<span>Part
A- Explain why the x-coordinates of the points where the graphs of the
equations y=2^-x and y=8^x+4 intersect are the solutions of the equation
2^-x=8^x+4
Because the intersection point has the a unique pair of (x,y) coordinates; such coordinates x,y belong to both equations.
Part B- Make tables to find the solution to 2^-x = 8^x+4. Take the integer values of x between -3 and 3.
x 2^ (-x) 8^(x + 4) <------ this is how I understand the right side
- 3 2^3 = 8 8^(1) = 8
- 2 2^2 = 4 8^(2) = 64
- 1 2^1 = 2 8^(3) = 512
0 2^0 = 1 8^(4) = 4,096
=> solution x = - 3
You can continue filling the table for x =1, x = 2 and x = 3, but the solution is already stated x = - 3.
Part C- How can you solve the equation 2^-x=8^x+4 graphically?
Draw the graphs of both equation is the same coordinate system and the solution will be the point where the two curves intersect each other.
</span>
Answer:
52.56% probability that eight or more of the flights will arrive on time.
Step-by-step explanation:
For each flight, there are only two possible outcomes. Either it is on time, or it is not. The probability of a flight being on time is independent from other flights. So we use the binomial probability distribution to solve this question.]
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
At a certain airport, 75% of the flights arrive on time.
This means that ![p = 0.75](https://tex.z-dn.net/?f=p%20%3D%200.75)
A sample of 10 flights is studied.
This means that ![n = 10](https://tex.z-dn.net/?f=n%20%3D%2010)
Find the probability that eight or more of the flights will arrive on time.
![P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%208%29%20%3D%20P%28X%20%3D%208%29%20%2B%20P%28X%20%3D%209%29%20%2B%20P%28X%20%3D%2010%29)
In which
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 8) = C_{10,8}.(0.75)^{8}.(0.25)^{2} = 0.2816](https://tex.z-dn.net/?f=P%28X%20%3D%208%29%20%3D%20C_%7B10%2C8%7D.%280.75%29%5E%7B8%7D.%280.25%29%5E%7B2%7D%20%3D%200.2816)
![P(X = 9) = C_{10,9}.(0.75)^{9}.(0.25)^{1} = 0.1877](https://tex.z-dn.net/?f=P%28X%20%3D%209%29%20%3D%20C_%7B10%2C9%7D.%280.75%29%5E%7B9%7D.%280.25%29%5E%7B1%7D%20%3D%200.1877)
![P(X = 10) = C_{10,10}.(0.75)^{10}.(0.25)^{0} = 0.0563](https://tex.z-dn.net/?f=P%28X%20%3D%2010%29%20%3D%20C_%7B10%2C10%7D.%280.75%29%5E%7B10%7D.%280.25%29%5E%7B0%7D%20%3D%200.0563)
![P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2816 + 0.1877 + 0.0563 = 0.5256](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%208%29%20%3D%20P%28X%20%3D%208%29%20%2B%20P%28X%20%3D%209%29%20%2B%20P%28X%20%3D%2010%29%20%3D%200.2816%20%2B%200.1877%20%2B%200.0563%20%3D%200.5256)
52.56% probability that eight or more of the flights will arrive on time.
Answer:
$63.06
Step-by-step explanation:
<em>Total Cost </em>
First, find the total cost for everything she bought
3 lamps at 23.59 each, and a sofa for 769.99
<u>Lamps </u>
Add 23.59 3 times, or multiply 3 times 23.59
23.59+23.59+23.59=70.77
23.59*3=70.77
<u>Total </u>
Add the lamps cost to the sofa cost
70.77+769.99=840.76
Sales Tax
Multiply the sales tax rate by her total cost
840.76 *7.5%
Convert 7.5% to a decimal by dividing by 100, or moving the decimal place 2 spots to the left
7.5/100=0.075
7.5--> .75-->0.075
840.76* 0.075=63.057
Round to the nearest cent, or hundreth: 63.06
The sales tax is: $63.06
Answer: 39,600
This is what the cars value is after 1 year.
Answer:
C. 38°
D. 30°
Step-by-step explanation:
The relevant relation in both cases is the inscribed angle measures half the measure of the arc it intercepts.
__
C. Angle TSQ intercepts arc TQ, so the measure of arc TQ is 2(86.5°) = 173°. The measure of arc TR is the difference between the measures of arcs TQ and RQ, so is ...
arc TR = 173° -135° = 38°
__
D. Inscribed angle PQR intercepts arc PR, so is half its measure.
angle PQR = 60°/2 = 30°