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klemol [59]
3 years ago
11

How to simplify 3x+2-x-4

Mathematics
1 answer:
Sladkaya [172]3 years ago
5 0

Answer:

2(x + 1)

Step-by-step explanation:

<u>Step 1:  Combine like terms </u>

<u />3x + 2 - x - 4

(3x - x) + (2 - 4)

2x + 2

2(x + 1)

Answer:  2(x + 1)

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Use the circle to answer the questions​
insens350 [35]

Answer:

Diameter: 10.8 cm

Circumference (in terms of π): 10.8π cm

Circumference (approximate): 33.91 cm

Step-by-step explanation:

Hi there!

<u>We're given:</u>

  • The radius (5.4 cm)

<u>1) Determine the diameter</u>

d=2r

Multiply the radius 5.4 cm by 2

5.4 × 2 = 10.8

Therefore, the diameter of the circle is 10.8 cm.

<u>2) Determine the circumference of the circle</u>

C=\pi d

Plug in the diameter 10.8

C=10.8\pi

Therefore, the circumference of the circle in terms of π is 10.8π cm.

<u />

<u>3) Determine the approximate circumference of the circle </u>

C=10.8\pi\\C=10.8(3.14)\\C=33.91

Therefore, the approximate circumference of the circle is 33.91 cm.

I hope this helps!

5 0
3 years ago
A popular resort hotel has 300 rooms and is usually fully booked. About 7% of the time a reservation is canceled before the 6:00
kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that n = 300

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied.  So we use p = 0.93

Approximating the binomial to the normal.

E(X) = np = 300*0.93 = 279

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{300*0.93*0.07} = 4.42

The probability that at least 285 rooms will be occupied is 1 subtracted by the pvalue of Z when X = 285. So

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

Z = \frac{285- 279}{4.42}

Z = 1.36

Z = 1.36 has a pvalue of 0.9131.

So there is a 1-0.9131 = 0.0869 = 8.69% probability that at least 285 rooms will be occupied.

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The answer would be the first one, 2s+6.

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