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dusya [7]
2 years ago
7

a regular hexagonal nut of side 1 cm and length 3 cm with a central hole of diameter 1 cm. 3 cm 1 cm 1 cm. Calculate the volume

of metal in the nut. (Ignore the thread and give your answer correct to 3 significant figures.) (WAEC]​
Mathematics
1 answer:
Bogdan [553]2 years ago
5 0

Answer:

  5.44 cm³

Step-by-step explanation:

The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.

The area of a hexagon with side length s is given by ...

  A = (3/2)√3·s²

For s=1 cm, the area is ...

  A = (3/2)√3(1 cm)² = (3/2)√3 cm²

__

The area of a circle is given by ...

  A = πr²

The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...

  A = π(0.5 cm)² = 0.25π cm²

__

The volume is the face area multiplied by the length, so is ...

  V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³

  V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³

The volume of the metal is about 5.44 cm³.

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Answer:

There is not enough evidence to conclude that  average starting salary for clerical employees in the state is less than ​$35,000 per year.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 35,000 dollars per year

Sample mean, \bar{x} = 34,700 dollars per year

Sample size, n = 100

Alpha, α = 0.10

Population standard deviation, σ = 3,500 dollars per year

First, we design the null and the alternate hypothesis

H_{0}: \mu = 35,000\text{ dollars per year}\\H_A: \mu < 35,000\text{ dollars per year}

We use one-tailed z test to perform this hypothesis.

Formula:

z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }

Putting all the values, we have

z_{stat} = \displaystyle\frac{34700 - 35000}{\frac{3500}{\sqrt{100}} } = -0.8571

Now, z_{critical} \text{ at 0.10 level of significance } = -1.28

Since,  

z_{stat} > z_{critical}

We fail to reject the null hypothesis and accept the null hypothesis.

Thus, there is not enough evidence to conclude that  average starting salary for clerical employees in the state is less than ​$35,000 per year.

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Help with this question please
mihalych1998 [28]

The number from standard form to decimal form is as follows:

2.077  ×  10⁻⁴ = 0.0002077

<h3>How to express number in standard form?</h3>

Standard form is a convenient way of writing very large or very small numbers.

Standard form is a way of writing a number so it is easier to read.

Standard form is like scientific notation and is typically used in science.

Standard form is like scientific notation and it is represented in the format as follows:

a × 10ᵇ

Therefore, the number is already in standard form but we can convert it back to decimal form as follows:

2.077  ×  10⁻⁴ = 2.077 × 1 / 10000 = 0.0002077

learn more on standard form here: brainly.com/question/17170676

#SPJ1

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