Complete the proof that TV || QS.

Mei is the manager of a hotel. She is placing rectangular rugs on the wood floors throughout the rectangular hotel lobby

uranmaximum [27]

Answer:

Mei is the manager of a hotel. She is placing rectangular rugs on the wood floors throughout the rectangular hotel lobby.

The lobby is 38 feet long and 24 feet wide.

Each rug is 4 feet long and 2 feet wide.

She places 7 rugs throughout the lobby. The rugs do not overlap.

How much of the lobby's floor is left uncovered by the rugs?

A.

806 square feet

B.

912 square feet

C.

856 square feet

D.

968 square feet

Step-by-step explanation:

6 0

3 years ago

Find x and y. <br><br> please help !

IrinaK [193]

Using linear pairs,

$115+5x=180\\\\5x=65\\\\x=\boxed{13}$

By the exterior angle theorem,

$2y=45+5(13)\\\\2y=45+65\\\\2y=110\\\\y=\boxed{55}$

3 0

2 years ago

A, B & C form a triangle where ∠ BAC = 90°. AB = 13.5 mm and CA = 3.2 mm. Find the length of BC, giving your answer rounded

adelina 88 [10]

Answer:

13.9

Step-by-step explanation:

Use Pythagorean Theorem:

Both of the lengths given are the legs,

13.5^2 + 3.2^2 = c^2

182.25 + 10.24 = c^2

192.49 = c^2

13.87 = c

8 0

3 years ago

4. One in four people in the US owns individual stocks. You randomly select 12 people and ask them if they own individual stocks

BartSMP [9]

Answer:

a. The mean is 3, the variance is 2.25 and the standard deviation is 1.5.

b. 0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.

c. 0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.

d. 0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two

e. Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they own stocks, or they do not. The probability of a person owning stocks is independent of any other person, which means that 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.

One in four people in the US owns individual stocks.

This means that $p = \frac{1}{4} = 0.25$

You randomly select 12 people and ask them if they own individual stocks.

This means that $n = 12$

a. Find the mean, variance, and standard deviation of the resulting probability distribution.

The mean of the binomial distribution is:

$E(X) = np$

So

$E(X) = 12(0.25) = 3$

The variance is:

$V(X) = np(1-p)$

So

$V(X) = 12(0.25)(0.75) = 2.25$

Standard deviation is the square root of the variance, so:

$\sqrt{V(X)} = \sqrt{2.25} = 1.5$

The mean is 3, the variance is 2.25 and the standard deviation is 1.5.

b. Find the probability that the number of people who own individual stocks is exactly six.

This is P(X = 6). So

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

$P(X = 6) = C_{12,6}.(0.25)^{6}.(0.75)^{6} = 0.0401$

0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.

c. Find probability that the number of people who say they own individual stocks is at least two.

This is:

$P(X \geq 2) = 1 - P(X < 2)$

In which

$P(X < 2) = P(X = 0) + P(X = 1)$

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

$P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317$

$P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267$

$P(X < 2) = P(X = 0) + P(X = 1) = 0.0317 + 0.1267 = 0.1584$

0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.

d. Find the probability that the number of people who say they own individual stocks is at most two.

This is:

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

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

$P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317$

$P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267$

$P(X = 2) = C_{12,2}.(0.25)^{2}.(0.75)^{10} = 0.2323$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0317 + 0.1267 + 0.2323 = 0.3907$

0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two.

e. Are the events in part c. and in part d. mutually exclusive

Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.

5 0

3 years ago

What are the coordinates of the point (-4,-10) after a 180 rotation about the orgin and then a translation 1 unit right

goblinko [34]

1. Rotation by 180° (clockwise or anti-clockwise) about the origin has a rule:

(x,y)→(-x,-y).

Then

(-4,-10)→(4,10).

2. Translation 1 unit to the right has a rule:

(x,y)→(x+1,y).

Then

(4,10)→(5,10).

3. After rotation and translation the image of point (-4,-10) is point (5,10).

Answer: (5,10).

5 0

4 years ago