Find the missing length in the right triangle.
If necessary, round to the nearest tenth.
18 mi 7 mi
Question 36 options:
A)
12.5 mi
B)
275 mi
C)
137.5 mi
D)
16.6 mi
Based on the given information, it is unclear which side of the right triangle is missing. Please provide more information or clarify the question.
Provide an appropriate response.
For the stem-and-leaf plot below, what are the maximum and minimum entries?
1 | 0 3
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 6 9
Question 37 options:
A)
max: 46; min: 10
B)
max: 47; min: 13
C)
max: 49; min: 10
D)
max: 38; min: 7
The maximum entry on the stem-and-leaf plot is 49, and the minimum entry is 10.
Therefore, the correct answer is:
C) max: 49; min: 10
Find the volume of the solid.
Use (22/7) for π.
4(1/2) cm 7 cm
Question 38 options:
A)
445(1/2) cu cm
B)
33 cu cm
C)
16(1/2) cu cm
D)
148(1/2) cu cm
To find the volume of a solid, we need to multiply the base area by the height.
In this case, the base is a circle with a radius of 4(1/2) cm, so the base area is (22/7)(4.5)^2 cm^2.
The height of the solid is 7 cm.
We can now calculate the volume:
Volume = Base area x Height
Volume = (22/7)(4.5)^2 cm^2 x 7 cm
Calculating this expression gives us approximately 445.5 cubic centimeters.
Rounding to the nearest tenth, the volume of the solid is 445.5 cubic centimeters.
Therefore, the correct answer is:
A) 445(1/2) cu cm
Solve the problem.
When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 51°49'.
If Joey is known to be standing 10 feet from the base of the tree, how tall is the tree (to the nearest foot)?
Question 39 options:
A)
17 ft
B)
19 ft
C)
15 ft
D)
13 ft
To solve this problem, we can use the tangent function to find the height of the tree.
The tangent of an angle is equal to the opposite side divided by the adjacent side.
In this case, the opposite side is the height of the tree and the adjacent side is the distance from Joey to the base of the tree.
Let's denote the height of the tree as h.
tan(51°49') = h / 10
Using a calculator, we find that tan(51°49') is approximately 1.312.
Now we can solve for h:
1.312 = h / 10
Multiplying both sides of the equation by 10, we get:
13.12 = h
Rounding to the nearest foot, the height of the tree is approximately 13 feet.
Therefore, the correct answer is:
D) 13 ft
Solve the problem.
A ramp leads up to a warehouse loft.
The path up the ramp is 21 ft long.
The base of the ramp is 16 ft long.
How high is the loft?
Round your answer to hundredths.
? 21 ft 16 ft
Question 40 options:
A)
13.60 ft
B)
18.50 ft
C)
92.50 ft
D)
6.80 ft
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the loft is the missing side, which we can denote as h. The base of the ramp is 16 ft, and the path up the ramp is 21 ft. Therefore, we have a right triangle with a base of 16 ft, height h, and hypotenuse 21 ft.
Applying the Pythagorean theorem:
16^2 + h^2 = 21^2
Simplifying:
256 + h^2 = 441
Subtracting 256 from both sides:
h^2 = 441 - 256
h^2 = 185
Taking the square root of both sides:
h = sqrt(185)
Calculating this value gives us approximately 13.60 ft.
Rounding to the nearest hundredth, the height of the loft is approximately 13.60 ft.
Therefore, the correct answer is:
A) 13.60 ft
To find the missing length in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have two sides given: 18 mi and 7 mi. Let's call the missing length "x". Now we can set up the equation using the Pythagorean theorem:
18^2 + 7^2 = x^2
Simplifying:
324 + 49 = x^2
373 = x^2
To find the value of x, we need to take the square root of both sides:
√373 = √x^2
Now we can use a calculator to find the approximate square root of 373:
√373 ≈ 19.3
Therefore, the missing length, rounded to the nearest tenth, is approximately 19.3 mi.
None of the given options match this result, so it seems there may be an error in the provided answer choices.