For Wyatt's recipe the rate is:
r1 = 3.15 / 9
r1 = 0.35
For Cora's recipe the rate is:
r2 = 2.4 / 8
r2 = 0.3
The difference between both recipes is:
r1-r2 = 0.35 - 0.3 = 0.05
Answer:
0.05 cups of flour per shortcake less is needed for Cora's recipe
The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
Learn more about prime numbers here:
brainly.com/question/145452
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Answer:
The correct answer is option C. 3
Step-by-step explanation:
It is given an expression in variable x
(x² + 3x²)/(x + 1) ÷ (x² - 9)/(3x + 3) * (x - 3)/x
<u>To find the simplified answer</u>
x² + 3x² = x(x + 3)
x² - 9 = (x + 3)(x - 3)
The given expression can be written as,
(x² + 3x²)/(x + 1) ÷ (x² - 9)/(3x + 3) * (x - 3)/x
= x(x + 3)/(x + 1) * 3(x + 1)/(x + 1)(x - 1) * (x -3)/x
=[ x(x +3) * 3(x +1) * (x -3)]/[(x + 1) * (x + 3)(x - 3) *x]
= 3
The correct answer is option C. 3
Best guess is it’s the second one but I believe it’s between A and B sorry If I’m wrong.
Answer:
7.43
Step-by-step explanation:
