Please can someone help with the question below

A $5,000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest f

jolli1 [7]

Answer:

$2600 was invested on the 1% account while $2400 was invested on the 6% account.

Step-by-step explanation:

For simple interest we must apply the following formula:

M = C*r*t

Where M is the amount of interest generated, C is the invested money, r is the rate of interest and t is the elapsed time.

The sum of capital investead in each account, "x" for the 1% interest one and "y" for the 6% interest one, must be equal to the original $5000. The same way as the interest generated from these investments must be equal to the earnt $170. So we have:

x + y = 5000

For the first account:

M1 = x*0.01*1 = 0.01*x

For the second account:

M2 = y*0.06*1 = 0.06*y

The sum of interests:

0.01*x + 0.06*y = 170

We have a system of equations as shown below:

x + y = 5000

0.01*x + 0.06*y = 170

Multiplying the first equation by -0.01 and adding both equations we have:

-0.01*x - 0.01*y = -50

0.01*x + 0.06*y = 170

0.05*y = 120

y = 120 / 0.05 = $2400

x = 5000 - 2400 = $2600

$2600 was invested on the 1% account while $2400 was invested on the 6% account.

3 0

3 years ago

Josh has 8 days to make pots and plates to sell at a local fair. Each pot weighs 2 pounds and each plate weighs 1 pound. Josh ca

sweet-ann [11.9K]

The optimal number of pots and plates Josh should make is given from

the graph of the inequalities.

Response:

a. 2·p + a ≤ 50

p ≤ 24

a ≤ 40

b. The coordinates of the vertices of the feasible region are; (24, 2), (40, 5), (0, 40), (24, 0), (0, 0)

c. 40 pots and 5 plates

<h3>How can the optimal number of plates and pots Josh should make be found?</h3>

Given:

Number of days Josh has to make pots and plates to sell = 8 days

Weight of each pot = 2 pounds

Weight of each plate = 1 pound

Weight Josh cannot carry = More than 50 pounds

Number plates he can make each da = At most 5 plates

Number of pots he can make each day = At most 5 pots

The profit Josh makes for each plate sold = $12

Profit from each pot sold = $25

a. Let <em>p</em> represent the number of pots Josh makes and let <em>a</em> represent the

number plates. The linear inequalities are;

2·p + a ≤ 50

p ≤ 8 × 3 = 24

p ≤ 24

a ≤ 5 × 8 = 40

a ≤ 40

b. When p = 24, we have;

2 × 24 + a = 50

a = 2

When <em>a</em> = 40, 2·p + 40 = 50, gives;

p = 5

The vertex points are;

The coordinates of the vertices of the feasible region are;

(24, 2), (40, 5), (0, 40), (24, 0), (0, 0)

c. The profit function is; P = 25·p + 12·a

The profit at the vertices are;

$\begin{tabular}{|c|c|c|}p&a&Profit\\0&0&0\\0&40&12 \times 40 = 480\\24&0&25 \times 24 = 600\\24&2&12 \times 2 + 25 \times 40 = 624\\40&5&12 \times 5 + 25 \times 40 = 660\end{array}\right]$

To maximize his potential profit, therefore;

<u>Josh should make 40 pots and 5 plates</u>.

Learn more about linear optimization here:

brainly.com/question/15356519

3 0

3 years ago

2,325 divided by 15 equals what I’m really confused ?)

lapo4ka [179]

Answer:

155

Step-by-step explanation:

5 0

3 years ago

A parallelogram with an area of 160.5 in^2 has a height that meansures 7.5 in. Find the length of the base.

Mrac [35]

Answer:

Length of the base is 21.34 inches.

Step-by-step explanation:

Area of parallelogram(A) is given by:

$A = b \cdot h$

where b is the length of the base and h is the height of the parallelogram respectively.

As per the statement:

A parallelogram with an area of 160.5 in^2 has a height that measures 7.5 in.

Area of a parallelogram(A) = 160.5 square inches.

height of a parallelogram(h) = 7.5 in.

Then by formula of area of parallelogram we have;

$160.5 = 7.5b$

Divide both sides by 7.5 we get;

21.34 = b

Therefore, the length of the base is 21.34 inches.

7 0

3 years ago

A radio station plays a total of 272 pop, rock, and hip-hop songs during a day. The number of pop songs is 3 times the number of

Norma-Jean [14]

Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.

i)
"A radio station plays a total of 272 pop, rock, and hip-hop songs during a day"

means that : P+R+H=272

ii)
"The number of pop songs is 3 times the number of rock songs. "

so, P=3R

iii)
"The number of hip-hop songs is 32 more than the number of rock songs."

means: H=32+R

iv)

since both P and H can be written in terms of R, we have:

P+R+H=272

(3R)+R+(32+R)=272

3R+R+32+R=272

5R+32=272

5R=272-32=240

R=240/5=48

vi)

thus: P=3R=3*48=144, H=32+R= 32+48=80

Answer:

48 Rock, 144 Pop and 80 Hip-hop

5 0

3 years ago