Procedure:
1) calculate the number of diferent teams of four members that can be formed (with the ten persons)
2) calculate the number of teams tha meet the specification (two girls and two boys)
3) Divide the positive events by the total number of events: this is the result of 2) by the result in 1)
Solution
1) the number of teams of four members that can be formed are:
10*9*8*7 / (4*3*2*1) = 210
2) Number of different teams with 2 boys and 2 girls = ways of chosing 2 boys * ways of chosing 2 girls
Ways of chosing 2 boys = 6*5/2 = 15
Ways of chosing 2 girls = 4*3/2 = 6
Number of different teams with 2 boys and 2 girls = 15 * 6 = 90
3) probability of choosing one of the 90 teams formed by 2 boys and 2 girls:
90/210 = 3/7
Answer:
He should change the number x is equal to. (i think)
Step-by-step explanation:
Answer:
(x - [-1])² + (y - [-1])² = [13]
Step-by-step explanation:
If P and Q are the end-points of the diameter PQ, midpoint of the segment PQ will be the center of the circle. (Definition of the center of a circle)
Midpoint of a segment having extreme ends
and ![(x_2,y_2)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29)
Coordinates of the center = ![(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5Cfrac%7By_1%2By_2%7D%7B2%7D%29)
Since, extreme ends of the diameter are P(-4, -3) and Q(2, 1)
Center of the circle = ![(\frac{-4+2}{2},\frac{-3+1}{2} )](https://tex.z-dn.net/?f=%28%5Cfrac%7B-4%2B2%7D%7B2%7D%2C%5Cfrac%7B-3%2B1%7D%7B2%7D%20%20%29)
= (-1, -1)
Radius of the circle = Distance between the center and Q,
Since distance between the two points
and
is,
d = ![\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Radius of the circle = ![\sqrt{(-1-2)^2+(-1-1)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-1-2%29%5E2%2B%28-1-1%29%5E2%7D)
= ![\sqrt{9+4}](https://tex.z-dn.net/?f=%5Csqrt%7B9%2B4%7D)
= ![\sqrt{13}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D)
Equation of the circle will be,
(x - h)² + (y - k)² = r²
Where (h, k) is the center and 'r' is the radius of the circle,
(x - [-1])² + (y - [-1])² = [13]
Using an exponential function, it is found that an appliance currently valued at $1,500 will be worth $150.17 in 8 years.
<h3>What is an exponential function?</h3>
A decaying exponential function is modeled by:
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
In this problem, we have that:
- The appliance is currently valued at $1,500, hence A(0) = 1500.
- It loses 25% of their resale value each year, hence r = 0.25.
Thus, the equation is given by:
![A(t) = A(0)(1 - r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281%20-%20r%29%5Et)
![A(t) = 1500(1 - 0.25)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%201500%281%20-%200.25%29%5Et)
![A(t) = 1500(0.75)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%201500%280.75%29%5Et)
In 8 years, the value will be given by:
![A(8) = 1500(0.75)^8 = 150.17](https://tex.z-dn.net/?f=A%288%29%20%3D%201500%280.75%29%5E8%20%3D%20150.17)
More can be learned about exponential functions at brainly.com/question/25537936
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