Answer:
3.2 cups
Step-by-step explanation:
Each serving needs 0.4 cups of milk.
Cups of milk / servings = Cups per serving
2 / 5 = 0.4 cups per serving
0.4 cups per serving * 8 servings = 3.2 cups
1/2 = 36/72
3/4 = 12/16
5/6 = 25/30
X/4 < = -3/2...multiply both sides by 4
x < = -3/2 * 4
x < = -12/2
x < = -6.......graph : 1 (because less then shades to the left....and an equal sign in the problem means the dot is solid)
7x/9 > - 14/3 ....multiply both sides by 9
7x > - 14/3 * 9
7x > -42...divide both sides by 7
x > -42/7
x > - 6......graph : 4 (because greater then shades to the right...and no equal sign means it is an open dot)
-75x/4 > 225/2...multiply both sides by 4
-75x > 225/2 * 4
-75x > 450...divide both sides by -75, and change the sign
x < -450/75
x < - 6.......graph : 2 (because less then is shaded to the left...and no equal sign means an open dot)
2x/3 > -16/3...multiply both sides by 3
2x > -16/3 * 3
2x > -16 ...divide both sides by 2
x > -16/2
x > -8......graph : 3 (because greater then shades to the right....and no equal sign means an open dot)
Answer:
1. The probability that the student will get exactly 6 correct answers is
.
2. The probability that the student will get more than 6 correct answers is
.
Step-by-step explanation:
From the given information it is clear that
The total number of equations (n) = 10
The probability of selecting the correct answer (p)= ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
The probability of selecting the incorrect answer (q)= ![1-p=1-\frac{1}{3}=\frac{2}{3}](https://tex.z-dn.net/?f=1-p%3D1-%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B2%7D%7B3%7D)
According to the binomial distribution, the probability of selecting r items from n items is
![P=^nC_rp^rq^{n-r}](https://tex.z-dn.net/?f=P%3D%5EnC_rp%5Erq%5E%7Bn-r%7D)
where, p is probability of success and q is the probability of failure.
The probability that the student will get exactly 6 correct answers is
![P(r=6)=^{10}C_6(\frac{1}{3})^6(\frac{2}{3})^{10-6}](https://tex.z-dn.net/?f=P%28r%3D6%29%3D%5E%7B10%7DC_6%28%5Cfrac%7B1%7D%7B3%7D%29%5E6%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-6%7D)
![P(r=6)=210(\frac{1}{3})^6(\frac{2}{3})^{4}=\frac{1120}{19683}](https://tex.z-dn.net/?f=P%28r%3D6%29%3D210%28%5Cfrac%7B1%7D%7B3%7D%29%5E6%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B4%7D%3D%5Cfrac%7B1120%7D%7B19683%7D)
Therefore the probability that the student will get exactly 6 correct answers is
.
The probability that the student will get more than 6 correct answers is
![P(r>6)=^{10}C_7(\frac{1}{3})^7(\frac{2}{3})^{10-7}+^{10}C_8(\frac{1}{3})^8(\frac{2}{3})^{10-8}+^{10}C_9(\frac{1}{3})^9(\frac{2}{3})^{10-9}+^{10}C_{10}(\frac{1}{3})^{10}(\frac{2}{3})^{10-10}](https://tex.z-dn.net/?f=P%28r%3E6%29%3D%5E%7B10%7DC_7%28%5Cfrac%7B1%7D%7B3%7D%29%5E7%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-7%7D%2B%5E%7B10%7DC_8%28%5Cfrac%7B1%7D%7B3%7D%29%5E8%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-8%7D%2B%5E%7B10%7DC_9%28%5Cfrac%7B1%7D%7B3%7D%29%5E9%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-9%7D%2B%5E%7B10%7DC_%7B10%7D%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B10%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B10-10%7D)
![P(r>6)=^{10}C_7(\frac{1}{3})^7(\frac{2}{3})^{3}+^{10}C_8(\frac{1}{3})^8(\frac{2}{3})^{2}+^{10}C_9(\frac{1}{3})^9(\frac{2}{3})^{1}+^{10}C_{10}(\frac{1}{3})^{10}(\frac{2}{3})^{0}](https://tex.z-dn.net/?f=P%28r%3E6%29%3D%5E%7B10%7DC_7%28%5Cfrac%7B1%7D%7B3%7D%29%5E7%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B3%7D%2B%5E%7B10%7DC_8%28%5Cfrac%7B1%7D%7B3%7D%29%5E8%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B2%7D%2B%5E%7B10%7DC_9%28%5Cfrac%7B1%7D%7B3%7D%29%5E9%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B1%7D%2B%5E%7B10%7DC_%7B10%7D%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B10%7D%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B0%7D)
![P(r>6)=120\times \frac{8}{59049}+45\times \frac{4}{59049}+10\times \frac{2}{59049}+1\times \frac{1}{59049}=\frac{43}{2187}](https://tex.z-dn.net/?f=P%28r%3E6%29%3D120%5Ctimes%20%5Cfrac%7B8%7D%7B59049%7D%2B45%5Ctimes%20%5Cfrac%7B4%7D%7B59049%7D%2B10%5Ctimes%20%5Cfrac%7B2%7D%7B59049%7D%2B1%5Ctimes%20%5Cfrac%7B1%7D%7B59049%7D%3D%5Cfrac%7B43%7D%7B2187%7D)
Therefore the probability that the student will get more than 6 correct answers is
.