If we place what the husband earns as h and what the wife earns as w, we can begin...
w + h = 110000
but w = 2h - 16000
We can turn it into..
2h - 16000 + h = 110000
Which we can then combine into..
3h - 16000 = 110000
Add 16000 and..
3h = 126000
Divide by three...
h = 42000
(nice)
The husband earns 42,000$ a year
Bonus: The wife then earns 68,000$
42,000 (or h) + 68,000 (or w) = 110,000
Because this is the original equation, we are correct.
Answer:
What are the choices?
Step-by-step explanation:
Answer: The answer is x = 6 units.
Step-by-step explanation: Please refer to the attached diagram
The diagram in the question shows two triangles placed on each other and for convenience sake has been labelled ABDCE. Triangle ABC is a right angled triangle, and so is triangle ADE. From the marks on the lines, we can infer that line AD is equal in measurement to line DB. Also line AE is equal in measurement to line EC.
Therefore we can see the similarity in both triangles, if AD and AE equals DB and EC, then it follows that DE equals BC.
Hence if AD = DB and
AE = EC, and
DE = BC
Then, x - 3 = ½x
(½x can also be expressed as x/2)
x - 3 = x/2
By cross multiplication we now have
2(x - 3) = x
2x - 6 = x
By collecting like terms we now have
2x - x = 6
x = 6
Answer:
The equation is
at a rate of -23%.
Step-by-step explanation:
Decay can be represented by the equation
. We can find the rate at which it decays by using t=3 hours and A=3000. This means
in this context.
After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.
We know
so we were able to cancel it out and divide both sides by 3.
We solve with a calculator
We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.
The equation is
Answer:
The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.

In which
z is the z-score that has a p-value of
.
The margin of error is of:

In a clinical test with 2161 subjects, 1214 showed improvement from the treatment.
This means that 
95% confidence level
So
, z is the value of Z that has a p-value of
, so
.
Margin of error:



The margin of error for the 95% confidence interval used to estimate the population proportion is of 0.0209.