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4 years ago

NEED HELP WITH THIS PROBLEM!!!!!!

Mathematics

1 answer:

zzz [600]4 years ago

3 0

Answer:

$\displaystyle\frac{\sqrt[4]{3x^2}}{2y}$

Step-by-step explanation:

It can work well to identify 4th powers under the radical, then remove them.

$\displaystyle\sqrt[4]{\frac{24x^6y}{128x^4y^5}}=\sqrt[4]{\frac{3x^2}{16y^4}}=\sqrt[4]{\frac{3x^2}{(2y)^4}}\\\\=\frac{\sqrt[4]{3x^2}}{2y}$

_____

The applicable rules of exponents are ...

1/a^b = a^-b

(a^b)(a^c) = a^(b+c)

The x-factors simplify as ...

x^6/x^4 = x^(6-4) = x^2

The y-factors simplify as ...

y/y^5 = 1/y^(5-1) = 1/y^4

The constant factors simplify in the usual way:

24/128 = (8·3)/(8·16) = 3/16

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In a certain population, body weights are normally distributed with a mean of 152 pounds and a standard deviation of 26 pounds.

Burka [1]

xBar ± z * sx / sqrt(n)

where xBar is the sample mean

z is the zscore for having α% of the data in the tails, i.e., P( |Z| > z) = α

sx is the sample standard deviation

n is the sample size

For sample size calcualtions we need the following. The width of the interval, from one end point to the center is:

z * sx / sqrt(n) =

w and solving for n gives:

n = (z * sx / w) ^ 2

remember that n needs to be an integer. Always take the ceiling, i.e., round up. If you round down then the width of the interval will not be correct, it will be too wide. By rounding up, the interval will be more narrow than asked for, but this is a good thing. It means there is more precision in the estimate.

here we have

z = 2.05

w = 0.04 * 152 = 6.08

n = (z * sx / w) ^ 2 n = (2.05 * 26 / 6.08)^2

n = 76.8506

Round of the answer since n must be an integer.

n = 77

7 0

4 years ago

The length of a rectangle is 2 foot less than 3 times its width. Find the the dimensions of this rectangle if the area is 96 squ

Xelga [282]

For example,area = a, length = l, width = w
First we write two equations. The easier equation is the area equation, which we know to be
a = l x w
So that the first equation is :
96 = l x w 

we make the second equation of the following statements :
The length of a rectangle is 2 foot less than 3 times its width.
so it becomes :
l = 3w - 2

To solve, we can use the substitution method.

$96 = l \times w\\96=(3w-2) \times w\\96=3w^{2}-2w\\3w^{2}-2w-96=0~~~~~~[now\ factor\ the\ equation]\\ (3w+16)(w-6)=0$

$3w+16=0\\3w=-16\\w= -\frac{16}{3}~~~~\Rightarrow~~~answer\ doesnt\ make\ sense\ , negative\ width.
$

$w-6=0\\\boxed{w=6~~~~~~~\Rightarrow~~~~positive\ answer\ for\ width\ makes\ sense }
$

So if our width is 6, Now substitute the value of w = 6 into equation 2 

$l=3w-2\\l=3(6)-2\\l=18-2\\l=16$

So "w" = 6 and "l" = 16, and if we multiply them together, we get the correct area, 96. So our dimensions are 6 by 16.

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3 years ago

4. A square court for playing the game four square has an area of 256 ft?. How long is one

shusha [124]

16ft
The square root of 256 is 16 which you square to find the area

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4 years ago

There are 10 marbles in a bag. 3 are red, 4 are blue, 2 are green, and 1 is yellow. You plan to draw 2 marbles from the bag with

schepotkina [342]

<h2>Probability that the second marble will be blue is 0.44</h2>

Step-by-step explanation:

There are 10 marbles in a bag. 3 are red, 4 are blue, 2 are green, and 1 is yellow.

Total number of marbles = 10

Given that first marble is yellow.

New total number of marbles = 10 - 1 = 9

Now we have 3 are red, 4 are blue, 2 are green.

Number of blue marbles = 4

We need to find drawing probability of blue marble from 9 marbles.

Let the probability be, p

$p=\frac{\texttt{Total blue marbles}}{\texttt{Total number of marbles}}\\\\p=\frac{4}{9}\\\\p=0.44$

Probability that the second marble will be blue is 0.44

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3 years ago

kelly lost 14.6 pounds over 4 weeks. if she lost the same each week, what was the weekly change in her weight.

Alisiya [41]

14.6 lbs/4 weeks = 3.65 lbs /week

she lost 3.65 pounds each week

6 0

3 years ago

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