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3 years ago

HELP ASAP

Mathematics

2 answers:

Aleks04 [339]3 years ago

8 0

Answer:

Answer: y - 37.5 = 2.5 ( x - 7)

Explanation:

1) The point-slope form is has this form:

y - y1 = m (x - x1)

Where m is the slope or rate of change and x1, y1 are the coordinates of the point.

2) you are told that the the rate of change of water (m) is 2.5

m = 2.5

3) The point is given by that after 7 min the rain barrel contains 37.5 gallons. This is:

x1 = 7

y1 = 37.5

4) Replace those value in the point-slope model:

y - 37.5 = 2.5 ( x - 7)

That is the point-slope model or equation.

Step-by-step explanation:

Solnce55 [7]3 years ago

5 0

So, first let's refill the barrel to the top:
37.5 + 7*2.5 = 55
Now that it's full again, let's divide the total amount by the rate of water loss:
55/2.5 = 22
It will take 22 minutes to completely empty the rain barrel

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3 years ago

2. In factored form, a quadratic function can be written as y= (-2- x) (x-8). This parabola goes through the points (-2, 0) and

Trava [24]

The vertex of the given parabola is the point (3, 25).

<h3>How to get the vertex of the parabola?</h3>

If the parabola has roots x₁ and x₂, then the vertex of the parabola is at:

xₙ = (x₁ + x₂)/2

Here the parabola is:

y = (-2 - x)*(x - 8)

We can rewrite that to:

y = -(x + 2)*(x - 8)

Then the two roots are:

x = -2 and x = 8

Then the vertex is at:

xₙ = (8 - 2)/2 = 6/2 = 3

To get the y-value of the vertex, we evaluate the equation in x = 3:

y = -(3+ 2)*(3 - 8) = -5*(-5) = 25

The vertex is (3, 25).

If you want to learn more about parabolas:

brainly.com/question/4061870

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2 years ago

Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean’s weekly income

Sauron [17]

Answer:

d. 0.303

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

In this question:

We want the probability of Sean having a greater income than Evan, which is the probability of the subtraction of Sean's income by Evan's income is greater than 0.

Distribution of the difference between Sean's and Evan's income:

Sean has mean 225, Evan 240. So

$\mu = 225 - 240 = -15$