Answer: 2
Step-by-step explanation:
try each value in the equation
2(0) + 1 = 3
0 + 1 = 3
1 ≠ 3
so 0 doesn’t work
2(1) + 1 = 3
2 + 1 = 3
3 = 3
this works, so the answer is 1
Answer: C.
Simple random sampling
Step-by-step explanation:
A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.
Answer:
a) 
Just one solution
b) 
But we know that the cosine can't be negative so then this equation no have solutions on the reals.
c) 
This is only the solution on the interval assumed.
d) 
Step-by-step explanation:
a. 5 cos(x) − 3 = 0
For this case we can do this:

Now we can divide both sides by 5 and we got:

If we apply arccos on both sides we got:

So for this case the possible solution is:

Just one solution. This is only the solution on the interval assumed.
b. 3 cos(x) + 5 = 0
We can do this:

Then we can divide by 3 both sides and we got:

But we know that the cosine can't be negative so then this equation no have solutions on the reals.
c. 3 sin(x) − 1 = 0
We can do this:

Then we can divide both sides by 3 and we got:

The general solutions would be:


This is only the solution on the interval assumed.
d. tan(x) = −0.115
For this case we can solve the value of x like this:

And then the only possible solution for this case is:

Answer:
11. MN = 4 m
12. LK = 8 m
Step-by-step explanation:
11. Apply pythagorean theorem to find MN:
MN = √(5² - 3²) = √(25 - 9) = √16
MN = 4 m
12. Recall: The ratio of the corresponding side lengths of any two given similar triangles are equal.
MN corresponds to LK
MO corresponds to KO
Therefore:
LK/MN = KO/MO
LK/4 = 10/5
LK/4 = 2
Multiply both sides by 4
LK = 2*4
LK = 8 m
Answer:
A) ![V =12500[1-\frac{17.2 \times t}{100} ]](https://tex.z-dn.net/?f=V%20%3D12500%5B1-%5Cfrac%7B17.2%20%5Ctimes%20t%7D%7B100%7D%20%5D)
B) ![V = 12500[1-\frac{19}{100} ]^{t}](https://tex.z-dn.net/?f=V%20%3D%2012500%5B1-%5Cfrac%7B19%7D%7B100%7D%20%5D%5E%7Bt%7D)
Step-by-step explanation:
In two years i.e. from 2013 to 2015 the car value decreases from $12500 to $8200.
a) If the rate of decrease is constant and it is r% per year, then
![8200 = 12500[1-\frac{r \times 2}{100}}]](https://tex.z-dn.net/?f=8200%20%3D%2012500%5B1-%5Cfrac%7Br%20%5Ctimes%202%7D%7B100%7D%7D%5D)
⇒ r = 17.2%
Therefore, the value of the car is given by
, where, t is in years since 2013. (Answer)
b) If the rate of decrease is exponential and it is r%, then
![8200 = 12500[1-\frac{r}{100} ]^{2}](https://tex.z-dn.net/?f=8200%20%3D%2012500%5B1-%5Cfrac%7Br%7D%7B100%7D%20%5D%5E%7B2%7D)
⇒ r = 19%
Therefore, the value of the car is given by
, where, t is in years since 2013. (Answer)