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2 years ago

Write the y-intercept of the graph of 9x + 6y = 27

Mathematics

1 answer:

stealth61 [152]2 years ago

4 0

Answer:

y= −3 /2 x+ 9/ 2

Step-by-step explanation:

Let's solve for y.

9x+6y=27

Step 1: Add -9x to both sides.

9x+6y+−9x=27+−9x

6y=−9x+27

Step 2: Divide both sides by 6.

6y /6=−9x+27 /6

y= −3 /2 x+ 9/ 2

Answer:

y= −3 /2 x+ 9/ 2

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Pls show me the work too

Ksenya-84 [330]

Answer:

1). Mean: 14.2

Median: 13.5

Step-by-step explanation:

To calculate the mean, sum all values and divide by the number of values:

(13+16+14+17+13+12) / 6 ≈ 14.2

To calculate the median, order the values from small to large and take the middle value. If there is no middle. average the two values in the middle:

12,13,13,14,16,17

The median is (13+14)/2 = 13.5.

Using this explanation you should be able to find the rest.

4 0

2 years ago

A selective college would like to have an entering class of 950 students. Because not all students who are offered admission acc

pogonyaev

Answer:

a) The mean is 900 and the standard deviation is 15.

b) 100% probability that at least 800 students accept.

c) 0.05% probability that more than 950 will accept.

d) 94.84% probability that more than 950 will accept

Step-by-step explanation:

We use the normal approximation to the binomial to solve this question.

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 $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

(a) What are the mean and the standard deviation of the number X of students who accept?

$n = 1200, p = 0.75$ . So

$E(X) = np = 1200*0.75 = 900$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.75*0.25} = 15$

The mean is 900 and the standard deviation is 15.

(b) Use the Normal approximation to find the probability that at least 800 students accept.

Using continuity corrections, this is $P(X \geq 800 - 0.5) = P(X \geq 799.5)$ , which is 1 subtracted by the pvalue of Z when X = 799.5. So

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

$Z = \frac{799.5 - 900}{15}$

$Z = -6.7$

$Z = -6.7$ has a pvalue of 0.

1 - 0 = 1

100% probability that at least 800 students accept.

(c) The college does not want more than 950 students. What is the probability that more than 950 will accept?

Using continuity corrections, this is $P(X \geq 950 - 0.5) = P(X \geq 949.5)$ , which is 1 subtracted by the pvalue of Z when X = 949.5. So

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

$Z = \frac{949.5 - 900}{15}$

$Z = 3.3$

$Z = 3.3$ has a pvalue of 0.9995

1 - 0.9995 = 0.0005

0.05% probability that more than 950 will accept.

(d) If the college decides to increase the number of admission offers to 1300, what is the probability that more than 950 will accept?

Now n = 1300. So

$E(X) = np = 1300*0.75 = 975$

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1200*0.75*0.25} = 15.6$

Same logic as c.

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

$Z = \frac{949.5 - 975}{15.6}$

$Z = -1.63$

$Z = -1.63$ has a pvalue of 0.0516

1 - 0.0516 = 0.9484

94.84% probability that more than 950 will accept

5 0

2 years ago

Find the unit rate. 5/8 ounce per 1/4 pint

Katena32 [7]

Answer: 2.5 ounces/ pint

You can firstly turn your fractions into decimals 5/8 is equal to .625 and 1/4 is .25

Then you can divide .625 by .25 which is 2.5, So the unit rate is 2.5 ounces per pint.

4 0

2 years ago

Help me please if you can

zheka24 [161]

Answer:

perimeter = 1 3/4

Step-by-step explanation:

1. 3/4 x 2 because there are two sides with the fraction 3/4. 3/4 x 2 is 1 1/2

2. 1/8 x 2 because there are two sides with the fraction 1/8. 1/8 x 2 is 1/4

3. 1 1/2 + 1/4 = 1 3/4

8 0

2 years ago

Please help!!!!!!!!

xxMikexx [17]

Answer:

1) 0.50

2) 1

using probability formula

6 0

2 years ago