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3 years ago

3 to the power 6 divided 3 to the power -2

1 answer:

8 0

First find out 3 to the power of 6 which is 729 then divide by 3 which is 243
then find out what's the power of -2 to 243 which is 0.00001693508

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Please help Find the volume of the triangular prism. I only have a few min

lawyer [7]

Answer:

18 +2 + 2.5 + 3 = 25.5

Step-by-step explanation:

just add

6 0

1 year ago

Read 2 more answers

The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by World One Research, included the question, "H

LenaWriter [7]

Answer:

A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

Step-by-step explanation:

We are given that x is normally distributed with a known standard deviation of 12.6.

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average mean response = 9 hours

$\sigma$ = population standard deviation = 12.6

n = sample of legal professionals = 250

$\mu$ = mean number of hours a legal professional works

Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $9-1.96 \times {\frac{12.6}{\sqrt{250} } }$ , $9+1.96 \times {\frac{12.6}{\sqrt{250} } }$ ]

= [7.44 hours, 10.56 hours]

Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

5 0

2 years ago

A family is trying to pick from different shades of paint for their living room. They have narrowed it down to 3 different blues

Olin [163]

To find the denominator:
3+6=9
There are 3 shades of blues so our fraction is 3/9

To get the percent you multiply 3/9×100/1=300/9
300÷9=33.33%
33.33 rounded to the nearest percent is 33%.

Your answer is 33%.

4 0

3 years ago

Read 2 more answers

The diagram shows the outline of a room. The owner has decided to make the room three times as large as it is now. How many feet

guapka [62]

Answer:

New width will be $6.807\ ft$ larger than old width.

Step-by-step explanation:

Given width of room is $9.3\ ft$

And length of room is $6.2\ ft$

Then the old area will be $(9.3\times 6.2)$

Also we have to make this room three times larger as it is now.

We can see the ratio between width and length of room is $\frac{9.3}{6.2}=1.5$

let us say the length of new room is $x$

So, width of room will be $1.5\times x$

And we know area of rectangle is $length\times width$

Also, the new area will be $3\times (9.3\times 6.2)$

Then the equation will be

$x\times 1.5\times x=3\times(9.3\times 6.2)\\1.5\times x^2=172.89\\x^2=\frac{172.89}{1.5}\\ x^2=115.32\\x=\sqrt{115.32}\\x=10.73\ ft$

So, the width of new room is

$1.5\times x=1.5\times 10.738\\width=16.107\ ft$

So, the increment in width is

$16.107-9.3=6.807\ ft$

5 0

3 years ago

Solve the system of equations: 10x+y=-18 0=5x+3y+4

Bas_tet [7]

So first you change the two equations into:
y = -18 - 10x and
-5x - 3y = 4

Then substitute y = -18 - 10x into the second equation for the y part

-5x - 3(-18 - 10x) = 4

Then simplify:

-5x + 54 + 30x = 4

Then put all the variables on one side while all the single numbers on the other:

-5x + 30x = 4 - 54

Then simplify:

25x = -50

Then divide 25 by both sides making it:

25x/25 = -50/25

Cancel out the 25’s on the left side… then your left with:

x = -50/25

so x = -2

And when you substitute x for -2 in either equation’s you get y as:

Work:

-5x - 3y = 4

-5(-2) -3y = 4

10 - 3y = 4
-10 -10

Cancel out the 10 on the left side
(since 10 -10 = 0)

Then your left with:

-3y = -6

Then divide -3 from both sides:

-3y/3 = -6/-3

The -3’s from the left side cancel out

So then y = 2 (since -6/-3 = 2)

THE ANSWER IS:

x = -2
y = 2

7 0

1 year ago