The line on a coordinate plane makes an angle of depression 32 degrees. What is the slope of the line

After solving equation, Katya needs 5 or 6 display cases to display all of her badges, depending on how she chooses to group them.

The number of badges Katya has is not explicitly given in the problem. Therefore, we need to first find the total number of badges Katya has earned by subtracting the number of parks for which she doesn't have badges from the total number of participating parks.

The equation to use for this is:

b = 207 - 165

where b is the total number of badges Katya has earned.

Option A is the correct equation, which simplifies to:

b = 42

This means Katya has earned 42 badges.

Next, we need to find out how many display cases Katya needs. We know that she can fit 8 badges in one case, so we can use division to find the number of cases needed:

c = b / 8

where c is the number of cases needed.

Substituting the value of b from the previous equation, we get:

c = 42 / 8

Option C is the correct equation, which simplifies to:

c = 5.25

This means that Katya needs 5 or 6 display cases to display all of her badges, depending on how she chooses to group them.

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Therefore, the linearization predicts that f(2.9, 4.1) is approximately 4.142.

To find the linearization of the function f(x, y) = √x^2 + y^2 at the point (3, 4), we need to find the partial derivatives of f with respect to x and y, evaluate them at (3, 4), and use them to write the equation of the tangent plane to the surface at that point.

First, we have:

∂f/∂x = x/√(x^2 + y^2)

∂f/∂y = y/√(x^2 + y^2)

Evaluating these at (3, 4), we get:

∂f/∂x(3, 4) = 3/5

∂f/∂y(3, 4) = 4/5

So the equation of the tangent plane to the surface at (3, 4) is:

z - f(3, 4) = (∂f/∂x(3, 4))(x - 3) + (∂f/∂y(3, 4))(y - 4)

Plugging in f(3, 4) = 5 and the partial derivatives, we get:

z - 5 = (3/5)(x - 3) + (4/5)(y - 4)

Simplifying, we get:

z = (3/5)x + (4/5)y - 1

This is the linearization of f(x, y) = √x^2 + y^2 at the point (3, 4).

To approximate f(2.9, 4.1), we plug in x = 2.9 and y = 4.1 into the linearization:

z = (3/5)(2.9) + (4/5)(4.1) - 1

z ≈ 4.142

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The values of the combination expressions are ¹²C₁₁ = 12, ¹²C₁₀ = 66, ¹²C₅ = 792, ¹²C₁ = 12, ¹²C₁₂ = 1, ⁵C₄ + ⁵C₃ = 15, ⁵C₃/⁵C₂ = 1 and 4⁷C₂ = 84

Also, the number of ways is 30045015

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

¹²C₁₁

The formula for combination is

ⁿCₓ = n!/[(n - x)! * x!]

So, we have

¹²C₁₁ = 12!/[(12 - 11)! * 11!]

Evaluate

¹²C₁₁ = 12

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

¹²C₁₀ = 12!/[(12 - 10)! * 10!]

¹²C₁₀ = 66

¹²C₅ = 12!/[(12 - 5)! * 5!]

¹²C₅ = 792

¹²C₁ = 12!/[(12 - 1)! * 1!]

¹²C₁ = 12

¹²C₁₂ = 12!/[(12 - 12)! * 12!]

¹²C₁₂ = 1

⁵C₄ + ⁵C₃ = 5!/[(5 - 4)! * 4!] + 5!/[(5 - 3)! * 3!]

⁵C₄ + ⁵C₃ = 15

⁵C₃/⁵C₂ = 5!/[(5 - 3)! * 3!] / 5!/[(5 - 2)! * 2!]

⁵C₃/⁵C₂ = 1

4⁷C₂ = 4 * 7!/[(7 - 2)! * 2!]

4⁷C₂ = 84

For the number of ways to get people hired, we have

n = 30

x = 10

So, we have

³⁰C₁₀ = 30!/[(30 - 10)! * 10!]

³⁰C₁₀ = 30045015

Hence, the number of ways to get them hired is 30045015 ways

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Answer:

Step-by-step explanation:

√4x^2=2x

Based on the given situation we can conclude that the sedan retains its value better than the pickup truck over time.The functions S(t) and P(t) represent the values of the sedan and pickup truck, respectively, as a function of the number of years t after their purchase.

The coefficient 24,400 in the function S(t) represents the initial value of the sedan, which is the value of the car at t=0. The base 0.82 represents the decay rate or the percentage decrease in the value of the sedan each year. Similarly, in the function P(t), the coefficient 35,900 represents the initial value of the pickup truck and the base 0.71 represents the decay rate of the value of the pickup truck.

Since the base of the sedan's value decay is 0.82, it indicates that the value of the sedan decreases by 18% each year. Whereas the base of the pickup truck's value decay is 0.71, indicating that the value of the pickup truck decreases by 29% each year. Therefore, we can observe that the value of the pickup truck depreciates faster than the sedan. After two years, the value of the sedan would be approximately $16,650, and the value of the pickup truck would be approximately $14,161. After five years, the value of the sedan would be approximately $9,237, and the value of the pickup truck would be approximately $6,155.

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We can use the ratio test to determine whether the series ∑(n=1[tex])^(infinity)[/tex][tex]13^n[/tex]/ [(n+1)[tex]6^(2n+1)[/tex]] is convergent or divergent.

We evaluate the limit:

lim n → ∞ [tex]|(13^(n+1) / [(n+2)6^(2n+3)]) / (13^n / [(n+1)6^(2n+1)])|[/tex]

= lim n → ∞ [tex]|(13^(n+1) / 13^n) * [(n+1)6^(2n+1) / (n+2)6^(2n+3)]|[/tex]

= lim n → ∞ [tex]|13 / 6^2| * |(n+1)/(n+2)|[/tex]

= 13/36

Since the limit is less than 1, by the ratio test, the series is convergent.

To find the value of a_n, we can substitute n = 1 into the formula:

a_n = [tex]13^n / [(n+1)6^(2n+1)][/tex]

a_1 = [tex]13 / [(1+1)6^(2+1)] = 13 / (2*6^3)[/tex]

Therefore, a_1 = 13 / 432.

Note that we only needed to find the value of a_1 to apply the ratio test and determine the convergence of the series.

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Step-by-step explanation:

To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.

The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:

3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1

Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).

Therefore, the students should use 1/8 as the fraction for the line plot.

The dimensions of the bookmark are length = 15 centimeters and width = 10 centimeters.

Let's denote the length of the bookmark as L and the width as W.

The area of a rectangle is given by the formula A = L * W, and the perimeter is given by P = 2L + 2W.

From the given information, we have two equations:

Equation 1: A = 150 square centimeters

Equation 2: P = 62 centimeters

Substituting the formulas for area and perimeter, we get:

Equation 1: L * W = 150

Equation 2: 2L + 2W = 62

To solve these equations, we can use substitution or elimination. Let's solve by substitution:

From Equation 1, we can express one variable in terms of the other:

L = 150 / W

Substituting this into Equation 2:

2(150 / W) + 2W = 62

300 / W + 2W = 62

300 + 2W^2 = 62W

2W^2 - 62W + 300 = 0

Now we have a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

[tex]2W^2 - 62W + 300 = 0[/tex]

(W - 10)(2W - 30) = 0

This gives us two possible solutions:

W - 10 = 0 -> W = 10

2W - 30 = 0 -> W = 15

Since the width cannot be longer than the length, we discard the solution W = 15.

So, the width of the bookmark is W = 10 centimeters.

Now, we can substitute this value into Equation 1 to find the length:

L * 10 = 150

L = 150 / 10

L = 15

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Nataly saved s/64.

The original prices for the items are:

Skirt: s/78

Blouse: s/65

Jacket: s/240

The discounted prices Nataly paid are:

Skirt: s/69

Blouse: s/52

Jacket: s/198

To find out how much Nataly saved, we need to calculate the difference between the original prices and the discounted prices, and then add them up:

savings = (78 - 69) + (65 - 52) + (240 - 198)

savings = 9 + 13 + 42

savings = s/64

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Answer:  First, we need to find the composite function (fg)(x):

(fg)(x) = f(g(x))

= f(-4x-3)

= (-4x-3)^2 + (-4x-3) + 9 (substituting g(x) into f(x))

= 16x^2 + 24x + 18

Therefore, (fg)(x) = 16x^2 + 24x + 18.

Next, we need to find the quotient function (f/g)(x):

(f/g)(x) = f(x) / g(x)

= (x^2 + x + 9) / (-4x - 3) (substituting f(x) and g(x))

To simplify this expression, we can use polynomial long division or synthetic division. Using synthetic division, we get:

  -4 |   1    1    9

      |_____-4__ 12

      |  1  -3   21

Therefore, (f/g)(x) = -4x + 3 - 21 / (-4x - 3)

Simplifying further, we get:

(f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4))

Therefore, (f/g)(x) = -4x + 3 + (21/4)(1/(x + 3/4)).

Step-by-step explanation:

Jorge's older brother's watering can holds approximately 165.33 cups of water. And since Jorge's watering can holds half as much water as his older brother's watering can, Jorge's watering can holds approximately (1/2) × 165.33 = 82.67 cups of water, which we can round to 4 cups.

Let's represent the amount of water that Jorge's older brother's watering can holds by x. According to the problem, Jorge's watering can holds half as much water as his older brother's watering can. Therefore, Jorge's watering can holds (1/2)x cups of water.

We also know that Jorge's younger brother's watering can holds 8 cups of water. Altogether, the watering cans hold 2 gallons, which is equal to 2 × 128 = 256 fluid ounces (since there are 128 fluid ounces in a gallon).

We can write an equation based on the given information:

x + (1/2)x + 8 = 256

Simplifying the equation, we get:

(3/2)x = 248

x = 248 × 2/3 = 165.33

Therefore, jorge's watering can holds 4 cups of water.

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The correct statement for p-value in chi-square is : Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger, option B.

A test that evaluates how well a model matches real observed data is the chi-square (2) statistic. A chi-square statistic can only be calculated with data that is random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a sizable enough sample. The outcomes of a fair coin flip, for instance, satisfy these requirements.

To test hypotheses, chi-square tests are frequently employed. Given the size of the sample and the number of variables in the relationship, the chi-square statistic examines the magnitude of any differences between the predicted findings and the actual results.

According to the total number of variables and samples used in the experiment, degrees of freedom are utilised in these tests to assess if a certain null hypothesis can be rejected. Like with any statistic, the results are more trustworthy the greater the sample size.

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Complete question:

A chi-square test for homogeneity was conducted to investigate whether the four high schools in a school district have different absentee rates for each of four grade levels. The chi-square test statistic and p-value of the test were 19.02 and 0.025, respectively. Which of the following is the correct interpretation of the p-value in the context of the test?

A) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or smaller.

B) Assuming that each high school has the same absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.

C) Assuming that each high school has a different absentee rate for each grade level, there is a 2.5 percent chance of finding a test statistic 19.02 or larger.

D) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is the same.

E) There is a 2.5 percent chance that the absentee rate for each grade level at the four schools is different.

our final estimate for the area under the curve f(x)=1/x on [1,2] using 4 approximating rectangles and taking the average of the left and right endpoints is 0.76.

To estimate the area under the curve f(x)=1/x on [1,2], we can use 4 approximating rectangles.

a) Using left endpoints, the width of each rectangle is (2-1)/4 = 0.25. The left endpoints of the rectangles are 1, 1.25, 1.5, and 1.75. The height of each rectangle is f(x) evaluated at the left endpoint.

So, the heights are f(1) = 1/1 = 1, f(1.25) = 1/1.25 = 0.8,

f(1.5)=1/1.5 = 0.67, and f(1.75) = 1/1.75 = 0.57.

The area of each rectangle is width times height, so the areas are

0.25*1 = 0.25, 0.25*0.8 = 0.2, 0.25*0.67 = 0.1675, and 0.25*0.57 = 0.1425.

Adding these areas together, we get an estimate of the total area under the curve as

0.25 + 0.2 + 0.1675 + 0.1425 = 0.76.

b) Using right endpoints, the width of each rectangle is the same as before. The right endpoints of the rectangles are

1.25, 1.5, 1.75, and 2.

The heights are f(x) evaluated at the right endpoint. So, the heights are

f(1.25) = 0.8, f(1.5) = 0.67, f(1.75) = 0.57, and f(2) = 0.5.

The areas of the rectangles are the same as before, so adding them up, we get an estimate of the total area as

0.2 + 0.1675 + 0.1425 + 0.25 = 0.76,  

which is the same as before.
c) To get the average of the two estimates, we add them together and divide by 2:

(0.76+0.76) / 2 = 0.76.

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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = base area × height

Area of playground, A = 45 × 20

Area of a playground, A = 900 square yards.

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Answer:

b

Step-by-step explanation:

point B has coordinates (0, 0 ) which is the origin

The linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x and for 10 comic books, the second store has the better deal.

A linear function is a mathematical function where the graph of the function is a straight line. It can be written in the form y = mx + b, where x and y are the variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis). The slope represents the rate of change of the function, while the y-intercept is the value of the function when x is equal to zero.

To write a linear function rule that models the cost y of a package containing any number x of comic books, we can use the given information to set up a system of equations:

Poster + 2 Comics = $7.50

Poster + 11 Comics = $16.50

We can solve for the cost of the poster and the cost of one comic book by subtracting the first equation from the second:

9 Comics = $9.00

1 Comic = $1.00

Then, we can use the cost of one comic to set up a linear function rule:

y = cost of poster + cost of x comics

y = $6.50 + $1.00x

Therefore, the linear function rule that models the cost y of a package containing any number x of comic books is y = $6.50 + $1.00x.

For the second store, the linear function rule is given as y = $5.75 + $1.00x.

To determine which store has the better deal, we can compare the cost of each package for a specific number of comic books. For example, if we want to buy 10 comic books, the cost at the first store would be:

y = $6.50 + $1.00(10) = $16.50

The cost at the second store would be:

y = $5.75 + $1.00(10) = $15.75

Therefore, for 10 comic books, the second store has the better deal. However, for a different number of comic books, the better deal may be at a different store. We can use the linear function rules to compare the costs for any number of comic books

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Answer:

x = 18

Step-by-step explanation:

We Know

(10x - 4) + (x - 14) must equal 180°

Find the value of x.

Let's solve

10x - 4 + x - 14 = 180

11x - 18 = 180

11x = 198

x = 18

So, x = 18 is the answer.

Answer: AB = 16.4

Step-by-step explanation:

You can use tan x = opposite/adjacent

tan 38 = AB/21

21 tan 38 = AB

AB = 16.4

The volume of the package which is 12 inches long, 12 inches wide, and 48 inches high is 6912 inches³ or 4 cubic feet.

Given length of the package which is in rectangular prism shape (L) = 12 inches

similarly, width of the package (W) = 12 inches

height of the package (H)  = 48 inches

To know the volume of the package which is in the rectangular prism shape the formula is V=  L x W x H

The substituting the given values in the above equation, we can obtain the volume of the package.

So,

L x W x H = 12 x 12 x 48 = 6912 inches³

To convert the cubic inches into the cubic feet we have to divide the obtained value by 1728.

So, [tex]\frac{6912}{1728}[/tex] = 4 feet³

From the above explanation, we can conclude that the volume of the given package of rectangular prism shape is 4 feet³.

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If kawan paints the visible outside faces of her shed, she paints two rectangle faces and two triangle faces then the total surface area that she paints is 88ft².

The area of a triangle of altitude h and base b is given by;

A = 0.5bh

Therefore the area of one triangle face ;

At = 0.5 × 8 × 5

At = 20ft²

Area of a rectangle of length l and breadth b is;

A = lb

Therefore the area of a rectangle face;

Ar = 8 × 3

Ar = 24ft²

We have 2 triangle faces and 2 rectangle face, therefore total surface area as;

A = 2At + 2Ar

A  = 2×20 + 2×24

A = 40 + 48

A = 88ft²

Therefore the answer is; 88ft².

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A comparison of the cost of each for 100 g indicates that the standard which costs about $1.13 per 100 grams is more expensive than the supersize which costs about $0.69 per 100 g and the supersize is more expensive than the economy which costs $0.575 per 100 g.

The order of the cost of the brands from cheapest to most expensive can be presented as follows;

The cost per unit is the cost of a number of items, divided by the number of units of the item.

The unit cost of the brands of cereal sold at the supermarket are therefore;

Unit cost per 100 gram for Standard = $2.49/220 g × 100 ≈ $1.13/g

Unit cost per gram for Economy = $5.00/725 g × 100 = $100/145/ g ≈ $0.69/g

Unit cost per gram for Supersize = $11.50/2kg × 100 = $1150/2,000 g ≈ $0.575/g

Based on the above unit cost, we get;

1.13 > 0.69 > 0.575

Therefore, the cheapest brand is the supersize with a cost per 100 gram of $0.575/g, followed by the economy, with a cost per 100 grams which is about $0.69/g then the most costly is the standard, with a cost per 100 gram of $1.13/g

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You must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.

To achieve a savings account balance of $23,000 in 5 years with an interest rate of 6.8% compounded continuously, you will need to use the formula for continuous compounding: A = P * e^(rt), where A is the future value, P is the principal amount (initial deposit), r is the interest rate, t is the time in years, and e is the base of the natural logarithm (approximately 2.71828).

In this case, A = $23,000, r = 0.068, and t = 5 years. You need to solve for P, the principal amount:

$23,000 = P * e^(0.068 * 5)

Now, you can solve for P:

P = $23,000 / e^(0.068 * 5)

P ≈ $16,465.55

So, you must have approximately $16,465.55 in your account now to achieve a balance of $23,000 in 5 years with a 6.8% interest rate compounded continuously.

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1. This is not an example of a quasi-experimental design because the researcher randomly assigned participants to the two groups. In a quasi-experimental design, the researcher does not have full control over the assignment of participants to groups.

2. The dependent variable in this study is the word recall. It is the variable that the researcher is interested in measuring and is expected to be affected by the independent variable.

3. The independent variable in this study is sugar consumption. It is the variable that the researcher manipulated by assigning participants to one of two groups, sugar vs. no sugar.

The purpose of manipulating the independent variable is to examine its effect on the dependent variable, word recall.

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To the nearest dollar, the business initially invested approximately $3,449 in 1991.

To determine the initial investment in 1991, we can use the formula F = P(1 + R/100)^T, where F is the final amount, P is the initial investment amount, R is the annual interest rate, and T is the time in years.

In this case, F = $4,000 (the amount in the account at the end of 1996), R = 3% (the annual interest rate), and T = 5 years (1996 - 1991). We need to solve for P, the initial investment amount.

First, let's rewrite the equation: P = F / (1 + R/100)^T

Now, we can plug in the known values: P = 4000 / (1 + 3/100)^5

Next, we calculate the denominator: (1 + 0.03)^5 = 1.159274

Then, we divide the final amount by the denominator to find the initial investment: P = 4000 / 1.159274

Lastly, rounding to the nearest dollar, we get: P ≈ $3,449

So, the business initially invested approximately $3,449 in 1991.

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Answer:

y=f(x) = log7x

Just trust me

The graph best represents the function y = f(x) = 7x, an exponential function.

The graph represents the function y = 7x, which is an exponential function. In an exponential function, the variable x is the base, and the exponent is a constant, which in this case is 7. This means that the function grows rapidly as x increases, creating a steep curve on the graph.

The other two options, y = f(x) = log7x and y = f(x) = x7, are not represented by the given graph.

The function y = f(x) = log7x is a logarithmic function, which has a different shape on the graph, with a horizontal asymptote and the x-axis acting as its asymptote.

The function y = f(x) = x7 is a polynomial function, where x is raised to the power of 7, and it would have a different pattern on the graph compared to the exponential function shown.

Thus, the graph best represents the function y = f(x) = 7x, an exponential function.

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Answer:

4

Step-by-step explanation:

You can cut it 4 ways to obtain equal parts on both sides. It's along the same as the symmetry of a square.

Answer:

Kerry could give her the range or the standard deviation of the data set.

Step-by-step explanation:

Coach Loren wants one number to describe how all of the values in the data set vary, so Kerry should tell her to use a measure of variability.

Kerry could give her the range or the standard deviation of the data set.

To find the area of each shaded sector and round to the hundredths place, I'll need some more information, such as the radius of the circle and the measure of the central angle of the sector. Please provide these details so I can assist you with the calculation.

The area of the shaded sector is 1330.81 ft²

Given, ∠GKH = 26° and ∠JKI = 90°

The area that is not shaded has a total of 90° + 26° = 116°.

A circle has a total angle of 360°, so the area that is shaded must be

360° - 116° =  244°

Given, HK = 25 ft

Radius of circle = 25 ft

We know that the formula for the area of the sector of a circle is

Area = [tex]\frac{\pi \theta r^2}{360^\circ}[/tex]

= (π × 244 × (25)² )/ 360

= 7625π/18

= 1330.81 ft²

Hence, the area of the shaded sector is 1330.81 ft²

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Given question is incomplete, the complete question is below

Find the area of each shaded sector. round to the hundredths place.

The average price of milk in 2018 was $6.45 per gallon.

The average price of milk in 2021 was $189.15 per gallon.

When x = 0 (which represents the year 2018), the function becomes:

3.55 + 2.90(1 + 0)³

= 3.55 + 2.90(1)³

= 3.55 + 2.90

= 6.45

The average price of milk in 2018 was $6.45 per gallon.

When x = 3 (which represents the year 2021), the function becomes:

3.55 + 2.90(1 + 3)³

= 3.55 + 2.90(4)³

= 3.55 + 2.90(64)

= 3.55 + 185.6

= 189.15

The average price of milk in 2021 was $189.15 per gallon.

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Answer:  B   28√15

Step-by-step explanation:

They want you to find the Area of the quadrilateral.  But if you can find the area of 1 trangle then you can double it because the 2 triangles are congruent.

We know the 2 triangles are congruent from the theorem  (see diagram

We also know that  QR=TR=SR  They are all radius

Let's solve for triangle PRS

PR = hypotenuse = 10+7 =17

SR=7  radius

Use pythagorean to find PS

c²=a²+b²

17²=7²+b²

289 = 49 + b²

b²=289 -49

b² = 240

b=√240

b=[tex]\sqrt{16*15}[/tex]

b= 4√15  This is PS

Area of triangle = 1/2 bh       b=PS   h=7

Area of triangle = 1/2 (4√15)(7)

Area of triangle = (2√15)(7)

Area of triangle = 14√15

Area of quadrilateral = 2 (14√15)        > 2 triangles make the quadrilateral

Area of quadrilateral =  28√15