Answer:
The answer to your question is width = 3
Step-by-step explanation:
Data
width = w = ?
length = l = ?
Area = 15 units
Process
1.- Write equations to help to solve this problem
Area of a rectangle = width x length
= w x l Equation l
width = length - 2
w = l - 2 Equation ll
2.- Substitution
A = w x l
15 = (l - 2)(l)
3.- Expand
15 = l² - 2l
l² - 2l - 15 = 0
2.- Solve for l
-Find the prime factors of -15
15 3
5 5
1
15 = 3 x 5
3.- Factor l² -2l - 15 = 0
(l - 5)(l + 3) = 0
4.- Find the values of l
l₁ - 5 = 0 l₂ + 3 = 0
l₁ = 5 l₂ = -3
The length if the rectangle = 5, it could not be -3, because there are no negative lengths.
5.- Find w
w = l -2
w = 5 - 2
w = 3 units
I am assuming that 114114 is actually 114.
Toni: 20 + 0.80/lap
Marcy: 15 + 0.85/lap
Marcy: x laps
Toni: 114x laps
[20 + 0.80(114x)] + [15 + 0.85x] = 257
20 + 91.2x + 15 + 0.85x = 257
92.05x = 257 - 35
92.05x = 222
x = 222/92.05
x = 2.41 laps
Marcy: x = 2.41 laps
Toni: 114x = 114(2.41) = 274.74 laps
20 + 0.80(274.74) = 20 + 219.79 = 239.79 or 240
15 + 0.85(2.41) = 15 + 2.05 = 17.05 or 17
240 + 17 = 257
Answer:
a) 0.0081975
b) 0.97259
Step-by-step explanation:
The line width for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. What is the probability that a line width is greater than 0.62 micrometer?
z = 0.62 - 0.5/0.05
z = 2.4
Probability value from Z-Table:
P(x<0.62) = 0.9918
P(x>0.62) = 1 - P(x<0.62)
= 0.0081975
b. What is the probability that a line width is between 0.4 and 0.63 micrometer?
For 0.4
z = 0.4 - 0.5/0.05
= -2
Probability value from Z-Table:
P(x = 0.4) = 0.02275
For 0.63
z = 0.63 - 0.5/0.05
= 2.6
Probability value from Z-Table:
P(x = 0.63) = 0.99534
P(x = 0.63) - P(x = 0.4)
= 0.99534 - 0.02275
= 0.97259
c. The line width of 90% of samples is below what value?
Answer:
C. 
Step-by-step explanation:
In order to find the slope knowing two points, use the slope formula 
. 
and 
represent the x and y values of one point the line intersects, and 
and 
represent the x and y values of another point the line intersects.
Knowing this, use the points (-4, -4) and (6, 4) for the formula. Substitute -4 for , -4 for , 6 for , and 4 for . Then, simplify:
Thus, is the slope of the line.
