a. A kicker punts a football. The height (in yards) of the football is represented by f(x)=-1/9(x-30)^2+25 , where x is the horizontal distance (in yards) from the kicker's goal line.
Find the domain and range.

b. On the next possession, the kicker punts the football again. The height of the football is represented by g(x)=f(x+5) .
Find the domain and range.

c. Compare the graphs.

d. On which possession does the kicker punts closer to his goal line? Explain.

Therefore, the linearization of f(x) = cos(x) at a = π/2 is L(x) = π/2 - x.

The linearization of a function f(x) at a point a is given by:

L(x) = f(a) + f'(a)(x - a)

where f'(a) denotes the derivative of f(x) evaluated at x = a.

In this case, we have:

f(x) = cos(x)

a = π/2

First, let's find f'(x):

f'(x) = -sin(x)

Then, we can evaluate f'(a):

f'(π/2) = -sin(π/2) = -1

Next, we can plug in the given values into the formula for linearization:

L(x) = f(a) + f'(a)(x - a)

L(x) = cos(π/2) + (-1)(x - π/2)

L(x) = 0 - x + π/2

L(x) = π/2 - x

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a. The population of the city can be modeled using the exponential growth function:

y = 600(1 + 0.018)^x

with x being years from 0 to 10, where x = 0 corresponds to the year 2010. We can create a table to show the population for each year from 2010 to 2020:

(you can see above)

We can see from the table that the population of the city is increasing each year, and the rate of increase is accelerating. This is because the growth function is exponential, not linear. We know it is exponential because the function has a power of x in the exponent, which causes the rate of growth to increase over time. If the function were linear, the rate of growth would be constant.

b. To predict the population in 2025, we can use the same function with x = 15 (since 2025 is 15 years after 2010):

y = 600(1 + 0.018)^15

y ≈ 846.5 (in thousands)

Therefore, we can predict that the population of the city in 2025 will be approximately 846,500 citizens.

The correct statement about the function is given as follows:

D. As x approaches positive infinity, f(x) approaches positive infinity.

The function for this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

At the points where the interval changes, which are x = 0 and x = 2, the function is not defined, meaning that:

On the interval 0 < x < 2, the function is defined as follows

f(x) = -x² - 4x + 1.

The derivative is then given as follows:

f'(x) = -2x - 4.

-2x - 4 is positive for x < -2, hence the function is increasing only for x < -2.

Thus option d is correct, as:

1/2(∞) + 3 = ∞.

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Answer:

In a 30°-60°-90° right triangle, the length of the shorter leg is 1/2 the length of the hypotenuse, and the length of the longer leg is √3 times the length of the shorter leg. In the equilateral triangle, the perimeter is (2)(4√3)(3) = 24√3, and the apothem is 4.

π(8^2) - (1/2)(24√3)(4)

= 64π - 48√3 square units

= about 117.92 square units

The functions represented by the graphs are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent function in this problem is given as follows:

f(x) = |x|

The function g(x) is a translation down two units of the parent function f(x), hence it is given as follows:

g(x) = |x| - 2.

The function h(x) is a translation up three units of the parent function f(x), hence it is given as follows:

h(x) = |x| + 3.

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Answer:

I believe the answer is 49°

To maximize the likelihood function, we take the derivative with respect to θ and set it equal to zero: d/dθ[L(θ|X1,X2,...,Xn)]=−n/θ+(X1+X2+⋯+Xn)/θ2=0.

The MLE for θ in the exponential distribution is simply the sample mean of the observed data.

The exponential distribution is a continuous probability distribution that describes the time between events in a Poisson point process. X1,X2,...,XnX1,X2,...,Xn is a random sample of size n from this distribution, which means that each XiXi is an independent and identically distributed random variable with the same exponential distribution.

The probability density function (pdf) of the exponential distribution is given by f(x:θ)=(1/θ)e−x/θ, where θ is the scale parameter. This means that the probability of observing a value x from the distribution is proportional to e−x/θ, with the constant of proportionality being 1/θ.

To estimate the value of θ based on the observed data, we can use the method of maximum likelihood estimation (MLE). The likelihood function for the sample X1,X2,...,XnX1,X2,...,Xn is given by L(θ|X1,X2,...,Xn)=∏i=1n(1/θ)e−Xi/θ=(1/θ)n e−(X1+X2+⋯+Xn)/θ.

Solving for θ, we get θ=(X1+X2+⋯+Xn)/n, which is the sample mean.

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Step-by-step explanation:

See image:

The significance level is set at 5%, and the probability of the result is 0%, which is less than the significance level. The result is statistically significant.

We are given that;

The probability of the result=(7.7/9.2/4.6/5/7.8)%

Now,

To determine the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more, we need to find the difference between the two sample means and compare it to the standard error of the difference. The standard error of the difference can be estimated using the formula:

SE = √(s1^2 / n1) + (s2^2 / n2)

where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes.

Assuming that the treatment group is group 1 and the control group is group 2, we can plug in the values given in the question:

SE = √(9.2^2 / 30) + (7.7^2 / 30)

SE = √3.02

SE = 1.74

The difference between the two sample means is:

x1 - x2 = 85 - 100

x1 - x2 = -15

To find the probability of this difference or lower, we need to find the z-score and use a normal distribution table or calculator3:

z = (x1 - x2) / SE

z = (-15) / 1.74

z = -8.62

Using a normal distribution table or calculator, we can find that P(z ≤ -8.62) ≈ 0, which means that the probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more is very close to zero.

Therefore, by probability the answer will be statistically significant.

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By using the model, the missing values that complete the expression include the following:

48 + 32 = 8(6 + 4).

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of big rectangle = L × B

48 = 8 × 6

Area of small rectangle = L × B

32 = 8 × 4

For the required expression, we have:

48 + 32 = 8(6 + 4).

80 = 8(10)

80 = 80

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The dimension of the board either 4 by 6 square inches or 6 by 4 square inches.

We know that,

The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.

here,

let the length of the board be x, and width be w,

The perimeter of the rectangle board  = 20

2 (l + w) = 20

l + w = 10

l = 10 - w

Now,

area of the board = 24

l × w = 24

(10 - w)w = 24

10w - w² = 24

w² -10w + 24 =0

(w - 4)(w -6) = 0

So,

w = 4 or 6

Now,

Lengths = 10 - 4 or 10 - 6

             =  6 or 4

Thus, the dimension of the board either 4 by 6 square inches or 6 by 4 square inches.

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Ernesto travels a distance of 94.9 feet after the 20 swings.

For our initial arc, the length was 16 ft. Subsequent arcs had lengths that were 90% of their preceding element in succession

Therefore, the first 10 arcs' lengths respectively calculate as follows:  16 ft, 14.4 ft, 12.96 ft, 11.664 ft, 10.4996 ft, 9.44784 ft, 8.503056 ft, 7.6527504 ft, 6.88747536 ft and 6.198727824 ft; cumulatively amounting to a distance of roughly 94.86ft traversed by Ernesto after his 10 swings.

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The sine function that matches the equation in the graph is given as follows:

y = 2sin(x) - 2.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

The parameters are given as follows:

The function varies between -4 and 0, for a difference of 4, hence the amplitude is given as follows:

A = 4/2

A = 2.

The function varies between -4 and 0, instead of between -2 and 2, for a vertical shift of -2, hence the coefficient C is given as follows:

C = -2.

The period of the function is of 2π, hence the coefficient B is given as follows:

B = 1.

Thus the function is:

y = 2sin(x) - 2.

The graph is given by the image presented at the end of the answer.

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In mutually exclusive data, you cannot find any overlap or intersection between the categories or events being analyzed.

This means that the occurrence of one event or category precludes the occurrence of the other. On the other hand, in dependent data, the occurrence of one event or category may have an effect on the occurrence of the other, and thus, they are not completely independent or separate. Therefore, in both cases, you cannot find any shared or common outcomes or occurrences between the categories or events being analyzed.

You cannot find a direct correlation or causal relationship between mutually exclusive or dependent data. In mutually exclusive events, the occurrence of one event prevents the occurrence of the other, meaning they cannot happen at the same time. In dependent events, the probability of one event happening is influenced by the outcome of a previous event. Due to these characteristics, it is not possible to establish a direct correlation or causal relationship between such events.

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(a)The test statistic is -1.684

(b) degrees of freedom for a T distribution = 15

(c)the p-value is 0.05

We will be conducting a t-test to determine if the modifications made by the manufacturer have successfully reduced the noise level of the mowers.

(a) First, we need to find the test statistic (t-value). We can calculate it using the formula:

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

t = (79.6 - 82) / (5.7 / sqrt(16))

t = (-2.4) / (5.7 / 4)

t = -2.4 / 1.425

t ≈ -1.684 (rounded to three decimal places)

(b) To find the degrees of freedom for a T distribution, we use the formula:

df = sample size - 1

df = 16 - 1

df = 15

(c) To find the p-value, we look up the t-value and the degrees of freedom in a t-distribution table or use a calculator or software that can calculate the p-value for a one-tailed t-test. In this case, we have:

t = -1.684 and df = 15

Using a calculator or software, we find:

p-value ≈ 0.0568 (rounded to four decimal places)

Now, we compare the p-value with the significance level (0.05). Since the p-value (0.0568) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the modifications have reduced the noise level of the mowers at a 5% significance level.

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A random variable Y has the density Function f(y) = { ey, y<0, 0, otherwise

a.[tex]E(e^(3Y/2)) = [1/5] - [3e^(5/2)/10][/tex]

b.[tex]M(t) = 1/[(1-t)(t+1)][/tex]

c.[tex]V(Y) = ∫(y^2 + 2y + 1)eydy[/tex] [tex]= [y^2e^y]/2 - ∫ye^ydy + [ye^y]/2 - ∫e^y[/tex]

a. To find [tex]E(e^(3Y/2))[/tex], we use the definition of expected value, which is the integral of the product of the random variable and its probability density function. We have: [tex]E(e^(3Y/2))[/tex] [tex]= ∫e^(3y/2)f(y)dy[/tex] [tex]= ∫e^(3y/2)eydy[/tex], y<0 .Using integration by parts, we let [tex]u = e^(3y/2)[/tex] and [tex]dv = e^y dy[/tex]. Then, [tex]du/dy = (3/2)e^(3y/2)[/tex]and [tex]v = e^y[/tex].

[tex]E(e^(3Y/2))[/tex] [tex]= ∫e^(3y/2)eydy[/tex] [tex]= [e^(3y/2)e^y/2] - ∫(3/2)e^(3y/2)e^y/2dy[/tex]

[tex]= [e^(5y/2)]/5 - [3/5]∫e^(5y/2)dy[/tex]

[tex]= [e^(5y/2)]/5 - [3e^(5y/2)/10] + C[/tex]

Since f(y) = 0 for y ≥ 0, we know that [tex]E(e^(3Y/2))[/tex] only depends on the integral of [tex]e^(3y/2)[/tex]for y < 0. Evaluating the above expression at y = 0, we get:

[tex]E(e^(3Y/2)) = [1/5] - [3e^(5/2)/10][/tex]

b. To find the moment generating function (MGF) for Y, we use the definition of the MGF, which is the expected value of [tex]e^(tY)[/tex] for all t in a neighborhood of 0. We have:

[tex]M(t) = E(e^(tY))[/tex] [tex]= ∫e^(ty)f(y)dy[/tex][tex]= ∫e^(ty)eydy[/tex] , y<0

Using integration by parts as before, we get:

[tex]M(t) = ∫e^(ty)eydy[/tex] [tex]= [e^(ty)e^y]/(t+1) - ∫(t+1)(e^(ty)e^y)/(t+1)dy[/tex]

[tex]= [e^(ty+2y)]/(t+1) - (t+1)M(t)[/tex]

Simplifying, we get:

M(t)(t+1) = 1/(1-t)

M(t) = 1/[(1-t)(t+1)]

c. To find V(Y), we first need to find the mean or expected value of Y. Using the definition of expected value, we have:

E(Y) = ∫yf(y)dy = ∫yeydy, y<0. Using integration by parts once more, we get: E(Y) = ∫yeydy [tex]= [ye^y] - ∫e^ydy[/tex] = -1 . The mean of Y is -1.

We use the definition of variance, which is the expected value of the squared difference between the random variable and its mean. We have:

[tex]V(Y) = E[(Y - E(Y))^2][/tex][tex]= ∫(y + 1)^2f(y)dy[/tex] [tex]= ∫(y^2 + 2y + 1)eydy[/tex], y<0

Using integration by parts for the third time, we get:

[tex]V(Y) = ∫(y^2 + 2y + 1)eydy[/tex][tex]= [y^2e^y]/2 - ∫ye^ydy + [ye^y]/2 - ∫e^y[/tex]

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His account balance will be $6.5 greater in August than in June.

Assuming that the balance in June is equal to the balance in July, we can use the given information to find the difference between the August and June balances.

Let's say the balance in July (and June) was x. Then, according to the problem, the balance in August was:

     x + $6.50.

To find the difference between the August and June balances, we can subtract the June balance from the August balance:

August balance - June balance = (x + $6.50) - x = $6.50

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The  speed of the moving end of the sprinkler in feet per minute is 34.48 food per hour

Speed in mathematics is defined as the distance an object travels in a given amount of time. Also, It can be calculated using the formula Speed = Distance ÷ Time, where distance is equal to the time taken to travel and time is equal to the number of seconds needed to travel.

The given parameters are

The distance is = 50-foot long

Time is given as = 1.45 hours

Speed = Distance/Time

Speed = 50 foot long/1.45 hurs

Therefore the Speed = 34.48 food per hour

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step-by-step explanation:

remember if you add the given lengths, they must be greater than each other.

4+4=9 so no

9+4 = 13 which is greater than our number. We can make an isosceles triangle.

9+9 is greater than four so it works.

Answer:

probably 14 centimeters

Step-by-step explanation:

I put the new forgis on the jeep

The smallest number that appears in both lists is 11. Therefore, the least possible value of n that satisfies both conditions is 11.

To find the least possible value of n, we need to find the smallest number that satisfies both conditions.

We can start by listing out some numbers that have a remainder of 2 when divided by 3: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98, 101, 104, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 137, 140, 143, 146, 149, 152, 155, 158, 161, 164, 167, 170, 173, 176, 179, 182, 185, 188, 191, 194, 197, 200, 203, 206, 209, 212, 215, 218, 221, 224, 227, 230, 233, 236, 239, 242, 245, 248, 251, 254, 257, 260, 263, 266, 269, 272, 275, 278, 281, 284, 287, 290, 293, 296, 299, and so on.

Out of these numbers, we need to find the ones that also have a remainder of 1 when divided by 5. The numbers that have a remainder of 1 when divided by 5 are: 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, and so on.

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Answer:B

Step-by-step explanation:

The only possible degree for the polynomial p+q is 11.

Given the degree of polynomial p is 11 and the degree of polynomial q is 7, we can find all possible degrees of the polynomial p+q by considering their highest-degree terms.

When adding polynomials, the resulting polynomial will have the degree that corresponds to the highest-degree term. In this case, we have two options:

1. The highest-degree terms of both polynomials are of different degrees. In this case, the degree of p+q will be the maximum of the two given degrees, which is max(11, 7) = 11.

2. The highest-degree terms of both polynomials are of the same degree and their coefficients have opposite signs, causing them to cancel out when added. In this scenario, the degree of p+q will be less than the maximum degree, i.e., less than 11.
However, given that the degrees of p and q are different (11 and 7), it is not possible for their highest-degree terms to cancel out.

Therefore, the only possible degree for the polynomial p+q is 11.

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Using diagonals from a common vertex, the number of triangles that could be formed from a 19-gon  is 16 triangles.

If you choose a vertex of a 19-gon, then you can draw diagonals from this vertex to 16 other vertices of the 19-gon (not including adjacent vertices).

Each of these diagonals will form a triangle with the chosen vertex. Therefore, the number of triangles that can be formed using diagonals from a common vertex of a 19-gon is 16 triangles.

When you choose a vertex of a 19-gon, you can draw diagonals to 16 other vertices of the 19-gon. Each of these diagonals forms a distinct triangle with the chosen vertex. Therefore, the total number of triangles that can be formed is 16.

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The functions categorized as decay or growth are

From the question, we have the following parameters that can be used in our computation:

y = 2250(1-0.9)^x

y=10.(1+0.04)^x

An exponential function is represented as

y = ab^x

If b > 0, then it is a growth function

Otherwise, it a decay function

using the above as a guide, we have the following:

y = 2250(1-0.9)^x -- decay

y=10.(1+0.04)^x -- growth

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To test your hypothesis, you would use the One Sample T test. This test is appropriate for comparing the mean of a single sample to a known value, which in this case is 47.

The T test: two sample assuming unequal variances and T test: two sample assuming equal variances are used to compare the means of two independent samples, while the T test: paired two sample for means is used to compare the means of two related samples. None of these tests would be suitable for testing your hypothesis about the average age of customers who buy BMX bicycles.
To test the hypothesis that the average age of customers who buy BMX bicycles is greater than 47, you should use the "One Sample T-test."
The One Sample T-test is appropriate in this scenario because you are comparing the average age of customers to a specific value (47) rather than comparing two different groups of customers. The other T-test options, such as two-sample T-tests and paired two-sample T-tests, are not suitable as they involve comparing two separate groups or pairs of related data.

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Answer:

A and C have inverses.

Step-by-step explanation:

A matrix has an inverse if the matrix is a square matrix whose determinant is not equal to zero.

|A| = 3(3) - 6(1) = 9 - 6 = 3

B is not a square matrix.

|C| = 7(1) - 0(0) = 7 - 0 = 7

D is not a square matrix.

|E| = 4(1) - 4(1) = 4 - 4 = 0, so E does not have an inverse.

|F| = 3(8) - 4(6) = 24 - 24 = 0, so F does not have an inverse.

Answer:

316.78

Step-by-step explanation:

area of 360 circle = pi*radius*radius

area of 360 circle = pi*11*11

area of 360 circle = pi*11*11

area of 360 circle = 380.13

360/300 = 380.13/x

114039/360 = x

x=316.775

Answer:

Ais 66 and B is 40% C is 60%

Step-by-step explanation:

I know A is correct but not b or c hope this helps

43 4/5 cups of cheese is needed to make 10 pizzas.

We will use the Unitary method, that is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit.

Given that it takes 4 3/4 cups of cheese, 7/8 cups of olives, and 2 5/8 cups of sausage to make a signature pizza.

For making one pizza, amount of cheese needed =  4 3/8 cups = 35/8  cups.

Now the total amount of cheese needed to make 10 pizzas, we need to multiply  35/8  cups by 10.

So, 350/8  cups = 43 4/5 cups

Thus,  43 4/5 cups of cheese is needed.

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  If we run this test with the data above, we would get a p-value of 0.1389. This means that there is no significant difference between the distribution of pod weight for inoculated vs. uninoculated plants at the 5% significance level.

A1. The nonparametric test that can be used to compare the distribution of pod weight for inoculated vs. uninoculated plants is the Mann-Whitney U test. This test is also known as the Wilcoxon rank-sum test and is used to compare two independent groups.

A2. To perform a permutation test approach using a computer, we can use R programming language. Here are the steps to conduct the Mann-Whitney U test:

1. Input the data into R. Let's say we have two groups, Group A (inoculated) and Group B (uninoculated), with sample sizes of n1 and n2, respectively.

2. Use the "wilcox.test" function in R to perform the Mann-Whitney U test. The syntax for this function is as follows:

  wilcox.test(x, y, alternative = "two.sided", exact = FALSE, conf.int = TRUE)

  where x and y are the vectors of observations for Group A and Group B, respectively. The "alternative" argument specifies whether the test is two-tailed ("two.sided"), one-tailed ("less" or "greater"), or "two.sided" by default. The "exact" argument is set to FALSE to use the asymptotic approximation, and "conf.int" is set to TRUE to compute the confidence interval.

3. Run the function with the appropriate inputs and obtain the p-value.

  For example, let's say we have the following data:

  Group A (inoculated): 10, 12, 15, 20, 22
  Group B (uninoculated): 5, 8, 11, 16, 18, 21

  We can input the data into R as follows:

  A <- c(10, 12, 15, 20, 22)
  B <- c(5, 8, 11, 16, 18, 21)

  Then, we can run the Mann-Whitney U test as follows:

  wilcox.test(A, B, alternative = "two.sided", exact = FALSE, conf.int = TRUE)

  The output will include the test statistic (U), the p-value, and the confidence interval, among other things. The p-value will be the two-tailed p-value we are interested in.

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