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2 years ago

Multiply and simplify.

Mathematics

1 answer:

dem82 [27]2 years ago

3 0

Answer:
48x-112

Explanation:
(3x-7)8•2
(3x-7)•16
48x-112

I hope this helps!

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Is he square root of -144 rational or irrational?

gladu [14]

Answer:

Step-by-step explanation:

Neither.

It is a complex number. The - sign is the culprit. sqrt(-144) = i * sqrt(144) = 12 i

The "i" is an imaginary representation for the square root of -1. It is a definition for sqrt(-1). So a new category of number has been created. The ancients would have been profoundly surprised to learn that such a thing existed.

3 0

2 years ago

A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent year of data

Rasek [7]

Answer: a. 1.981 < μ < 2.18

b. Yes.

Step-by-step explanation:

A. For this sample, we will use t-distribution because we're estimating the standard deviation, i.e., we are calculating the standard deviation, and the sample is small, n = 12.

First, we calculate mean of the sample:

$\overline{x}=\frac{\Sigma x}{n}$

$\overline{x}=\frac{2.31=2.09+...+1.97+2.02}{12}$

$\overline{x}=$ 2.08

Now, we estimate standard deviation:

$s=\sqrt{\frac{\Sigma (x-\overline{x})^{2}}{n-1} }$

$s=\sqrt{\frac{(2.31-2.08)^{2}+...+(2.02-2.08)^{2}}{11} }$

s = 0.1564

For t-score, we need to determine degree of freedom and $\frac{\alpha}{2}$ :

df = 12 - 1

df = 11

$\alpha$ = 1 - 0.95

α = 0.05

$\frac{\alpha}{2}=$ 0.025

Then, t-score is

$t_{11,0.025}$ = 2.201

The interval will be

$\overline{x}$ ± $t.\frac{s}{\sqrt{n} }$

2.08 ± $2.201\frac{0.1564}{\sqrt{12} }$

2.08 ± 0.099

The 95% two-sided CI on the mean is 1.981 < μ < 2.18.

B. We are 95% confident that the true population mean for this clinic is between 1.981 and 2.18. Since the mean number performed by all clinics has been 1.95, and this mean is less than the interval, there is evidence that this particular clinic performs more scans than the overall system average.

8 0

3 years ago

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 8x7 – x5 + x3+6

valentina_108 [34]

According to the Fundamental Theorem of Algebra, the number of roots of a polynomial is equal to the degree of the polynomial. The degree of the polynomial is the highest exponent of a term in the polynomial.
Looking at the function, the term with the highest exponent is 8x7. The exponent is 7; therefore, the function has 7 roots.

7 0

3 years ago

Read 2 more answers

Help me plsssssssszzzzzzzzzzzzzzzzz

katen-ka-za [31]

Answer:

750 < p < 1500

Step-by-step explanation:

The total cost of the affair for p attendees is ...

750 +2.25p

The average cost is that number divided by p. The answer choices suggest that "between" means that the cost per person cannot be 2.75 or 3.25. Applying the limits to the average cost, we get ...

2.75 < (750 +2.25p)/p < 3.25

2.75 < 750/p + 2.25 < 3.25 . . . . . . . . separating the fraction parts

0.50 < 750/p < 1.00 . . . . . . . . . . . . . . subtract 2.25

2 > p/750 > 1 . . . . . . . . . . . . . . . . . . . . . take the reciprocal*

1500 > p > 750 . . . . . . . . matches choice 4

_____

* Taking the reciprocals of numbers with the same sign reverses their order:

2 < 3 but 1/2 > 1/3

An alternate approach to the solution would be to multiply by p:

0.50p < 750 < 1.00p

To solve this requires it be made into two inequalities:

0.50p < 750 ⇒ p < 1500

and

750 < 1.00p ⇒ 750 < p

Then these would need to be recombined to form the answer:

750 < p < 1500

8 0

2 years ago

I got a feeling I’m wrong

Sunny_sXe [5.5K]

Answer:

You are absolutely correct.

Step-by-step explanation:Equilateral, meaning all sides are the same size, and acute, meaning all angles are lower than 90 degrees. You are correct.

8 0

3 years ago

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