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Pavlova-9 [17]
3 years ago
13

Describe how you would use the rules of exponents to simplify (7x?yz) 3. You may indicate an exponent in your answer with ^. For

Mathematics
1 answer:
SVETLANKA909090 [29]3 years ago
5 0

Answer:

343x^6y^3z^3

Step-by-step explanation:

One of the rules of exponents demands:

(abc)^m=a^mb^mc^m

where a, b, c and m are coefficients.

Furthermore, you use the following rule for exponents of variables that already have an exponent:

(a^n)^m=a^{m*n}

Thus, you can apply this rules in the following way:

(7x^2yz)^3=(7)^3(x^2)^3(y)^3(z)^3=7*7*7x^{2*3}y^3z^3=343x^6y^3z^3

hence, the answer is 343x^6y^3z^3

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Choose the correct answer below.
Bumek [7]

Answer:

B. Descriptive statistics describes sets of data. Inferential statistics draws conclusions about the sets of data based on sampling.

Step-by-step explanation:

Let's explain on why the others are not,

A. Descriptive statistics is a characteristic or property of an individual experimental unit. Inferential statistics is the process used to assign numbers to variables of individual population units.

Descriptive statistics needs a set of data, not just an individual experimental unit, since it uses statistical methods like tendency, mean, median, mode, dispersion ranges, deviation, etc. That cannot be gathered from an individual set unit. In the same way, Inferential statistics, is about using a sample of data to infer, as the name says, behavior of larger groups, it doesn't assign numbers or variables, it studies behavior of samples, that being said, a variable might be "assigned" by testing an hypothesis, yet not from an unit, but from a set.

C. Descriptive statistics draws conclusions about the sets of data based on sampling. Inferential statistics summarizes the information revealed in data sets.

It is the complete oposite, Descriptive Statistics (DS), studies data to represent numerical analysis in charts and graphs, but not samples. While Inferential Statistics (IS), is about samples, and how they COULD represent a larger group.

D. Descriptive statistics are measurements that are recorded on a naturally occurring numerical scale. Inferential statistics are measurements that cannot be measured on a natural number​ scale; they can only be classified into one of a group of categories.

In IS, its not that the measurements cannot be measured on a natural number scale, it is that the size of the date is too large, so it needs to be broken down in order to be studied, it can have several categories but a smaller data set (thus a sample)

5 0
3 years ago
Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 14 small cakes per hour. The kitchen i
PolarNik [594]

Answer:

8

Step-by-step explanation:

In 2 hours

1 cook makes 10 large cakes

24/10 = 2.4

You need 3 cooks to make the large cakes.

In 2 hours

1 cook makes 28 small cakes

130/28 = 4.64

You need 5 cooks to make the small cakes.

3 + 5 = 8

Answer: 8

5 0
3 years ago
Determine whether Rolle's Theorem can be applied to f(x)=(x-1) (x-2)(x-3) on the closed interval [1,3]. Of Rolle's Theorem can b
NeX [460]

Answer:56

Step-by-step explanation:

6 0
3 years ago
Find all the solutions for the equation:
Contact [7]

2y^2\,\mathrm dx-(x+y)^2\,\mathrm dy=0

Divide both sides by x^2\,\mathrm dx to get

2\left(\dfrac yx\right)^2-\left(1+\dfrac yx\right)^2\dfrac{\mathrm dy}{\mathrm dx}=0

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2\left(\frac yx\right)^2}{\left(1+\frac yx\right)^2}

Substitute v(x)=\dfrac{y(x)}x, so that \dfrac{\mathrm dv(x)}{\mathrm dx}=\dfrac{x\frac{\mathrm dy(x)}{\mathrm dx}-y(x)}{x^2}. Then

x\dfrac{\mathrm dv}{\mathrm dx}+v=\dfrac{2v^2}{(1+v)^2}

x\dfrac{\mathrm dv}{\mathrm dx}=\dfrac{2v^2-v(1+v)^2}{(1+v)^2}

x\dfrac{\mathrm dv}{\mathrm dx}=-\dfrac{v(1+v^2)}{(1+v)^2}

The remaining ODE is separable. Separating the variables gives

\dfrac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=-\dfrac{\mathrm dx}x

Integrate both sides. On the left, split up the integrand into partial fractions.

\dfrac{(1+v)^2}{v(1+v^2)}=\dfrac{v^2+2v+1}{v(v^2+1)}=\dfrac av+\dfrac{bv+c}{v^2+1}

\implies v^2+2v+1=a(v^2+1)+(bv+c)v

\implies v^2+2v+1=(a+b)v^2+cv+a

\implies a=1,b=0,c=2

Then

\displaystyle\int\frac{(1+v)^2}{v(1+v^2)}\,\mathrm dv=\int\left(\frac1v+\frac2{v^2+1}\right)\,\mathrm dv=\ln|v|+2\tan^{-1}v

On the right, we have

\displaystyle-\int\frac{\mathrm dx}x=-\ln|x|+C

Solving for v(x) explicitly is unlikely to succeed, so we leave the solution in implicit form,

\ln|v(x)|+2\tan^{-1}v(x)=-\ln|x|+C

and finally solve in terms of y(x) by replacing v(x)=\dfrac{y(x)}x:

\ln\left|\frac{y(x)}x\right|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C

\ln|y(x)|-\ln|x|+2\tan^{-1}\dfrac{y(x)}x=-\ln|x|+C

\boxed{\ln|y(x)|+2\tan^{-1}\dfrac{y(x)}x=C}

7 0
3 years ago
Jeremy swims 5 3/5 kilometers in a 7 day period. He swims the same distance each day. What distance does he swim?
PIT_PIT [208]
Since 5 3/5 can be turned into 28/5, then divided by 7/1, you will get 4/5. So Jeremy swims 4/5 of a kilometer each day.
4 0
3 years ago
Read 2 more answers
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