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3 years ago

8

The Robot Factory is a learning center where children can build robots. The project fee per visit is $18, and each hour of time

(x) at the factory costs $6. Jesse goes to the Robot Factory one afternoon, and the total charge for his visit is $33. What is the equation that models the situation where x is the number of hours Jesse spends at the Robot Factory?

1 answer:

ipn [44]3 years ago

5 0

The answer is 2 and a half. Because 18 + 6 + 6 + 3 is 33. This is because $18 to get in then $6 for one hour another $6 for an hour and $3 for an half hour.

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A roller coaster starts with the cars being pulled up a ramp. The mass of the cars is estimated by the function m(p) = 175p + 1,

KiRa [710]

Answer:

$E(p)=51,450p+346,920$

Step-by-step explanation:

The function

$m(p) = 175p + 1,180$

gives the mass of the car as a function of the number of passengers in it.

And the function

$E(m) = 9.8m*h$

gives the potential energy of the car as a function of the car's mass.

Now if the height of the ramp is 30 meters, we have

$E(m) =9.8m*(30)$

$E(m) =294m$

And to find the potential energy as a function of the number of passengers, we just substitute $m(p)$ into $E(m)$ to get:

$E(m(p))=294(175p+1180)$

$\boxed{ E(p)=51,450p+346,920}$

which gives the potential energy as a function of the number of passengers.

7 0

4 years ago

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

How would you write 105% as a decimal.

Luba_88 [7]

Answer:

1.05

Step-by-step explanation:

number starts as .105

slide the decimal over 1 space

1.05

6 0

4 years ago

Read 2 more answers

If 2 inches are equivalent to 5 centimeters, how many square centimeters are in one square inch?

umka2103 [35]

There are 6.45 or 6.5 square cm in one square in.

5 0

2 years ago

The perimeter of a shape is 25.71 cm calculate the value of the radius X takes pie to be 3.142

Mariulka [41]

Answer:

5 cm

Step-by-step explanation:

Given a semicircle with perimeter 25.71 cm, we are required to find the radius of the circle.

Circumference of a Semicircle

=Length of the Circular part+Length of the diameter

$=\pi r+2r$

$If \: \pi=3.142, C=25.71\\Then:\\25.71=3.142r+2r\\r(3.142+2)=25.71\\5.142r=25.71\\r=25.71 \div5.142\\r=5cm$

3 0

3 years ago