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RideAnS [48]
2 years ago
7

Find the smallest non-zero whole number n such that 756n is a perfect cube.

Mathematics
1 answer:
Kitty [74]2 years ago
5 0

Step-by-step explanation:

756 = 2² * 3³ * 7.

For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.

How to get from 2² to 2³: Multiply by 2.

3³ has already a power that is a multiple of 3.

How to get from 7 to 7³: Multiply by 7².

Hence n = 2 * 7² = 98.

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What is the average rate of change of f over the interval -7 < or equal to x Give an exact number
Annette [7]

Answer:

\frac{4}{3}

Step-by-step explanation:

The average rate of change can be found by using the following formula

\frac{f(x_{2}) - f(x_{1}) }{x_{2} - x_{1}}

Since the interval goes from -7 to 2, we should find the y-values that correspond to x=-7 and x=2.

By inspection of the graph, we can clearly see that when x is -7, y is -7 as well and when x is 2, y is 5.

Now that we know this, we can simply plug these values into the formula!

\frac{f(2) - f(-7) }{2 - (-7)} = \frac{5 - (-7)}{2 - (-7)} = \frac{5 +7}{2+7} = \frac{12}{9} = \frac{4}{3}

Good luck!

3 0
2 years ago
Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?
sasho [114]

Answer:

y=12x-16

Step-by-step explanation:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

4 0
3 years ago
The probability for event A is 0.3, the probability for event B is 0.6, and the probability of events A or B is 0.8. Why are the
Sedaia [141]

Answer:

A.

Step-by-step explanation:

I think it makes the most sense sorry if i got it wrong

6 0
2 years ago
If $64,000 is invested in an IRA account with an annual interest rate of 8% compounded once a year, what is the value of the acc
Iteru [2.4K]

Answer: the value of the account after 6 years is $101559.96

Step-by-step explanation:

If $64,000 is invested in an IRA account, then

Principal = $64,000

So P = 64,000

The rate at which $64000 was compounded is 8%

So r = 8/100 = 0.08

If it is compounded once in a year, this means that it is compounded annually (and not semi annually, quarterly or others). So

n = 1

We want to determine the value of the account after 6 years, this means

time, t = 6

Applying the compound interest formula,

A = P(1 + r/n)^nt

A = amount after n number of years

A = 64000( 1 + 0.08/1)^1×6

A = 64000(1.08)^6

A= 64000×1.58687432294

A= 101559.956668416

Approximately $101559.96 to 2 decimal places

4 0
3 years ago
as part of the carnival the school will hold a factor game marathon, it takes Archie and kel an average of 12 minutes to finish
aliina [53]
Archie and kel would have played 27 1/2 games
5 0
3 years ago
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