PLEASE HELP WILL MARK BRANLIEST

If a scale dilates a two-dimensional object by a factor of 2/3, it means that the image of the object will be reduced by a factor of 2/3. In other words, the length and width of the image will be 2/3 of the length and width of the original object.

For instance, consider a rectangle with length L and width W. If we dilate this rectangle by a factor of 2/3, the new length and width of the rectangle will be (2/3)L and (2/3)W, respectively. The area of the new rectangle will be (2/3)L x (2/3)W = (4/9)LW, which is 4/9 of the original area. This means that the image is smaller than the original rectangle, and this type of dilation is called a reduction.

Dilations can be used in different applications of mathematics, such as geometry, trigonometry, and algebra. They are useful for changing the scale or size of an object in a proportional way, without altering its basic shape or characteristics.

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To build a series for the given function f(x) = (e^(2x) - 1 - 2x)/2x^2, we can start by finding the MacLaurin series for e^(2x) and then manipulate it to obtain the desired series.

The MacLaurin series for e^(2x) is given by:

e^(2x) = Σ (2x)^n / n! for n = 0 to ∞

Expanding the series, we get:

e^(2x) = 1 + 2x + 2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ...

Now, we can substitute this back into the original function:

f(x) = (e^(2x) - 1 - 2x)/2x^2 = (1 + 2x + 2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ... - 1 - 2x) / 2x^2

Simplifying, we have:

f(x) = (2x^2/2! + 2^3x^3/3! + 2^4x^4/4! + ...) / 2x^2

Now, we can divide by 2x^2 to obtain the series for f(x):

f(x) = 1/2! + 2x/3! + 2^3x^2/4! + 2^4x^3/5! + ...

Finally, we can write the final answer in proper summation notation:

f(x) = Σ (2^(n-1)x^(n-2)) / n! for n = 2 to ∞

To begin, we can write f(x) as:

f(x) = (1/2x^2)[e^(2x) - 1 - 2x]

Next, we will use the Maclaurin series for e^x, which is:

e^x = 1 + x + (x^2)/2! + (x^3)/3! + ...

Substituting 2x for x, we have:

e^(2x) = 1 + 2x + (4x^2)/2! + (8x^3)/3! + ...

Expanding the first two terms of the numerator in f(x), we have:

f(x) = (1/2x^2)[(1 + 2x + (4x^2)/2! + (8x^3)/3! + ...) - 1 - 2x]

Simplifying, we get:

f(x) = (1/2x^2)[2x + (4x^2)/2! + (8x^3)/3! + ...]

Now we can simplify the coefficients in the numerator by factoring out 2x:

f(x) = (1/x)[1 + (2x)/2! + (4x^2)/3! + ...]

Finally, we can write the series in summation notation:

f(x) = Σ[(2n)!/(2^n*n!)]x^n, n=1 to infinity.

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The probability of choosing exactly 13 students who dressed up as the 40s out of the 16 selected students is approx. 0.4334.

We can model this situation as a hypergeometric distribution, where we have a population of 19 students, 15 of whom dressed up as the 40s.

We want to choose a sample of 16 students and find the probability that exactly 13 of them dressed up as the '40s.

The probability of choosing exactly 13 students who dressed up as the 40s can be calculated:

(number of ways to choose 13 students who dressed up as the 40s) * (number of ways to choose 3 students who dressed up as other decades) / (total number of ways to choose 16 students)

The number of ways to choose 13 students who dressed up as the '40s is the number of combinations of 15 choose 13:

(15 choose 13) = 105

The number of ways to choose 3 students who dressed up as other decades is the number of combinations of 4 choose 3, which is:

(4 choose 3) = 4

The total number of ways to choose 16 students from 19 is the number of combinations of 19 choose 16, which is:

(19 choose 16) = 969

105 * 4 / 969 = 0.4334

Therefore, the probability of choosing exactly 13 students who dressed up as the 40s = 0.4334 (rounded to four decimal places)

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Answer:

B

Step-by-step explanation:

Every fifth people means one person from 5 people in total. So when we convert that into numbers, it becomes  [tex]\frac{1}{5}[/tex].

And in total there are 85 people involved, so the answer is

[tex]85[/tex] × [tex]\frac{1}{5}[/tex]

Answer:

Step-by-step explanation:

correct asnswer b

a) ∫ (1/x + 3/x^2 - 4/x^3) dx
To solve this indefinite integral, we need to use the power rule and the fact that the derivative of ln(x) is 1/x.

∫ (1/x + 3/x^2 - 4/x^3) dx = ln|x| - 3/x + 2/x^2 + C

b) ∫ (x^2 + 2x - 5) / √x dx
To solve this indefinite integral, we can simplify the integrand by multiplying the numerator and denominator by √x. Then, we can use the power rule and u-substitution.

∫ (x^2 + 2x - 5) / √x dx = ∫ (x^(5/2) + 2x^(3/2) - 5x^(1/2)) dx

= (2/7)x^(7/2) + (4/5)x^(5/2) - (10/3)x^(3/2) + C

c) ∫ x e^x dx
To solve this indefinite integral, we need to use integration by parts.

Let u = x and dv/dx = e^x. Then, we can find v by integrating dv/dx.

v = e^x

Using integration by parts, we get:

∫ x e^x dx = xe^x - ∫ e^x dx

= xe^x - e^x + C

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the partial derivative ∂z/∂y using implicit differentiation of e^z + sin(5x^2) + 2y = 0 is:
To calculate the partial derivative ∂z/∂y using implicit differentiation of e* + sin (5x^2) + 2y = 0, we first need to differentiate both sides of the equation with respect to y.

We get:

d/dy(e^z + sin(5x^2) + 2y) = d/dy(0)

Using the chain rule, the left-hand side becomes:

∂(e^z)/∂z * ∂z/∂y + ∂(sin(5x^2))/∂y + 2

We can simplify this by recognizing that ∂(sin(5x^2))/∂y = 0, since sin(5x^2) does not depend on y. Thus, we are left with:

∂(e^z)/∂z * ∂z/∂y + 2 = 0

Now, we need to solve for ∂z/∂y:

∂z/∂y = -2 / ∂(e^z)/∂z

To find ∂(e^z)/∂z, we differentiate e^z with respect to z, giving:

∂(e^z)/∂z = e^z

Substituting this into the expression for ∂z/∂y, we get:

∂z/∂y = -2 / e^z

Therefore, the partial derivative ∂z/∂y using implicit differentiation of e^z + sin(5x^2) + 2y = 0 is:

∂z/∂y = -2 / e^z

Note that we cannot simplify this any further without knowing the value of z.
To find the partial derivative ∂z/∂y using implicit differentiation for the equation e^z + sin(5x^2) + 2y = 0, we will first differentiate the equation with respect to y, treating z as a function of x and y.

Differentiating both sides with respect to y:

∂/∂y (e^z) + ∂/∂y (sin(5x^2)) + ∂/∂y (2y) = ∂/∂y (0)

Using the chain rule for the first term, we get:

(e^z) * (∂z/∂y) + 0 + 2 = 0

Now, solve for ∂z/∂y:

∂z/∂y = -2 / e^z

So, the partial derivative ∂z/∂y for the given equation is:

∂z/∂y = -2 / e^z

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Answer:

324π

Step-by-step explanation:

Area of circle = r² · π

r = 18 in

Find its area in terms of pi.

We Take

18² · π = 324π

So, the area of the circle is 324π.

Answer:

A = 324π

Step-by-step explanation:

A = πr²

A = π(18)²

A = π(324)

A = 324π

the length, in inches, of the other leg of his triangle is 9. 8inches

Using the Pythagorean theorem which states that the square of the longest leg or side of a given triangle is equal to the sum of the squares of the other two sides of the triangle.

From the information given, we have that;

a² + b² = c² represents the relationship between the three sides of a right triangle

Also,

Hypotenuse side = 11 inches

One of the other side = 5 inches

Substitute the values, we have;

11² = 5² + c²

collect like terms

c² = 121 - 25

Subtract the values

c = √96

c = 9. 8 inches

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the determinant of the matrix is e1e4-e3e2

The determinant of a matrix is a scalar value that is a function of the entries. It characterizes some properties of the matrix and the linear map represented by it. The determinant is nonzero if and only if the matrix is invertible and an isomorphism exists.

Determinants are only defined for square matrices and encode certain properties of the matrices.

The determinant of a matrix is defined by the difference betweern the product of the right diagonal to the the product of the left diagonal

From the given question. the determinant of the matrix is e1*e4 -e3-e2 = e1e4-e3e2

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Since there are multiple colors, the theoretical probability of selecting any one color would be 1/total number of colors, which is 1/6.

Theoretical probability is the probability of an event occurring based on all possible outcomes. In this case, if the bag contained an equal number of each color of bead, then the theoretical probability of selecting any one color of bead would be 1/total number of colors.

To find the experimental probability, we need to calculate the number of times each color was selected and divide by the total number of selections. Since each student is replacing the bead, the probability of selecting any one color of bead remains the same. Therefore, the experimental probability of selecting any one color of bead should also be 1/6.

However, due to the randomness of the selection process, the experimental probability may not be exactly equal to the theoretical probability. The color for which the experimental probability is closest to the theoretical probability would be the color that has been selected the most number of times, as this would provide the most accurate representation of the experimental probability.

Therefore, we need to record the number of times each color has been selected and calculate the experimental probability for each color. The color with the experimental probability closest to 1/6 would be the color for which the theoretical probability is closest to the experimental probability.

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a. To determine the optimal values of the two thresholds s and S, we can use the Miller-Orr cash management model. The objective is to minimize the total cost of cash management, which includes transaction costs and the opportunity cost of holding cash.

Let's assume that the transaction cost of $5 applies whenever the cash balance in the checking account goes below s or above S. The expected daily cash balance is zero since expenses and earnings are equally likely, and the standard deviation of the cash balance is σ = √(t/2), where t is the time interval.

The optimal value of s is given by:

s* = √(3rT/4C) - σ/2,

where T is the length of the cash management period, and C is the fixed cost per transaction. The optimal value of S is given by:

S* = 3s*,

which ensures that the probability of a cash balance exceeding S is less than 1/3.

Using r = 0.1, T = 1 day, and C = $5, we obtain:

s* = √(30.11/4*5) - √(1/2)/2 = $16.82

S* = 3*$16.82 = $50.47

Therefore, the optimal values of the two thresholds are s* = $16.82 and S* = $50.47.

b. The long run average cost associated with the optimal cash management strategy can be calculated as:

Total cost = (s*/2 + S*) * σ * √(2r/C) + C * E(N),

where E(N) is the expected number of transactions per day. Since expenses and earnings are equally likely, E(N) = (S* - s*)/2 = $16.83. Therefore, the total cost is:

Total cost = ($16.82/2 + $50.47) * √(1/2) * √(2*0.1/$5) + $5 * $16.83 = $1.38 per day.

Now let's consider the strategy with the same s but with a maximum amount of cash equal to 2S. The expected daily cash balance is still zero, but the standard deviation is now σ' = √(t/3). The optimal value of S' is given by:

S' = √(3rT/2C) - σ'/2 = $35.35.

The long run average cost associated with this strategy is:

Total cost' = (s/2 + S') * σ' * √(2r/C) + C * E(N'),

where E(N') is the expected number of transactions per day. Since the maximum amount of cash is now 2S, we have E(N') = (2S - s)/2 = $34.59. Therefore, the total cost is:

Total cost' = ($16.82/2 + $35.35) * √(1/3) * √(2*0.1/$5) + $5 * $34.59 = $1.30 per day.

Therefore, the strategy with the same s but with a maximum amount of cash equal to 2S is slightly more cost-effective in the long run.

c. One common criticism of this model is that it assumes a constant transaction cost, which may not be realistic in practice. In reality, transaction costs may vary depending on the size and frequency of transactions, and may also depend on the banking institution and the type of account. Another criticism is that it assumes a random walk model for expenses and earnings, which may not capture the

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The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.

To find the probability that a customer who buys a washer also buys a dryer, we need to use conditional probability.

Let's start by finding the probability of a customer buying a washer and a dryer, which is given as 11%.

Now, we know that 11% of customers buy both a washer and a dryer. We also know that 37% of customers buy a washer.

Using these two pieces of information, we can find the probability of a customer buying a dryer given that they have already bought a washer. This is the conditional probability we are looking for.

The formula for conditional probability is:

P(D | W) = P(D and W) / P(W)

where P(D | W) is the probability of buying a dryer given that a washer has already been purchased, P(D and W) is the probability of buying both a dryer and a washer, and P(W) is the probability of buying a washer.

Substituting the values we have:

P(D | W) = 0.11 / 0.37

P(D | W) = 0.297

The probability that a customer who buys a washer also buys a dryer is 0.297 or approximately 30%.

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The difference between the outcomes when selected with or without replacement is B. 10 outcomes.

With Replacement:

When you select two coins with replacement, you put the first coin back in the jar before selecting the second coin. This means that there are 10 possibilities for each selection. So, the number of outcomes for selecting two coins with replacement is 10 x 10 = 100 outcomes.

Without Replacement:

When you select two coins without replacement, you don't put the first coin back in the jar before selecting the second coin. This means that after selecting the first coin, there are 9 coins left in the jar for the second selection. So, the number of outcomes for selecting two coins without replacement is 10 x 9 = 90 outcomes.

Difference = 100 outcomes - 90 outcomes

Difference = 10 outcomes

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If Jesse can mow 3 yards in 8 hours. Jackson can mow twice as many yards per hour the constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.

To find the constant of proportionality between the number of yards Jackson can mow and the number of hours, we can use the formula:

k = y/x

where k is the constant of proportionality, y is the number of yards, and x is the number of hours.

We know that Jesse can mow 3 yards in 8 hours, which means his rate of mowing is: 3 yards/8 hours = 3/8 yards per hour

We also know that Jackson can mow twice as many yards per hour as Jesse, which means his rate of mowing is:

2 * (3/8) yards per hour = 3/4 yards per hour

Now we can use the formula to find the constant of proportionality for Jackson:

k = y/x = (3/4) yards per hour / 1 hour = 3/4

Therefore, the constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.

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"t" increases, and the number of digital subscriptions grows exponentially at a rate of 3.4% per month.

The function s(t) = 31,500(1.034)^t gives an approximation of the number of digital subscriptions s as a function of t months after the launch of the advertising campaign.

The parameters of the function s(t) are:

31,500: This is the initial number of digital subscriptions at t = 0, when the advertising campaign is launched.

1.034: This is the growth rate of the number of digital subscriptions per month. It represents the percentage increase in the number of subscriptions each month due to the advertising campaign. Specifically, each month the number of subscriptions is multiplied by 1.034, which is the same as increasing it by 3.4%.

t: This is the time in months after the launch of the advertising campaign. It is the independent variable of the function that determines the number of digital subscriptions at any given time t.

Statements interpreting the parameters of the function s(t) are:

The initial number of digital subscriptions at t = 0 is 31,500.

For every month after the launch of the advertising campaign, the number of digital subscriptions increases by 3.4%, or a factor of 1.034.

The parameter t represents the time in months after the launch of the advertising campaign. As t increases, the number of digital subscriptions grows exponentially at a rate of 3.4% per month.

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The volume of the cone to the nearest tenth is 263.8 cm^3.

To find the volume of the cone, we first need to use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

We are given that the radius is 6 centimeters and the height is 7 centimeters, so we can substitute these values into the formula.

The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.

Using the given values, we can plug them into the formula and solve:

V = (1/3)π(6 cm)^2(7 cm)

V ≈ 263.7 cm^3

Rounding this to the nearest tenth gives us the final answer of 263.8 cm^3, which is option (C).

Since 3 is less than 5, we round down, which means the answer is 263.8 cm^3, as shown in option (C).

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1 is linear variation and 2 is direct proportionality. In 1 it is linear variation since from the beginning the zeros do not correspond and in 2 if the zeros correspond.

Variation refers to the differences that exist among individuals or groups within a population. These differences can be genetic, environmental, or a combination of both, and can manifest in various traits, such as physical characteristics, behavior, or disease susceptibility.

Genetic variation arises from differences in the DNA sequence among individuals, which can result in different traits being expressed. This variation can occur naturally or be induced by mutations, genetic recombination, or genetic drift. Environmental variation arises from differences in the conditions experienced by individuals or groups, such as differences in climate, nutrition, or exposure to toxins. Environmental variation can also interact with genetic variation to produce complex traits.

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Complete Question:-

Look at the following tables and analyze the values ​​they contain. Then, pose a problem that can be solved with these data, also argue why one table corresponds to linear variation and the other to direct proportional variation.​

TABLE 1:

X 0 1 2 3

and 2 17 32 47

TABLE 2:

X 0 1 2 3

AND 0 15 30 45​

The polynomial is factored to y²(x³ - 7³y³)

Note that polynomials are described as expressions that are made up of terms, variables, coefficients, factors and constants.

Also, they have a degree greater than one.

Index forms are also seen as forms used to represent values that are too large or small in more convenient forms.

From the information given, we have that;

x³y²-343y⁵

Now, find the cube value of 343, we have;

343 = 7³

Substitute the value

x³y²- 7³y⁵

Factorize the common terms, we have;

y²(x³ - 7³y³)

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Answer:20 feet by 10 feet

Step-by-step explanation:

Answer:

I think the answer might be -4 = 3x.

Step-by-step explanation:

-2 times x + 2 = -4 and 5 - 2x = 3x so i think the answer is -4 = 3x. Also, you're welcome if this helps.

The inequalities represented are:

In mathematics, an inequality is a statement that two values or expressions are not equal. It is used to compare two values and determine the relationship between them. Inequalities use symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Inequalities can be solved and graphed on a number line to show all possible solutions that satisfy the inequality. They are commonly used in algebra and calculus to express a range of values for a variable.

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Answer:

bad photo quality

Step-by-step explanation:

The function is transformed by a vertical stretching or compression by a factor of 5, a horizontal shift of 6 units to the right, and a vertical shift of 2 units downward.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

In the given function y = 5/(x - 6) - 2, the values of a, h, and k can be identified as follows:

a = 5

h = 6

k = -2

Now , the original function is y = a/(x - h) + k, and the reciprocal family of this function is y = a/(x - h) + k

And , value of 'a' determines the vertical scaling factor of the reciprocal function

Now , the value of 'h' determines the horizontal shift of the reciprocal function. If 'h' is positive, the graph of the reciprocal function is shifted horizontally to the right

And , if 'k' is negative, the graph is shifted vertically downward

Hence , the transformation of the function is solved

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The square root of units is sqrt (80), and the area of the kite to the nearest unit is 74 square units.

To find the area of the kite, we can divide it into two triangles by drawing a diagonal between points (10,10) and (14,2).
First, we need to find the length of this diagonal. We can use the distance formula:

d = sqrt((14-10)^2 + (2-10)^2)
d = sqrt(16 + 64)
d = sqrt(80)

So the length of the diagonal is square root(80) units.

Next, we can find the area of each triangle:

Triangle 1:
Base = 10 units
Height = 10 units
Area = 1/2 * base * height = 1/2 * 10 * 10 = 50 square units

Triangle 2:
Base = 6 units (the difference between the x-coordinate plane of (10,10) and (14,2))
Height = 8 units (the difference between the y-coordinate plane of (10,10) and (16,8))
Area = 1/2 * base * height = 1/2 * 6 * 8 = 24 square units

So the total area of the kite is 50 + 24 = 74 square units.

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Answer:    

On a coordinate plane, kite G D E F has points (0, 0), (10, 10), (16, 8), (14, 2).

Complete the steps to find the area of the kite.

What is GE?

Square root of

units

What is DF?

Square root of

units

What is the area of the kite to the nearest unit?

square units

The initial height of the ball after launch is 14ft.

A vertical motion is a motion due to gravity. This means the velocity and height will depend on the acceleration due to gravity.

The height of vertical motion is given as;

H = ut ± 1/2 gt²

where u is the initial velocity and t is the time to reach max height.

The height of a ball is given by;

h(t) = -16t²+14

where t represents the time in seconds after launch.

The initial height after launch is when t = 0

h(t) = -16(0)² +14

h(t) = 14ft

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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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The probability of the adults being chosen this way by chance is less than 0.01 interprets that group is more likely to choose men over women

A group conducting a survey randomly selects adults in a certain region. Of the 2,500 adults selected, 1,684 are men. The men and women have an equal chance The result of the survey is significant at the 0.01 level which means that the probability of group selection being the result of chance is 0.01 or less because the event is least likely to happen the group is more likely to select men over women.

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Ruben painted a total area of [tex]130.5 square feet.[/tex]

To determine the total area that Ruben painted, we need to find the area

of each wall and then add them together. Since the dimensions of the

walls are given in different units (yards and feet), we will first need to

convert them to a common unit.The first wall is 3 1/2 yards long by 9 feet

tall, which is equivalent to 10 1/2 feet long by 9 feet tall (since 1 yard = 3

feet).

The area of this wall is:

[tex]10 1/2 feet * 9 feet = 94.5 square feet[/tex]

The second two walls are each 4 feet tall by 1 1/2 yards long, which is

equivalent to 4 feet tall by 4.5 feet long (since 1 yard = 3 feet).

The area of each of these walls is:

[tex]4 feet* 4.5 feet = 18 square feet[/tex]

Since Ruben painted one coat on each wall, the total area he painted is:

[tex]94.5 square feet + 2 * 18 square feet = 130.5 square feet[/tex]

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The measure of angle U to the nearest tenth is 39.6°

The cosine Rule says that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

C² = a²+b²-2abcosC

450² = 360²+110²+2(110)(360)cosU

202500 = 129600+ 12100+ 79200cosU

202500 = 141700+79200cosU

79200cosU = 202500-141700

79200cosU = 60800

cos U = 60800/79200

cos U = 0.77

U = 39.6°( nearest tenth)

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