All categories

3 years ago

Write and equation of the line that passes through the point (2,-6) and is parallel to the line x-2y=8

Mathematics

1 answer:

mestny [16]3 years ago

5 0

Answer:

y=0.5x-7

Step-by-step explanation:

x-2y=8

2y=x-8

y=0.5x-4 m1=0.5

m1=m2=0.5 - the slope for parallel lines are equaly

y=m2x+b

-6=0.5*2+b

b=-7

y=0.5x-7

You might be interested in

Guys If you buy me a private island with a pterodactyl..:.. i’ll let you be in my Dino club for free :)

Vikki [24]

Ofc! Private island incoming...

️

5 0

3 years ago

Read 2 more answers

According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening.† (a) For

SpyIntel [72]

Answer:

a) 0.2741 = 27.41% probability that at least 13 believe global warming is occurring

b) 0.7611 = 76.11% probability that at least 110 believe global warming is occurring

Step-by-step explanation:

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.

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:

$p = 0.71$

(a) For a sample of 16 Americans, what is the probability that at least 13 believe global warming is occurring?

Here $n = 16$ , we want $P(X \geq 13)$ . So

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16)$

In which

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

$P(X = 13) = C_{16,13}.(0.71)^{13}.(0.29)^{3} = 0.1591$

$P(X = 14) = C_{16,14}.(0.71)^{14}.(0.29)^{2} = 0.0835$

$P(X = 15) = C_{16,15}.(0.71)^{15}.(0.29)^{1} = 0.0273$

$P(X = 16) = C_{16,16}.(0.71)^{16}.(0.29)^{0} = 0.0042$

$P(X \geq 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) = 0.1591 + 0.0835 + 0.0273 + 0.0042 = 0.2741$

0.2741 = 27.41% probability that at least 13 believe global warming is occurring

(b) For a sample of 160 Americans, what is the probability that at least 110 believe global warming is occurring?

Now $n = 160$ . So

$\mu = E(X) = np = 160*0.71 = 113.6$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{160*0.71*0.29} = 5.74$

Using continuity correction, this is $P(X \geq 110 - 0.5) = P(X \geq 109.5)$ , which is 1 subtracted by the pvalue of Z when X = 109.5. So

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

$Z = \frac{109.5 - 113.6}{5.74}$

$Z = -0.71$

$Z = -0.71$ has a pvalue of 0.2389

1 - 0.2389 = 0.7611

0.7611 = 76.11% probability that at least 110 believe global warming is occurring

3 0

3 years ago

Please answer the following<br><br>please explain how you got your answer

Liula [17]

Answer:

P(1) = 4/20 or 1/5

P(2) = 3/20

P(3) = 7/20

P(4) = 6/20 or 3/10

Step-by-step explanation:

Crystal spun the spinner 20 times. 1 was the outcome 4 times out of 20 spins, so the experimental probability would be 4/20 or 1/5. Same goes for all the other ones.

4 0

3 years ago

HELP URGENT!!!!

Vikki [24]

The equation should be y= -2x+5.

7 0

3 years ago

Please Help! 30 points! Real answers pls The box plot below shows the total amount of time, in minutes, the students of a class

padilas [110]

Hii!

So I did this and I have A!

A: You cannot get the mean from the graph but you CAN get the third quartile!

B: To find the interquartile range (IQR) we subtract the third and first quartiles:

60-35 = 25

C: An outlier would be much larger than the rest of the data or much smaller than the rest of the data. An outlier would make the "whisker" portion longer and could potentially slightly shift the box.

6 0

4 years ago

Read 2 more answers