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1 year ago

What value of x makes the equation -5 - (-7-4x) = -2 (3x-4) true?

Mathematics

1 answer:

MrMuchimi1 year ago

5 0

-5 - (-7 - 4x) = -2(3x - 4) |use distributive property

-5 -(-7) - (-4x) = (-2)(3x) + (-2)(-4)

-5 + 7 + 4x = -6x + 8

2 + 4x = -6x + 8 |-2

4x = -6x + 6 |+6x

10x = 6 |:10

x = 0.6

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After years of maintaining a steady population of 32,000, the population of a town begins to grow exponentially. After 1 year an

galben [10]

Answer:

$y=32000(1+0.08)^x$

Step-by-step explanation:

Exponential growth function is $y=a(1+r)^x$

Where 'a' is the initial population

r is the rate of growth and x is the time period in years

a steady population of 32,000. So initial population is 32,000

an increase of 8% per year. the rate of increase is 8% that is 0.08

a= 32000 and r= 0.08

Plug in all the values in the general equation

$y=a(1+r)^x$

$y=32000(1+0.08)^x$

$y=32000(1+0.08)^x$

4 0

2 years ago

Read 2 more answers

The local skating rink pays marry a fixed rate per pupil plus a base amount to work as a skating instructor. she earns $90 for i

Ganezh [65]

You have to make a system of equations: lets make a equal the amount marry makes per student and b be her base amount.
90=15a+b (you have to subtract the top equation by the bottom equation)
62=8a+b (90-62=28, 15a-8a=7a, and b-b=0)
Since b canceled out, you are left with 7a=28 which means a=4. you can than plug a into the equation 62=8a+b to find that b=30.

since Lisa makes half of the base amount marry, her base amount is 15. However, she also make twice the amount per kid so she makes 8 per kid.
using the found values found you can make the equations (m=the amount Marry makes, l=the amount Lisa makes, and c is the number of children)
m=4c+30
l=8c+15
set c=20 and you should get m=110 and l=175. Based off of that information, we can say that Lisa makes more money instructing a class of 20 students.
I hope this helps.

8 0

1 year ago

If 2.5 mol of dust particles were laid end to end along the equator, how many times would they encircle the planet? The circumfe

Natalka [10]

Answer:

They encircle the planet $3.76\times 10^{11}$ times.

Step-by-step explanation:

Consider the provided information.

We have 2.5 mole of dust particles and the Avogadro's number is $6.022\times 10^{23}$

Thus, the number of dust particles is:

$2.5\times 6.022\times 10^{23}=15.055\times 10^{23}$

Diameter of a dust particles is 10μm and the circumference of earth is 40,076 km.

Convert the measurement in meters.

Diameter: $10\mu m\times \frac{10^{-6}m}{\mu m} =10^{-5}m$

If we line up the particles the distance they could cover is:

$15.055\times 10^{23}\times 10^{-5}=15.055\times 10^{18}=1.5055\times 10^{19}$

Circumference in meters:

$40,076km\times \frac{1000m}{1km}=40,076,000 m$

Therefore,

$\frac{1.5055\times 10^{19}}{40,076,000} = 3.76\times 10^{11}$

Hence, they encircle the planet $3.76\times 10^{11}$ times.

8 0

2 years ago

Elijah and Jonathan play on the same soccer team. They have played 3 of their 15,

Lynna [10]

Answer:

Only Elijah's model is correct

Step-by-step explanation:

The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play

This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play

Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.

5 0

2 years ago

Suppose two different methods are available for eye surgery. The probability that the eye has not recovered in a month is 0.002

umka21 [38]

Answer:

0.4007

Step-by-step explanation:

Let's define the following events:

A: method A is used

B: method B is used

NR: the eye has not recovered in a month

R: the eye is recovered in a month

The probability that the eye has not recovered in a month is 0.002 if method A is used, i.e., P(NR|A) = 0.002, so P(R|A) = 0.998.

When method B is used, the probability that the eye has not recovered in a month is 0.005, i.e., P(NR|B) = 0.005, so P(R|B) = 0.995.

40% of eye surgeries are done with method A, i.e., P(A) = 0.4

60% of eye surgeries are done with method B, i.e., P(B) = 0.6

If an eye is recovered in a month after surgery is done in the hospital, what is the probability that method A was performed? We are looking for P(A|R), then, by Bayes' Formula

P(A|R) = P(R|A)P(A)/(P(R|A)P(A) + P(R|B)P(B)) = 0.998*0.4/(0.998*0.4 + 0.995*0.6) = 0.4007

4 0

2 years ago