If a coin is flipped and then a twenty part spinner is spun how many possible outcomes are in the sample space for the compound

In right ∆PQR, P and Q are acute angles, and cos P is 3/5. What is sin Q? Answers: 4/5 3/5 2/5 3/4

Andrews [41]

$Look\ at\ the\ picture.\\\\cos\alpha=\frac{3}{5};\ cos\alpha=\frac{b}{c}\\\\sin\beta=\frac{b}{c}=cos\alpha\\\\therefore\\\\sin\beta=\frac{3}{5}\\\\Answer:\huge\boxed{\frac{3}{5}}$

4 0

3 years ago

Find the area of the shaded portion in the equilateral triangle with sides 6.

VashaNatasha [74]

First, let's get the area of the entire triangle since we'll need it later. The area of a triangle is A=1/2*b*h

We can find the height with the Pythagorean theorem by splitting the triangle in half.
3^2+b^2=6^2
9+b^2=36
b^2=27
b=√27

Then we can find the area:
A=1/2*6*√27
A=3√27 or =9√3 or 15.59

Now we can find the area of each region in the triangle other than the shaded region because they are all portions of a circle.

Each region has an angle of 60 because this is an equilateral triangle. Therefore the area of each region other than the shaded region will be 1/6 the area of a circle with a radius of 3 because a full circle is 360 degrees.
A=pi*r^2/6
A=pi*9/6
A=4.71

So three of these regions would have an area of 14.14

We do the area of the triangle minus the area of these regions to get the area of the shaded region
15.59-14.14 = 1.45

Hope this helps!

<span />

3 0

3 years ago

In the Numbers Game, a state lottery, four numbers are drawn with replacement from an urn containing balls numbered 0-9, inclusi

Fantom [35]

There are 10 digits from 0 to 9, inclusive.

Thus, number of ways in which four numbers will be drawn from an urn containing balls numbered 0-9, inclusive is given by $10^4=10,000$

The number of ways in which a ticket holder will have the first two digits in the correct order is the same as the number of ways in which two numbers will be drawn from the urn containing balls numbered 0-9, inclusive and is given by $10^2=100$

Therefore, <span>the probability that a ticket holder has the first two digits in exact order is given by $\frac{100}{10,000} = \frac{1}{100} =0.01$ </span>

7 0

3 years ago

The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 ye

trasher [3.6K]

Answer:

66.98% probability that the mean gain for the sample was between 250 and 500.

Step-by-step explanation:

To solve this problem, it is important to know the Normal probability distribution and the Central limit theorem.

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 432, \sigma = 722, n = 40, s = \frac{722}{\sqrt{40}} = 114.16$

What is the probability that the mean gain for the sample was between 250 and 500?

This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 250.

So

X = 500

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

By the Central Limit Theorem

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

$Z = \frac{500 - 432}{114.16}$

$Z = 0.6$

$Z = 0.6$ has a pvalue of 0.7257.

X = 250

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

By the Central Limit Theorem

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

$Z = \frac{250 - 432}{114.16}$

$Z = -1.59$

$Z = -1.59$ has a pvalue of 0.0559.

So there is a 0.7257 - 0.0559 = 0.6698 = 66.98% probability that the mean gain for the sample was between 250 and 500.

8 0

3 years ago

3. A rock is lying on a rock ledge that is 3 m high. The rock as 120 J of potential energy.

n200080 [17]

Answer:

For the gravitational force the formula is P.E. = mgh, where m is the mass in kilograms, g is the acceleration due to gravity (9.8 m / s2 at the surface of the earth) and h is the height in meters. Notice that gravitational potential energy has the same units as kinetic energy, kg m2 / s2.

Step-by-step explanation:

6 0

3 years ago