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Andreyy89
2 years ago
12

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

Mathematics
1 answer:
Molodets [167]2 years ago
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)

Read more:

brainly.com/question/21549068

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Which of the following can be used to describe the location that is 9 units to the right of zero on the number line?
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You will use the word absolute value. The absolute value describes a distance from zero. Here is how you would write this in math terms and symbols:

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3 years ago
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Maria has 90$ in a saving account.The interest rate rise a 5% compounded annually.to the nearest cent, how much will he have in
-Dominant- [34]

Answer:

$104.19

Step-by-step explanation:

We will use the compound interest formula to solve this:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

<em />

First, lets change 5% into a decimal:

5% -> \frac{5}{100} -> 0.05

Now, plug the values into the equation:

A=90(1+\frac{0.05}{1})^{1(3)}

A=104.19

After 3 years, Maria will have $104.19

8 0
2 years ago
What is an equation of the line that passes through the points (-1, 6) and<br> (-1, –5)?
miskamm [114]

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

------    =   ----------      or  y ₋ y₁ =    ---------  ˣ  ( x - x₁ )

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.

y - 6           -5 - 6       -11             -11

------      =   --------    =  ----      =    -----

x - (-1)         -1 - (-1)      -1 + 1          0

y - 6          -11

------    =    -----

x + 1           0   ,

Now we cross multiply to have a linear equation

0( y - 6 )  =  -11( x + 1 )

0   =   -11x - 11, now multiply by -1

The equation now becomes

11x + 11

   

3 0
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))
sergejj [24]

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, <em>f</em> and <em>g</em> are inverses, then:

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

So, we can let <em>j</em> be the inverse function of <em>h</em>.

Function <em>h</em> is given by:

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

Find its inverse. Flip variables:

x = 3y - 2

Solve for <em>y. </em>Add:

\displaystyle x + 2 = 3y

Hence:

\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}

Therefore, <em>a</em> = 1/3 and <em>b</em> = 2/3.

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}

And:

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

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2 years ago
Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need
Mars2501 [29]

Answer:

\text{Average diameter is 1.65 mm and we decide that it is not 1.65 mm.}                

Step-by-step explanation:

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.

We design the null and the alternate hypothesis

H_{0}: \mu = 1.65\text{ mm}\\H_A: \mu \neq 1.65\text{ mm}

Sample size, n = 35

Sample mean, \bar{x} = 1.64 mm

Sample standard deviation, s = 0.07 mm

Type I error:

  • It is the error of rejecting the null hypothesis when it is true.
  • It is also known as false positive error.
  • It is the rejecting of a true null hypothesis.

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.

Thus, average diameter is 1.65 mm and we decide that it is not 1.65 mm.

8 0
3 years ago
Read 2 more answers
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