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3 years ago

Solve the following equation, and check your solution. Be sure to show all work.

Mathematics

1 answer:

sweet-ann [11.9K]3 years ago

3 0

1. Subtract 24 from both sides

-3x = -27 - 24

Simplify -27 - 24 to -51

-3x = -51

Divide both sides by -3

x = -51/-3

Two negatives make a positive

x = 51/3

Simplify 51/3 to 17

x = 17

2. Regroup terms

n/5 - 17 = 33

Add 17 to both sides

n/5 = 33 + 17

Simplify 33 + 17 to 50

n/5 = 50

Multiply both sides by 5

n = 50 * 5

Simplify 50 * 5 to 250

n = 250

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A regular pyramid has a square base with sides of length 1. The four triangular faces are isosceles triangles whose equal sides

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Answer:

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Step-by-step explanation:

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5 0

3 years ago

Calculate the area of the quarter circle estimate using 3.14 for pi

mars1129 [50]

The area of the quarter circle with radius 3ft is $7.065 ft^2$

Area of a quarter circle is given by the formula:

$Area = \frac{\pi r^2}{4}$

Where r represents the radius of the circle

In the quarter circle shown, the radius, r = 3 feet

π = 3.14

Substitute π = 3.14 and r = 3 into the formula $Area = \frac{\pi r^2}{4}$

$Area = \frac{3.14 \times 3^2}{4}\\\\Area = \frac{3.14 \times 9}{4}\\\\Area = \frac{28.26}{4}\\\\Area = 7.065 ft^2$

The area of the quarter circle with radius 3ft is $7.065 ft^2$

Learn more here: brainly.com/question/25843249

6 0

2 years ago

Can you find what each of the answers are

Ksju [112]

$▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$

1. Find Angle A :

$x + 24 = 3x$

$3x - x = 2 4$

$2x = 24$

$x = 12$

Angle A :

$3x$

$3 \times 12$

$36 \degree$

2. Find Angle B :

$10x - 27 = 7x$

$10x - 7x = 27$

$3x = 27$

$x = 9$

Angle B :

$10x - 27$

$(10 \times 9) - 27$

$90 - 27$

$63 \degree$

Find Angle C :

$5x + 1 = 6x - 13$

$6x - 5 x = 1 + 13$

$x = 14$

Angle C :

$5x + 1$

$(5 \times 14) + 1$

$70 + 1$

$71 \degree$

Find Angle D :

$6x + 3 = 4x + 39$

$6x - 4x = 39 - 3$

$2x = 36$

$x = 18$

Angle D :

$4x + 39$

$(4 \times 18) + 39$

$72 + 39$

$111\degree$

And it's given :

36° = Angle A = B

63° = Angle B = A

71° = Angle C = H

111° = Angle D = E

Therefore, the answer will be " BAHE "

4 0

2 years ago

The number of people arriving at a ballpark is random, with a Poisson distributed arrival. If the mean number of arrivals is 10,

Stella [2.4K]

Answer:

a) 3.47% probability that there will be exactly 15 arrivals.

b) 58.31% probability that there are no more than 10 arrivals.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

If the mean number of arrivals is 10

This means that $\mu = 10$

(a) that there will be exactly 15 arrivals?

This is P(X = 15). So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 15) = \frac{e^{-10}*(10)^{15}}{(15)!} = 0.0347$

3.47% probability that there will be exactly 15 arrivals.

(b) no more than 10 arrivals?

This is $P(X \leq 10)$

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-10}*(10)^{0}}{(0)!} = 0.000045$

$P(X = 1) = \frac{e^{-10}*(10)^{1}}{(1)!} = 0.00045$

$P(X = 2) = \frac{e^{-10}*(10)^{2}}{(2)!} = 0.0023$

$P(X = 3) = \frac{e^{-10}*(10)^{3}}{(3)!} = 0.0076$

$P(X = 4) = \frac{e^{-10}*(10)^{4}}{(4)!} = 0.0189$

$P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378$

$P(X = 6) = \frac{e^{-10}*(10)^{6}}{(6)!} = 0.0631$

$P(X = 7) = \frac{e^{-10}*(10)^{7}}{(7)!} = 0.0901$

$P(X = 8) = \frac{e^{-10}*(10)^{8}}{(8)!} = 0.1126$

$P(X = 9) = \frac{e^{-10}*(10)^{9}}{(9)!} = 0.1251$

$P(X = 10) = \frac{e^{-10}*(10)^{10}}{(10)!} = 0.1251$

$P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.000045 + 0.00045 + 0.0023 + 0.0076 + 0.0189 + 0.0378 + 0.0631 + 0.0901 + 0.1126 + 0.1251 + 0.1251 = 0.5831$

58.31% probability that there are no more than 10 arrivals.

8 0

3 years ago

PLEASE ANSWER QUICK One year, the population of a city was 164,000. Several years later it was 182,040. Find the percent increas

Katena32 [7]

Answer:

There was an 11% increase.

Step-by-step explanation:

The formula to find a percent increase is this: (original amount - new amount / original amount) * 100

If you fill in the formula, you get this:

(164,000 - 182,040 / 164,000) * 100

Solve:

(-18,040 / 164,000) * 100 ---> If the number being divided is negative, find the absolute value.

(18,040 / 164,000) * 100 =

0.11 * 100

11%

5 0

2 years ago