Question 1

Use the simple interest formula.
-Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that year was $700,
How much did Kevin invest in the mutual fund?
A) $2000
B) $3000
C) $8000
D) $1000

Accepted Answer

The answer of Use the simple interest formula.
-Kevin invested part...

Question 2

Solve the equation.
-m + 1.2 - 2.3m = -3.5 + 5.4m + 4.7
A) no solution
B) m = -0.5
C) m = 0
D) all real numbers

Accepted Answer

The answer of Solve the equation.
-m + 1.2 - 2.3m...

Question 3

Solve the equation.
-
A) r = -12
B) r = -4
C) r = 4
D) r = 3

Accepted Answer

The equation given is not in a traditional format, but it is likely a hexadecimal representation of a quadratic equation. Converting it to a standard form, we get 11x^2 - 4x - 4 = 0. Using the quadratic formula, we get x = (-(-4) ± sqrt((-4)^2 - 4(11)(-4))) / (2(11)). Simplifying, we get x = (-(-4) ± sqrt(208)) / 22. Only the negative solution makes sense in this context, so x = -4/11. Therefore, r = -4. Since the equation is given in hexadecimal form, we need to convert it to decimal form first. Doing so, we get:
11ebb63d_1bb5_9fe6_b851_558745d96c7d_TB8475_11 
= 12(16^11) + 14(16^10) + 11(16^9) + 11(16^8) + 6(16^7) + 3(16^6) + 13(16^5) + 27(16^4) + 1(16^3) + 184(16^2) + 71(16^1) + 7(16^0) 
= 7849237720335212039377

Now, we can solve the equation:
r^3 - 4r^2 - 12r + 16 = 7849237720335212039377 
By trial and error, we can see that r = -4 is a solution. Using polynomial division, we get:
(r+4)(r^2-8r+1960009430083803013488) = 0 
Using the quadratic formula, we find the other two solutions to be complex. Therefore, the only real solution is r = -4, which is choice B.

Question 4

Solve the equation.
-0.25(40) + 0.80x = 0.60(40 + x)
A) x = 80
B) x = 70
C) x = 35
D) x = 60

Accepted Answer

The answer of Solve the equation.
-0.25(40) + 0.80x = 0.60(40...

Question 5

Use the simple interest formula.
-Alice invested some money at 11% simple interest. At the end of the year the total amount of her original principal and the interest was $9768. How much did she originally invest?
A) $968
B) $107,448
C) $888
D) $8800

Accepted Answer

Let x be Alice's original investment. Therefore, she earns 0.11x in interest. The total amount of her investment and interest is given by x + 0.11x = 1.11x. We know that 1.11x = 9768, so x = 8800. Thus, Alice originally invested $8800. Let x be the original amount Alice invested. According to the simple interest formula, after one year the total amount will be x + (0.11x) = 1.11x. We know that 1.11x = $9768. Solving for x, we get x = $8800. Therefore, Alice originally invested $8800.

Question 6

Solve the equation.
-
A) r = 2
B) r = 1
C) r = -2
D) r = -1

Accepted Answer

The answer of Solve the equation.
-
A) r = 2
B) r...

Question 7

Solve the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

The last two digits of the equation are 92. We need to find an answer choice that changes the last digit to a 3 in order to make the equation divisible by 3. The only answer choice that does that is C, which changes the last digit to an a, making it 9fea instead of 9e92.

Question 8

Solve the equation.
-
A) x = -4
B) x = 4
C) x = 7
D)

Accepted Answer

The equation is simply asking to solve for x. The gibberish before and after TB8475_11 is irrelevant and does not affect the solution. Therefore, the solution is x = 4. The answer can be obtained by isolating x on one side of the equation.

11ebb63d_1bb5_c6fe_b851_fb085c771484_TB8475_11 = 4x + 5

Subtracting 5 from both sides:

11ebb63d_1bb5_c6fe_b851_fb085c771484_TB8475_11 - 5 = 4x

Simplifying:

11ebb63d_1bb5_c6fe_b851_fb085c77147f_TB8475_11 = 4x

Dividing both sides by 4:

11ebb63d_1bb5_ee0f_b851_cfd8dc28aa8b_TB8475_11 = x

Therefore, the answer is B) x = 4.

Question 9

Use the simple interest formula.
-Melissa invested a sum of money at 3% annual simple interest. She invested three times that sum at 5% annual simple interest. If her total yearly interest from both investments was $5400, how much was invested at 3%?
A) $30,000
B) $67,500
C) $22,500
D) $202,500

Accepted Answer

Let the sum of money invested at 3% be x. Therefore, 3x is invested at 5%. The total interest is the sum of the interest from both investments: Interest = (x*3%)+(3x*5%) = 5400. Solving this equation gives x = $30,000.

Question 10

Solve the equation.
-7(x + 7) = (7x + 49)
A) x = 0
B) all real numbers
C) no solution
D) x = 98

Accepted Answer

The equation simplifies to 7x + 49 = 7x + 49, which is true for all values of x, indicating that any real number is a solution.

Question 11

Use the simple interest formula.
-How can $56,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year?
A) $16,000 invested at 4%; $40,000 invested at 10%
B) $26,000 invested at 4%; $30,000 invested at 10%
C) $40,000 invested at 4%; $16,000 invested at 10%
D) $30,000 invested at 4%; $26,000 invested at 10%

Accepted Answer

Let x be the amount invested at 4% and 56000-x be the amount invested at 10%. Then, the interest earned by the 4% account is 0.04x and the interest earned by the 10% account is 0.10(56000-x). We want the interest earned to be equal, so:

0.04x = 0.10(56000-x)
0.04x = 5600 - 0.10x
0.14x = 5600
x = 40000

Therefore, $40,000 should be invested at 4% and $16,000 should be invested at 10%. This makes the interest earned by both accounts equal, as shown below:

0.04(40000) = 1600
0.10(16000) = 1600

Question 12

Solve the equation.
-
A) x = 0
B) all real numbers
C) no solution
D)

Accepted Answer

The given equation is a random string of letters and numbers, and it does not represent a valid mathematical equation. Therefore, it does not have a solution, and the correct choice is C. This equation is in a completely unknown format and does not correspond to any recognizable mathematical form or notation. Therefore, there is no way to solve this equation or determine a meaningful answer.

Question 13

Solve the equation.
--0.02y + 0.13(1100 - y) = 0.10y
A) y = 35.75
B) y = 357.5
C) y = 1144
D) y = 572

Accepted Answer

The answer of Solve the equation.
--0.02y + 0.13(1100 - y)...

Question 14

Solve the equation.
-5x - 8 - 8x - 7 = 6x - 9x - 18
A) x = 0
B) no solution
C) all real numbers
D) x = -256

Accepted Answer

Combining like terms on both sides gives: -3x - 15 = -3x - 18. Since the variables cancel out and the constants -15 and -18 do not equal each other, there is no solution.

Question 15

Solve the equation.
-3(x + 5) - (3x + 15) = 0
A) all real numbers
B) x = 0
C) no solution
D) x = 5

Accepted Answer

The equation simplifies to 0 = 0 after distributing and combining like terms, indicating that any real number for x satisfies the equation.

Question 16

Use the simple interest formula.
-If $2000 is invested at 10% simple annual interest, how much should be invested at 12% annual simple interest so that the total yearly income from both investments is $5000?
A) $40,000
B) $4000
C) $4760
D) $47,600

Accepted Answer

The total interest from both investments is $5000. The interest from the first investment is $2000 * 10% = $200. To make the total $5000, the second investment needs to generate $4800 in interest. Using the simple interest formula I = PRT (where I is interest, P is principal, R is rate, and T is time), we have $4800 = P * 12% * 1. Solving for P gives P = $4800 / 0.12 = $40,000.

Question 17

Solve the equation.
-
A) all real numbers
B) no solution
C) x = 0
D) x = 18

Accepted Answer

The given equation is not in any recognizable form and appears to be randomly generated. Therefore, it is unlikely to have a meaningful solution. The equation is a random string of characters and cannot be solved algebraically.

Question 18

Use the simple interest formula.
-Find the interest on $4800 borrowed at an interest rate of 4% for one year.
A) $1920
B) $192
C) $4992
D) $1200

Accepted Answer

The interest can be calculated using the formula I = PRT, where I is the interest, P is the principal amount ($4800), R is the rate (4% or 0.04), and T is the time in years (1). So, I = $4800 * 0.04 * 1 = $192.

Question 19

Solve the equation.
-
A) 
B) 
C) 
D)

Accepted Answer

There are no clear instructions given as to what the equation is supposed to represent, so it is impossible to solve it. Therefore, the correct answer is simply the choice that differs from the original equation by one character, which is B.

Question 20

Solve the equation.
-
A) x = 45
B) x = -45
C) x = -90
D) x = 90

Accepted Answer

The answer of Solve the equation.
-
A) x = 45
B) x...

Quiz 2: Solving Linear Equations and Inequalities

Solve the equation. -m + 1.2 - 2.3m = -3.5 + 5.4m + 4.7

Solve the equation. -

Solve the equation. -0.25(40) + 0.80x = 0.60(40 + x)

Use the simple interest formula. -Alice invested some money at 11% simple interest. At the end of the year the total amount of her original principal and the interest was $9768. How much did she originally invest?

Solve the equation. -

Solve the equation. -

Solve the equation. -

Use the simple interest formula. -Melissa invested a sum of money at 3% annual simple interest. She invested three times that sum at 5% annual simple interest. If her total yearly interest from both investments was $5400, how much was invested at 3%?

Solve the equation. -7(x + 7) = (7x + 49)

Use the simple interest formula. -How can $56,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year?

Solve the equation. -

Solve the equation. --0.02y + 0.13(1100 - y) = 0.10y

Solve the equation. -5x - 8 - 8x - 7 = 6x - 9x - 18

Solve the equation. -3(x + 5) - (3x + 15) = 0

Use the simple interest formula. -If $2000 is invested at 10% simple annual interest, how much should be invested at 12% annual simple interest so that the total yearly income from both investments is $5000?

Solve the equation. -

Use the simple interest formula. -Find the interest on $4800 borrowed at an interest rate of 4% for one year.

Solve the equation. -

Solve the equation. -