All categories

3 years ago

Select the correct answer.

Mathematics

1 answer:

ratelena [41]3 years ago

5 0

Answer:

A. $x(x+12) -7(x+12)$

Step-by-step explanation:

Factoring is the process of taking common terms out of an expression such that one can represent the expression as the result of smaller values. When given the following expression:

$x^2 +5x - 84$

First, represent the linear term as the sum of two terms such that each term shares a common factor with the other terms in the expression.

$x^2 +12x - 7x - 84$

Now take out the common factors,

$x(x+12) -7(x+12)$

Thus, the correct option is choice (A).

You might be interested in

$5,000 is invested in two different accounts yielding 3% and 3.5% interest. The interest earned on the two accounts is $155. Let

Artist 52 [7]

I am almost sure it is A

hope this helps (;

3 0

3 years ago

Read 2 more answers

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

KatRina [158]

Answer:

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.

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

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

3 years ago

Glenda and Fiero are at a restaurant eating meal that costs $30. They have a discount coupon that gets them 10% off the cost. If

yaroslaw [1]

The cost of meal = $$30$

The tip to the waiter = $8%$ %

Discount = $10%$ %

Cost = $30 + 0.08 * 30 - 0.1 * 30$

Cost = $30(1 + 0.08 - 0.1)$

Cost = $ $$29.4$ 0

8 0

2 years ago

2<br> .<br> 2<br> 12n = 42<br> NEED HELP ASAP⬆️

Anni [7]

Answer:

—————

n + 8

Step-by-step explanation:

Step by Step Solution:

More Icon

STEP

Equation at the end of step 1

((12•(n3))-(24•(n2))) (12n-42)

—————————————————————•———————————————————

(((4•(n2))-22n)+28) ((6•(n3))+(24•3n2))

STEP

Equation at the end of step

((12•(n3))-(24•(n2))) (12n-42)

—————————————————————•——————————————————

(((4•(n2))-22n)+28) ((2•3n3)+(24•3n2))

STEP

12n - 42

Simplify ——————————

6n3 + 48n2

STEP

Pulling out like terms

4.1 Pull out like factors :

12n - 42 = 6 • (2n - 7)

STEP

Pulling out like terms

5.1 Pull out like factors :

6n3 + 48n2 = 6n2 • (n + 8)

Equation at the end of step

((12•(n3))-(24•(n2))) (2n-7)

—————————————————————•————————

(((4•(n2))-22n)+28) n2•(n+8)

STEP

Equation at the end of step

((12•(n3))-(24•(n2))) (2n-7)

—————————————————————•————————

((22n2-22n)+28) n2•(n+8)

STEP

Equation at the end of step

((12•(n3))-(23•3n2)) (2n-7)

————————————————————•————————

(4n2-22n+28) n2•(n+8)

STEP

Equation at the end of step

((22•3n3) - (23•3n2)) (2n - 7)

————————————————————— • ————————————

(4n2 - 22n + 28) n2 • (n + 8)

STEP

12n3 - 24n2

Simplify ——————————————

4n2 - 22n + 28

STEP

Pulling out like terms

10.1 Pull out like factors :

12n3 - 24n2 = 12n2 • (n - 2)

STEP

Pulling out like terms

11.1 Pull out like factors :

4n2 - 22n + 28 = 2 • (2n2 - 11n + 14)

Trying to factor by splitting the middle term

11.2 Factoring 2n2 - 11n + 14

The first term is, 2n2 its coefficient is 2 .

The middle term is, -11n its coefficient is -11 .

The last term, "the constant", is +14

Step-1 : Multiply the coefficient of the first term by the constant 2 • 14 = 28

Step-2 : Find two factors of 28 whose sum equals the coefficient of the middle term, which is -11 .

-28 + -1 = -29

-14 + -2 = -16

-7 + -4 = -11 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -4

2n2 - 7n - 4n - 14

Step-4 : Add up the first 2 terms, pulling out like factors :

n • (2n-7)

Add up the last 2 terms, pulling out common factors :

2 • (2n-7)

Step-5 : Add up the four terms of step 4 :

(n-2) • (2n-7)

Which is the desired factorization

Canceling Out :

11.3 Cancel out (n-2) which appears on both sides of the fraction line.

Equation at the end of step

6n2 (2n - 7)

—————— • ————————————

2n - 7 n2 • (n + 8)

STEP

Canceling Out

12.1 Cancel out (2n-7) which appears on both sides of the fraction line.

Canceling Out :

12.2 Canceling out n2 as it appears on both sides of the fraction line

Final result :

—————

n + 8

8 0

4 years ago

What is the Mean of this question I need the answer ASAP

o-na [289]

Pretty sure the mean is 5

5 0

4 years ago