X/3 -4 = -29 what does X equal? Plz help

What is the measure of angle f

Leni [432]

Answer:

C) 116

Step-by-step explanation:

<F = x

x + 64 = 180

x = 116

6 0

3 years ago

The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A fir

Kazeer [188]

Answer:

(1) (c) 5.30 years.

(2) (b) 0.289.

(3) (b) 0.80.

(4) (d) 0.50.

(5) (a) 5.25 years.

Step-by-step explanation:

Let X = age of the children in kindergarten on the first day of school.

The random variable X follows a continuous Uniform distribution with parameters a = 4.8 years and b = 5.8 years.

The probability density function function of X is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a}} ;\ a$

(1)

The expected value of a Uniform random variable is:

$E(X)=\frac{1}{2}(a+b)$

Compute the mean of X as follows:

$E(X)=\frac{1}{2}(a+b)=\frac{1}{2}\times (4.8+5.8)=5.3$

Thus, the mean of the distribution is (c) 5.30 years.

(2)

The standard deviation of a Uniform random variable is:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}=\sqrt{\frac{1}{12}\times (5.8-4.8)^{2}}=0.289$

Thus, the standard deviation of the distribution is (b) 0.289.

(3)

Compute the probability that a randomly selected child is older than 5 years old as follows:

$P(X>5)=\int\limits^{5.8}_{5} {\frac{1}{5.8-4.8}}\, dx\\$

$=\int\limits^{5.8}_{5} {1}\, dx\\=[x]^{5.8}_{5}\\=(5.8-5)\\=0.8$

Thus, the probability that a randomly selected child is older than 5 years old is (b) 0.80.

(4)

Compute the probability that a randomly selected child is between 5.2 years and 5.7 years old as follows:

$P(5.2$

$=\int\limits^{5.7}_{5.2} {1}\, dx\\=[x]^{5.7}_{5.2}\\=(5.7-5.2)\\=0.5$

Thus, the probability that a randomly selected child is between 5.2 years and 5.7 years old is (d) 0.50.

(5)

It is provided that a randomly selected child is at the 45th percentile.

This implies that:

P (X < x) = 0.45

Compute the value of x as follows:

$P (X < x) = 0.45$

$\int\limits^{x}_{4.8} {\frac{1}{5.8-4.8}}\, dx=0.45$

$\int\limits^{x}_{4.8} {1}\, dx=0.45$

$[x]^{x}_{4.8}=0.45$

$x-4.8=0.45\\$

$x=0.45+4.8\\x=5.25$

Thus, the age of the child at the 45th percentile is (a) 5.25 years.

6 0

3 years ago

A line has y intercept -6 and a x-intercept - 12. what is the equation of the line

koban [17]

Answer:

$\boxed{y = -\dfrac{1}{2}x-6}}$

Step-by-step explanation:

The equation for a straight line is

y = mx + b

where m is the slope of the line and b is the y-intercept.

The line passes through the points (-12, 0) and (0, 6)

(a) Calculate the slope of the line

$\begin{array}{rcl}m & =&\dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\ & = &\dfrac{6 - 0 }{0 - (-12)}\\\\& = &\dfrac{6}{-12}\\\\& = & -\dfrac{1}{2}\\\end{array}$

(b) Write the equation

The y-intercept is at x = -6.

$\text{The equation for the line is $\boxed{\mathbf{y = -\dfrac{1}{2}x-6}}$}$

The diagram shows the graph of the line passing through the two intercepts.

5 0

3 years ago

A house is purchased for $150,000 in 2002. The value of the house

Sunny_sXe [5.5K]

9514 1404 393

Answer:

$67,516

Step-by-step explanation:

"Depreciates" means the value is getting smaller. The function that describes the situation is a decay function:

y= a(1-r)^x

Here, a=150000, r = 0.07, and x=11. The value is predicted to be ...

y = 150000(1 -0.07)^11 = 150000(0.93^11) = 67,515.53

The house is worth about $67,516 in 2013.

4 0

3 years ago

What it is the equivalent of 7:2

Law Incorporation [45]

Answer:

7:2

7/2

Step-by-step explanation:

7:2 is also equivalent to 7/2

4 0

3 years ago