Which angle is complementary to ∠X?
1 answer:
You might be interested in
Answer:
The probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424
Step-by-step explanation:
The variable that assigns the value 1 if a person had its original major and 0 otherwise is a Bernoulli variable with paramenter 0.65. Since she asked the question to 1850 people, then the number of students that will have their original major is a Binomial random variable with parameters n = 1850, p = 0.65.
Since the sample is large enough, we can use the Central Limit Theorem to approximate that random variable to a Normal random variable, which we will denote X.
The parameters of X are determined with the mean and standard deviation of the Binomal that we are approximating. The mean is np = 1850*0.65 = 1202.5, and the standard deviation is √np(1-p) = √(1202.5*0.35) = 20.5152.
We want to know the probability that X is between 0.64*1850 = 1184 and 0.66*1850 = 1221 (that is, the percentage is between 64 and 66). In order to calculate this, we standarize X so that we can work with a standard normal random variable W ≈ N(0,1). The standarization is obtained by substracting the mean from X and dividing the result by the standard deviation, in other words
The values of the cummulative function of the standard normal variable W, which we will denote are tabulated and they can be found in the attached file.
Now, we are ready to compute the probability that X is between 1184 and 1221. Remember that, since the standard random variable is symmetric through 0, then \phi(-z) = 1-\phi(z) for each positive value z.
Therefore, the probability that Polly's Sample will give a result within 1% of the value 65% is 0.6424.
Answer:
Step-by-step explanation:
Let be the cost in dollars of the puck.
You need to analize carefully the information given in the exercise.
It is important to remember that the word "twice" indicates multiplication. Then "<em>Twice the cost of the puck</em>" can be represented with the following expression:
The word "more" indicates Addition.
So, "<em>$9 more than twice the cost of the puck</em>" means that must add 9 to the product of to find the cost of purchasing a hockey stick. Then, this can be written as:
Based on the explained above, you can determine that the given phrase <em>"The cost of purchasing a hockey stick and puck if the stick costs $9 more than twice the cost of the puck"</em> can be represented as the sum of and
.
Therefore, the algebraic expression is: