20 students.
10% chose tennis, and .10(200)=20
No these polygons are not similar or equal
Answer:
(a)
(b) ![\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D)
Step-by-step explanation:
GIVEN: Suppose that two cards are randomly selected from a standard
card deck.
TO FIND: (a) What is the probability that the first card is a club and the second card is a club if the sampling is done without replacement? (b) What is the probability that the first card is a club and the second card is a club if the sampling is done with replacement.
SOLUTION:
(a)
Probability that first card is club ![P(A)=\frac{\text{total club cards}}{\text{total cards}}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B%5Ctext%7Btotal%20club%20cards%7D%7D%7B%5Ctext%7Btotal%20cards%7D%7D)
![=\frac{13}{52}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B13%7D%7B52%7D)
![=\frac{1}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D)
As sampling is done without replacement.
probability that second card is club ![P(B)=\frac{\text{total club cards}}{\text{total cards}}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7B%5Ctext%7Btotal%20club%20cards%7D%7D%7B%5Ctext%7Btotal%20cards%7D%7D)
![=\frac{12}{51}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B12%7D%7B51%7D)
![=\frac{4}{17}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%7D%7B17%7D)
Probability that first card is club and second card is club ![=P(A)\times P(B)](https://tex.z-dn.net/?f=%3DP%28A%29%5Ctimes%20P%28B%29)
![=\frac{1}{4}\times\frac{4}{17}=\frac{1}{17}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%5Cfrac%7B4%7D%7B17%7D%3D%5Cfrac%7B1%7D%7B17%7D)
(b)
Probability that first card is club ![P(A)=\frac{\text{total club cards}}{\text{total cards}}](https://tex.z-dn.net/?f=P%28A%29%3D%5Cfrac%7B%5Ctext%7Btotal%20club%20cards%7D%7D%7B%5Ctext%7Btotal%20cards%7D%7D)
![=\frac{13}{52}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B13%7D%7B52%7D)
![=\frac{1}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D)
As sampling is done with replacement.
probability that second card is club ![P(B)=\frac{\text{total club cards}}{\text{total cards}}](https://tex.z-dn.net/?f=P%28B%29%3D%5Cfrac%7B%5Ctext%7Btotal%20club%20cards%7D%7D%7B%5Ctext%7Btotal%20cards%7D%7D)
![=\frac{13}{52}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B13%7D%7B52%7D)
![=\frac{1}{4}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D)
Probability that first card is club and second card is club ![=P(A)\times P(B)](https://tex.z-dn.net/?f=%3DP%28A%29%5Ctimes%20P%28B%29)
![=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%5Cfrac%7B1%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B16%7D)
Py +7 = 6y + qp
Solve the equation for y
To solve the equation for y we need to get y alone
Py +7 = 6y + qp
Subtract 6y from both sides
Py - 6y +7 = + qp
Subtract 7 from both sides
Py - 6y = + qp - 7
Now factor out y
(P - 6)y = qp - 7
Divide by P - 6 from both sides
![y =\frac{qp - 7}{(P - 6)}](https://tex.z-dn.net/?f=y%20%3D%5Cfrac%7Bqp%20-%207%7D%7B%28P%20-%206%29%7D)
Answer:
Jewel is 7 years old
John is 1 year old
Dave is 17 years old
Step-by-step explanation:
From the question we are told that:
Jewel age is ![J=7 years](https://tex.z-dn.net/?f=J%3D7%20years)
John age ![J'=(D-16)years](https://tex.z-dn.net/?f=J%27%3D%28D-16%29years)
Dave's age a Year ago
![D-1=2(J-1+J'-1)](https://tex.z-dn.net/?f=D-1%3D2%28J-1%2BJ%27-1%29)
So that Dave.s age this Year could be
![D=2((J-1)+(J'-1))+1](https://tex.z-dn.net/?f=D%3D2%28%28J-1%29%2B%28J%27-1%29%29%2B1)
Simplifying Equation for Dave's age we have
![D=2((7)-1+(D-16)-1)+1](https://tex.z-dn.net/?f=D%3D2%28%287%29-1%2B%28D-16%29-1%29%2B1)
![D=2(6+D-15)+1](https://tex.z-dn.net/?f=D%3D2%286%2BD-15%29%2B1)
![D=2(D-9)+1](https://tex.z-dn.net/?f=D%3D2%28D-9%29%2B1)
![D=2D-18+1](https://tex.z-dn.net/?f=D%3D2D-18%2B1)
![D=17 Years](https://tex.z-dn.net/?f=D%3D17%20Years)
Dave is 17 years old
Therefore
Johns age is
![J'=(D-16)](https://tex.z-dn.net/?f=J%27%3D%28D-16%29)
![J'=17-16](https://tex.z-dn.net/?f=J%27%3D17-16)
![J'=1year old](https://tex.z-dn.net/?f=J%27%3D1year%20old)
John is 1 year old