Find the sum of the first 10 terms of the following series, to the nearest integer.


8,20/3,50/9

Using the Pythagorean theorem, the value of x, rounded to the nearest tenth, is 11.5 units.

In the given right triangle ABC with right angle B, you are given the lengths of sides BC (8 units) and AC (14 units). You are asked to find the length of side AB (x units). To do this, you can use the Pythagorean theorem, which states that the square of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC).

So, the equation for this triangle is:

AC² = AB² + BC²

Plug in the given values:

14² = x² + 8²

196 = x² + 64

Subtract 64 from both sides:

132 = x²

Now, find the square root of 132:

x ≈ 11.5

So, the value of x, rounded to the nearest tenth, is 11.5 units.

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The value of s - 85 cannot be determined based on the given information as we do not know the value of s.

Alternating Series Test states that if a series satisfies three conditions, namely the terms alternate in sign, the absolute value of the terms decreases as n increases, and the limit of the terms approaches zero as n approaches infinity, then the series converges.

The given series (-1)^n satisfies the first two conditions as the terms alternate in sign and the absolute value of the terms is decreasing. To check the third condition, we take the limit of the terms as n approaches infinity: lim n→∞ |(-1)^n+1/n+1| = lim n→∞ 1/(n+1) = 0.

Since all three conditions are satisfied, the series converges. We can also see from the given partial sums that the sum s lies between 83 and 85. Therefore, s - 85 is negative or zero.

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Proportionately, if 8 cm represents​ 10%, the length of a line segment that is​ 100% is 80 cm.

Proportion is the ratio of two quantities equated to each other.

Proportion also represents the portion or part of a whole.

Proportions can be represented using decimals, fractions, or percentages, like ratios.

The percentage of 8 cm length = 10%

The whole length = 100%

Proportionately, 100% = 80 cm (8 ÷ 10%) or (8 x 100 ÷ 10)

Thus, we can conclude that 100% of the line segment will be 80 cm if 8 cm is 10%.

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If 8 cm represents​ 10%, what is the length of a line segment that is​ 100%? Explain.

Amount that will be in the account after 2 years with daily compounding is $28,484.03.

Amount that will be in the account after 2 years with continuous compounding is $28,498.84.

The appropriate compound interest formula is:

[tex]A = P(1 + r/n)^{nt[/tex]

A is the amount.

P is the principal.

r is the annual interest rate.

n is the number of times the interest is compounded all year.

t is the number of years.

(a) For daily compounding (n = 365), we have:

A = 26000(1 + 0.0365/365)³⁶⁵*²
A = 26000(1 + 0.0001)⁷³⁰
A = 26000(1.0001)⁷³⁰
A = 28,484.03

Therefore, the amount that will be in the account after 2 years with daily compounding is $28,484.03.

(b) For continuous compounding, we have:

A = P[tex]e^{rt[/tex]

e is the mathematical constant almost equal to 2.71828.

A = 26000[tex]e^{0.0365*2[/tex]
A = 26000[tex]e^{0.073[/tex]
A = 28,498.84

Therefore, the amount that will be in the account after 2 years with continuous compounding is $28,498.84.

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If two fair dice are rolled, the probability that the total showing is either even or less than five is 17/36. The correct answer is B.

There are 36 possible outcomes when rolling two dice, since each die has 6 possible outcomes.

To find the probability that the total showing is either even or less than five, we can first find the probability that the total showing is even, and then add to that the probability that the total showing is less than five, excluding the outcomes where the total showing is even.

To find the probability that the total showing is even, we can consider the following possibilities:

both dice show even numbers (probability 1/4)

both dice show odd numbers (probability 1/4)

So the probability of rolling an even total is 1/4 + 1/4 = 1/2.

To find the probability that the total showing is less than five, excluding the outcomes where the total showing is even, we can consider the following possibilities:

So the probability of rolling a total less than five, excluding the outcomes where the total showing is even, is 1/36 + 1/18 + 1/18 + 1/12 + 1/12 + 1/9 + 1/9 + 1/9 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 11/36.

Therefore, the probability that the total showing is either even or less than five is 1/2 + 11/36 = 17/36.

So the correct answer is (b) 17/36.

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1. Write out the given equation: 8/10 + unknown fraction = 97/100

2. Subtract 8/10 from both sides of the equation to isolate the unknown fraction:

  8/10 + unknown fraction - 8/10 = 97/100 - 8/10

  Simplifying the left side: unknown fraction = 97/100 - 8/10

3. Convert both fractions to have a common denominator of 100:

  97/100 - 8/10 = 97/100 - 80/100

  Simplifying the right side: unknown fraction = 17/100

4. Therefore, the unknown fraction is 17/100.

So, the correct answer is "seventeen hundredths".

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The cost of a plumber's one-hour visit is $51, determined by the linear equation C = 51d, where C is the cost and d is the duration of the visit in hours.

If a plumber's visit lasts for a certain duration, the cost can be determined using the equation

                           C = 51d

where C is the cost and d is the duration of the visit in hours.

In this case, the duration of the plumber's visit is given as 1 hour. Substituting d = 1 in the equation, we get

                             C = 51(1) = $51

as the cost of the plumber's visit.

Therefore, if the plumber's visit lasts for one hour, it would cost $51 according to the given equation.

This cost may vary if the duration of the visit changes, as it is directly proportional to the duration of the visit.

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2x - 3 would be 92 - 3 = 89 inches, which is the length of the table

The table needs to be 2 times longer than it is wide, so its length is 2 times its width, or 2x.

The table also needs to be 3 inches shorter than it is wide, so its width is x + 3 inches.

The area of the table is 4,608 square inches, so we can set up an equation:

2x(x + 3) = 4,608

Simplifying this equation:

2x²+ 6x = 4,608

Dividing both sides by 2:

x²+ 3x - 2,304 = 0

We can solve for x using the quadratic formula:

x = (-b ±  √(b² - 4ac)) / 2a

In this case, a = 1, b = 3, and c = -2,304. Substituting these values:

x = (-3 ±  √(3² - 4(1)(-2,304))) / 2(1)

Simplifying:

x = (-3 ±  √(9 + 9,216)) / 2

x = (-3 ±  √(9,225)) / 2

x = (-3 ± 95) / 2

x = 46 or x = -49

Since the width of the table cannot be negative, we can ignore the negative solution. Therefore, x needs to be 46 inches to fit the given requirements.

The length of the table is 2x, or 2(46) = 92 inches, and the width is x + 3, or 46 + 3 = 49 inches. The area is 92 * 49 = 4,508 square inches, which matches the given area requirement.

So, 2x - 3 would be 92 - 3 = 89 inches, which is the length of the table.

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The value of the expression 11C7 is 330. This can be calculated using the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of objects and r is the number of objects being selected. So, the correct answer is A).

To calculate the value of the expression 11C7, we need to use the formula for combinations or binomial coefficients, which is

nCr = n! / (r! * (n-r)!)

where n is the total number of items, r is the number of items to be chosen, and ! denotes the factorial operation (the product of all positive integers up to n).

In this case, we have

n = 11 and r = 7

So, we can substitute these values into the formula

11C7 = 11! / (7! * (11-7)!)

= 11! / (7! * 4!)

= (11 * 10 * 9 * 8 * 7 * 6 * 5) / (4 * 3 * 2 * 1)

= 330

Therefore, the value of the expression 11C7 is 330. So, the correct answer is A).

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--The given question is incomplete, the complete question is given

"Pls respond quick | what is the value of the expression? ₁₁C₇

a)330

b)1,663,200

c)5040

d)7920"--

The value of x is 5/3.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

We have equation in fraction are:

[tex]\frac{3x-2}{3x+1} = \frac{1}{2}[/tex]

To solve the value of x

In the above equation, Solve by cross multiplication:

2(3x - 2) = 3x + 1

Open the bracket and multiply by 2 :

6x - 4 = 3x +1

Combine the like terms:

6x - 3x = 1 + 4

Add and subtract the terms:

3x = 5

x = 5/3

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The rent of the apartment during the 10th year of living in the apartment would be $4940.79

To solve the problem, we need to use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

where:

A is the final amount

P is the initial principal

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, the "principal" is the initial rent of $1600 per month, and the "interest rate" is the 12.5% increase per year. We want to find out the rent during the 10th year, so t = 10.

Let's plug in the values and solve for A:

A = 1600 * (1 + 0.125/12)^(12*10)

A = 1600 * (1.01042)^120

A = 1600 * 3.086

A = 4940.79

So the rent during the 10th year would be $4940.79 per month, rounded to the nearest tenth.

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The backpack forms an angle of approximately 15 degrees with the ground.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle.

To find the angle that Luis's backpack forms with the ground, we can use the inverse tangent function.

The height of the backpack when the handle is extended is 3.5 feet, and the distance from the ground to Luis's hand is 3 feet. So the opposite side of the triangle is 3.5 - 3 = 0.5 feet, and the adjacent side is the distance from Luis's hand to the backpack, which we can call x.

Using the tangent function, we have:

tan(theta) = opposite/adjacent

tan(theta) = 0.5/x

To solve for x, we can use the Pythagorean theorem:

x² + 3² = (3.5)²

x² = 3.5² - 3²

x² = 3.25

x = sqrt(3.25)

x ≈ 1.8 feet

Now we can substitute x into our tangent equation and solve for theta:

tan(theta) = 0.5/1.8

theta = arctan(0.5/1.8)

theta ≈ 15 degrees

Therefore, the backpack forms an angle of approximately 15 degrees with the ground.

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Answer:

  C = (-1, -2)

  D = (2, 0)

Step-by-step explanation:

You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).

The diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:

  E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC

  C = 2E -A = 2(0, 2) -(1, 6)

  C = (-1, -2)

and

  D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern

  D = (2, 0)

The surface area of the given regular pyramid is 84 cm^2.

To find the surface area of a regular pyramid, we need to calculate the area of each face and add them together. A regular pyramid has a base that is a regular polygon, and its lateral faces are triangles that meet at a common vertex. We can use the Pythagorean theorem to find the slant height of the pyramid, which is the height of each lateral face.

Let's assume that the base of the regular pyramid is a square with side length 6 cm, and the slant height is 4 cm.

First, we need to find the area of the base of the pyramid:

Area of the base = (side length)^2

                = 6 cm x 6 cm

                = 36 cm^2

Next, we need to find the area of each triangular lateral face. Since the pyramid is a regular pyramid, all the triangular faces are congruent.

We can find the area of each triangular face using the formula:

Area of a triangle = (1/2) x base x height

The base of each triangular face is equal to the side length of the square base, which is 6 cm. The height of each triangular face is equal to the slant height, which is 4 cm.

Area of each triangular face = (1/2) x 6 cm x 4 cm

                            = 12 cm^2

Since the pyramid has 4 triangular faces, we need to multiply the area of one triangular face by 4 to get the total area of all the triangular faces:

Total area of the triangular faces = 4 x 12 cm^2

                                 = 48 cm^2

Finally, we can find the total surface area of the pyramid by adding the area of the base and the area of the triangular faces:

Total surface area = Area of the base + Total area of the triangular faces

                  = 36 cm^2 + 48 cm^2

                  = 84 cm^2

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The partial derivative of z with respect to x is 5xy + 5xz, and the partial derivative of z with respect to y is 5xz + 5yz.

To find the partial derivatives of z with respect to x and y, we use the chain rule. The chain rule allows us to find the rate of change of a function with respect to one of its independent variables while holding all other independent variables constant.

Using the chain rule, we can find the partial derivatives of z with respect to x and y as follows:

∂z/∂x = 5(yz) + 5x(1)(z)

∂z/∂x = 5xy + 5xz

∂z/∂y = 5(xz) + 5y(1)(z)

∂z/∂y = 5xz + 5yz

Therefore, the partial derivative of z with respect to x is 5xy + 5xz, and the partial derivative of z with respect to y is 5xz + 5yz.

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The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases.

what is exponent ?

In mathematics, an exponent (also known as a power or index) is a number that indicates how many times a given number (the base) must be multiplied by itself.

In the given question,

The given exponential model is:

y = 200(0.80)ˣ

where:

y is the output (dependent variable)

x is the input (independent variable)

To determine whether the model represents exponential growth or decay, we need to examine the base of the exponent, which is 0.80 in this case.

If the base is greater than 1, then the model represents exponential growth, and if the base is between 0 and 1, then the model represents exponential decay.

In this case, the base of the exponent is 0.80, which is between 0 and 1. Therefore, the model represents exponential decay.

The growth/decay factor is the base of the exponent, which is 0.80 in this case. The factor is less than 1, indicating that the output (y) decreases as the input (x) increases. The factor represents the rate of decay per unit of the independent variable, which in this case is 0.80.

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OD. M = log(I/10,000)

How can the magnitude of an earthquake be calculated when its intensity is 10,000 times that of the reference earthquake?

The correct equation that calculates the magnitude, M, of an earthquake with an intensity 10,000 times that of the reference earthquake is option B: M = log(10,000/Io).

In the given equation M = log(I/IO), I represents the intensity of the earthquake being measured, and IO represents the intensity of the reference earthquake. Since the intensity of the earthquake in question is 10,000 times that of the reference earthquake, we substitute I with 10,000 times IO.

Therefore, the equation becomes M = log(10,000/Io), which is option B. This equation allows us to calculate the magnitude of the earthquake based on the relative intensity compared to the reference earthquake.

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The area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

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

Radii = 21 cm, 81 ft, 45/2 cm

The area of a circle is calculated as

Area = πr²

substitute the known values in the above equation, so, we have the following representation

Area = 3.14 * 21² = 1384.74

Area = 3.14 * 81² = 20601.54

Area = 3.14 * (45/2)² = 1589.625

Hence, the area of the circles are 1384.74 cm², 20601.54 cm² and 1589.625 cm²

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Answer:

The equation to represent Fernando's job offer is:

y = 15 + x

Where y is the hourly wage and x is the number of months worked.

The equation to represent Amelia's job offer is:

y = 8(1 + 0.1)^x

Where y is the hourly wage and x is the number of months worked.

To determine the time period for which Fernando's offer is better, we need to find the point where his hourly wage is greater than Amelia's. We can set the two equations equal to each other and solve for x:

15 + x = 8(1 + 0.1)^x

15 + x = 8(1.1)^x

x ≈ 20.44

Therefore, Fernando's offer is better for any time period greater than 20.44 months.

To determine the time period for which Amelia's offer is better, we need to find the point where her hourly wage is greater than Fernando's. We can set the two equations equal to each other and solve for x:

8(1 + 0.1)^x = 15 + x

8(1.1)^x = 15 + x

x ≈ 14.45

Therefore, Amelia's offer is better for any time period less than 14.45 months.

For the long run, we need to determine which offer has a higher hourly wage after a certain number of months. We can compare the two equations by finding their limits as x approaches infinity:

lim (y = 15 + x) as x → ∞ = ∞

lim (y = 8(1 + 0.1)^x) as x → ∞ = ∞

Therefore, both offers have the same long-term hourly wage of infinity. However, Fernando's offer has a faster rate of increase, so it may be more beneficial in the long run.

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To solve this equation, we first simplify both sides of the equation by using the distributive property to expand the right-hand side:

4x + 5 = 6(x + 3) - 20 - 2x

4x + 5 = 6x + 18 - 20 - 2x

Next, we can combine like terms on the right-hand side:

4x + 5 = 4x - 2

Now, we can subtract 4x from both sides to isolate the variable on one side of the equation:

4x - 4x + 5 = 4x - 4x - 2

5 = -2

This is a contradiction since 5 cannot be equal to -2. Therefore, there is no solution to this equation.

In other words, the equation is inconsistent and there is no value of x that can make it true.

The number of different menu combinations Mr. Carlos' family can choose is 60.

To find the total menu combinations, you need to use the multiplication principle. Since there are 3 choices of appetizers, 5 choices of entrees, and 4 choices of cake, you simply multiply these numbers together. Here's the step-by-step explanation:

1. Multiply the number of appetizer choices (3) by the number of entree choices (5): 3 x 5 = 15
2. Multiply the result (15) by the number of cake choices (4): 15 x 4 = 60

So, there are 60 different menu combinations possible for Mr. Carlos' family to choose for their reception.

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The cost of a small cup of coffee is $2.97, and the cost of a piece of banana bread is $5.13.

Let x represent the cost of a small coffee and y represent the cost of a piece of banana bread. We know:

Cost of muffin: $3.51

y = x + $2.16

5(x + $3.51) + 2(x + y) = $48.60

Substitute y with x + $2.16:

5(x + $3.51) + 2(x + (x + $2.16)) = $48.60

Solve for x:

9x + $21.87 = $48.60

9x = $26.73

x = $2.97

Find y:

y = x + $2.16

y = $2.97 + $2.16

y = $5.13

A slice of banana bread costs $5.13, while a small coffee costs $2.97.

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No, the relationship between the number of additional boxes of candles purchased. C = 14.00 + 10.00b. The person would spend $34.00 on 3 boxes of candles.

a. No, the relationship between the number of additional boxes of candles purchased and the total money spent is not linear. This is because the cost of the first box is $14.00 and the cost of each additional box is $10.00.

A linear relationship implies that the change in the dependent variable (total money spent) is proportional to the change in the independent variable (number of additional boxes purchased), but in this case, the cost does not change at a constant rate.

b. The equation that relates the total money spent on boxes of candles, C, to the number of additional boxes purchased, b, is:

C = 14.00 + 10.00b

This equation takes into account the cost of the first box, which is $14.00, and the cost of each additional box, which is $10.00.

c. If someone buys 3 boxes of candles, they are purchasing 2 additional boxes (since the first box is already included in the $14.00). Using the equation from part (b), the total money spent by a person who bought 3 boxes of candles for the fundraiser would be:

C = 14.00 + 10.00(2) = $34.00

Therefore, the person would spend $34.00 on 3 boxes of candles.

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The function represents exponential decay with a percentage rate of decrease of 9.8%.

The given exponential function y = 660(0.902) represents decay because the base of the exponent is less than one.

This means that the output value of the function will decrease as the input value increases.

To determine the percentage rate of decrease, we need to find the value of the base of the exponent subtracted from one and then multiply it by 100.

The base of the exponent is 0.902, so we subtract it from one to get 0.098.

Multiplying by 100 gives us a percentage rate of decrease of 9.8%.

This means that for every unit increase in the input value, the output value of the function will decrease by approximately 9.8%.

For example, if the input value increases from 1 to 2, the output value will decrease by 9.8%, and if the input value increases from 2 to 3, the output value will again decrease by 9.8%.

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The area under the curve at the given points is 3.758 sq.units.

The area under the curve at the given points is calculated as follows;

y = -3/x ; (-7, -2)

To find the area under the curve y = -3/x between x = -7 and x = -2, we need to integrate the function from x = -7 to x = -2.

∫[-7,-2] (-3/x) dx

= [-3 ln|x|]_(-7)^(-2)

= [-3 ln|-2| - (-3 ln|-7|)]

= [-3 ln(2) + 3 ln(7)]

= 3 ln(7/2)

= 3.758 sq.units

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p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:

x + 5 + 2 / (x + 2)

To express the given expression x^2 + 7x + 12 / (x + 2) in the form p(x) + k / (x + 2), we will perform polynomial division.

1. Divide the numerator (x^2 + 7x + 12) by the denominator (x + 2):

(x^2 + 7x + 12) ÷ (x + 2)

2. Perform long division:

       x + 5
       ________________
x + 2 | x^2 + 7x + 12
       - (x^2 + 2x)
       ________________
             5x + 12
             - (5x + 10)
       ________________
                 2

3. Write the result:

p(x) + k / (x + 2) = x + 5 + 2 / (x + 2)

So, p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:

x + 5 + 2 / (x + 2)

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Part a: f(x) = (x-3)^2 + 5

Part b: f(x) = (x+10)^2 + 5

Part a: To shift the function f(x) = x^2 + 5 right 3 units, we need to subtract 3 from the x-coordinate of the vertex. The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h,k) is the vertex. Thus, the function in vertex form that shifts f(x) right 3 units is:

f(x) = (x-3)^2 + 5

Part b: To shift the function f(x) = x^2 + 5 left 10 units, we need to add 10 to the x-coordinate of the vertex. Using the same vertex form as before, the function in vertex form that shifts f(x) left 10 units is:

f(x) = (x+10)^2 + 5

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The total number of students who were surveyed is 575

The graph likely displays a horizontal axis and a vertical axis.

In this graph, the horizontal axis may indicate two categories, such as "juniors" and "seniors," and the vertical axis shows the number of students in each category who responded "yes," "no," or "not sure."

To find the total number of students surveyed, we need to look for the bar that represents the entire group of juniors and seniors. Typically, this bar will be labeled as "total," "all," or something similar. Once we locate this bar, we can add up the number of students represented by the bar. The value will be displayed on the vertical axis, and it should correspond to the sum of the bars for juniors and seniors separately.

=> 100 + 200 + 125 + 150 = 575

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The second wedge has a greater volume by 4.125 cubic inches. Therefore, the correct option is 4.

To determine which cheese wedge has a greater volume, you need to calculate the volume of each triangular prism using the given dimensions.

For the first wedge:

1. Calculate the area of the base (isosceles triangle):

(base x height) / 2 = (2.5 in x 4.5 in) / 2 = 5.625 square inches

2. Calculate the volume of the prism:

base area x thickness = 5.625 sq in x 3 in = 16.875 cubic inches

For the second wedge:

1. Calculate the area of the base (isosceles triangle):

(base x height) / 2 = (3 in x 4 in) / 2 = 6 square inches

2. Calculate the volume of the prism:

base area x thickness = 6 sq in x 3.5 in = 21 cubic inches

To find which wedge has a greater volume and by how much, subtract the smaller volume from the larger volume:

21 cu in - 16.875 cu in = 4.125 cu in.

Therefore, the correct answer is option 4: The second wedge has a greater volume by 4.125 cubic inches.

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U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:

Find the slopes of sides UQ, QA, and UA:

Determine which segments are perpendicular and how we know they are perpendicular:

To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.

Find the lengths of each side:

Use the Pythagorean Theorem to show that it is a right triangle:

Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.

Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.

U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

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