Step-by-step explanation:
For example, you use {10}^{2}. That's representing 10 times 10, which equals 100. So basically, all you do is convert {10}^{2} into 10 times 10 and solve, which gives you 100 as the final answer.
Tim began with 40 comics
Further explanation:
The equation involve linear equation as there is only one object i.e. comic books
So,
Let x be the number of comic books Tim began with
Then after selling half comics Tim will have x/2 comics remaining
Now when he buys 16 more the expression will be:
![\frac{x}{2}+16](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B16)
He has total 36 books, then
![\frac{x}{2}+16= 36](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B16%3D%2036)
Subtracting 16 from both sides
![\frac{x}{2}+16-16= 36-16](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%2B16-16%3D%2036-16)
![{\frac{x}{2}}= 20\\](https://tex.z-dn.net/?f=%7B%5Cfrac%7Bx%7D%7B2%7D%7D%3D%2020%5C%5C)
Multiplying 2 on both sides
![{\frac{x}{2}}* 2= 20*2\\x=40](https://tex.z-dn.net/?f=%7B%5Cfrac%7Bx%7D%7B2%7D%7D%2A%202%3D%2020%2A2%5C%5Cx%3D40)
<u>We can recheck, if he had 40, half of them will be 20 and adding 16 makes them 36.</u>
Tim began with 40 comics
Keywords: Equation in one variable, linear equations
Learn more about linear equations at:
#LearnwithBrainly
Answer:
-1/3
Step-by-step explanation:
→ Write down 2 coordinate pairs
(-9 , 11) and (-3 , 9)
→ Write down the slope formula
(y₂ - y₁) ÷ ( x₂ - x₁ )
→ Substitute in the numbers
( 9 - 11 ) ÷ ( 9 - - 9 )
→ Simplify
-1/3
15+8x=2x+7-5x
Subtract 8x from both sides.
15=2x+7-5x-8x
Combine like terms.
15=-11x+7
Subtract 7 from both sides.
8=-11x
Divide -11 from both sides.
.73=x
Your answer is .72
Answer:
a) Expected amount of the gambler's win = $0.209
b) SD = 2.26
c)P (X >1) = P(z >0.35) = 0.36317
Step-by-step explanation:
The probability of winning, p = 12/38 =6/19
Probability of losing, q = 1 -p = 1-6/19
q = 13/19
Win amount = $5
Loss amount = $2
a) Expected total amount of win = ((6/19)*5) - ((13/19)*2)
Expected total amount of win = 1.579 - 1.369
Expected amount of win, E(X) = $0.209
b) Standard Deviation for the total amount of the gambler's win
![SD = \sqrt{E(X^{2}) - (E(X))^{2} }](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7BE%28X%5E%7B2%7D%29%20-%20%28E%28X%29%29%5E%7B2%7D%20%7D)
E(X²) = (6/19)*5² - (13/19)*2²
E(X²) = 5.158
![SD = \sqrt{5.158 - 0.209^2}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B5.158%20-%200.209%5E2%7D)
SD = 2.26
c) probability that, in total, the gambler wins at least $1.
P(X >1)
![z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
μ = E(x) = 0.209
z = (1-0.209)/2.26
z = 0.35
P( X >1) = P(z >0.35)
P(z >0.35) = 1 - P(z <0.35)
P(z >0.35) = 1 - 0.63683
P(z >0.35) = 0.36317