Answer:
$7.50; $18.36; $11.48
Step-by-step explanation:
FICA = 7.65 %
A. <em>Weekly pay $98.00
</em>
Tax deduction = 98.00 × 7.65/100
Tax deduction = $7.50
B. <em>Weekly pay $240.00
</em>
Tax deduction = 240.00 × 7.65/100
Tax deduction = $18.36
C. Weekly pay $150.00
Tax deduction = 150.00 × 7.65/100
Tax deduction = $11.48
Answer:
|Z| = |-1.36| < 1.645 at 0.1 level of significance
The null hypothesis is accepted
A manufacturer of banana chips are filling machine works correctly at the mean 449
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given mean of the Population(μ) = 449
The Standard deviation of the population(σ) = 22
size of the sample 'n' = 36
mean of the sample(x⁻) = 444
Given the level of significance(α) = 0.1
Critical value Z = 1.645
<u><em>Step(ii):</em></u>-
<em>Null hypothesis</em>:H₀:
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 449.0
(μ) = 449
<em>Alternative Hypothesis</em>:H₁: (μ) ≠ 449
Test statistic
= -1.36
<em>Final answer:-</em>
|Z| = |-1.36| < 1.645 at 0.1 level of significance
The null hypothesis is accepted
A manufacturer of banana chips are filling machine works correctly at the mean 449
1. -x+9y=-5
x-5y=1
-----------------
x=1+5y
-(1+5y)+9y=-5
-1-5y+9y=-5
-1+4y=-5
4y=-5-(-1)
4y=-5+1=-4
4y=-4
y=-4/4=-1
So x=1+5y=1+5(-1)=1-5=-4
Answer: x=-4, y=-1. (-4, -1).
2) -7x-y=13
8x+y=-14
------------------
y=-14-8x
-7x-(-14-8x)=13
-7x+14+8x=13
14+x=13
x=13-14=-1
y=-14-8(-1)=-14+8=-6.
Answer: x=-1, y=-6. (-1, -6).
3) x+7y=24
x-9y=-24
----------------
x=24-7y
24-7y-9y=-24
24-16y=-24
16y=24-(-24)=24+24=48
y=48/16=3
x=24-7(3)=24-21=3
Answer: x=3, y=3. (3, 3).
4). 3x+y=-21
x+y=-5
-------------------
x=-5-y
3(-5-y)+y=-21
-15-3y+y=-21
-15-2y=-21
2y=-15-(-21)=-15+21=6
y=6/2=3
x=-5-3=-8.
Answer: x=-8, y=3. (-8, 3).
5) 3x+6y=6
9x-12y=18
---------------
Simplify 3x+6y=6 will get you x+2y=2,
x=2-2y,
9(2-2y)-12y=18
18-18y-12y=18
18-30y=18
30y=18-18=0
y=0/30=0
x=2-2(0)=2-0=2
Answer: x=2, y=0. (2, 0).
6) 6x+8y=26
-7x+2y=-19
-----------------
-4(-7x+2y)=-4(-19)
28x-8y=76
---------------------------
6x+8y=26
28x-8y=76
-----------------
34x=102
x=102/34=3
6(3)+8y=26
18+8y=26
8y=26-18=8
y=8/8=1
Answer: x=3, y=1. (3, 1)
BONUS:
-5x+5y=-25
3x+2y=10
---------------
Simplify -5x+5y=-25 you will get x-y=5
x=y+5
3(y+5)+2y=10
3y+15+2y=10
5y+15=10
5y=10-15=-5
y=-5/5=-1
x=-1+5=4
Answer: x=4, y=-1. (4, -1).
Step-by-step explanation:
2×9n=18n
2×-6=-12
52-12+18n= 38 +18n
2×7n=14n
8×2=16
14n+16
38+18n=14n+16
subtract 14n from 14n and 18n
38+4n=16
subtract 38 from 38 and 16
4n=-22
divide each side by 4
n= -5.5
<span>Let the width of the rectangular plot of land be 'x' yards.
Given that the length of the rectangular plot of land is 10 yards more than its width.
So, width of the rectangular plot of land = (x + 10) yards.
Also given that the area of the rectangular plot of land is 600 square yards.
We know that, area of a rectangle = length * width
That is, (x+10) * x = 600
x^2 + 10x = 600
x^2 + 10x - 600 = 0
x^2 + 30x - 20x -600 = 0
x(x + 30) - 20(x + 30) = 0
(x +30)(x -20) =0
Therefore, either (x + 30) = 0 or (x - 20) = 0
If x + 30 = 0, then x = -30 and
If x - 20 = 0, then x = 20
Since 'x' represents the width of a rectangular plot of land it cannot be negative.
Therefore,
width of the rectangular plot of land = 20 yards
length of the rectangular plot of land= x + 10 = 30 yards</span>
