Translate the word phrase into a variable expression. please helpEight less than the quotient of x and 3.

A.
3x – 8

B.x/3-8

C.x-8/3

D.8-x/3

Answers

Answer 1

Answer: Quotient means the answer to a division problem. 8 less than the quotient indicates that we have to subtract 8 AFTER we do the division... so your expression would be

(x ÷ 3) - 8 or

x/3 - 8

Answer B

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1. Find the products. Show your thinking. An example of how to show your thinking is provided.a. 1,400 × 20
b. 8,000 × 50
c. 120 × 300

2. Fill in the missing factors to find the given estimated product. The first one is done for you.

a. 582 x 23 ≈ __600________ x ___20_______ = 12,000

b. 325 x 454 ≈ __________ x __________ = 150,000

c. 6,397 x 349 ≈ __________ x __________ = 1,800,000

3. Round the factors and estimate the products. Round to the highest place value.

a. 656 × 106 ≈ __________ x __________ = __________

b. 3,108 × 7,942 ≈ __________ x __________ = __________

c. 425 × 9,311 ≈ __________ x __________ = __________

Answers

So number 1 is B number 2 is A number 3 is B

The volume of a cylinder with height to radius ratio of 4:1 is 108 pie centimeters cubed. Find the radius and height of the cylinder.

Answers

$H:r=4:1\n\n(H)/(r)=(4)/(1)\to H=4r\ (*)\n\nV=108\pi\ cm^3\n\nV=\pi r^2H\n\nsubstitute\ (*)\n\n\pi r^2\cdot4r=108\pi\ \ \ \ /:4\pi\n\nr^3=27\n\nr=\sqrt[3]{27}\n\nr=3\ (cm)\n\nH=4r=4\cdot3=12\ (cm)\n\nAnswer:radius=3\ cm\ and\ height=12\ cm.$

4:1 height to radius
let x be radius
let 4x be height

V=(pi)(r)^2h
108(pi)=(pi)x^2(4x)
divide both sides by pi
108=x^2(4x)
108=4x^3
divide both sides by 4
27=x^3
cube root both sides
x=3

therefore the radius is 3 and the height is 12

Can somebody please help me with my discrete math sudoku puzzles.

Answers

Use trial and error, best way to start when trying to play sudoku for the first time.

Form an equation to help you solve this problem.A school bus is full as it sets off. At the first stop 3 children get off and at the next stop a third
of the remaining children get off, leaving the bus only half full.
How many children were on the bus at the start?

Answers

Answer:

Step-by-step explanation:

If there are x children on the bus at the start, after the first stop, there are (x-3) remaining. After two stops, the number on the bus is ...

x/2 = x -3 -(1/3)(x -3)

Multiplying by 6, we have ...

3x = 6x -18 -2(x -3)

3x = 4x -12 . . . . simplify

12 = x . . . . . . . . add 12-3x

There were 12 children on the bus at the start.

_____

Check

After 3 got off at the first stop, there were 12-3 = 9 remaining. 1/3 of those, or 9/3=3 got off at the second stop, so 9 -3 = 6 remained. This is half the original number, as required.

Final answer:

Let X represent the number of children on the bus originally. The equation formed is 2/3*(X - 3) = X/2, and when we solve it, we find that X equals 12 which indicates that there were 12 children on the bus at the start.

Explanation:

Let's denote the number of children on the bus at the start as X. After the first stop, the number of children on the bus became X - 3, because 3 children got off. After the second stop, a third of the remaining children got off, so the number of children on the bus became 2/3*(X - 3). According to the problem, after all the stops, the bus was half full. Therefore, we can set up an equation: 2/3*(X - 3) = X/2.

To solve the equation, we can multiply all terms by 6 to clear out the fractions and obtain the equation: 4*(X - 3) = 3X. This simplifies to 4X - 12 = 3X which simplifies further to X = 12, meaning there were initially 12 children on the bus.

Learn more about Problem Solving here:

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PLEASE HELP!!!The equation for the line of best fit is shown below.

Y=5/6 x+ 10

Based on the line of best fit, if an employee works at a company for six years, how much vacation time will he or she accrue?
A.
20 days
B.
15 days
C.
13 days
D.
6 days