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3 years ago

What is the range of the data set

Mathematics

1 answer:

Vinil7 [7]3 years ago

3 0

The data set isn’t there

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Solve the following and explain your steps. Leave your answer in base-exponent form. (3^-2*4^-5*5^0)^-3*(4^-4/3^3)*3^3 please st

Naily [24]

Answer:

$\boxed{2^{\frac{802}{27}} \cdot 3^9}$

Step-by-step explanation:

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$(3^{-2} \cdot 4^{-5} \cdot 5^0)^{-3} \cdot (4^{-\frac{4}{3^3} })\cdot 3^3$

Note that

$\boxed{a^{-b} = \dfrac{1}{a^b}, a\neq 0 }$

The denominator can't be 0 because it would be undefined.

So, we can solve the expression inside both parentheses.

$\left(\dfrac{1}{3^2} \cdot \dfrac{1}{4^5} \cdot 5^0 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{3^3} } }\right)\cdot 3^3$

Also,

$\boxed{a^{0} = 1, a\neq 0 }$

$\left(\dfrac{1}{9} \cdot \dfrac{1}{1024} \cdot 1 \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27$

Note

$\boxed{\dfrac{1}{a} \cdot \dfrac{1}{b}= \frac{1}{ab} , a, b \neq 0}$

$\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{1}{4^{\frac{4}{27} } }\right)\cdot 27$

$\left(\dfrac{1}{9216} \right)^{-3} \cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)$

$\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)$

$\left( \dfrac{1}{\left(\dfrac{1}{9216}\right)^3} \right)\cdot \left(\dfrac{27}{4^{\frac{4}{27} } }\right)$

Note

$\boxed{\dfrac{1}{\dfrac{1}{a} } = a}$

$9216^3\cdot \left(\dfrac{27}{4^{\frac{4}{9} } }\right)$

$\left(\dfrac{ 9216^3\cdot 27}{4^{\frac{4}{27} } }\right)$

Once

$9216=2^{10}\cdot 3^2 \implies 9216^3=2^{30}\cdot 3^6$

$\boxed{(a \cdot b)^n=a^n \cdot b^n}$

And

$4^{\frac{4}{27}} = 2^{\frac{8}{27}$

We have

$\left(\dfrac{ 2^{30} \cdot 3^6\cdot 27}{2^{\frac{8}{27} } }\right)$

Also, once

$\boxed{\dfrac{c^a}{c^b}=c^{a-b}}$

$2^{30-\frac{8}{27}} \cdot 3^6\cdot 27$

$30-\dfrac{8}{27} = \dfrac{30 \cdot 27}{27}-\dfrac{8}{27} =\dfrac{802}{27}$

$2^{30-\frac{8}{27}} \cdot 3^6\cdot 27 = 2^{\frac{802}{27}} \cdot 3^6 \cdot 3^3$

$2^{\frac{802}{27}} \cdot 3^9$

4 0

2 years ago

Katie earns $8 per hour at her paint job. Her boss gives her a raise of 15%. What is Katie’s hourly wage after her raise? How mu

kodGreya [7K]

Answer: $9.20 hourly 230 dollars for 25 hour work week

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Wiat number should be added to both sides of the equation to complete the square? X^2+x=11

Ivahew [28]

Answer:

add 1/4 to each side

Step-by-step explanation:

x^2+x=11

We take the coefficient of the x term

Then divide it by 2

1/2

Then square it

(1/2) ^2 = 1/4

Add this to both sides of the equation

x^2 + x + 1/4 = 11+1/4

(x+1/2)^2 = 11 1/4

7 0

3 years ago

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A student says that a correlation coefficient of −0.93 indicates that the two quantities of a data set have a weak correlation.

zloy xaker [14]

Answer:

Step-by-step explanation:

Recall that correlation coefficients range from -1 to +1. So, -0.93 is a strong negative relationship. Two interpretations: 1) the correlation is actually very strong, and 2) the correlation is negative. When the correlation is negative, the dependent variable DECREASES when the independent variable INCREASES.

8 0

2 years ago

Why does the fact family for 81 and 9 have only two number sentences

Julli [10]

It only has two number sentences because 81 divided by anything else wont work only 9 would. Also since 9 times 9 is equal to 81

8 0

2 years ago

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