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o-na [289]
3 years ago
5

A railway tunnel 147m long is to be bored with a circular cross section of radius 5m.what volume of soil has to be excavated?

Mathematics
1 answer:
skad [1K]3 years ago
8 0
We have to find the volume of the cylinder, where: r = 5 m and h = 147 m.
V = r² h π
V = 5² · 147 · 3.14 = 25 · 147 · 3.14 = 11,539.5 m³
Answer:
11,539.5 m³ of soil has to be excavated.
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A recent national survey found that high school students watched an average (mean) of 7.8 movies per month with a population sta
notka56 [123]

Answer:

Step-by-step explanation:

Given that :

Mean = 7.8

Standard deviation = 0.5

sample size = 30

Sample mean = 7.3 5.4772

The null and the alternative hypothesis is as follows;

\mathbf{ H_o: \mu  \geq  7.8}

\mathbf{ H_1: \mu  <  7.8}

The test statistics can be computed as :

z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}

z = \dfrac{7.3- 7.8}{\dfrac{0.5}{\sqrt{30}}}

z = \dfrac{-0.5}{\dfrac{0.5}{5.4772}}

z = - 5.4772

The p-value at  0.05 significance level is:

p-value = 1- P( Z < -5.4772)

p value = 0.00001

Decision Rule:

The decision rule is to reject the null hypothesis if  p value is less than 0.05

Conclusion:

At  the 0.05 significance level,  there is sufficient information to reject the null hypothesis. Therefore ,we  conclude that college students watch fewer movies a month than high school students.

8 0
3 years ago
Give the equation of the circle centered at the origin and<br> passing through the point (4,0)
zimovet [89]

Answer:

x² + y² = 4²

Step-by-step explanation:

The standard equation of a circle centered at the origin and with radius r is

x² + y² = r²

Note that the point (4, 0) is 4 units horizontally and to the right of the center (0, 0).  Thus, we know immediately that the radius is 4.

Thus the equation of this circle is x² + y² = 4²

4 0
3 years ago
A civil engineer is mapping the overhead clearance of his family’s property on a coordinate grid. The ground is represented by t
Rudik [331]
We are given
x1 = 10 ft
y1 = 14 ft
x2 = 13 ft
y2 = 9 ft

We are asked to find the distance between the base of the house to the closest treetop.

So,
d1 = √(10² + 14²) = 17.20
d2 √(13² + 9²) = 15.81

The distance is 15.81 ft to the closest treetop which is the tree 13 feet from the base of the house.
7 0
2 years ago
Read 2 more answers
If would be great if someone answered this I'm sorry if its blurry the set of numbers are (4,4) (5'5)
Morgarella [4.7K]

Answer:

I think its 3752 but i might be wrong not sure

Step-by-step explanation:

or its 15008

5 0
3 years ago
If RS = 17, ST = x + 6, and RT = 3x - 5, What is ST.
tigry1 [53]

Answer:

ST = 20

Step-by-step explanation:

Line segment RS and segment ST must add up to line segment RT

Step 1: Define

RS = 17

ST = x + 6

RT = 3x - 5

Step 2: Set up equation

mRS + mST = mRT

17 + x + 6 = 3x - 5

Step 3: Solve for <em>x</em>

x + 23 = 3x - 5

23 = 2x - 5

28 = 2x

x = 14

Step 3: Find mST

ST = x + 6

ST = 14 + 6

ST = 20

3 0
3 years ago
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