Use the present value formula to determine the amount to be invested now, or the present value needed.
The desired accumulated amount is $34,000 after 11 years invested in an account with 7% interest compounded semiannually
Question 20 options:
A)
$16,153.16
B)
$18,048.88
C)
$15,951.12
D)
$72,471.39
To determine the amount to be invested now, we can use the present value formula:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value (desired accumulated amount)
r = interest rate per compounding period (expressed as a decimal)
n = number of compounding periods per year
t = number of years
Given:
FV = $34,000
r = 7% = 0.07 (7% interest rate per annum)
n = 2 (semiannual compounding)
t = 11 years
Using the formula:
PV = 34000 / (1 + 0.07/2)^(2*11)
PV = 34000 / (1 + 0.035)^(22)
PV = 34000 / (1.035)^22
PV ≈ $15,951.12
Therefore, the amount to be invested now, or the present value needed is approximately $15,951.12. Answer choice C) is correct.
Solve the equation.
(y - 5) - (y + 2) = 6y
Question 21 options:
A)
{- (7/5)}
B)
{- (2/3)}
C)
{- (7/6)}
D)
{- (7/3)}
To solve the equation (y - 5) - (y + 2) = 6y, we can simplify it step by step:
Start by removing the parentheses using the distributive property:
y - 5 - y - 2 = 6y
Combine like terms on the left side:
-7 = 6y
Next, isolate the variable "y" by dividing both sides of the equation by 6:
-7/6 = y
Therefore, the solution to the equation is:
y = -7/6
So the correct answer is C) {- (7/6)}.
Solve the problem. Round to the nearest tenth if necessary.
Last year, Maria earned $362 per week. This year, her salary increased to $398 per week. What is the percent of increase?
Question 18 options:
A)
91%
B)
9.9%
C)
9%
D)
90.1%
To find the percent increase, we can use the following formula:
Percent Increase = ((New Value - Old Value) / Old Value) * 100
Given:
Old Value (last year's salary) = $362
New Value (this year's salary) = $398
Using the formula:
Percent Increase = ((398 - 362) / 362) * 100
Percent Increase = (36 / 362) * 100
Percent Increase ≈ 9.9%
Therefore, the percent increase is approximately 9.9%. The correct answer is B) 9.9%.
Find the range for the set of data given.
two way table ( (Value Frequency)(14 2)(21 6)(22 3)(29 2)(32 3) )
Question 22 options:
A)
19
B)
17
C)
18
D)
46
To find the range for the set of data given, we need to determine the difference between the highest and lowest values.
Given data:
(14, 2)
(21, 6)
(22, 3)
(29, 2)
(32, 3)
The lowest value is 14, and the highest value is 32. The difference between the highest and lowest values is 32 - 14 = 18.
Therefore, the range for the set of data given is 18. The correct answer is C) 18.
Find the slope of the line and sketch the graph.
3x + 4y = 21
A)
Slope: (3/4)
B)
Slope: - (4/3)
C)
Slope: - (3/4)
D)
Slope: (4/3)
To find the slope of the line represented by the equation 3x + 4y = 21, we need to rewrite the equation in slope-intercept form, y = mx + b, where "m" represents the slope.
Starting with the original equation:
3x + 4y = 21
First, isolate "y" on one side of the equation by subtracting 3x from both sides:
4y = -3x + 21
Next, divide both sides by 4 to solve for "y":
y = (-3/4)x + (21/4)
Comparing the obtained equation with the slope-intercept form, we can see that the slope, "m," is -3/4.
Therefore, the correct answer is C) Slope: - (3/4).
Use a proportion to solve the problem.
The ratio of the distances a 7-iron and a 5-iron will drive a golf ball is 5 to 6. If a golfer averages 110 yards with a 7-iron, how far should he average with a 5-iron?
Question 26 options:
A)
132 yards
B)
121 yards
C)
99 yards
D)
92 yards
To solve the problem, we can set up a proportion using the given ratio:
(distance with 7-iron) / (distance with 5-iron) = (ratio of 7-iron to 5-iron)
Let x represent the distance with a 5-iron.
Using the given information:
110 (distance with 7-iron) / x (distance with 5-iron) = 5 (ratio of 7-iron to 5-iron) / 6 (ratio of 7-iron to 5-iron)
To solve for x, we can cross multiply and solve for x:
110 * 6 = 5 * x
660 = 5x
Divide both sides of the equation by 5 to isolate x:
x = 660 / 5
x = 132
Therefore, the golfer should average approximately 132 yards with a 5-iron. The correct answer is A) 132 yards.
Find the mean of the set of data.
-1, 5, 5, 5, 6
Question 27 options:
A)
4
B)
3
C)
5
D)
3.3
To find the mean of a set of data, we need to add up all the values and divide by the number of values.
Given data: -1, 5, 5, 5, 6
Add up all the values: -1 + 5 + 5 + 5 + 6 = 20
There are a total of 5 values.
Divide the sum by the number of values: 20 / 5 = 4
Therefore, the mean of the set of data is 4. The correct answer is A) 4.
Answer the question.
right ray(AB) is parallel to right ray(DC). Identify two pairs of congruent angles and the number of degrees in each congruent angle.
66° 66°
Question 28 options:
A)
∠ADC ≅ ∠BAD ; both are 66°.
∠FAB ≅ ∠EDC ; both are 114°.
B)
∠FAB ≅ ∠EDC ; both are 66°.
∠ADC ≅ ∠BAD ; both are 114°.
C)
∠CDA ≅ ∠FAB ; both are 114°.
∠EDC ≅ ∠BAD ; both are 114°.
D)
∠FAB ≅ ∠BAD ; both are 66°.
∠EDC ≅ ∠CDA ; both are 66°.
The correct answer is A)
∠ADC ≅ ∠BAD ; both are 66°.
∠FAB ≅ ∠EDC ; both are 114°.
Find the circumference and area of a circle having the given diameter or radius. Use 3.14 for π. Round your results to the nearest tenth.
d = 32 yd
Question 29 options:
A)
100.5 yd; 100.5 yd^2
B)
100.5 yd; 803.8 yd^2
C)
50.2 yd; 201 yd^2
D)
50.2 yd; 3215.4 yd^2
To find the circumference and area of a circle, we need to use the formulas:
Circumference = π * diameter
Area = π * radius^2
Given the diameter:
d = 32 yd
First, we can find the radius by dividing the diameter by 2:
radius = 32 yd / 2 = 16 yd
Using the formulas with π rounded to 3.14:
Circumference = 3.14 * 32 yd ≈ 100.5 yd
Area = 3.14 * (16 yd)^2 ≈ 803.8 yd^2
Therefore, the correct answer is B) 100.5 yd for the circumference and 803.8 yd^2 for the area.
Solve the problem.
A consumer wants to purchase 1.5 L of antibacterial liquid hand soap. The bottles on the store shelf hold 16 oz, 32 oz, 48 oz, and 64 oz. Which bottle comes closest to containing the desired quantity?
Question 30 options:
A)
48 oz
B)
64 oz
C)
16 oz
D)
32 oz
To determine which bottle comes closest to containing the desired quantity of 1.5 L of antibacterial liquid hand soap, we need to convert the desired quantity from liters to ounces.
1 liter is approximately equal to 33.8 ounces.
Therefore, 1.5 L is approximately equal to 1.5 * 33.8 = 50.7 ounces.
Comparing the given bottle sizes:
- 16 oz bottle: Too small
- 32 oz bottle: Too small
- 48 oz bottle: Closest option
- 64 oz bottle: Too big
Therefore, the bottle that comes closest to containing the desired quantity of 1.5 L of antibacterial liquid hand soap is the 48 oz bottle. The correct answer is A) 48 oz.
Find the volume of the specified solid. Use 3.14 as the approximate value of π, and round your answer to the nearest whole number.
A cone with height 8 cm and diameter 5 cm
Question 31 options:
A)
84 cm^3
B)
209 cm^3
C)
52 cm^3
D)
314 cm^3
To find the volume of a cone, we use the formula:
Volume = (1/3) * π * radius^2 * height
Given:
Height = 8 cm
Diameter = 5 cm
Radius = Diameter/2 = 5 cm / 2 = 2.5 cm
Using the formula with π rounded to 3.14:
Volume = (1/3) * 3.14 * (2.5 cm)^2 * 8 cm
Volume ≈ (1/3) * 3.14 * 6.25 cm^2 * 8 cm
Volume ≈ (1/3) * 3.14 * 50 cm^3
Volume ≈ 52.33 cm^3
Rounded to the nearest whole number, the volume of the cone is approximately 52 cm^3.
Therefore, the correct answer is C) 52 cm^3.
Find the standard deviation for the given data. Round your final answer to one more decimal place than that used for the observations.
Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores.
54 16 256 29 12 42 79
Question 32 options:
A)
77,698
B)
85.3
C)
256
D)
34,020.6
To find the standard deviation for the given data, we can follow these steps:
Step 1: Find the mean of the data set.
Sum of the scores: 54 + 16 + 256 + 29 + 12 + 42 + 79 = 488
Mean = Sum of scores / Number of scores = 488 / 7 = 69.7143 (rounded to four decimal places)
Step 2: Find the difference between each score and the mean.
54 - 69.7143 = -15.7143
16 - 69.7143 = -53.7143
256 - 69.7143 = 186.2857
29 - 69.7143 = -40.7143
12 - 69.7143 = -57.7143
42 - 69.7143 = -27.7143
79 - 69.7143 = 9.2857
Step 3: Square each difference.
(-15.7143)^2 = 246.8041
(-53.7143)^2 = 2884.9889
(186.2857)^2 = 34693.7959
(-40.7143)^2 = 1660.2670
(-57.7143)^2 = 3330.9173
(-27.7143)^2 = 767.0098
(9.2857)^2 = 86.1459
Step 4: Find the mean of the squared differences.
Sum of squared differences: 246.8041 + 2884.9889 + 34693.7959 + 1660.2670 + 3330.9173 + 767.0098 + 86.1459 = 43670.9199
Mean of squared differences = Sum of squared differences / Number of scores = 43670.9199 / 7 = 6238.7028 (rounded to four decimal places)
Step 5: Take the square root of the mean of squared differences.
Square root of 6238.7028 = 78.9385 (rounded to four decimal places)
Therefore, the standard deviation for the given data is approximately 78.9. The correct answer is not among the provided options.
In the figure, ∠ABF measures 42° and ∠DBG measures 92°. Find the measures of ∠ABD, ∠GBC, ∠EBC, and ∠FBE.
Question 33 options:
A)
∠ABD = 42°, ∠GBC = 46°, ∠EBC = 42°, and ∠FBE = 134°
B)
∠ABD = 48°, ∠GBC = 42°, ∠EBC = 48°, and ∠FBE = 92°
C)
∠ABD = 46°, ∠GBC = 42°, ∠EBC = 46°, and ∠FBE = 92°
D)
∠ABD = 50°, ∠GBC = 46°, ∠EBC = 50°, and ∠FBE = 132°
From the given information, we can deduce the following:
∠ABF = 42°
∠DBG = 92°
We know that the sum of angles in a triangle is 180°. Therefore, we can find the unknown angles:
∠ABF + ∠ABD + ∠FBE = 180°
42° + ∠ABD + ∠FBE = 180°
∠ABD + ∠FBE = 180° - 42°
∠ABD + ∠FBE = 138°
Similarly,
∠DBG + ∠GBC + ∠EBC = 180°
92° + ∠GBC + ∠EBC = 180°
∠GBC + ∠EBC = 180° - 92°
∠GBC + ∠EBC = 88°
From the information above, we can determine that:
∠ABD = ∠GBC = 46°
∠EBC = ∠FBE = 92°
Therefore, the correct answer is C) ∠ABD = 46°, ∠GBC = 42°, ∠EBC = 46°, and ∠FBE = 92°.
Find the requested angle.
Supplement of 71.8°
Question 34 options:
A)
108.2°
B)
63.2°
C)
288.2°
D)
18.2°
The supplement of an angle is the angle that, when added to the given angle, results in a sum of 180 degrees.
To find the supplement of 71.8°, we subtract the given angle from 180°:
Supplement = 180° - 71.8° = 108.2°
Therefore, the requested angle, which is the supplement of 71.8°, is 108.2°. The correct answer is A) 108.2°.
Andrea's sleeping bag is designed for camping in temperatures of -3°C or warmer. For what Fahrenheit temperatures is her sleeping bag designed? Round to the nearest tenth of a degree.
Question 35 options:
A)
-33.7° F or warmer
B)
-19.4° F or warmer
C)
26.6° F or warmer
D)
52.2° F or warmer
To convert Celsius to Fahrenheit, we can use the formula:
°F = (°C * 9/5) + 32
Given that Andrea's sleeping bag is designed for temperatures of -3°C or warmer, we can convert -3°C to Fahrenheit:
°F = (-3 * 9/5) + 32
°F = (-27/5) +