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4 years ago

Y=6x^-4, if x is halved what happens to y?

1 answer:

5 0

X^-m=1/(x^m)
y=6/(x^4) is the equation
if x is halves
replace x with x/2
y=6/((x/2)^4)
y=6/((x^4)/16)
y=6/((x^4)(1/16))
y=((6)(16))/(x^4)
y=16(6/(x^4))

y increases by 16 times

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A population of values has a normal distribution with μ=204.9μ=204.9 and σ=81.9σ=81.9. You intend to draw a random sample of siz

marin [14]

Answer:

7. μ=204.9 and σ=5.4968

8. μ=75.9 and σ=0.7136

9. p=0.9452

Step-by-step explanation:

7. - Given that the population mean =204.9 and the standard deviation is 81.90 and the sample size n=222.

-The sample mean, $\mu_x$ is calculated as:

$\mu_x=\mu=204.9, \mu_x=sample \ mean$

-The standard deviation, $\sigma_x$ is calculated as:

$\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{81.9}{\sqrt{222}}\\\\=5.4968$

8. For a random variable X.

-Given a X's population mean is 75.9, standard deviation is 9.6 and a sample size of 181

-#The sample mean, $\mu_x$ is calculated as:

$\mu_x=\mu\\\\=75.9$

#The sample standard deviation is calculated as follows:

$\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{9.6}{\sqrt{181}}\\\\=0.7136$

9. Given the population mean, μ=135.7 and σ=88 and n=59

#We calculate the sample mean;

$\mu_x=\mu=135.7$

#Sample standard deviation:

$\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\=\frac{88}{\sqrt{59}}\\\\=11.4566$

#The sample size, n=59 is at least 30, so we apply Central Limit Theorem:

$P(\bar X>117.4)=P(Z>\frac{117.4-\mu_{\bar x}}{\sigma_x})\\\\=P(Z>\frac{117.4-135.7}{11.4566})\\\\=P(Z>-1.5973)\\\\=1-0.05480 \\\\=0.9452$

Hence, the probability of a random sample's mean being greater than 117.4 is 0.9452

7 0

3 years ago

What is the inverse function f(x)=1/4x-2

Cloud [144]

The inverse function of the function above is f(x) = 4x + 8

You can find the inverse to any function by switching the x and f(x) values. After that, solve for the new f(x) value. The result will be the inverse function. The step-by-step process for this one is done below for you.

f(x) = 1/4x - 2 ----> Start by switching the f(x) and x

x = 1/4f(x) - 2 ----> Now add 2 to both sides

x + 2 = 1/4f(x) ----> Now multiply both sides by 4

f(x) = 4x + 8

Now that you've solved it for the new f(x), you have your inverse function.

3 0

4 years ago

Which method could be used to factor 4x^2-50

IrinaVladis [17]

Take the 4 out to get 4(x^2-12.5)

3 0

3 years ago

A basketball player has a 50 chance of making each free throw. what is the probability that the player makes at least eleven out

Katyanochek1 [597]

It would be about 1.89 or 1 5/6

4 0

4 years ago

An 8 kg box is at rest and is pushed for 10 m with a 60 N force. If it's accelerated to 10 m/s, calculate the efficiency of the

wlad13 [49]

Answer:

2/3

Step-by-step explanation:

The work done on the box is ...

Fd = (60 N)(10 m) = 600 N·m = 600 J

The amount of energy the box has as a result is ...

KE = 1/2mv² = (1/2)(8 kg)(10 m/s)² = 400 kg·m²/s² = 400 J

The ratio of box energy to energy input is ...

η = (400 J)/(600 J) = 2/3 . . . ≈ 66.7%

4 0

3 years ago