Answer:
A worked 20 hours and B worked 15 hours.
Step-by-step explanation:
Given:
Mechanic A hourly rate = $55
Mechanic B hourly rate = $45
Total charged = $1775
Let's assume Mechanic A worked 'A' amount of hours and Mechanic B worked 'B' amount of hours, then
Step 1:
First equation: A + B = 35
Second equation: 55xA + 45xB = 1775
Step 2:
First equation can be written as: A = 35 - B
Step 3: Replace value of A in second equation
Second equation: 55x(35-B) + 45B = 1775
: 1925 - 55B + 45B = 1775
: (1925 - 1775 )/10 = B
: B = 15 hours
A worked = 35 - 15
= 20 hours
Because the sum and product will always have to flipped
Example
4x5=5x4
9+6=6+9
Answer:
14, 20, 0, 0, 0
Step-by-step explanation:
The notation indicates the absolute value of x, therefore it can be rewritten as:
if x 0
if x < 0
In this problem, we have the expression
Therefore, we can rewrite it as:
if x ≥ 0:
(a)
If x < 0:
(b)
So now we can substitute the given values into the two expressions:
x = 7 (positive value, so we use expression (a):
x = 10 (positive values, so we use expression (a):
x = 0 (zero, so we can use expression (a):
x = -3 (negative value, so we use expression (b):
x = -8 (negative value, so we use expression (b):
Answer:
The 95% confidence interval would be given by (96.98;100.82)
Step-by-step explanation:
Information given
represent the sample mean
population mean (variable of interest)
s=0.62 represent the sample standard deviation
n=103 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
The degrees of freedom are given by:
Since the Confidence is 0.95 or 95%, the significance is and , and the critical value for this case would be
And replacing we got:
The 95% confidence interval would be given by (96.98;100.82)