Write an expression for the lengths of each segment AB = BC = DE = EF =

OverLord2011 [107]

1. We are given:
$a^2 = 64$

The only a which squared gives you 64 is 8. The perimeter of an 8 by 8 square will be 32. Half of that is 16. Now, let's see what we can do. We can set up:
$4a = 16$

Obviously, each side length has to be 4. So, the area of this square will be 16 units².

2. Let n equal her son's age. So, her age right now will be (S = her age):
$S = 18n$
1 year ago it was:
$S-1 = 3n$

We have 2 equations, let's substitute. We can rewrite this as:
$18n-1 = 3n$
Solve for n:
$15n-1=0$
$n= \frac{1}{15}$

We know the value of n, which is her son's age. So, her son is 1/15 of a year old or about 24 days old.

8 0

4 years ago

2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.01

Pie

Answer:

On average it will take 13 hrs 53 minutes before the van is filled

Step-by-step explanation:

The first thing we need to do here is to find find the number of defective light bulbs

Using the poisson process, that would be;

λ * p

where λ is the poisson rate of production which is 300 per hour

and p is the probability that the produced bulb is defective = 0.012

So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour

Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)

What we need to find however is E(X)

Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;

E(X) = r/λ = 50/3.6 = 13.89

Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes

5 0

4 years ago

Math geometry pls help:) Find all missing angles

Naily [24]

Answer:

m<1 = 51 degrees

m<2 = 18 degrees

m<3 = 123 degrees

m<4 = 39 degrees

Step-by-step explanation:

To solve this problem, let's first try to find the measure of angle 1.

To do this, we must remember that the sum of the interior angles of a triangle must equal 180 degrees. Using this knowledge, we can set up the following equation:

72 + 57 + m<1 = 180

Our first step in solving this equation is to simplify the left side by adding together the two constant terms.

129 + m<1 = 180

Next, we can subtract 129 from both sides of the equation.

m<1 = 51 degrees

Now, we can solve for angle 2.

We can see that angle 2 and the angle measuring 72 degrees together make a right angle, which is 90 degrees. From this observation, we can set up the following equation:

m<2 + 72 = 90

To solve, we subtract 72 from both sides of the equation.

m<2 = 18 degrees

Now, we can solve for angle 3.

We can see from the diagram that angle 3 and the angle measuring 57 degrees are supplementary. This means that their sum should equal 180 degrees, and the two angles together make a straight line. This lets us set up the following equation:

m<3 + 57 = 180

To solve, we subtract 57 from both sides of the equation.

m<3 = 123 degrees

Finally, we can solve for angle 4.

We can solve for angle 4 using the same strategy we used to solve for angle 1. Our equation for angle 4 is as follows:

m<2 + m<3 + m<4 = 180

18 + 123 + m<4 = 180

Let's first simplify the left side of the equation.

141 + m<4 = 180

We can subtract 141 from both sides of the equation as our next step.

m<4 = 39 degrees

Therefore, the correct answers are m<1 = 51 degrees, m<2 = 18 degrees, m<3 = 123 degrees, and m<4 = 39 degrees.

Hope this helps!

8 0

3 years ago

If you have 10 red, 10 blue, 10 orange and 10 black socks in a drawer, how many socks must you pull out of the drawer (assume it

Orlov [11]

Answer:

Step-by-step explanation:

The probability of u choosing two orange socks from the sock drawer WITHOUT REPLACEMENT:

= P(the first one is Orange) * P(the second one is Orange)

= 10/40 * 9/39 = 3/52.

6 0

3 years ago

Helpp urgent evaluate if k= -4, p=7, q=-8 p + 4 (-p) + (-13)

ExtremeBDS [4]

Answer:

-34

Step-by-step explanation:

p + 4 (-p) + (-13)

Let p = 7

7 + 4 (-7) + (-13)

Multiply

7 -28 -13

-21-13

-34

8 0

3 years ago