What is the probability?

Brrunno [24]

The area of the kite is 70 square cm.

Step-by-step explanation:

Step 1:

From the given question, the diagonals measure 14 cm and 10 cm. The longer diagonal of the kite is taken as q and the shorter one is taken as p.

So for the given kite, p is 10 cm long and q is 14 cm long.

The area of a kite is half the product of the diagonals of the kite.

The area of the kite $= \frac{(p)(q)}{2}.$

Step 2:

Substituting the known values, we get

The area of the kite $= \frac{(p)(q)}{2} = \frac{(10)(14)}{2},$

$\frac{(10)(14)}{2}= \frac{140}{2} = 70.$

So the area of the kite is 70 square cm.

7 0

3 years ago

Vail Resorts pays part-time seasonal employees at ski resorts on an hourly basis. At a certain mountain, the hourly rates have a

notsponge [240]

Answer:

$z=0.842$

And if we solve for a we got

$\mu=13.16 +0.842*3=15.69$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the hourly rates of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,3)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>13.16)=0.20$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. On this case P(Z<0.842)=0.8 and P(z>0.842)=0.20

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.842$

And if we solve for a we got

$\mu=13.16 +0.842*3=15.69$

3 0

3 years ago

Which measure of central tendency is found by calculating the sum of all data in the set divided by the number of data values in

aivan3 [116]

The answer would be A, Mean

The mean is the Average of a data set.

I hope that this helps. If it does, please rate Brainliest :D

6 0

4 years ago

Read 2 more answers

Find the value of x please

VladimirAG [237]

Answer:

x= -8

Step-by-step explanation:

you combined the two equations to equal 180 since CIA are supplementary and the you solve the equation.

7 0

3 years ago

Prove the formula for (d/dx)(cos−1(x)) by the same method as for (d/dx)(sin−1(x)). Let y = cos−1(x). Then cos(y) = and 0 ≤ y ≤ π

gtnhenbr [62]

Answer:

$\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$

Step-by-step explanation:

Given the differential (d/dx)(cos−1(x)), to find the equivalent formula we will differentiate the inverse function using chain rule as shown below;

let;

$y = cos^{-1} x \\\\taking \ cos\ of\ both\ sides\\\\cosy = cos(cos^{-1} x)\\\\cosy = x\\\\x = cosy\\\\\frac{dx}{dy} = -siny\\$

$\frac{dy}{dx} = \frac{-1}{sin y} \\\\from\ trigonometry\ identity,\ sin^{2} x+cos^{2}x = 1\\sinx = \sqrt{1-cos^{2} x}$

Therefore;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-cos^{2}y } }$

Since x = cos y from the above substitute;

$\frac{dy}{dx} = \frac{-1}{\sqrt{1-x^{2}} }$

Hence, $\frac{d(cos^{-1}x )}{dx} = \frac{-1}{\sqrt{1-x^2} }$ gives the required proof

5 0

4 years ago