A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.29 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.01 level of significance. Assume normality.a) What are the appropriate null and alternative hypotheses?H0: ? = 5 versus Ha: ? ? 5H0: x = 5 versus Ha: x ? 5 H0: ? = 5 versus Ha: ? < 5H0: ? = 5 versus Ha: ? > 5b) What is the test statistic? Give your answer to four decimal places. c) What is the P-value for the test? Give your answer to four decimal places. d) What is the appropriate conclusion?

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

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!!!

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:-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]

Read more on geometric sequence here: brainly.com/question/16423479

#SPJ3

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:

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%

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:

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

1 meter = 100 cm

So a 800 cm roll can cover 8 meters

(800/100 = 8)

She has 5 rolls so 5 x 8 = 40 meters total.

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:

from what I understand a 200% increase is tripling the number the increase is on

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:

The answer is B

Step-by-step explanation:

Just did the assignment on Egn.

Answer:

(B) all numbers less than 7

Step-by-step explanation:

Given the inequality:

x<7

It means that:

Therefore, x<7 consists of all numbers less than 7.

Answer:

B

Step-by-step explanation:

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".

Learn more:

brainly.com/question/22553360

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:

-13a+10b

Step-by-step explanation:

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:

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.

Step-by-step explanation:

Three m minus eight n divided by thirteen

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.

To learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6

Answer:

The length of shadow of the woman is 14.375 ft.

Step-by-step explanation:

Here we are given that

Height of the woman = 5.75 ft

Height of the lamp post = 12 ft

Shadow of the lamp post = 30 ft

Let the angle of elevation of the light source be θ

By definition, in a right triangle, with respect to angle θ, we have;

tan(θ) = Opposite÷Adjacent

Therefore, tan(θ) = (Height of the lamp post)÷(Shadow of the lamp post)

and tan(θ) = 12 ft ÷ 30 ft = 0.4

θ = Actan(0.4) = tan⁻¹(0.4) = 21.8°

Since, angle of elevation of the light = Angle of depression of the light (alternate angles) = 21.8° we have

tan(θ) = (Height of the woman) ÷ (Length of shadow of the woman)

∴ Length of shadow of the woman = (Height of the woman) ÷ tan(θ)

Length of shadow of the woman = 5.75 ft ÷ tan(21.8) = 5.75 ft ÷ 0.4

Length of shadow of the woman = 5.75 ft ÷ 0.4 = 14.375 ft.

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:

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 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.

https://brainly.com/question/34633110

#SPJ3

Answer:

465

Step-by-step explanation:

424+41=465

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:

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

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:

(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.