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3 years ago

Find the range of the given function y = 5x + 2, where x > -2.

Mathematics

1 answer:

andrew-mc [135]3 years ago

8 0

Answer:

Its -3,2,7

Step-by-step explanation:

Simply put, you plug in all values greater than -2. Which is what thst function tells you.

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In parallelogram RSTU, what is SU?

serious [3.7K]

Because S and U are the opposite vertices of the <span>parallelogram RSTU,
so SU is a diagonal of this </span>parallelogram.

5 0

3 years ago

Solve the problem. Use the Central Limit Theorem.The annual precipitation amounts in a certain mountain range are normally distr

bazaltina [42]

Answer:

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

Step-by-step explanation:

To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 109.0 inches, and a standard deviation of 12 inches.

This means that $\mu = 109, \sigma = 12$

Sample of 25.

This means that $n = 25, s = \frac{12}{\sqrt{25}} = 2.4$

What is the probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches?

This is the p-value of Z when X = 112. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{112 - 109}{2.4}$

$Z = 1.25$

$Z = 1.25$ has a p-value of 0.8944.

0.8944 = 89.44% probability that the mean annual precipitation during 25 randomly picked years will be less than 112 inches.

7 0

3 years ago

A motorcar is running at the rate of 66 km per hour. Each

amm1812

Answer:

Given:

The radius of a wheel =r=35 cm=0.35 cm.

The speed it must keep =s=66 km/h=

66×1000

m/min=1100 m/min

To find out:

The number of revolution =n, it makes per minute to maintain that speed.

Solution:

The circumference =C of the wheel =2πr=2×

×0.35 m=2.2 m=C

The distance the wheel covers in 1 min=d=1100 m.

Now the distance =d covered by a wheel in one revolution = the circumference of the wheel.

∴ Here the number of revolution =n=

2.2

1100

=500.

3 0

3 years ago

Solve the equation v^3=80

Luba_88 [7]

Answer:

4.31

Step-by-step explanation:

Find the cube root of both sides of the equation.

$^3\sqrt{v^3}$ = $^3\sqrt{80}$

The cube root will cancel out the cubed in the variable.

v = $^3\sqrt{80}$

Find the cube root of 80. I rounded to the nearest hundredth.

v = 4.31

3 0

3 years ago

Read 2 more answers

Let c be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. find the exact length of c from t

Mandarinka [93]

Parameterize the intersection by setting $x(t)=t$ , so that

$x^2=2y\iff y=\dfrac{x^2}2\implies y(t)=\dfrac{t^2}2$
$3z=xy\iff z=\dfrac{xy}3\implies z(t)=\dfrac{t^3}6$

The length of the path $C$ is then given by the line integral along $C$ ,

$\displaystyle\int_C\mathrm dS$

where $\mathrm dS=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dz}{\mathrm dt}\right)^2}\,\mathrm dt$ . We have

$\dfrac{\mathrm dx}{\mathrm dt}=1$
$\dfrac{\mathrm dy}{\mathrm dt}=t$
$\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{t^2}2$

and so the line integral is

$\displaystyle\int_{t=0}^{t=2}\sqrt{1^2+t^2+\dfrac{t^4}4}\,\mathrm dt$

This result is fortuitous, since we can write

$1+t^2+\dfrac{t^4}4=\dfrac14(t^4+4t^2+4)=\dfrac{(t^2+2)^2}4=\left(\dfrac{t^2+2}2\right)^2$

and so the integral reduces to

$\displaystyle\int_{t=0}^{t=2}\frac{t^2+2}2\,\mathrm dt=\dfrac{10}3$

3 0

3 years ago