Question 1

The owner of a candy store wants to make a(n) 16-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for $0.90 per pound and lemon gumdrops sell for $1.30 per pound, how many pounds of each should be used? NOTE: All the values were rounded to the nearest whole number.

Accepted Answer

To solve this, we can set up a system of equations. Let $x$ be the pounds of lemon gumdrops and $y$ be the pounds of red licorice bits. We have two equations:1. $x + y = 16$ (the total weight of the mixture)2. $1.30x + 0.90y = 16$ (the total cost of the mixture)Solving this system, we find that $x = 4$ and $y = 12$, meaning 4 pounds of lemon gumdrops and 12 pounds of red licorice bits are needed.

Question 2

Paint costing $21 per gallon is to be mixed with 5 gallons of paint thinner costing $3 per gallon to make a paint that can be sold for $16 per gallon. Refer to the table below and compute how much of the new paint mixture will be produced.  Paint   gal  Thinner   gal  Mixture   gal

Accepted Answer

The answer of Paint costing $21 per gallon is to...

Question 3

Graph the solution set.

Accepted Answer

The answer of Graph the solution set. 
...

Question 4

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,450 has grown to be $4,720?

Accepted Answer

The answer of The amount A in an account is...

Question 5

Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 2 mph, and the other team, on foot, heads south at 1 mph. How long will it take them to search a distance of 9 miles between them?

Accepted Answer

The teams are moving apart at a combined speed of 3 mph (2 mph north + 1 mph south). To cover a distance of 9 miles at 3 mph, it will take 3 hours.

Question 6

If one of two supplementary angles is  larger than the other, find the measure of the smaller angle.

Accepted Answer

The answer of If one of two supplementary angles is...

Question 7

Solve the inequality. Use interval notation to describe the solution.

Accepted Answer

The answer of Solve the inequality. Use interval notation to...

Question 8

Graph the solution set.

Accepted Answer

The answer of Graph the solution set. 
...

Question 9

Lured by the ad in the illustration below, a woman invested $11,100, some in a money market account and the rest in a 5-year CD. How much was invested in each account if the income from both investments is $978 per year? First Republic Savings and Loan Account Rate NOW 5.5% Savings 7.5% Money market 8.0% Checking 4.0% 5-year CD 9.0%

Accepted Answer

The income from the money market account at 8.0% and the CD at 9.0% should total $978. Solving the equations: 0.08x + 0.09(11100-x) = 978 gives x = $2,100 in the money market and $9,000 in the CD.

Question 10

An amount P , invested at a simple interest rate r , will grow to an amount A in t years, according to the formula A = P ( 1 + r t ). Suppose a man invested some money at 5.9%. If after 5 years, he had $6,151.25 on deposit, what amount did he originally invest? Round your answer to the nearest integer.

Accepted Answer

The answer of An amount P , invested at a...

Question 11

A solution contains 0.2 liters of sulfuric acid. If this represents 8% of the total amount, find the total amount.

Accepted Answer

To find the total amount, divide the amount of sulfuric acid by the percentage it represents: 0.2 liters / 0.08 = 2.5 liters.

Question 12

At lunchtime, a man called his wife from his office to tell her that they needed to switch vehicles so that he could use the family van to pick up some building materials after work. The wife then left their home, traveling towards his office in their van at 32 mph. At the same time, the husband left his office in his car, traveling towards their home at 47 mph. If his office is 47.4 miles from their home, how long will it take them to meet so that they can switch vehicles?

Accepted Answer

To find the time it takes for the couple to meet, we need to first determine how far they are from each other initially. We do this by adding their individual distances traveled, which we can find using the formula:

distance = rate × time

Let t be the time it takes for them to meet. Then, the wife travels a distance of 32t miles, while the husband travels a distance of 47t miles. So, initially, they are:

47.4 - (32t + 47t) miles apart

Simplifying this expression, we get:

47.4 - 79t miles apart

To find the time it takes for them to meet, we need to set this expression equal to zero (i.e., when they are at the same location). Thus, we have:

47.4 - 79t = 0

Solving for t, we get:

t = 0.6 hours

Therefore, the answer is C) 0.6 hr.

Question 13

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as  and  , are called adjacent angles. Angles that are nonadjacent, such as  and  or  and  , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If   and  , find x . Read  as "the measure of  ".

Accepted Answer

The answer of When two lines intersect as in the...

Question 14

Find x .

Accepted Answer

The letter "x" in the given string is representing a hexadecimal digit. We need to convert this digit to its decimal equivalent to find the value of x. 
The hexadecimal digit in question is "c1", which is equivalent to 193 in decimal. 
Now, we need to find a number out of the given options which is divisible by 193. 
Option D (32) is divisible by 193, and the quotient is 6. 
Therefore, x = 6, which corresponds to option D.

Question 15

Mary bought pound of two sorts of cookies for $1 per pound. If cookie with apricot jam $0.90 per pound and cookies with lemon jam $1.20 per pound, how many pounds of cookies with apricot jam did she buy? NOTE: Round your answer to the nearest tenth.

Accepted Answer

Let x be the pounds of apricot cookies and y be the pounds of lemon cookies. We have the equations: x + y = 1 and 0.9x + 1.2y = 1. Solving these, we find x = 0.7.

Question 16

A garden store sells Kentucky bluegrass seed for $6 per pound and ryegrass seed for $3 per pound. How much rye must be mixed with 180 pounds of bluegrass to obtain a blend that will sell for $5 per pound?

Accepted Answer

The price of the blend ($5 per pound) is exactly in the middle of the prices of Kentucky bluegrass ($6 per pound) and ryegrass ($3 per pound). This means the blend should have equal amounts of Kentucky bluegrass and ryegrass to achieve the average price. Therefore, to mix with 180 pounds of bluegrass, 180 pounds of ryegrass are needed to get a blend that sells for $5 per pound. However, the correct answer is not listed, indicating a mistake in the question or answer choices. Given the options, none directly match the correct calculation based on the provided prices and desired blend price.

Question 17

Granville and Preston are 522 miles apart. A car leaves Preston bound for Granville at 44 mph. At the same time, another car leaves Granville bound for Preston at 43 mph. How long will it take them to meet?

Accepted Answer

The answer of Granville and Preston are 522 miles apart....

Question 18

Solve the inequality. Use interval notation to describe the solution.

Accepted Answer

The answer of Solve the inequality. Use interval notation to...

Question 19

Graph the inequality.

Accepted Answer

The answer of Graph the inequality. 
...

Question 20

Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 23 gallons of milk containing 6% butterfat? __________ gallons

Accepted Answer

The answer of Cream is approximately 22% butterfat. How many...

Quiz 2: Equations and Inequalities

The owner of a candy store wants to make a(n) 16-pound mixture of two candies to sell for $1 per pound. If red licorice bits sell for $0.90 per pound and lemon gumdrops sell for $1.30 per pound, how many pounds of each should be used? NOTE: All the values were rounded to the nearest whole number.

Paint costing $21 per gallon is to be mixed with 5 gallons of paint thinner costing $3 per gallon to make a paint that can be sold for $16 per gallon. Refer to the table below and compute how much of the new paint mixture will be produced. Paint gal Thinner gal Mixture gal

Graph the solution set.

The amount A in an account is given by the formula A = p + i where p is the principal and i is the interest. How much interest was earned if an original deposit (the principal) of $4,450 has grown to be $4,720?

Two search-and-rescue teams leave base camp at the same time, looking for a lost child. The first team, on horseback, heads north at 2 mph, and the other team, on foot, heads south at 1 mph. How long will it take them to search a distance of 9 miles between them?

If one of two supplementary angles is larger than the other, find the measure of the smaller angle.

Solve the inequality. Use interval notation to describe the solution.

Graph the solution set.

A solution contains 0.2 liters of sulfuric acid. If this represents 8% of the total amount, find the total amount.

Find x .

Mary bought pound of two sorts of cookies for $1 per pound. If cookie with apricot jam $0.90 per pound and cookies with lemon jam $1.20 per pound, how many pounds of cookies with apricot jam did she buy? NOTE: Round your answer to the nearest tenth.

A garden store sells Kentucky bluegrass seed for $6 per pound and ryegrass seed for $3 per pound. How much rye must be mixed with 180 pounds of bluegrass to obtain a blend that will sell for $5 per pound?

Granville and Preston are 522 miles apart. A car leaves Preston bound for Granville at 44 mph. At the same time, another car leaves Granville bound for Preston at 43 mph. How long will it take them to meet?

Solve the inequality. Use interval notation to describe the solution.

Graph the inequality.

Cream is approximately 22% butterfat. How many gallons of cream must be mixed with milk testing at 2% butterfat to get 23 gallons of milk containing 6% butterfat? __________ gallons