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A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.

A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?


Enter your answer, to the nearest tenth, in the box.

Based on the amounts that Geraldo Saldana deposited in the month of May, the total simple interest comes to $18.98.

the simple interest earned can be found as:

= (3,600 x 3.5%/360 days x 30 days) + (3,000 x 3.5%/360 days x 20 days) x (5,000 x 3.5%/360 days x 6 days)

= 10.5 + 5.83 + 2.65

= $18.98

rest of the question is:

How much simple interest did his money earn?

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Answer:

[tex]a=\sqrt{40.768}[/tex]

Step-by-step explanation:

Given a leg and a hypotenuse we can find the third side by substituting the known values using Pythagorean theorem, let the unknown be a.

[tex]a^2+3.24^2=7.16^2[/tex]

Now all we must do is solve for a:

[tex]a^2+3.24^2=7.16^2\\a^2+10.4976=51.2656\\a^2=40.768\\a=\sqrt{40.768}[/tex]

Answer [tex]=7085760[/tex]

Step-by-step explanation:

Use order of operations and evaluate the exponent first

[tex]30*4*3^{10}[/tex]

[tex]30*4(59049)[/tex]

[tex]30*236192[/tex]

[tex]=7085760[/tex]

Answer: 1920

Step-by-step explanation:

4x4x4=64

64x30=1920

Based on the information provided in the first table, we have the following angle and trigonometric function:

Based on the information provided in the first table, we have the following trigonometric function:

tanθ = √3

θ = tan⁻¹(√3)

θ = 60°.

In radians, we have:

θ = 60 × π/180

θ = 1.0472 radian.

sin60 = √3/2

cos60 = 1/2

csc60 = 2/√3

sec60 = 2

cot60 = 1/√3

Based on the information provided in the second table, we have the following trigonometric function:

θ = 30 × π/180

θ = 0.5236 radian.

sin30 = 1/2

cos30 = √3/2

tan30 = 1/√3

csc30 = 2

sec30 = 2/√3

cot30 = √3

Based on the information provided in the third table, we have the following trigonometric functions:

sinθ = √2/2                                   tanθ = 1

θ = sin⁻¹(√2/2)                               θ = tan⁻¹(1)

θ = 45°.                                          θ = 45°.

In radians, we have:

θ = 45 × π/180

θ = 0.7854 radian.

cos45 = √2/2

csc45 = √2

sec45 = √2

cot45 = 1

Based on the information provided in the fourth table, we have the following trigonometric function:

sinθ = 1                                

θ = sin⁻¹(1)                      

θ = 90°.

θ = 90 × π/180

θ = 1.5708 radian.

cos90 = 0

tan90 = not defined

csc90 = 1

sec90 = not defined

cot90 = 0

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Answer: [tex]x=11, y=9[/tex]

Step-by-step explanation:

Corresponding sides of similar figures are proportional, so:

[tex]\frac{x-2}{6}=\frac{15}{10}\\\\\frac{x-2}{6}=\frac{3}{2}\\\\x-2=9\\\\x=11[/tex]

[tex]\frac{y+3}{8}=\frac{15}{10}\\\\\frac{y+3}{8}=\frac{3}{2}\\\\y+3=12\\\\y=9[/tex]

Answer:

M = 4.5

N = 2.1

Step-by-step explanation:

angle p would be 25.  180 - 155 = 25

M = 5cos25 =4.5 rounded to the tenths place.

M = 5sin25 = 2.1 rounded.

Answer:

y = (1/3)x + 7

Step-by-step explanation:

The general structure form of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The slope of a perpendicular line is the opposite-signed, reciprocal of the original line's slope. Therefore, if the slope of the original line is m = -3, the new slope is m = 1/3.

The y-intercept can be found by plugging the new slope and the values from the point (-3, 6) into the slope-intercept form equation.

m = 1/3

x = -3

y = 6

y = mx + b                                  <----- Slope-intercept form

6 = (-3)(1/3) + b                           <----- Insert values

6 = -1 + b                                    <----- Multiply -3 and 1/3

7 = b                                           <----- Add 1 to both sides

Now, that you have the slope and y-intercept, you can construct the equation of the perpendicular line.

y = (1/3)x + 7

Answer:

58%

Step-by-step explanation:

47/81 x 100%

≈ 58%

Hope it helps : )

The function given can be classified as a function. That is option C.

Function can be defined as the expression that has both an x domain value and a y range value and it's being classified based on the quality of these values.

A function can be represented based on their roster forms.

Using the function equation given, f(X) = 10.2^2

Here, the first element is the domain or the x value and the second element is the range or the f(x) value of the function.

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Answer:

(2, -1).

Step-by-step explanation:

y = 1/4x^2 - x - 1

First convert to vertex form:

y = 1/4(x^2 - 4x) - 1

y = 1/4[(x - 2)^2 - 4] - 1

y =  1/4(x - 2)^2 - 2

The formula for the focus of the parabola y = a(x - h)^2 + k is (h, k+1/4a)

So here it is:

(2, -2+1/ 4*1/4)

=  (2, -1).

For a population where the distribution is unknown, the sampling distribution of the sample mean will be b which is approximately normal for all sample sizes.

Given options regarding sample sizes.

We have to choose the correct option which shows the sample mean characteristics when the distribution is unknown.

Based on the central limit theorem the sampling distribution of the sample mean for either skewed variable ir normally distributed variable can be approximated given the mean and standard deviation.

The central limit theorem is said to be  true when n greater than or equal to 30.

When n is greater than 30 ,z test is used, when n is less than 30 ,t test is used.

Hence for a population where the distribution is unknown ,the sampling distribution of the sample mean will be approximately normal for all sample sizes.

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Question is incomplete as it includes options in a right way:

1)exactly normal for large sample,

2) approximately normal for all sample sizes,

3) exactly normal for all sample sizes.

Beta = Correlation x (Variance of Z)^0.5 / (Variance of Market)^0.5

Beta = 0.18 x (0.3185)^0.5 / (0.0282)^0.5

Beta = 0.604927

CAPM equation:

Expected return = Risk free rate + Beta x (Market return - Risk free rate)

Expected return = 3.2% + 0.604927 x (9.9% - 3.2%)

Expected return = 7.25% is the answer.

Portfolio return refers to the return or loss realized on an investment portfolio that includes multiple types of investments. The portfolio is intended to provide returns based on the defined objectives of the investment strategy and the risk tolerance of the type of investor covered by the portfolio.

The basic formula for expected return is to multiply the weight of each asset in the portfolio by the expected return and then add up all these numbers. In other words, the expected return of a portfolio is a weighted average of the returns of the individual components.

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The correct labels are matched to their appropriate locations on the graph as shown in the image attached below.

A graph refers to a type of chart that's used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.

In this exercise, you're required to drag the correct labels to their appropriate locations on the graph as shown in the image attached below.

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Part A:

According to a life cycle analysis of the U.S. food system conducted by the University of Michigan, the U.S. consumes 13.9 quads of mostly fossil fuel energy to produce 1.75 quads of food energy annually. A quad is a unit of energy equal to 1 quadrillion (10¹⁵) British thermal units (BTUs). One quad is equal to the energy of 183 million barrels of petroleum.

There are 20 $5 bills and 10 $2 coins.

He bought a radio for $120. He paid for it with 2 coins and $5 bills.

let

the number of $5 bills = x

the number of $2 coins = y

Therefore,

y = 1 / 2 x

2y + 5x = 120

2(1  /2 x) + 5x = 120

x + 5x = 120

6x = 120

x = 120 / 6

x = 20

y = 1 / 2 × 20

y = 10

Therefore, there are 20 $5 bills and 10 $2 coins.

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For this, multiply 150 × .20 = 30

Therefore, 20% of 150 is 30.

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Answer:

The equation is ×=-3

Step-by-step explanation:

Let x be the number

Difference between a number tines 3 and 6 is 9

3x-6x=9

-3x=9

x=-3

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The volume of the frozen figure is 736 cm³

From the question, we are to determine the volume of the frozen figure

In the given diagram,

The volume of the frozen figure = a³ + 1/2(a²b)

From the given information,

a = 8 cm

b = 7 cm

∴ Volume of the frozen figure = 8³ + 1/2(8² ×7)

Volume of the frozen figure = 512 + 1/2(448)

Volume of the frozen figure = 512 + 224

Volume of the frozen figure = 736 cm³

Hence, the volume of the frozen figure is 736 cm³

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The polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of

f(x) = [tex]2x^{3} - 5 x^{2} + x +2[/tex]

According to the question,

f(x)  [tex]=2x^{3} - 5 x^{2} + x + 2[/tex]

[tex]f(2)= 2(2)^{3} - 5 (2)^{2} + 2 + 2 \\= 2(8) - 5(4) +4\\= 16 - 20 + 4\\= -4 + 4\\= 0.[/tex]

Hence, the polynomial equation [tex]2x^{3} - 5 x^{2} + x + 2 = 0[/tex] given that 2 is zero of f(x)  [tex]=2x^{3} - 5 x^{2} + x + 2[/tex].

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Answer:

Step-by-step explanation:

Discussion

A: incorrect. the minus turns the parabola upside down and you would get a maximum, not a minimum.

B: incorrect. The + 1 moves the parabola upwards not downwards.

C: incorrect. The - 3 turns the parabola upside down. You get a maximum, not a minimum.

D: correct. The parabola moves right (x - 3)^2 which anti intuitive, but it is correct. - 5 moves the parabola down. +8 the plus makes a minimum.

If the graph of the line falls from left to right the slope is negative.

Slope = (y2 - y1)/(x2 - x1)

---> y = -2x + 3

The entrance fee is proportional to the number of visitors at A)museum a.

In arithmetic, two sequences of numbers, often experimental statistics, are proportional or at once proportional if their corresponding factors have a regular ratio, that's called the coefficient of proportionality or proportionality consistent.

The definition of proportional is something that has an incredibly correct dating of length or that is appropriate. An example of something proportional is a woman's tiny toes to her quick stature. An instance of something proportional is the quantity of pay a worker receives for the hours that they installed.

While something is proportional to something else, it does no longer suggest the values are equal, simply that they trade with admiration for each other. The regular of proportionality serves as a multiplier.

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Answer:

Museum C

Step-by-step explanation:

If you divide them all (like 3/4) you get .75

Step-by-step explanation:

find the slope:

[tex]\frac{y2-y1}{x2-x1}=\frac{-4+2}{1+3} =\frac{-2}{4} =-\frac{1}{2}[/tex]

Now our equation looks like:

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

To solve for b, plug in one of the coordinates

[tex]-4=-\frac{1}{2} (1)+b[/tex]

[tex]-4=-\frac{1}{2} +b[/tex]

[tex]b=-3.5[/tex]

Put our equation together to get y = -1/2x-3.5

The length of the missing length in the triangle is 53.6 units

The given triangle is a right triangle.

Right triangles are triangles that have a measure of angle that is 90 degrees.

The missing side is x, and the value of x is calculated using the following sine rule

We have

sin(angle) = opposite/hypotenuse

This gives

sin(66) = 49/x

Divide both sides by sin(66)

1 = 49/x sin(66)

Multiply both sides by x

x = 49/sin(66)

Divide the expression

x = 53.6

Hence, the length of the missing length is 53.6 units

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Answer: 13 feet

Step-by-step explanation:

Answer:

12.37 ft

Step-by-step explanation:

Hypotenuse(c): the ladder

Cathetus: the wall (a=12) and the floor (b=3)

Equation:

[tex]c^{2} =a^{2} +b^{2}[/tex]

[tex]c^{2} =(12)^{2}+ (3)^{2} =144+9[/tex]

[tex]c^{2} =153[/tex]

[tex]c=\sqrt{153}[/tex]

[tex]c=12.37[/tex]

The ladder is 12.37 feet long

Hope this helps

Answer:

Addition form: x = 75 + √3 (675 − P) / 3

or

Subtract form: x = 75 − √3 (675 − P) / 3

Answer:

The field is 1 and 4/10 mile long.

Step-by-step explanation:

If I understand the question:

(1/2) + (9/10) =

(5/10) + (9/10) = (14/10)

(14/10) is 1 and 4/10

The field is 1 and 4/10 mile long.

Answer:22-0.22y

Step-by-step explanation: we have to decrease 22 by y%

we need to calculate what is y% of 22. y% of 22 simply means y% into 22 that is y% x 22

= 0.01(y) x 22

= 0.22y

= 22 - 0.22y

Answer:

[tex]y = -x^{2} +4x-10[/tex]

Step-by-step explanation:

I used a graphing calculator to calculate the points so I'm not sure how to do it without, but I hope this helped!

The weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.

Let

3x + 5y = 62.5

3x + 2y = 52

5y - 2y = 62.5 - 52

3y = 10.5

y = 10.5/3

y = 3.5 lbs

Substitute y = 3.5 into

3x + 2y = 52

3x + 2(3.5) = 52

3x + 7 = 52

3x = 52 - 7

3x = 45

x = 45/3

x = 15 lbs

Therefore, the weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.

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The solution of the system of equation is x = 7 and y = 12.5.

2y + 4x = 18

2y - 3x = 4

2y = 4 + 3x

y = 2 + 3 / 2 x

Hence, let's substitute the value of y in equation(1)

2( 2 + 3 / 2 x) + 4x = 18

4 + 3x + 4x = 18

4 + 7x = 18

7x = 14

x = 14 / 2

x = 7

2y - 3(7) = 4

2y - 21 = 4

2y = 25

y = 25 / 2

y = 12.5

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