Answer:
1,7
Step-by-step explanation:
x1 y1 x2 y2
5 , 11 -3 , 4
, ![\frac{11+4}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B11%2B4%7D%7B2%7D)
,
= 1,7
The correct answer is option B: There are between 15 and 20 green pieces in all 5 packages
The most important factor has been given which is, "Which statement about the candy pieces in the remaining packages is best supported by this information."
The information given is such that, the first package she opened had 4 green pieces and on this basis we can safely assume that all other packages have 4 green pieces as well. The second package had 3 green pieces and this based on this too we can safely assume that all other packages had 3 green pieces. Hence, all 5 packages can either have a total of 4 x 5 green candies which equals a total of 20 green pieces or, all 5 packages can have a total of 3 x 5 green candies which equals a total of 15 green pieces.
So according to Suzi's experiment, there are between 15 and 20 green pieces in all 5 packages.
Answer:
3(x-6)
Step-by-step explanation:
i love math
Area of a rectangle is A = L*W.
Here, A = 56 cm^2 (not 56 cm).
= (56 cm^2)=( L )( W ) = (x+2)*(2x-5) = 2x^2 - 5x + 4x - 10
Simplifying, 2x^2 - 5x + 4x - 10 = 56, or 2x^2 - x - 66 = 0.
Solve this using the quadratic formula:
-(-1) plus or minus sqrt ( (-1)^2 - 4(2)(-66) )
x = -------------------------------------------------------------
2(2)
Finish the work: find x. Most likely you will need to check both of the roots. Keep in mind that x will likely be a positive number.
Answer:
The probability that no more than 6 students belong to a ethnic minority is 0.9815.
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, what is the probability that no more than 6 belong to an ethnic minority?</em>
We can model this with a random variable, with sample size n=10 and probability of success p=0.33.
The probability that k answers are guessed right in the sample is:
![P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{10}{k}\cdot0.33^k\cdot0.67^{10-k}](https://tex.z-dn.net/?f=P%28x%3Dk%29%3D%5Cdbinom%7Bn%7D%7Bk%7Dp%5Ek%281-p%29%5E%7Bn-k%7D%3D%5Cdbinom%7B10%7D%7Bk%7D%5Ccdot0.33%5Ek%5Ccdot0.67%5E%7B10-k%7D)
We have to calculate the probability that 6 or less students belong to a ethnic minority. This can be calculated as:
![P(x\leq6)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)+P(x=5)+P(x=6)\\\\\\](https://tex.z-dn.net/?f=P%28x%5Cleq6%29%3DP%28x%3D0%29%2BP%28x%3D1%29%2BP%28x%3D2%29%2BP%28x%3D3%29%2BP%28x%3D4%29%2BP%28x%3D5%29%2BP%28x%3D6%29%5C%5C%5C%5C%5C%5C)
![P(x=0)=\dbinom{10}{0}\cdot0.33^{0}\cdot0.67^{10}=1\cdot1\cdot0.0182=0.0182\\\\\\P(x=1)=\dbinom{10}{1}\cdot0.33^{1}\cdot0.67^{9}=10\cdot0.33\cdot0.0272=0.0898\\\\\\P(x=2)=\dbinom{10}{2}\cdot0.33^{2}\cdot0.67^{8}=45\cdot0.1089\cdot0.0406=0.1990\\\\\\P(x=3)=\dbinom{10}{3}\cdot0.33^{3}\cdot0.67^{7}=120\cdot0.0359\cdot0.0606=0.2614\\\\\\](https://tex.z-dn.net/?f=P%28x%3D0%29%3D%5Cdbinom%7B10%7D%7B0%7D%5Ccdot0.33%5E%7B0%7D%5Ccdot0.67%5E%7B10%7D%3D1%5Ccdot1%5Ccdot0.0182%3D0.0182%5C%5C%5C%5C%5C%5CP%28x%3D1%29%3D%5Cdbinom%7B10%7D%7B1%7D%5Ccdot0.33%5E%7B1%7D%5Ccdot0.67%5E%7B9%7D%3D10%5Ccdot0.33%5Ccdot0.0272%3D0.0898%5C%5C%5C%5C%5C%5CP%28x%3D2%29%3D%5Cdbinom%7B10%7D%7B2%7D%5Ccdot0.33%5E%7B2%7D%5Ccdot0.67%5E%7B8%7D%3D45%5Ccdot0.1089%5Ccdot0.0406%3D0.1990%5C%5C%5C%5C%5C%5CP%28x%3D3%29%3D%5Cdbinom%7B10%7D%7B3%7D%5Ccdot0.33%5E%7B3%7D%5Ccdot0.67%5E%7B7%7D%3D120%5Ccdot0.0359%5Ccdot0.0606%3D0.2614%5C%5C%5C%5C%5C%5C)
![P(x=4)=\dbinom{10}{4}\cdot0.33^{4}\cdot0.67^{6}=210\cdot0.0119\cdot0.0905=0.2253\\\\\\P(x=5)=\dbinom{10}{5}\cdot0.33^{5}\cdot0.67^{5}=252\cdot0.0039\cdot0.135=0.1332\\\\\\P(x=6)=\dbinom{10}{6}\cdot0.33^{6}\cdot0.67^{4}=210\cdot0.0013\cdot0.2015=0.0547\\\\\\\\\\\\](https://tex.z-dn.net/?f=P%28x%3D4%29%3D%5Cdbinom%7B10%7D%7B4%7D%5Ccdot0.33%5E%7B4%7D%5Ccdot0.67%5E%7B6%7D%3D210%5Ccdot0.0119%5Ccdot0.0905%3D0.2253%5C%5C%5C%5C%5C%5CP%28x%3D5%29%3D%5Cdbinom%7B10%7D%7B5%7D%5Ccdot0.33%5E%7B5%7D%5Ccdot0.67%5E%7B5%7D%3D252%5Ccdot0.0039%5Ccdot0.135%3D0.1332%5C%5C%5C%5C%5C%5CP%28x%3D6%29%3D%5Cdbinom%7B10%7D%7B6%7D%5Ccdot0.33%5E%7B6%7D%5Ccdot0.67%5E%7B4%7D%3D210%5Ccdot0.0013%5Ccdot0.2015%3D0.0547%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C)
![P(x\leq6)=0.0182+0.0898+0.1990+0.2614+0.2253+0.1332+0.0547\\\\\\P(x\leq6)=0.9815](https://tex.z-dn.net/?f=P%28x%5Cleq6%29%3D0.0182%2B0.0898%2B0.1990%2B0.2614%2B0.2253%2B0.1332%2B0.0547%5C%5C%5C%5C%5C%5CP%28x%5Cleq6%29%3D0.9815)
The probability that 6 or less students belong to a ethnic minority is 0.9815.