A clown is shot out of cannon with a velocity of 200 feet per second at an angle of 24°
with the horizontal. Find the vertical and horizontal components of the velocity of this clown.

Answer:

The answer is B

Step-by-step explanation:

Just did the assignment on Egn.

Answer:

465

Step-by-step explanation:

424+41=465

Answer:

-13a+10b

Step-by-step explanation:

Answer:

A, B, D

Step-by-step explanation:

The linear parent function is a straight line with equation x=y, which means that it has a slope of 1 and goes through the origin. However, it does not go through quadrants 2 and 4, only 1 and 3. Hope this helps!

Answer: x = 0 or x = 2

Step-by-step explanation:

To solve this, we must note that the two equations speaks of a single function of y. So

y = 2x - 3 = x² - 3

So from.here we can equate the two together and solve for x.

x² - 3 = 2x - 3, biw convert to a quadratic expression

x² - 2x - 3 + 3 = 0

x² - 2x = 0

Now factorize

x( x - 2 ) = 0, so solving for x

x = 0 or x = 2. .I believed getting the 2 won't be a problem

When x - 2 = 0

Then x = 2.

Answer: A. Mean.

Explanation:

Mean is the only measure of central tendency that is always affected by an outlier. Mean, the average is the most popular measure of central tendency.

The mean is strongly influenced by outliers because it is the average of the scores and it is not resistant.

Answer:

A) mean

Step-by-step explanation:

Mean is a measure of central tendency, it is the sum of all data divided by the number of data. Because the mean take into consideration each of the data in its calculations, it is generally affected by outliers (extremely high or low values)

Answer:

  68.44%

Step-by-step explanation:

You compute the average the way you compute any average: add up the numbers and divide by their number.

Multiplication is a useful way to shorten the effort of repeated addition.

  (64% × 3 + 58% × 7 + 88% × 3 +33% + 100% × 2)/(3 +7 +3 + 1 + 2)

  = 1095%/16 = 68.4375%

  ≈ 68.44% . . . the average mark for the class

The volume of Christina's cube-shaped coin bank is calculated by cubing the length of one of its sides, which is 7 inches. The volume is therefore 7 × 7 × 7, or 343 cubic inches.

The volume of Christina's cube-shaped coin bank can be calculated using the formula for the volume of a cube, which is Volume = side × side × side. As all sides of a cube are equal and the coin bank is 7 inches wide and 7 inches tall, we can calculate the volume by multiplying 7 inches by 7 inches by 7 inches.

Calculation:

Volume = 7 in. × 7 in. × 7 in. = 343 cubic inches

Hence, the volume of Christina's coin bank is 343 cubic inches.

Final answer:

The volume of Christina's cube-shaped coin bank is calculated using the cube volume formula and is found to be 343 cubic inches.

Explanation:

To calculate the volume of Christina's coin bank, we use the formula for the volume of a cube, which is Volume = side³, where 'side' is the length of one side of the cube. Since the coin bank is 7 inches wide and 7 inches tall, each side is 7 inches. Thus, the volume of the coin bank is:

Volume = 7 in. × 7 in. × 7 in. = 343 in.³

Therefore, Christina's coin bank has a volume of 343 cubic inches.

Answer:

[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]    

Critical value

The degreed of freedom are given by:

[tex]df=n-1=57-1=56[/tex]  

We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:

[tex] t_{\alpha}= -1.297[/tex]

And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes

P value

The p value for this case would be given by:

[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]  

Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes

Step-by-step explanation:

Information provided

[tex]\bar X=6.5[/tex] represent the sample mean for tje waiting times

[tex]s=2.1[/tex] represent the sample standard deviation

[tex]n=57[/tex] sample size  

[tex]\mu_o =7[/tex] represent the value to verify

[tex]\alpha=0.1[/tex] represent the significance level

t would represent the statistic

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

System of hypothesis

We want to verify if the true mean for this case is less than 7 minutes, the system of hypothesis for this case sre:  

Null hypothesis:[tex]\mu \geq 7[/tex]  

Alternative hypothesis:[tex]\mu < 7[/tex]  

Since we don;t know the population deviation the statistic for the t test is given by:

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

If we replace the info given we got:

[tex]t=\frac{6.5-7}{\frac{2.1}{\sqrt{57}}}=-1.798[/tex]    

Critical value

The degreed of freedom are given by:

[tex]df=n-1=57-1=56[/tex]  

We are looking for a critical value in the t distribution with 56 degrees of freedom who accumulates 0.10 of the area in the left and we got:

[tex] t_{\alpha}= -1.297[/tex]

And since the calculated value is lower than the critical value we have enough evidence to reject the null hypothesis for this case and makes sense conclude that the true mean is less than 7 minutes

P value

The p value for this case would be given by:

[tex]p_v =P(t_{(56)}<-1.798)=0.0388[/tex]  

Since the p value is lower than the significance level provided of 0.1 we have enough evidence to conclude that the true mean is significantly lower than 7 minutes

Following are the solution to the given question:

Given:

size [tex](n) = 58[/tex]

mean [tex]\mu = 7.4 \ minutes[/tex]

standard deviation [tex]\sigma = 2.3 \ minutes[/tex]

null and alternative hypotheses:

[tex]H_0 : \mu = 8 \ minutes\\\\H_a : \mu < 8 \ minutes\\\\[/tex]

Calculating the test statistic:

So, the observed value

Calculating the degrees of freedom:

[tex]\to 58 - 1 = 57[/tex]

Calculating the range of p-value:

Therefore the t is the critical value at the significance level that is 0.05 with of freedom is,

Therefore,

[tex]\to test \ statistic = -1.987 < -1.672[/tex]  rejecting the null hypothesis.

Therefore, the conclusion of the manager's claim is "True".

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To find the p-value from the given data in Excel, populate your data in Excel sheet into various columns for each variable. Then, use the 'Regression' tool under 'Data Analysis' in the 'Data' tab, selecting the appropriate ranges for dependent and independent variables. Ensure that the 'P-Values' box is checked before clicking 'OK'. Excel will then generate the regression analysis with the p-value.

In Excel, you can perform regression analysis to deduce the p-value from this data using the following steps:

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Answer:

$3,256.2

Step-by-step explanation:

First, we need to get 3% of 3,460. Find the decimal value of 3%:

3% -> [tex]\frac{3}{100}[/tex] -> 0.03

Next, lets multiply 3,460 by 0.03:

[tex]x=3,460(0.03)[/tex]

[tex]x=103.8[/tex]

Now subtract that number from 3,460:

[tex]3,460-103.8=3,356.2[/tex]

Lastly, lets take the $100 fee off of the number we just got:

[tex]3,356.2-100=3,256.2[/tex]

The new amount is $3,256.2

Answer:

3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of $3,256.2.

explanation:

To find the length of the band holding four pencils together, calculate the circumference of each pencil using the formula C = 2πr, where C is the circumference and r is the radius. Multiply the circumference of each pencil by 4 to find the total length of the band.

To find the length of the band holding four pencils together, you need to calculate the circumference of the pencils. The diameter of each pencil is given as 10 mm, so the radius is half of the diameter, which is 5 mm. The formula for calculating the circumference of a circle is C = 2πr, where C is the circumference, π is a constant approximately equal to 3.14159, and r is the radius. Therefore, the circumference of each pencil is 2π(5 mm) = 10π mm. Since there are four pencils, the total length of the band is 10π mm x 4 = 40π mm. This is your answer in terms of π.

Answer:an isosceles triangle cannot be an equilateral triangle

Step-by-step explanation:

An isosceles triangle cannot be an equilateral triangle

Final answer:

An isosceles triangle has at least 2 equal sides and an equilateral triangle has all sides equal. All equilateral triangles are isosceles triangles, but not all isosceles triangles are equilateral triangles.

Explanation:

An isosceles triangle has at least 2 equal sides, while an equilateral triangle has all sides equal. Therefore, the sentence 'All isosceles triangles are equilateral triangles' is not true because not all isosceles triangles have all sides equal. On the other hand, the sentence 'All equilateral triangles are isosceles triangles' is true because every equilateral triangle automatically has at least 2 equal sides. Furthermore, it is possible for an equilateral triangle to not be an isosceles triangle if all three sides are not equal in length. So, the sentence 'An isosceles triangle cannot be an equilateral triangle' is not true.

Answer:

19

Step-by-step explanation:

plug in 5 for x so f(5)=4(5)-1 = 20-1 = 19

The solution of expression f (x) = 4x - 1at x = 5 would be 19.

Given that the expression is,

f (x) = 4x - 1

Used the concept of substitution method to solve the expression.

Now, substitute x = 5 in the expression,

f (x) = 4x - 1

f (5) = 4(5) - 1

f (5) = 20 - 1

f (5) = 19

Therefore, the value of the expression is f (5) = 19.

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Answer:

Step-by-step explanation:

For a two tailed alternative hypothesis, it involves the "not equal to symbol,≠ ". This can never be in the null hypothesis.

The curve is symmetrical and the rejection regions would be in the left and right tails

In order to reject the null hypothesis, the test statistic must be smaller than the critical value on the left tail or greater than the critical value on the right tail.

Therefore, the following statements are false

B. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution.

D. When the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution and when the alternative hypothesis is two-tailed, the rejection region is split between the two tails of the test statistic's sampling distribution.

Final answer:

Statement d is false because it combines parts of two separate true statements, which could be misleading. A two-tailed test is indicated by a not equals symbol in the alternative hypothesis, and the rejection region is split between the two tails of the test statistic's sampling distribution.

Explanation:

The false statement is d. While it's true that when the alternative hypothesis is two-tailed, the null hypothesis is rejected for values of the test statistic located in either tail of that statistic's sampling distribution, statement d is false because it repeats the earlier part of the statement and combines it with a correct statement from option c, which can be misleading. The correct information is provided in separate statements b and c.

The alternative hypothesis indicates the type of test to be conducted. If the alternative hypothesis has a not equals symbol (≠), it indicates a two-tailed test. In a two-tailed test, the rejection region is split between the two tails of the test statistic's sampling distribution. In terms of p-value, it represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. A small p-value (< 0.05) typically indicates strong evidence against the null hypothesis, leading to its rejection.

Answer:

.18 % increase

Step-by-step explanation:

First you would find what the difference is between the school enrollment

you would do 1456 - 1234 =  222

Then you would divide 1234/1456 = 84.75% to see the total percentage

The increase however has a percentage of .18%

To check your work you would do .18 x 1234 = 222.12 ( round to the nearest whole number so it would just be 222) then add 1234+ 222 = 1456!

Answer:

A) (1,456-1,234) ÷ 1,456

Answer:

The test statistic = 2.51

Step-by-step explanation:

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.

While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.

For this question, Dr. Vegapunk wants to test the claim that watching anime decreases social skills in college students.

So, the null hypothesis would be that there isn't significant evidence to conclude that watching anime decreases social skills in college students. That is, watching anime does not decrease social skills in college students.

And the alternative hypothesis is that there is significant evidence to conclude that watching anime decreases social skills in college students.

If the previous known mean social skills of college students is 6.2 and the new population mean social skills of college students who watch anime is μ,

Mathematically,

The null hypothesis is represented as

H₀: μ ≥ 6.2

The alternative hypothesis is given as

Hₐ: μ < 6.2

To do this test, we will use the t-distribution because no information on the population standard deviation is known

So, we compute the t-test statistic

t = (x - μ)/σₓ

x = sample mean = 7.3

μ₀ = Standard to be compared against = 6.2

σₓ = standard error of sample mean = [σ/√n]

where n = Sample size = 30

σ = Sample standard deviation = 2.4

σₓ = (2.4/√30) = 0.4382

t = (7.3 - 6.2) ÷ 0.4382

t = 2.51

Hope this Helps!!!

Answer:

(1, 1), (2.4), (0.5) (470)

Step-by-step explanation:

Honestly, I only know it's this one because the first one is a linear function. If you think about it on a graph, all of the points on the first one can connect with a straight line.

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

The value of the limit is 12.

Step-by-step explanation:

Small typing mistake, the limit is of h tending to 0.

We have that:

[tex]f(x) = x^{3}[/tex]

Then

[tex]f(2+h) = (2+h)^{3} = 8 + 12h + 6h^{2} + h^{3}[/tex]

[tex]f(2) = 2^{3} = 8[/tex]

Calling the limit L

[tex]L = \frac{f(2+h) - f(2)}{h}[/tex]

[tex]L = \frac{8 + 12h + 6h^{2} + h^{3} - 8}{h}[/tex]

[tex]L = \frac{h^{3} + 6h^{2} + 12h}{h}[/tex]

h is the common term in the numerator, then

[tex]L = \frac{h(h^{2} + 6h + 12)}{h}[/tex]

Simplifying by h

[tex]L = h^{2} + 6h + 12[/tex]

Since h tends to 0.

[tex]L = 0^{2} + 6*0 + 12[/tex]

[tex]L = 12[/tex]

So the answer is 12.

Using the definition of a derivative, the expression lim h→0 [f(2+h)-f(2)]/h for f(x)=x^3 simplifies to 12, which is the derivative of the function at x=2.

The limit you are trying to find is representative of the definition of a derivative at a point. In this case, the function is f(x) = x^3 and we're trying to find the derivative at x = 2. This is the definition of the derivative at a point:

lim h→0 [f(x+h) - f(x)] / h

Now, we plug in the equation for f(x):

lim h→0 [(2+h)^3 - 2^3] / h = lim h→0 [8+12h+6h^2+h^3 - 8] / h

Simplify that to get:

lim h→0 h [12+6h+h^2] / h

Then, by cancelling the h's, you have:

lim h→0 [12+6h+h^2]

As h→0, 6h and h^2 become 0, so finally, you obtain 12 as the derivative of f at x=2.

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Question:

A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per​ tie, where

MP(x) =1.85 + 0.12x - 0.0024x². ​Also, the shop will lose ​$65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.

Answer:

P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65

Step-by-step explanation:

MP(x) = 1.85 + 0.12(x) - 0.0024(x^2)

At sales level, x=0, loss = $65

P(0) = - $65

Integrating MP(x) with respect to x

P(x) = ∫MP(x) dx = ∫ 1.85 + 0.12(x) - 0.0024(x^2)

P(x) = 1.85x + 0.06x^2 - 0.0008x^3 + C

Therefore :

P(x) = 1.85x + 0.06x^2 - 0.0008x^3 - 65

Correct question:

A small tie shop finds that at a sales level of x ties per day its marginal profit is MP(x )dollars per​ tie, where

MP(x) =1.85 + 0.12x - 0.0024x². ​Also, the shop will lose ​$65 per day at a sales level of x= 0. Find the profit from operating the shop at a sales level of x ties per day.

Answer:

P(x) =1.85x +0.06x² - 0.0008x³ - 65

Step-by-step explanation:

Given the marginal profit function:

MP(x) =1.85 +0.12x - 0.0024x², P(0)= -65

We are to find P(x).

P(x) = ∫MP(x) dx

P(x) = ∫(1.85 + 0.12x - 0.0024x²) dx

= ∫1.85 dx+∫0.12x dx+∫(-0.0024x²)dx + C

= 1.85x + 0.06x² - 0.0008x³ + C

Initial condition at P(0) = - 65

where x(0), P(x) = -65

we have:

-65 = 1.85(0)+0.06(0)² - 0.0008x(0)³ + C

-65 = 0 + 0 - 0 + C

-65 = C

C = -65

P(x) =1.85x + 0.06x² - 0.0008x³ - 65

Answer:

c. 139

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

How large a sample should be taken to estimate the average age of out-of-state guests with a margin of error no larger than 5 and with a 95% level of confidence?

We need a sample size of n.

n is found when [tex]M = 5, \sigma = 30[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.96*\frac{30}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.96*30[/tex]

Simplifying by 5

[tex]\sqrt{n} = 1.96*6[/tex]

[tex](\sqrt{n})^{2} = (1.96*6)^{2}[/tex]

[tex]n = 138.30[/tex]

We round up,

So the correct answer is:

c. 139

Answer:

[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]

And if we round up to the nearest integer we got n =139, and the best answer for this case is:

c. 139

Step-by-step explanation:

For this case we have this previous info:

[tex]\sigma = 30[/tex] represent the previous estimation for the population deviation

[tex]Confidence =0.95[/tex] represent the confidence level

The margin of error for the true mean is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

The desired margin of error is ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The critical value for a 95% of confidence interval given now can be founded using the normal distribution. For this case the critical value would be given by [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:

[tex]n=(\frac{1.960(30)}{5})^2 =138.30 \approx 139[/tex]

And if we round up to the nearest integer we got n =139, and the best answer for this case is:

c. 139

Answer:-2048

Step-by-step explanation:

First term(a)=1

Common ratio(r)=-2/1 or 4/-2

Common ratio(r)=-2

nth term=a x r^(n-1)

12th term=1 x (-2)^(12-1)

12th term=1 x (-2)^11

12th term=(-2)^11

12th term=-2048

The 12th term of the geometric sequence 1, −2, 4, .... is equal to -2048.

In Mathematics and Geometry, the nth term of any geometric sequence can be determined by using the following formula:

[tex]a_n=a_1(r)^{n-1}[/tex]

Where:

In this context, the common ratio would be determined as follows;

Common ratio, r = a₂/a₁

Common ratio, r = -2/1

Common ratio, r = -2

Now, we can determine the 12th term in the sequence defined by this explicit rule;

[tex]a_n=a_1(r)^{n-1}\\\\a_{12}=1(-2)^{12-1}\\\\a_{12}=(-2)^{-11}\\\\a_{12}=-2048[/tex]

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Answer:

3.14 miles but that doesn't sound right

Step-by-step explanation:

Assuming you have to find area of the circle its

A = πr² Radius is half of diameter so half of 2 = 1

A = 3.14 x 1²

A = 3.14 x 1

A = 3.14

If you have to find area than its 3.14 it just sounds odd

Sorry if its wrong

Answer:

The distribution is approximately normal.

The mean and standard deviation are 15 and 0.98 respectively.

Step-by-step explanation:

The population of the random variables X₁ and X₂ are distributed as follows:

[tex]X_{1}\sim (\mu_{1}=35, \sigma_{1}^{2}=3^{2})\\\\X_{2}\sim (\mu_{2}=20, \sigma_{2}^{2}=4^{2})[/tex]

Two independent random samples of sizes,

[tex]n_{1}=47\\\\n_{2}=54[/tex]

are selected form the two populations.

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

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

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

And the standard deviation of the sample means is given by,

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

Both the sample selected from the two populations are quite large, i.e. [tex]n_{1}=47>30\\\\n_{2}=54>30[/tex]

So, according to the central limit theorem the sampling distribution of sample means [tex]\bar X_{1}\ \text{and}\ \bar X_{2}[/tex] can be approximated by the Normal distribution.

Then, the distribution of [tex]\bar X_{1}[/tex] is:

[tex]\bar X_{1}\sim N(35,\ 0.44)[/tex]

And the distribution of [tex]\bar X_{2}[/tex] is:

[tex]\bar X_{2}\sim N(20,\ 0.54)[/tex]

If two random variables are normally distributed then their linear function is also normally distributed.

So, the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is Normal and the shape of the distribution is bell-shaped.

The mean of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:

[tex]E(\bar X_{1}\ -\ \bar X_{2})=E(\bar X_{1})-E(\bar X_{2})\\=35-20\\=15[/tex]

The standard deviation of the distribution of [tex]\bar X_{1}\ - \bar X_{2}[/tex] is:

[tex]SD(\bar X_{1}-\bar X_{2})=SD(\bar X_{1})+SD(\bar X_{2})\\=0.44+0.54\\=0.98[/tex]

*X₁ and X₂ are independent.

Thus, the mean and standard deviation are 15 and 0.98 respectively.

Answer:

The 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Step-by-step explanation:

The (1 - α)% confidence interval for population mean when the population standard deviation is not known is:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=24\\\bar x=3.19\ \text{hours}\\s=0.2903\ \text{hours}[/tex]

Confidence level = 99%.

Compute the critical value of t for 99% confidence interval and (n - 1) degrees of freedom as follows:

[tex]t_{\alpha/2, (n-1)}=t_{0.01/2, (24-1)}=t_{0.005, 23}=2.807[/tex]

*Use a t-table.

Compute the 99% confidence interval for the true mean amount of time Americans spend social networking each day as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}[/tex]

     [tex]=3.19\pm 2.807\times \frac{0.2903}{\sqrt{24}}\\\\=3.19\pm 0.1663\\\\=(3.0237, 3.3563)\\\\\approx (3.02, 3.36)[/tex]

Thus, the 99% confidence interval for the true mean amount of time Americans spend social networking each day is (3.02 hours, 3.36 hours).

Answer:

48% was sold

Step-by-step explanation:

Let the percent sold be x

x/100 * 150 = 72

(This equation basically means...what percentage of 150 bundles will give us 72 bundles remaining? and that's the answer we need)

Simplifying...

150x/100 = 72

3x/2 = 72

3x = 144

x = 48%

Answer:

Was the answer possibly C)  4,671 sq.cm. ?


Explanation:
Since the expert didn't get it right from what I'm seeing.

The surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.

To calculate the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm, we follow these steps:

1. Determine the dimensions of the equilateral triangle base:
   - The diameter of the cylinder (10 cm) is equal to the side length of the equilateral triangle base.

2. Calculate the height of the equilateral triangle:
   - The height \( h \) of an equilateral triangle with side length \( a \) is given by:
     [tex]\[ h = \frac{\sqrt{3}}{2} a \] For \( a = 10 \) cm: \[ h = \frac{\sqrt{3}}{2} \times 10 \approx 8.66 \text{ cm} \][/tex]

3. Calculate the area of the equilateral triangle base:
   - The area \( A \) of an equilateral triangle with side length \( a \) is given by:
     [tex]\[ A = \frac{\sqrt{3}}{4} a^2 \] - For \( a = 10 \) cm: \[ A = \frac{\sqrt{3}}{4} \times 10^2 \approx 43.30 \text{ cm}^2 \][/tex]

4. Calculate the lateral surface area of the prism:
   - The lateral surface area is given by the perimeter of the triangular base times the length of the prism.
   - The perimeter \( P \) of an equilateral triangle with side length \( a \) is:
     [tex]\[ P = 3a \] For \( a = 10 \) cm: \[ P = 3 \times 10 = 30 \text{ cm} \][/tex]
   - The length of the prism is 85 cm.
   - The lateral surface area \( L \) is:
     [tex]\[ L = P \times \text{length} = 30 \times 85 = 2550 \text{ cm}^2 \][/tex]

5. Calculate the total surface area of the prism:
   - The total surface area \( S \) includes the lateral surface area and the area of the two triangular bases.
   - Total surface area \( S \) is given by:
     [tex]\[ S = L + 2 \times A \] - Substitute the values: \[ S = 2550 + 2 \times 43.30 = 2550 + 86.60 = 2636.60 \text{ cm}^2 \][/tex]

6. Round the total surface area to the nearest square centimeter:
[tex]\( S \approx 2637 \text{ cm}^2 \)[/tex]

So, the surface area of the triangular prism container needed to enclose a rolled document with a diameter of 10 cm and a length of 85 cm is approximately 2637 square centimeters.

Answer:

We conclude that the reaction time is increased or remains same by frequent alcohol use.

Step-by-step explanation:

We are given that a substance abuse researcher wants to know whether reaction time is decreased by frequent alcohol use. He randomly selects 164 alcoholics and finds that their mean reaction time (in ms) to a stimulus equals 283.

Reaction times to the stimulus in the general population are distributed normally with a mean equal to 281 and a standard deviation equal to 28.

Let [tex]\mu[/tex] = mean reaction time after alcohol use.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 281      {means that the reaction time is increased or remains same by frequent alcohol use}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 281      {means that the reaction time is decreased by frequent alcohol use}

The test statistics that would be used here One-sample z test statistics as we know about population standard deviation;

                    T.S. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean reaction time (in ms) = 283

            [tex]\sigma[/tex] = population standard deviation = 28

            n = sample of alcoholics = 164

So, test statistics  =  [tex]\frac{283-281}{\frac{28}{\sqrt{164}}}[/tex]  

                              =  0.915

The value of z test statistics is 0.915.

Now, at 0.01 significance level the z table gives critical value of -2.3263 for left-tailed test. Since our test statistics is more than the critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the reaction time is increased or remains same by frequent alcohol use.

Answer:

The of the pentagon is A=232.48cm²

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes, a pentagon

Now given the apothem the area can be expressed as

A=a²n tan (180/n)

where

a = the length of the apothem (in radius)

n = the number of sides= 5 for pentagon

tan is the tangent function calculated in degrees

Substituting our given data we can solve for the area A

A= 8²*5 tan (180/5)

A= 64*5 tan 36

A= 320tan 36

A= 320*0.7265

A=232.48cm²