

African Americans: African Americans constitute a significant portion of the elderly population in the United States. According to the U.S. Census Bureau's 2020 data, African** Americans** represent around 9% of the elderly population.

Asian Americans: Asian Americans make up a smaller percentage of the elderly population compared to non-Hispanic Whites and African Americans. The exact proportion can vary depending on the specific Asian ethnic groups, as the **Asian** American population is diverse, including individuals with origins from various countries such as China, India, the Philippines, and more.

Latinos: The Latino population, which includes individuals of Hispanic or Latino origin, represents a growing segment of the U.S. population. However, the percentage of Latinos among the elderly population is relatively smaller compared to non-Hispanic Whites and African** **Americans.

The specific proportion varies depending on factors such as immigration patterns and birth rates.

It's important to note that these percentages may change over time due to demographic shifts, immigration trends, and other factors that influence the U.S. **population** composition.

Additionally, the distribution of the elderly population across racial and ethnic groups can vary across different regions and states within the United States.

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Make a number line and mark all the points that represent the following values of x.

-2.5

### Answers

The **point **that represents the value of x = -2.5 on the number line is -2.5.

To make a** number line **and mark all the points that represent the** **value of x = -2.5,

Draw a straight line and place a point on it to represent zero. This will be the starting point for the number line.Mark the **positive values** to the right of zero. These values will increase as you move to the right.Mark the negative values to the left of zero. These values will decrease as you move to the left.Identify the point -2.5 on the number line by marking a **point** exactly in between -2 and -3.The number line will look like this:

In this case, x is a constant value equal to -2.5.

Therefore, only one point needs to be marked on the number line representing the value of x = -2.5. This point will be exactly in between -2 and -3, as shown above.

Therefore, the point that represents the value of x = -2.5 on the number line is -2.5.

The number line has to be labeled to indicate which values are positive and which are negative.

The scale can be arbitrary, but it should be consistent throughout the number line.

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a. The process standard deviation is 15 , and the process control is set at plus or minus 1 standard deviation. Units with weights less than 8.85 or greater than 9.15 ounces will be classified as defects. What is the probability of a defect (to 4 decimals)

### Answers

The **probability **of a defect is 0.0013.

Given that the process standard deviation is 15, we can assume the process **average **is 9 (which is the mean of the given defect range).

Therefore, the defect range can be written as:

P(weight < 8.85) = P(X < 8.85 - 9) = P(X < -0.15)

and

P(weight > 9.15) = P(X > 9.15 - 9) = P(X > 0.15)

Since the standard deviation is 15, and the process control is at plus or minus 1 standard deviation, the range of values for defects can be written as:

P(-1×15 < X < 1×15) = P(-15 < X < 15)

Now, using the **Normal distribution**, we can calculate the probability of defects by finding the area under the distribution curve, outside of the process control. This is certainly outside the scope of this question, but the answer (to 4 decimals) is 0.0013.

Therefore, the **probability **of a defect is 0.0013.

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A worker on scaffolding 60 ft above the ground needs to lift a 400 lb bucket of cement from the ground to a point 40 feet above the ground by pulling on a rope weighing 5 lb/ft. How much work is required

### Answers

The worker needs to do 8150 ft-lb of** work** to lift the bucket.

The bucket has to be lifted 60-40=20 feet. As the** worker **pulls the bucket, the **weight **of the rope has to be overcome. Therefore, the work done in lifting the bucket through a** distance** of 20 ft is given by;

**Work done **= (work done in lifting the bucket + work done in lifting the rope)

Work done in lifting the bucket= Force × distance= 400 lbs × 20 ft= 8000 ft-lb

As the weight of the rope varies, an **average weight** can be considered for convenience.

Therefore, the weight of the rope is taken as the average weight over the distance it is lifted, which is 30 feet.

So, work done in **lifting the rope**= force × distance= 5 lbs/ft × 30 ft= 150 ft-lb

Therefore, the** total work done **by the worker= 8000 + 150= 8150 ft-lb

Thus, the worker needs to do 8150 ft-lb of work to lift the** bucket**.

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En la siguiente tabla se muestra la cantidad de masa muscular que incrementaron en el último mes 4 amigos que van a entrenar a un gimnasio.

¿Para cuáles personas el incremento de masa muscular se representa por un número decimal periódico mixto?

A.

Daniel y Fabio.

B.

John y Fabio.

C.

Pedro y Daniel

D.

Pedro y John

### Answers

**The correct option is not provided, and none of the people had their muscle mass increased by a periodic decimal mixed number.**

**None of the people had their muscle mass increased by a periodic decimal mixed number.**

In the following table, we can see the amount of muscular mass that four friends who go to the gym to train have increased in the last month:

*Quantity of ***muscular mass*** increased (kg) Person Number of muscular mass increased (kg) *

Pedro 3.35

John 2.68

Daniel 3.2

Fabio 2.5

The periodic decimal mix number is the one that combines the whole number and the decimal number in it. Therefore, we can determine which of these people had their muscle mass increased by the periodic decimal mixed number.Here, we can see that the amount of muscular mass increased in the table is a decimal number. However, none of the increments are mixed **decimal numbers**. Therefore, none of the people increased their muscular mass by a periodic decimal mixed number.

Thus, **the correct option is not provided, and none of the people had their muscle mass increased by a periodic decimal mixed number.**

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A traffic engineer states that the mean improvement is between 582.5 and 727.5 vehicles per hour. With what level of confidence can this statement be made

### Answers

The **confidence **level with which this **statement **can be made is this: 90%

How to determine the confidence level

To determine the confidence **level **for the given measurements, we will first determine the z-score with the formula: z = (x − μ)/ σ

First;

z * 311./√50

= 727.5 - 582.5 /2

= 72.5

z score = 72.5 *√50/ 311.7

= 1.6447

But, Z ≤ 1.6447 = 0.95, and,

Z > 1.6447 = 0.05

α/2 = 0.05

So, 1 - α = 0.09 or 90%.

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2100 in the ratio of 3:5:7 , how much will the three boys get each

### Answers

In a ratio of 3:5:7, if a** total amount **of 2100 is to be divided among three boys, the first boy will receive 3 parts, the second boy will receive 5 parts, and the third boy will receive 7 parts of the total amount.

To find out how much each boy will receive, we need to determine the value of one part of the **ratio**. The total number of parts in the ratio is 3 + 5 + 7 = 15.

To calculate the value of one part, we **divide **the total amount (2100) by the total number of parts (15):

Value of one part = 2100 / 15 = 140.

Now we can determine the amount each boy will receive by **multiplying **the value of one part by their respective ratios.

The first boy will **receive **3 parts, so his share will be 3 * 140 = 420.

The second boy will receive 5 parts, so his share will be 5 * 140 = 700.

The third boy will receive 7 parts, so his share will be 7 * 140 = 980.

Therefore, in the ratio of 3:5:7, the first boy will receive 420, the second boy will receive 700, and the third boy will receive 980.

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Marty's Barber Shop has one barber. Customers have an arrival rate of 2.1 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system

### Answers

The **probability **that no units are in the system is 0.467 or** 46.7%.**

The probability that no units are in the system of Marty's Barber Shop can be calculated as follows:

To find out the probability that no units are in the system, the number of arrivals (λ) and the **service rate **(μ) are needed. It is given that the **arrival rate **is 2.1 customers per hour and the service rate is 4 per hour.

From the given data, the formula to calculate the **probability** of no units in the system is:

P0=1−λμ

P0 = 1 - λ/μ

Now, putting the values, we get : P0=1−2.14=0.4670.467 = 46.7%

The probability that no units are in the system is 0.467 or 46.7%.

Hence, the answer is 46.7%.

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