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Stels [109]
2 years ago
10

The length of the rectangle is 7/(x-4) feet, while its width is 5/x feet. Find its perimeter. Please help asap!!!!! :(

Mathematics
1 answer:
damaskus [11]2 years ago
3 0

The perimeter would be (24x - 40)/(x^2 - 4x).

In order to find this, first double the length and width as you would to find any perimeter.

7/(x - 4) * 2 = 14/(x - 4)

5/x * 2 = 10/x

Now to add those together, we need to give them common denominators. In order to do that with the first one, we need to multiply by x/x

14/(x - 14) * x/x = 14x/(x^2 - 14x)

Then we can do the same with the second part by multiplying by (x - 4)/(x - 4)

10/x * (x - 4)/(x - 4) = (10x - 40)/(x^2 - 14x)

Now we can add the two together

14x/(x^2 - 14x) + (10x - 40)/(x^2 - 14x) = (24x - 40)/(x^2 - 14x)

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Exercise 11.21) Many smartphones, especially those of the LTE-enabled persuasion, have earned a bad rap for exceptionally bad ba
stiv31 [10]

Answer:

Step-by-step explanation:

Hello!

The researcher suspects that the battery life between charges for the Motorola Droid Razr Max differs if its primary use is talking or if its primary use is for internet applications.

Since the means for talk time usage (20hs) is greater than the mean for internet usage (7hs) the main question is if the variance in hours of usage is also greater when the primary use is talk time.

Be:

X₁: Battery duration between charges when the primary usage of the phone is talking. (hs)

n₁= 12

X[bar]₁= 20.50 hs

S₁²= 199.76hs² (S₁= 14.13hs)

X₂: Battery duration between charges when the primary usage of the phone is internet applications.

n₂= 10

X[bar]₂= 8.50

S₂²= 33.29hs² (S₂= 5.77hs)

Assuming that both variables have a normal distribution X₁~N(μ₁;σ₁²) and X₂~N(μ₂; σ₂²)

The parameters of interest are σ₁² and σ₂²

a) They want to test if the population variance of the duration time of the battery when the primary usage is for talking is greater than the population variance of the duration time of the battery when the primary usage is for internet applications. Symbolically: σ₁² > σ₂² or since the test to do is a variance ratio: σ₁²/σ₂² > 1

The hypotheses are:

H₀: σ₁²/σ₂² ≤ 1

H₁: σ₁²/σ₂² > 1

There is no level of significance listed so I've chosen α: 0.05

b) I've already calculated the sample standard deviations using a software, just in case I'll show you how to calculate them by hand:

S²= \frac{1}{n-1}*[∑X²-(∑X)²/n]

For the first sample:

n₁= 12; ∑X₁= 246; ∑X₁²= 7240.36

S₁²= \frac{1}{11}*[7240.36-(246)²/12]= 199.76hs²

S₁=√S₁²=√199.76= 14.1336 ≅ 14.13hs

For the second sample:

n₂= 10; ∑X₂= 85; ∑X₂²= 1022.12

S₂²= \frac{1}{9}*[1022.12-(85)²/10]= 33.2911hs²

S₂=√S₂²=√33.2911= 5.7698 ≅ 5.77hs

c)

For this hypothesis test, the statistic to use is a Snedecors F:

F= \frac{S_1^2}{S_2^2} *\frac{Sigma_1^2}{Sigma_2^2} ~~F_{n_1-1;n_2-1}

This test is one-tailed right, wich means that you'll reject the null hypothesis to big values of F:

F_{n_1-1;n_2-1; 1-\alpha }= F_{11;9;0.95}= 3.10

The rejection region is then F ≥ 3.10

F_{H_0}= \frac{199.76}{33.29} * 1= 6.0006

p-value: 0.006

Considering that the p-value is less than the level of significance, the decision is to reject the null hypothesis.

Then at a 5% level, there is significant evidence to conclude that the population variance of the duration time of the batteries of Motorola Droid Razr Max smartphones used primary for talk is greater than the population variance of the duration time of the batteries of Motorola Droid Razr Max smartphones used primary for internet applications.

I hope this helps!

8 0
2 years ago
84. Use properties of exponents to rewrite each expression with only positive, rational exponents. Then find the numerical value
Yakvenalex [24]

Answer:

a) 1/27

b) 16

c) 1/8

Step-by-step explanation:

a) x^{-3/2}

One of the properties of the exponents tells us that when we have a negative exponent we can express it in terms of its positive exponent by turning it into the denominator (and changing its sign), so we would have:

x^{-3/2}=\frac{1}{x^{3/2} }

And now, solving for x = 9 we have:

\frac{1}{x^{3/2}}=\frac{1}{9^{3/2} }  =\frac{1}{27}

b) y^{4/3}

This is already a positive rational exponent so we are just going to substitute the value of y = 8 into the expression

y^{4/3}=8^{4/3}=16

c) z^{-3/4}

Using the same property we used in a) we have:

z^{-3/4}=\frac{1}{z^{3/4} }

And now, solving for z = 16 we have:

\frac{1}{z^3/4} } =\frac{1}{16^{3/4} } =\frac{1}{8}

4 0
3 years ago
Simple math, please help, have to turn in soon
mezya [45]

Answer:1

Step-by-step explanation:

8 0
3 years ago
6) (after 2.3) Consider the infinite system of linear equations in two variables given by ax + by = 0 where (a, b) moves along t
Paraphin [41]

Answer:

Step-by-step explanation:

Given infinite system of linear equations is ax + by = 0

when (a,b) moves along unit circle in plane.

a) system having unique system (0, 0)

Since two of equation in thus system will be

1.x+0.y=0\\x=0

and

0.x+1.y=0\\y=0

It is clear that x = 0, y= 0 is the only solution

b) Linear independent solution in this system gives some set of solutions

1.x+0.y=0\\\x=0

and

0.x+1.y=0\\y=0

Vector form is

\left[\begin{array}{ccc}1&0\\0&1\end{array}\right] =I

c) for this equation if add 0x +0y = 0 to system , Nothing will change

Because [0,0] satisfies that equation

d) If one of the equation is ax + by = 0.00001

where 0.00001 is small positive number

so, the system will be inconsistent

Therefore, the system will have no solution.

6 0
3 years ago
What is the value of r?
s2008m [1.1K]

Answer:

Since opposite sides of parallelogram are equal therefore

9r-6=8r+3

r=9

EF=4r+19{opposite sides of parallelogram are equal}

=4×9+19

36+19

=55

Here is you answer.

Step-by-step explanation:

5 0
3 years ago
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