Tyrone has 51 movies in his collection. He wants to estimate the average length, in minutes, per movie in his collection. So, he wrote down the length of 10 random movies. The lengths are listed below.
107, 130, 151, 82, 151, 107, 130, 107, 151, 82
Assuming that the sample was representative of the entire collection, what was the mean number of minutes per movie?
A.
140.5
B.
94.5
C.
119.8
D.
129
To find the mean number of minutes per movie, we must first calculate the total number of minutes for all 10 movies:
107 + 130 + 151 + 82 + 151 + 107 + 130 + 107 + 151 + 82 = 1098
Next, we divide the total number of minutes by the number of movies to find the average:
1098 / 10 = 109.8
Therefore, the mean number of minutes per movie in Tyrone's collection is 109.8, which is closest to option C. 119.8.
you sure
Apologies for the mistake in my previous response. Let's recalculate the mean using the correct steps.
First, sum up the lengths of the 10 random movies:
107 + 130 + 151 + 82 + 151 + 107 + 130 + 107 + 151 + 82 = 1098
Next, divide this sum by the number of movies (10) to find the average length per movie:
1098 / 10 = 109.8
Therefore, the correct mean number of minutes per movie in Tyrone's collection is 109.8 minutes, which is closest to option C. 119.8. Thank you for bringing that to my attention.
Garett wants to design a spinner for a game that has the same probability of landing on each color. Which spinner could he use?
A.
B.
C.
D.
..
I'm unable to view or interpret images, so I can't identify the spinner you're referring to based on the letters alone. However, to ensure that each color on the spinner has the same probability of landing, each color should occupy an equal amount of space on the spinner.
If you describe the design or specify the colors on the spinner, I can help you determine which spinner Garett could use to ensure equal probability of landing on each color.
Select the expression below that is equal to 5(12 - m).
A.
60 - m
B.
5m - 60
C.
17 - m
D.
60 - 5m
To simplify the expression 5(12 - m), we distribute the 5 across the terms inside the parentheses:
5 * 12 - 5 * m
60 - 5m
Therefore, the expression 5(12 - m) is equal to 60 - 5m, which is option B. 5m - 60.
What is the total surface area, in square inches, of the rectangular box shown below, given the values for x, y, and z?
Note: picture not drawn to scale.
Assume x = 10, y = 8, and z = 8.
A.
148 in2
B.
640 in2
C.
448 in2
D.
598 in2
To find the total surface area of the rectangular box, we need to sum the areas of all six faces.
Given x = 10, y = 8, and z = 8, the six faces of the box can be described as follows:
- The top and bottom faces have areas of x * y and x *y respectively.
- The front and back faces have areas of x * z and x * z respectively.
- The left and right faces have areas of y * z and y * z respectively.
Let's calculate the areas of each face and then sum them to find the total surface area:
Top and bottom faces: 2(xy) = 2(10 * 8) = 2(80) = 160 sq. in.
Front and back faces: 2(xz) = 2(10 * 8) = 2(80) = 160 sq. in.
Left and right faces: 2(yz) = 2(8 * 8) = 2(64) = 128 sq. in.
Total surface area = 2(xy) + 2(xz) + 2(yz)
Total surface area = 160 + 160 + 128
Total surface area = 448 sq. in.
Therefore, the total surface area of the rectangular box is 448 square inches, which corresponds to option C. 448 in².
Note: picture not drawn to scale
Triangles ABC and XYZ are similar figures, because angles A, B, and C are congruent to angles X, Y, and Z, respectively.
If side AC equals 6 cm, BC equals 11 cm, and XZ equals 18 cm, what is the length of side YZ?
A.
43 cm
B.
33 cm
C.
66 cm
D.
56 cm
In similar triangles, the corresponding sides are proportional. Therefore, we can set up a proportion to find the length of side YZ.
Given:
AC = 6 cm, BC = 11 cm, XZ = 18 cm
We need to find YZ.
Using the proportionality of corresponding sides:
AC / XZ = BC / YZ
Substitute the given values:
6 / 18 = 11 / YZ
1/3 = 11 / YZ
Cross multiply to solve for YZ:
3 * 11 = YZ
YZ = 33 cm
Therefore, the length of side YZ is 33 cm, which corresponds to option B. 33 cm.