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Summer School 2020 Math 8 NWLSD

Ray Of Light [21]

Answer:

8 granola bars in each box

Step-by-step explanation:

The equation is 4x+5x=72

4x and 5x are like terms, so combine those 9x=72

Use the division property of equality to solve for x, x=8

5 0

2 years ago

A leprechaun places a magic penny under a girls pillow. The next night there are 2 magic pennies under her pillow. The following

kiruha [24]

Answer:

After 47 days she will have more than 90 trillion pennies.

Step-by-step explanation:

At the beginning there was 1 penny. At the second day the amount of pennies under the pillow became 2.

The amount of pennies doubled each day. So the series is,

$1,2,4,8,16,32,.....$

This series is in geometric progression.

As the pennies from each of the previous days are not being stored away until more pennies magically appear so the sum of series will be,

$S_n=\dfrac{a(r^n-1)}{r-1}$

where,

a = initial term = 1,

r = common ratio = 2,

As we have find the number of days that would elapse before she has a total of more than 90 trillion, so

$\Rightarrow 90\times 10^{12}\le \dfrac{1(2^n-1)}{2-1}$

$\Rightarrow 90\times 10^{12}\le \dfrac{2^n-1}{1}$

$\Rightarrow 90\times 10^{12}\le 2^n-1$

$\Rightarrow 2^n\ge 90\times 10^{12}+1$

$\Rightarrow \log 2^n\ge \log (90\times 10^{12}+1)$

$\Rightarrow n\times \log 2\ge \log (90\times 10^{12}+1)$

$\Rightarrow n \ge \dfrac{\log (90\times 10^{12}+1)}{\log 2}$

$\Rightarrow n \ge 46.4$

$\Rightarrow n\approx 47$

8 0

3 years ago

Shawna found coins worth $4.32. One- fourth of the found coins are pennies and one- sixth are quarters. The number of nickels fo

eduard

Answer:

8 quarters

12 nickels

12 pennies

16 dimes

Step-by-step explanation:

The trick is to ASSUME the dimes.

Start by thinking about the three explicit premises and the one implicit premise.

1) Quarters = 1/6 of total coins

2) Nickels = 1.5 the number of quarters

3) Pennies = 1/4 of total coins

Also, ASSUME an unknown number of dimes to fill in the gap.

48 Total Coins = $4.32

⅙ of 48 = 8 8 quarters = $2.00

1.5 x 8 = 12 12 nickels = $0.60

¼ of 48 = 12 12 pennies = $0.12

Add those coins = $2.72

Take the known total and minus this sum.

$4.32 - $2.72 = $1.60

16 dimes = $1.60

Thus, you have the following:

8 quarters (⅙ of total coins) $2.00

12 nickels (1.5 the number of quarters) $0.60

12 pennies (¼ the number of total coins) $0.12

+ 16 dimes $1.60

Total Coins 48 $4.32

8 0

3 years ago

Angle 7 and angle 8 are complementary. angle 5 equals angle 8 and angle 6=29.

olya-2409 [2.1K]

Answer:

Angle 7 + Angle 8 = 90°

Angle 5 = Angle 8

Angle 6 = 29°

5 0

3 years ago

If $-2 < x \le 3,$ then find all possible values of $5x + 1.$ Give your answer in interval notation PLEASE ANSWER THUS PLEASE

exis [7]

Answer:

$(-9,16]$

Step-by-step explanation:

we know that

The domain of x is equal to the interval--------> $(-2,3]$

$-2< x \leq 3$

All real numbers greater than $-2$ and less than or equal to $3$

Let

$y=5x+1$

For $x=3$

$y=5x+1\\y=5(3)+1=16$

For $x>-2$

$y >5(-2)+1\\y > -9$

so

The range of the function is the interval--------> $(-9,16]$

5 0

3 years ago

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