There are 10 apples in the fridge and 2 of them are bad. if you grab 3 apples, what is the expected number of bad apples

A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex

Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

$I=P*r*t$

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

$I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1$

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

$I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y$

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

$x+y=50000$

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

$y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500$

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

$x+y=50000\\12500+y=50000\\y=50000-12500=37500$

Therefore, the loan at 8% is $37500

5 0

3 years ago

To solve for y in the equation 2y + y = 5, what first step would need to be taken? Subtract 2 from each side. Add 2y and y. Subt

cricket20 [7]

Answer:

Add 2y and y.

Step-by-step explanation:

you have to combine what is common

plz give brainliest

4 0

3 years ago

Need help with graph

andre [41]

Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

The domain is the values of x between 1 and 7

The range

4 0

1 year ago

7-ounce package costs $2.59. A 12 ounce package costs $4.56. An 18 ounce package costs $6.30. Which package is the best buy?

Yanka [14]

Answer:

18 ounce package for $6.30

Step-by-step explanation:

For each one, you divide the money by the package to see how much it is per ounce.

2.59 / 7 = $0.37 per oz

4.56 / 12 = $0.38 per oz

6.30 / 18 = $0.35 per oz

4 0

3 years ago

4✓6 × 3✓6<br>multiply and simplify <br>show work

mafiozo [28]

Answer:

3

√

2

Explanation:

First put change the words into an equation:

√

3

×

√

6

Now you can multiply them together as you would normally multiply:

√

3

×

√

6

=

√

18

Now let's prime factor 18 and see if there are any squares that we can take out of it to simplify. All we have to see is if there are 2 numbers that are the same:

18

/ \

6

3

/ \

2

3

As you can see, we have a square:

3

×

3

=

9

So take

√

9

out of

√

18

. You should have:

√

9

√

2

But since

√

9

=

3

we can simplify further to make:

√

9

√

2

→

3

√

2

Step-by-step explanation:

3 0

2 years ago