All categories

3 years ago

What is the length of the indicated arc?

Mathematics

1 answer:

Ksivusya [100]3 years ago

6 0

Answer:

E. None of the above

Step-by-step explanation:

Arc length = radius • angle in radians

30 deg = 0.523599 rad

L = 12 • 0.523599 = 6.28319

2π = 6.28319

Answer is E. None of the above

You might be interested in

What is this equation x2 – 2x – 6 in vertex form?

Lena [83]

Answer:

In vertex form, the parabola's equation is y=(x−1)^2 +5.

Step-by-step explanation:

7 0

3 years ago

Convert the polar equation to rectangular form: r = 2 / [1 + sin(theta)]

iren2701 [21]

R = 2 / (1 + sin θ)

Using the following relations:

R = sqrt (x^2 + y^2)
sin θ = y/R

R = 2 / (1 + y/R)
R(1 + y/R) = 2
R + y = 2
R = 2 - y
sqrt(x^2 + y^2) = 2 - y

Squaring both sides:
x^2 + y^2 = (2 - y)^2
x^2 + y^2 = 4 - 4y + y^2

x^2 + 4y - 4

8 0

3 years ago

The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15.

evablogger [386]

Answer:

4.4% of the population with IQ between 120 and 125.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution of IQ scores is a bell shaped distribution that is a normal distribution.

a) Let X be a person's IQ score.

Then, density functions for IQ scores is given by:

$P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{z^2}{2}}\\\\\text{where,}\\\\z = \frac{x-\mu}{\sigma}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-100)^2}{450}}$

b) P(population with IQ between 120 and 125.)

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

$P(120 \leq x \leq 125) = P(\displaystyle\frac{120 - 100}{15} \leq z \leq \displaystyle\frac{125-100}{15}) = P(1.33 \leq z \leq 1.66)\\\\= P(z \leq 1.66) - P(z < 1.33)\\= 0.952 - 0.908 = 0.044 = 4.4\%$

$P(120 \leq x \leq 125) = 4.4\%$

6 0

3 years ago

Find the length of the missing side. The triangle is not drawn to scale.

suter [353]

Answer:

D.) 8

Step-by-step explanation:

You can use the Pythagorean theorem because this is a right triangle:

$a^2+b^2=c^2$

a and b are the legs and c is the hypotenuse. The hypotenuse is always the longest side in a right triangle (since it is opposite the biggest angle). The two legs squared have to add up to the hypotenuse squared.

Fill in values:

$a^2+15^2=17^2$