Given EP = FP and GQ = FQ, what is the perimeter of ΔEFG?

Answer:

We need a sample of size at least 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage.

We need a sample of size at least n.

n is found when [tex]M = 0.02[/tex]

We don't know the exact proportion, so we use [tex]\pi = 0.5[/tex], which is the case for which we are going to need the largest sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.02})^{2}[/tex]

[tex]n = 2401[/tex]

We need a sample of size at least 2401.

Answer:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]  

And rounded up we have that n=2401

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".  

Solution to the problem

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 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/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 0.02[/tex] or 2% points 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 use an prior estimation for p [tex]\hat p=0.5[/tex]. And replacing into equation (b) the values from part a we got:

[tex]n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401[/tex]  

And rounded up we have that n=2401

Answer:

20°

Step-by-step explanation:

Given:

Angle of Intercepted arc = 40°

If an angle is inscribed in a circle, the measure of the inscribed angle is half the measure of the intercepted arc.

Therefore, since the angle of Intercepted arc is 40°, the measure of inscribed angle will be:

[tex] \frac{1}{2} * 40 [/tex]

= 20

Answer:

the answer is 20 degrees

Step-by-step explanation:

just took it

Answer:

1,600

Step-by-step explanation:

3000/75=40

40*40=1,600

Final answer:

The best prediction for the number of people who will vote for Mr. Beston out of 3,000 voters is found through a simple proportion, resulting in an estimated 1,600 votes for Mr. Beston.

Explanation:

The question asks for a prediction of the number of people who will vote for Mr. Beston if 3,000 people vote, based on the results of a survey where 40 out of 75 people indicated they would vote for him. To find this prediction, we use a simple proportion. We set up a ratio of the number of people who plan to vote for Mr. Beston to the total number surveyed and set this equal to the unknown number of people who will vote for Mr. Beston out of 3,000 total voters.

The ratio or survey proportion is 40/75. We set up the following proportion to find the predicted number of votes:

40/75 = x/3000,

where x is the number we want to find. By cross-multiplying, we get:

40 * 3000 = 75 * x,

which simplifies to:

120,000 = 75x.

Now, we divide both sides by 75 to isolate x:

x = 120,000 / 75,

x = 1600.

Therefore, the best prediction is that 1,600 people out of 3,000 will vote for Mr. Beston.

Answer:

3

Step-by-step explanation:

First, find the midline by averaging the highest value (2) and the lowest value (-4). In other words, do (2+-4)/2. You get the midline as -1. Now find the distance from the midline to the top. Distance from -1 to 2 is 3. Amplitude is therefore 3.

Final answer:

The amplitude of a function is represented by the symbol A, which is the maximum displacement from the equilibrium position in a sine wave function. The sinusoidal wave equation y(x) = Asin(ax) makes it clear that A is the amplitude.

Explanation:

The amplitude of a function, often represented by the symbol A, is the maximum displacement from the equilibrium position of an object oscillating around that equilibrium position. In the case of a sine function such as y(x) = Asin(ax), where x is the positional coordinate, the amplitude A is the distance from the equilibrium point to either the highest or lowest point of the wave. It is important to note that amplitude is different from peak-to-peak amplitude, which is the total vertical distance between the crest and the trough of a wave.

The equation provided, & (x) = Asin (ax), indicates that the function's amplitude is A. Specifically, for a sinusoidal wave like this, A represents the maximum vertical distance from the midpoint of the wave (equilibrium) to its crest (or trough).

Answer:

100 goes into 540 5 times

Step-by-step explanation:

which leaves a remainder of 40

hi and hope this helps!!

Answer:

5 remainder: 40 or 5.4

Step-by-step explanation:

when dividing 540 to 100, you need to know how many times 540 can go into 100. 100 can go into 540 5 times, so, you'll multiply 100 by 5. That should give you 500, then, you'll subtract 540 to 500, and that should give you a remainder of 40.

If you want to divide it to a decimal, you need to add an additional zero . to 40. That should give you 400. Then, 100 can go into 400, 4 times. So, you'll subtract 400 to 400, and that should give you 0. Now, you're done!

Problem 1

----------------

Work Shown:

There are n = 6 red marbles and r = 5 ways to pick them (order does not matter). Use the combination formula to find that

n C r = (n!)/(r!(n-r)!)

6 C 5 = (6!)/(5!*(6-5)!)

6 C 5 = (6!)/(5!*1!)

6 C 5 = (6*5!)/(5!*1!)

6 C 5 = (6)/(1!)

6 C 5 = (6)/(1)

6 C 5 = (6)/(1)

6 C 5 = 6

Now repeat for n = 6+9+8 = 23 and r = 5

n C r = (n!)/(r!(n-r)!)

23 C 5 = (23!)/(5!*(23-5)!)

23 C 5 = (23!)/(5!*18!)

23 C 5 = (23*22*21*20*19*18!)/(5!*18!)

23 C 5 = (23*22*21*20*19)/(5!)

23 C 5 = (23*22*21*20*19)/(5*4*3*2*1)

23 C 5 = (4037880)/(120)

23 C 5 = 33649

We have 6 ways of getting what we want (picking five red marbles) out of 33649 ways total (to get five marbles of any color). Again order does not matter.

Divide: 6/33649 = 0.00017831139112

This rounds to 0.0002 when rounding to four decimal places.

=========================================

Problem 2

----------------

Work Shown:

There are 6 C 2 = 15 ways to pick 2 red marbles

There are 17 C 3 = 680 ways to pick 3 non-red marbles.

There are 15*680 = 10,200 ways to pick 5 marbles such that 2 are red, the rest aren't.

There are 33649 ways to select 5 marbles where color doesn't matter

So,

10200/33649 = 0.30312936491427

which rounds to 0.3031

=========================================

Problem 3

----------------

Work Shown:

There are 17 marbles that aren't red, so there are 17 C 5 = 6188 ways to pull out five of them

This is out of 33649 ways to pull out five marbles in general.

6188/33649 = 0.18389848138131

which rounds to 0.1839

The probability of drawing all marbles red is extremely low (0.0002), while the probability of drawing exactly two red marbles is much higher (0.2865). If no red marbles are drawn, the probability is 0.1839.

To solve these problems, we will use the basic principles of probability and combinations, since we are dealing with the probability of drawing marbles without replacement.

1. Probability that all marbles are red

We have a total of 23 marbles (6 red, 9 white, 8 blue). Since we're drawing 5 marbles without replacement, to get the probability that all marbles are red, we need to calculate the combinations of choosing 5 out of 6 red marbles and divide that by the combinations of choosing 5 out of all 23 marbles.

Probability = (⁶C₅) / (²³C₅) = 6/33649 = 0.0002

2. Probability that exactly two of the marbles are red

Here, we want two red marbles and the remaining three to be non-red (either white or blue). We calculate this by multiplying the combination of choosing 2 reds out of 6, 3 non-reds out of 17 (total marbles minus red marbles), and divide by the total combinations of choosing 5 out of 23.

Probability = (⁶C₂ × ¹⁷C₃) / (²³C₅) = (15 × 680) / 33649 = 0.2865

3. Probability that none of the marbles are red

To find the probability of drawing no red marbles, we only consider the white and blue ones, so we want all 5 to be from the 17 non-red marbles.

Probability = (¹⁷C₅) / (²³C₅) = 6188 / 33649 = 0.1839

m=6.50t

6.50 per ticket so you multiply 6.50 by t. The money collected is the answer to the equation. Hope this helps!

To find the probabilities of a randomly selected U.S. adult using social media and being aged 18-29, we can use probability concepts and the given information.

To solve this problem, we can use the concept of probability. Let's define the following events:

From the information given, we have P(A' ∩ B') = 35%, P(A' ∩ B) = 0, P(A ∩ B') = 67.2%. We need to find the probabilities P(A) and P(B).

Therefore, the probability that a randomly selected U.S. adult uses social media is 102.2%, the probability that a randomly selected U.S. adult is aged 18-29 is 22%, and the probability that a randomly selected U.S. adult is 18-29 and a user of social media is 67.2%.

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a. Probability of a randomly selected U.S. adult using social media is 45.2%.

b. Probability of a randomly selected U.S. adult being aged 18-29 is 65%.

c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media is approximately 29.38%.

a. Probability a randomly selected U.S. adult uses social media:

Probability of being 18-29 or use social media = 67.2%

Percentage of US adults aged 30 and older = 78%

Thus, percentage of US adults aged 18-29 = 100% - 78% = 22%

Probability of using social media = 67.2% - 22% = 45.2%

b. Probability of a randomly selected U.S. adult being aged 18-29:

Percentage of adults not using social media = 35%

Thus, percentage of adults aged 18-29 = 100% - 35% = 65%

c. Probability of a randomly selected U.S. adult being 18-29 and a user of social media:

Probability of using social media = 45.2%

Probability of being 18-29 = 65%

Probability of being 18-29 and using social media = 0.452 * 0.65 = 29.38%

Step-by-step explanation:

Arranging in ascending order

2 , 4 , 7 , 9 , 11 , 15

No of data (N) = 6

Now

Position of median

= (N+1)/2 th item

= ( 6 + 1) /2 th item

= 7/2 th item

= 3.5 th item

Exact Median

= 3 + 0.5 ( 4th term - 3rd term)

= 3 + 0.5( 9 - 7)

= 3 + 0.5 * 2

= 3 + 1

= 4

Hope it will help :)

Answer:

(a) Engineers with greater than 36 months of full-time employment.

(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter

(c) Measurements of the diameter of forged pistons that conform to engineering specifications.

(d) Cholesterol levels that measure less than 180 and greater than 220.

Step-by-step explanation:

The complement of a set refers to elements that does not exist in that set. It means what does not exist in the set but exist in the universal set.

(a) Engineers with greater than 36 months of full-time employment.

In this case, the Universal set is a set of engineers in full-time employment. The given set is for engineers with less than 36 months of full-time employment. The complement is engineers with greater than 36 months of full-time employment.

(b) Samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter

In this case, the universal set is a set of samples of cement block having compressive strength. The given set is a set of cement block having compressive strength less than 6000 kilograms per square centimeter. The complement is samples of cement blocks with compressive strength greater than 6000 kilograms per square centimeter.

(c) Measurements of the diameter of forged pistons that conform to engineering specifications.

In this case, the universal set is a set of measurements of the diameter of forged pistons. The given set is a set of measurements of the diameter of forged pistons that do not conform to engineering specifications. The complement is a set of measurements of the diameter of forged pistons that conforms to engineering specification.

(d) Cholesterol levels that measure less than 180 and greater than 220.

In this case, the universal set is a set of Cholesterol levels. The given set is Cholesterol levels that measure greater than 180 and less than 220. The complement is Cholesterol levels that measure less than 180 and greater than 220.

the complement sets are engineers with 36 months or more of full-time employment, samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more, measurements of the diameter of forged pistons that do conform to engineering specifications and cholesterol levels that measure 180 or less, or 220 or more.

Complement sets are those that are not a part of collection of set. For example, if a set contains the numbers from 1 to 5 and set a = {1, 3, 5} then complement of set A will have {2, 4}. Now applying this concept we get:

Thus, the complement sets are engineers with 36 months or more of full-time employment, samples of cement blocks with compressive strength of 6000 kilograms per square centimeter or more, measurements of the diameter of forged pistons that do conform to engineering specifications and cholesterol levels that measure 180 or less, or 220 or more.

Complete question:

A manufacturer has determined that a model of its washing machine has an expected life that is Exponential with a mean of four years to failure and irrelevant board burn-in period. He wants to testthe system and complete data collection. Find the probability that one of these washing machines will have a life that ends: (Note you can find the reliability of the washing machine life)

a) After an initial four years of washing machine service

b) Before four years of washing machine service are completed

c) Not before six years of washing machine service.

Answer:

a) 0.3679

b) 0.6321

c) 0.2231

Step-by-step explanation:

Given:

Mean, u= 4

/\ = 1/u

= 1/4 = 0.25

The cummulative distribution function, will be:

For x≥0,

[tex] F(x) = 1 - e^-^0^.^2^5^X[/tex]

[tex]P(x<X) = F(X)[/tex]

a) After an intial four years:

[tex]P(x>4) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]

P(x>4) = 0.3679

b) Before four years:

[tex]P(x<4) = 1-(e^-^0^.^2^5^*^4^.^0)[/tex]

P(x<4) = 0.6321

c) Not before 6 years:

[tex]P(x>6) = 1-(1-e^-^0^.^2^5^*^4^.^0)[/tex]

P(x>6) = 0.2231

Answer:

.69 or c

Step-by-step explanation:

Answer:

I think it's 55.

Step-by-step explanation:

11-n/5

n=11*5

n=55

Answer:

[tex]\frac{n-11}{5}[/tex]

Step-by-step explanation:

1) Subtract 11 from n to get [tex]n-11[/tex]   You cannot find a solution for it because there is no value for n.

2) You divide that by 5 so you would just put n-11 over 5 to create a fraction that would look like [tex]\frac{n-11}{5}[/tex]

I am not sure if this is what you were asking but this is the most I can do for you with the information that you gave.

Answer: $11,155

Step-by-step explanation: For this problem, first we will use the "Simple Interest" equation to find the total interest earned after three years.

First, convert 3.85% to a decimal, 0.0385.

I, interest = 10,000 x 0.0385 x 3

I = 1,155

Now add the total interest $1,155 to the total deposit $10,000.

1,155 + 10,000 = $11,155

By using  the formula for amount of Compound Interest the result is

Ending balance after 3 years = $11224.29

What is compound Interest?

If the interest on a certain principal increases exponentially rather than  linearly on a certain rate over a certain period of time, then the interest obtained is known as compound interest.

If the principal be P, rate is r%, time is n years,

Amount = [tex]P(1 + \frac{r}{100})^n[/tex]

CI = Amount - Principal

Here,

Principal = $10000

Rate = 3.85%

Time = 3years

Amount =

[tex]10000(1+\frac{3.85}{36500})^{3\times 365}\\10000(1 + \frac{385}{3650000})^{1095}\\[/tex]

11224.29

Ending balance after 3 years = $11224.29

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Answer:

Correct option is (A). H₀: [tex]\mu_{d}[/tex] = 0.5

Step-by-step explanation:

The (1 - α)% confidence interval for a population parameter can be used to determine whether to reject a null hypothesis or not.

The decision rule is:

If the (1 - α)% confidence interval for a population parameter consists of the null value of the parameter then the null hypothesis will be accepted or else it will be rejected.

A hypothesis test is performed to determine the difference between the ideal and actual heights of college males.

The 95% confidence interval for the mean difference, [tex]\mu_{d}[/tex] is:

CI = (0.8, 2.2)

The four null hypothesis provided are:

The 95% confidence interval for the mean difference consists of the value, 1.0, 1.5 and 2.0.

But it does not consist the value 0.5.

So, the null hypothesis that can be rejected is:

H₀: [tex]\mu_{d}[/tex] = 0.5

Thus, the correct option is (A).

Based on the 95% confidence interval given, we can only reject null hypothesis H0: μd= 0.5. The rest of the null hypotheses fall within the interval and therefore, cannot be rejected.

Based on the 95% confidence interval, which ranges from 0.8" to 2.2", we are interested in whether 0 falls within this range. When it falls within this range, we cannot reject the null hypothesis. Going through the provided null hypotheses, we can reject the null hypothesis which falls outside the confidence interval.

Considering:
A. H0: μd= 0.5
B. H0: μd= 1.0
C. H0: μd= 1.5
D. H0: μd= 2.0

Only hypothesis A falls outside the confidence interval, thus we can reject null hypothesis H0: μd= 0.5. The null hypotheses stating μd= 1.0, μd= 1.5, and μd= 2.0 fall within this range and therefore, cannot be rejected based on this confidence interval.

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Answer: the character of king Henry, or Harry

Step-by-step explanation:

Answer:

46.142857143

Step-by-step explanation:

10×2+(30-15)÷7+3×8

=10×2+15÷7+3×8

=20+15÷7+3×8

=20+2.142857143+3×8

=20+2.142857143+24

=46.142857143

Step-by-step explanation:

In ascending order

100 , 102 , 103 , 106, 109

No of data (N) = 5

Now

Position of median

= ( N + 1) /2 th item

=( 5+1 )/2 th item

= 6 / 2 th item

= 3rd item

Therefore exact median = 103

Hope it will help you :)

Answer:

103

Step-by-step explanation:

100,102,103,106,109

Median position: (n+1)/2

(5+1)/2 = 3rd value

Median = 103

Answer:

? necesitamos  más  información..  ¿dónde están los fracciones?

Step-by-step explanation:

Answer:

38 > 36

it is true it shows that 38 is greater than 36

Answer:

33.333%.

Step-by-step explanation:

Take the cost changed ($4) and divide it by it's normal price ($12).

$4/$12 = .33333

Multiply that by 100 to get its percent. 33.333%

Answer:

- 33.3%

Step-by-step explanation:

You calculate percent change by dividing the change by the absolute value of the original. In this instance, it would be -4/12 which equals -0.3333. Multiply that by 100 and you get the percent.

Answer:

Because our p-value of .023 is lower than the alpha-level of .05, we reject the null hypothesis. There is sufficient evidence to conclude that the proportion of subjects who have the necessary qualities is less than .2. Our test provided a statistically significant result.

Answer:

The calculated value t = 5.608 > 2.3988 at 0.1 level of significance with 53 degrees of freedom.

The null hypothesis is rejected at 0.1 level of significance

The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries

Step-by-step explanation:

Step(i):-

Given data the size of sample n=54

Given "D" size batteries produced by MNM Corporation have had a life expectancy of 85.8 hours

therefore mean of Population μ = 85.5 hours

Given a sample of 54 batteries showed an average life of 88.7 hours with a standard deviation of 3.8 hours

The mean of the sample x⁻ = 88.7 hours

The standard deviation of the sample (S) = 3.8 hours

Step(ii):-

Null hypothesis : H₀:μ > 85.5 hours

Alternative hypothesis: H₁:μ < 85.5 hours

Level of significance : ∝= 0.1

Degrees of freedom γ =n-1 = 54-1 =53

The test statistic

[tex]t= \frac{x^{-}-u }{\frac{S}{\sqrt{n} } }=\frac{88.7-85.8}{\frac{3.8}{\sqrt{54} } }[/tex]

t = 5.608

The tabulated value t = 2.3988 at 0.1 level of significance with 53 degrees of freedom.

Conclusion:-

The calculated value t = 5.608 > 2.3988at 0.1 level of significance with 53 degrees of freedom.

The null hypothesis is rejected at 0.1 level of significance

The company do not believes that there has been an INCREASE in the life expectancy of its D size batteries

Prism B has larger volume than Volume of prims A.

Volume is the scalar quantity of any object that specified occupied space in 3D.

For example, the space in our room is referred to as volume.

Volume has units of cube example meter³,cm³, etc.

Given that;

Prism A has a length of 2 units, height of 7 units, and width of 1 unit. Prism B has a length of 3 units, height of 2 units, and width of 3 units.

Since, The volume of the rectangular prism is given as,

V = length × height × width

Put length as 2 unit cubes, height as 7 unit cubes, and width as 1 unit cubes.

For prism A;

V = 2 x 7 x 1 = 14 units³.

Put length as 3 unit cubes, height as 2 unit cubes, and width as 3 unit cubes.

For prism B;

V = 3 x 2 x 3 = 18 units³.

Hence, Prism B has larger volume than Volume of prims A.

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Answer:

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

The mean is given by:

[tex] \mu_{\hat p} = 0.55[/tex]

And the deviation:

[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]

Step-by-step explanation:

For this case we assume that the true population proportion of Americans do not know that GOP stands for Grand Old Party is 0.55 and we select a random sample of n = 953 americans

For this case we assume that we satisfy the conditions to use the normal approximation for [tex]\hat p[/tex]

1) np >10 , n(1-p)>10

2) Independence

3) Random sample

4) The sample size is less than 10% of the population size

We assume that all the conditions are satisfied and the distribution for [tex]\hat p[/tex] would be:

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

The mean is given by:

[tex] \mu_{\hat p} = 0.55[/tex]

And the deviation:

[tex] \sigma_{\hat p} =\sqrt{\frac{0.55*(1-0.55)}{953}}= 0.0161[/tex]

(1) 132.67 square meters

(2) 379.94 square meters

Step-by-step explanation:

A barn is in the shape of a rectangle with each corner angle a right angle.

[tex] \therefore Central\: \angle \:(\theta) =90°[/tex]

Since, goat is tied at a corner of the barn, so she would be able to graze the grass of sector of circle with radius (r) = 13 m.

Area of field grazed by goat = area of sector of circle

[tex] = \frac{ \theta}{360 \degree} \times \pi {r}^{2} \\ \\ = \frac{90 \degree}{360 \degree} \times 3.14 \times {13}^{2} \\ \\ = \frac{1}{4} \times 3.14 \times 169\\ \\ = \frac{1}{4} \times530.66 \\ = 132.665 \\ = 132.67 \: {m}^{2} [/tex]

[tex] (2) \\ similarly \: for \: r \: = 22 \: m \\ area \: of \: sector = 379.94 \: {m}^{2} [/tex]

Answer:

At t=1, Rate of Change=-36.86

At t=10 hours, Rate of Change =-0.0088

Step-by-step explanation:

The function which describes the number of facts of a certain type which are remembered after t hours is given as:

[TeX]f(t)=\frac{85t}{99t-85}[/TeX]

To determine the Rate of Change at the given time, we first look for the derivative of f(t).

Applying quotient rule:

[TeX]f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}[/TeX]

At t=1

[TeX]f^{'}(1)=\frac{-7225}{(85-99)^{2}}[/TeX]

=-36.86

At t=10 hours

[TeX]f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}[/TeX]

=-0.0088

The rate of change of the function is calculated by finding its derivative and evaluated by substituting the respective hours (1 hour and 10 hours). The rate of change after 1 hour is approximately -106.25, implying a decline per hour, and after 10 hours is approximately -0.918, indicating a slower rate of decline per hour.

The rate of change of a function is calculated by finding the derivative of the function. The derivative of a function gives the rate of change of the function at any given point. Let's calculate the derivative of the function f(t) = 85 t / (99 t - 85).

We get f'(t) = (85*(99 t - 85) - (85 t)*99) / (99 t -85)² = (-850)/ (99 t - 85)². This is the rate of change of the function f(t).

To find the rate of change after 1 hour and 10 hours, substitute t = 1 and t = 10 into f'(t).

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Answer:

The socks cost $2.44 per pair

Step-by-step explanation:

Everything costs $21.85 in total. The given values are $6.75 for each jersey (which adds to make both jerseys together make $13.50). There is also a given value of $1.03 for total sales tax. If you add the jerseys and tax, you get $14.53. Subtract that from $21.85 to get $7.2. That is the total for all three pairs of socks, so divide that by three and you get $2.44 for each pair of socks :)