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4 years ago

9

A fee of $12.50 is deducted each month from Aubryn’s bank account. She currently has a balance of $75.00 in her account. She mus

t maintain a balance of $0.

1 answer:

xxTIMURxx [149]4 years ago

4 0

Current balance - 12 months a year times the monthly fee

=75-12(12.50)
=75-150
=-75

She will have negative $75 so she will be below zero.

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

mamaluj [8]

Answer:

$x = 10$ . In other words, there number of girls is $10$ .

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

$\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}$ .

Rewrite to obtain:

$\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}$ .

For this question:

$\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}$ .

$\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}$ .

Therefore:

$\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}$ .

On the other hand, there are $(15 + x)$ boys and girls in total. Using the formula for average:

$\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}$ .

From the question, this average should be equal to $123$ . In other words:

$\displaystyle \frac{1875 + 120\, x}{15 + x} = 123$ .

Solve this equation for $x$ to obtain:

$1875 + 120\, x= 123\, (15 + x)$ .

$(123 - 120)\, x = 1875 - 123 \times 15$ .

$x = 10$ .

In other words, the number of girls here is $10$ .

5 0

3 years ago

Roberto’s cat weighed 6 3/4 pounds last year.Then the cat gained 1 1/2 pounds.How much does the cat weigh now?

hammer [34]

Add the gain and the last weight together
new weight = 6 3/4 + 1 1/2
or we can write it as
new weight = 6 + 3/4 + 1 + 1/2

Separate whole numbers and fraction
new weight = 6 + 3/4 + 1 + 1/2
new weight = 6 + 1 + 3/4 + 1/2

Simplify the whole numbers
new weight = 6 + 1 + 3/4 + 1/2
new weight = 7 + 3/4 + 1/2

Equalize the denominators of the fraction
new weight = 7 + 3/4 + 1/2
new weight = 7 + 3/4 + 2/4
new weight = 7 + 5/4

Because 5/4 is improper fraction, change it to mixed fraction
new weight = 7 + 5/4
new weight = 7 + 1 1/4
new weight = 7 + 1 + 1/4
new weight = 8 + 1/4
new weight = 8 1/4

The cat weights 8 1/4 pounds now

4 0

3 years ago

Find the area of triangle DEF with vertices D(-1,2), E(3,-2) and F(-2,-2).*

Veronika [31]

Answer:

<em>The area of the triangle DEF is 10.</em>

Step-by-step explanation:

<u>Area of a Triangle:</u>

A triangle of base B and height H (both must be perpendicular) has an area of:

$\displaystyle A=\frac{BH}{2}$

The image below shows the triangle formed by the points DEF. It's important to notice the points E and F lie on the same horizontal line because they both have the same y-coordinate.

This fact simplifies the calculations since we can easily compute the length the of base as the difference of their x-coordinates:

B=3-(-2)=3+2=5

Being the base of a horizontal line, the height of the triangle can be calculated as the difference of y-coordinates of D and the height of that line.

H=2-(-2)=4

With these two values, we calculate the area:

$\displaystyle A=\frac{5*4}{2}=10$

The area of the triangle DEF is 10.

4 0

4 years ago

A store is having a 20% off sale on all merchandise If Mai buys one item and save $13 what was the original price of her purchas

katrin [286]

Answer:

Step-by-step explanation:

20% off...and she saves $13

so 20% of what number is 13

0.20x = 13

x = 13/0.20

x = 65 <== original price

7 0

3 years ago

Read 2 more answers

An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest cir

finlep [7]

Answer:

The area of the copper circle is <u>31.4 inches</u>.

Step-by-step explanation:

Given:

An artist used silver wire to make a square that has a perimeter of 40 inches.

She then used copper wire to make the largest circle that could fit in the square, with perimeter of 40 inches.

Use 3.14 to represent π.

Now, to find the area of the copper circle.

Perimeter of square = 40 inches.

So, we get the side of square by putting formula:

$Perimeter=4\times side$

$40=4\times side$

Dividing both sides by 4 we get:

$10=side.$

$Side=10\ inches.$

Now, as the side of square is 10 inches it is the diameter of the circle as the square is fit inside the circle:

For getting the area of circle we find the radius:

Radius (r) = $\frac{Diameter}{2} \\=\frac{10}{2}= 5\ inches.$

Now, putting the formula to get the area of the circle:

$Area=2\times \pi \times r$

$Area=2\times 3.14\times 5$

$Area=31.4\ inches.$

Therefore, the area of the copper circle is 31.4 inches.

6 0

3 years ago