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2 years ago

Help me please!! Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Mathematics

1 answer:

igor_vitrenko [27]2 years ago

8 0

Answer:

Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Step-by-step explanation:

We know that:

48 + 8(b) = Carly's expenditure
10(b) = Carly's expenditure
48 + 8b = 10b
B = Boxes of cards

Work:

48 + 8b = 10b
=> 48 + 8b - 8b = 10b - 8b
=> 48 = 2b
=> b = 24

Now, let's substitute the value of b into any equation.

10(24)
=> 240

Hence, Carly's expenditure was $240 and the number of boxes of cards was required is 24 boxes.

Hoped this helped.

$BrainiacUser1357$

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A simple random sample of 125 SAT scores has a mean of 1522. Assume that SAT scores have a population standard deviation of 335.

Fed [463]

Answer:

$1463.3\:$

Step-by-step explanation:

Since the population standard deviation $\sigma$ , is known, we use the z confidence interval for the mean.

This is given by:

$\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:$

For a 95% confidence interval we use $z=1.96$ .

It was also given that: $n=125$ , $\bar X=1522$ and $\sigma=335$

Let us substitute the values to get:

$1522-1.96(\frac{335}{\sqrt{125} } )\:$

$1463.3\:$

Interpretation:

We can say with 95% confidence that the interval between 1463.3 and 1580.7 SAT scores contains the population mean based on the sample 125 SAT scores.

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3 years ago

What is the prime factorization of 72?

Bingel [31]

Ik that 9 is one of em
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3 years ago

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What is the percent of change in 6 yards to 36 yards

BaLLatris [955]

Answer:

The percent of change in 6 yards to 36 yards is 500% .

Step-by-step explanation:

Formula

$Percentage = \frac{Change\ in\ value\times 100}{initial\ value}$

Where

Change in value = Final value - initial value

As given

The percent of change in 6 yards to 36 yards.

Final value = 36 yards

initial value = 6 yards

Change in value = 36 - 6

= 30 yards

Put in the formula

$Percentage = \frac{30\times 100}{6}$

$Percentage = \frac{3000}{6}$

Percentage = 500%

Therefore the percent of change in 6 yards to 36 yards is 500% .

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4 years ago

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A fish swims upstream a distance of 16 miles in a river with a current of 3 miles per hour. The fish returns swimming

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Answer:

9 mph = the speed in still water

Step-by-step explanation:

Let r = the speed in still water

Then the speed going down stream is r + 3

and the speed going upstream is r - 3

d = rt or t = d/r

time going downstream is 16/(r + 3) and time going upstream is 16/(r - 3)

The total time was 4 hours, so

$\frac{16}{r + 3} + \frac{16}{r - 3} = 4$ Multiply thru the equation by (r + 3)(r - 3)

Then 16(r - 3) + 16(r + 3) = 4(r + 3)(r - 3)

16r - 48 + 16r + 48 = $4r^{2}$ - 36

$4r^{2}$ - 36 = 32r

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$4(r^{2} - 8r - 9) = 0$

4(r - 9)(r + 1) = 0

r = 9 or -1

But a rate of speed cannot be negative, so x ≠ -1

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3 years ago

A rectangle retaining wall has area of 15 square feet.The height of the wall is two feet less than its length.find the height an

Aleksandr-060686 [28]

Answer:

The wall is 3 ft high and 5 ft long.

Step-by-step explanation:

Recall: Area of the rectangular wall is A = (length)(height).

Let the height be represented by h. Then the length is represented by h + 2.

The formula A = (length)(height) then becomes A = h(h+2) = 15 ft², which, written in the standard form of a quadratic equation, is h² + 2h - 15 = 0.

Let's solve this last equation for h using completing the square:

h² + 2h - 15 = 0 becomes h² + 2h + 1 -1 - 15 = 0, or (h + 1)² = 16. Taking the square root of both sides, we get:

h + 1 = ±4, which is equivalent to h = 3 and h = -5. Discard the negative result. Then h = 3 and w = 3+2 = 5.

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