I dont know how to answer this question

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

What are the factors of 150 and 40? Please help me.

posledela

Answer:

40: 1, 2, 4, 5, 8, 10, 20, 40

150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

Step-by-step explanation:

6 0

3 years ago

(b) Out of 200 students in an examination of class IX, 140 passed in Maths, 120 passed in Scien

iren [92.7K]

Answer:

n(U)=200

n(M)=140

n(S)=120

n(MuS)complement=40

n(MuS)=n(U)-n(MuS)complement

=200-40

=160

n(MnS)=n(M)+n(S)-n(MuS)

=140+120-160

=260-160

=100

3 0

3 years ago

Read 2 more answers

Halppppppppppppppppppp

Hatshy [7]

Answer:

Yes

Step-by-step explanation:

$y\leq 3x+9\\\\8\leq 3(7)+9\\\\8\leq 21+9\\\\8\leq 30$

Yes, the given point makes the inequality true. We end up with a true statement.

Hope this helps.

4 0

3 years ago

6. A car dealership would like to estimate the mean mpg of its new model car with 90% confidence. The population is normally dis

Yakvenalex [24]

Answer:

92.9997< $\mu$ <99.5203

Step-by-step explanation:

Using the formula for calculating the confidence interval expressed as:

CI = xbar ± Z * S/√n where;

xbar is the sample mean

Z is the z-score at 90% confidence interval

S is the sample standard deviation

n is the sample size

Given parameters

xbar = 96.52

Z at 90% CI = 1.645

S = 10.70.

n = 25

Required

90% confidence interval for the population mean using the sample data.

Substituting the given parameters into the formula, we will have;

CI = 96.52 ± (1.645 * 10.70/√25)

CI = 96.52 ± (1.645 * 10.70/5)

CI = 96.52 ± (1.645 * 2.14)

CI = 96.52 ± (3.5203)

CI = (96.52-3.5203, 96.52+3.5203)

CI = (92.9997, 99.5203)

<em>Hence a 90% confidence interval for the population mean using this sample data is 92.9997<</em> $\mu$ <em><99.5203</em>

4 0

3 years ago

I dont know how to answer this question​

I dont know how to answer this question