Answer:
![f(x)=7(b)^{x}-2](https://tex.z-dn.net/?f=f%28x%29%3D7%28b%29%5E%7Bx%7D-2)
![f(x)=-5(b)^{x}+10](https://tex.z-dn.net/?f=f%28x%29%3D-5%28b%29%5E%7Bx%7D%2B10)
Step-by-step explanation:
we know that
The y-intercept is the value of y when the value of x is equal to zero
<em>Verify each case</em>
case 1) we have
![f(x)=7(b)^{x}-2](https://tex.z-dn.net/?f=f%28x%29%3D7%28b%29%5E%7Bx%7D-2)
so
For x=0
![f(0)=7(b)^{0}-2](https://tex.z-dn.net/?f=f%280%29%3D7%28b%29%5E%7B0%7D-2)
![f(0)=7(1)-2=5](https://tex.z-dn.net/?f=f%280%29%3D7%281%29-2%3D5)
therefore
The function has a y-intercept of (0,5)
case 2) we have
![f(x)=3(b)^{x}-5](https://tex.z-dn.net/?f=f%28x%29%3D3%28b%29%5E%7Bx%7D-5)
so
For x=0
![f(0)=3(b)^{0}-5](https://tex.z-dn.net/?f=f%280%29%3D3%28b%29%5E%7B0%7D-5)
![f(0)=3(1)-5=-2](https://tex.z-dn.net/?f=f%280%29%3D3%281%29-5%3D-2)
therefore
The function does not have a y-intercept of (0,5)
case 3) we have
![f(x)=5(b)^{x}-1](https://tex.z-dn.net/?f=f%28x%29%3D5%28b%29%5E%7Bx%7D-1)
so
For x=0
![f(0)=5(b)^{0}-1](https://tex.z-dn.net/?f=f%280%29%3D5%28b%29%5E%7B0%7D-1)
![f(0)=5(1)-1=4](https://tex.z-dn.net/?f=f%280%29%3D5%281%29-1%3D4)
therefore
The function does not have a y-intercept of (0,5)
case 4) we have
![f(x)=-5(b)^{x}+10](https://tex.z-dn.net/?f=f%28x%29%3D-5%28b%29%5E%7Bx%7D%2B10)
so
For x=0
![f(0)=-5(b)^{0}+10](https://tex.z-dn.net/?f=f%280%29%3D-5%28b%29%5E%7B0%7D%2B10)
![f(0)=-5(1)+10=5](https://tex.z-dn.net/?f=f%280%29%3D-5%281%29%2B10%3D5)
therefore
The function has a y-intercept of (0,5)
case 5) we have
![f(x)=2(b)^{x}+5](https://tex.z-dn.net/?f=f%28x%29%3D2%28b%29%5E%7Bx%7D%2B5)
so
For x=0
![f(0)=2(b)^{0}+5](https://tex.z-dn.net/?f=f%280%29%3D2%28b%29%5E%7B0%7D%2B5)
![f(0)=2(1)+5=7](https://tex.z-dn.net/?f=f%280%29%3D2%281%29%2B5%3D7)
therefore
The function does not have a y-intercept of (0,5)
Answer:
9 hours or 9.9 hours
Step-by-step explanation:
просто думай :/
Answer:
a) P{W>0} = 0.5
b) P{W<0} = 0.5
c) E[W] = 0
Step-by-step explanation:
Solution:
a) P(W > 0) is 0.5 because there is a 0.5 chance the player will win on their first gamble and stop with a net profit.
b) P(W = 0) is 0.25 because there is a 0.5 chance the player will lose on their first gamble, then also a 0.5 chance they will win on their second gamble and stop with a profit of 0.
All other combinations of gambles result in a net loss, so P(W < 0) = 1−P(W > 0)−P(W = 0)
c) The expected value can be obtained by summing the products of each profit and the probability of that profit. In this case, you have 1∗0.5+0∗0.25+(−1)∗0.125+(−2)∗0.0625, etc. So E(W) is the sum to infinity:
= (1 - n) / 2^( n + 1 )
= 0
The three angles on top are supplementar. This means that
![56+y+51 = 107+y = 180 \implies y = 180-107 = 73](https://tex.z-dn.net/?f=%2056%2By%2B51%20%3D%20107%2By%20%3D%20180%20%5Cimplies%20y%20%3D%20180-107%20%3D%2073)
So, the angles of the triangle are x, 72 and 73. Again, we know that the sum of the interior angles of a triangle is 180, so we have something similas as before:
![72+x+73 = 145+x = 180 \implies y = 180-145 = 35](https://tex.z-dn.net/?f=%2072%2Bx%2B73%20%3D%20145%2Bx%20%3D%20180%20%5Cimplies%20y%20%3D%20180-145%20%3D%2035)
So, the measure of angle x is 35.
Answer:
3/10
Step-by-step explanation:
3/8×4/5= 12/40
To reduce to the Lowest fraction =3/10