Eric is adding water to a 60-gallon pool.

The given value below figure find the value of x

tino4ka555 [31]

Answer:

Step-by-step explanation:

We know:

The sum of the quadrilateral angles measures 360°.

Therefore we have the equation:

$30^o+39^o+48^o+m\angle D=360^o\qquad(1)$

The sum of angles x and D is equal to 360°. Therefore we have the other equation:

$x+m\angle D=360^o\qquad(2)$

From (1) and (2) we have:

$x+m\angle D=30^o+39^o+48^o+m\angle D\qquad\text{subtract}\ m\angle D\ \text{from both sides}\\\\x=30^o+39^o+48^o\\\\x=117^o$

6 0

3 years ago

A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the

iris [78.8K]

Answer:

They are not independent

Step-by-step explanation:

Given

E = Occurrence of 1 on first die

F = Sum of the uppermost occurrence in both die is 5

Required

Are E and F independent

First, we need to list the sample space of a roll of a die

$Event\ 1 = \{1,2,3,4,5,6\}$

Next, we list out the sample space of F

$Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\$

$6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}$

In (1): the sample space of E is:

$E = \{1\}$

So:

$P(E) = \frac{n(E)}{n(Event\ 1)}$

$P(E) = \frac{1}{6}$

In (2): the sample space of F is:

$F = \{5,5,5,5\}$

So:

$P(F) = \frac{n(F)}{n(Event\ 2)}$

$P(F) =\frac{4}{36}$

$P(F) =\frac{1}{9}$

For E and F to be independent:

$P(E\ and\ F) = P(E) * P(F)$

Substitute values for P(E) and P(F)

This gives:

$P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}$

$P(E\ and\ F) = \frac{1}{54}$

However, the actual value of P(E and F) is 0.

This is so because $E = \{1\}$ and $F = \{5,5,5,5\}$ have 0 common elements:

So:

$P(E\ and\ F) = 0$

Compare $P(E\ and\ F) = \frac{1}{54}$ and $P(E\ and\ F) = 0$ .

These values are not equal.

Hence: the two events are not independent

6 0

3 years ago

Joe is training for a race in 30 days. He needs to run a total of 135 miles. How many miles will joe need to run each day to be

marin [14]

He needs to run 4.5 miles each day.

4 0

3 years ago

The mean height of 10 girls is 154cm. The mean height of 8 boys is 162cm. What is the mean height of the class?

olganol [36]

Answer:

158cm

Step-by-step explanation:

154+162=316

316/2=158

8 0

3 years ago

Which mathematical equation represents the solution for k in the equation h + 3 = jk + 6k ?

Tomtit [17]

Answer:

The answer is<u> D.</u> h+3/j+6.

Step-by-step explanation:

Given:

The equation h + 3 = jk + 6k.

Now, to get the mathematical expression.

$h + 3 = jk + 6k$

So, taking $k$ common on R.H.S we get:

$h + 3 = k(j + 6)$

Then, dividing both sides by $j+6$ we get:

$\frac{h+3}{j+6} =k$

Thus,

$k=\frac{h+3}{j+6}$

Therefore, the answer is D. h+3/j+6.

5 0

3 years ago