Step 1 :
53x3 - 8
Step 2 :
Trying to factor as a Difference of Cubes:
2.1 Factoring: 125x3-8
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0+b3 =
a3+b3
Check : 125 is the cube of 5
Check : 8 is the cube of 2
Check : x3 is the cube of x1
Factorization is :
(5x - 2) • (25x2 + 10x + 4)
Trying to factor by splitting the middle term
2.2 Factoring 25x2 + 10x + 4
The first term is, 25x2 its coefficient is 25 .
The middle term is, +10x its coefficient is 10 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 25 • 4 = 100
Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is 10 .
-100 + -1 = -101
-50 + -2 = -52
-25 + -4 = -29
-20 + -5 = -25
-10 + -10 = -20
-5 + -20 = -25
For tidiness, printing of 12 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
(5x - 2) • (25x2 + 10x + 4)
Answer:
For every one pound there are 16 ounces.
Step-by-step explanation:
We can simply see that by dividing the ounces by pounds, 32/2 = 16, and 48/3 = 16.
Number of ounces: 16, 32, 48, 64, 80, 96
Number of pounds: 1, 2, 3, 4, 5, 6
Answer:
[0.875;0.925]
Step-by-step explanation:
Hello!
You have a random sample of n= 400 from a binomial population with x= 358 success.
Your variable is distributed X~Bi(n;ρ)
Since the sample is large enough you can apply the Central Limit Teorem and approximate the distribution of the sample proportion to normal
^ρ≈N(ρ;(ρ(1-ρ))/n)
And the standarization is
Z= ^ρ-ρ ≈N(0;1)
√(ρ(1-ρ)/n)
The formula to estimate the population proportion with a Confidence Interval is
[^ρ ± 
*√(^ρ(1-^ρ)/n)]
The sample proportion is calculated with the following formula:
^ρ= x/n = 358/400 = 0.895 ≅ 0.90
And the Z-value is 
≅ 1.65
[0.90 ± 1.65 * √((0.90*0.10)/400)]
[0.875;0.925]
I hope you have a SUPER day!
Answer: 35gh, 40mn
Step-by-step explanation:
You just multiply the numbers!
