Find the mode or modes.
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mode(s).
51 62 59
54 56 66
67 58 50
Question 29 options:
A)
51, 62, 59, 54, 56, 66, 67, 58, 50
B)
No mode
C)
58.1
D)
58
To find the slope of the line, we need to rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope.
Starting with the given equation:
3x + 5y = 19
We isolate y on one side by subtracting 3x from both sides:
5y = -3x + 19
Now we divide both sides by 5 to solve for y:
y = (-3/5)x + 19/5
Comparing this equation with y = mx + b, we can see that the slope is -3/5.
To sketch the graph, we can plot two points and draw a line through them.
1. Let's choose x = 0:
y = (-3/5)(0) + 19/5
y = 19/5
The point (0, 19/5) is on the line.
2. Now let's choose another value for x, such as x = 5:
y = (-3/5)(5) + 19/5
y = -3 + 19/5
y = -3 + 19/5
y = 2/5
The point (5, 2/5) is also on the line.
Now we can plot these two points on a coordinate plane and draw a straight line passing through them.
The graph will have a slope of -3/5 and will go through the points (0, 19/5) and (5, 2/5).
Here is a rough sketch of the graph:
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0 5
Note that the line is downward sloping from left to right, indicating a negative slope of -3/5.
Solve the equation.
(y - 9) - (y + 5) = 5y
Let's simplify the equation step by step to solve for y:
(y - 9) - (y + 5) = 5y
First, let's simplify the expression inside the parentheses:
y - 9 - y - 5 = 5y
Next, simplify the equation by combining like terms:
-y - 14 = 5y
To get rid of the negative sign in front of y, we can multiply the entire equation by -1:
1y + 14 = -5y
Combine like terms again:
14 = -6y
To solve for y, divide both sides of the equation by -6:
14 / -6 = -6y / -6
-7/3 = y
Therefore, the solution to the equation is y = -7/3.
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
(-1.7, -2.3) and (1.6, -0.5)
To find the slope of a line passing through two points (x1, y1) and (x2, y2), we can use the formula:
Slope = (y2 - y1) / (x2 - x1)
Using the given points (-1.7, -2.3) and (1.6, -0.5), we can substitute the values into the formula:
Slope = (-0.5 - (-2.3)) / (1.6 - (-1.7))
= (-0.5 + 2.3) / (1.6
The mode is the value(s) that appear(s) most frequently in the data set. In this case, the numbers that appear most frequently are 58 and 51, both appearing twice. Therefore, the mode is 58 and 51.
The correct answer is D) 58.
Solve the problem.
A radio transmission tower is 230 feet tall. How long should a guy wire be if it is to be attached 14 feet from the top and is to make an angle of 27° with the ground? Give your answer to the nearest tenth of a foot.
Question 30 options:
A)
475.8 ft
B)
258.1 ft
C)
506.6 ft
D)
242.4 ft
To solve this problem, we can use trigonometry. The length of the guy wire can be found using the sine function.
The length of the guy wire (h) can be calculated using the formula:
h = 230 / sin(angle)
Using the given information, we can substitute the values into the formula:
h = 230 / sin(27°)
h ≈ 506.6 ft
Therefore, the correct answer is C) 506.6 ft.
Solve the equation.
4m + 6 + 5(4m - 4) = 4(m + 4)
Answers:
A1/10
B 3/2
C15/14
D 21/10
To solve the equation, we will simplify and collect like terms.
Starting with the left side of the equation:
4m + 6 + 5(4m - 4)
= 4m + 6 + 20m - 20
= 24m - 14
Now let's simplify the right side of the equation:
4(m + 4)
= 4m + 16
Now let's rewrite the equation:
24m - 14 = 4m + 16
To isolate the variable m, we can subtract 4m from both sides and add 14 to both sides:
24m - 4m - 14 + 14 = 4m + 16 - 4m + 14
20m = 30
Finally, divide both sides by 20:
m = 30/20
m = 3/2
Therefore, the correct answer is B) 3/2.
Find the median.
22, 26, 38, 44, 71, 71, 86
Question 32 options:
A)
71
B)
44
C)
38
D)
51
To find the median, we need to arrange the numbers in ascending order:
22, 26, 38, 44, 71, 71, 86
Now, we can see that the middle number is 44. Since there is an odd number of values, there is only one middle value, which is the median.
Therefore, the correct answer is B) 44.
Find the simple interest. Round your answer to the nearest cent.
Principal = $170
Rate = 8%
Time in years = 4(1/2)
Question 33 options:
A)
$95.63
B)
$61.20
C)
$6.12
D)
$3.02
To find the simple interest, we can use the formula:
Interest = Principal * Rate * Time
Given:
Principal = $170
Rate = 8%
Time = 4(1/2) years
First, we need to convert the time to a decimal. 4(1/2) can be written as 4.5 years.
Now we can plug the values into the formula:
Interest = $170 * 0.08 * 4.5
Calculating the simple interest:
Interest ≈ $61.20
Therefore, the correct answer is B) $61.20.
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 34 options:
A)
32 oz
B)
48 oz
C)
64 oz
D)
16 oz
To find the bottle that comes closest to containing the desired quantity of 1.5 L, we need to convert 1.5 L to fluid ounces (oz).
Since 1 L is equivalent to 33.814 fluid ounces, we can calculate the desired quantity in fluid ounces:
1.5 L * 33.814 oz/L ≈ 50.721 oz
Now let's compare this value to the different bottle sizes:
- 16 oz is too small
- 32 oz is closer, but still less than the desired quantity
- 48 oz is closer than 32 oz, but still less than the desired quantity
- 64 oz is larger than the desired quantity
Therefore, the bottle that comes closest to containing the desired quantity of 1.5 L is C) 64 oz.
Solve the problem.
The man weighed 146 lb. How many kilograms is this?
Question 35 options:
A)
370.8 kg
B)
154.8 kg
C)
321.2 kg
D)
65.7 kg
To convert pounds to kilograms, we can use the conversion factor: 1 lb = 0.4536 kg.
Given that the man weighed 146 lb, we can calculate the weight in kilograms:
Weight in kg = 146 lb * 0.4536 kg/lb ≈ 66.224 kg
Therefore, the correct answer is D) 65.7 kg.
Solve the problem.
A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter?
Question 37 options:
A)
57.75 m
B)
0.9 m
C)
1.11 m
D)
46.82 m
To solve this problem, we can use trigonometry. The height of the window (h) can be found using the tangent function.
The height of the window (h) can be calculated using the formula:
h = distance * tan(angle)
Using the given information, we can substitute the values into the formula:
h = 52 m * tan(42°)
Calculating the value using a calculator:
h ≈ 46.82 m
Therefore, the correct answer is D) 46.82 m.
Find the range for the set of data given.
two way table ( (Value Frequency)(14 2)(21 2)(26 5)(27 6)(35 3) )
Question 38 options:
A)
20
B)
49
C)
22
D)
21
To find the range for a set of data, we need to subtract the smallest value from the largest value.
The smallest value in the given data set is 14 and the largest value is 35.
Range = Largest value - Smallest value
Range = 35 - 14
Range = 21
Therefore, the correct answer is D) 21.
Fill in the missing value.
916,900 m^2 = km^2
Question 39 options:
A)
91.69
B)
9.169
C)
9169
D)
0.9169
To convert from square meters (m²) to square kilometers (km²), we divide by 1,000,000.
916,900 m² ÷ 1,000,000 km²/m² = 0.9169 km²
Therefore, the missing value is D) 0.9169.
Find the requested angle.
Supplement of 82.2°
Question 40 options:
A)
277.8°
B)
7.8°
C)
52.8°
D)
97.8°
The supplement of an angle is the angle that, when added to the given angle, results in a total of 180°.
To find the supplement of 82.2°, we subtract it from 180°:
180° - 82.2° = 97.8°
Therefore, the requested angle is D) 97.8°.
(y - 9) - (y + 5) = 5y
To solve the equation, we'll simplify and combine like terms on each side.
Starting with the left side:
(y - 9) - (y + 5)
Distribute the negative sign:
y - 9 - y - 5
Combine like terms:
(y - y) + (-9 - 5)
0y + (-14)
-14
Now let's rewrite the equation:
-14 = 5y
To isolate the variable y, we can divide both sides by 5:
-14 / 5 = 5y / 5
-2.8 = y
Therefore, the solution to the equation is y = -2.8.
Possible answers:
A{-2}
B{-14/9}
C{0}
D{-14/5}
None of the provided answer choices, A{-2}, B{-14/9}, C{0}, D{-14/5}, are equivalent to the value we found.
The correct solution is y = -2.8.
Use the order of operations to simplify the expression.
3/4 x (1/10 + 1/5) x 16/3
To simplify this expression using the order of operations, we follow the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's simplify the expression inside the parentheses:
1/10 + 1/5 = 1/10 + 2/10 = 3/10
Now, let's simplify the multiplication:
3/4 * 3/10 = (3 * 3)/(4 * 10) = 9/40
Finally, let's multiply the resulting fraction by 16/3:
9/40 * 16/3 = (9 * 16)/(40 * 3) = 144/120 = 6/5
Therefore, the simplified expression is 6/5.
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
(-1.7, -2.3) and (1.6, -0.5)
To find the slope between two points (x1, y1) and (x2, y2), we use the formula:
Slope = (y2 - y1) / (x2 - x1)
Given the points (-1.7, -2.3) and (1.6, -0.5), we can substitute the values into the formula:
Slope = (-0.5 - (-2.3)) / (1.6 - (-1.7))
= (-0.5 + 2.3) / (1.6 + 1.7)
= 1.8 / 3.3
≈ 0.545
The slope is approximately 0.545.
Since the slope is positive, the line through the points rises from left to right.
0.545 as a fraction
To convert 0.545 to a fraction, we can write it as a fraction with the decimal as the numerator and a power of 10 as the denominator.
0.545 = 545/1000
To simplify this fraction, we divide both the numerator and denominator by their greatest common factor, which is 5.
545/1000 ÷ 5/5 = 109/200
Therefore, 0.545 as a fraction is 109/200.
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 12 224 21 13 46 79
To find the standard deviation of a set of data, we follow these steps:
1. Calculate the mean (average) of the data set.
2. Subtract the mean from each observation and square the result.
3. Calculate the mean of the squared differences.
4. Take the square root of the mean of the squared differences.
Step 1: Calculate the mean:
Mean = (54 + 12 + 224 + 21 + 13 + 46 + 79) / 7
= 449 / 7
≈ 64.14
Step 2: Subtract the mean and square the differences:
(54 - 64.14)^2 = 103.1396
(12 - 64.14)^2 = 2607.6196
(224 - 64.14)^2 = 22226.2196
(21 - 64.14)^2 = 1863.6996
(13 - 64.14)^2 = 2595.6196
(46 - 64.14)^2 = 332.0996
(79 - 64.14)^2 = 219.9196
Step 3: Calculate the mean of the squared differences:
Mean of squared differences = (103.1396 + 2607.6196 + 22226.2196 + 1863.6996 + 2595.6196 + 332.0996 + 219.9196) / 7
= 15949.1154 / 7
≈ 2278.4451
Step 4: Take the square root of the mean of squared differences:
Standard deviation = √2278.4451
≈ 47.7947
Rounding to one more decimal place than used for the observations, the standard deviation is approximately 47.8.
Therefore, the standard deviation for the given data is 47.8 (rounded to one decimal place).
Find the slope of the line and sketch the graph.
3x + 5y = 19
Find the surface area and volume of a sphere with radius 9 yards.
Use 3.14 for π.
RESPOND TO EACH STATEMENT
BE SURE TO LABEL YOUR RESPONSES WITH THE APPROPRIATE LETTER
A) What formula will you use for the surface area of the sphere
B) What is the surface area
C) What formula will you use for the volume of the sphere
D) What is the volume of the sphere
Question 6 options:
Well?
Solve the problem.
Use 3.14 for π.
A figure skater must trace a figure eight on the ice that consists of two perfect circles, each with a radius of 12 feet.
What distance does the skater cover, tracing one time around the figure eight?
Round results to the nearest tenth of a unit.