An online gaming site conducted a survey to determine the types of games people play online. if 1500 people participated in the study how many more would play card games than arcade games (Page 824)

Answer:

Claim is rejected

Step-by-step explanation:

Solution:-

- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.

- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.

- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.

- State the hypothesis for the effectiveness of medication:

          Null Hypothesis: p = 0.75   ... Claim

          Alternate hypothesis: p < 0.75   .... Test

- The conditions of standard normality:

Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.

- We will estimate the population proportion with the sample proportion ( p* ):

                          p* = n / N

                          p* = 100 / 150

                          p* = 2/3 = 0.667

- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:

                         [tex]Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607 \\[/tex]

- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.

- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.

- So for lower tailed test the critical value of statistics is:

                       P ( Z < Z-critical ) = α = 0.05

                       Z-critical = - 1.645

- The rejected values all lie to the left of the Z-critical value -1.645          

- The claim test value is compared the rejection region:

                      -2.35607 < -1.645

                       Z-test < Z-critical

Hence, Null hypothesis rejected because test lies in the rejection region.

Conclusion:

The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.

By calculating the Z-score and corresponding p-value for the statistical test, we found that there is significant evidence at the 0.05 level to suggest that the medication's effectiveness is less than the 75% claimed.

The subject we're dealing with here is hypothesis testing in statistics, where we have a claim (the effectiveness of the medication is 75%) and we are testing whether the observations (effectiveness in 100 out of 150 individuals) support this claim.

Firstly, the parameter of interest here is the proportion (p) of individuals for whom the medication is effective. Our null hypothesis (H0) is that p = 0.75 and our alternate hypothesis (Ha) is that p < 0.75.

To conduct the hypothesis test, let's check the conditions:

The sample proportion (p-hat) = 100/150 = 0.67

Next, we calculate the Z score, which is (p-hat - p) / sqrt[p(1-p)/n] = (0.67 - 0.75) / sqrt[0.75 * (0.25) / 150] = -1.65. The p-value associated with a Z score of -1.65 is 0.0495.

Since the p-value is less than the significance level of 0.05, we reject H0 and conclude that there is statistically significant evidence at the 0.05 level that the effectiveness of medication is less than 75% as claimed by the manufacturer.

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The temperature values for which the interpolation would be limited to is given by: Option B: Between 0 and 60

One of such equations we can use for interpolation is given as:

[tex]y - y_0 = \dfrac{y_1 - y_0}{x_1 - x_0} \times (x -x_0)[/tex]

The question seems bit incomplete. From the given options, the second option is correct for the completed question.

Thus, the temperature values for which the interpolation would be limited to is given by: Option B: Between 0 and 60

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Final answer:

Interpolation estimates values within the range of known data points. For temperature values, interpolation would be limited to the temperature ranges provided, such as -60 to 65 degrees. Values outside these intervals would require extrapolation instead.

Explanation:

The question about interpolation is set in the context of Mathematics, specifically focusing on data interpretation or statistics. Interpolation is a method used to estimate values within the range of a discrete set of known data points.

Given the provided information, it seems that temperature values for interpolation are specified within certain ranges. To deduce which temperature values interpolation would be limited to, we must understand the data and context in which interpolation is applied. Since interpolation only makes sense between known data points, it is limited to the ranges of temperatures for which we have data.

For instance, the given ranges such as -60 to -55, -55 to -50, ..., 55 to 60, 60 to 65 suggest that interpolation would be appropriate for estimating temperature values within these intervals. If the known data is between 0 and 60 degrees, the interpolation would be valid only within that range and not outside it since extrapolation, not interpolation, is used to predict values outside the range of known data points.

Answer:

For 99% of confidence interval is 67.5±1.3524

Step-by-step explanation:

Given:

Mean height =67.5 inches

Standard deviation:2.1 inches

Z at 99%.

No of samples 16.

To find:

confidence interval

Solution:

We have formula for confidence interval,

=mean ±Z*{standard deviation/sqrt(no.of observation)}

Now

Z=99%

has  standard  value as ,

Z=2.576

Confidence interval= mean±Z{standard deviation/sqrt(No. of samples)}

=67.5±2.57{(2.1/sqrt(16)}

=67.5±2.576(2.1/4)

=67.5±1.3524

To determine the probabilities of the project manager receiving bonuses, calculate the z-scores for the project completion times and use the normal distribution to find the associated probabilities. The process relies on the project completion times being normally distributed, with the given means and standard deviations used in calculations.

The task involves calculating the probability of a project manager receiving different bonus amounts based on the project completion time. To find the probability of each bonus, we need to consider the distribution of the project completion times along different paths and use the given means and standard deviations. Although the actual values of the probabilities are not provided, the general approach would be to use the normal distribution (since project completion times can be assumed to follow it) and calculate the respective z-scores for 26 weeks and 27 weeks.

For a bonus of $1,000 (project finished within 26 weeks), the z-score calculation would be:

And for a bonus of $500 (project finished within 27 weeks), it would be a similar z-score calculation. After calculating the z-scores, we would use normal distribution tables or a calculator to find the probability associated with those z-scores.

If the provided probability of receiving a $1,000 bonus is 0.4099, this implies that the z-score associated with completing the project within 26 weeks corresponds to a probability of 0.4099 in the normal distribution.

Answer:

Option D, 72 cubic inches

Step-by-step explanation:

The formula for the volume of a rectangular prism is length*width*height, which in this case is 3*3*8=72 cubic inches, or option D. Hope this helps!

Answer: D) 72

Step-by-step explanation: To get the volume of the rectangular prism all you got do is multiply the width x length x height. Therefore:

3 x 3 x 8 = 72

The answer is D) 72

(Hope this helps)

Answer:

Step-by-step explanation:

A 90° CCW rotation makes the transformation ...

  (x, y) ⇒ (-y, x)

A translation 3 left and 2 down makes the transformation ...

  (x, y) ⇒ (x -3, y-2)

The two transformations together are ...

  (x, y) ⇒ (-y-3, x -2)

Then the given points are transformed to ...

 A'(-6, -8)

  B'(-7, -6)

  C'(-6, -4)

  D'(-5, -6)

Answer:

a = 1, b = 10, c = 9

Step-by-step explanation:

x is increasing by positive two from each number and y is increasing by 1 from each number.

mx+n=y

m*3+n=8

m*5+n=9

=>m*5+n-(m*3+n)=9-8

      2m=1  => m=1/2

½ *3+ n =8  

n=8-3/2

n=13/2

=> y=x/2 +13/2

y=(x+13)/2

7=(a+13)/2; a+13=14  => a=1

b=(7+13)/2; b=20/2; b=10

11=(c+13)/2, c+13=22 => c=9

Answer:

d = 2

Step-by-step explanation:

We have four unknown numbers a, b, c, d

It is given that the mode is 3,

Since the mode is 3 then at least two numbers are 3.

It is given that the median is 3,

Since the median is 3 which means the middle two values must be 3

a, 3, 3, d

It is given that the mean of the four numbers is 4,

Since the mean of the four number is 4 then

mean = (a + 3 + 3 + d)/4

4 = (a + 6 + d)/4

4*4 = a + 6 + d

16 = a + 6 + d    eq. 1

It is given that the range is 6,

Since the range is 6 which is the difference between highest and lowest number that is

a - d = 6

a = 6 + d    eq. 2

Substitute the eq. 2 into eq. 1

16 = a + 6 + d

16 = (6 + d) + 6 + d

16 = 12 + 2d

2d = 16 - 12

d = 4/2

d = 2

Substitute the value of d into eq. 2

a = 6 + d

a = 6 + 2

a = 8

so

a, b, c, d = 8, 3, 3, 2

Verification:

a ≤ b ≤ c ≤ d

8 ≤ 3 ≤ 3 ≤ 2

mean = (a + b + c + d)/4

mean = (8 + 3 + 3 + 2)/4

mean = 16/4

mean = 4

range = a - d

range = 8 - 2

range = 6

Answer:

360

Step-by-step explanation:

Divide by two on both numbers to get how many out of 100, or a percentage.

72 / 2 = 36

200 / 2 = 100

Multiply times ten to get 1000

100 x 10 = 1000

36 x 10 = 360

Answer:20000ft^3

Step-by-step explanation:

volume of triangular prism:

Base area x height

1/2 x 20 x 20 x40

(1x20x20x40) ➗ 2

16000 ➗ 2=8000ft^3

Volume of rectangular prism:

Length x width x height

40 x 15 x 20=12000ft^3

Total volume=8000+12000

Total volume=20000ft^3

The total amount of volume inside the parking garage = 20,000 cu. ft.

The volume of the triangular prism = base area × height

V = l × b × h, where 'l' represents the length, 'w' represents the width and 'h' represents the height of the rectangular prism

For given example,

Let V1 represents the volume of the triangular prism and V2 represents the volume of the rectangular prism.

Dimensions of the triangular prism are:

Base - 20 feet by 20 feet and Height - 40 feet

The base of the triangular prism is a triangle.

So, the area of the base would be,

⇒ A = 1/2 × 20 × 20

⇒ A = 200 sq. ft.

The volume of the triangular prism would be,

⇒ V1 = base area × height

⇒ V1 = 200 × 40

⇒ V1 = 8,000 cubic feet

Now, the dimensions of the rectangular prism are:

Base - 15 feet by 40 feet and Height - 20 feet

⇒ l = 40ft., w = 15 ft., h = 20 ft.

The volume of the rectangular prism would be,

⇒ V2 = l × w × h

⇒ V2 = 40 × 15 × 20

⇒ V2 = 12,000 cu. ft.

So, the total amount of volume inside the parking garage would be,

⇒ V = V1 + V2

⇒ V = 8000 + 12000

⇒ V = 20,000 cu. ft.

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Answer:12.57

Step-by-step explanation:

Answer:

12.566370614359 rounded to the nearest hundreth is 12.57

Answer:

please like and Mark as brainliest

don't mind my messy handwriting

the explanation is in the picture

Answer:

Correct option: (C) Yes, because the sample sizes are both greater than 30.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

For the first sample, the sample size of the sample selected is:

n₁ = 32 > 30

Ans for the second sample, the sample size of the sample selected is:

n₂ = 41 > 30

Both the samples selected are quite large.

So, the Central limit theorem can be used to approximate the distribution of of the two sample means.

Ans since the distribution of the two sample means follows a normal distribution, the difference of the two means will also follows normal distribution.

Thus, the correct option is (C).

C Yes, because the sample sizes are both greater than 30.

The following information should be considered;

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Answer:

Part a

For the given study, the explanatory variable or independent variable is given as regularity or frequency of exercise. This variable is classify as categorical variable because variable is divided into two categories such as whether participant exercise 5 or more days a week or not.

Part b

For the given study, the response variable or dependent variable is given as frequency of colds. This variable is classified as quantitative variable because we measure the quantities or frequency of number of colds.

Part c

A confounding variable for this research study is given as incidence of upper respiratory tract infections that provides an alternative explanation for the lower frequency of colds among those who exercised 5 or more days per week, compared to those who were largely sedentary. This confounding variable is categorical in nature.

Answer:5/3 jars left

Step-by-step explanation:

Convert the total number of jars to improper fraction from mixed fraction

The subtract the total number of jars from the total number of empty jars

16/3 -11/3

5/3

Answer:

D. 24/7

Step-by-step explanation:

SOH CAH TOA

we doing the tangent so

tan (α) = opposite / adjacent

tan (α) = 24/7

Answer:

Correlation coefficient 'r' would be lower.

Step-by-step explanation:

Correlation is co movement relationship between two variables.

Correlation coefficient 'r' is positive, when variables move in same direction. 'r' is negative when variables move in opposite direction. So, 'r' lies between -1 (perfect negative correlation) & +1 (perfect positive correlation). High 'r' magnitude reflects strong correlation between the variables, Low 'r' reflects  weak weak correlation between the variables.

Correlation studied between amount of daily exercise and weight  : It is negative as exercise & weight are negatively correlated - more exercise, less weight & less exercise, more weight. 'r' is given = -0.21

If sample is restricted to people weighing less than 180 pounds : It would lead to fall in 'r'. Such because these low weight people are likely to have good natural metabolic rate, naturally slim body physique / figure. So, in their case, exercise & body weight are likely to be less (weakly) correlated than normal case.

Answer:

The restocking level is 113 tins.

Step-by-step explanation:

Let the random variable X represents the restocking level.

The average demand during the reorder period and order lead time (13 days) is, μ = 91 tins.

The standard deviation of demand during this same 13- day period is, σ = 17 tins.

The service level that is desired is, 90%.

Compute the z-value for 90% desired service level as follows:

[tex]z_{\alpha}=z_{0.10}=1.282[/tex]

*Use a z-table for the value.

The expression representing the restocking level is:

[tex]X=\mu +z \sigma[/tex]

Compute the restocking level for a 90% desired service level as follows:

[tex]X=\mu +z \sigma[/tex]

   [tex]=91+(1.282\times 17)\\=91+21.794\\=112.794\\\approx 113[/tex]

Thus, the restocking level is 113 tins.

Final answer:

The restocking level for Jimmy's Delicatessen is calculated using the average demand, standard deviation, desired service level, and the z-score for a 90% service level, resulting in a restocking level of 113 tins.

Explanation:

Calculating the Restocking Level for Jimmy's Delicatessen

To calculate the restocking level, we need to use the information given about the average demand, the standard deviation of demand, and the desired service level. The average demand during the reorder period and order lead time (13 days) is 91 tins. Given the standard deviation of 17 tins and a 90% service level, we would typically look up the z-value that corresponds to a 90% service level in a standard normal distribution table, which is approximately 1.28.

Now, to find the restocking level, we use the formula: Restocking Level = Average Demand + (Z-score * Standard Deviation). Plugging in the numbers, we get:

Restocking Level = 91 tins + (1.28 * 17 tins) = 91 + 21.76 = 112.76 tins.

Therefore, the restocking level should be rounded up to 113 tins to ensure that there is a 90% probability that the stock on hand will be sufficient until the next delivery arrives.

Answer:

  for independent A and B, P(A|B) = P(A)

Step-by-step explanation:

The definition of  conditional probability is ...

  P(A|B) = P(A&B)/P(B)

When A and B are independent, ...

  P(A&B) = P(A)·P(B)

so the conditional probability is ...

  P(A|B) = (P(A)·P(B))/P(B) = P(A) . . . . . for independent A and B

In words, when A and B are independent, the probability of A given B is the same as the probability of A. That is, the probability of B has no effect on the probability of A.

Use PEMDAS and do the multiplication first.

Answer:

All steps below

Step-by-step explanation:

27 - t × 3

27 - 3t

t = 6

27 - 3(6)

27 - 18

9

Answer: 1.6

Order the numbers

5,6,6,8,10

Add

5+6+6+8+10=35

Divide

35÷5=7

Mean: 7

Sum divided by the count.

Final Answer: 1.6

Answer:

1.6

Step-by-step explanation:

Mean: 5 + 6 + 6 + 8 + 10 = 35/5 = 7

7 - 5 = 2

7 - 6 = 1

7 - 6 = 1

7 - 8 = 1

7 - 10 = 3

1 + 1 + 1 + 2 + 3 = 8/5 = 1.6

Answer:

choice a....625 = [tex]5^{4}[/tex] in exponential form

Step-by-step explanation:

625 = 25*25 =  [tex]25^{2}[/tex]  =  [tex]5^{4}[/tex]

Answer:

choice A well be correct !! (did it on usa test prep)

Step-by-step explanation:

Answer:

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.

The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.

Step-by-step explanation:

This is a case in which, from a sample os size n=16, a confidence interval is constructed.

The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.

Answer:

C = 1029.92 ft

Step-by-step explanation:

C = πd              Use the equation for circumference

C = 3.14(328)       Multiply

C = 1029.92 ft

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Answer:

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

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.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 40, p = 0.2[/tex]

So

[tex]\mu = E(X) = np = 40*0.2 = 8[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40*0.2*0.8} = 2.53[/tex]

What is the probability that a randomly selected bag of this size has 10 or more green candies

Using continuity correction, this is [tex]P(X \geq 10 - 0.5) = P(X \geq 9.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 9.5. So

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

[tex]Z = \frac{9.5 - 8}{2.53}[/tex]

[tex]Z = 0.59[/tex]

[tex]Z = 0.59[/tex] has a pvalue of 0.7224

1 - 0.7224 = 0.2776

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Answer:

[tex]P(x\geq 10)=0.2682[/tex]

Step-by-step explanation:

The number x of green candies in a bag of 40 candies follows a binomial distribution, because we have:

So, the probability that in a bag of 40 candies, x are green is calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Replacing, n by 40 and p by 0.2, we get:

[tex]P(x)=\frac{40!}{x!(40-x)!}*0.2^{x}*(1-0.2)^{40-x}[/tex]

So, the probability that a randomly selected bag of this size has 10 or more green candies is equal to:

[tex]P(x\geq 10)=P(10)+P(11)+...+P(40)\\P(x\geq 10)=1-P(x<10)[/tex]

Where [tex]P(x<10)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)[/tex]

So, we can calculated P(0) and P(1) as:

[tex]P(0)=\frac{40!}{0!(40-0)!}*0.2^{0}*(1-0.2)^{40-0}=0.00013\\P(1)=\frac{40!}{1!(40-1)!}*0.2^{1}*(1-0.2)^{40-1}=0.00133[/tex]

At the same way, we can calculated P(2), P(3), P(4), P(5), P(6), P(7), P(8) and P(9) and get that P(x<10) is equal to:

[tex]P(x<10)=0.7318[/tex]

Finally, the probability [tex]P(x\geq 10)[/tex] that a randomly selected bag of this size has 10 or more green candies is:

[tex]P(x\geq 10)=1-P(x<10)\\P(x\geq 10)=1-0.7318\\P(x\geq 10)=0.2682[/tex]

Answer:

There are 3 hundredths

Step-by-step explanation:

0.63

. tenths   hundredths

There are 3 hundredths

Answer:

[tex]z=\frac{23-21}{\frac{3.5}{\sqrt{49}}}=4[/tex]    

[tex]p_v =2*P(z>4)=0.0000633[/tex]  

When we compare the significance level [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can reject the null hypothesis at 10% of significance. So the  the true mean is difference from 21 at this significance level.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=23[/tex] represent the sample mean

[tex]\sigma=3.5[/tex] represent the population standard deviation

[tex]n=49[/tex] sample size  

[tex]\mu_o =21[/tex] represent the value that we want to test

[tex]\alpha=0.1[/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 (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the average age of the evening students is significantly different from 21, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 21[/tex]  

Alternative hypothesis:[tex]\mu \neq 21[/tex]  

The statistic is given by:

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

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]z=\frac{23-21}{\frac{3.5}{\sqrt{49}}}=4[/tex]    

P-value

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

[tex]p_v =2*P(z>4)=0.0000633[/tex]  

Conclusion  

When we compare the significance level [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can reject the null hypothesis at 10% of significance. So the  the true mean is difference from 21 at this significance level.

Final answer:

To determine whether the average age of the evening students is significantly different from 21, we can conduct a hypothesis test using a z-test with a known population standard deviation.

Explanation:

To determine whether the average age of the evening students is significantly different from 21, we can conduct a hypothesis test.

First, we need to state our hypotheses:

Null hypothesis (H0): The average age of the evening students is equal to 21.

Alternative hypothesis (Ha): The average age of the evening students is not equal to 21.

Since the population standard deviation is known, we can use a z-test. We calculate the test statistic using the formula:

z = (sample mean - hypothesized mean) / (population standard deviation / sqrt(sample size))

Once we have the test statistic, we can compare it to the critical value at a significance level of 0.1. If the test statistic falls within the critical region, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In this case, the test statistic is 2.8571, which falls outside the critical region. Therefore, we reject the null hypothesis and conclude that the average age of the evening students is significantly different from 21.

The surface area of a square pyramid is found by adding the area of the square base to the area of the four triangular faces. If the side of the square base is 's' and the length of the slant height of the triangles is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex]

The net described in the question would form a square pyramid. To calculate the surface area of a square pyramid, you add the area of the square base to the combined areas of the four triangular faces. If the side of the square is 's' and the length of the slant height of the triangular faces is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex] The surface area is expressed in square units. For example, if the side of the square is 4 units and the slant height is 6 units, the surface area of the pyramid is [tex]4^2 + 2 * 4 * 6 = 16 + 48 = 64[/tex] square units.

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Answer:

We showed that if we have the position of the particle [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex] the velocity of the particle at time t is given by [tex]v(t)=\frac{70t}{\left(3t^2+8\right)^2}[/tex].

Step-by-step explanation:

Velocity is defined as the rate of change of position with respect to time.

                                                  [tex]v(x)=\frac{dx}{dt}[/tex]

To find velocity, we take the derivative of the position function [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex]

[tex]\mathrm{Apply\:the\:Quotient\:Rule}:\quad \left(\frac{f}{g}\right)'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]

[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{\frac{d}{dt}\left(t^2-9\right)\left(3t^2+8\right)-\frac{d}{dt}\left(3t^2+8\right)\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]

Next, we find the values of [tex]\frac{d}{dt}\left(t^2-9\right)[/tex] and [tex]\frac{d}{dt}\left(3t^2+8\right)[/tex]

[tex]\frac{d}{dt}\left(t^2-9\right)=\frac{d}{dt}\left(t^2\right)-\frac{d}{dt}\left(9\right)=2t-0=2t[/tex]

[tex]\frac{d}{dt}\left(3t^2+8\right)=\frac{d}{dt}\left(3t^2\right)+\frac{d}{dt}\left(8\right)=6t+0=6t[/tex]

So,

[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{2t\left(3t^2+8\right)-6t\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]

Next, we expand [tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)[/tex]

[tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)=6t^3+16t-6t\left(t^2-9\right)=6t^3+16t-6t^3+54t=70t[/tex]

Therefore,

[tex]v(t)=\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{70t}{\left(3t^2+8\right)^2}[/tex]

This question lies in high school level Mathematics, more specifically in calculus. The process includes finding the derivative of a function x(t) to get v(t), which is the velocity of the particle. There appears to be an error in the provided equations in the question.

The subject of this question falls under calculus, a branch of Mathematics, and the grade level would most likely be High School. The equation for the particle's position in terms of time x(t)=(t^2 - 9)/(3t^2 + 8) indicates the focus is on particle motion.

To find the velocity of a particle moving along a line at a given time, we find the derivative of the position function. This principle comes from the fact that velocity is the rate of change of position with respect to time. In this case, the derivative of the position function x(t) gives the velocity function v(t).

However, it seems there might be a mistake in the question because the derivative of x(t) is not v(t)=70t/(30t^2 + 8)^2. Please double-check the original problem to ensure the equations are correctly provided.

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Answer:

The way you worded this he should buy at either store because the price is 20 at both and he won't have any savings because they have the same price.

Step-by-step explanation:

Answer:

Well correct me if I am wrong but I think something is missing in this problem because I do not see another number to compare $20 to...