Power usage is measured in kilowatt-hours, kWh. After 7 a.m., the power usage on a college campus increases at a rate of 21% per hour. Prior to 7 a.m., 15,040 kWh have been used. The university has a daily goal to keep their power usage less than or equal to 100,000 kWh.

Which of the following inequalities can be used to determine the number of hours, t, after 7 a.m. when the power usage on campus will be less than or equal to 100,000?A.
15,040(0.79)t ≤ 100,000
B.
15,040(1.79)t ≤ 100,000
C.
15,040(1.021)t ≤ 100,000
D.
15,040(1.21)t ≤ 100,000

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

We have given that,

it is possible to form a triangle with the given side lengths.

We have to determine the side of the triangle

[tex]Area \ of \ the \ triangle=\frac{1}{2} \times height\times base[/tex]

No, The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

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Step-by-step explanation:

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Answer:

30°

Step-by-step explanation:

Remember, all the interior angles of a triangle add up to 180 degrees. Therefore, we can find the value of x by subtracting the values of the other angles from 180:

[tex]x = 180-97-53[/tex]

[tex]x=30[/tex]

Answer:

Soln:

x+53+97=180(sum of interior angle of a triangle is 180)

or,x+150=180

or,x=180-150

or,x=30

Hence, the value of x is 30.

Answer:

Common ratio is 6.

Step-by-step explanation:

The geometric sequence is being multiplied by 6 each time because 6x6=36, and 36x6=216.

Answer: Find the common ratio of the geometric sequence 6, 36, 216,...6,36,216,...

a_1=6                                       a_2=36                               a_3=216

a

1

​

=6a

2

​

=36a

3

​

=216

\text{Common Ratio:}

Common Ratio:

r=\frac{a_2}{a_1}

r=

a

1

​

a

2

​

​

r=\frac{36}{6}

r=

6

36

​

r=6

r=6

Answer:

[tex]-9a^3b^2[/tex]

Step-by-step explanation:

Your Welcome!

Answer: C

explanation : It is because the answer supposed to be equivalent to

[tex]\frac{-e}{f}[/tex]  

Instead of this, answer a and b are positive

a is completely positive as it has no negatives at all

b is positive as 2 negative makes up as positive

Answer:

The closest to the output when the input is approximately 12

Step-by-step explanation:

The given (x, y) coordinates are;

The line of best fit is

x, 0, 3, 6, 6, 8, 10, 11

y, -2, 7, 16, 15, 21, 28, 31

The line of best fit can be obtained from the scatter plot of the given data from where a linear pattern is apparent

A linear line of best fit is a trend line that gives an overall cumulative minimum distance of all the points from the line

The method for constructing a line of best fit includes;

1) The least Squares Method

2) The method of linear regression

3) Construction of line of best fit

a) The area method

b) The dividing method

The least squares equation is given as follows;

[tex]\hat y[/tex] = a + b·x

[tex]b = \dfrac{\Sigma (x_i - \overline x) \cdot (y_i - \overline y)}{\Sigma (x_i - \overline x)^2 }[/tex]

From MS Excel, we have;

[tex]{\Sigma (x_i - \overline x) \cdot (y_i - \overline y)}{ }[/tex] = 266.8571

[tex]{\Sigma (x_i - \overline x)^2 }[/tex] = 89.42857

∴ b = 266.8571/89.42857 ≈ 2.984

[tex]a =\overline y- b \cdot \overline x[/tex]

From MS Excel, with the given data, we get;

[tex]\overline y[/tex] = 16.57143

[tex]\overline x[/tex] = 6.285714

Therefore;

a = 16.57143 - 2.984 × 6.285714 = -2.185

Therefore, we get the following regression equation;

[tex]\hat y[/tex] = -2.185 + 2.9·x

Where;

x = The input

[tex]\hat y[/tex] = The output

Therefore, when x = 5, we get;

[tex]\hat y[/tex] = -2.185 + 2.9 × 5 = 12.315

Therefore, the closest to the output when the input is 5, y ≈ 12

Answer: its B

Step-by-step explanation:

Answer: The third option

Step-by-step explanation:

(6) (5) is the area of the quadrilateral, therefore you subtract that value by the area of the semi-circle.

to find the area of a semi circle the formula is: (1/2) π ( [tex]r^{2}[/tex])

The radius is 2.5 because the diameter is 5, and the radius is half the diameter.

Answer:

x=−3 or x=7

Step-by-step explanation:

Step 1: Factor left side of equation.

2(x+3)(x−7)=0

Step 2: Set factors equal to 0.

x+3=0 or x−7=0

x=−3 or x=7

Answer:

(-3,7)

Step-by-step explanation:

Answer:

.........................

Step-by-step explanation:

.................................................

Answer:

99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 18 minutes

Standard Deviation, σ = 3 minutes

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Empirical Formula:

Almost all the data lies within three standard deviation from the mean for a normally distributed data.

About 68% of data lies within one standard deviation from the mean.

About 95% of data lies within two standard deviations of the mean.

About 99.7% of data lies within three standard deviation of the mean.

Thus, 99.7% of the customers have to wait:

`

Thus, 99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

hope this helps

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Answer: 2/3 cups

Step-by-step explanation:

Answer:

24 inches

Step-by-step explanation:

30 divided 5

that equals 6

then times 6 with 4

you get 24 inches

Answer:

x = 3 units

SV = 2 units

Step-by-step explanation:

In[tex] \odot Z[/tex] QR and ST are chords such that:

QR = ST = 4

That is both the chords are equal in measure.

Equal chords are at equal distance from the center of the circle. Therefore,

VZ = UZ

4x - 6 = 6

4x = 6 + 6

4x = 12

x = 12/4

x = 3 units

Since, perpendicular dropped from the center of the circle bisects the chord.

[tex] \therefore SV = \frac{1}{2} ST[/tex]

[tex] \therefore SV = \frac{1}{2} \times 4[/tex]

[tex] \therefore SV = 2\: units[/tex]

Answer:

Step-by-step explanation:

The cylinder on the right, its volume = 9 bi * 10 = 90 bi

The volume of the left cylinder = 9 bi * 10 = 90 bi

They are equal because the radius and length of 2 cylinders are equal

Answer:

x = 5

Step-by-step explanation:

Let

x = the unknown variable

The difference of 11 and 2 times a number "x" is 1

11 - 2x = 1

Find x

11 - 2x = 1

Add 2x to both sides

11 - 2x + 2x = 1 + 2x

11 = 1 + 2x

Subtract 1 from both sides

11 - 1 = 1 + 2x - 1

10 = 2x

Divide both sides by 2

10 / 2 = 2x / 2

5 = x

x = 5

Answer:

answer is A

Step-by-step explanation:

as /_ 1 + /_ 2 =180 degree

and /_6 +/_5 = 180 degree

so they are equal

Answer:

1) ten subtracted from the product of a number and -3 is 29

2) the difference between a number and nine , divided by 4 , is -7

Answer:

Si la pendiente ([tex]m[/tex]) disminuye 3 unidades, entonces tenemos que [tex]y = -4[/tex].

Step-by-step explanation:

Sea la función lineal [tex]d(x) = 3\cdot x - 4[/tex], una función está definida por la siguiente expresión matemática:

[tex]y = m\cdot x + b[/tex] (1)

Donde:

[tex]x[/tex] - Variable independiente.

[tex]y[/tex] - Variable dependiente.

[tex]m[/tex] - Pendiente.

[tex]b[/tex] - Intercepto.

Por comparación directa, tenemos que [tex]y = d(x)[/tex], [tex]m = 3[/tex] y [tex]b = -4[/tex]. Si [tex]m[/tex] disminuye en 3 unidades, entonces tenemos la siguiente ecuación lineal:

[tex]y = -4[/tex]

Answer:

w = 18

Step-by-step explanation:

Given

[tex]\frac{1}{3}[/tex] (w + 18) = 12 ← distribute parenthesis on left side

[tex]\frac{1}{3}[/tex] w + 6 = 12 ( subtract 6 from both sides )

[tex]\frac{1}{3}[/tex] w = 6 ( multiply both sides by 3 to clear the fraction )

w = 18

Answer:

she can buy 4 pizzas and five drinks with 2.50 to spare or 4 pizzas and 6 drinks

Step-by-step explanation:

Answer:

I'm pretty sure its D if not I'm sry

Answer:

A

Step-by-step explanation:

Compound interest is p (1+r)^T

5,375(1+0.062)^3 = 6,438.02

You have to convert the months into years.

Answer:

Yes

Step-by-step explanation:

A polygon is a 2D figure with at least three straight sides and angles. A pentagon has five sides and angles, so it qualifies as a polygon.

I hope this helped ^^ Good luck

Answer:

4(1 - 4x + 7y)

Step-by-step explanation:

The only factor common to all three terms is 4.

Factoring out the 4, we get    4(1 - 4x + 7y)

Answer:

a.) 64

b.) 2401

Step-by-step explanation:

Answer:

a.) 64

b.) 2401

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Answer:

15 × 5

Step-by-step explanation:

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