Roll the number cube 20 times to represent 20 purchases. What is the experimental probability of receiving a 50% coupon? Write the probability as a decimal.

Answer:

0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 1217, \sigma = \sqrt{10414} = 102, n = 116, s = \frac{102}{\sqrt{116}} = 9.475[/tex]

What is the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd?

This is 2 multiplied by the pvalue of Z when X = 1217 - 11 = 1206. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1206 - 1217}{9.475}[/tex]

[tex]Z = -1.16[/tex]

[tex]Z = -1.16[/tex] has a pvalue of 0.1230

2*0.1230 = 0.2460

0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.

To calculate the probability, we can use the Central Limit Theorem. Calculate the standard error using the formula: standard error = standard deviation / sqrt(n), then use the z-score formula to find the probability.

To find the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs, we can use the Central Limit Theorem. Since the sample size is large (n > 30), the distribution of sample means will be approximately normally distributed. First, we calculate the standard deviation of the sampling distribution, also known as the standard error, using the formula: standard error = standard deviation / sqrt(n). In this case, the standard error is sqrt(10404)/sqrt(116).

Finally, we can use the z-score formula to calculate the probability. The z-score is given by z = (x - mean) / standard error. We want to find the probability that the mean weight differs from the population mean by more than 11 lbs, so we calculate the z-score for both 11 and -11 and use the z-table or a calculator to find the probability of z being greater than the positive z-score and less than the negative z-score. Adding these two probabilities gives us the final answer.

https://brainly.com/question/898534

#SPJ3

Answer:

129

Step-by-step explanation:

Answer:

315

Step-by-step explanation:

The missing percentages of the given scenario are;

Adventure Games: 22%

Puzzles: 28%

Card Games: 30%

Arcade Games: 9%

Board Games: 11%

So in order to solve the problem, we simply use the pie chart distributions to get the result

Now if look at the percentages, we that card games percentage is 30 while arcade games is 9 so, 21 % of people play more card games.

In terms of number of people = 21/100 x 1500 = 315

Hence out of 1500, 315 people play card games more than arcade

Answer:

The number of more people that played card games than arcade games is 150 people

Step-by-step explanation:

Here  we have a pie chart showing games people play in the following proportions

Assumption; Card games = 49%

Arcade games = 32%

Classic = 15%

Kids = 4%

Therefore. if 49%  played card games, we have 49% of 1500 which is 735 people, while 32% that played arcade games, we have 39% of 1500 = 0.39×1500 = 585

Therefore, the number of more people that played card games than arcade games = 735 - 585 = 150 people.

Answer:

210.22

Step-by-step explanation:

first you need to divide 3785 divided by 18 which is 210.22222222 then u need to round to the nearest tenth which is equaled to 210.22. I hope this helped

Answer:

Step-by-step explanation:

Let represent the edge of the tank with x and the radius of the first sphere with x/2;

The amount of the water = Volume of the tank - Volume of the sphere

= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]

on the second cube ; the radius of the sphere = [tex]\frac{x}{4} \ units[/tex] ;

Also the number of sphere here is = 8

The amount of water = [tex]x^3 -8*\frac{4}{3} \pi (\frac{x}{4})^3[/tex]

For the third figure ; the radius of the sphere is = [tex]\frac{x}{8} \ units[/tex]

Also the number of sphere here is = 64

The amount of water = [tex]x^6 -64*\frac{4}{3} \pi (\frac{x}{8})^3[/tex]

= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]

In the fourth tank ; 512 sphere illustrates that in a single row; that more than one 8 sphere is present i.e 8³ = 512

then the radius will be = [tex]\frac{x}{16}[/tex]

The amount of water = [tex]x^3 -512*\frac{4}{3} \pi (\frac{x}{16})^3[/tex]

= [tex]x^3 -\frac{4}{3} \pi (\frac{x}{2})^3[/tex]

This implies that alll the three cube shaped tanks are identical and hold equal amount of water.

Answer:

24 feet

Step-by-step explanation:

sorry I'm so late

Answer:

s would be the dependent variable, and g the independent.

Step-by-step explanation:

Whatever the score is, it would depend on how many goals the team has scored.

Final answer:

The independent variable is typically the one that is manipulated, like the number of goals scored (g), and the dependent variable is the one that responds, like the team's score (S). A scatter plot can reveal patterns, and the correlation coefficient indicates the strength of the relationship. The least-squares line represents a best-fit line through the data.

Explanation:

The independent variable is typically the one that is controlled or manipulated, whereas the dependent variable is the one that responds to changes in the independent variable. In the context of a team's score (S) and the number of goals scored (g), the independent variable is usually the number of goals scored (g) because it can be controlled or affected through the team's actions. The dependent variable is the team's score (S), because it depends on the number of goals scored.

In a broader context, such as analyzing the relationship between the ranking of a state and the area of the state, the independent variable could be the ranking (since it is not influenced by the area), and the dependent variable would be the area of the state (since it could be influenced by a variety of factors, including ranking).

When creating a scatter plot, it is common to place the independent variable on the x-axis and the dependent variable on the y-axis. This scatter plot could reveal correlations or trends between the two variables. The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A correlation coefficient close to 1 or -1 indicates a strong relationship, while a number close to 0 indicates a weak relationship. The least-squares line is a regression line that minimizes the sum of the squared differences between the observed values and the values predicted by the line.

Answer: The surface is (4*n + 2)*L^2

Step-by-step explanation:

The surface of a cube is equal to 6 times the area of one of the sides.

So if the sides of the cube have a length L, we have that the area of one face is L^2, and the surface of the cube is 6*L^2

Now, if we put n of those cubes in a tower, we will have a shape were the bottom and the top still have an area of L^2, then the total area of the bottom and the top is 2*L^2

But each one of the sides has two sides of length L, and two sides of length n*L (n times the length of one of the sides), then the area of each side is equal to n*L*L = n*L^2

and we have 4 sides, then the total area of the sides is 4*n*L^2

Then the total surface of the tower is:

A = 4*n*L^2 + 2*L^2 = (4*n + 2)*L^2

Answer:

49

Step-by-step explanation:

36 minus -18 is 49

Answer:

-1/2

Step-by-step explanation:

The fraction is not reduced to lowest terms. We can reduce this fraction to lowest

terms by dividing both the numerator and denominator by 18.

Given Information:

Smoothing constant = α = 0.25

Initial forecast salary = F₀ = $55,000

Actual salaries = A = $60,000, $72,000, $84,500, and $96,000

Required Information:

Forecast salaries = F = ?

Answer:

[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]

Step-by-step explanation:

The exponential smoothing model is given by

[tex]F_{n} = \alpha \cdot A_{n - 1} + (1 - \alpha ) F_{n - 1}[/tex]

Where

[tex]F_{n}[/tex] is the forecast salary for nth graduate class

α is the smoothing constant

[tex]A_{n-1}[/tex] is the actual salary of n - 1 graduate class

[tex]F_{n-1}[/tex] is the forecast salary of n - 1 graduate class

For n = 1

[tex]F_{1} = 0.25 \cdot A_0} + (1-0.25) \cdot F_{0}\\F_{1} = 0.25 \cdot 60,000} + (0.75) \cdot 55,000\\F_{1} = 56,250[/tex]

For n = 2

[tex]F_{2} = 0.25 \cdot A_1} + (1-0.25) \cdot F_{1}\\F_{2} = 0.25 \cdot 72,000} + (0.75) \cdot 56,250\\F_{2} = 60,187.5[/tex]

For n = 3

[tex]F_{3} = 0.25 \cdot A_2} + (1-0.25) \cdot F_{2}\\F_{3} = 0.25 \cdot 84,500} + (0.75) \cdot 60,187.5\\F_{3} = 66,265.625[/tex]

For n = 4

[tex]F_{4} = 0.25 \cdot A_3} + (1-0.25) \cdot F_{3}\\F_{4} = 0.25 \cdot 96,000} + (0.75) \cdot 66,265.625\\F_{4} = 73,699.218[/tex]

Therefore, the foretasted starting salaries are

[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]

Using an exponential smoothing model with α = 0.25, we sequentially calculate the forecasted starting salary for each year, then use that to estimate the starting salary for the next graduating class.

To predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25 and an initial forecast of $55,000, we follow these steps:

By applying this model, we will obtain the predicted starting salary for the next class after performing these calculations for each given salary data point in sequence.

Answer:

0.000773 is the probability that atleast 12 out of 14 will have brown eyes.

Step-by-step explanation:

We are given the following information:

We treat people having brown eyes as a success.

P(people have brown eyes) = 41% = 0.41

Then the number of people follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 14

We have to evaluate:

[tex]P(x \geq 12) = P(x = 12) + P(x = 13) + P(X = 14) \\= \binom{14}{12}(0.41)^{12}(1-0.41)^2 + \binom{14}{13}(0.41)^{13}(1-0.41)^1 + \binom{14}{14}(0.41)^{14}(1-0.41)^0\\= 0.0007 + 0.00007 + 0.000003\\= 0.000773[/tex]

0.000773 is the probability that atleast 12 out of 14 will have brown eyes.

Yes, it is an unusual event due to small probability values.

Answer:

a) p-hat (sampling distribution of sample proportions)

b) Symmetric

c) σ=0.058

d) Standard error

e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Step-by-step explanation:

a) This distribution is called the sampling distribution of sample proportions (p-hat).

b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.

This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.

c) The variability of this distribution, represented by the standard error, is:

[tex]\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058[/tex]

d) The formal name is Standard error.

e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:

[tex]\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667[/tex]

If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Using the Central Limit Theorem, we get that:

a) Sampling distribution of sample proportions of size 40.

b) Symmetric.

c) 0.0580.

d) Standard error.

e) It would decrease.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard erro .

For a skewed variable, we need n of 30 and greater.

For a proportion p in a sample of size n, we have that:  and standard deviation .

In this problem:

Item a:

We are working proportions, and sample of 40, thus:

Sampling distribution of sample proportions of size 40.

Item b:

Item c:

This is the standard error, thus:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.16(0.84)}{40}} = 0.0580[/tex]

It is of 0.0580.

Item d:

Item e:

The formula is:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

A similar problem is given at https://brainly.com/question/14099217

Answer:

There are many possible solutions. For example,

(2^3)^4 = ((2^5)^12)/((2^6)^8) = 2^10 x 2^2 = (2^19)/(2^7)

(2^2)^5 = ((2^6)^11)/((2^7)^8) = 2^1 x 2^9 = (2^20)/(2^10)

Step-by-step explanation:

You need to fill in boxes with the digits 1 to 20 to create equations where both sides yield the same numerical result. This will involve understanding of basic arithmetic operations and a bit of trial and error.

The subject of this question is Mathematics. Specifically, it relates to the concept of equivalent expressions, which are an essential component of algebra and arithmetic. First, it's crucial to understand the concept of equivalent expressions: two expressions are considered equivalent if they share the same numerical value for each possible value of their variable(s).

Now, let's make an example with the numbers 1 to 10 (just to simplify the explanation). Consider the equations: 1+2+3+4 and 5+3+2+1. Even though the order of operations is different, both expressions yield the final numerical value of 10, making them equivalent expressions.

In the context of the question, you are being asked to fill in boxes with the digits 1-20, such that the expressions on either side of the equation sign are equivalent. This might involve a combination of operations like addition, subtraction, multiplication, and division.

It's a challenging task because it involves a bit of trial and error. Start by deciding on the operations for the expressions and then fill in the numbers. Make sure you check your results by calculating the numerical value of each expression.

https://brainly.com/question/32827451

#SPJ3

Answer:

78,750 pages

Step-by-step explanation:

225 books each with 350 paged

225 x 350

78,750 pages

Answer:

[tex]132\pi[/tex]

Step-by-step explanation:

The lateral area is the area of a rectangle. Think of a soup can with the label removed and laid out flat on a table.  The height of the rectangle is the same as the height of the can (cylinder).  Where does the base of the rectangle come from?  It's the circumference of the can "unrolled."

Area of a rectangle = base x height

Circumference of a circle [tex]C=2\pi r[/tex]

Lateral Area [tex]=2\pi r \times h[/tex] [tex]=2 \pi (6)(11) =132\pi[/tex]

Answer:

$0.90 per kilogram

Step-by-step explanation:

4.5/5=.9

Answer:

The answer is 30% off

Step-by-step explanation:

if you do 21.50 - 30% = 15.05

Answer:

Mean = 2.7

In a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.

Step-by-step explanation:

We are given that the rate of cancer in children is 37 children in 1 million. So the probability of cancer in a child is P(C) = 0.000037

Poisson distribution is used to approximate the number of cases of diseases and we have to find what will be the mean number of cases for 74,090.

In simple words we have to find the expected number of children with cancer in a group of 74,090 children.

The mean value of expected value can be obtained by multiplying the probability with the sample size. So, in this case multiplying probability of child having a cancer with total group size will give us the expected or mean number of children in the group with cancer.

Mean = E(x) = P(C) * Group size

Mean = 0.000037 x 74090

Mean = 2.7

This means in a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.

Final answer:

The mean of the Poisson distribution for the number of cancer cases among 74,090 children in Normalville is approximately 2.7413 cases.

Explanation:

To find the mean of the appropriate Poisson distribution for the number of cases in groups of 74,090 children in Normalville, we multiply the probability of the disease by the number of children. Thus, the mean (μ) is:

μ = probability of one child having the disease × total number of children

μ = 0.000037 × 74,090 = approximately 2.7413

The mean of the Poisson distribution, in this case, indicates the average number of children who would have this rare form of cancer in groups of 74,090 children in Normalville.

Answer:

Expected cost = $6,750

Variance of the cost = $373,500

Step-by-step explanation:

During normal 9 work hours: average number of calls = 7.0

Cost of each call = $50

During 15 off hours:

average number of calls = 4.0

Cost of each call = $60

Let's take U as the number of calls during the normal 9 hours.

I.e, [tex] U = U_1+U_2+U_3+U_4....+ U_9[/tex]

Therefore,

[tex] E(U) = E(U_1)+E(U_2)+E(U_3)+E(U_4)....+E(U_9)[/tex]

= 7+7+7+7+7+7+7+7+7

= 63

In Poisson random variable, Variance= mean, thus:

[tex] Var(U) =Var(U_1)+Var(U_2).....+Var(U_9) [/tex]

= 7+7+7+7+7+7+7+7+7

=63

Let's take V as the number of calls during the day's remaining 15 hours.

E(V) = Var(V)

= 15(4)

=60

The expected cost and the variance of cost associated with the calls received during a 24 hour day:

The expected cost =

$50U + $60V

= $50(63) + $60(60)

= $3150 + $3600

= $6750

The variance of the cost :

= Var(50U + 60V)

= 50²Var(U) + 60²Var(V)

= 2500*63 + 3600*60

= $373,500

Therefore, the expected cost is $6,750 and the variance of the cost is $373,500

Answer:(-5,0) , (-6,0)

Y= (0,30)

Step-by-step explanation:

Answer:

[tex]47.36\%[/tex]

Step-by-step explanation:

The equation that governs how the insect population dies is

[tex]p' = - \mu p[/tex]

We need to solve this differential equation for p.

We separate variables to get:

[tex] \frac{p'}{p} = - \mu[/tex]

We integrate both sides to get:

[tex] \int\frac{p'}{p} dt = - \mu \int \: dt[/tex]

[tex] ln( |p| ) = - \mu \: t + ln(k) [/tex]

[tex]p = c{e}^{ \ - ut} [/tex]

If 1200 insects hatch, and only 70 remain after 6 days,

Then we have:

[tex]70 = 1200 {e}^{ - 6 \mu} [/tex]

[tex] \frac{70}{1200} = {e}^{ - 6 \mu} [/tex]

[tex] - 6 \mu = ln( \frac{7}{120} ) [/tex]

[tex] \mu = \frac{ln( \frac{7}{120} ) }{ - 6} [/tex]

[tex] \mu = 0.4736[/tex]

[tex]47.36\%[/tex]

Answer:

x = 5

Step-by-step explanation:

x² -3x -4 = x² - 5x + 6.

-x² - x²

-3x -4 = -5x + 6

+3x + 3x

-4 = -2x +6

-6 -6

-10 = -2x

÷-2 ÷-2

5 = x

Hope this Helps

Answer:

x = 5

Step-by-step explanation:

hope this helps!

The solution of ''9 more than the quotient of 52 divided by 4'' is 22.

Now,

Given statement is,  ''9 more than the quotient of 52 divided by 4''

What is Quotient?

A quotient is the answer a division problem. The divisor is the number of parts you divide the dividend by.

Now,

The quotient of 52 divided by 4 is,

52 ÷ 4 = 13

And, 9 more than the quotient of 52 divided by 4 is,

( 52 ÷ 4 )+ 9 = 13 + 9 = 22

Hence, The solution of ''9 more than the quotient of 52 divided by 4'' is 22.

Learn more about the Quotient visit:

https://brainly.in/question/848408

#SPJ2

To solve the expression, divide 52 by 4 to get 13, then add 9 to the quotient, resulting in the final answer of 22.

The question asks to find '9 more than the quotient of 52 divided by 4'.

First, we need to calculate the quotient of 52 divided by 4, which is done by performing the division.

So, 52 ÷ 4 equals 13. Next, we add 9 to this quotient to get the final result.

Adding 9 to 13 gives us 22.

Therefore, 9 more than the quotient of 52 divided by 4 is 22.

Answer:

Probability that a randomly selected bill will be at least $39.10 is 0.03216.

Step-by-step explanation:

We are given that the daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.

Let X = daily dinner bills in a local restaurant

So, X ~ N([tex]\mu=28,\sigma^{2} =6^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean amount = $28

            [tex]\sigma[/tex] = standard deviation = $6

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, the probability that a randomly selected bill will be at least $39.10 is given by = P(X [tex]\geq[/tex] $39.10)

  P(X [tex]\geq[/tex] $39.10) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{ 39.10-28}{6}[/tex] ) = P(Z [tex]\geq[/tex] 1.85) = 1 - P(Z < 1.85)

                                                           = 1 - 0.96784 = 0.03216

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.85 in the z table which has an area of 0.96784.

Hence, the probability that a randomly selected bill will be at least $39.10 is 0.03216.

The probability that a randomly selected bill will be at least $39.10 is approximately 0.0323.

First, we calculate the z-score for a bill of $39.10 using the formula:

[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]

where X is the value for which we want to find the probability, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.

Given:

[tex]\[ \mu = 28 \] \[ \sigma = 6 \] \[ X = 39.10 \][/tex]

Plugging in the values:

[tex]\[ z = \frac{39.10 - 28}{6} \] \[ z = \frac{11.10}{6} \] \[ z \approx 1.85 \][/tex]

Now, we look up the z-score of 1.85 in the standard normal distribution table or use a calculator to find the probability of a z-score being at least 1.85. This gives us the area to the right of the z-score on the standard normal curve.

Using a standard normal distribution table or calculator, we find:

[tex]\[ P(Z \geq 1.85) \approx 0.0323 \][/tex]

Answer:

Radius 6.5cm

Diameter  13cm

Step-by-step explanation:

Diameter ia a straight line passing from side to side through the center  a circle or sphere.

Radius formula is simply derived by halving the diameter of the circle

13/2=6.5

Answer:

C. 7269108

D. 0689271

E. 7042351

Step-by-step explanation:

If the number is 0,1 or 2, it is a win.

Otherwise, it is a loss.

Each number is a match.

A. 8531905

Two wins(0,1), 5 losses(8,5,3,9,5)

B. 4963184

One win(1), 6 losses(4,9,6,3,8,4)

C. 7269108

Three wins(2,1,0) and four losses (7,6,9,8)

D. 0689271

Three wins (0,2,1) and four losses (6,8,9,7)

E. 7042351

Three wins (0,2,1), four losses (7,4,3,5)

F. 9094562

Two wins (0,2) and five losses (9,9,4,5,6)

Answer:

C.

D.

E.

Step-by-step explanation:

Answer:

First, apply the power of a product rule by which you raise each factor to the power 3, and then multiply all the factors, to obtain:

       [tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]

Next,  apply the power of a power rule, in virtue of which you raise the factor x² to the power 3 and obtain:

       [tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]

Finally, compute the numerical values, doing 7³ = 7×7×7 = 343.

Therefore, the final result is:

                                                  [tex]343x^6y^3z^3[/tex]

Explanation:

The expression you have to simplify is:

     [tex](7x^2yz)^3[/tex]

You have to apply two rules:

1. Power of a product

This rule states that the power of a product is equal to the product of each factor raised to the same exponent of the whole prduct:

For instance:

         [tex](abc)^z=a^z\cdot b^z\cdot c^z[/tex]

Using this with the expression   [tex](7x^2yz)^3[/tex] it is:

        [tex](7x^2yz)^3=7^3\cdot (x^2)^3\cdot y^3\cdot z^3[/tex]

In complete sentences that is: raise every factor, 7, x², x, and z to the exponent 3 and, then, multiply them.

2. Power of a power:

This rule states that to raise a power to a power, you must multiply the exponents.

For instance:

              [tex](a^n)^m=a^{m\times n}[/tex]

You must apply that rule to the factor [tex](x^2)^3[/tex]

That is:

        [tex](x^2)^3=x^{(3\times 2)}=x^6[/tex]

3. Final result and description using complete sentences:

The first step is to apply the power of a product rule by rasing each factor to the power 3, and then multiply all the factors, to obtain:

       [tex](7x^2yz)^3=7^3(x^2)^3y^3z^3[/tex]

The second step is to apply the power of a power rule, in virtue of which you raise the factor x² to the power 3, in this way:

       [tex]7^3(x^2)^3y^3z^3=7^3x^6y^3z^3[/tex]

The last step is to calculate the numerical values, doing 7³ = 7×7×7 = 343.

The final result is: [tex]343x^6y^3z^3[/tex]

Answer:

-8 and 1

Step-by-step explanation:

the x is going by 5 and the y is going by 2

so add 5 to the x and 2 to the y

hope this help <(*__*)>

Answer:

(-7,1)

Step-by-step explanation:

(1+x/2) = -3     (-3+y/2) = -1

2(1+x/2) = -3(2)    2 (-3+y/2) = -1(2)

multiple each side by two to cancel the two's.

1+x= -6   -3+y= -2

x=-7      y= 1

Answer:

The percent of juniors whose score is at or above the mean is 50%

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 80, \sigma = 8[/tex]

Find the percent of juniors whose score is at least 80.

This is 1 subtracted by the pvalue of Z when X = 80. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 80}{8}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

1 - 0.5 = 0.5

So

The percent of juniors whose score is at or above the mean is 50%