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3 years ago

In n + 10 =40, then what is the value of the expression n - 25?

Mathematics

2 answers:

damaskus [11]3 years ago

8 0

Find n first.

n+10= 40

Subtract 10.

n= 30

Plug in n.

30-25= 5

The answer is 5.

I hope this helps!
~cupcake

andriy [413]3 years ago

5 0

N + 10 = 40
n = 30
30 - 25 = x
5 = x

n = 30
x = 5

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2 years ago

The resting heart rate for an adult horse should average about µ = 47 beats per minute with a (95% of data) range from 19 to 75

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a. 0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. 0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

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Step-by-step explanation:

Empirical Rule:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

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.

Mean:

$\mu = 47$

(95% of data) range from 19 to 75 beats per minute.

This means that between 19 and 75, by the Empirical Rule, there are 4 standard deviations. So

$4\sigma = 75 - 19$

$4\sigma = 56$

$\sigma = \frac{56}{4} = 14$

a. What is the probability that the heart rate is less than 25 beats per minute?

This is the p-value of Z when X = 25. So

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

$Z = \frac{25 - 47}{14}$

$Z = -1.57$

$Z = -1.57$ has a p-value of 0.0582.

0.0582 = 5.82% probability that the heart rate is less than 25 beats per minute.

b. What is the probability that the heart rate is greater than 60 beats per minute?

This is 1 subtracted by the p-value of Z when X = 60. So

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

$Z = \frac{60 - 47}{14}$

$Z = 0.93$

$Z = 0.93$ has a p-value of 0.8238.

1 - 0.8238 = 0.1762

0.1762 = 17.62% probability that the heart rate is greater than 60 beats per minute.

c. What is the probability that the heart rate is between 25 and 60 beats per minute?

This is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 25. From the previous two items, we have these two p-values. So

0.8238 - 0.0582 = 0.7656

0.7656 = 76.56% probability that the heart rate is between 25 and 60 beats per minute

3 0

2 years ago

Find the equation of a line passing through points (-7, -10) , (-5, -20)

LuckyWell [14K]

You want to find the equation for a line that passes through the two points:

(-7,-10) and (-5,-20).

First of all, remember what the equation of a line is:

y = mx+b

here, m is the slope, b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through.

Consider (-7,-10) as point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-7 and y1=-10.

Consider (-5,-20), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-5 and y2=-20.

Now, just plug the numbers into the formula for m above, like this:

m= (-20 - -10)/(-5 - -7)

m= -10/2

m=-5

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=-5x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(-7,-10). When x of the line is -7, y of the line must be -10.

(-5,-20). When x of the line is -5, y of the line must be -20.

Because line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-5x+b. b is what we want, the -5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the two points (-7,-10) and (-5,-20).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want.The answer will be the same:

(-7,-10). y=mx+b or -10=-5 × -7+b, or solving for b: b=-10-(-5)(-7). b=-45.

(-5,-20). y=mx+b or -20=-5 × -5+b, or solving for b: b=-20-(-5)(-5). b=-45.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points (-7,-10) and (-5,-20) is y=-5x-45.

8 0

3 years ago