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2 years ago

Consider the line segment below that is five feet long. Is Q the midpoint of PR? Justify your answer.

Mathematics

1 answer:

givi [52]2 years ago

4 0

Answer:

Q is not the midpoint of PR

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If Q is the midpoint of PR

then

PQ=QR

substitute the given values and solve for x

$15x-2=5x+3\\15x-5x=3+2\\10x=5\\x=0.5$

Remember that

$PR=5\ ft$ ----> given problem

$PR=PQ+QR\\PR=(15x-2)+(5x+3)$

substitute the value of x

$PR=(15(0.5)-2)+(5(0.5)+3)$

$PR=(5.5)+(5.5)$

$PR=11\ ft$

Compare with the given value of PR

$5\ ft\neq 11\ ft$

therefore

Q is not the midpoint of PR

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The probability that a person in the United States has type B+ blood is 12%. Three unrelated people in the United States are s

V125BC [204]

Answer:

The probability that all three have type B+ blood is 0.001728

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have type B+ blood, or they do not. The probability of a person having type B+ blood is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

The probability that a person in the United States has type B+ blood is 12%.

This means that $p = 0.12$

Three unrelated people in the United States are selected at random.

This means that $n = 3$

Find the probability that all three have type B+ blood.

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{3,3}.(0.12)^{3}.(0.88)^{0} = 0.001728$

The probability that all three have type B+ blood is 0.001728

4 0

2 years ago

The cost of producing x bags of dog food is given by C(x) = 800 + 400 + 10x - x where 0 SX 55000. Find the marginal-cost functio

nikdorinn [45]

Answer:

The marginal-cost function is;

c'(x)= (20x-1)/(2√(400 + 10x² - x))

Completed question;

The cost of producing x bags of dog food is given by C(x) = 800 + √(400 + 10x² - x) where 0≤x≤55000. Find the marginal-cost function.

The marginal-cost function is c'(x)=

(Use integers or fractions for any numbers in the expression.)

Step-by-step explanation:

The marginal-cost function is c'(x)= = dC(x)/dx

Where;

C(x) = 800 + √(400 + 10x² - x)

c'(x) = d(800 + √(400 + 10x² - x) )/dx

Using function of function rule of differentiation or chain rule;

c'(x) = (20x-1)×(1/2√(400 + 10x² - x))

c'(x) = (20x-1)/(2√(400 + 10x² - x))

The marginal-cost function is;

c'(x)= (20x-1)/(2√(400 + 10x² - x))

3 0

2 years ago

How many pounds of water must be evaporated from 50 pounds of a 3% salt solution so that the the remaining solution will be 5 %

svlad2 [7]

Answer:

Step-by-step explanation:

This is kinda tricky, but not nearly as bad as d = rt problems. Those are a nightmare!

We will make a table for this:

#lbs solution * % salt = lbs. salt

3% solution

- Water

New solution

And we will now fill in what we know. The 3% solution part is easy. The number of pounds of that is 50 and the percent salt in 3% salt is....well, 3%. As a decimal, it is .03:

#lbs solution * %salt = lbs salt

3% solution 50 * .03 = 1.5

- Water

New solution

The last column there with a 1.5 in it is the product of 50 times .03, since that is what the formula at the top of the table tells us we have to use. Now for the water. That's easy, too, since the amount of water we are evaporating (notice the subtraction sign out front of the word "water"; that indicates we are removing water) is our unknown, and we also know that water has 0% salt in it:

#lbs solution * %salt = lbs. salt

3% solution 50 * .03 = 1.5

- Water x * 0 = 0

New solution

Now all we have left is the new solution row and the equation. Finding the equation from a mixture table is as easy as it can be! Super easy!

The new solution will be 50 - x since, going down column 1, we are subtracting the water from the 3% solution, the % salt is to be 5%:

#lbs. solution * %salt = lbs. salt

3% solution 50 * .03 = 1.5

- Water x * 0 = 0

New solution 50 - x * .05 = 2.5 - .05x

Now we're ready for our equation. I got the 2.5 - .05x from multiplying

.05(50 - x), just so you know.

if we had to subtract the water from the salt solution and set it equal to the new solution in the first column, we also have to do it in the third column:

1.5 - 0 = 2.5 - .05x and solve for x:

-1 = -.05x so

x = 20 pounds of water

4 0

2 years ago

Convert the following into scientific notation: 0.00001.

Anna35 [415]

The answer would be D 1 x 10-5..

8 0

2 years ago

Each leg of a 45°-45°-90° triangle measures 14 cm. What is the length of the hypotenuse? 7 cm cm 14 cm cm

Mashutka [201]