Question 1

A cleaning service offers packages up to 6 full hours of cleaning. The company charges $20 per hour for the first 4 hours and $35 per hour after that.
Which of the following graphs best represents the relationship between the cost and total number hours of cleaning service provided?

Accepted Answer

The price per hour starts at $20 per hour for the first 4 hours. This means that for each added hour, the price increases at a constant rate of $20. Because the increase is constant with each hour, the graph should be linear before 4 hours with a slope of 20. 
After 4 hours, the rate increases to $35 per hour. This means the slope of the line will increase and become steeper. For each mile added after 4 hours, $35 will be added to the total cost. The rate of increase is still constant, it is just increasing at a different constant rate. 
A graph that matches these conditions would be linear both before and after 4 with a bend at 4. The line after 4 will have a steeper slope than the line before. The only graph that satisfies these requirements is the answer.

Question 2

The area of a bedroom is 12m². What is the area of the bedroom in feet when 1 meter is 3.28 feet?

Accepted Answer

In order to convert between different units of measurement, we use what is called a conversion factor. A conversion factor is a ratio (written as a fraction) where one of the units is the numerator and one is the denominator. In order to convert one type of unit to another, you will cross-multiply the starting value by the conversion factor. *We decide which unit goes on the top based on what we are trying to convert. Basically, the units have to match - the units of one numerator should be the same as the numerator of the second fraction. In this case, we know the conversion factor to be the number of feet in one meter. This can be written as either of the following: ^{1 m} / _{3.28 ft} OR ^{3.28 ft} / _{1 m} These can both be used as conversion factors because the ratio of feet to meters is the SAME in both. In order to decide which version to use, we come to our problem. We are told that the area of a bedroom is 12m², and we're trying to convert the meters to feet. Since the number of feet (the area of the bedroom in feet) is unknown, we're going to represent It as x. In order to solve using ratios, we need to write the first ratio as a fraction. We know that the area in meters is 12m², so that will be the numerator in our fraction (ratio) to start. We have decided to use x to represent the unknown number of feet (which will also be squared), so our fraction (ratio) will look like this: ^{12 meters2}/_x Now, we know which version of the conversion factor to use. Meters is the unit used in the numerator, so we will use the conversion factor that also has meters in the numerator: ^{1 meter}/_{3.28 feet} Now we can set the ratios equal to one another in preparation to solve. ^{12 meters2}/_x= ^{1 meter}/_{3.28 feet} However, before we can move forward, we have to make sure the units match. Even though we're using meters and feet in each, the left hand side of the equation has squared units, while the right hand side does not. We cannot combine terms if they don't have the same units. Remember that when something is "squared," it means that it has been multiplied by itself. For example: 2²= 4 3²= 9 2 meters • 2 meters = 4m² Therefore, in order to "square" the right side of the equation, we are going to multiply the entire ratio (fraction) by itself (and round any decimals to the nearest tenth to make the math easier!) ^{1 meter}/_{3.28 feet}• ^{1 meter}/_{3.28 feet =}^{1 meter2}/_{10.76 ft²} Now, we can move forward and solve. ^{12 meters2}/_x= ^{1 meter2}/_{10.76 ft²} Cross multiply across the equal sign to eliminate the ratios. This means you multiply the first numerator by the second denominator, and the first denominator by the second numerator. 12 m² • 10.76 ft² = x • 1m² 129.12m²ft² = x • 1m² Now, we can see that we have the 1m² multiplying the x, so we have to divide both sides by 1m² . Note that when you divide, you also divide by the units. This cancels out the m² on the left hand side as well. 129.12m²ft² ÷ 1m² = x • 1m²÷ 1m² 129.12 ft²= x

Question 3

Solve the following equation for x. 4x - ⁵⁄₄ = 4.75

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: 4x - ⁵⁄₄ = 4.75 Since you have both fractions and decimals, you can convert the fraction to a decimal to help you solve. To convert a fraction to a decimal, divide the numerator by the denominator (5 ÷ 4 = 1.25). 4x - 1.25 = 4.75 Next, move the ( - 1.25) to the other side of the equation by adding - 1.25 (opposite operation) to both sides. 4x - 1.25 + 1.25 = 4.75 + 1.25 4x = 6 Then, you need to move the 4, which is multiplying x. You do this by dividing (opposite operation) both sides by 4. 4x = 6 4x ÷ 4 = 6 ÷ 4 x = 6 ÷ 4 x = 1.5

Question 4

Jeremy places in the top 98% of students for a standardized test. If there were approximately 35 million students took the exam, how many students did he score better than?

Accepted Answer

We can use the percent formula to solve. The percent formula is below: ^part⁄_whole = ^%⁄₁₀₀ We are given the whole (the 35,000,000 students) and are asked to find the part, which is the number of students Jeremy scored higher than (x): ^x⁄_35,000,000 = ⁹⁸⁄₁₀₀ Cross multiply and solve for x: 100 * x = 35,000,000 * 98 100x = 343,000,000 100x/100 = 343,000,000/100 x = 34,300,000 So, 34,300,000 is 98% of 35,000,000

Question 5

Solve the following equation for x. 10x- ²⁄₃ = -⁴⁄₅

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: 10x- ²⁄₃ = -⁴⁄₅ The first thing you want to do is move the ( - ²⁄₃) to the other side of the equation by adding ²⁄₃ (opposite operation) to both sides. 10x - ²⁄₃ = -⁴⁄₅ 10x - ²⁄₃ + ²⁄₃ = -⁴⁄₅+ ²⁄₃ 10x = -⁴⁄₅+ ²⁄₃ ext, we need to add the fractions. In order to do this, we need to find a common denominator for both fractions. This will be the least common multiple between the two denominators. You can easily find this by listing the multiples of each number: 3: 3, 6, 9, 12, 15, 18… 5: 5, 10, 15, 20… The lowest common multiple between 3 and 5 is 15. In order for the fractions to have the same denominator, we need to multiply each fraction by a fractional version of "1" which is basically any number over itself (e.g. ⁵/₅= 1). In order to get from 3 to 15, we need to multiply it by 5. Therefore, we multiply the entire fraction by ⁵/₅. In order to get from 5 to 15, we need to multiply it by 3. Therefore, we multiply the entire fraction by ³/₃. 10x = -⁴⁄₅ + ²⁄₃ So, 10x = (-⁴⁄₅• ³⁄₃) + (²⁄₃ • ⁵⁄₅) 10x = -¹²⁄₁₅ + ¹⁰⁄₁₅ Now that you have a common denominator, you simply add the numerators. Remember that you are adding a negative number here, so it's actually 12-10. 10x = -¹²⁄₁₅ + ¹⁰⁄₁₅ 10x = -²⁄₁₅ Finally, you need to move the 10, which is multiplying x. You do this by dividing (opposite operation) both sides by 10. 10x ÷ 10 = -²⁄₁₅ ÷ 10 x = -²⁄₁₅ ÷ 10 Remember that when you are dividing a fraction by a whole number, you have to make the whole number a fraction by putting it over 1. x = -²⁄₁₅ ÷ 10 x = -²⁄₁₅÷ ¹⁰⁄₁ Then, to divide, we multiply by the reciprocal (flip the second fraction and multiply): x = -²⁄_{15 •} ¹⁄₁₀ Remember that you multiply across the fraction: multiply the two numerators and the two denominators. Since you are multiplying one negative number by one positive number, the answer will also be negative. x = -²⁄₁₅₀ Reduce the final fraction by finding the largest common factor between the numerator and denominator and divide both by that number. 2: 1, 2 150: 1, 2, 3… Divide both 2 and 150 by 2 to get your reduced fraction. x = -¹/₇₅

Question 6

A student answers 60% of the questions right on the test. If there were 25 questions on the test, how many did the student answer correctly?

Accepted Answer

We can use the percent formula to solve. The percent formula is below: ^part⁄_whole = ^%⁄₁₀₀ We are given the whole (the 25 total test questions) and are asked to find the part, which is the number of questions answered correctly (x): ^x⁄₂₅ = ⁶⁰⁄₁₀₀ Cross multiply and solve for x: 100 * x = 25 * 60 100x = 1500 100x/100 = 1500/100 x = 15 So, 15 is 60% of 25

Question 7

Solve the following equation for x. ³⁄₅x - 3 = 9

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: Step 1: Begin to isolate variable by moving numbers that are being added or subtracted to the other side of the equation. Note: We want to move numbers NOT attached to a variable first, if possible. The first thing you want to do is move the ( - 3) to the other side of the equation by adding 3 (opposite operation) to both sides. ³⁄₅x - 3 + 3 = 9 + 3 ³⁄₅x = 12 Step 2: Continue to isolate variable by moving numbers that are being multiplied or divided to the other side of the equation. Then, you need to move the ³⁄₅, which is multiplying x. You do this by dividing (opposite operation) both sides by ³⁄₅. *Remember that when you divide by a fraction, you multiply by its reciprocal, which in this case is ⁵/₃. ⁵/₃• ³⁄₅x = 12 • ⁵/₃ When you multiply two fractions, you can cross-reduce before you multiply across: 11ec0fb7_2739_21f9_95f0_c3973e745aef_NR0002_00 Reduce the numbers diagonal from one another by finding the lowest common factor between the two numbers, then dividing each number by the lowest common factor. The lowest common factor for 12 and 3 is 3. You can reduce both 3's by dividing by 3. This results in each 3 being reduced to 1. You can also reduce both 5's by dividing by 5. This results in each 5 being reduced to 1. 11ec0fb7_2739_21fa_95f0_e3d61bf28ae4_NR0002_00 Now, your new fraction is: 11ec0fb7_2739_21fb_95f0_9f8f4aebf4b0_NR0002_00 We know that this comes out equal to 1, so now we have 1x, which is the same as just x. Step 3: Complete the remaining operations on the opposite side of the equation. x = 12 • ⁵/₃ Since 12 is a whole number, we make it a fraction by making 12 the numerator and 1 the denominator. Reduce the numbers diagonal from one another by finding the lowest common factor between the two numbers, then dividing each number by the lowest common factor. 11ec0fb7_2739_21fc_95f0_4952650bbabd_NR0002_00 In this case, the lowest common factor between 12 and 3 is 3, so we divide both numbers by 3. 5 and 1 do not have any common multiples other than 1, so these numbers cannot be reduced. 11ec0fb7_2739_490d_95f0_af5f7371f10d_NR0002_00 Finally, we multiple the two numerators and two denominators together to reach the final answer. 11ec0fb7_2739_490e_95f0_59717d60aa51_NR0002_00 Answer: 20

Question 8

A car dealership has sold 9 cars from the lot. They had 24 cars at the beginning of the month. What percentage of their lot cars have they sold?

Accepted Answer

We can use the percent formula to solve. The percent formula is below: ^part⁄_whole = ^%⁄₁₀₀ First, we have to determine the part. In this problem, the part is the number of cars that have been sold. We know that the dealership started off with 24 cars (the whole) and sold 9 (the part). So, the part of the percent formula is 9. The whole of the percent formula (the total number of cars) is 24. Now, we have to determine our percent. Since we we don't know the percent, this is where we are going to put our variable (x). ^part⁄_whole = ^%⁄₁₀₀ ⁹⁄₂₄ = ^x⁄₁₀₀ Cross multiply and solve for x: ⁹⁄₂₄ = ^x⁄₁₀₀ 24 * x = 9 * 100 24x = 900 24x/24 = 900/24 x = 37.5 So, 9 is 37.5% of 24.

Question 9

Solve the following equation for x.
-1)4x - 6.3 = 9.1

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite side of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. 
For this problem:
The first thing you want to do is move the ( - 6.3) to the other side of the equation by adding 6.3 (opposite operation) to both sides.
-1.4x - 6.3 = 9.1
-1.4x - 6.3 + 6.3 = 9.1 + 6.3
1.4x = 15.4
Then, you need to move the ( -1.4), which is multiplying x. You do this by dividing (opposite operation) both sides by -1.4.
-1.4x = 15.4
-1.4x ÷ -1.4 = 15.4 ÷ -1.4
x = 15.4 ÷ -1.4
x = -11

Question 10

Solve the following equation for x. 2x + ¹⁄₂ = -¹⁄₇

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: The first thing you want to do is move the ( ¹⁄₂) to the other side of the equation by subtracting ¹⁄₂ (opposite operation) from both sides. 2x + ¹⁄₂ = -¹⁄₇ 2x + ¹⁄₂ - ¹⁄₂ = -¹⁄₇ - ¹⁄₂ 2x = -¹⁄₇ - ¹⁄₂ Next, we need to subtract the fractions. In order to do this, we need to find a common denominator for both fractions. This will be the least common multiple between the two denominators. You can easily find this by listing the multiples of each number: 7: 7, 14, 21, 28, 35… 2: 2, 4, 6, 8, 10, 12, 14, 16… The lowest common multiple between 7 and 2 is 14. In order for the fractions to have the same denominator, we need to multiply each fraction by a fractional version of "1" which is basically any number over itself (e.g. ⁵/₅= 1). In order to get from 7 to 14, we need to multiply it by 2. Therefore, we multiply the entire fraction by ²/₂. In order to get from 2 to 14, we need to multiply it by 7. Therefore, we multiply the entire fraction by ⁷/₇. 2x = (-¹⁄₇ • ²⁄₂) - (¹⁄₂ • ⁷⁄₇) 2x = -²⁄₁₄ - ⁷⁄₁₄ Now that you have a common denominator, you simply subtract the numerators. 2x = -²⁄₁₄ - ⁷⁄₁₄ 2x = -⁹⁄₁₄ Finally, you need to move the 2, which is multiplying x. You do this by dividing (opposite operation) both sides by 2. 2x ÷ 2 = -⁹⁄₁₄ ÷ 2 x = -⁹⁄₁₄ ÷ 2 Any whole number written as a fraction is simply that number over 1. So we have: x = -⁹⁄₁₄ ÷ ²⁄₁ To divide fractions, we multiply by the reciprocal (flip the second fraction and multiply): x = -⁹⁄₁₄ ÷ ²⁄₁ x = -⁹⁄₁₄ • ¹⁄₂ x = -⁹⁄₂₈

Question 11

Simplify the expression: ⁹⁄₅ • 1 ²⁄₃

Accepted Answer

Step 1: Convert Mixed Number to Improper Fraction You can use this formula to convert mixed numbers to improper fractions: a ^b/_c = ^{ac + b}/_c 1 ²⁄₃= ^{(1 • 3) + 2}/₃ = ^{3 + 2}/₃ = ⁵/₃ So, our new expression is: ⁹/₅• ⁵⁄₃ Step 2: Multiply Use the following formula when multiplying fractions: ^a/_b • ^c/_d = ^ac/_bd ⁹/₅• ⁵/₄= ^{(9 • 5)} / _{(5 • 3)}= ⁴⁵ / ₁₅ Step 3: Convert Improper Fractions to Mixed Numbers Next, we change the improper fraction to a mixed number. We do this by first dividing the numerator by the denominator. 45 ÷ 13 = 3 In this case, the numbers divide equally, so the answer is 3.

Question 12

Solve the following equation for x.
2)5x - 1.5 = 3 + 0.5

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. 
For this problem:
The first thing you want to do is move the ( - 1.5) to the other side of the equation by adding 1.5 (opposite operation) to both sides.
2.5x - 1.5 + 1.5 = 3.5 + 1.5
2.5x = 5
Then, you need to move the 2.5, which is multiplying x. You do this by dividing (opposite operation) both sides by 2.5.
2.5x = 5
2.5x ÷ 2.5 = 5÷ 2.5
x =  5÷ 2.5
x = 2

Question 13

Simplify the expression: 4 ³⁄₄ • 1 ¹⁄₂

Accepted Answer

Step 1: Convert First Mixed Number to Improper Fraction You can use this formula to convert mixed numbers to improper fractions: a ^b/_c = ^{ac + b}/_c 4 ³⁄₄= ^{(4 • 4) + 3}/₄ = ^{16 + 3}/₄ = ¹⁹/₄ So, our new expression is: ¹⁹/₄• 1 ¹⁄₂ Step 2: Convert Second Mixed Number to Improper Fraction Use the same formula to convert the second mixed number to an improper fraction: a ^b/_c = ^{ac + b}/_c 1 ¹⁄₂= ^{(1 • 2) + 1}/₂ = ^{2 + 1}/₂ = ³/₂ So, our new expression is: ¹⁹/₄• ³/₂ Step 3: Multiply Use the following formula when multiplying fractions: ^a/_b • ^c/_d = ^ac/_bd ¹⁹/₄• ³/₂= ^{(19 •3)} / _{(4 • 2)}= ⁵⁷ / ₈ Step 4: Convert Improper Fractions to Mixed Numbers Next, we change the improper fraction to a mixed number. We do this by first dividing the numerator by the denominator. 57 ÷ 8 = 7 r1 (7 with a remainder of 1) Then, we identify the whole number. In this example, the whole number of the answer is 7. This means that the whole number in our fractional answer will be 7. Next, we determine what our fraction will be by placing the remainder (1) over the denominator from the original fraction (8). So we now have: 7 ¹ / ₈ Finally, if possible, we reduce the fraction. In this case, it is not possible.

Question 14

Solve the following equation for x:
12x - 3 = 1

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: The first thing you want to do is move the ( - 3) to the other side of the equation by adding 3 (opposite operation) to both sides. 12x - 3 = 1 12x - 3 +3 = 1 +3 12x = 4 Then, you need to move the 12, which is multiplying x. You do this by dividing (opposite operation) both sides by 12. 12x = 4 12x ÷ 12 = 4 ÷ 12 x = 4 ÷ 12 x = ¹⁄₃

Question 15

A businesswoman needs to fly to Bulgaria for a conference. She watches the prices for flights and records the prices each Monday on the graph below.
 The x-axis (horizontal) shows the number of weeks leading up to the flight. Therefore, if x = 5, it means that the flight is in 5 weeks. If x = 10, the flight is in ten weeks, and so on.
Which of the following is affecting the price of the ticket in the graph above?

Accepted Answer

The graph only uses time until departure as a factor in the price of a flight.
The graph does not compare which days of the week you can purchase the tickets.
The person only recorded data on Mondays so we have no comparison to other days of the week. The graph does not compare different days of the week.
We also have no comparison to other destinations. The person only recorded data for one destination. The person did not look at the impact of different destinations on the price of the ticket.
Even though the number of seats is affected by the number of weeks until the flight, this is not what the person used as a variable that affected the price of the ticket.

Question 16

Solve the following equation for x. -18x - 23 = -³⁷⁄₂

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: The first thing you want to do is move the ( - 23) to the other side of the equation by adding 23 (opposite operation) to both sides. -18x - 23 + 23 = -³⁷⁄₂ + 23 -18x = -³⁷⁄₂ + 23 Now let's simplify the right side of the equation. Remember that any whole number in fractional form is that number over 1. -18x = -³⁷⁄₂ + 23 -18x = -³⁷⁄₂ + ²³⁄₁ Next, we need to add the fractions. In order to do this, we need to find a common denominator for both fractions. This will be the least common multiple between the two denominators. You can easily find this by listing the multiples of each number: 1: 1, 2, 3, 4, 5, 6… 2: 2, 4, 6, 8, 10, 12, 14, 16… The lowest common multiple between 1 and 2 is 2. In order for the fractions to have the same denominator, we need to multiply each fraction by a fractional version of "1" which is basically any number over itself (e.g. ⁵/₅= 1). In order to get from 1 to 2, we need to multiply it by 2. Therefore, we multiply the entire fraction by ²/₂. Since the other denominator is already 2, you do not need to multiply the fraction by any number. -18x = -³⁷⁄₂ + ²³⁄₁ -18x = -³⁷⁄₂ + (²³⁄₁ • ²⁄₂) -18x = -³⁷⁄₂ + ⁴⁶⁄₂ Now that you have a common denominator, you simply add the numerators. Remember that you are adding a negative number here, so it's actually 46-37. -18x = -³⁷⁄₂ + ⁴⁶⁄₂ -18x = ⁹⁄₂ Finally, you need to move the -18, which is multiplying x. You do this by dividing (opposite operation) both sides by -18. -18x ÷ -18 = ⁹⁄₂ ÷ -18 Any whole number written as a fraction is simply that number over 1. So we have: x = ⁹⁄₂ ÷ -¹⁸⁄₁ Simplify the right side of the equation. To divide fractions, we multiply by the reciprocal (flip the second fraction and multiply): x = ⁹⁄₂ ÷ -¹⁸⁄₁ x = ⁹⁄₂ • -¹⁄₁₈ Remember that you multiply across the fraction: multiply the two numerators and the two denominators. Since you are multiplying one negative number by one positive number, the answer will also be negative. x = -⁹⁄₃₆ Reduce the final fraction by finding the largest common factor between the numerator and denominator and divide both by that number. 9: 1, 3, 9 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Divide both 9 and 36 by 9 to get your reduced fraction. x = -⁹⁄₃₆ x = -¹⁄₄

Question 17

Solve the equation for x. -2x + 0.25 = ³⁄₄

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. For this problem: The first thing you want to do is move the ( 0.25) to the other side of the equation by subtracting 0.25 (opposite operation) to both sides. -2x + 0.25 - 0.25 = ³⁄₄ - 0.25 -2x = ³⁄₄ - 0.25 Now, let's simplify the right side of the equation. We know 0.25 in fraction form is ¹⁄_4: -2x = ³⁄₄ - 0.25 -2x = ³⁄₄ - ¹⁄₄ -2x = ²⁄₄ -2x = ¹⁄₂ Then, you need to move the (-2), which is multiplying x. You do this by dividing (opposite operation) both sides by -2. -2x = ¹⁄₂ -2x ÷ -2 = ¹⁄₂÷ -2 When dividing with fractions, we need to convert any whole numbers to fractions as well. All whole numbers can be written as a fraction by putting the whole number over 1. So, -2 = -²⁄₁. x = ¹⁄₂ ÷ -²⁄₁ Also remember that when dividing by a fraction, we multiply by the reciprocal. In this case, the reciprocal of -²⁄₁ is -¹⁄₂. x = ¹⁄₂ • -¹⁄₂ x = -¹⁄₄

Question 18

285 people were asked about their favorite type of blanket and the results were graphed below.
 Which of the following is true about the information provided by the graph?

Accepted Answer

14% of people prefer electric and only 10% like fleece. More people like electric.
More than half of people prefer down comforters and electric blankets combined. This is not true. Down and electric together only account for 46% which is not more than half.
The number of people that prefer quilts and down comforters is the same. 32% of people prefer down and 37% prefer quilts. These are not equal.
Overall, most people prefer down comforters. This is not true. 32% of people prefer down comforters, but 37% of people prefer quilts.

Question 19

A small BBQ restaurant in Kansas City, Missouri sells three set meals during their lunchtime rush. They gather data and graph the percentage of orders at each type of meal set, as shown below.
 Which of the following is not true, concerning the graph above?

Accepted Answer

According to the graph, over 50% of guests chose to have Meal Set B, whereas less than 40% chose to have Meal Set A. Therefore, this statement is incorrect.
If you picked a customer at random, there would be a less than 40% chance the guest ate Meal Set A. Meal Set A had slightly less than 40% of the customers order it. This means if you picked a customer at random, there would be a slightly less than 40% chance that they picked Meal Set A. 
The most popular meal set that day was Meal Set B. Meal Set B was ordered by over 50% of the guests that day. It is the most popular meal set for that day.
The popularity of both meal set A and meal set C combined is less than meal set B. Meal set A was ordered by slightly less than 40% of the guests. Meal set B was ordered by approximately 55% of guests.  Meal Set C was ordered by less than 10% of guests. This means the popularity of A and C combined is still less than B.
All of the above are true.

Question 20

Solve the following equation for x.
-4x - 3 = 9

Accepted Answer

When solving an equation with one variable, your goal is to isolate the variable on one side of the equal sign. You do this by moving all of the other numbers to the opposite of the equal sign. You move numbers by performing the opposite operation (subtraction/addition and multiplication/division), on both sides of the equation to keep it balanced. 
For this problem:
The first thing you want to do is move the ( - 3) to the other side of the equation by adding 3 (opposite operation) to both sides.
-4x - 3 = 9
-4x - 3 + 3 = 9 + 3
-4x = 12
Then, you need to move the 4, which is multiplying x. You do this by dividing (opposite operation) both sides by 4.
-4x = 12
-4x ÷ -4 = 12 ÷ -4
x = 12 ÷ -4
x = - 3

Exam 2: ATI-TEAS-Math

A cleaning service offers packages up to 6 full hours of cleaning. The company charges $20 per hour for the first 4 hours and $35 per hour after that. Which of the following graphs best represents the relationship between the cost and total number hours of cleaning service provided?

The area of a bedroom is 12m². What is the area of the bedroom in feet when 1 meter is 3.28 feet?

Solve the following equation for x. 4x - ⁵⁄₄ = 4.75

Jeremy places in the top 98% of students for a standardized test. If there were approximately 35 million students took the exam, how many students did he score better than?

Solve the following equation for x. 10x- ²⁄₃ = -⁴⁄₅

A student answers 60% of the questions right on the test. If there were 25 questions on the test, how many did the student answer correctly?

Solve the following equation for x. ³⁄₅x - 3 = 9

A car dealership has sold 9 cars from the lot. They had 24 cars at the beginning of the month. What percentage of their lot cars have they sold?

Solve the following equation for x. -1) 4x - 6.3 = 9.1

Solve the following equation for x. 2x + ¹⁄₂ = -¹⁄₇

Simplify the expression: ⁹⁄₅ • 1 ²⁄₃

Solve the following equation for x. 2) 5x - 1.5 = 3 + 0.5

Simplify the expression: 4 ³⁄₄ • 1 ¹⁄₂

Solve the following equation for x: 12x - 3 = 1

Solve the following equation for x. -18x - 23 = -³⁷⁄₂

Solve the equation for x. -2x + 0.25 = ³⁄₄

285 people were asked about their favorite type of blanket and the results were graphed below. Which of the following is true about the information provided by the graph?

A small BBQ restaurant in Kansas City, Missouri sells three set meals during their lunchtime rush. They gather data and graph the percentage of orders at each type of meal set, as shown below. Which of the following is not true, concerning the graph above?

Solve the following equation for x. -4x - 3 = 9

Exam 2: ATI-TEAS-Math

A cleaning service offers packages up to 6 full hours of cleaning. The company charges $20 per hour for the first 4 hours and $35 per hour after that. Which of the following graphs best represents the relationship between the cost and total number hours of cleaning service provided?

The area of a bedroom is 12m2. What is the area of the bedroom in feet when 1 meter is 3.28 feet?

Solve the following equation for x. 4x - 5⁄4 = 4.75

Jeremy places in the top 98% of students for a standardized test. If there were approximately 35 million students took the exam, how many students did he score better than?

Solve the following equation for x. 10x- 2⁄3 = -4⁄5

A student answers 60% of the questions right on the test. If there were 25 questions on the test, how many did the student answer correctly?

Solve the following equation for x. 3⁄5 x - 3 = 9

A car dealership has sold 9 cars from the lot. They had 24 cars at the beginning of the month. What percentage of their lot cars have they sold?

Solve the following equation for x. -1) 4x - 6.3 = 9.1

Solve the following equation for x. 2x + 1⁄2 = -1⁄7

Simplify the expression: 9⁄5 • 1 2⁄3

Solve the following equation for x. 2) 5x - 1.5 = 3 + 0.5

Simplify the expression: 4 3⁄4 • 1 1⁄2

Solve the following equation for x: 12x - 3 = 1

Solve the following equation for x. -18x - 23 = -37⁄2

Solve the equation for x. -2x + 0.25 = 3⁄4

285 people were asked about their favorite type of blanket and the results were graphed below. Which of the following is true about the information provided by the graph?

A small BBQ restaurant in Kansas City, Missouri sells three set meals during their lunchtime rush. They gather data and graph the percentage of orders at each type of meal set, as shown below. Which of the following is not true, concerning the graph above?

Solve the following equation for x. -4x - 3 = 9

The area of a bedroom is 12m². What is the area of the bedroom in feet when 1 meter is 3.28 feet?

Solve the following equation for x. 4x - ⁵⁄₄ = 4.75

Solve the following equation for x. 10x- ²⁄₃ = -⁴⁄₅

Solve the following equation for x. ³⁄₅x - 3 = 9

Solve the following equation for x. 2x + ¹⁄₂ = -¹⁄₇

Simplify the expression: ⁹⁄₅ • 1 ²⁄₃

Simplify the expression: 4 ³⁄₄ • 1 ¹⁄₂

Solve the following equation for x. -18x - 23 = -³⁷⁄₂

Solve the equation for x. -2x + 0.25 = ³⁄₄