A bag of a certain type of sand weighs 42 pounds and has a volume of 0.5 cubic feet. A sandbox has a volume of 16 cubic feet.
Approximately how many pounds of sand will it take to fill the sandbox?
Answer options with 5 options
A.
5 pounds
B.
32 pounds
C.
336 pounds
D.
672 pounds
E.
1,344 pounds
To find the approximate weight of sand needed to fill the sandbox, we can set up a proportion using the volumes of the bag and the sandbox:
Volume of bag / Weight of bag = Volume of sandbox / Weight of sand for the sandbox
Simplifying this proportion:
0.5 / 42 = 16 / x
Cross-multiplying:
0.5x = 42 * 16
0.5x = 672
Dividing by 0.5 to solve for x:
x ≈ 1,344
Therefore, it will take approximately 1,344 pounds of sand to fill the sandbox.
The answer is E. 1,344 pounds.
Jillian collected data about the average daily temperatures for two cities. She organized her data in the given table.
Average Daily Temperature (° Fahrenheit)
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
City A 2 12 30 38 55 62 85 90 78 60 35 11
City B 30 52 58 67 72 80 85 88 82 75 55 35
Question
Click on ,begin emphasis,all,end emphasis, the true statements about the data.
Answer options with 5 options
A.
Over the course of the year, the mean temperature is the same for both cities.
B.
Over the course of the year, the mean temperature is greater in City A than City B.
C.
Over the course of the year, the mean temperature is greater in City B than City A.
D.
Over the course of the year, the range of temperatures is greater in City A than City B.
E.
Over the course of the year, the range of temperatures is greater in City B than City A.
To determine the true statements about the data, let's analyze the given information:
1. Mean Temperature:
City A: To find the mean temperature, we sum up all the temperatures and divide by 12 (the number of months):
(2 + 12 + 30 + 38 + 55 + 62 + 85 + 90 + 78 + 60 + 35 + 11) / 12 = 48.67
City B: To find the mean temperature, we sum up all the temperatures and divide by 12 (the number of months):
(30 + 52 + 58 + 67 + 72 + 80 + 85 + 88 + 82 + 75 + 55 + 35) / 12 = 66.25
Therefore, the mean temperature is greater in City B than City A.
So, the true statement is:
B. Over the course of the year, the mean temperature is greater in City A than City B.
2. Range of Temperatures:
City A: The range is the difference between the highest and lowest temperatures.
Range = 90 - 2 = 88
City B: The range is the difference between the highest and lowest temperatures.
Range = 88 - 30 = 58
Therefore, the range of temperatures is greater in City A than City B.
So, the true statement is:
D. Over the course of the year, the range of temperatures is greater in City A than City B.
The options A, C, and E are false based on the analysis above.
Which graph shows the image of the triangle after a transformation defined by the rule Z transforms the point x comma y into the point x minus 3 comma y?
Answer options with 4 options
A.
On a graph, transformed triangle P Q R has point P prime (negative 6, 4); point Q prime (negative 6, 1); and point R prime (negative 4, 1).
C.
On a graph, transformed triangle P Q R has point P prime (0, 4); point Q prime (0, 1); and point R prime (negative 2, 1).
B.
On a graph, transformed triangle P Q R has point P prime (0, 4); point Q prime (0, 1); and point R prime (2, 1).
D.
On a graph, transformed triangle P Q R has point P prime (6, 4); point Q prime (6, 1); and point R prime (4, 1).
To determine the image of the triangle after the transformation defined by the rule Z transforms the point (x, y) into the point (x - 3, y), we need to subtract 3 from the x-coordinate of each point.
Let's compare the coordinates of the original triangle PQR with the coordinates given in each answer option:
A. (-6, 4), (-6, 1), (-4, 1)
C. (0, 4), (0, 1), (-2, 1)
B. (0, 4), (0, 1), (2, 1)
D. (6, 4), (6, 1), (4, 1)
By applying the transformation rule (subtracting 3 from the x-coordinate), the correct image of the triangle should have the following coordinates:
P' = P - 3 = (x - 3, y)
Q' = Q - 3 = (x - 3, y)
R' = R - 3 = (x - 3, y)
Comparing the given answer options, the only option that satisfies this transformation is:
C. On a graph, transformed triangle PQR has point P' (0, 4); point Q' (0, 1); and point R' (-2, 1).
Therefore, the correct answer is option C.
The distance from the Earth to the Sun is approximately 93,000,000 miles.
What is this distance expressed in scientific notation?
Answer options with 5 options
A.
9.3 times 10 Superscript 6 Baseline miles
B.
9.3 times 10 Superscript 7 Baseline miles
C.
9.3 times 10 Superscript 8 Baseline miles
D.
93 times 10 Superscript 6 Baseline miles
E.
93 times 10 Superscript 7 Baseline miles
To express the distance from the Earth to the Sun in scientific notation, we need to represent it in the form of a number between 1 and 10 multiplied by a power of 10.
The distance is 93,000,000 miles. To convert this to scientific notation, we can move the decimal point to the left until we have a number between 1 and 10. Each time we move the decimal point to the left, we increase the exponent of 10 by 1.
Moving the decimal point 7 places to the left, we get 9.3. The exponent of 10 is 7 because we moved the decimal point 7 places to the left.
Therefore, the distance from the Earth to the Sun expressed in scientific notation is:
9.3 x 10^7 miles
The correct answer is B. 9.3 times 10^7 miles.
Find the area of this parallelogram.
Information
The parallelogram has a base of 12 inches and a side of 7 inches. The height is 6 inches.
Answer options with 5 options
A.
42 inches
B.
42 square inches
C.
84 square inches
D.
72 square inches
E.
72 inches
To find the area of a parallelogram, we multiply the base by the height. In this case, the base is 12 inches and the height is 6 inches.
Area of parallelogram = base x height = 12 inches x 6 inches = 72 square inches
Therefore, the area of the parallelogram is 72 square inches.
The answer is D. 72 square inches.
An educational research company randomly surveyed 10 high school teachers and 10 middle school teachers and recorded how many years they have been teaching.
Years Teaching
,begin bold,High School,end bold,
,begin bold,Middle School,end bold,
10 5
8 7
11 10
15
4
6
11
18
12
13
8
14
9
9 15
20 12
Question
Based on the survey data, how much greater is the mean years of teaching for high school teachers than for middle school teachers? Round the answer to the nearest tenth. Enter the answer in the box.
Response area with 1 text input box
years
To find the difference in the mean years of teaching between high school teachers and middle school teachers, we need to calculate the mean or average separately for each group and then find the difference.
For high school teachers:
Sum of years of teaching = 10 + 8 + 11 + 15 + 4 + 6 + 11 + 18 + 12 + 13 = 108
Number of high school teachers surveyed = 10
Mean years of teaching for high school teachers = Sum of years of teaching / Number of high school teachers surveyed = 108 / 10 = 10.8
For middle school teachers:
Sum of years of teaching = 5 + 7 + 10 + 15 + 12 = 49
Number of middle school teachers surveyed = 5
Mean years of teaching for middle school teachers = Sum of years of teaching / Number of middle school teachers surveyed = 49 / 5 = 9.8
To find the difference, we subtract the mean years of teaching for middle school teachers from the mean years of teaching for high school teachers:
Difference = Mean years of teaching for high school teachers - Mean years of teaching for middle school teachers = 10.8 - 9.8 = 1
The difference in mean years of teaching between high school teachers and middle school teachers is 1 year.
The relationship between the number of years x that have passed and the population y for a small town is shown in the table.
Population Count Per Year
Number of Years x 1 2 3 4 5 6 7 8
Population y
14401,440 1,728 2,074 2,488 2,986 3,583 4,300 5,160
Question
A regression equation for this data is y equals 1,200 left-parenthesis 1.2 right-parenthesis Superscript x Baseline.
Based on this data, which value is the ,begin emphasis,best,end emphasis, prediction for the town's population after 12 years?
Answer options with 4 options
A.
6,020
B.
8,600
C.
8,916
D.
10,699
To find the best prediction for the town's population after 12 years using the regression equation y = 1,200 * 1.2^x, we substitute x = 12 into the equation.
y = 1,200 * 1.2^12
Calculating this value:
y ≈ 1,200 * 8.916
y ≈ 10,699.2
Rounding to the nearest whole number, the best prediction for the town's population after 12 years is 10,699.
Therefore, the correct answer is D. 10,699.
What is the value of this expression?
4 plus 6 left-parenthesis 4.3 plus 8 right-parenthesis minus 2.1
Answer options with 4 options
A.
35.7
B.
48.9
C.
75.7
D.
120.9
To calculate the value of the expression 4 + 6(4.3 + 8) - 2.1, we follow the order of operations.
First, we simplify the expression inside the parentheses:
4.3 + 8 = 12.3
Then, we perform the multiplication:
6 * 12.3 = 73.8
Next, we perform the addition and subtraction from left to right:
4 + 73.8 - 2.1 = 77.8 - 2.1 = 75.7
Therefore, the value of the expression 4 + 6(4.3 + 8) - 2.1 is 75.7.
The answer is option C. 75.7.
Solve this system of equations:
1st row Y equals 3 X. 2nd row 2 Y plus X equals 14.
Answer options with 5 options
A.
the point negative 2 comma negative 6
B.
the point 6 comma negative 2
C.
the point 6 comma 2
D.
the point negative 2 comma 6
E.
the point 2 comma 6
To solve the system of equations:
1st row: Y = 3X
2nd row: 2Y + X = 14
We can substitute the value of Y from the first equation into the second equation:
2(3X) + X = 14
6X + X = 14
7X = 14
X = 14/7
X = 2
Now that we have the value of X, we can substitute it back into the first equation to find the value of Y:
Y = 3(2)
Y = 6
Therefore, the solution to the system of equations is the point (2, 6).
The correct answer is E. the point 2, 6.
Which set of measures could be the side lengths of a right triangle?
Answer options with 5 options
A.
5 centimeters comma 10 centimeters comma 13 centimeters
B.
7 centimeters comma 20 centimeters comma 25 centimeters
C.
8 centimeters comma 15 centimeters comma 17 centimeters
D.
10 centimeters comma 21 centimeters comma 26 centimeters
E.
12 centimeters comma 14 centimeters comma 21 centimeters
To determine if a set of side lengths can form a right triangle, we can apply the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's check each set of side lengths:
A. (5 cm, 10 cm, 13 cm)
5^2 + 10^2 = 25 + 100 = 125
13^2 = 169
Since 125 is not equal to 169, this set of side lengths cannot form a right triangle.
B. (7 cm, 20 cm, 25 cm)
7^2 + 20^2 = 49 + 400 = 449
25^2 = 625
Since 449 is not equal to 625, this set of side lengths cannot form a right triangle.
C. (8 cm, 15 cm, 17 cm)
8^2 + 15^2 = 64 + 225 = 289
17^2 = 289
Since 289 is equal to 289, this set of side lengths can form a right triangle.
D. (10 cm, 21 cm, 26 cm)
10^2 + 21^2 = 100 + 441 = 541
26^2 = 676
Since 541 is not equal to 676, this set of side lengths cannot form a right triangle.
E. (12 cm, 14 cm, 21 cm)
12^2 + 14^2 = 144 + 196 = 340
21^2 = 441
Since 340 is not equal to 441, this set of side lengths cannot form a right triangle.
Therefore, the answer is C. 8 centimeters, 15 centimeters, 17 centimeters.