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2 years ago

15. Which expression shows the sum of 72 and 96 as the product of the GCF

1 answer:

3 0

Here, we are required to determine which expression shows the sum of 72 and 96 as the product of the GCF and a sum of two numbers with no common factor?

The answer is Choice B: 24(3 + 4)

Factors of 72 are;

2 × 2 × 2 × 3 × 3

Factors of 96 are;

2 × 2 × 2 × 2 × 2 × 3

The factors in bold above are common to 72 and 96 and therefore gives a total of 24 which is the GCF of 72 and 96.

The remaining factor of 72 and 96 are 3 and 4 respectively.

And, since 3 and 4 have no common factor,

Therefore, the expression which shows the sum of 72 and 96 as the product of the GCF

and a sum of two numbers with no common factor is:

24(3 + 4)

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$104.19

Step-by-step explanation:

We will use the compound interest formula to solve this:

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2 years ago

What is an equation of the line that passes through the points (-1, 6) and (-1, –5)?

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Answer: 11x + 11

Step-by-step explanation:

This is two points equation. It could be done in various ways depending on the level of understanding of the topics. The formula goes thus

y - y₁ y₂ ₋ y₁ y₂ ₋ y₁

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x - x₁ x₂ ₋ x₁ x₂ ₋ x₁

Where x₁ = -1, x₂ = -1, y₁ = 6, y₂ = -5. Now substitute for the values in the formula above and solve.

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3 years ago

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

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Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

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$\displaystyle h(x) = y = 3x-2$

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We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

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We are given the following in the question:

The needle size should not be too big and too small.

The diameter of the needle should be 1.65 mm.

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Type I error:

It is the error of rejecting the null hypothesis when it is true.
It is also known as false positive error.
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Thus, type I error in this study would mean we reject the null hypothesis that the average diameter is 1.65 mm but actually the average diameters of the needle is 1.65 mm.

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