define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.

Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the la

sattari [20]

Answer:

C

Step-by-step explanation:

4x-5+x=180. Add 5 to both sides

5x=185. Divide by 6

X=37

180-37=143

143

4 0

3 years ago

Finn changes his mind and, from now on, decides to take the normal route to work everyday. On any given day, the time (in minute

Margaret [11]

Answer:

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

Step-by-step explanation:

This can be solved by the the z-score formula:

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

Each z-score value has an equivalent p-value, that represents the percentile that the value X is:

The problem states that:

Mean = 35, so $\mu = 35$

Variance = 81. The standard deviation is the square root of the variance, so $\sigma = \sqrt{81} = 9$ .

Find the 33rd percentile of the time it takes Finn to get to work on any given day. Do not include any units in your answer.

Looking at the z-score table, $z = -0.44$ has a pvalue of 0.333. So what is the value of X when $z = -0.44$ .

$Z = \frac{X - \mu}{\sigma}$

$-0.44 = \frac{X - 35}{9}$

$X - 35 = -3.96$

$X = 31.04$

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

Over the next 2 days, find the probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

$P = P_{1} + P_{2}$

$P_{1}$ is the probability that Finn took more than 40.5 minutes to get to work on the first day. The first step to solve this problem is finding the z-value of $X = 40.5$ .

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40.5 - 35}{9}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of 0.7291. This means that the probability that it took LESS than 40.5 minutes for Finn to get to work is 72.91%. The probability that it took more than 40.5 minutes if $P_{1} = 100% - 72.91% = 27.09% = 0.2709$

$P_{2}$ is the probability that Finn took more than 38.5 minutes to get to work on the second day. Sine the probabilities are independent, we can solve it the same way we did for the first day, we find the z-score of

$X = 38.5$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{38.5 - 35}{9}$

$Z = 0.39$

$Z = 0.39$ has a pvalue of 0.6517. This means that the probability that it took LESS than 38.5 minutes for Finn to get to work is 65.17%. The probability that it took more than 38 minutes if $P_{1} = 100% - 65.17% = 34.83% = 0.3483$

So:

$P = P_{1} + P_{2} = 0.2709 + 0.3483 = 0.6192$

There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

7 0

3 years ago

How do I do these? I don’t need the answers to them, I would just like to know how I go about solving them, thank you in advance

Sindrei [870]

Convert the percentage into a number then divide it by the income.

4 0

3 years ago

Sofia has 12 cups of yogurt to make smoothies. Each smoothie uses a cup of

olga55 [171]

Answer:

12

Step-by-step explanation:

If she has 12 cups of yogurt and each cup only uses 1 cup then she can make 12 smoothies

4 0

2 years ago

Read 2 more answers

a gardener has 322 tulip bulbs she wants to plant rows of 15 bulbs how many bulbs can be planted how many bulbs will she have le

Elden [556K]

Answer:315 bulbs planted and 7 left over

Step-by-step explanation:322/15 = 21.44

Roughly around 21 rows.

21 x 15 = 315 bulbs planted

322 - 315 = 7 bulbs left over

3 0

3 years ago