The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 17 in-state applicants results in a SAT scoring mean of 1046 with a standard deviation of 37. A random sample of 10 out-of-state applicants results in a SAT scoring mean of 1118 with a standard deviation of 50. Using this data, find the 90% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Step 2 of 3 : Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Answer:

Step-by-step explanation:

The smaller/closer the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are correct concluding that the data fits that particular distribution given.

Answer:

B) Mia Hamm helped her soccer team at the University of North Carolina at Chapel Hill win four NCAA titels.

Step-by-step explanation:

The first option is an opinion, not a fact.

Answer:

The number of pencils in the box A is 70

The number of pencils in the box B is 42

Step-by-step explanation:

The number of pencils in the box A is a

The number of pencils in the box B is b

We have:

a + b = 112

a - (1/5)a = b + (1/5)a

or

a + b = 112

a - (2/5)a = b

or

a + b = 112

(3/5)a = b

or

a + (3/5)a = 112

or

(8/5)a = 112

or

a = 112*(5/8)

or

a = 70

=> b = 112 - 70 = 42

Hope this helps!

Answer:

Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. Repeat step two using the quotient found with synthetic division.

Step-by-step explanation:

One of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

The methods to finding zeros and factors of higher degree polynomial functions

Hence, one of the methods to finding zeros and factors of higher degree polynomial functions is using the Remainder theorem.

To learn more about the polynomial function visit:

https://brainly.com/question/12976257.

#SPJ3

Answer:

260

20

Step-by-step explanation:

speed of plane= p

speed of wind =w

and

added up the 2 equations we get:

then

Answer:

Chemical rocks form when minerals dissolve in a solution and crystalize.

Answer:

Chemical rocks don't form from solidification from a melt

Step-by-step explanation:

Answer:

alternative hypothesis : H₁ :

Recent  Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

Alternative Hypothesis : H₁: μ < $1.298 a gallon

Step-by-step explanation:

Explanation:-

Given A recent gasoline survey said that the national average price of gasoline was $1.298 a gallon

Population average μ= $1.298 a gallon

sample size 'n' = 37

Sample mean (x⁻) = $1.192 a gallon

Sample standard deviation 'S' = $0.0436

Null hypothesis :H₀ : μ =  $1.298 a gallon

Alternative Hypothesis : μ < $1.298 a gallon

Degrees of freedom : ν = n-1= 37-1=36

t₀.₀₂₅ = 1.688

Test statistic

                       [tex]t = \frac{x^{-}-mean }{\frac{S}{\sqrt{n} } }[/tex]

                       [tex]t = \frac{1.192-1.298 }{\frac{0.0436}{\sqrt{37} } }[/tex]

                     t =  -14.8044

|t| = |-14.8044| > 1.688

Null hypothesis is rejected

Alternative hypothesis is accepted

Recent  Gasoline surveys felt that gasoline price in Texas was significantly lower than the national average

Answer:

The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 0.5

Middle 95% of weights:

By the Empirical Rule, within 2 standard deviations of the mean.

6 - 2*0.5 = 5

6 + 2*0.5 = 7

The interval that would represent weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

The Empirical Rule states that for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

The empirical rule says that, in a standard data set, virtually every piece of data will fall within three standard deviations of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 6

Standard deviation = 0.5

Middle 95% of weights

By the Empirical Rule, within 2 standard deviations of the mean.

6 - 2*0.5 = 5

6 + 2*0.5 = 7

The interval representing the weights of the middle 95% of all oranges from this orchard is from 5 oz to 7 oz.

To learn more about the empirical rule visit:

https://brainly.com/question/24244232

#SPJ5

Answer:

The population density is 618.93 per square mile.

Step-by-step explanation:

It is given that,

No. of people, N = 70,000

The radius of a city's town hall, r = 6 miles

We need to find the population density. It can be calculated by the formula i.e. number of people divided by area of land such that,

[tex]P=\dfrac{N}{A}\\\\P=\dfrac{N}{\pi r^2}\\\\P=\dfrac{70000}{\pi (6)^2}\\\\P=618.93\ \text{per square mile}[/tex]

So, the population density is 618.93 per square mile.

Answer:

Step-by-step explanation:

Hello!

Distribution in attachment.

The variable of interest is:

X: Number of successes after flipping a coin 5 times.

If you check the binomial criteria:

The number of trials is fixed: n=5

There are only two possible outcomes "success" or "failure"

Each flip of the coin is independent of the others.

The probability of success in the same from one trial to another, in this case, if we consider the coin to be balanced, the probability of success is p=0.5

The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis)

Statements:

1) The bar for any number k represents the probability of getting k successes in 5 flips. Correct. The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis). Each bar represents the probability of success for each possible value.

2) The number of successes, k, can range from 0 (no success) to 5 (all successes). Correct. The variable count the number of successes after flipping a coin 5 times. It can happen that you flip it and all the flips turn to be failures (X=0), that you flip it 5 times and only one turns out to be a success and the other 4 are failures (X=1), and so on until you flip it 5 times and all flips are successes (X=5)

3) Each coin flip is independent; it is not affected by any other coin flip. Correct, if not, this variable wouldn't have a binomial distribution as specified in the text.

4) For 5 coin flips, P(2 heads) = P(3 heads). Correct

Looking at the histogram, the bars for "2 successes" and "3 successes" have the same height, a little above 0.3, this means that both values have the same probability of occurrence.

5) The sum of the probabilities shown in the binomial distribution is p.

Incorrect.

For the binomial distribution "p" represents the probability of success for each trial, in this case, flipping the coin once.

For this distribution, as well as for other probability distribution, the sum of all probabilities is always 1, if not, then it is not a probability distribution.

I hope this helps!

Answer:

Lets make this easier for you guys. The correct answers are 1 through 4.

The bar for any number k represents the probability of getting k successes in 5 flips.

The number of successes, k, can range from 0 (no success) to 5 (all successes).

Each coin flip is independent; it is not affected by any other coin flip.

For 5 coin flips, P(2 heads) = P(3 heads

Step-by-step explanation:

Correct on edge :))

Answer:

Yes- these answers are equivalent.

Step-by-step explanation:

In the expression 7(2d+3), the 7 is outside the parentheses, meaning everything inside the parentheses is multiplied by 7.

2d X 7 = 14 d

3 X 7 = 21

7(2d+3) = 14d + 21

Yes, the expressions are equivalent.

By combining numbers, variables, functions in mathematics we get an expression.

Example : 4p+2, 3x-4y etc

Given expressions are 14d+21 and 7(2d+3)

Here, simplifying the expression 7(2d+3) we get,

7(2d+3) = (7×2d)+(7×3) = 14d+21

Therefore, the given two expressions are equal to each other, i.e same.

Learn more about expression here :

https://brainly.com/question/723406

#SPJ2

Answer:

[tex]P(A|B) = \frac{32}{49}[/tex]

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)}[/tex]

In which

P(A|B) is the probability of event A happening, given that B happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(B) is the probability of B happening.

We have that:

[tex]P(A \cap B) = \frac{4}{7}, P(B) = \frac{7}{8}[/tex]

So

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{4}{7}}{\frac{7}{8}} = \frac{4}{7}*\frac{8}{7} = \frac{32}{49}[/tex]

Then

[tex]P(A|B) = \frac{32}{49}[/tex]

Answer:

A= (0,0) and B = (6,3)

We can find the length AB with the following formula:

[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]

And replacing we got:

[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]

So then the length AB would be [tex] 3\sqrt{5}[/tex]

Step-by-step explanation:

For this case we have the following two points:

A= (0,0) and B = (6,3)

We can find the length AB with the following formula:

[tex] d = \sqrt{(x_B -x_A)^2 +(y_B -y_A)^2}[/tex]

And replacing we got:

[tex] d = \sqrt{(6-0)^2 +(3-0)^2} = \sqrt{45}= 3\sqrt{5}[/tex]

So then the length AB would be [tex] 3\sqrt{5}[/tex]

Answer:6.71

Step-by-step explanation: awesomeness

The answer is 1/3

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer: 1/3

Step-by-step explanation: To subtract mixed numbers, first subtract the fractions.

Notice here however that we have 1/6 - 5/6

which will give us a negative fraction.

Since this will cause us a lot of trouble, instead,

let's rewrite the first mixed number.

We can do this by thinking of 3 and 1/6 as 2 + 1 and 1/6 or 2 + 7/6

by changing 1 and 1/6 into an improper fraction.

So 3 and 1/6 can be written as 2 and 7/6.

So we have 2 and 7/6 -  2 and 5/6.

Now, subtract the fractions.

So we have 7/6 - 5/6 which is 2/6.

Then subtract the whole numbers.

2 - 2 is 0.

However, we don't need to include 0 in our answer.

We can write our answer as 2/6.

However, 2/6 is not in lowest terms.

So divide the numerator and denominator by 2 to get 1/3.

So 3 and 1/6 - 2 and 5/6 is 1/3.

Answer:

a) The null hypothesis is given as

H₀: μ₀ ≥ 38.2 minutes

The alternative hypothesis is given as

Hₐ: μ₀ < 38.2 minutes

b) The null hypothesis is given as

H₀: μ₀ = $58,291

The alternative hypothesis is given as

Hₐ: μ₀ ≠ $58,291

c) The null hypothesis is given as

H₀: μ₀ ≤ 133.0 mg

The alternative hypothesis is given as

Hₐ: μ₀ > 133 mg

d) The null hypothesis is given as

H₀: μ₀ = 161.9 bushels

The alternative hypothesis is given as

Hₐ: μ₀ ≠ 161.9 bushels

e) The null hypothesis is given as

H₀: μ₀ ≤ 42.8 years

The alternative hypothesis is given as

Hₐ: μ₀ > 42.8 years

Step-by-step explanation:

In hypothesis testing, 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. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.

Taking the statements one at a time

a) The assertion is that the new average time workers spent commuting to work in Verona is now less than the old average.

The null hypothesis would be there isn't enough evidence to conclude that the new average time workers spent commuting to work in Verona is now less than the old average. That is, the new average time workers spent commuting to work in Verona is now equal to or more than the old average.

The alternative hypothesis is that the new average time workers spent commuting to work in Verona is now less than the old average.

Mathematically, if μ₀ = new average time workers spent commuting to work in Verona.

The null hypothesis is given as

H₀: μ₀ ≥ 38.2 minutes

The alternative hypothesis is given as

Hₐ: μ₀ < 38.2 minutes

b) Although the question isn't complete,

The null hypothesis is that there isn't a significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.

The alternative hypothesis is that there is significant difference between whatever is being compared in the complete question and the mean salary for all men in that profession.

Mathematically, if μ₀ = Mean of whatever is being compared in the complete question

The null hypothesis is given as

H₀: μ₀ = $58,291

The alternative hypothesis is given as

Hₐ: μ₀ ≠ $58,291

c) The claim to be proved is that the average caffeine content for coffee served in a local restaurants is higher.

The null hypothesis is that the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup. That is, the average caffeine content for coffee served in a local restaurants is not higher than the standard figure of 133 mg for an 8 ounce cup.

The alternative hypothesis is that average caffeine content for coffee served in a local restaurants is higher than the standard figure of 133 mg for an 8 ounce cup.

Mathematically, if μ₀ = average caffeine content for coffee served in a local restaurants.

The null hypothesis is given as

H₀: μ₀ ≤ 133.0 mg

The alternative hypothesis is given as

Hₐ: μ₀ > 133 mg

d) The economist claims that the average yield per acre this year is different from the average yield per acre in recent years.

Hence, the null hypothesis is that there is no significant difference between the average yield per acre this year and the average yield per acre in recent years.

The alternative hypothesis is that there is significant difference between the average yield per acre this year and the average yield per acre in recent years.

Mathematically, if μ₀ = the average yield per acre this year

The null hypothesis is given as

H₀: μ₀ = 161.9 bushels

The alternative hypothesis is given as

Hₐ: μ₀ ≠ 161.9 bushels

e) The sociologist suspects that the average age of all self-described fly fishermen is higher than 42.8 years.

Hence, the null hypothesis is that the average age of all self-described fly fishermen is not higher than 42.8 years. That is, the average age of all self-described fly fishermen is equal to less than 42.8 years.

The alternative hypothesis is that the average age of all self-described fly fishermen is higher than 42.8 years.

Mathematically, if μ₀ = average age of all self-described fly fishermen.

The null hypothesis is given as

H₀: μ₀ ≤ 42.8 years

The alternative hypothesis is given as

Hₐ: μ₀ > 42.8 years

Hope this Helps!!!

Answer:

1680 is the answer.

Step-by-step explanation:

Here, we have 11 letters in the word MISSISSIPPI.

Repetition of letters:

M - 1 time

I - 4 times

S - 4 times

P - 2 times

As per question statement, we need a substring MISS in the resultant strings.

So, we need to treat MISS as one unit so that MISS always comes together in all the strings.

The resultant strings will look like:

xxxxMISSxxx

xxMISSxxxxx

and so on.

After we treat MISS as one unit, total letters = 8

Repetition of letters:

MISS - 1 time

I - 3 times

S - 2 times

P - 2 times

The formula for combination of letters with total of n letters:

[tex]\dfrac{n!}{p!q!r!}[/tex]

where p, q and r are the number of times other letters are getting repeated.

p = 3

q = 2

r = 2

So, required number of strings that contain MISS as substring:

[tex]\dfrac{8!}{3!2!2!}\\\Rightarrow \dfrac{40320}{6\times 2 \times 2}\\\Rightarrow 1680[/tex]

So, 1680 is the answer.

Answer:

47.50

Step-by-step explanation:

According to the question above Salid bought 30 feet of window at a hardware trim store

The trim cost of each window is $1.75 per foot with an inclusion of sales tax added to this amount

= $1.75×30

= 52.5

Since Salid paid for the trim service with a cash of $100.00, his change is calculated as follows

=$100-52.5

= $47.50

Hence Salid change is $47.50

Answer:

A)  [tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]

B) [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]

Step-by-step explanation:

Let [tex]A = \left[\begin{array}{ccc}a&b\\c&d \end{array}\right][/tex] where a, b, c and d are real numbers

Since A is said to be a half magic square matrix, a = d, b = c.

The matrix A therefore becomes  [tex]A = \left[\begin{array}{ccc}a&b\\b&a \end{array}\right][/tex] where [tex]a,b \epsilon R[/tex]

A can therefore be manipulated as:

[tex]A = a \left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

The matrices [tex]\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right][/tex] and [tex]\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex] are apparently linearly independent and therefore form a basis B for V

[tex]B = \{\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right], \left[\begin{array}{ccc}0&1\\1&0 \end{array}\right] \}[/tex]

B) Find the coordinate vector [M]_B of M [-2 -7, -7 -2]

 [tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right][/tex]

[tex]M[/tex] can be written in the form [tex]M = a\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] + b\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

[tex]M = \left[\begin{array}{ccc}-2&-7\\-7&-2 \end{array}\right] = -2\left[\begin{array}{ccc}1&0\\0&1 \end{array}\right] -7\left[\begin{array}{ccc}0&1\\1&0 \end{array}\right][/tex]

The coordinate vector is therefore, [tex]M_{B} = \left[\begin{array}{ccc}-2\\-7\end{array}\right][/tex]

Answer:

1600

please see the attached picture for full solution

Hope it helps...

Answer:

2.8 hours or 2hrs 8 min

Step-by-step explanation:

money paid per hour=16+9=$25

money paid by luis=70

time=70/25= 2.8 hrs

=2 hours and 8 minutes

hope this helps u :)

Answer:

a) The 99% confidence interval is from 14.8% to 23.2%.

b) The confidence interval tells us that the true proportion of mislabeled is within 14.8% and 23.2%, with a 99% confidence. In other words, if we take samples of the same size, 99% of the samples will have a proportion within 0.148 and 0.232.

c) The confidence interval calculation take into account the sample size, so the width (or precision) of the interval depends on the sample size.

The only criticism that could be analyzed is to see if the sample is representative of the population.

Step-by-step explanation:

a) We have to calculate a 99% confidence interval for the proportion.

The sample proportion is p=0.19.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.19*0.81}{585}}\\\\\\ \sigma_p=\sqrt{0.000263}=0.016[/tex]

The critical z-value for a 99% confidence interval is z=2.576.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=2.576 \cdot 0.02=0.042[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.19-0.042=0.148\\\\UL=p+z \cdot \sigma_p = 0.19+0.042=0.232[/tex]

The 99% confidence interval for the population proportion is (0.148, 0.232).

Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

Answer:

The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.

Step-by-step explanation:

The random variable X can be defined as the number of swarms of honeybees seen each spring.

The average value of the random variable X is, λ = 13.

A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.

For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.

So, the random variable X follows a Poisson distribution with parameter λ = 13.

The probability mass function of X is as follows:

[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]

Compute the  the probability of observing between 9 and 15 (inclusive) swarms as follows:

P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)

                      [tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]

Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.

Answer:

Solve   -x2+11xandg+6x-6  = 0

Step-by-step explanation:

Answer:−2x=−8

4sin2(x)−1=0

2x+3=3

Step-by-step explanation:

Answer:

26 feet

Step-by-step explanation:

Let the length of the required wire =l

The height of the tree =24 cm

We want the tree to fall to the ground 10 feet away from the base.

Ths problem forms a right triangle which I have drawn and attached below.

To determine the length of the wire l required, we use Pythagoras theorem to solve for the hypotenuse of the right triangle.

[tex]B$y Pythagoras theorem: Hypotenuse^2=Opposite^2+Adjacent^2\\$Therefore:\\l^2=24^2+10^2\\l^2=676\\$Take the square root of both sides\\l=\sqrt{676}\\ l=26$ feet[/tex]

Thw wire must be 26 feet long to reach the ground.

Answer: 35

Step-by-step explanation:

The number of combinations of r things selected out of n things is given by

[tex]^nC_r= \dfrac{n!}{r!(n-r)!}[/tex]

Given , the total number of types of toppings available = 7

The number of toppings needed to be selected = 4

Then, the number of ways to do this would be

[tex]^7C_4=\dfrac{7!}{4!(7-4)!}\\\\=\dfrac{7\times6\times5\times4!}{4!3!}\\\\=\dfrac{7\times5}{1}=35[/tex]

Hence, the number of combinations of 5 scoops of ice cream and 4 toppings are possible = 35.

Answer:

Area of rectangle = [tex]196\,m^2[/tex]

Length of rectangle = 14 m

Width of rectangle = 14 m

Step-by-step explanation:

Given:

Perimeter of rectangle is 56 m

To find: the maximized area of a rectangle and the length and width

Solution:

A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]

Let x, y denotes length and width of the rectangle.

Perimeter of rectangle = 2( length + width )

[tex]=2(x+y)[/tex]

Also, perimeter of rectangle is equal to 56 m.

So,

[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]

Let A denotes area of rectangle.

A = length × width

[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]

Differentiate with respect to x

[tex]\frac{dA}{dx}=28-2x[/tex]

Put [tex]\frac{dA}{dx}=0[/tex]

[tex]28-2x=0\\2x=28\\x=14[/tex]

Also,

[tex]\frac{d^2A}{dx^2}=-2<0[/tex]

At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]

So, x = 14 is a point of maxima

So,

[tex]y=28-x=28-14=14[/tex]

Area of rectangle:

[tex]A=xy=14(14)=196\,m^2[/tex]

Length of rectangle = 14 m

Width of rectangle = 14 m

Answer:

Step-by-step explanation:

Midline is the horizontal line that passes exactly in the middle between the graph's maximum and minimum points.

Amplitude is the vertical distance between the midline and one of the extremum points.

Period is the distance between two consecutive maximum points, or two consecutive minimum points (these distances must be equal).

To find the formula for [tex]g(x)[/tex]. First, let's use the given information to determine the function's amplitude, midline, and period.

The midline of a sinusoidal function passes exactly in the middle of its extreme values. So we can find the midline by finding the average of the maximum and minimum values.

The midline passes exactly between the minimum value 1, and the maximum value 11, so the midline equation is

[tex]midline=y=\frac{11+1}{2} =6[/tex]

The extremum points are 5 units above or below the midline, so the amplitude is 5.

The maximum point is 0.5 units to the right of the minimum point, so the period is [tex]2\cdot 0.5 =1[/tex]. We multiply by 2 because the distance between consecutive minimum and maximum points is always [tex]\frac{1}{2}[/tex] of the period.

The general sinusoidal equation [tex]y=a\cos(bx)+d[/tex] is the result of horizontal and vertical shifts, reflections, and stretches of the parent equation [tex]y=\cos(x)[/tex] where

The amplitude is 5, so [tex]|a|=a=5[/tex].

The midline is y = 6, so d = 6.

The period is 1, so b = [tex]\frac{2\pi }{1}=2\pi[/tex].

The formula for [tex]g(x)=5\cos(2\pi x)+6[/tex].