MATHEMATICS COLLEGE

Question 1x + 6 = 23 x = ____

Question 2
Solve.
x - 7 = 12 x = ___

Question 3
Solve. Round your answer to the nearest tenth.

4x = 13 x = ____

Question 4
Solve. Round your answer to the nearest tenth.

3x + 1 = 15

Answers

Answer 1
Answer:

Answer:

1. x=17

2. x=19

3. x=3

4. x=4
Answer 2
Answer:

Answer:

question 1:

3/11

question 2:

-  7/11

Step-by-step explanation:

in

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The average sales per customer at a home improvement store during the past year is $75 with a standard deviation of $12. The probability that the average sales per customer from a sample of 36 customers, taken at random from this population, exceeds $78 is:

Oct 16, 10:30:54 AMA rocket is shot into the air. The function f (x) = -16x2 + 64x + 8 gives the
height of the rocket (in feet) as a function of the rockets horizontal distance from
where it was initially shot.
a. What was the initial height of the rocket when it was shot?
b. What is the maximum height the rocket reaches in the air?
a. The initial height of the rocket was
feet.
b. The maximum height the rocket reaches is
feet.

Answers

Answer:

A) 8 feet.

B) 72 feet

Step-by-step explanation:

We have the function f(x)=-16x^2+64x+8 which gives the height of the rocket (in feet) as a function of the rocket's horizontal distance.

Part A)

We want to find the initial height of the rocket when it was shot.

At the initial height, the rocket has not moved anywhere. So, the horizontal distance will be 0.

Therefore, to find the initial height, we will substitute 0 into our function. This yields:

f(0)=-16(0)^2+64(0)+8

Evaluate:

f(0)=8

Therefore, the initial height was 8 feet.

Part B)

Notice that our function is a quadratic.

Therefore, the maximum height will be given by the vertex of our quadratic.

To find the vertex, we use:

(-(b)/(2a),f(-(b)/(2a)))

Let's label our coefficients. We have -16x^2+64x+8

Therefore, a=-16, b=64, and c=8.

Substitute them into the vertex formula to find the x-coordinate:

x=-(64)/(2(-16))\n\Rightarrow x=64/32=2

Now, to find the maximum height, substitute 2 back into our function f(x):

f(2)=-16(2)^2+64(2)+8

Evaluate:

f(2)=-16(4)+64(2)+8\n\Rightarrow f(2)=-64+128+8\n\Rightarrow f(2)=72\text{ feet}

Therefore, the rocket reaches a maximum height of 72 feet.

The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 15 percent will enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved

Answers

Answer:

The steady state proportion for the U (uninvolved) fraction is 0.4.

Step-by-step explanation:

This can be modeled as a Markov chain, with two states:

U: uninvolved

M: matched

The transitions probability matrix is:

\begin{pmatrix} &U&M\nU&0.85&0.15\nM&0.10&0.90\end{pmatrix}

The steady state is that satisfies this product of matrixs:

[\pi] \cdot [P]=[\pi]

being π the matrix of steady-state proportions and P the transition matrix.

If we multiply, we have:

(\pi_U,\pi_M)*\begin{pmatrix}0.85&0.15\n0.10&0.90\end{pmatrix}=(\pi_U,\pi_M)

Now we have to solve this equations

0.85\pi_U+0.10\pi_M=\pi_U\n\n0.15\pi_U+0.90\pi_M=\pi_M

We choose one of the equations and solve:

0.85\pi_U+0.10\pi_M=\pi_U\n\n\pi_M=((1-0.85)/0.10)\pi_U=1.5\pi_U\n\n\n\pi_M+\pi_U=1\n\n1.5\pi_U+\pi_U=1\n\n\pi_U=1/2.5=0.4 \n\n \pi_M=1.5\pi_U=1.5*0.4=0.6

Then, the steady state proportion for the U (uninvolved) fraction is 0.4.

PLEASEEE HELP FAST! One solution each is given on four quadratic equations. Assuming that each quadratic equation has two solutions, what is the second solution for each equation?

Answers

Answer:

Step-by-step explanation:

If one solution of a quadratic equation is a complex number (a + bi),

Other solution of the equation will be the conjugate of the first solution.

So the other solution will be in the form of (a - bi)

If one solution is, x = -4 - 5i

Other solution will be, x = -4 + 5i

If one solution is, x = 4 + 5i

Other solution will be, x = 4 - 5i

If one solution is, x = 5 - 4i

Other solution will be, x = 5 - 4i

A line passes through the point (2, 7) and has a slope of 4. What is the equation of the line?

Answers

Answer:

y=4x-1

Step-by-step explanation:

Remember the point slope form equation y-y1=m(x-x1) where m is the slope and the given point is (x1,y1)

y-7=4(x-2) . Plug in the numbers for the equation

y-7=4x-8   distributive property

y = 4x-1
y=4x-1 is the equation that passes through (2,7)

Simplify (x + 4)(x2 − 6x + 3). x3 − 14x2 + 3x + 12 x3 − 6x2 − 17x + 12 x3 − 10x2 − 27x + 12 x3 − 2x2 − 21x + 12

Answers

Answer:

36 x^3 - 32 x^2 + (x + 4) (x^2 - 6 x + 3).x^3 - 62 x + 12

Step-by-step explanation:

Answer:

x^6-2x^5-21x^4+48x^3-32x^2-62x+12

Step-by-step explanation:

Mark me as brainliest!!!!

3.A train can travel 360 miles in 4 hours. How much time will it take
travelling 585 miles?​

Answers

Answer:

6.5 hours

Step-by-step explanation:

We can write a ratio to solve

360 miles      585 miles

---------------- = ------------

4 hours         x hours

Using cross products

360 * x = 4* 585

360 x = 2340

Divide each side by 360

x = 2340/360

x =6.5
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