Question 1

Solve the problem.
-A college student earned $5,700 during summer vacation working as a waiter in a popular restaurant. Thestudent invested part of the money at 7% and the rest at 6%. If the student received a total of $378 ininterest at the end of the year, how much was invested at 7%?
A)$3,600
B)$2,100
C)$2,850
D)$950

Accepted Answer

The student invested $3,600 at 7% and $2,100 at 6%. The interest from the 7% investment is $3,600 * 0.07 = $252, and from the 6% investment is $2,100 * 0.06 = $126. The total interest is $252 + $126 = $378, which matches the given total interest.

Question 2

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-Express that x differs from -7 by more than 3 as an inequality involving absolute value. Solve for x.

Accepted Answer

The answer of Write the word or phrase that best...

Question 3

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-Momentum is the product of the mass of an object and its velocity.
A)If M represents momentum, m mass, and v velocity, then M = mv.
B)If M represents momentum, m mass, and v velocity, then 
C)If M represents momentum, m mass, and v velocity, then 
D)If M represents momentum, m mass, and v velocity, then M = m + v.

Accepted Answer

The equation M = mv represents the product of the mass of an object (m) and its velocity (v) equaling its momentum (M). The equation M = mv represents momentum as the product of the mass (m) of an object and its velocity (v).

Question 4

Write the word or phrase that best completes each statement or answers the question.
-Martin purchased some municipal bonds yielding 8% annually and some certificates of deposit yielding11% annually. If Martinʹs investment amounts to $23,000 and the annual income is $2230, how muchmoney is invested in bonds and how much is invested in certificates of deposit?

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-The force of gravity between two objects is the gravitational constant times the product of their massesdivided by the square of the distance between them.
A)If F is the force of gravity, G the gravitational constant,  the mass of one object,  the mass of the second, and d the distance between them, then 
B)If F is the force of gravity, G the gravitational constant,  he mass of one object,  the mass of the second, and d the distance between them, then 
C)If F is the force of gravity, G the gravitational constant, m1 the mass of one object,  the mass of the second, and d the distance between them, then 
D)If F is the force of gravity, G the gravitational constant,  the mass of one object,  the mass of the second, and d the distance between them, then

Accepted Answer

The answer of Translate the sentence into a mathematical equation....

Question 6

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-The profit derived from the sale of x video cameras is $330 per unit less the sum of $2,100 costs plus $120per unit.
A)If P is profit and x the units sold, then 
B)If P is profit and x the units sold, then 
C)If P is profit and x the units sold, then 
D)If P is profit and x the units sold, then

Accepted Answer

The answer of Translate the sentence into a mathematical equation....

Question 7

Find a and b.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find a and b.
-
A) 
B) 
C) 
D)...

Question 8

Solve the problem.
-A loan officer at a bank has $97,000 to lend and is required to obtain an average return of 12% per year. Ifhe can lend at the rate of 13% or the rate of 11%, how much can he lend at the 11% rate and still meet hisrequired return?
A)$48,500.00
B)$4,041.67
C)$1,212,500.00
D)$7,461.54

Accepted Answer

Let x be the amount of money the loan officer can lend at 13% and y be the amount of money he can lend at 11%. We can set up a system of equations to represent the given information:

x + y = $97,000 (total amount lent)
0.13x + 0.11y = 0.12($97,000) (required average return)

Simplifying the second equation, we get:

0.13x + 0.11y = $11,640

Multiplying both sides by 100 to eliminate the decimals, we get:

13x + 11y = $1,164,000

Now we can use substitution to solve for y:

x + y = $97,000
x = $97,000 - y

Substituting into the equation above, we get:

13($97,000 - y) + 11y = $1,164,000

Simplifying and solving for y, we get:

$1,261,000 - 2y = $1,164,000
$97,000 = 2y
y = $48,500

Therefore, the loan officer can lend $48,500 at 11% and still meet his required return of 12%. Let's assume the loan officer lends $x at 13% and $(97,000-x) at 11%.

The annual return from lending $x at 13% is 0.13x.
The annual return from lending $(97,000-x) at 11% is 0.11(97,000-x).

We know that the overall annual return must be 12%, so:

0.13x + 0.11(97,000-x) = 0.12(97,000)

Simplifying this equation, we get:

0.02x = 1,050

x = $52,500

Therefore, the loan officer can lend $(97,000-$52,500) = $44,500 at 11% and still meet his required return.

So, the answer is A) $48,500.00.

Question 9

Solve the inequality. Express your answer in set notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality. Express your answer in...

Question 10

Solve the inequality. Express your answer in set notation.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Solve the inequality. Express your answer in...

Question 11

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-The volume of a right prism is the area of the base times the height of the prism.
A)If V represents the volume, B the area of the base, and h the height, then V = Bh.
B)If V represents the volume, B the area of the base, and h the height, then V = B + h.
C)If V represents the volume, B the area of the base, and h the height, then 
D)If V represents the volume, B the area of the base, and h the height, then

Accepted Answer

The equation V = Bh represents the volume of a right prism, where V is the volume, B is the area of the base, and h is the height. The multiplication symbol is implied between B and h. In this equation, V represents the volume, which is a measure of the space enclosed by the prism. B represents the area of the base, which is the measure of the surface area of the base of the prism. h represents the height, which is the measure of the distance from the base to the top of the prism. Therefore, the equation V = Bh is stating that the volume of the prism is equal to the product of the area of the base and the height of the prism.

Question 12

Solve the problem.
-Don James wants to invest $65,000 to earn $6,600 per year. He can invest in B-rated bonds paying 15% peryear or in a Certificate of Deposit (CD)paying 6% per year. How much money should be invested in eachto realize exactly $6,600 in interest per year?
A)$30,000 in B-rated bonds and $35,000 in a CD
B)$35,000 in B-rated bonds and $30,000 in a CD
C)$31,000 in B-rated bonds and $34,000 in a CD
D)$34,000 in B-rated bonds and $31,000 in a CD

Accepted Answer

To earn $6,600 per year, let x be the amount invested in B-rated bonds at 15%, and y be the amount invested in a CD at 6%. We have the equations: x + y = $65,000 and 0.15x + 0.06y = $6,600. Solving these equations gives x = $30,000 and y = $35,000.

Question 13

Solve the problem.
-A bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 6% per year. If theinterest received was $6,040, how much was loaned at 13%?
A)$28,000
B)$40,000
C)$29,000
D)$39,000

Accepted Answer

The total interest for the year can be represented by the equation: 0.13x + 0.06(68,000 - x) = 6,040, where x is the amount loaned at 13%. Solving this equation for x gives the amount loaned at 13% as $28,000.

Question 14

Solve the problem.
-Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9%annually. If Susanʹs investment amounts to $19,000 and the annual income is $1590, how much money isinvested in bonds and how much is invested in certificates of deposit?
A)$5500 in bonds; $13,500 in certificates of deposit
B)$13,000 in bonds; $6000 in certificates of deposit
C)$13,500 in bonds; $5500 in certificates of deposit
D)$6000 in bonds; $13,000 in certificates of deposit

Accepted Answer

The answer of Solve the problem.
-Susan purchased some municipal bonds...

Question 15

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-Speed is measured by distance divided by time.
A)If S represents speed, d distance, and t time, then 
B)If S represents speed, d distance, and t time, then 
C)If S represents speed, d distance, and t time, then 
D)If S represents speed, d distance, and t time, then

Accepted Answer

The answer of Translate the sentence into a mathematical equation....

Question 16

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differfrom the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value thatexpresses the relationship between the actual weight x of a bag and 40 pounds. Over what range may theweight of a 40-pound bag of to soil vary?

Accepted Answer

The answer of Write the word or phrase that best...

Question 17

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-The surface area of a sphere is 4π times the square of the radius.
A)If S represents the surface area and r the radius, then 
B)If S represents the surface area and r the radius, then 
C)If S represents the surface area and r the radius, then 
D)If S represents the surface area and r the radius, then

Accepted Answer

The answer of Translate the sentence into a mathematical equation....

Question 18

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols.
-The total cost of producing refrigerators in one production line is $3,600 plus $270 per unit produced.
A)If C is the total cost and x is the number of units produced, then C = 3,600 + 270x.
B)If C is the total cost and x is the number of units produced, then C = 3,600x + 270.
C)If C is the total cost and x is the number of units produced, then C = (3,600 + 270)x.
D)If C is the total cost and x is the number of units produced, then

Accepted Answer

The equation should start with the total cost (C) equals a fixed cost ($3,600) plus a variable cost (270x) for each unit produced. Therefore, the correct equation is C = 3,600 + 270x. Option B is incorrect because it implies that the fixed cost is multiplied by the number of units produced (3,600x), which is not the case. Option C is incorrect because it mistakenly puts the addition inside the parentheses, changing the meaning of the equation. Option D is invalid because it is not a complete equation. The equation needs to represent the total cost (C) as a function of the number of units produced (x), which means multiplying the per-unit cost by the number of units produced and adding the fixed cost. Therefore, the correct equation is C = 3,600 + 270x.

Question 19

Find a and b.
-
A)a = 5, b = 9
B)a = 1, b = 5
C)a = 2, b = 6
D)a = -5, b = -1

Accepted Answer

The answer of Find a and b.
-
A)a = 5, b...

Question 20

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-Chi is assigned to construct a triangle with the measure b of the base and the measure h of the heightdiffering by no more than 0.2 centimeters. Express the relationship between b and h as an inequalityinvolving absolute value.

Accepted Answer

The answer of Write the word or phrase that best...

Quiz 1: Equations and Inequalities

Solve the problem. -A college student earned $5,700 during summer vacation working as a waiter in a popular restaurant. Thestudent invested part of the money at 7% and the rest at 6%. If the student received a total of $378 ininterest at the end of the year, how much was invested at 7%?

Write the word or phrase that best completes each statement or answers the question. Solve the problem. -Express that x differs from -7 by more than 3 as an inequality involving absolute value. Solve for x.

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -Momentum is the product of the mass of an object and its velocity.

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -The force of gravity between two objects is the gravitational constant times the product of their massesdivided by the square of the distance between them.

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -The profit derived from the sale of x video cameras is $330 per unit less the sum of $2,100 costs plus $120per unit.

Find a and b. -

Solve the problem. -A loan officer at a bank has $97,000 to lend and is required to obtain an average return of 12% per year. Ifhe can lend at the rate of 13% or the rate of 11%, how much can he lend at the 11% rate and still meet hisrequired return?

Solve the inequality. Express your answer in set notation. -

Solve the inequality. Express your answer in set notation. -

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -The volume of a right prism is the area of the base times the height of the prism.

Solve the problem. -Don James wants to invest $65,000 to earn $6,600 per year. He can invest in B-rated bonds paying 15% peryear or in a Certificate of Deposit (CD) paying 6% per year. How much money should be invested in eachto realize exactly $6,600 in interest per year?

Solve the problem. -A bank loaned out $68,000, part of it at the rate of 13% per year and the rest at a rate of 6% per year. If theinterest received was $6,040, how much was loaned at 13%?

Solve the problem. -Susan purchased some municipal bonds yielding 7% annually and some certificates of deposit yielding 9%annually. If Susanʹs investment amounts to $19,000 and the annual income is $1590, how much money isinvested in bonds and how much is invested in certificates of deposit?

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -Speed is measured by distance divided by time.

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -The surface area of a sphere is 4π times the square of the radius.

Translate the sentence into a mathematical equation. Be sure to identify the meaning of all symbols. -The total cost of producing refrigerators in one production line is $3,600 plus $270 per unit produced.

Find a and b. -