7 less than the difference of 12 and 5

Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4% interest on

boyakko [2]

Answer:

Mathew invested $600 and $2400 in each account.

Solution:

From question, the total amount invested by Mathew is $3000. Let p = $3000.

Mathew has invested the total amount $3000 in two accounts. Let us consider the amount invested in first account as ‘P’

So, the amount invested in second account = 3000 – P

Step 1:

Given that Mathew has paid 3% interest in first account .Let us calculate the simple interest $(I_1)$ earned in first account for one year,

$\text {simple interest}=\frac{\text {pnr}}{100}$

Where

p = amount invested in first account

n = number of years

r = rate of interest

hence, by using above equation we get $(I_1)$ as,

$I_{1}=\frac{P \times 1 \times 3}{100}$ ----- eqn 1

Step 2:

Mathew has paid 8% interest in second account. Let us calculate the simple interest $(I_2)$ earned in second account,

$I_{2} = \frac{(3000-P) \times 1 \times 8}{100} \text { ------ eqn } 2$

Step 3:

Mathew has earned 4% interest on total investment of $3000. Let us calculate the total simple interest (I)

$I = \frac{3000 \times 1 \times 4}{100} ----- eqn 3$

Step 4:

Total simple interest = simple interest on first account + simple interest on second account.

Hence we get,

$I = I_1+ I_2 ---- eqn 4$

By substituting eqn 1 , 2, 3 in eqn 4

$\frac{3000 \times 1 \times 4}{100} = \frac{P \times 1 \times 3}{100} + \frac{(3000-P) \times 1 \times 8}{100}$

$\frac{12000}{100} = \frac{3 P}{100} + \frac{(24000-8 P)}{100}$

12000=3P + 24000 - 8P

5P = 12000

P = 2400

Thus, the value of the variable ‘P’ is 2400

Hence, the amount invested in first account = p = 2400

The amount invested in second account = 3000 – p = 3000 – 2400 = 600

Hence, Mathew invested $600 and $2400 in each account.

3 0

2 years ago

Read 2 more answers

M is inversely proportional to r if m= 9 when r= 4 find m when r=2

bazaltina [42]

m=18 when r = 2.

Step-by-step explanation:

Given,

m∝ $\frac{1}{r}$

So,

m = k× $\frac{1}{r}$ ,--------eq 1, here k is the constant.

To find the value of m when r = 2

At first we need to find the value of k

Solution

Now,

Putting the values of m=9 and r = 4 in eq 1 we get,

9 = $\frac{k}{4}$

or, k = 36

So, eq 1 can be written as m= $\frac{36}{r}$

Now, we put r =2

m = $\frac{36}{2}$

or, m= 18

Hence,

m=18 when r = 2.

4 0

2 years ago

(8x^3 - x) - (10x - 5x^2 - 3x^3) Show your work.

sergeinik [125]

Let's simplify step-by-step.
8
x
3
−
x
−
(
10
x
−
5
x
2
−
3
x
3
)
Distribute the Negative Sign:
=
8
x
3
−
x
+
−
1
(
10
x
−
5
x
2
−
3
x
3
)
=
8
x
3
+
−
x
+
−
1
(
10
x
)
+
−
1
(
−
5
x
2
)
+
−
1
(
−
3
x
3
)
=
8
x
3
+
−
x
+
−
10
x
+
5
x
2
+
3
x
3
Combine Like Terms:
=
8
x
3
+
−
x
+
−
10
x
+
5
x
2
+
3
x
3
=
(
8
x
3
+
3
x
3
)
+
(
5
x
2
)
+
(
−
x
+
−
10
x
)
=
11
x
3
+
5
x
2
+
−
11
x
Answer:
=
11
x
3
+
5
x
2
−
11
x

Brainliest Please:)

6 0

3 years ago

Read 2 more answers

What is the x of 2/3x squared minus 6x plus 15

iogann1982 [59]

(2/3)x^2 -6x + 15 = 0
Using the quadratic formula:
x = [-b +-sq root(b^2 - 4 *a*c)] / 2a
x= [--6 +-sq root(36 -4*(2/3)*15] / 2*(2/3)
x= [6 +-sq root 36 -40] / (4/3)

x1 = 4.5 + (2i / (4/3))
x1 = 4.5 + 1.5i
x2 = 4.5 - (2i / (4/3))
x2 = 4.5 - 1.5i

4 0

3 years ago

Automobile fuel efficiency is often measured in miles that the car can be driven per gallon of fuel (mpg). Heavier cars tend to

Maksim231197 [3]

Answer:

Correct option: A. Weight.

Step-by-step explanation:

In regression analysis there are two kinds of variables: Explanatory and Response variable.

The explanatory variable are used to predict the changes in the response variable. They are also known as independent or predictor variable.

The response variable are observed for any changes caused by the explanatory variable. They are also known as the dependent or experimental variable.

In this case it is provided that heavier cars have lower fuel efficiencies.

It implies that there is linear inverse relationship between the variables weight of the car and fuel efficiency.

The response variable is the fuel efficiency and the explanatory variable is the weight of the car. Since the weight of the car is used to determine the fuel efficiency.

Thus, the explanatory variable is the weight of the car.

4 0

3 years ago