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svet-max [94.6K]

3 years ago

6

Mason is driving on a long road trip. He currently has 12 gallons of gas in his car. Each hour that he drives, his car uses up 1

.5 gallons of gas. How much gas would be in the tank after driving for 2 hours? How much gas would be left after tt hours?

1 answer:

egoroff_w [7]3 years ago

6 0

After 2 hours it should have 9 gallons of gas left

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Prove or disprove that the point (3, 2) lies on the circle centered at (-1. -1) and containing the point (4,-1)

melisa1 [442]

Need a picture of the plot

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3 years ago

Choose the statement that best describes a solution of a system of linear inequalities.(1 point)

yan [13]

Answer: A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.

Step-by-step explanation:

A system of linear inequalities can be written as:

y < a*x + b

y < c*x + d

or

y ≤ a*x + b

y ≤ c*x + d

In the first case, the borders are not included in the solutions, and in the second case, the borders are included.

Where the solutions will be points like (x, y), where these points must be solutions for both inequalities.

Then the only option that is correct for a general system of inequalities is:

A solution of a system of linear inequalities is an ordered pair that satisfies each inequality in the system.

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3 years ago

What is the volume of this rectangular prism?

nika2105 [10]

Answer:

The volume of this rectangular prism is D. 60 $cm^{3}$ .

Step-by-step explanation:

In order to find the volume of a rectangular prism, we need to multiply the length by the width, and then multiply their product by the height of the prism. We can write what I said above as a formula...

V = l × w × h

(In the formula above "V" is the volume, "l" is the length, "w" is the width, and "h" is the height).

Now we just substitute the values into the formula and we get...

V = l × w × h

V = 4cm × 3cm × 5cm

V = 60 $cm^{3}$

Therefore, the volume of this rectangular prism is D. 60 $cm^{3}$ .

6 0

3 years ago

Identify each point as a solution of the system or not a solution of the system.

lubasha [3.4K]

Answer:

see below

Step-by-step explanation:

Plot the points on the given graph. The ones that fall in on a solid line at the edge of the doubly-shaded area, or fall in the doubly-shaded area, are part of the solution set.

(0, 4) on the dashed line — not a solution

(-2, 4) on red line in blue area — solution

(0, 5) in doubly-shaded area — solution

(–2, 7) in doubly-shaded area — solution

(–4, 1) in blue area — not a solution

(–1, 1) on red line outside blue area — not a solution

(–1.5, 3.5) in doubly-shaded area — solution

6 0

3 years ago

The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 ye

trasher [3.6K]

Answer:

66.98% probability that the mean gain for the sample was between 250 and 500.

Step-by-step explanation:

To solve this problem, it is important to know the Normal probability distribution and the Central limit theorem.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 432, \sigma = 722, n = 40, s = \frac{722}{\sqrt{40}} = 114.16$

What is the probability that the mean gain for the sample was between 250 and 500?

This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 250.

So

X = 500

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{500 - 432}{114.16}$

$Z = 0.6$

$Z = 0.6$ has a pvalue of 0.7257.

X = 250

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{250 - 432}{114.16}$

$Z = -1.59$

$Z = -1.59$ has a pvalue of 0.0559.

So there is a 0.7257 - 0.0559 = 0.6698 = 66.98% probability that the mean gain for the sample was between 250 and 500.

8 0

3 years ago