When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
The gross profit margin is calculated using the following rule:
gross profit margin = total profit / total sales
Now, we need to get the values of total profit and total sale:
total profit = <span>9*8-(40+8)=24$
total sales = 9*8 = 72$
Now, we will substitute in the above equation:
gross profit margin = 24/72 = 1/3 = 0.3333334
% = 0.33333334*100 = 33.3334%</span>
Mean: 10.5
Median: 10.5
Range: 5
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To find the mean you order the numbers then add then divide.
<u>Add</u>
8+9+10+10+10+11+11+11+12+13=105
<u>Divide</u>
105÷10=10.5
Mean = 10.5
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Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers.
Find the middle number. Put your left finger on 8 and your right finger on 13. Move your left finger to the right to 10 and move your right finger to 11.
the middle number is 10.5 so therefore it is the median.
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To find the range you subtract the biggest number to the smallest number.
<u>Subtract</u>
13-8=5
Therefore 5 is the range
Four hundred thousand two hundred five
Answer:
20
Step-by-step explanation:
(6x3=18) (6x1/3=2) (18+2=20)
