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3 years ago

A triangle has an area of 72 square feet. The height is 12 feet. What is the length of the base (in feet)?

Mathematics

1 answer:

SashulF [63]3 years ago

4 0

Answer:

6ft

Step-by-step explanation:

we went over this in class

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Decide if each expression is equivalent to 2^6 or 4^4

Mandarinka [93]

Answer:

Step-by-step explanation:

2^6=64

4^4=256

4 0

2 years ago

while shopping at a clearence sale samantha finds a $60 dress on sale for 25% off. samantha also finds a 50% off coupon.

tatuchka [14]

She would pay 15 dollars for the dress because it would be 75 percent off.

6 0

3 years ago

SOHCAHTOA can anyone help me with this

zvonat [6]

Root of ( 20^2 - 16^2 ) = 12

5 0

3 years ago

If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi

Sophie [7]

Answer:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

$P(Z>0.8)=1-P(Z\leq 0.8)$

$P(Z>0.8)=1-0.788=0.212$

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly, the actual volume of oil loaded into each barrel by the filling equipment at the port is approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5 gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

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".

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

$X \sim N(55,0.5)$

Where $\mu=55$ and $\sigma=0.5$

We are interested on this probability

$P(X>55.4)$

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:

$P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)$

And we can find this probability using the complement rule:

$P(Z>0.8)=1-P(Z\leq 0.8)$

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

$P(Z>0.8)=1-0.788=0.212$

8 0

3 years ago

The linear inequality y<-2/3x+2 is graphed. Determine a solution for the inequality. A) (0,2) B) (3,0) C) (0,0) D) (0,3)

jenyasd209 [6]

Hello!

The graph y < -2/3x + 2 has a dotted line. That means that any points on the dotted line or not shaded, is not a solution to this inequality. Since we are given 4 choices, we can substitute those values into the given inequality to see if it is true.

A) (0, 2)

2 < -2/3(0) + 2

2 < 2, this is false.

B) (3, 0)

0 < -2/3(3) + 2

0 < -2 + 2

0 < 0, this is false.

C) (0, 0)

0 < -2/3(0) + 2

0 < 2, this is true.

D). (0, 3)

3 < -2/3(0) + 2

3 < 2, this is false.

To check if choice C) (0, 0) is true, we should look at the given graph.

Since (0, 0) is in the shaded area, and is not graphed on the dotted line, therefore, a solution to this linear inequality is C, (0, 0).

5 0

3 years ago