The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 2007 and 277 million megawatt hours in 2012. Write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007.

Answer:22

Step-by-step explanation:22

The expressions based on the information given are illustrated below

3/4 ÷ 1/2 = 1.5 = quotient is grater than 1

1/2 ÷ 3/4 = 2/3 = quotient is less than 1

2/9 ÷ 1/27 = 6 = quotient is grater than 1

5/3 ÷ 20/6 = 1/2 = quotient is less than 1

4/3 ÷ 3/5 = 20/9 = quotient is grater than 1

19/8 ÷ 2 3/8 = 1 = quotient is equal to 1.

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If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026

Total orders both accurate and not accurate = 1131

Total orders from restaurant B (both accurate and not accurate) = 337

Probability of first order from B = 337/1131

Probability of second order from B = 336/1130

Probability of third order from B = 335/1129

Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129

Probability of the first three orders from B = 0.026

Complete question is;

Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A

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The points are (7, 13/3).

Lets simplify the equation,

The equation of first line: y = 1/3 x + 2

the equation of second line: y= 4/3x - 5

Solve the system of equations by elimination,

Multiply equation A by -4 both sides

-4y = -4(1/3x +2)

-4y = -4/3x-8

After eliminating the equation we get,

y = 13/3

So now have to find x

13/3 = 1/3x + 2

Lets multiply above by 3
x = 13-6

x = 7.

Hence the points are (7, 13/3)

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Answer:

B

Step-by-step explanation:

What is the solution to the system of equations?

(7, 4)

(7, StartFraction 13 over 3 EndFraction)

(8, StartFraction 14 over 3 EndFraction)

(9, 7)

Answer:

C. (32/4)*2

Step-by-step explanation:

C is the correct answer because when we divide 4/2 it equals 2.

Hope this helps!

Answer:

D

Step-by-step explanation:

Given expression:

[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]

Evaluation of the given expression:

[tex] = 8 \times 2 \times 2 [/tex]

[tex] = 32 [/tex]

A.     [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]

B.     [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]

C.     [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]

D.     [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]

Only expression D evaluates to the same value as the given expression.

Answer: D

Answer: -1/2

Step-by-step explanation:

The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.

We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.

Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.

[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]

Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]

The volume of the composite solid shown in the diagram is: 80 ft.³.

Volume of the composite solid = volume of triangular prism + volume of triangular pyramid.

Volume = 0.5 × base of triangle × height of triangle × length of prism + 1/3 × Base area × Height = 0.5 × 8 × 5 × 3 + 1/3 × 0.5 × 8 × 5 × 3

Volume = 60 + 20

Volume of the composite solid = 80 ft.³.

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Answer:

S₁₂ = - 654

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9

this indicates the series is arithmetic with sum to n terms

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 5 and d = - 9 , then

S₁₂ = [tex]\frac{12}{2}[/tex] [ (2 × - 5) + (11 × - 9) ]

     = 6(- 10 - 99 )

    = 6 × - 109

    = - 654

The altitudes of equal length, BE and CF gives AB = AC, from which we have;

From the given description, we have;

BE = CF

<CFB = <BEC = 90° All right angles are congruent

BC = BC by reflexive property of congruency

BC = The hypotenuse side of triangles ∆BFC and ∆CEB

Therefore;

∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.

Therefore;

BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC

Similarly, we have;

∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency

Which gives;

FA = AE by CPCTC

BF + FA = CE + AE, by substitution property of equality

BF + FA = AB

CE + AE = AC

Therefore;

Therefore;

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Solving a linear equation, we conclude that Margo's paycheck is of 96 dollars.

We know that she spends one quarter on a dress, one eight on shoes, and $24 on a birthday present.

We also know that she spent a total of $60.

If we define P as Margo's paycheck, then we know that:

(1/4)*P + (1/8)*P + $24 = $60

Now we just need to solve that linear equation for P, we will get:

(2/8)*P + (1/8)*P = $60 - $24 = $36

(3/8)*P = $36

P = (8/3)*$36 = $96

In this way, we conclude that Margo's paycheck is of 96 dollars.

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Answer:

[tex] {3}^{x} [/tex]

Step-by-step explanation:

[tex] {x}^{3} = 8[/tex]

[tex] {3}^{x} = 9[/tex]

The median will change; the mode will stay the same.

The median is the number that is at the center of a data set when the data are arranged either in ascending or descending order.

Median = 23

When 68 and 75 are added, the median would change.

Mode refers to a value that appears most frequently in a data set.

The mode = 75

So, when 75 is added, the mode does not change.

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The only set that only has rational numbers is the first one:

{1/3, -3.45, √9}

A rational number is a number that can be written as the quotient of two integers.

If we look at the first set, the elements are:

In the other sets we can see elements like:

√37, √44, or √2 which are all irrational numbers, then the only correct option is the first one.

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By using the triple integral, the wedge's volume is 4/15.

A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.

The wedge's volume, which the parabolic cylinder encloses, must be determined.

Consequently, as a result of the z=y form,

In addition to the specified boundary, the plane y=0 x = 0, z = 0.

For all of this, we are therefore in the first octant. additionally, the plane

x + y = 1 is a constraint.

Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.

The following would be written as a triple integral:

∫x=0 ∫y=0

∫z=0 dy dz dx

Once the values have been entered and the problem has been solved, we obtain the

[−4/15(1−x)^5/2] at x=0

The answer will then change to 4/15.

As a result, using the triple integral, the wedge's volume comes out to 4/15.

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Answer:

306 square meters

Step-by-step explanation:

The maximum area is when the length and width are the closest together.

70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle

35/2=17.5, find the 2 closest integers, they are 17 and 18

17*18=306

Answer:

A.

Step-by-step explanation:

i'm 99% sure!

Answer:

B

Step-by-step explanation:

Plug in the coordinates.

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of big sector = (60/360) * π(10)² = (50π /3) cm²

Area of small sector = (60/360) * π(x)² = (x²π /6) cm²

Unshaded area = (x²π /6) cm²

Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6

Shaded area = unshaded area

(100π - x²π) /6 = (x²π /6) cm²

x = 7.07

The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.

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The length of x in the sector is 7.08 cm.

area of a sector = ∅ / 360 × πr²

where

Therefore,

area of a sector = 60 / 360 × π × 10²

area of a sector = 60 / 360 × π × 100

area of a sector = 6000 / 360 π

Hence,

area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 =  26.1666666667 = 26.2 cm

Hence,

26.2 = 60 / 360 × 3.14 × x²

x² = 26.2 / 0.52333333333

x = √50.0637261552

x = 7.07557064836

x = 7.08 cm

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Answer: C

Step-by-step explanation:

There is a vertical asymptote at x=3, so the denominator should have a factor of (x-3).

This eliminates everything except for C.

Answer:

315

Step-by-step explanation:

-3ac7

-3x-3=9x5=45x7=315

❄ Hi there,

evaluate this expression by using substitution:

If

then

[tex]\sf{-3(-3)(5)}[/tex]

[tex]\sf{9\times5}[/tex]

[tex]\triangleright \ \sf{45}[/tex]

That's it!

❄

Step-by-step explanation:

we first divide fourteen by four

14/4= 3.5

then we change 0.5 to hours by multiplying by 60

0.5 * 60 = 30

so in conclusion it would take 3hrs 30mins to finish each activity

Based on the graph of the cupcakes done, we find that w(2) = 5.

Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.

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Answer:

72°

Step-by-step explanation:

3x = 4x - 24 (alternate exterior angles theorem)

x = 24

So, angle RST measures 72°.

Answer:

200 yd²

Step-by-step explanation:

A = 17 yd

B  = 15 yd

C = 2 yd

D = 8 yd

b) Area of rectangle = length * width

 [tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]

Area of right triangular prism = Areas of two triangle +  area of the upper rectangle + area of middle rectangle + area of below rectangle

          = 8 * 15 +  17 * 2 + 15 *2 + 8*2

          = 120 + 34 + 30 + 16

          = 200 yd²

Answer: $37.50

Step-by-step explanation:

Answer:

I and II only

The formula for the volume of a cube is-side length^3.

For your problem, side length=4, so the answer is 4^3=64

ANSWER: 64 CUBIC CENTIMETERS hope this helped you

(T-Tb)

The general equation of a circle is written like [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h,k) is the centre and r is the radius.

Firstly, we're given that the centre is (8,6).

Plug this into the general equation:

[tex](x-h)^2+(y-k)^2=r^2\\(x-8)^2+(y-6)^2=r^2[/tex]

We're given this other point on the circumference of the circle, (8,0), which is 6 units away from the center.

Therefore, the radius is 6 units. Plug this into the general equation too:

[tex](x-8)^2+(y-6)^2=r^2\\(x-8)^2+(y-6)^2=6^2\\(x-8)^2+(y-6)^2=36[/tex]

[tex](x-8)^2+(y-6)^2=36[/tex]

The volume of the composite figure is of 425 m³.

The volume of a prism is given by the base area multiplied by the height.

In this problem:

Hence the volume in m³ is:

V = 5² x 13 + 5² x 4 = 25 x 17 = 425 m³.

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r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.

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Answer:

D

Step-by-step explanation: