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geniusboy [140]
3 years ago
13

The graph below shows the price of different numbers of beach balls at a store: Which equation can be used to determine p, the c

ost of b beach balls? b = 5.50p p = 5.50b p = 11b b = 11p

Mathematics
1 answer:
lys-0071 [83]3 years ago
7 0

Answer:

p = 5.50b

Step-by-step explanation:

2 beach balls cost 11

4 beach balls cost 22

6 beach balls cost 33

So each (1) ball b costs 5.50 ($) p

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The score on an exam from a certain MAT 112 class, X, is normally distributed with μ=78.1 and σ=10.8.
salantis [7]

a) X

b) 0.1539

c) 0.1539

d) 0.6922

Step-by-step explanation:

a)

In this problem, the score on the exam is normally distributed with the following parameters:

\mu=78.1 (mean)

\sigma = 10.8 (standard deviation)

We call X the name of the variable (the score obtained in the exam).

Therefore, the event "a student obtains a score less than 67.1) means that the variable X has a value less than 67.1. Mathematically, this means that we are asking for:

X

And the probability for this to occur can be written as:

p(X

b)

To find the probability of X to be less than 67.1, we have to calculate the area under the standardized normal distribution (so, with mean 0 and standard deviation 1) between z=-\infty and z=Z, where Z is the z-score corresponding to X = 67.1 on the s tandardized normal distribution.

The z-score corresponding to 67.1 is:

Z=\frac{67.1-\mu}{\sigma}=\frac{67.1-78.1}{10.8}=-1.02

Therefore, the probability that X < 67.1 is equal to the probability that z < -1.02 on the standardized normal distribution:

p(X

And by looking at the z-score tables, we find that this probability is:

p(z

And so,

p(X

c)

Here we want to find the probability that a randomly chosen score is greater than 89.1, so

p(X>89.1)

First of all, we have to calculate the z-score corresponding to this value of X, which is:

Z=\frac{89.1-\mu}{\sigma}=\frac{89.1-78.1}{10.8}=1.02

Then we notice that the z-score tables give only the area on the left of the values on the left of the mean (0), so we have to use the following symmetry property:

p(z>1.02) =p(z

Because the normal distribution is symmetric.

But from part b) we know that

p(z

Therefore:

p(X>89.1)=p(z>1.02)=0.1539

d)

Here we want to find the probability that the randomly chosen score is between 67.1 and 89.1, which can be written as

p(67.1

Or also as

p(67.1

Since the overall probability under the whole distribution must be 1.

From part b) and c) we know that:

p(X

p(X>89.1)=0.1539

Therefore, here we find immediately than:

p(67.1

7 0
3 years ago
according to "Black Hole Beginnings," the destruction of some stars results in inbursts of light. an intense gravitational pull.
Colt1911 [192]

According to "Black Hole Beginnings," the destruction of some stars results in an an intense gravitational pull.

To answer the question, we need to know what Black Holes are.

<h3>What are Black Holes?</h3>

Blackholes are regions of space in which no matter can escape

<h3>Characteristics of black holes</h3>
  • Black holes are formed from the remnants of  large star that dies in a supernova
  • As long as the star is three times or more larger than the sun, it will collapse
  • The gravitational force on the star causes it to collapse into a black hole

So, when black holes are formed, some stars are destroyed and collapse due to intense gravitational forces.

So, according to "Black Hole Beginnings," the destruction of some stars results in an an intense gravitational pull.

Learn more about black holes here:

brainly.com/question/6037502

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5 0
2 years ago
A. the series is absolutely convergent.
Dovator [93]
\displaystyle\sum_{n=1}^\infty\left(1+\frac5n\right)^n

Notice that

\displaystyle\lim_{n\to\infty}\left(1+\frac5n\right)^n=e^5\neq0

which means the series is divergent. So if this is one of those "select all that apply" questions, then both (c) and (j) are the only choices that do.
7 0
3 years ago
Find x in the diagram
sukhopar [10]

Answer: where’s the diagram

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Enter the equation of the line in the form y=mx+b where m is the slope and b is the y-intercept.
rusak2 [61]

y=1.5x-2

Hope this helps

7 0
3 years ago
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