Solve the inequality. 53(2x + 2) – 10 ≥ 2x + 2(23x + 2) please help

An investor invested a total of $2500 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If th

7nadin3 [17]

Answer:

$500 and $2000

Step-by-step explanation:

Let x represent the total investment = $2500

also, this total is split into two different funds

Lets represent these funds as a and b, such that fund a yields a profit of 3% and fund b yield a profit of 5%

So,

a + b = x

a + b = 2500 ......eq 1

Profit from each fund gives;

0.03 a + 0.05b = 115 ....eq 2

Solve simultaneously using substitution method

From eq 1;

b = 2500 - a

Slot in this value in eq 2

0.03a + 0.05 (2500 - a) = 115

expand

0.03a + 125 - 0.05a = 115

collect like terms

0.03a - 0.05a = 115 - 125

-0.02a = -10

Divide both sides by -0.02

a = $500

Put this value of a in eq 1

500 + b = 2500

Subtract 500 from both sides

b = 2500 - 500

b = $2000

3 0

3 years ago

Diagram shows a section of a bridge between the points A and K. The length of line segment is 640 meters. ∆ABC, ∆CDF, and ∆FJK a

Marta_Voda [28]

AK = 640
Δ ABC and ΔFJK are similar. They are small triangles.
ΔCDF is the big triangle.

640 / 2 = 320 m= CF
AC & FK= 320/2 = 160 m each

2AC = CF = 2FK
2(160) = 320 = 2(160)

BG = 20 m

20/160 = x / 320
20*320 = 160x
6400 = 160x
6400/160 = x
40 = x

Area of CDF = (40 m * 320 m)/2 = 12,800 / 2= 6,400 m²

3 0

3 years ago

In a certain region, about 6% of a city's population moves to the surrounding suburbs each year, and about 4% of the suburban po

Sedbober [7]

Answer:

City @ 2017 = 8,920,800

Suburbs @ 2017 = 1, 897, 200

Step-by-step explanation:

Solution:

- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:

0.94*p_c + 0.04*p_s = p_c'

0.06*p_c + 0.96*p_s = p_s'

- Assuming 6% moved while remaining 94% remained settled at the time of migrations.

- The matrix representation is as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right]$

- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1$

- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:

$\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1$

- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o$

- Where,

$x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right]$

- The population in 2017 x_2 would be:

$x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right]$

5 0

4 years ago

A cookie factory produced 2,435,956 packages of cookies. There were 52 cookies in each package. How many cookies did the factory

Viktor [21]

Answer: The factory produced 46845.3076923 cookies, though in context the answer does not make sense. If you were to estimate then it'll be 46845 cookies.

8 0

3 years ago

Read 2 more answers

You find a car that costs $18,500. If the interest rate on a 5-year loan is 6.25% and you make monthly payments on the car, what

OlgaM077 [116]

The answer is $24,281.25.

5 0

3 years ago