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x^3 – 27 = 0

Answer:

A=150

Step-by-step explanation:

1/2ab=A

1/2 15x20 = 1/2 300 = 150 = A

Hope this Helps! :)

Answer:

Hypotenuse = 25

Step-by-step explanation:

Pythagorean theorem: a^2+b^2 = c^2

15^2+20^2 = c^2

225+400 = c^2

625 = c^2

25 = c

Answer: [tex]\$11.5[/tex]

Step-by-step explanation:

Given

Demand function is [tex]p=22-2q[/tex]

The average cost function is [tex]c=2+q[/tex]

Total revenue is the product of demand and the price per unit.

[tex]r=\left(22-2q\right)q[/tex]

Profit is given by the difference of the total revenue and the cost

[tex]\Rightarrow P=r-c\\\Rightarrow P=22q-2q^2-2-q\\\Rightarrow P=-2q^2+21q-2[/tex]

Find the derivative of profit to get the maximum profit

[tex]\Rightarrow P'=-4q+21\\\text{Put the derivative equal to 0 to get the maximum profit}\\\\\Rightarrow q=\dfrac{21}{4}[/tex]

Put q in the equation of demand to get the price

[tex]\Rightarrow p=22-2\times \dfrac{21}{4}\\\\\Rightarrow p=22-10.5\\\Rightarrow p=\$11.5[/tex]

Answer:

yes

Step-by-step explanation:

yes

Answer:

y = 2/3x - 2

Step-by-step explanation:

Lines on the graph: (0, -2) and (3, 0)

Slope:

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

m=(0+2)/(3-0)

m= 2/3

Slope-intercept:

y - y1 = m(x - x1)

y + 2 = 2/3(x - 0)

y + 2 = 2/3x

y = 2/3x - 2

Answer:

Given:

-> Area of the wall: 500sq. feet

-> 1 gallon of paint covers 160sq. feet of area

-> By unitary method:

-> 1 ft. square of wall requires 1/160 gallon of paint

Thus,

-> 500 ft. square of wall will require = 500 x 1/160 gallons of paint

= 3.0125 gallons

Hope it helps :)

Though my answer may be wrong :(

Have a great day!

Answer: C

Step-by-step explanation: 52 weeks in a year. 61870/52 is 1,189.81.

Answer:

C. 1/4

Step-by-step explanation:

The probability of landing tails is 50%, since coins are two sided.

If a cube has 6 numbers, the probability of getting an even number is also 50% since 2,4,and 6 are even while 1,3, and 5 are odd.

The probability of getting both would be 25% (I multiplied 1/2 by 1/2)

Answer:

your answer is 36 counting by 4s

Step-by-step explanation:

4

16

20

24

28

32

36

Answer:

28

Step-by-step explanation:

4, 8, 12, 16, 20, 24, 28

The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;

x⁴ divided by x equals x³

x + 1 multiplied by x³ equals x⁴ + x³

subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2

2x³ divided by x equals 2x²

x + 1 multiplied by 2x² equals 2x³ + 2x²

subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2

2x² divided by x equals 2x

x + 1 multiplied by 2x equals 2x² + 2x

subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2

-3x divided by x equals -3

x + 1 multiplied by -3 equals -3x - 3

subtract -3x - 3 from -3x - 2 will result to a remainder of 1.

Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).

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Answer:

1.05

Step-by-step explanation:

it is 105 divided by 1000

Answer:

0.105 metres

Step-by-step explanation:

105 divided by 1000

h^2 = 9^2 + 4^ 2

= 81 + 16

= 97

h =97 ^ 1/2

= 9.849

= 10 ml

Answer: Its cube is six times the

cube of the given number.

Step-by-step explanation:

Let's assume we have a number which is 2. The cube will be:

= 2³

= 2 × 2 × 2

= 8

Let's now assume, we double the number 2, we'll have 2 × 2 = 4. Therefore, the cube will be:

= 4³

= 4 × 4 × 4

= 64

Therefore, from the explanation above, 2 raise to power 6 is 64. This means, if a number is doubled, then its cube is six times the cube of the given number.

Answer:

33

Step-by-step explanation:

48 - 15 = 33

Answer:

33??

Step-by-step explanation:

Step-by-step explanation:

Answer:

6/5

Step-by-step explanation:

5x + 14 = 20

Subtract 14 from 20

5x = 6

Divide both sides by 5

x = 6/5

Answer: its 18.27  

Step-by-step explanation:

Answer:

140

Step-by-step explanation:

B 10/33.

Step-by-step explanation:

becouse you first have to add all the chocolates together, with would be 33. Out of the 33, 10 of them are dark chocolate, so your answer would be 10/33

Answer:

x = 15

Step-by-step explanation:

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 9² + 12² = 81 + 144 = 225 ( take square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

x = 15

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

From inspection of the given right triangle:

Substitute the given values into Pythagoras Theorem and solve for x:

[tex]\implies 9^2+12^2=x^2[/tex]

[tex]\implies 81+144=x^2[/tex]

[tex]\implies 225=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{225}[/tex]

[tex]\implies x=15[/tex]

Answer:

The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.

Step-by-step explanation:

The average teaching salary in Georgia is $48,553 per year. The school districts in the metro Atlanta area boast that they pay more.

At the null hypothesis, we test if they pay the average, that is:

[tex]H_0: \mu = 48553[/tex]

At the alternate hypothesis, we test if they pay more, that is:

[tex]H_1: \mu > 48553[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

48553 is tested at the null hypothesis:

This means that [tex]\mu = 48553[/tex]

Sample of 228 teachers from the metro Atlanta area and record their salaries. The sample mean is $49,021, with a standard deviation of $3,127.

This means that [tex]n = 228, X = 49021, \sigma = 3127[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{49021 - 48553}{\frac{3127}{\sqrt{228}}}[/tex]

[tex]z = 2.26[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 49021, which is 1 subtracted by the p-value of z = 2.26.

Looking at the z-table, z = 2.26 has a p-value of 0.9881

1 - 0.9881 = 0.0119

The p-value of the test is 0.0119 < 0.06, which means that the data provides statistically significant evidence at the 0.06 level that the average teaching stay in the metro Atlanta area is greater than the state average.

Answer:

it's D

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

Distribute 2 to the parentheses:

2(x + 3) = x + 10

2x + 6 = x + 10

Subtract x from both sides:

x + 6 = 10

Subtract 6 from both sides:

x = 4

So, x = 4

Answer: x = 4

Step-by-step explanation:

Answer:

Option B, 5/48 yd³

Step-by-step explanation:

[tex] \frac{5}{6} \times \frac{1}{4} \times \frac{1}{2} [/tex]

[tex] = \frac{5}{4} [/tex]

Answer: it is 90,000 i believe

Answer: 90,000

Step-by-step explanation: I think it is 90,000 because if the number was for an example 95,000 it would be 100,000 so the number after the 9 is deciding either it goes up or down

(sorry for the grammar and stuff because I'm from Germany so its not very easy to explain, thanks for understanding)

Answer: A ≈ 74.35

Step-by-step explanation: Explanation below.

According to the solving If the room's width is 6 meter's, then its length must be 10 meter's.

Distance is measured by length. The quantity of length has the dimension of distance there in International System of Quantities. Most measurement systems choose a base unit for length from which all subsequent units are derived. The metre serves as the fundamental unit of length in the International System of Units.

If you have an area A and a width w, you can calculate the length w by using the formula h = A/w. Its length can indeed be calculated using the formula h = P/2w if you know its perimeter (P) and width (W). If you have the width w and the diagonal

According to the give information:

Let length be x By Given Condition

5/3=x/6

x=5/3*6

x=30/3=10

Therefore length of room is 10.

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Answer:

They are similar in a way. Perpendicular lines can intersect, but they must make a 90 degree angle to be prerpendicular lines. A cross is an example of this.

Step-by-step explanation:

Answer:

She makes 2.50 $ a hour and she will make 20 $ at 8 hours

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Answer:

18 more students preferred pepperoni pizza over cheese pizza in the survey.

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] x [tex]\frac{72}{1}[/tex] Can be rewritten

[tex]\frac{3}{1}[/tex] x [tex]\frac{9}{1}[/tex] = [tex]\frac{27}{1}[/tex] = 27   I cross canceled the 8 and 72.  They have a common factor of 8.  8 goes into 8 once and 8 goes into 72 9 times.

27 students preferred pepperoni pizza.

[tex]\frac{1}{8}[/tex] x [tex]\frac{72}{1}[/tex] = [tex]\frac{1}{1}[/tex] x [tex]\frac{9}{1}[/tex] = 9

9 students preferred cheese pizza.

27 - 9 = 18