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3 years ago

Can someone help? 25 points

Mathematics

2 answers:

gregori [183]3 years ago

3 0

Answer:

t ≥ 18

Step-by-step explanation:

He has run 12 miles plus some more miles t. He need to run at least 30 miles

12+t ≥ 30

Subtract 12 from each side

12+t-12 ≥ 30-12

t ≥ 18

4vir4ik [10]3 years ago

3 0

Answer:

t 》18

Step-by-step explanation:

t + 12 》30

t 》30 - 12

t 》18

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Gale wants to compare the cost of the events.

Lera25 [3.4K]

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The carnival always costs the least.

No its possible but not always .
Aquarium fee is 14.50 on the other hand carnival fee starts at 15.55.

The aquarium always costs the move.

Impossiible

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2 years ago

The midpoint of AB is M(3, -1). If the coordinates of A are (5,1), what are the

Vera_Pavlovna [14]

Given parameters:

Midpoint of AB = M(3, -1)

Coordinates of A = (5,1)

Unknown:

Coordinates of B = ?

Solution:

To find the mid point of any line, we use the expression below;

$x_{m} = \frac{x_{1} + x_{2} }{2}$ and $y_{m} = \frac{y_{1} + y_{2} }{2}$

where $x_{m}$ and $y_{m}$ = coordinates of the mid points = 3 and -1

x₁ = 5 and y₁ = 1

x₂ = ? and y₂ = ?

Now let us input the variables and solve,

3 = $\frac{5 + x_{2} }{2}$ and -1 = $\frac{1 + y_{2} }{2}$

5 + x₂ = 6 -2 = 1 + y₂

x₂ = 1 y₂ = -2 -1 = -3

The coordinates of B = 1, -3

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3 years ago

What is the correct answer?

Vedmedyk [2.9K]

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3 years ago

What is the volume of this composite solid?<br> 16 m<br> 5 m<br> 12 m<br> 9 m

son4ous [18]

Answer:

864 cubic meters

Step-by-step explanation:

Rectangular prism = 5x9x12=540

Triangular prism = 1/2(9)(6)(12)=324

540+324=864 cubic meters

3 0

3 years ago

SAT scores are normed so that, in any year, the mean of the verbal or math test should be 500 and the standard deviation 100. as

vovangra [49]

Answer:

a) $P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

$P(Z>1.25)=1-P(Z$

b) $P(400$

$P(-1$

c) $z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

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 SAT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(500,100)$

Where $\mu=500$ and $\sigma=100$

We are interested on this probability

$P(X>625)$

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:

$P(X>625)=P(\frac{X-\mu}{\sigma}>\frac{625-\mu}{\sigma})=P(Z>\frac{625-500}{100})=P(Z>1.25)$

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

$P(Z>1.25)=1-P(Z$

Part b

We are interested on this probability

$P(400$

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:

$P(400$

And we can find this probability with this difference:

$P(-1$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1$

Part c

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

$P(X>a)=0.8$ (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 0.2 of the area on the left and 0.8 of the area on the right it's z=-0.842. On this case P(Z<-0.842)=0.2 and P(Z>-0.842)=0.8

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:

$z=-0.842$

And if we solve for a we got

$a=500 -0.842*100=415.8$

So the value of height that separates the bottom 20% of data from the top 80% is 415.8.

8 0

3 years ago