So r+c=42
c=4+r
subsitute c=4+r for r in r+c=42
r+4+r=42
add like terms
2r+4=42
subtract 4 from both sides
2r=38
divide both sides by 2
r=19
rob=19
subsitute r=19 for r in c=4+r
c=19+4
carly=23
Answer: The percentage of legal quarters will be rejected by the vending machine = 2.275%
Step-by-step explanation:
Given: The weights of legal U.S. quarters have a normal distribution with a mean of 5.67 grams and a standard deviation of 0.07 gram.
Let x be the weights of legal U.S. quarters .
Required probability: 
![=P(\dfrac{x-\mu}{\sigma}\dfrac{5.81-5.67}{0.07})\\\\=P(z2)\approx0.02275 \ \ \ [By\ P-value\ calculator]](https://tex.z-dn.net/?f=%3DP%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3C%5Cdfrac%7B5.33-5.67%7D%7B0.07%7D%29%2BP%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3E%5Cdfrac%7B5.81-5.67%7D%7B0.07%7D%29%5C%5C%5C%5C%3DP%28z%3C-4.857%29%2BP%28z%3E2%29%5Capprox0.02275%20%20%20%20%5C%20%5C%20%5C%20%5BBy%5C%20%20P-value%5C%20calculator%5D)
The percentage of legal quarters will be rejected by the vending machine = 2.275%
Answer:
3
Step-by-step explanation:
3
I think that a linear equation can have no solution, one solution, or infinitely solutions. It just depends on what is the equation. That's what I think
Answer:
Step-by-step explanation:
We will use the binomial distribution. Let X be the random variable representing the no. of boxes Hannah buys before betting a prize.
Our success is winning the prize, p =40/100 = 0.4
Then failure q = 1-0.4 = 0.6
Hannah keeps buying cereal boxes until she gets a prize. Then n be no. times she buys the boxes.
P(X ≤ 3) = P(X=0) +P(X=1)+P(X=2)+P(X=3)
=
+
+
+ 
=
+
+
= ![(0.6)^{n}+n(0.4)(0.6)^{n-1}+[tex]\frac{n(n-1)(0.4)^{2}0.6^{n-2}}{2} +\frac{n(n-1)(n-2)0.4^{3}0.6^{n-3}}{6}](https://tex.z-dn.net/?f=%280.6%29%5E%7Bn%7D%2Bn%280.4%29%280.6%29%5E%7Bn-1%7D%2B%5Btex%5D%5Cfrac%7Bn%28n-1%29%280.4%29%5E%7B2%7D0.6%5E%7Bn-2%7D%7D%7B2%7D%20%2B%5Cfrac%7Bn%28n-1%29%28n-2%290.4%5E%7B3%7D0.6%5E%7Bn-3%7D%7D%7B6%7D)