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3 years ago

Rachel runs 4 miles in 23 minutes. How many miles does she run per minute?

Mathematics

1 answer:

KIM [24]3 years ago

8 0

Answer:

To calculate how many total miles Rachel runs per minute, setting up a unit rate, that is a rate with a denominator of 1, would be helpful.

Step-by-step explanation:

Use the current problem to determine a rate.

23 minutes/4 miles

Now, set up a unit rate.

1 minute/x miles = 23 minutes/4 miles

To solve for x, we can use simple division strategies. We divide 23 by 23 to receive 1 minute. Likewise, dividing the current milage by 23 would wield the correct unit rate. To do this, divide 4 by 23.

4/23 = 0.1739130434782609

Finally, simplify your answer to receive 0.17.

Therefore, Rachel runs ~0.17 miles per minute. (Note that this answer is only a rounded answer of her actual milage per minute)

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andreyandreev [35.5K]

The series converges to 1/(1-9x) for -1/9<x<1/9

Given the series is ∑ $9x^{n} x^{n}$

We have to find the values of x for which the series converges.

We know,

∑ $ar^{n-1}$ converges to (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ $(9x)^{n}$ is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

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2 years ago

A line passes through the points (–1, –5) and (4, 5). The point (a, 1) is also on the line.

IgorC [24]

Answer:

a = 2

Step-by-step explanation:

Let's find the equation of the line using the 2 points given.

Let's call -1 as x_1 and -5 as y_1

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The equation of line is :

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Let's plug the points and get the equation of the line:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\y+5=\frac{5+5}{4+1}(x+1)\\y+5=2(x+1)\\y+5=2x+2\\y=2x-3$

Now, to find a, we substitute a in x and 1 in y of the equation of the line we just got:

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3 years ago

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3 years ago

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Anarel [89]

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3 years ago

to avoid a large shallow reef a ship set a course from point a and traveled 24 miles east to point b . the ship them turn and tr

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Next, we are going to use the Pythagorean theorem to find the distance from $a$ to $c$ :
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Finally, we are going to subtract the two distances:
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4 years ago

Rachel runs 4 miles in 23 minutes. How many miles does she run per minute?​

Rachel runs 4 miles in 23 minutes. How many miles does she run per minute?