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3 years ago

Find the surface area of the shape below

Mathematics

1 answer:

Juliette [100K]3 years ago

3 0

Answer:

464 in²

Step-by-step explanation:

Surface area of a figure is the total area of its sides.

We shall assume that the shape is a solid.

2 × (5 × 10) = 2 × 50 = 100

2 × 1/2 × 4(10+16) = 4 × 26 = 104

10 × 10 = 100

10 × 16 = 160

Total area = 100 + 104 + 100 + 160

= 464 in²

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To obtain the area of a sector, what fraction is multiplied by the area of a circle (A = πr2)?

romanna [79]

Let r be a radius of a given circle and α be an angle, that corresponds to a sector.

The circle area is $A=\pi r^2$ and denote the sector area as $A_1$ .
Then $\dfrac{A_1}{A}= \dfrac{\alpha}{2\pi}$ (the ratio between area is the same as the ratio between coresponding angles).

$A_1=\dfrac{\alpha}{2\pi} \cdot A=\dfrac{\alpha}{2\pi} \cdot \pi r^2= \dfrac{r^2\alpha}{2}$ .

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3 years ago

Evaluate the expression for the given values. 12x+5y/3z, where x + 1/2, y = 6 and z = 3

Semmy [17]

Answer:

Step-by-step explanation:

Substitute: $\frac{\frac{12}{2} +5*6}{3*3}$

Cross out the common factor: $\frac{6+5*6}{3*3}$

Calculate the product or quotient: $\frac{6 +30}{3*3}$

Calculate the product or quotient: $\frac{6+30}{9}$

Calculate the sum or difference: $\frac{36}{9}$

Cross out the common factor: $4$

Answer: $4$

6 0

2 years ago

Read 2 more answers

Suppose you do an analysis of the starting salaries of 100 recent Lehman graduates. You find that the average starting salary is

madreJ [45]

Answer:

a) (59180,60820)

b) (59020,60980)

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = $60,000

Standard Deviation, σ = $5,000

Sample size, n = 100

a) 90% critical values

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.10} = 1.64$

$60000 \pm 1.64(\frac{5000}{\sqrt{100}} ) = 60000 \pm 820 = (59180,60820)$

b) 95% critical values

$\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}$

Putting the values, we get,

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

$60000 \pm 1.96(\frac{5000}{\sqrt{100}} ) = 60000 \pm 980= (59020,60980)$

5 0

3 years ago

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)