Lucia hit a golf ball 240 feet. How many yards did she hit the ball?

A) 80 yards

B) 60 yards

C) 120 yards

D) 300 yards

Answer:

yes

Step-by-step explanation:

no

maybe

perhaps

done

Answer:

You have every right to be angry, but that doesn't give you the right to be mean.

He drank life before spitting it out.

My Mum tries to be cool by saying that she likes all the same things that I do.

Step-by-step explanation:

Pauline can purchase 3 grey parrots and 7 blue lovebirds with her budget of $1040 to fulfill the requirement of buying a total of 10 birds.

To figure out how many of each bird Pauline can buy, we can setup and solve a system of equations:

Solving the system:

Therefore, Pauline should purchase 3 grey parrots and 7 blue lovebirds.

To find the total amount in an investment account after 13 years with continuous compounding, use the formula for continuous compound interest. Substitute the given values into the formula and compute.

The question deals with the concept of continuous compound interest. The formula for this is given by the equation V=P * e^{rt}, where V is the total value of the investment after time t, P is the principal amount, r is the rate of interest, and e is the base of the natural logarithm.

Plug these values into the equation: V = $934 * e^{0.061 * 13} . Using the value of e, which is approximately 2.71828, compute to get V. Therefore the total amount in the account after 13 years, when rounded to the nearest cent, will be V.

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The amount of money in an account with continuously compounded interest, substitute the given principal, interest rate, and time values in the formula V = Pert. Convert the interest rate to a decimal before using. Calculate the exponent using a scientific calculator or similar tool.

You're looking to calculate the future value of an investment using the formula for continuous compounding, V = Pert. In this case, P = $934, r = 6.1%, and t = 13 years.

First, convert the percent interest rate to a decimal by dividing by 100, which gives r = 0.061.

Then, substitute the given values into the formula:

V = $934 * e(0.061 * 13).

Calculator the exponent to find the value V. Round the final answer to the nearest cent.

In summary, computing the amount of money in a continuously compounded account involves substituting the given values into the proper formula and calculating using an appropriate method such as a scientific calculator or algorithm.

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The cone is the correct answer.

A cone is the shape that could be slice perpendicular to its base/face to create a cross-section whose shape has two edges, one straight and one curved.

cone, in mathematics, the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

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Answer:

r(x) = 56x + 99

Step-by-step explanation:

You need to add the two equations together:

r(x) = (24x+48) + (51+32x)

r(x) = 24x + 32x + 48 + 51

r(x) = 56x + 99

Answer:

Step-by-step explanation:

Took the test

Answer:

Probability that a battery will last more than 19 hours is 0.0668.

Step-by-step explanation:

We are given that the lifetime of a battery in a certain application is normally distributed with mean μ = 16 hours and standard deviation σ = 2 hours.

Let X = lifetime of a battery in a certain application

So, X ~ N([tex]\mu=16,\sigma^{2} =2^{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 lifetime = 16 hours

            [tex]\sigma[/tex] = standard deviation = 2 hours

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 battery will last more than 19 hours is given by = P(X > 19 hours)

  P(X > 19) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] > [tex]\frac{19-16}{2}[/tex] ) = P(Z > 1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)

                                              = 1 - 0.9332 = 0.0668

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 = 1.50 in the z table which has an area of 0.9332.

Hence, the probability that a battery will last more than 19 hours is 0.0668.

The probability that a battery with a mean lifetime of 16 hours and a standard deviation of 2 hours will last more than 19 hours is approximately 6.68%, calculated using the z-score for a normal distribution.

Probability of Battery Lasting More Than 19 Hours

The question asks about the probability that a battery with a normal distribution will last more than 19 hours, given a mean μ = 16 hours and standard deviation σ = 2 hours. To find this probability, we calculate the z-score using the formula:

[tex]Z = (X - \mu) / \sigma[/tex]

For X = 19 hours:

[tex]Z = (19 - 16) / 2 = 1.5[/tex]

Next, we use a standard normal distribution table or a calculator to find the probability associated with this z-score. The area to the right of Z = 1.5 represents the probability that a battery lasts more than 19 hours. Assuming we've looked up the value in the standard normal distribution table:

[tex]P(X > 19) = 1 - P(Z \leq 1.5) = 1 - 0.9332 = 0.0668[/tex]

Thus, the probability that a battery will last more than 19 hours is approximately 6.68%.

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Answer:

2x

Step-by-step explanation:

[8x² - 4x] ÷ [4x - 2]

[4x(x - 2)] ÷ [2(x - 2)]

[2x × 2(x - 2)] ÷ [2(x - 2)]

2x

Answer:

The decay rate expressed as a percentage is of 24%.

Step-by-step explanation:

The equation for the value of the car has the following format:

[tex]y(t) = y0(1-r)^{t}[/tex]

In which y(t) is the value of the car after t years, y0 is the initial value and r is the decay rate, as a decimal.

In this problem:

y=48000(0.76)^t

So

Comparing to the general formula:

1 - r = 0.76

r = 1 - 0.76

r = 0.24

To convert from decimal to percentage, we multiply by 100

The decay rate expressed as a percentage is of 24%.

Answer: 28

Step-by-step explanation:

Answer:

28 pints

Step-by-step explanation:

There are 4 quarts in a gallon

There are 2 pints in a quart

We know 10 guarts = 10/4 = 2 .5 gallons = 2 gallons 2 guarts

Subtracting the 10 quarts in the kitchen

9 gallons - 2 gallons 2 quarts

Changing 1 gallon to 4 quarts

8 gallons 4 quarts - 2 gallons 2 quarts = 6 gallons 2 quarts

Then he used 3 gallons in the living room

6 gallons 2 quarts - 3 gallons = 3 gallons 2 quarts

Changing gallons to quarts

3*4 = 12 12 quarts + 2 quarts = 14 quarts

Now we need to change to pints

14 quarts * 2 pints = 28 pints

Answer:

Null hypothesis:[tex]\mu = 52.6[/tex]  

Alternative hypothesis:[tex]\mu \neq 52.6[/tex]  

[tex]z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976[/tex]    

[tex]p_v =2*P(z>1.976)=0.0482[/tex]  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

Step-by-step explanation:

Information provided

[tex]\bar X=52.8[/tex] represent the sample mean  for the MPG of the cars

[tex]\sigma=1.6[/tex] represent the population standard deviation

[tex]n=250[/tex] sample size  of cars

[tex]\mu_o =52.6[/tex] represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test

Hypothesis

We need to conduct a hypothesis in order to check if the true mean of MPG is different from 52.6 MPG, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 52.6[/tex]  

Alternative hypothesis:[tex]\mu \neq 52.6[/tex]  

Since we know the population deviation the statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

Calculate the statistic

Replacing we have this:

[tex]z=\frac{52.8-52.6}{\frac{1.6}{\sqrt{250}}}=1.976[/tex]    

Decision

Since is a two tailed test the p value would be:  

[tex]p_v =2*P(z>1.976)=0.0482[/tex]  

Since the p value is lower than the significance level wedon't have enough evidence to conclude that the true mean is significantly different from 52.6 MPG.

Answer:

A) Pd = 13/28

B) Pd = 7/16

Step-by-step explanation:

Given;

Drama = 2

Comedy = 1

Science fiction = 5

Total = 8

a) The probability of selectingat least one drama movie Pd;

Pd = 1 - Pd'

Without replacement;

Probability of not selecting a drama movie Pd' is;

Pd' = 6/8 × 5/7 = 15/28

Pd = 1 - 15/28

Pd = 13/28

b) with replacement;

Probability of not selecting a drama movie Pd' is;

Pd' = 6/8 × 6/8 = 9/16

Pd = 1 - 9/16

Pd = 7/16

To test the effectiveness of touch therapists, a hypothesis test can be conducted using a significance level of 0.05. The test statistic is calculated by comparing the observed success rate to the expected success rate under the null hypothesis. If the test statistic falls within the critical region, the null hypothesis can be rejected and it can be concluded that the touch therapists are effective.

To test the claim that touch therapists use a method equivalent to random guesses, a hypothesis test can be conducted using a significance level of 0.05. In this case, the null hypothesis would state that the therapists' success rate is no better than random chance, while the alternative hypothesis would state that the therapists are effective. The test statistic can be calculated using the observed success rate and the expected success rate under the null hypothesis. If the test statistic falls within the critical region, which is determined by the significance level, then the null hypothesis can be rejected, suggesting that the touch therapists are indeed effective.

First, let's calculate the expected success rate under the null hypothesis. Since the therapists are guessing randomly, the probability of guessing correctly is 0.5. Therefore, the expected success rate can be calculated by multiplying the total number of trials by the probability of guessing correctly:

Expected success rate = 0.5 * 264 = 132

Next, we can calculate the test statistic using the observed success rate and the expected success rate:

Test statistic = (observed success rate - expected success rate) / sqrt(expected success rate * (1 - expected success rate) / number of trials)

Substituting the values into the formula:

Test statistic = (105 - 132) / sqrt(132 * (1 - 132/264) / 264) = -3.181

Finally, we can compare the test statistic to the critical value. The critical value can be obtained from the Z-table or using statistical software. If the test statistic falls within the critical region (i.e., if it is less than the negative critical value), then we can reject the null hypothesis and conclude that the touch therapists are effective.

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To test the claim that touch therapists use a method equivalent to random guesses, a hypothesis test can be conducted. The data provided is used to calculate the p-value, which is found to be less than 0.05. This suggests that touch therapists are effective.

To test the claim that touch therapists use a method equivalent to random guesses, we can use a hypothesis test. The null hypothesis is that the therapists' accuracy is due to random chance, while the alternative hypothesis is that they are effective. We can use a binomial hypothesis test with a significance level of 0.05. Using the given data, the therapists were correct in 105 out of 264 trials. Calculating the p-value, we find that it is less than 0.05, which means we reject the null hypothesis. Therefore, the results suggest that touch therapists are effective.

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Answer:

The student GPA is 3.1875

Step-by-step explanation:

First we calculate the grade point by multiplying the grade with the weight;

= (3.9 * 5) + (2.1 * 3) + (2.9 * 4) + (3.4 * 4)

= 19.5 + 6.3 + 11.6 + 13.6

= 51

Total weight = 5+3+4+4=16

GPA = 51/16=3.1875

To calculate the student's GPA, we multiply each course grade by its credit hours, sum those totals to get the quality points, and then divide by the total number of credits. In this case, the student's GPA is 3.1875.

To calculate a student's Grade Point Average (GPA) for a term, each course grade is multiplied by the course's credit hours to get the total quality points for that course. Then, the sum of all quality points is divided by the total number of credit hours taken.

Step-by-Step GPA Calculation

For each course, multiply the grade by the number of credits:

(3.9 × 5) + (2.1 × 3) + (2.9 × 4) + (3.4 ×4).

Sum the results of these multiplications to get the total quality points.

Sum the total number of credits: 5 + 3 + 4 + 4.

Divide the total quality points by the total number of credits.

Let's do the math:

(3.9 × 5) = 19.5

(2.1 × 3) = 6.3

(2.9 × 4) = 11.6

(3.4 × 4) = 13.6

Total quality points = 19.5 + 6.3 + 11.6 + 13.6 = 51

Total credits = 5 + 3 + 4 + 4 = 16

The student's GPA for the term is the total quality points divided by the total credits:

GPA = 51 / 16 = 3.1875.

Answer:

Check the explanation

Step-by-step explanation:

US has a comparative advantage in producing rice.

This means US's opportunity cost of producing rice is less than that of Korea.

Korea's opportunity cost of producing rice will be given as:

For producing 9 units of Rice, Korea gives up 5 cars.

For producing 1 unit of rice's, Korea will give up 5/9 units of car.

Kindly check the image below.

If the U.S. has a comparative advantage in producing rice, then [tex]\( X > \frac{54}{7} \).[/tex]

The correct answer is option B.

Comparative advantage in the context of international trade is determined by the opportunity cost of producing one good over another. If the U.S. has a comparative advantage in producing rice, it implies that the U.S. can produce rice at a lower opportunity cost compared to Korea. To analyze the situation, let's consider the production figures provided:

In the U.S., the opportunity cost of producing one unit of rice is 6/7 units of cars. In Korea, the opportunity cost of producing one unit of rice is X/9 units of cars. Since the U.S. has the comparative advantage in rice production, X/9 (opportunity cost for Korea) should be greater than 6/7 (opportunity cost for the U.S.).

Mathematically, this can be expressed as:

[tex]\[ \frac{X}{9} > \frac{6}{7} \][/tex]

To simplify the comparison, multiply both sides of the inequality by 9 to get:

[tex]\[ X > \frac{54}{7} \][/tex]

Therefore, the correct statement is [tex]\( X > \frac{54}{7} \)[/tex] making option B the correct option.

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Answer:

No it is not

Step-by-step explanation:

B is a subset of A but not all the elements in Set A are in B hence they don't contain equal elements

Answer:

3

Step-by-step explanation:

The region representing the solution to a system of inequalities is where the shading of all individual inequalities overlap on a graph. In this case, the provided inequalities should be graphed individually, and the overlapping shaded area is the solution.

The region that represents the solution to a system of inequalities is the area in a graph where all the inequality solutions overlap. In the given inequalities:

First, graph each inequality individually on the coordinate plane using a method that makes sense (linear inequality graphing for this case). The region that is shaded by both inequalities, or resides in the overlap of the shading of the individual inequalities, represents the solution to the system of inequalities.

Do recall that when dealing with 'greater than' or 'less than' signs, we use dashed lines to represent the boundary where inequality is not equal to the boundary. If the sign was 'greater than or equal to' or 'less than or equal to', we would use solid lines.

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Answer:

The 90% confidence interval for the mean consumption of milk among males over age 25 is (2.8 lt, 3.0 lt).

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

 [tex]CI=\bar x\pm z_{\alpha /2}\ \frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

 [tex]n=715\\\bar x=2.9\ \text{lt}\\\sigma=1.2\ \text{lt}[/tex]

Confidence level = 90%

Then, α = 10%

Compute the critical value of z for α = 10% as follows:

 [tex]z_{\alpha/2}=z_{0.10/2}=z_{0.05}=1.645[/tex]

*Use a z-table.

Compute the 90% confidence interval for population mean as follows:

[tex]CI=\bar x\pm z_{\alpha /2}\ \frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=2.9\pm 1.645\times \frac{1.2}{\sqrt{715}}\\\\=2.9\pm 0.074\\\\=(2.826, 2.974)\\\\\approx (2.8\ \text{lt}, 3.0\ \text{lt})[/tex]

Thus, the 90% confidence interval for the mean consumption of milk among males over age 25 is (2.8 lt, 3.0 lt).

Answer:

[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]    

[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]    

We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2  is between (2.793; 3.951)

Step-by-step explanation:

Data provided

2.69, 5.76, 2.67, 1.62, and 4.12

We can calculate the sample mean with this formula:

[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X=3.372[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma=0.66[/tex] represent the population standard deviation

n=5 represent the sample size  

Confidence interval :

The two sided confidence interval for the true mean is given by:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

We have the confidence level given of 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that [tex]z_{\alpha/2}=1.96[/tex]

Replacing into the formula for the interval we have this:

[tex]3.372-1.96\frac{0.66}{\sqrt{5}}=2.793[/tex]    

[tex]3.372+1.96\frac{0.66}{\sqrt{5}}=3.951[/tex]    

We are 95% confident that the true mean for the adhesion to solid surfaces in dyne-cm2  is between (2.793; 3.951)

Final answer:

The 95% confidence interval for the mean adhesion of the bacterial strain Acinetobacter, based on the given measurements and standard deviation, is [2.795, 3.949] dyne-cm².

Explanation:

The question asks us to find a 95% confidence interval for the mean adhesion of the bacterial strain Acinetobacter based on five given measurements and a known standard deviation. To calculate the confidence interval, we can use the formula for the confidence interval of the mean when the standard deviation is known:

mean ± Z*(standard deviation/√n),

where Z is the Z-value corresponding to the desired level of confidence from the standard normal distribution, and n is the sample size.

First, we need to calculate the mean of the given measurements:

Since we are looking for a 95% confidence interval and the standard deviation (σ) is 0.66 dyne-cm² with a sample size (n) of 5, our formula becomes:

3.372 ± (Z * 0.66 / √5)

To find the appropriate Z-value, we look at the standard normal distribution table for a two-sided 95% confidence interval, which gives us a Z-value of approximately 1.96.

Plugging this Z-value into the formula, we can calculate the confidence interval:

3.372 ± (1.96 * 0.66 / √5) = 3.372 ± 0.577

Therefore, the 95% confidence interval for the mean adhesion is [2.795, 3.949] dyne-cm².

Answer:

The answer is 24 inches

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

Answer:

  34 would be a Rational number

Step-by-step explanation:

it's clean number and not sloppy like 0.888883

The final inequality that defines the shaded region on the graph is y ≥ -2 + 2x. Here option A is correct.

Given Linear Equation:

The general form of a linear equation is y = mx + c, where c is the y-intercept (the value of y when x = 0). Given that the point (0, -2) lies on the line, c = -2. The equation is then y = mx - 2.

Equation: y = mx - 2

Using Another Point on the Line:

The point (2, 2) is also on the line. Substitute x = 2 and y = 2 into the equation:

2m - 2 = 2

Solve for m:

2m = 4

m = 2

Now we know m = 2, so the equation becomes:

y = 2x - 2

Inequality for Shaded Region:

The inequality sign ≥ suggests that the shaded region is above the line. Therefore, the inequality for the shaded region is:

y ≥ 2x - 2

Rewriting the Inequality:

To match the given form y ≥ -2 + 2x, rearrange terms:

y ≥ -2 + 2x. Here option A is correct.

Complete question:

Which inequality describes the graph?

Answer:

If solving an equation yields a statement that is true for a single value for the variable, like x = 3, then the equation has one solution. If solving an equation yields a statement that is always true, like 3 = 3, then the equation has infinitely many solutions.

Step-by-step explanation:

Final answer:

Equations can have differing numbers of solutions: linear equations typically have one, while quadratic equations usually have two, but may have one or none depending on their discriminant. Inequalities often have a range of solutions, representing values that satisfy the inequality condition.

Explanation:

The number of solutions an equation has can vary depending on the type of equation. Linear equations typically have one solution, representing where the line intersects the x-axis on a graph. Equations that involve an unknown squared, also known as quadratic equations, generally have two solutions; these solutions represent the x-intercepts or the points where the parabola crosses the x-axis. However, there are cases where a quadratic equation might have one or no real solutions depending on its discriminant (b2 - 4ac).

Inequalities are different from equations. They often have a range of solutions rather than exact values, because they represent values that are less than (<), less than or equal to (≤), greater than (>), or greater than or equal to (≥) a certain number, rather than being exactly equal to it. A simple linear inequality, for instance, has a set of all possible solutions that make the inequality true, which can be illustrated as a region on a number line or in coordinate space.

The experimental probability that the band will play an encore at its next show is 7/12 or approximately 0.5833.

To find the experimental probability that the band will play an encore at its next show, we need to divide the number of times the band played an encore by the total number of shows. In this case, the band played an encore at 7 out of 12 shows. To calculate the experimental probability, divide 7 by 12. So, the experimental probability that the band will play an encore at its next show is 7/12 or approximately 0.5833.

Answer:

x = 1.67 about  and y = 4.67 about

Step-by-step explanation:

y = 4x-2 and y = x+3

4x - 2 = x + 3

3x = 5

x = 5/3 = 1.67  about

y = 5/3 + 3 = 5/3 + 9/3 = 14/3 = 4.667

Answer:

-11

Step-by-step explanation:

I got it wrong, sorry! T-T

Answer:

[tex]n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13[/tex]  

And rounded up we have that n=173

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

[tex]p[/tex] represent the real population proportion of interest

[tex]\hat p[/tex] represent the estimated proportion for the sample

n is the sample size required (variable of interest)

[tex]z[/tex] represent the critical value for the margin of error

Solution to the problem

The population proportion have the following distribution  

[tex]p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})[/tex]  

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by [tex]\alpha=1-0.90=0.10[/tex] and [tex]\alpha/2 =0.05[/tex]. And the critical value would be given by:  

[tex]z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64[/tex]  

The margin of error for the proportion interval is given by this formula:  

[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)  

And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)

We can assume that the estimates proportion is [tex]\hat p=\frac{14}{70}=0.2[/tex]. And replacing into equation (b) the values from part a we got:  

[tex]n=\frac{0.2(1-0.2)}{(\frac{0.05}{1.64})^2}=172.13[/tex]  

And rounded up we have that n=173

Answer: the first one

Step-by-step explanation: base×width×height

Answer:

The first choices.

Step-by-step explanation:

The solid is a rectangular prism which means V=l × w × h