Answer: 6 pounds of French roast coffee and 14 pounds of Sumatran coffee was used.
Step-by-step explanation:
Let x represent the number of pounds of French roast coffee that should be added in the blend.
Let y represent the number of pounds of Sumatran coffee that should be added in the blend.
The total number of pounds of the mixture made is 20 lb. This means that
x + y = 20
The mixture sells for $8.30 a pound. The total cost of the mixture would be
8.3 × 20 = 166
This means that
9x + 8y = 166 - - - - - - - - -1
Substituting x = 20 - y into equation 1, it becomes
9(20 - y) + 8y = 166
180 - 9y + 8y = 166
- 9y + 8y = 166 - 180
- y = - 14
y = 14
x = 20 - y = 20 - 14
x = 6
<u>Original</u>
Length (L): L
width (w): w
Perimeter (P) = 2L + 2w
48 = 2(L) + 2(w)
24 = L + w
24 - L = w
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<u>New</u>
Length (L): L + 24
width (w): 2w ⇒2(24 - L) = 48 - 2L
Perimeter (P) = 2L + 2w
112 = 2(L + 24) + 2(48 - 2L)
112 = 2L + 48 + 96 - 4L
112 = -2L + 140
-28 = -2L
14 = L
Answer: 14 m
Answer:
P(1833 < X < 1975) = 7.55%
Step-by-step explanation:
From the given information:
Let X be the random variable that obeys a normal distribution and which represents the monthly electric consumption during winter by all households in the Boston area.
X N ( μ = 1650 , σ² = 320² )
The probability that a monthly consumption of 1883 to 1975 kilowatt is given as:
P(1833 < X < 1975) = P(Z< 1.0156) - P(Z< 0.738)
P(1833 < X < 1975) = 0.8452 - 0.7697
P(1833 < X < 1975) = 0.0755
P(1833 < X < 1975) = 7.55%
10.5 - 8.7 = 1.8
There is 1.8 feet of pipe left
(Note: this is hard to explain without graphing. You might want to graph both of these lines just to make sure I did this correctly. :))
Y = -4(x) is the y = mx + b where m = slope and b = the y intercept.
So the slope of line A is -4 / 1 and the y intercept is 0. (If it's 0 there is no point in writing it down, so it was left out of the equation.)
The slope of line B with be equal to the slope of line A, so we can fill that in our equation. y = -4 x + ??
We know that y increases as x decreases.
Now we just need to scale 8, -3 down until x = 0.
(8 - 4, -3 + 1) = (4, -2)
(4 - 4, -2 + 1) = (0, -1)
y = -4x -1 is your final answer. Hope that helps! :)