Answer:
y = ⅔x - 5
Step-by-step explanation:
The line that is parallel to 2x - 3y = 24, would have the same slope as the line, 2x - 3y = 24.
Rewrite;
2x - 3y = 24
-3y = -2x + 24
Divide both sides by -3
y = ⅔x - 8
Thus, the slope of 2x - 3y = 24 is ⅔.
Therefore the line that is parallel to 2x - 3y = 24, will have a slope (m) of ⅔.
Using point-slope form, we can generate an equation that passes through (-3, -7) and is parallel to 2x - 3y = 24.
Thus, substitute (a, b) = (-3, -7) and m = ⅔ into y - b = m(x - a)
Therefore:
y - (-7) = ⅔(x - (-3))
y + 7 = ⅔(x + 3)
Rewrite in slope-intercept form.
Multiply both sides by 3
3(y + 7) = 2(x + 3)
3y + 21 = 2x + 6
3y = 2x + 6 - 21
3y = 2x - 15
Divide both sides by 3
y = ⅔x - 5
Answer:
Russell family's sprinkler: 40 hours
Gonzales family's sprinkler: 20 hours
Step-by-step explanation:
Let's call the amount of time the Russell family's sprinkler was on by X, and the Gonzales family's sprinkler by Y.
We can then formulate the equations:
X + Y = 60
X*35 + Y*40 = 2200
We can solve this system multiplying the first equation by 35, and then subtracting the result from the second equation:
35*X + 35*Y = 2100
5*Y = 100
Y = 20
from the first equation:
X + 20 = 60
X = 40
Russell family's sprinkler: 40 hours
Gonzales family's sprinkler: 20 hours
Answer:
you should accept the $1,000 bill
Step-by-step explanation:
Given the information:
- $500 for rolling 1 or 2
- $400 for rolling 3
- lose $300 for rolling 4,5,6
P (rolling 1 or 2) = 1/6 + 1/6 = 2/6 = 1/3
P (rolling a 3) = 1/6
P (rolling 4 or 5 or 6) = 3/6 = 1/2
Hence, the expected value for 1 time is:
E = (1/3)*500 + (1/6)*400 - (1/2)*300
E = $166 + $66 - $150
E = $82
Expected value is linear so if you roll the die 10 times, expected value is: 10*82 = $820
The expected value is $82, meaning you should accept the $1,000 bill
Answer:
1.98
Step-by-step explanation:
sin(26) = EF/4.5 -->
.44 = EF/4.5 -->
.44 * 4.5 = EF -->
1.98 = EF
