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3 years ago

Mrs. Torres’s class has 28 students. The class includes 12 boys. What is the

Mathematics

2 answers:

diamong [38]3 years ago

7 0

Answer:

4:3

Step-by-step explanation:

Because there are 12 boys out of the 28 students in the class, there would have to be 16 girls in the class. This information would make the ratio 16:12. Although that is not the lowest you can go, so you would divide both numbers by the same value, to get both as low as possible, in this case, you would divide both by 4. Now your ratio is 4:3, which can also be said as, for every 4 girls in the class, there are 3 boys.

Maslowich3 years ago

6 0

Answer:

16:12 or 4:3

Step-by-step explanation:

Girls + boys = 28

Girls + 12 = 28

Girls = 16

Girls to boys:

16:12

16/12

4:3

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Kelly has $20000 to invest, and hopes to earn $1390 in interest in the first year. She wants her investment in treasury bills to

liq [111]

Answer:

$8,000 in Treasury bills

$7,000 in Treasury bonds

$5,000 in corporate bonds

Step-by-step explanation:

Let the amount to be invested in treasury bills be $x , the amount to be invested in treasury bonds be $y

From the question, we understand that the amount she will invest in corporate bonds will be $3000 less than the amount in treasury bills;

So mathematically, this will be $(x - 3000)

So therefore, the amount invested in each will be;

x + y + x-3000 = 20,000

2x + y = 20,000 + 3000

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For treasury bills;

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10% = 10/100 * (x -3000) = (x-3000)/10

For Treasury bonds 7%

7% = 7/100 * y = 7y/100

Adding all gives the total interest;

5x/100 + 7y/100 + (x-3000)/10 = 1390

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5x + 7y + 10(x-3000) = 1390 * 100

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5x + 7y + 10x -30,000 = 139,000

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From i, y = 23,000 - 2x

Put this into ii

15x + 7(23,000 -2x) = 169,000

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x + 161,000 = 169,000

x = 169,000 - 161,000

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y = 23,000 - 2(8,000)

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What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3) ? Enter your answer in t

nikdorinn [45]

Let

$A(-12,2)\\B(6,2)\\C(-2,-3) \\D(-20.-3)\\E(-12.-3)$

using a graphing tool

see the attached figure to better understand the problem

we know that

Parallelogram is a quadrilateral with opposite sides parallel and equal in length

$AB=CD \\AD=BC$

The area of a parallelogram is equal to

$A=B*h$

where

B is the base

h is the height

the base B is equal to the distance AB

the height h is equal to the distance AE

Step 1

Find the distance AB

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-12,2)\\B(6,2)$

substitute the values

$d=\sqrt{(2-2)^{2}+(6+12)^{2}}$

$d=\sqrt{(0)^{2}+(18)^{2}}$

$dAB=18\ units$

Step 2

Find the distance AE

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(-12,2)\\E(-12.-3)$

substitute the values

$d=\sqrt{(-3-2)^{2}+(-12+12)^{2}}$

$d=\sqrt{(-5)^{2}+(0)^{2}}$

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Step 3

Find the area of the parallelogram

The area of a parallelogram is equal to

$A=B*h$

$A=AB*AE$

substitute the values

$A=18*5=90\ units^{2}$

therefore

the answer is

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