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3 years ago

Why is cube root of 9 equal to 9 to the one third power question mark

Mathematics

2 answers:

alexira [117]3 years ago

7 0

Answer:

See below

Step-by-step explanation:

$\sqrt[3]{9}=9^{\frac{1}{3}}$

$(\sqrt[3]{9})^3=(9^{\frac{1}{3}})^3$

$9=9^{\frac{1}{3}*3$

$9=9^\frac{3}{3}$

$9=9^1$

$9=9$

Remember that $(a^b)^c=a^{b*c}$

kozerog [31]3 years ago

3 0

Answer:

just because

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10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.

erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

$p = \frac{4}{6} = 0.6667$

10 normal six sided dice are thrown.

This means that $n = 10$

Find the probability of obtaining at least 8 failures.

This is:

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951$

$P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867$

$P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174$

Then

$P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992$

0.2992 = 29.92% probability of obtaining at least 8 failures.

8 0

3 years ago

Find the measurement of each segment.

zavuch27 [327]

To find the measurement of PS, you would add the lengths of PQ and PS. 18.4+4.7=23.1. The answer is 23.1 cm

6 0

4 years ago

Line L has equation y = 4x - 7, and line M is parallel to line L and passes through the point (2, 15). Determine the equation of

Artist 52 [7]

Answer:

A: y = 4x + 7

Step-by-step explanation:

Step 1: Our line is parallel to this line, so it has the same slope, but a different y-intercept, so set up the equation...

y = 4x + b

We are given a point (x, y) of (2, 15), so plug that in and solve for b.

15 = 4(2) + b

15 = 8 + b (simplify)

7 = b (subtract 8 from both sides to isolate b)

So the equation of our line is y = 4x + 7

3 0

3 years ago

Simplify the expression x8 y-26/x14 y-5 X x-39 y-21.

KonstantinChe [14]

$\frac{x^8y^{-26}}{x^{14}y^{-5}}[x^{-36}y^{-21}]$

We will apply these following power rule

$x^m*x^n = x^{m+n}$
$x^m/x^n=x^{m-n}$

$[ \frac{x^8}{x^{14}}][ \frac{y^{-26}}{y^{-5}}][x^{-39}y^{-21}]$
$[x^{8-14}][y^{-26-5}][x^{-39}y^{-21}]$
$x^{-6}y^{-21}[x^{-39}y^{-21}]$
$[x^{-6-39}][y^{-21-21}]$
$x^{-45}y^{-42}$

8 0

4 years ago

Danny rented a truck for one day. There was a base fee of $15.99, and there was an additional charge of 92 cents for each mile d

Kitty [74]

Answer:

194 miles

Step-by-step explanation:

The base fee of $15.99 is going to have to be paid, whether any miles are put on the truck or not. If the number of miles driven is our unknown, if we rent the truck for the base fee of $15.99 and drive it 0 miles, we still have to pay the $15.99. If we do drive it and we have to pay .92 a mile, the expression for that is .92x, where x is the number of miles driven (it is also the variable we are solving for!). The expression for this total cost is .92x + 15.99, and since we paid a total of $194.47, we set our cost equation equal to that number and solve for x:

.92x + 15.99 = 194.47 and

.92x = 178.48 so

x = 194 miles driven

5 0

3 years ago