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kaheart [24]
2 years ago
11

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10

units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units. Which expression represents the volume, in cubic units, of the shaded region of the composite figure?
Mathematics
2 answers:
Anuta_ua [19.1K]2 years ago
8 0

Answer:

Step-by-step explanation:

bogdanovich [222]2 years ago
8 0

Answer:

One-half(14)(10)(8) – π(2.52)(8)

Step-by-step explanation:

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Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate
Elan Coil [88]

Answer:

The answer is B) 0.57.

Step-by-step explanation:

In this problem we have to apply queueing theory.

It is a single server queueing problem.

The arrival rate is  \lambda=4 and the service rate is \mu=7.

The proportion of time that the server is busy is now as the "server utilization"and can be calculated as:

p=\frac{\lambda}{c\mu} =\frac{4}{1*7}=0.57

where c is the number of server (in this case, one server).

3 0
2 years ago
Conor has a roll of fence that is 25 feet long. He needs 8 yards of fence to go around a flower bed. Does he have enough fence t
vlabodo [156]

Answer:

Yes he has enough fence to go round the flower bed.

Step-by-step explanation:

1 yard = 3 feet

25 feet = 25/3 = 8.33 yards

Yes he has enough fence to go round the flower bed.

8 0
2 years ago
The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism. Find the volume of each
Art [367]

Answer:

Step-by-step explanation:

Let the volume of a rectangular prism be VR and that of right triangular prism be VT. If The volume of the rectangular prism is 32 cubic feet more than the volume of the right triangular prism, then VR = 32 + VT

Since VR = length * width and height

VR = 6*x*3

VR = 18x ft³

Also VT =  Length *width * Height/2

VT = (7 * x * 4)/2

VT = 28x/2

VT = 14xft³

Since VR = 32 + VT

18x = 32+(14x)

collect like terms

18x-14x = 32

4x = 32

divide both sides by 4

4x/4 = 32/4

x = 8

Volume of the rectangular prism = 18x

Volume of the rectangular prism = 18*8

Volume of the rectangular prism = 144ft³

Volume of the right triangular prism = 14x

Volume of the rectangular prism = 14*8

Volume of the rectangular prism = 112ft³

4 0
2 years ago
Read 2 more answers
A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance tra
alina1380 [7]

Answer:

1.734

Step-by-step explanation:

Given that:

A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles).

The fitted regression is Time = −7.126 + .0214 Distance

Based on a sample size n = 20

And an Estimated standard error of the slope = 0.0053

the critical value for a right-tailed test to see if the slope is positive, using ∝ = 0.05 can be computed as follows:

Let's determine the degree of freedom df = n - 1

the degree of freedom df = 20 - 2

the degree of freedom df =  18

At the level of significance ∝ = 0.05 and degree of freedom df =  18

For a right tailed test t, the critical value from the t table is :

t_{0.05, 18} = 1.734

5 0
2 years ago
Which statements are true about the graph of y ≤ 3x + 1 and y ≥ –x + 2? Check all that apply. 1.The slope of one boundary line i
zloy xaker [14]

Answer:

2.Both boundary lines are solid.

3.A solution to the system is (1, 3)

5.The boundary lines intersect.

Step-by-step explanation:

we have

y\leq 3x+1 ----> inequality A

The solution of the inequality A is the shaded area below the solid line y=3x+1

The slope of the solid line is 3

The point (1,3) is  a solution of inequality A (lie in the shaded area of the solution set)

y\geq -x+2 ----> inequality B

The solution of the inequality B is the shaded area above the solid line y=-x+2

The slope of the solid line is -1

The point (1,3) is a solution of inequality B (lie in the shaded area of the solution set)

The solution of the system of inequalities is the shaded area between the two solids lines

see the attached figure

<u><em>Verify each statement</em></u>

1.The slope of one boundary line is 2

The statement is False

2.Both boundary lines are solid.

The statement is True

3.A solution to the system is (1, 3)

The statement is True

4.Both inequalities are shaded below the boundary lines

The statement is False

5.The boundary lines intersect.

The statement is True

The intersection point is (0.25,1.75)

see the attached figure

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2 years ago
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