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Shalnov [3]
2 years ago
12

one school purchased 18 gallons of blue paint to decorate several of its classrooms. if each classroom needs 1 4/5 gallons of pa

int, then how many classrooms will get painted.
Mathematics
1 answer:
Elis [28]2 years ago
5 0

Answer:

18 gallons of paint could paint 10 classrooms.

Step-by-step explanation:

Given that the school bought 18 gallons of paint, and that each classroom requires 1 4/5 of paint to be painted, to determine how many classrooms can be painted with that amount of paint, the following calculation must be performed:

4/5 = 0.8

1 + 0.8 = 1.8

18 / 1.8 = 10

Therefore, 18 gallons of paint could paint 10 classrooms.

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What is log of 1/100
sesenic [268]
Log of 1 / 100 is - 2 because 10^( - 2 ) = 1 / 10^2 = 1 / 100 ;
5 0
2 years ago
Solve the triangle. Round your answers to the nearest tenth.
wel

Answer:

m∠A ≈ 43°

m∠B ≈ 55°

mBC ≈ 20

Step-by-step explanation:

Law of Sines: \frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

Step 1: Find m∠B

\frac{29}{sin82} =\frac{24}{sinB}

Step 2: Solve for ∠B

29sinB = 24sin82°

sinB = 24sin82°/29

B = sin⁻¹(24sin82°/29)

B = 55.038°

Step 3: Find m∠A

180 - (55.038 + 82)

180 - 137.038

m∠A = 42.962°

Step 4: Find BC

\frac{29}{sin82} =\frac{BC}{sin42.962}

Step 5: Solve for BC

29sin42.962° = BCsin82°

BC = 29sin42.962°/sin82°

BC = 19.9581

4 0
2 years ago
Define z_alpha to be a z-score with an area of alpha to the right. For Example: z_0.10 means P(Z > z_0.10) = 0.10. We would a
Reptile [31]

Answer:

a) P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

"=NORM.INV(0.025,0,1)"

And for this case the two values are :z_{crit}= \pm 1.96

b) P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates \alpha/2 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

"=NORM.INV(alpha/2,0,1)"

c) For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got z_{\alpha/2}=1.64

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Part a

P(-z_0.025 < Z < z_0.025)

For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(0.025,0,1)"

"=NORM.INV(0.025,0,1)"

And for this case the two values are :z_{crit}= \pm 1.96

Part b

P(-z_{\alpha/2} < Z < z_{\alpha/2})

For this case we want a quantile that accumulates \alpha/2 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:

"=NORM.INV(alpha/2,0,1)"

"=NORM.INV(alpha/2,0,1)"

Part c

For this case we want to find a value of z that satisfy:

P(Z > z_alpha) = 0.05.

And we can use the following excel code:

"=NORM.INV(0.95,0,1)"

And we got z_{\alpha/2}=1.64

6 0
3 years ago
8p+5=-6p+1 what's the answer to this equation?​
Olin [163]

Answer:

-2/7

Step-by-step explanation:

8 0
3 years ago
A city council consists of seven Democrats and five Republicans. If a committee of four people is selected, find the probability
Hoochie [10]

Answer:

The probability  of selecting two Democrats and two Republicans is 0.4242.

Step-by-step explanation:

The information provided is as follows:

  • A city council consists of seven Democrats and five Republicans.
  • A committee of four people is selected.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!\times (n-k)!}

Compute the number of ways to select four people as follows:

{12\choose 4}=\frac{12!}{4!\times (12-4)!}=495

Compute the number of ways to selected two Democrats as follows:

{7\choose 2}=\frac{7!}{2!\times (7-2)!}=21

Compute the number of ways to selected two Republicans as follows:

{5\choose 2}=\frac{5!}{2!\times (5-2)!}=10

Then the probability  of selecting two Democrats and two Republicans as follows:

P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242

Thus, the probability  of selecting two Democrats and two Republicans is 0.4242.

6 0
2 years ago
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