x^3 - 5x^2 + 6x - 30
| 1 - 5 6 - 30
|
|
5 | 5 0 30
----------------------------------------------
| 1 0 6 0 <------ the resiude is 0.
Resiude 0 means that the polynomial is divisible by x - 5, and that means the root is x = 5.
That is the only rooto because the quotient is x^2 + 6, which does not have real roots.
Answer: x = 5
Answer:
...what are the following for reference?
Step-by-step explanation:
Answer:
a. 3⁄10 + 6⁄10 = 9/10
b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4
c. 5⁄6 – 3⁄6 = 1/3
d. 2⁄3 – 6⁄10 = 1/15
e. 4⁄10 × 3⁄7 = 6/35
f. 1⁄6 × 6⁄15 = 1/15
g. 1⁄8 ÷ 4⁄9 = 9/32
h. 1⁄5 ÷ 3⁄4 = 4/15
Step-by-step explanation:
a. 3⁄10 + 6⁄10
= 3*1 + 6*1 / 10
= 3+6/10
= 9/10
b. 1⁄3 + 1⁄4 + 1⁄6
since denominators are different we take LCM of 3,4,6 which is 12
= 1*4 + 1*3 + 1*2 / 12
= 4+3+2/12
= 9 ÷ 3 / 12 ÷ 3
= 3 / 4
c. 5⁄6 – 3⁄6
= 5 - 3 / 6
= 2 ÷ 2 / 6 ÷ 2 = 1/3
d. 2⁄3 – 6⁄10
LCM of 3 and 10 is 30
= 2 * 10 - 6 * 3 / 30
= 20 - 18 / 30
= 2 ÷ 2 / 30 ÷ 2 = 1/15
e. 4⁄10 × 3⁄7
= 12 ÷ 2 / 70 ÷ 2 = 6/35
f. 1⁄6 × 6⁄15
= 6 ÷ 6/90 ÷ 6 = 1/15
g. 1⁄8 ÷ 4⁄9
= 1/ 8 * 9/4
=9/32
h. 1⁄5 ÷ 3⁄4
=1/5 * 4/3
= 4/15
Answer:
(0.30, 0.42)
Step-by-step explanation:
Given the sample proportion is = 0.36
Number of trials required for determining the margin of the error = 100
Sample size, n = 50
The point estimate = 0.36
The minimum sample proportion form the simulation = 0.28
The maximum sample proportion from the simulation = 0.40
Also the margin of the error of population proportion is found by using the half of the range.
Therefore, the interval estimate for the true population proportion is = (0.30, 0.42)
Answer:
Box X
Step-by-step explanation:
In order to find which box holds the most material, you have to find the volume of each box.
The formula for volume of a prism (or box) is [area of the base] * height. So, you can solve the problem as follows:
Step 1) Find the area of the base for box X (7 * 3). You can use any side as your base, as long as the opposite side of the shape is congruent (which in this case, it is)
Step 2) Multiply the area of your base (21) times the distance between the opposite congruent side (6). (21 * 6) = 126
Step 3) By repeating this process with box Y, you will find that the volume of box Y (10*11) = 110, which is less than the volume of box X.
Since the volume of box X is greater than that of box Y, box X can hold more material.