Answer: B. the 1101 people interviewed.
Step-by-step explanation:
- A sample is a subset of an entire population that we take to perform analysis regarding the required information.
Given : An opinion poll contacts 1101 adults and asks them, " Which political party do you think has better ideas for leading the country in the 21st century?" In all, 613 of the 1101 say, " The Democrats."
Here, 1101 adults are representing the subset of entire population of adults in US.
Therefore, The sample in this setting is 1101 people interviewed.
Hence, the correct answer is option(B).
Refer to the diagram shown below.
The shaded area satisfies the two inequalities
y > x - 1
and
y < 1 -x
Answer: A and D
Answer:
Option- one is correct.
The given system of equations have one solution that is (7,-21)
Step-by-step explanation:
Given system of equations are
![y=-3x\hfill (1)](https://tex.z-dn.net/?f=y%3D-3x%5Chfill%20%281%29)
![-9x-4y=21\hfill (2)](https://tex.z-dn.net/?f=-9x-4y%3D21%5Chfill%20%282%29)
Now to the solution:
To solve the given system of equations using substitution method.
That is substitute equation(1) in equation (2) we get
(here y=-3x)
![-9x+12x=21](https://tex.z-dn.net/?f=-9x%2B12x%3D21)
(adding the like terms)
![x=\frac{21}{3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B21%7D%7B3%7D)
Therefore x=7
Now substitute x=7 in equation (1) we get
![y=-3x](https://tex.z-dn.net/?f=y%3D-3x)
![y=-3(7)](https://tex.z-dn.net/?f=y%3D-3%287%29)
![y=-21](https://tex.z-dn.net/?f=y%3D-21)
Therefore the solution is (7,-21)
Therefore Option- one is correct.
The given system of equations have one solution that is (7,-21)
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.
Answer: the first graph
Reasoning: When a graph is going left to right it is a decay while when it’s going right to left it is an increase... think of linear equations where if it is going from left to right the slope is negative, it’s the same for the exponential decay and increase.