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Westkost [7]
3 years ago
11

A drive-in theater costs $20 per car, plus an additional fee of $4 per person. The cost, C, of the movie when p people are in th

e car can be represented by this equation: C = 20 + 4p Solve the equation for p to show How many people were in the car when the movie costed C dollars.
Mathematics
1 answer:
ozzi3 years ago
8 0

Answer:

P=\frac{C}{4} -5

Step-by-step explanation:

Step one:

given

cost  per drive= $20

additional fee per person= $4

let the number of persons be p

and the total cost be C

The total cost function is expressed as

C=20+4p

Step two:

Required:

<u><em>We want to make P subject of the cost function </em></u>

Take 20 to the other side we have

C-20=4p

divide through by 4

P=C-20/4

simplify

P=C/4-5

P=\frac{C}{4} -5

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Would i solve this doing 14+5 or 14-5 to get the missing length?
nataly862011 [7]

Answer:

The answer to your question is 10 ft

Step-by-step explanation:

We can observe that all the sides have a length but the first to the left.

Also, we know the corners meet at right triangles, so to calculate the length of the missing side, we must add to sides.

But these sides must be the ones that are in front of it (6 ft and 4 ft)

Then    ? = 6 + 4

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3 years ago
A culture started with 5,000 bacteria. After 8 hours, it grew to 6,000 bacteria. Predict how many bacteria will be present after
Vlad [161]

Answer:

6,250

Step-by-step explanation: 6,000 - 5,000 = 1000

1,000/8 = 125

125 X 10 = 1,250

5,000 + 1,250 = 6,250

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5 0
3 years ago
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It is known that the life of a particular auto transmission follows a normal distribution with mean 72,000 miles and standard de
scoray [572]

Answer:

a) P(X

P(z

b) P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)

P(z>-0.583)=1-P(Z

c) P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)

P(z>2.33)=1-P(Z

Sicne this probability just represent 1% of the data we can consider this value as unusual.

d) z=1.28

And if we solve for a we got

a=72000 +1.28*12000=87360

So the value of height that separates the bottom 90% of data from the top 10% is 87360.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the life of a particular auto transmission of a population, and for this case we know the distribution for X is given by:

X \sim N(72000,12000)  

Where \mu=72000 and \sigma=12000

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using excel or the normal standard table and we got:

P(z

Part b

P(X>65000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>65000)=P(\frac{X-\mu}{\sigma}>\frac{65000-\mu}{\sigma})=P(Z>\frac{65000-72000}{12000})=P(z>-0.583)

And we can find this probability using the complement rule and excel or the normal standard table and we got:

P(z>-0.583)=1-P(Z

Part c

P(X>100000)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>100000)=P(\frac{X-\mu}{\sigma}>\frac{100000-\mu}{\sigma})=P(Z>\frac{100000-72000}{12000})=P(z>2.33)

And we can find this probability using the complement rule and excel or the normal standard table and we got:

P(z>2.33)=1-P(Z

Sicne this probability just represent 1% of the data we can consider this value as unusual.

Part d

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.1   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=1.28

And if we solve for a we got

a=72000 +1.28*12000=87360

So the value of height that separates the bottom 90% of data from the top 10% is 87360.  

5 0
3 years ago
Brad says that if a second number is 125% of the first number than the second number must be 75% of the second number is he corr
elena-s [515]

Answer:

Incorrect.

Step-by-step explanation:

Let, the first number is x, and the second number is y. Given, the second number is 125% of the first number. So, the equation will be

y = 1.25 x

Or, y= 5/4x

Now, multiplying it with 4/5, we get, x= 4/5y

Or, x= 0.80 y

But, Brad is saying the first number must be 75% of the second number. But here we see that the first number is 80% of the second number. That's why Brad is incorrect.

5 0
2 years ago
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