Answer:
y=3
y=9
Step-by-step explanation:
y=3×0+3
=3
y=3×1+3
=9
The answer would be 26.25
Since sample size is > 40, we use the z-score
in calculating for the confidence interval.
The formula is given as:
Confidence Interval = X ± z * σ / sqrt (n)
Where,
X = mean = $50,340
z = z-score which is taken from standard distribution
tables at 90% confidence interval = 1.645
σ
= standard deviation = $10,780
n = sample size = 45
Substituting to the equation:
Confidence Interval = 50,340 ± 1.645 * 10,780 / sqrt (45)
Confidence Interval = 50,340 ± 1,607
Confidence Interval = $48,733 to $51,947
<span>Therefore the salary range of the personnel is $48,733 to $51,947.</span>
Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
