Please help asap 22 pts

How many gallons of paint are needed to paint one coat, if a gallon of paint covers 400ft squared?

bixtya [17]

Answer:

6.28 gallons

Step-by-step explanation:

first we need to find the area of a half sphere, and then find how much paint will be needed for that area.

The area of a sphere:

$a=4 \pi r^2$

thus, the area of half a sphere is:

$a=2 \pi r^2$

we know that the radius is:

$r=20ft$

we substitute this to find the area of the half sphere (the area they need to paint):

$a=2\pi (20ft)^2\\a=2(3.1416) (400ft^2)\\a=2,513.27ft^2$

now the question is how many gallons of paint are needed to paint 2,513.27 square feet.

We are told that 1 gallon covers 400 square feet

thus, we must divide 2,513.27 by 400:

$\frac{2,513.27ft^2}{400ft^2} =6.28$

6.28 gallons of paint are needed.

5 0

3 years ago

Two corporate baseball teams are scheduled to play a game together. They agree that if both teams attend or if neither team atte

sp2606 [1]

Answer:

2.99% probability that the cost will be paid by only one team

Step-by-step explanation:

The binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Probability that a team plays:

A team plays if it has at most 2 injured players out of 11.

11 players, so $n = 11$

Each player with a 5% probability of injury, so $p = 0.05$

Then

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{11,0}.(0.05)^{0}.(0.95)^{11} = 0.5688$

$P(X = 1) = C_{11,1}.(0.05)^{1}.(0.95)^{10} = 0.3293$

$P(X = 2) = C_{11,2}.(0.05)^{2}.(0.95)^{9} = 0.0867$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.5688 + 0.3293 + 0.0867 = 0.9848$

Each team has a 0.9848 probability of showing up to play.

What is the probability that the cost will be paid by only one team?

This happens if one team shows up and the other do not.

2 teams, so $n = 2$

Each team has a 0.9848 probability of showing up to play, so $p = 0.9848$ .

This probability is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{2,1}.(0.9848)^{1}.(0.0152)^{1} = 0.0299$

2.99% probability that the cost will be paid by only one team

7 0

4 years ago

Which equation represents the linear relationships shown in the table?

saveliy_v [14]

Answer:

idk

Step-by-step explanation:

4 0

3 years ago

Lisa's favorite chocolate candies are wrapped in the shape of a triangular prism with shiny gold paper as shown below. If all si

Tatiana [17]

Answer:

Surface Area = 150

Step-by-step explanation:

The surface area of this triangular prism is the sum of area of all the sides.

Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)

Triangle 1 area: $\frac{1}{2}bh=\frac{1}{2}(8)(3)=12$
Triangle 2 area: $\frac{1}{2}bh=\frac{1}{2}(8)(3)=12$
Lateral surface 1 (rectangle): $l*w=(7)(5)=35$
Lateral surface 2 (rectangle): $l*w=(7)(5)=35$
Bottom surface (rectangle): $l*w=(7)(8)=56$