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3 years ago

Find the inequalities represented by the graph?

Mathematics

1 answer:

nekit [7.7K]3 years ago

7 0

Answer:

Step-by-step explanation:

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Find the volume, in cubic centimeters, of the rectangular prism pictured below.

never [62]

Answer:

V= 18.75 cm^3

Step-by-step explanation:

The formula for finding the volume for any given shape is V = L x W x H.
So, multiply 2 1/2 cm x 2 1/2 cm x 3 cm.
This gives you 18.75 cm^3

6 0

3 years ago

Find the equation of the circle with a diameter whose end points are (-1,-2) and (-3,2)

Sergeeva-Olga [200]

Answer:

The equation of the circle with a diameter whose end points are (-1,-2) and (-3,2) is

$x^{2} +y^{2}+4x-1=0$

Step-by-step explanation:

Explanation:-

Step 1:-

The equation of the circle having center and radius is

$(x-h)^2+(y-k)^2=r^2$

here center is (h,k) and radius is r

Given diameter whose end points are (-1,-2) and (-3,2)

The diameter of the circle is passing through the center of the circle

so center of the circle = midpoint of two end points

$(\frac{-1 +(-3) }{2} ,\frac{-2+2 }{2} )$

$(-2,0)$

therefore center (h,k) = (-2,0)

Step 2:-

we have to find the radius of the circle

the radius of the circle = the distance from center to the one end point

i.e., C P = r

Given one end point is P(-3,2) and center C(-2,0)

The distance formula of two points are

$\sqrt{(x_{2}-x_{1} ) ^{2}+ (y_{2}-y_{1} ) ^{2}}$

$r=\sqrt{{(-3)-(-1) ) ^{2}+ (2-(-2)) ^{2}}$

$r=\sqrt{5}$

Step 3:-

center (h,k) = (-2,0) and

radius $r=\sqrt{5}$

The standard form of circle equation

$(x-h)^2+(y-k)^2=r^2$

$(x-(-2))^2+(y-0)^2=\sqrt{5} ^2$

on simplification is

$x^{2} +y^{2}+4 x-1=0$

5 0

3 years ago

Three girls are selling cases of popcorn to earn money for a band trip in their first week Emily sold 2 3/4 cases Brenda sold 4

ss7ja [257]

They have sold ten full cases
but have sold 10 and a half cases in total

8 0

3 years ago

2) In order to receive a passing grade in your math class, you must attain an average of at least 65. If your scores on 5 exams

Xelga [282]

Answer:

Step-by-step explanation:

to get the average you add all five together and divide by the number of scores, which is five

7 0

3 years ago

Suppose that the probability that a person is killed by lightning, in a year is, independently of other people, 1/(500 million).

Katen [24]

Answer:

a) $P(X \geq 3) = 1- P(X$

The individual pprobabilities are:

$P(X=0)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.548812$

$P(X=1)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.329287$

$P(X=2)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.098786$

And if we replace we got:

$P(X \geq 3) = 1- [0.548812+0.329287+0.098786]=0.023115$

b) $P(X \geq 3) = 1- P(X$

And we can calculate this with the following excel formula:

$=1-BINOM.DIST(2;300000000;(1/500000000);TRUE)$

And we got:

$P(X\geq 3) = 0.023115$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=300000000, p=\frac{1}{500000000})$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

(a) Write down the exact expression for the probability P(3 or more people will be killed by lightning in the U.S. next year). Evaluate this expression to 6 decimal places.

For this case we want this probability, we are going to use the complement rule:

$P(X \geq 3) = 1- P(X$

The individual probabilities are:

$P(X=0)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.548812$

$P(X=1)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.329287$

$P(X=2)=(300000000C0)(\frac{1}{500000000})^3 (1-\frac{1}{500000000})^{300000000-0}=0.098786$

And if we replace we got:

$P(X \geq 3) = 1- [0.548812+0.329287+0.098786]=0.023115$

(b) Write down a relevant approximate expression for the probability from (a). Justify briefly the approximation. Evaluate this expression to 6 decimal places.

For this case we want this probability, we are going to use the complement rule:

$P(X \geq 3) = 1- P(X$

And we can calculate this with the following excel formula:

$=1-BINOM.DIST(2;300000000;(1/500000000);TRUE)$

And we got:

$P(X\geq 3) = 0.023115$

7 0

4 years ago