Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-15s + 38 + 3(5s - 10) = 0
Question 21 options:
A)
Conditional; {5}
B)
Identity; {all real numbers}
C)
Contradiction; ∅
D)
Conditional; {1}
To determine the solution set for the equation, let's simplify it:
-15s + 38 + 3(5s - 10) = 0
-15s + 38 + 15s - 30 = 0
38 - 30 = 0
8 = 0
Since 8 does not equal 0, this implies that there is no value of s that satisfies the equation. Therefore, the equation is a contradiction, and the solution set is the empty set (∅).
So, the correct answer is:
C)
Contradiction; ∅
Convert.
56 in. = underbar( ) ftunderbar( ) in.
Question 22 options:
A)
4 ft 7 in.
B)
4 ft 8 in.
C)
3 ft 20 in.
D)
8 ft 4 in.
To convert 56 inches to feet and inches, divide the total number of inches by 12.
56 inches ÷ 12 = 4 feet remainder 8 inches
So, 56 inches is equivalent to 4 feet and 8 inches.
The correct answer is:
B)
4 ft 8 in.
Solve.
The tree in the Morton's back yard is 7.8 m tall. Because it blocks too much light, they ask a tree trimmer to remove the top (1/3) of the tree. How tall will the tree be after being shortened?
Question 23 options:
A)
5.2 m
B)
5.1 m
C)
7.5 m
D)
2.6 m
To find the height of the tree after being shortened, we need to subtract 1/3 of the original height from the original height.
Original height of the tree = 7.8 m
1/3 of the original height = 1/3 * 7.8 = 2.6 m
Height of the tree after being shortened = 7.8 - 2.6 = 5.2 m
So, the tree will be 5.2 meters tall after being shortened.
The correct answer is:
A)
5.2 m
Solve the problem. Round to the nearest tenth if necessary.
Enrollment in a business seminar increased from 70 people to 94 people. What was the percent of increase?
Question 24 options:
A)
65.7%
B)
25.5%
C)
74.5%
D)
34.3%
To find the percent increase, we need to find the difference between the final enrollment and the initial enrollment, then divide that difference by the initial enrollment, and finally multiply by 100.
Initial enrollment = 70
Final enrollment = 94
Difference = Final enrollment - Initial enrollment = 94 - 70 = 24
Percent increase = (Difference / Initial enrollment) * 100 = (24 / 70) * 100 ≈ 34.3%
So, the percent of increase is approximately 34.3%.
The correct answer is:
D)
34.3%
Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
4(24t + 16) = 16(2t - 4)
Question 25 options:
A)
Conditional; {-0}
B)
Conditional; {-2}
C)
Contradiction; ∅
D)
Identity; {all real numbers}
To determine the solution set for the equation, let's simplify it:
4(24t + 16) = 16(2t - 4)
96t + 64 = 32t - 64
96t - 32t = -64 - 64
64t = -128
t = -128/64
t = -2
So, the equation is conditional and the solution set is:
A)
Conditional; {-2}
Use dimensional analysis to convert the unit indicated.
6 m to ft
Question 26 options:
A)
6.7 ft
B)
19.7 ft
C)
5.4 ft
D)
1.8 ft
To convert from meters to feet, we can use the conversion factor 1 m = 3.281 ft.
So, to convert 6 meters to feet:
6 m * (3.281 ft/1 m) = 19.686 ft
Rounding to the nearest tenth, the result is approximately 19.7 ft.
The correct answer is:
B)
19.7 ft
Solve the problem.
Sarah has grades of 74 and 99 on his first two tests. If she wants an average of at least 80 after her third test, what score must she make on that test?
Question 27 options:
A)
84 or more
B)
80 or more
C)
87 or more
D)
67 or more
Let's denote the score Sarah must make on her third test as "x".
To find the score she must make on the third test in order to have an average of at least 80, we can set up an equation:
(74 + 99 + x)/3 ≥ 80
Combining like terms and multiplying both sides by 3, we have:
(173 + x) ≥ 240
Subtracting 173 from both sides, we get:
x ≥ 240 - 173
x ≥ 67
Therefore, Sarah must score 67 or more on her third test.
The correct answer is:
D)
67 or more
Solve the problem.
What percent of 110 is 40.7?
Question 28 options:
A)
37%
B)
370%
C)
0.37%
D)
3.7%
To find the percentage, we divide the part (40.7) by the whole (110), and then multiply by 100 to get the percentage.
Percentage = (40.7 / 110) * 100 ≈ 37%
Therefore, 40.7 is approximately 37% of 110.
The correct answer is:
A)
37%
Solve the problem.
A container of motor oil has a volume of 7000 cubic centimeters. How many liters of oil does the container hold?
Question 30 options:
A)
70 L
B)
7 L
C)
700 L
D)
7000 L
To convert from cubic centimeters (cm³) to liters (L), we divide by 1000.
7000 cm³ ÷ 1000 = 7 L
Therefore, the container holds 7 liters of oil.
The correct answer is:
B)
7 L
The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money will be in the account after the given number of years (Assume 360 days in a year.), and how much interest was earned.
A = P(1 + (r/n))nt P = (A/((1 + (r/n))) with superscript (nt)) A = Pert Y = (1 + (r/n))n - 1
Principal: $8500
Rate: 7%
Compounded: quarterly
Time: 3 years
A)
amount in account: $19,143.63; interest earned: $10,643.63
B)
amount in account: $10,467.23; interest earned: $1967.23
C)
amount in account: $12,756.21; interest earned: $4256.21
D)
amount in account: $8954.10; interest earned: $454.10
To find the amount of money in the account after the given number of years and the amount of interest earned, we can use the formula:
A = P(1 + (r/n))^(nt)
where:
A = amount in the account
P = principal
r = annual interest rate (in decimal form)
n = number of times the interest is compounded per year
t = number of years
Given:
Principal (P) = $8500
Rate (r) = 7% = 0.07 (in decimal form)
Compounded (n) = quarterly = 4 times per year
Time (t) = 3 years
Substituting these values into the formula:
A = $8500(1 + (0.07/4))^(4*3)
Calculating this expression, we get:
A ≈ $19,143.63
So, the amount in the account after 3 years is approximately $19,143.63
To find the interest earned, we subtract the principal from the amount in the account:
Interest earned = A - P
Interest earned ≈ $19,143.63 - $8500
Interest earned ≈ $10,643.63
Therefore, the correct answer is:
A)
amount in account: $19,143.63; interest earned: $10,643.63
Solve the problem.
If a boat uses 21 gallons of gas to go 77 miles, how many miles can the boat travel on 105 gallons of gas?
Question 32 options:
A)
770 miles
B)
405 miles
C)
15 miles
D)
385 miles
To find out how many miles the boat can travel on 105 gallons of gas, we can set up a proportion based on the given information:
21 gallons / 77 miles = 105 gallons / x miles
Cross-multiplying, we have:
21 * x = 105 * 77
Dividing both sides by 21, we get:
x = (105 * 77) / 21
Performing the calculation:
x ≈ 385
Therefore, the boat can travel approximately 385 miles on 105 gallons of gas.
The correct answer is:
D) 385 miles
The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent.
P = $300
r = 4.75%
t = 5 months
Question 33 options:
A)
$305.94
B)
$71.25
C)
$6.48
D)
$5.94
To find the simple interest owed, we can use the formula:
Interest = P * r * t
where:
P = principal (amount borrowed)
r = interest rate (in decimal form)
t = time (in years)
Given:
P = $300
r = 4.75% = 0.0475 (in decimal form)
t = 5 months = 5/12 years
Substituting these values into the formula:
Interest = $300 * 0.0475 * (5/12)
Calculating this expression, we have:
Interest ≈ $5.94
Therefore, the simple interest owed for the use of the money is approximately $5.94.
The correct answer is:
D)
$5.94
Solve the problem.
Find the best buy and the unit price.
Brand X 16 oz for $4.80
Brand Y 20 oz for $6.20
Question 34 options:
A)
Brand X, $0.30
B)
Equal value
C)
Brand Y, $0.30
D)
Brand Y, $0.31
To find the best buy and the unit price, we need to calculate the unit price for each brand.
For Brand X:
Unit price for Brand X = Total price / Total quantity
Unit price for Brand X = $4.80 / 16 oz
Unit price for Brand X = $0.30/oz
For Brand Y:
Unit price for Brand Y = Total price / Total quantity
Unit price for Brand Y = $6.20 / 20 oz
Unit price for Brand Y = $0.31/oz
From the calculations, we can see that Brand X has a lower unit price of $0.30 per ounce, while Brand Y has a unit price of $0.31 per ounce.
Therefore, the best buy and the brand with the lower unit price is:
A)
Brand X, $0.30
Use 1 mi = 1.6 km to solve the problem.
Express 75 kilometers per hour in miles per hour.
Question 35 options:
A)
2812.5 mi/hr
B)
120.0 mi/hr
C)
46.9 mi/hr
D)
72,000 mi/hr
To convert kilometers per hour to miles per hour, we can use the conversion factor 1 mi = 1.6 km.
To express 75 kilometers per hour in miles per hour:
75 km/hr * (1 mi / 1.6 km) = 46.875 mi/hr
Rounded to the nearest tenth, the result is approximately 46.9 mi/hr.
Therefore, 75 kilometers per hour is equivalent to approximately 46.9 miles per hour.
The correct answer is:
C)
46.9 mi/hr
The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent.
P = $300.00
r = 4%
t = 4 months
Question 36 options:
A)
$304.00
B)
$348.00
C)
$48.00
D)
$4.00
To find the simple interest owed, we can use the formula:
Interest = P * r * t
where:
P = principal (amount borrowed)
r = interest rate (in decimal form)
t = time (in years)
Given:
P = $300.00
r = 4% = 0.04 (in decimal form)
t = 4 months = 4/12 years
Substituting these values into the formula:
Interest = $300.00 * 0.04 * (4/12)
Calculating this expression, we have:
Interest = $4.00
Therefore, the simple interest owed for the use of the money is $4.00.
The correct answer is:
D) $4.00
Solve the problem.
0.24 is 48% of what number?
Question 37 options:
A)
0.1152
B)
0.5
C)
0.005
D)
0.05
To find the number that 0.24 is 48% of, we can set up a proportion:
0.24 / x = 48 / 100
To solve for x, we can cross-multiply:
0.24 * 100 = x * 48
24 = 48x
Then divide both sides by 48:
24 / 48 = x
x = 0.5
Therefore, 0.24 is 48% of 0.5.
The correct answer is:
B)
0.5
Solve the equation.
4 - (x - 1) = -4x + 3(x + 3)
Let's simplify and solve the equation step by step:
4 - (x - 1) = -4x + 3(x + 3)
Using the distributive property on the right side:
4 - x + 1 = -4x + 3x + 9
Combine like terms:
5 - x = -x + 9
Add x to both sides to eliminate the negative x:
5 = 9
Since the equation 5 = 9 is not true, there is no solution to the equation.
Therefore, the equation has no solution.
The correct answer is:
No solution
Solve the problem.
For each kilogram of a person's weight, 60 milligrams of a drug is to be given. What dosage should be given to an adult who weighs 170 pounds?
Question 39 options:
A)
4590 mg
B)
10,200 mg
C)
22,666.67 mg
D)
1.02 mg
To solve this problem, we need to convert the weight of the adult from pounds to kilograms. Then we can multiply the weight in kilograms by the given dosage.
Given:
1 kilogram = 2.20462 pounds
To convert 170 pounds to kilograms:
170 pounds * (1 kilogram / 2.20462 pounds) ≈ 77.1107 kilograms
To calculate the dosage:
77.1107 kilograms * 60 milligrams/kilogram = 4,626.642 milligrams ≈ 4,626.64 milligrams
Therefore, the dosage that should be given to an adult who weighs 170 pounds is approximately 4,626.64 milligrams.
The correct answer is:
C)
22,666.67 mg
Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
2(5g + 13) - 10g - 26 = 0
Question 40 options:
A)
Conditional; {0}
B)
Conditional; {5}
C)
Identity; {all real numbers}
D)
Contradiction; ∅
To determine the solution set for the equation, let's simplify it:
2(5g + 13) - 10g - 26 = 0
10g + 26 - 10g - 26 = 0
0 = 0
Since 0 always equals 0, this implies that the equation is an identity. In other words, the equation is true for all real numbers.
Therefore, the equation is an identity and the solution set is:
C)
Identity; {all real numbers}
The formula C = 23d + 25 describes the total cost of renting a truck, where C is the total cost and d is the number of days the truck is rented. How many days can the truck be rented for $117?
Question 11 options:
A)
4 days
B)
5 days
C)
2 days
D)
14 days
To find the number of days the truck can be rented for $117, we can rearrange the formula:
C = 23d + 25
Substituting