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3 years ago

George’s car can drive 30 miles on 1/2 gallon of gas. How many gallons of gas will he use to drive 20 miles?

1 answer:

8 0

The best way to do this is to set up a proportion

30 20
---- = -----
0.5 x

then cross multiply and divide

20 × 0.5 = 10/30=1/3

he needs 1/3 tank of gas to drive 20 miles

I hope I've helped!

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Mike has a large tropical fish collection.He gives 2/3 of his fish to a local high school. Then gives 2/5 of the remaining fish

joja [24]

If you divide the 2 in 3 you get .6 and if you divide 2 in 5 ou get ,4 now add them you and get 1 now add that 1 to 30 your answer should be 31

3 0

2 years ago

The market and Stock J have the following probability distributions:

denis-greek [22]

Answer:

1) $E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%$

2) $E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%$

3) $E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1$

And the variance would be given by:

$Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89$

And the deviation would be:

$Sd(M) = \sqrt{13.89}= 3.73$

4) $E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8$

And the variance would be given by:

$Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56$

And the deviation would be:

$Sd(M) = \sqrt{55.56}= 7.45$

Step-by-step explanation:

For this case we have the following distributions given:

Probability M J

0.3 14% 22%

0.4 10% 4%

0.3 19% 12%

Part 1

The expected value is given by this formula:

$E(X)=\sum_{i=1}^n X_i P(X_i)$

And replacing we got:

$E(M) = 14*0.3 + 10*0.4 + 19*0.3 = 13.9 \%$

Part 2

$E(J)= 22*0.3 + 4*0.4 + 12*0.3 = 11.8 \%$

Part 3

We can calculate the second moment first with the following formula:

$E(M^2) = 14^2*0.3 + 10^2*0.4 + 19^2*0.3 = 207.1$

And the variance would be given by:

$Var (M)= E(M^2) -[E(M)]^2 = 207.1 -(13.9^2)= 13.89$

And the deviation would be:

$Sd(M) = \sqrt{13.89}= 3.73$

Part 4

We can calculate the second moment first with the following formula:

$E(J^2) = 22^2*0.3 + 4^2*0.4 + 12^2*0.3 =194.8$

And the variance would be given by:

$Var (J)= E(J^2) -[E(J)]^2 = 194.8 -(11.8^2)= 55.56$

And the deviation would be:

$Sd(M) = \sqrt{55.56}= 7.45$

8 0

2 years ago

Which of the following is a solution of y - x < -3?

azamat

Answer:

Step-by-step explanation:

$Subtract- y- from- both -sides.\\-x (less than)-3-y\\2 Multiply both sides by -1.\\x (greater than ) 3+y$

5 0

3 years ago

Read 2 more answers

Solve the system by elimination 1: x+5y-4z=-10, 2x-y+5z=-9, 2x-10y-5z=0 .. . 2. Solve the system by substitution: 2x-y+z=-4, z=5

Kryger [21]

1 )
1st and 2nd equation (multiply 1st by -2 ):
-2x - 10 y + 8 z = 20
2 x - y + 5 z = -9
---------------------------
- 11 y + 13 z = 11 / * ( -20 )
1st and 3rd:
- 2 x - 10 y + 8 z = 20
2 x - 10 y - 5 z = 0
-----------------------------
- 20 x + 3 z = 20 / * 11
----------------------------------
220 y - 260 z = -220
- 220 y + 33 z = 220
------------------------------
z = 0, y = -1, x = - 5
2 )
2 x - y + 5 = -4
- 2 x + 3 y - 5 = - 10
Substitution: y = 2 x + 9
- 2 x + 3(2 x + 9 ) = -5
4 x = - 32, x = -8, y = -7, z = 5
3 )
x + y + z = 11
1.5 x+3 y +1.5 z = 21
x = 2 y
------------------------
3 y + z = 11 / * (-2)
6 y + 1.5 z = 21
------------------------
- 6 y - 2 z = -22
6 y + 1.5 z = 21
------------------------
-0.5 z = -1, z = 2, y = 3, z = 6
Answer: the store used 6 pounds of peanuts, 3 pounds of almonds and 2 pounds of raisins.

8 0

3 years ago

The sum of the measures of two adjacent angles is 72 degrees. The ratio of the smaller angle to the

Goryan [66]

Answer:

The larger angle is 54°

Step-by-step explanation:

Given

Let the angles be: θ and α where

θ > α

Sum = 72

α : θ = 1 : 3

Required

Determine the larger angle

First, we get the proportion of the larger angle (from the ratio)

The sum of the ratio is 1 + 3 = 4

So, the proportion of the larger angle is ¾.

Its value is then calculated as:.

θ = Proportion * Sum

θ = ¾ * 72°

θ = 3 * 18°

θ = 54°

4 0

2 years ago