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Answer:

  442 ft²

Step-by-step explanation:

The amount of insulation needed is the amount that covers the area of the side walls and the ceiling. The area of the side walls is the product of the perimeter and height. The area of the ceiling is the product of length and width.

__

Lateral area = Ph = 2(L+W)h = 2(15 ft +8 ft)(7 ft) = 322 ft²

Ceiling area = LW = (15 ft)(8 ft) = 120 ft²

__

Insulation needed = lateral area + ceiling area = 322 ft² +120 ft²

Insulation needed = 442 ft²

Using the Pythagorean Theorem, it is found that Barrie is 12 miles from Luke's house, in a straight line.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

This problem can be modeled by a right triangle, with [tex]l_1 = 16, l_2 = d, h = 20[/tex], hence:

[tex]h^2 = l_1^2 + l_2^2[/tex]

[tex]16^2 + d^2 = 20^2[/tex]

[tex]d^2 = 144[/tex]

[tex]d = 12[/tex]

Barrie is 12 miles from Luke's house, in a straight line.

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The rate of interest required to achieve the conditions set forth is 7.1773%.

The interest rate is the rate at which the investment increases. The formula that can be used to determine interest rate is:

g = (FV / PV)^(1/N) - 1

Where:

4^(1/20) - 1 = 7.1773%

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Answer: 55.20$

Step-by-step explanation:

1. Add up 35% with the 15% since Mario is paying for it

2. Multiply 120(the cost without any discount/tax) with the new discount percentage

3. Now with the answer from multiplying subtract it from 120.

4. With the answer, multiply the tax percentage(0.08)

5. Now add It to the discounted price.

6. Round it to the nearest hundredth

Answer: Length = 9 in

Width = 12 in

Step-by-step explanation:

Length L = 3 + W

Perimeter P = 42 in

Perimeter = 2L + 2W

plugin values:

42 = 2(3 + W) + 2W

42 = 6 + 2W + 2W

42-6 = 4W

W = 36 / 4

W = 9  

solve L by substituting the value of W=9 into the equation:

L = 3 + W

L = 3 + 9

L = 12

therefore, the dimensions of the rectangle:

               Length = 9 in

               Width = 12 in

Answer:

Answer:

length = 9 in

width = 12 in

Step-by-step explanation:

You have to use the formula for the perimeter of a rectangle

P=2(l+w)

The semi-annual net cash flow that the company must achieve in order for the purchase to be made is $5041.

Maximum amount that can be invested = $32348.

Less: Present value of salvage value = $5927

Present value of cash inflow = $32348 - $5927 = $26421.

Net cash flow will be:

= $26421 / PV factor

= $26421/5.242

= $5041

In conclusion, the correct option is $5041.

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Answer:

9.852

Step-by-step explanation:

First, Graph all three functions and find where they intersect and the shape that they make through their intersection. Note that since the shape does not touch the y= -1 line, we will use the "washer" method (where the volume equals  [tex]\pi\int\limits^a_b {R(x)\x^{2} - r(x)^{2} } \, dx[/tex].

The next step is to find a and b. Since the function that the area is going to be rotated about is a " y =" equations, the boundaries will be the x coordinates where the three functions intersect, b=1 for (1,1) and a=3 for (3,1).

Next we have to find R(x) and r(x). In this case, R(x) is the difference between the function furthest away from the axis of rotation and the function of the axis of rotation (or visa versa depending on which is on top), and r(x) is the difference between the function closest to the axis of rotation and the function of the axis of rotation (or visa versa depending on which is on top.

For this problem R(x) = 1 - (-1) and r(x) = 1/x - (-1) since when you look at the graph, Y = 1  is further from y = -1 than y = 1/x is, and both functions are on top of y = -1.

Finally plug in R(x) and r(x) and solve either using a calculator or through integration. If you solve through integration you should get [tex]\pi (-2ln(3) + \frac{16}{3} )[/tex].

The height of the right circular cylinder with volume of 500π cubic centimetre and radius of 5 centimetre is 20 cm.

volume = πr²h

where

Therefore,

volume = 500π cm³

r = 5 cm

Therefore,

volume of the cylinder = πr²h

500π = 5²πh

500π = 25πh

divide both sides by 25π

500π / 25π = 25πh / 25π

h = 20 cm

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Answer:

A) 20 cm

Step-by-step explanation:

Answer:

12 pieces of cake

Step-by-step explanation:

4 pieces for each cake

there is a total of three cakes

needed to find total pieces of cakes

multiply 4 by 3 and you will get 12 pieces of cake.

Answer:

Miko has 12 pieces of cake

Answer: 19 and 14

Step-by-step explanation:

19-14 = 5

19x14 =266

Answer:

-1/2

Step-by-step explanation:

2/5 * - 3/7 - 1/14 - 3/7 * 3/5

= - 6/35 - 1/14 - 9/35

= - (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)

= - 12/70 - 5/70 - 18/70

= (-12 - 5 - 18)/70

=- 35/70

= - 1/2

Answer:

none of the above

Step-by-step explanation:

Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.

x + (x + 2) + (x + 4) = 72

3x + 6 = 72

3x = 66

x = 22.

This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.

The answer is 13728.

Answer:

5.60 pounds each

Step-by-step explanation:

This is the dry mixture problem.

Let x = the number of pounds of the first type of candy

Therefore, number of pounds of second type of candy = 10-x

Value of first candy + value of second candy = value of mixture

Value of any candy = cost per pound of candy * weight of candy

Thus:

4x + 6(10 - x) = 5.60(10)

4x + 60 - 6x = 56

-2x + 60 = 56

-2x = -4

x = -4/-2

x = 2

Therefore, the number of pounds of first type of candy = 2 pounds

The number of pounds of second type of candy = 10 - 2 = 8 pounds

Check

$4(2) + $6(8) =

           8 + 48 = $5.60(10)

               $56 = $56

Answer:

624

Step-by-step

480+(480(30%))

=624

Answer:

162

30/100 * 480

3/10 * 480

3/1 * 48

3 * 48

162

Answer:

33.15

Step-by-step explanation:

65% is 0.65

102/2=51

0.65*51=33.15 which is the answer

Answer:

option b

Step-by-step explanation:

It is option b

Your answer is 4(x+1)²

Answer:

B

Step-by-step explanation:

Given functions:

[tex](f \circ g)(x) & =f[g(x)][/tex]

This means substitute the x of f(x) with the function g(x).

[tex]\implies f[g(x)]=4(x+1)^2[/tex]

Answer:

Step-by-step explanation:

Answer:

78 is the number

Step-by-step explanation:

(65*6)÷5 = 78.

5/6 of a number is 65.

And the number is 78.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

A phrase: 5/6 of a number is 65.

To find the number:

Let the number be n.

Applying multiplication operation,

5/6 of n is 65.

(5/6)n = 65.

Applying cross multiplication,

n = 65 x 6/5

n = 390/5

n = 78.

Therefore, the number is 78.

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Answer:

x = 15

Step-by-step explanation:

the easiest way to do this is 5 times 3 and with that we get 15 :)

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Answer:

Step-by-step explanation:

answer: x = 15

explanation in picture

Answer:

6.856

Step-by-step explanation:

8² + x² = 17

8² - 17 = -x²

64 - 17 = -x²

-47 = -x²

x² = 47

x = 6.856

Answer:

[tex]\sf (x+2)^2+(y-2)^2=2[/tex]

Step-by-step explanation:

If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.

[tex]\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)[/tex]

             [tex]\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)[/tex]

             [tex]\sf =(-2, 2)[/tex]

Equation of a circle:   [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]

(where (h, k) is the center and r is the radius)

Substituting found center (-2, 2) into the equation of a circle:

[tex]\sf \implies (x-(-2))^2+(y-2)^2=r^2[/tex]

[tex]\sf \implies (x+2)^2+(y-2)^2=r^2[/tex]

To find [tex]\sf r^2[/tex], simply substitute one of the points into the equation and solve:

[tex]\sf \implies (-3+2)^2+(1-2)^2=r^2[/tex]

[tex]\sf \implies 1+1=r^2[/tex]

[tex]\sf \implies r^2=2[/tex]

Therefore, the equation of the circle is:

[tex]\sf (x+2)^2+(y-2)^2=2[/tex]

Answer:

V = V0 e^-k t     where V is the value of the car and t the time in years

ln (V/V0) = - k t

k = -1/4 ln (96/280) = .268

V = V0 e^-k t = 28000 e^-.268 * 6 = 28000 e^-1.606 = $5621

Answer:

1,600

Step-by-step explanation:

I did a bit of guessing becuase I don't know the exact way to reverse the formula, but here is what I did!

I guessed around 1,550 at first, but it was too low. I kept increasing the base number until I reached 1,600, and came to the conclusion by doing the equation;

1,600(0.6)=960

Then, since it increases each month by 60% of the previous month's value, you do

1,600+960=2,560

Answer:

hello

15 x 0.4 = 6

6 sunflower

Step-by-step explanation:

Answer:

6 of them have sprouted

Step-by-step explanation:

(15/100)x40

0.15x40

6

The conditions for this type of sampling test regarding the wait times at two branches of a bank include:

It should be noted that sampling simply means a statistical process where a predetermined number of observations are taken from a larger population.

In this case, the samples are both randomly selected and the wait times within each group are approximately symmetric without outliers. When there's a symmetric distribution with no outliers, the mean and standard deviation will be used.

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Answer:

491 red apples

Step-by-step explanation:

1/6 are apples

then 5/6 are oranges

red apples = green apples + 291

there are 3455 oranges

total amount of fruits is :

3455 / (5/6) = (3455 x 6)/5 = 4146

4146 - 3455 = 691 apples ( total )

so red + green = 691

and red - green = 291

add the two equations

red + red + green - green = 691 + 291

2red = 982

red = 982 / 2 = 491 red apples

green = 691 - 491 = 200 green apples

so red is 291 more than green

then red = 491

Answer:

You can solve this by setting up an exponential growth equation.

Now we solve for b

Now that we have found b, we can use the equation  to predict how many bacteria will be present after 10 hours.

t = 10

Answer = 4732

Step-by-step explanation:

Answer:

12 meters

Step-by-step explanation:

You have to use the inverse of the pythagorean theorem to do this so you do square root of (20x20-16x16) which is 12

The geometric series with 4th term as 10 and 7th term as 80 has the sum of the first tenth terms as 1278.75.

aₙ = arⁿ⁻¹

where

Therefore,

10 = ar³

80 = ar⁶

Hence,

a = 10 / r³

80 = (10 / r₃) r⁶

80 = 10r³

r³ = 80 / 10

r = ∛8

r = 2

a = 10 / 2³

a = 10 / 8 = 5 / 4

The sum of 10 terms can be calculated as follows:

Sₙ = a(rⁿ - 1) / r - 1

Sₙ = 5 / 4 (2¹⁰ - 1) / 2 - 1

Sₙ = 5 / 4 (1024 - 1) / 1

Sₙ = 1.25(1023)

Sₙ = 1278.75

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Answer:

  a) 96 = 3.57√h

  b) h ≈ 723.11 m

Step-by-step explanation:

The equation you want to solve is the model with the given values filled in.

  D(h) = 3.57√h . . . . model

  96 = 3.57√h . . . . . equation for seeing 96 km to the horizon

__

We solve this equation by dividing by the coefficient of the root, then squaring both sides.

  96/3.57 = √h

  h ≈ 26.891² ≈ 723.11 . . . . meters above sea level

Dustin would need to have an elevation of 723.11 meters above sea level to see 96 km to the horizon.