Question

80% of the students voted for John as class president. If he received 128 votes, how many students voted?

Answer 1

Which equation represents the line that passes through the points (0, 3) and (4, 2)

Answer 2

Which equation represents the line that passes through the points (0, 3) and (4, 2) ?

A. (y - 2) = - 1/4 * (x - 4)

B. (y + 2) = - 1/4 * (x + 4)

C. (y - 4) = - 1/4 * (x - 2)

D. (y + 4) = - 1/4 * (x + 2)

Answer 3

Estimate: 20 is 22% of what number?

Answer 4

Determine the vertex form and the maximum or minimum value of the function. f(x) = 2x ^ 2 + 8x + 3

Answer 5

10/9 - 7/6 =

Answer 6

1.6 divided by 100

Answer 7

40 1/10 × 2 1/2 =

Answer 8

If the replacement set is the set of integers, find the solution set for the inequality: x - 9 < - 15

Answer 9

If the replacement set is the set of integers, find the solution set for the inequality: x - 9 < - 15

A. { - 8, - 7, - 6 ,...}

B. { - 9, - 8, - 7 ,...}

C. {...,-8,-7,-6}

D. {...,-9,-8,-7}

Answer 10

Convert 23 L / m * in to milliliters per second (mL / s)

Answer 11

A bag contains 4 green marbles, 3 red marbles, and 7 blue marbles. One marble is taken from the bag and put back after checking its color. A second marble is then taken out. What is the probability that the first is blue and the second red?

Answer 12

What is the area of a circular region whose diameter is 12 centimeters?

A. 36pi square cm
B. 36pi cm
C. 12pi cm
D. 24pi square cm

Answer 13

Find the x-intercept of the line: 8x - 4y = - 24

A. 3
B. -3
C. 6
D. -6

Answer 14

Find the slope of the line through the points (- 1, - 4) and (2, - 2)

Answer 15

Evaluate: 5 - 3|3(- 6)|

A. -49
B. 49
C. -59
D. 59

Answer 16

(8.1 × 10 ^ 3)/(2.7 × 10 ^ 6) =

A. 3 × 10 ^ 11
B. 3 × 10 ^ - 5
C. 3 × 10 ^ 6
D. 3 × 10 ^ - 11

Answer 17

25 7/12 A tree is feet high. Richard cuts off the 8 7/8 top feet. How tall is the tree now?

A. 17 17/24 feet
B. 16 17/24 feet
C. 17 7/24 feet
D.16 7/24 feet

Answer 18

Let's use a proportion to solve for the total number of students who voted:

80% = 128/x

Here, x represents the total number of students who voted. To solve for x, we'll cross-multiply:

0.8x = 128

And now we'll divide both sides by 0.8:

x = 160

So there were 160 students who voted in the election.

Answer 19

We can use the point-slope form of a linear equation to find the equation of the line that passes through the points (0, 3) and (4, 2).

Point-slope form: y - y1 = m(x - x1)

We first need to find the slope of the line using the two points:

slope = (y2 - y1) / (x2 - x1)
slope = (2 - 3) / (4 - 0)
slope = -1/4

Now we can choose either point and substitute the values into the point-slope form:

y - 3 = (-1/4)(x - 0)

Simplifying:

y - 3 = (-1/4)x

y = (-1/4)x + 3

So the equation that represents the line passing through the points (0, 3) and (4, 2) is:

y = (-1/4)x + 3.

Answer 20

The correct equation is A. (y - 2) = - 1/4 * (x - 4).

Answer 21

To solve the problem, we can use the formula:

part/whole = percentage/100

where "part" is the number we are trying to find, "whole" is the total number we're looking for (in this case), and "percentage" is 22.

So, we can write:

20/whole = 22/100

To solve for "whole", we can cross-multiply:

20 * 100 = 22 * whole

2000 = 22 * whole

To isolate "whole", we can divide both sides by 22:

whole = 2000/22

whole ≈ 90.91

Therefore, 20 is approximately 22% of 90.91.

Answer 22

We can convert the quadratic function f(x) = 2x^2 + 8x + 3 to vertex form by completing the square:

f(x) = 2(x^2 + 4x) + 3

f(x) = 2(x^2 + 4x + 4 - 4) + 3

f(x) = 2((x + 2)^2 - 4) + 3

f(x) = 2(x + 2)^2 - 5

Therefore, the vertex form of the function is f(x) = 2(x + 2)^2 - 5, and the vertex is (-2, -5).

Since the coefficient of the x^2 term is positive, the parabola opens upwards. Therefore, the vertex is the minimum point of the function, and the minimum value of the function is -5.

Answer 23

We need to find a common denominator to subtract these fractions. The denominator should be the least common multiple (LCM) of 9 and 6, which is 18.

10/9 - 7/6 can be written as:

(10/9) * (2/2) - (7/6) * (3/3)

= 20/18 - 21/18

Now we can subtract the numerators:

= (20 - 21)/18

= -1/18

Therefore, 10/9 - 7/6 = -1/18.

Answer 24

To divide 1.6 by 100, we can simply move the decimal point two places to the left:

1.6 ÷ 100 = 0.016

Answer 25

To multiply 40 1/10 by 2 1/2, we need to convert the mixed numbers to improper fractions:

40 1/10 = 401/10

2 1/2 = 5/2

Now we can multiply these fractions:

401/10 × 5/2

We can simplify the fractions before multiplying:

401/10 = 40 + 1/10 = 400/10 + 1/10 = 401/10

So we have:

401/10 × 5/2 = 401/10 × 5/2

= (401 × 5)/(10 × 2)

= 2005/20

We can simplify the fraction by dividing both the numerator and denominator by 5:

2005/20 = 401/4

Therefore, 40 1/10 × 2 1/2 = 401/4 or 100.25.

Answer 26

To solve for x in the inequality x - 9 < - 15, we'll isolate x by adding 9 to both sides:

x - 9 + 9 < - 15 + 9

x < - 6

Therefore, the solution set for the inequality when the replacement set is the set of integers is all integers less than -6.

In set-builder notation, we can write the solution set as:

{x | x < -6, x ∈ ℤ}.

Answer 27

The solution set for the inequality x - 9 < - 15, when the replacement set is the set of integers, is the set of integers less than -6.

The correct set is A. { - 8, - 7, - 6 ,...}.

Answer 28

We can use dimensional analysis to convert 23 L/m*in to mL/s:

23 L/m*in * (1000 mL/L)/(60 s/min)

First, we multiplied by the conversion factor (1000 mL/L) to convert liters to milliliters.

Then, we multiplied by the conversion factor (1 min/60 s) to convert minutes to seconds.

Simplifying:

= 383.333... mL/s

Therefore, 23 L/m*in is equivalent to 383.333... mL/s (rounded to three decimal places).

Answer 29

Since a marble is put back in the bag after the first draw, the number of marbles in the bag remains the same for the second draw. Therefore, the probability of drawing a blue marble on the first draw is:

P(blue on first draw) = 7/14 = 1/2

Since the marble is put back in the bag, the probability of drawing a red marble on the second draw is:

P(red on second draw) = 3/14

Now we can multiply the probabilities of the individual events to get the combined probability of both events happening:

P(blue on first draw and red on second draw) = P(blue on first draw) × P(red on second draw)

P(blue on first draw and red on second draw) = (1/2) × (3/14)

P(blue on first draw and red on second draw) = 3/28

Therefore, the probability that the first marble drawn is blue and the second marble drawn is red is 3/28.

Answer 30

The formula for the area (A) of a circle is:

A = πr^2

where r is the radius of the circle. We can use the diameter (d) to find the radius (r) using the formula:

d = 2r

or

r = d/2

In this case, the diameter is 12 centimeters, so the radius is:

r = 12/2 = 6 centimeters

Now we can use the formula for the area of a circle:

A = πr^2

A = π(6^2)

A = 36π

Therefore, the area of the circular region with a diameter of 12 centimeters is 36π square centimeters, which is answer choice A.

Answer 31

To find the x-intercept of the line 8x - 4y = -24, we substitute 0 for y and solve for x:

8x - 4(0) = -24

8x = -24

x = -24/8

x = -3

Therefore, the x-intercept of the line is -3, which is answer choice B.

Answer 32

The formula for the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is:

m = (y2 - y1) / (x2 - x1)

We can use this formula to find the slope of the line passing through the points (-1, -4) and (2, -2):

m = (-2 - (-4)) / (2 - (-1))

m = 2 / 3

Therefore, the slope of the line passing through the points (-1, -4) and (2, -2) is 2/3.

Answer 33

First, we need to simplify the absolute value expression inside the parentheses:

|3(-6)| = |-18| = 18

Now we can substitute the absolute value result into the original expression:

5 - 3|3(-6)| = 5 - 3(18)

= 5 - 54

= -49

Therefore, the value of the expression 5 - 3|3(-6)| is -49, which is answer choice A.

Answer 34

To divide two numbers in scientific notation, we divide their coefficients and subtract their exponents.

So for (8.1 × 10^3) / (2.7 × 10^6), we have:

(8.1 / 2.7) × 10^(3-6)

3 × 10^(-3)

Therefore, (8.1 × 10^3) / (2.7 × 10^6) = 3 × 10^(-3), which is answer choice B.

Answer 35

To find the height of the tree after Richard cuts off the top 8 7/8 feet, we need to subtract 8 7/8 from 25 7/12:

25 7/12 - 8 7/8

We can convert both mixed numbers to improper fractions to make the subtraction easier:

25 7/12 = (25 × 12 + 7) / 12 = 307 / 12

8 7/8 = (8 × 8 + 7) / 8 = 71 / 8

Now we can subtract the fractions:

307/12 - 71/8

We need to find a common denominator for 12 and 8. The LCM of 12 and 8 is 24, so we can convert both fractions to have a denominator of 24:

(307/12) × (2/2) = 614/24

(71/8) × (3/3) = 213/24

Now we can subtract the fractions:

614/24 - 213/24 = 401/24

We can convert the improper fraction back to a mixed number to get the answer in the required format:

401/24 = 16 17/24

Therefore, the tree is now 16 17/24 feet tall, which is answer choice B.