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3 years ago

Which expression is equivalent to?????

Mathematics

2 answers:

Ket [755]3 years ago

8 0

I will do it step by step
(3xy^-5)^3= 27x^3y^-15
(x^-2y^2)^-4= x^8y-8
So the fraction is (27x^3y^-15)/ x^8 y^8= 27 x^-5y^-7
and the whole thing to power of -2 equals to x^10y^14/ 729
answer is A

qwelly [4]3 years ago

7 0

Your first choice is the correct answer and I am 100% sure.

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A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups

HACTEHA [7]

Answer: b. 8.56 to 21.44

Step-by-step explanation:

Let $\mu$ be the mean number of pushups that can be done.

As per given , we have

Sample size : n= 10

Degree of freedom = n-1=9

Sample mean : $\overline{x}=15$

Sample standard deviation : $s=9$

Significance level : α=1-0.95=0.05

From t- distribution table ,

Critical two -tailed t-value for α=0.05 and df = 9 is

$t_{\alpha/2, 9}=t_{0.025,9}=2.2622$

Confidence interval for $\mu$ is given by :-

$\overline{x}\pm t*\dfrac{s}{\sqrt{n}}$

$=15\pm (2.2622)\dfrac{9}{\sqrt{10}}\\\\\approx 15\pm 6.44=(15-6.44,\ 15+6.44)\\\\=(8.56,\ 21.44)$

Hence, the 95% confidence interval for the true mean number of pushups that can be done is 8.56 to 21.44.

5 0

3 years ago

Calculate 1.6 ∙ 103 times 3.0 ∙ 10-6. (Box after the "10" in answer is for the exponent.)

Nutka1998 [239]

(1.6 * 10^3) * (3.0 * 10^-6) =
(1.6 * 3.0) * (10^3 * 10^-6)
4.8 * 10^(3 - 6) =
4.8 * 10^-3 =
4.8 * 1/10^3 =
4.8 / 10^3 =
4.8 / 1000 =
0.0048 <==

7 0

3 years ago

Read 2 more answers

Determine the center and radius of the following circle equation:<br> x2 + y2 – 10x + 8y + 40 = 0

antiseptic1488 [7]

Answer:

The center of this circle is (5, -4) and the radius is 1.

Step-by-step explanation:

First regroup these terms according to x and y :

x^2 - 10x + y^2 + 8y = -40

Next, complete the square for x^2 - 10x: x^2 - 10x + 5^2 - 5^2.

and the same for y^2 + 8y: y^2 + 8y + 16 - 16

Substituting these results into x^2 - 10x + y^2 + 8y = -40, we get:

x^2 - 10x + 5^2 - 5^2 y^2 + 8y + 16 - 16 = -40.

Next, rewrite x^2 - 10x + 25 and y^2 + 8y + 16 as squares of binomials:

Then x^2 - 10x + 5^2 - 5^2 y^2 + 8y + 16 - 16 = -40 becomes:

(x - 5)^2 + (y + 4)^2 - 25 - 16 = -40, or:

(x - 5)^2 + (y + 4)^2 = 1

This equation has the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius. Matching like terms, we get h = 5, k = -4 and r = 1.

The center of this circle is (5, -4) and the radius is 1.

6 0

3 years ago

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Stacy fails 1/2 cup measuring cup seven times to have enough flour for cake recipe how much flour does the cake recipe call for

Gala2k [10]

7 times of 1/2 cup = 7 x 1/2
7 times of 1/2 cup = 7/2
7 times of 1/2 cup = 3 1/2 cups.

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The recipe called for 3 1/2 cups of flour
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3 0

3 years ago

Find the slope between these two points: (3, -10) and (-2, -30). Show all of your work. what the answer

Harlamova29_29 [7]

$\huge\text{$m=\boxed{4}$}$

Hey there! Start with the slope formula, where $(x_1,y_1)$ and $(x_2,y_2)$ are the two known points.

$\begin{aligned}m&=\dfrac{y_2-y_1}{x_2-x_1}\\&=\frac{-30-(-10)}{-2-3}\end{aligned}$

Simplify.

$\begin{array}{c|l}\textbf{Solving}&\textbf{Reason}\\\cline{1-2}\\m=\dfrac{-30+10}{-2-3}&x-(-y)=x+y\\\\m=\dfrac{-20}{-5}&\text{Addition and subtraction}\\\\m=\dfrac{20}{5}&\text{The negatives cancel out}\\\\m=\dfrac{4}{1}&\text{Divide the numerator and denominator by $5$}\\\\m=\boxed{4}&\dfrac{x}{1}=x\end{aligned}$

3 0

3 years ago

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