In a fruit punch drink the 3 ingredients are apple juice orange juice and cranberry juice. If 1/4 of the drink is apple juice an
1 answer:
Answer: The required ratio in simplest form is 7 : 5 : 8.
Step-by-step explanation: Given that in a fruit punch drink, the 3 ingredients are apple juice orange juice and cranberry juice. of the drink is apple juice and
is orange juice.
We are to find the ratio of cranberry juice to apple juice to orange juice in its simplest form.
Let x, y and z be the fractions of the cranberry juice, apple juice and orange juice in the fruit punch drink.
Then, according to the given information, we have
Now,
Therefore, the ratio of cranberry juice to apple juice to orange juice is given by
Thus, the required ratio in simplest form is 7 : 5 : 8.
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Answer:
b. 0.864
Step-by-step explanation:
Let's start defining the random variables.
Y1 : ''Number of customers who spend more than $50 on groceries at counter 1''
Y2 : ''Number of customers who spend more than $50 on groceries at counter 2''
If X is a binomial random variable, the probability function for X is :
Where P(X=x) is the probability of the random variable X to assume the value x
nCx is the combinatorial number define as :
n is the number of independent Bernoulli experiments taking place
And p is the success probability.
In counter I :
Y1 ~ Bi (n,p)
Y1 ~ Bi(2,0.2)
With y1 ∈ {0,1,2}
And P( Y1 = y1 ) = 0 with y1 ∉ {0,1,2}
In counter II :
Y2 ~ Bi (n,p)
Y2 ~ Bi (1,0.3)
With y2 ∈ {0,1}
And P( Y2 = y2 ) = 0 with y2 ∉ {0,1}
(1Cy2) with y2 = 0 and y2 = 1 is equal to 1 so the probability function for Y2 is :
Y1 and Y2 are independent so the joint probability distribution is the product of the Y1 probability function and the Y2 probability function.
With y1 ∈ {0,1,2} and y2 ∈ {0,1}
P( Y1 = y1 , Y2 = y2) = 0 when y1 ∉ {0,1,2} or y2 ∉ {0,1}
b. Not more than one of three customers will spend more than $50 can mathematically be expressed as :
when Y1 = 0 and Y2 = 0 , when Y1 = 1 and Y2 = 0 and finally when Y1 = 0 and Y2 = 1
To calculate we must sume all the probabilities that satisfy the equation :
Answer:
0% probability that at least 1,500 will agree to respond
Step-by-step explanation:
I am going to use the binomial approximation to the normal to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the probability that at least 1,500 will agree to respond
This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So
has a pvalue of 1.
1 - 1 = 0
0% probability that at least 1,500 will agree to respond
Answer:
Suzie walks faster by 0.27 miles per hour.
Step-by-step explanation:
Addie walked miles in 45 minutes and Suzie covered
miles in
of an hour.
So, Addie walked 2.5 miles in 45 minutes i.e. hours.
Therefore, the walking speed of Addie is miles per hour.
Again, Suzie covered i.e. 2.4 miles in
i.e. 0.67 hours.
So, the walking speed of Suzie is miles per hour.
Hence, Suzie walks faster by (3.6 - 3.33) = 0.27 miles per hour. (Answer)