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2 years ago

The diagram shows the entrance to a tunnel.

Mathematics

1 answer:

gladu [14]2 years ago

5 0

Step-by-step explanation:

it filled up half the circle (up to the center point) - if we had a full circle. but a little bit is cut off (below AB).

what we see is that the shaded area is the sum of the area of the triangle AOB and 2 equally sized circle segment areas left and right of AOB.

since we are dealing with a half-circle, we have 180° in total. 120° are taken by AOB, so, that leaves us with 180-120 = 60° for both circle segments (so, one has an angle of 30°).

and 2×30° = 1×60°, so we can calculate the area of one 60° segment instead of two 30° segments.

AOB is an isoceles triangle (the legs are equally long, and therefore also the 2 side angles are equal).

the area of this triangle AOB is

1/2 × a × b × sin(C) = 1/2 × 3 × 3 × sin(120) =

= 3.897114317... m²

a circle segment area of 60° is 60/360 = 1/6 of the full circle area (as a full circle = 360°).

so, it's area is

pi×r² × 1/6 = pi×3²/6 = pi×3/2 = 4.71238898... m²

so, the total area of the shaded area is

3.897114317... m² + 4.71238898... m² =

= 8.609503297... m²

You might be interested in

The rectangular prism is to be sliced perpendicular to the shaded face and is to pass through point B, parallel to the front fac

kodGreya [7K]

The dimensions of the rectangular cross section will be 10 centimeters by 18 centimeters

Step-by-step explanation:

As ,we know

The rectangular cross section is parallel to the front face

Which clearly states that

The dimensions of the rectangular cross section is congruent with the dimensions of the front face

Lets assume that dimensions of the front face are 10 centimeters by 18 centimeters

Then ,The dimensions of the cross section will also be 10 centimeters by 18 centimeters

Hence we can say that the dimensions of the rectangular cross section will be 10 centimeters by 18 centimeters

4 0

3 years ago

Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of

tia_tia [17]

Answer:

Using a formula, the standard error is: 0.052

Using bootstrap, the standard error is: 0.050

Comparison:

The calculated standard error using the formula is greater than the standard error using bootstrap

Step-by-step explanation:

Given

Sample A Sample B

$x_A = 30$ $x_B = 50$

$n_A = 100$ $n_B =250$

Solving (a): Standard error using formula

First, calculate the proportion of A

$p_A = \frac{x_A}{n_A}$

$p_A = \frac{30}{100}$

$p_A = 0.30$

The proportion of B

$p_B = \frac{x_B}{n_B}$

$p_B = \frac{50}{250}$

$p_B = 0.20$

The standard error is:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}$

$SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}$

$SE_{p_A-p_B} = \sqrt{0.00274}$

$SE_{p_A-p_B} = 0.052$

Solving (a): Standard error using bootstrapping.

Following the below steps.

Open Statkey
Under Randomization Hypothesis Tests, select Test for Difference in Proportions
Click on Edit data, enter the appropriate data
Click on ok to generate samples
Click on Generate 1000 samples ---- see attachment for the generated data

From the randomization sample, we have:

Sample A Sample B

$x_A = 23$ $x_B = 57$

$n_A = 100$ $n_B =250$

$p_A = 0.230$ $p_A = 0.228$

So, we have:

$SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}$

$SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}$

$SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}$

$SE_{p_A-p_B} = \sqrt{0.002475064}$

$SE_{p_A-p_B} = 0.050$

5 0

2 years ago

Aha please help!!!!! im a bit confused lol

Stels [109]

Answer:

e : g = 2 : 7

Step-by-step explanation:

e/f = 3/7

e = 3f/7

f/g = 2/3

g = 3f/2

e/g = (3f/7)/(3f/2) = 2/7

3 0

2 years ago

What is the distance in units between (−11, −20) and (−11, 5)

Morgarella [4.7K]

Distance = √(x₂-x₁)² + (y₂-y₁)²
d = √(-11-(-11)) + (5-(-20))²
d = √0² + 25²
d = √625
d = 25

In short, Your Answer would be 25 units

Hope this helps!

6 0

3 years ago

Read 2 more answers

Type the correct answer in each box. If necessary, use / for the fraction bar(s).

Mila [183]

Answer:

12x + 15y=34

x=34/12 = 17/6

y=34/15

____________________

-6x + 5y=3

x=3/-6 = 1/-2

y= 3/5

Step-by-step explanation:

5 0

3 years ago