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2 years ago

Find the length of the arc. A. 15π mi B. 5400π mi C. 135π mi D. 125π16 mi

Mathematics

1 answer:

weqwewe [10]2 years ago

7 0

Answer:

A. 15π mi

Step-by-step explanation:

First find the circumference

C = 2*pi*r

C = 2 * pi*18

C = 36pi

The arc is 150 degrees

The fraction of the circle is

150/360 = 5/12

Multiply this by the circumference

5/12 * 36 pi

15 pi

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In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous we

const2013 [10]

Answer:

1) Increase the sample size

2) Decrease the confidence level

Step-by-step explanation:

The 95% confidence interval built for a sample size of 1100 adult Americans on how much they worked in previous week is:

42.7 to 44.5

We have to provide 2 recommendations on how to decrease the margin of Error. Margin of error is calculated as:

$M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}$

Here,

$z_{\frac{\alpha}{2} }$ is the critical z-value which depends on the confidence level. Higher the confidence level, higher will be the value of critical z and vice versa.

$\sigma$ is the population standard deviation, which will be a constant term and n is the sample size. Since n is in the denominator, increasing the value of n will decrease the value of Margin of Error.

Therefore, the 2 recommendations to decrease the Margin of error for the given case are:

Increase the sample size and make it more than 1100
Decrease the confidence level and make it lesser than 95%.

7 0

3 years ago

The blue dot is at what value on the number line?

Paladinen [302]

Answer: 1

Step-by-step explanation: it goes -7 -5 -3 -1 1

8 0

3 years ago

Please Help me need help

daser333 [38]

Answer:

-1 * (x/y)

Step-by-step explanation:

-x/y = x /-y

Factor out the negative

-(x/y) = -(x/y)

This is equal to -1 * (x/y)

8 0

3 years ago

above ground electric wires and transformers are mounted on utility poles. a support cable, called a guy wire, is sometimes atta

kifflom [539]

The angle measure is 30 degrees.

Drawing out an image, the angle the is between the ground at the hypotenuse (the slanted guy wire), it creates a triangle with the utility pole that was already on the side. The angle between the utility pole and the ground is obviously 90 degrees because it is assumed to be at a straight standing stance.
Normally these two given angles would be added and then subtracted from 180 degrees (the law of Sum of Angles in a Triangle).
60 + 90 = 150 ... 180 - 150 = 30
Also, this can be supported by the 30-60-90 Theorem, which states that if a triangle contains 2 of the 3 angles, the other angle will be the missing one.

3 0

3 years ago

Which transformations could be performed to show that △ABC is similar to △A"B"C"?

Angelina_Jolie [31]

Answer:

A 180° rotation of then a dilation by a scale factor of one-third

Step-by-step explanation:

The coordinates of the vertices of ΔABC are;

A(-9, 3), B(-9, 6), and C(0, 3)

The coordinates of the vertices of ΔA'B'C' are;

A'(3, -1), B'(3, -2), and C'(0, -1)

We note that for a 180° rotation transformation about the origin, we get;

Coordinates of preimage = (x, y)

Coordinates of image after 180° rotation about the origin = (-x, -y)

Therefore, a 180° rotation of ΔABC about the origin, would give ΔA''B''C'' as follows;

A(-9, 3), B(-9, 6), and C(0, 3) = A''(9, -3), B''(9, -6), and C''(0, -3)

The formula for a dilation of a point about the origin is given as follows;

$D_{O, \, k} (x, \, y) = (k\cdot x, \, k\cdot y)$

Where;

k =The scale factor = 1/3, (one-third) we have;

A dilation of ΔA''B''C'', by a scale factor of 1/3, we get ΔA'B'C' as follows;

$D_{O, \, \frac{1}{3} } A''(9, \, -3) = A'(\frac{1}{3} \times 9, \, \frac{1}{3} \times -3) = A'(3, -1)$

$D_{O, \, \frac{1}{3} } B''(9, \, -6) = B'(\frac{1}{3} \times 9, \, \frac{1}{3} \times -6) = A'(3, -2)$

$D_{O, \, \frac{1}{3} } C''(0, \, -3) = C'(\frac{1}{3} \times 0, \, \frac{1}{3} \times -3) = C'(0, -1)$

The coordinates of the vertices of ΔA'B'C' are A'(3, -1), B'(3, -2), and C'(0, -1), which is the same as the required coordinates of the image;

Therefore, the transformation that can be performed to show that ΔABC and ΔA'B'C' are similar are rotating ΔABC by 180° then a dilating the image derived after rotation by a scale factor of one-third (1/3) we get ΔA'B'C'.

7 0

3 years ago