Using Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
Substituting the first three equations into the fourth allows us to solve for
:
For each possible value of
, we get two corresponding critical points at
.
At these points, respectively, we get a maximum value of
and a minimum value of
.
Answer:
g= 6
j = 2
r= 4
Step-by-step explanation:
Gummy bears = $1.50 per pound
Jelly beans = $1.00 per pound
Runt = $1.00 per pound
Total cost of the mixture = $15.00
Let
g = quantity of gummy bears
j = quantity of jelly beans
r = quantity of runts
g + j + r=12 (1)
1.5g + 1.0j + 1.0r = 15 (2)
three times as many gummy bears as jelly beans.
g=3j
Substitute g=3j into 1
g + j + r = 12
3j + j + r =12
4j + r =12 (3)
Substitute g=3j into 2
1.5g + 1.0j + 1.0r = 15
1.5(3j) + 1.0j + 1.0r =15
4.5j + 1.0j + 1.0r = 15
5.5j + 1.0r =15 (4)
4j + r =12 (3)
5.5j + 1.0r =15 (4)
Subtract (3) from (4)
5.5j - 4j = 15-12
1.5j = 3
Divide both sides by 1.5
j = 3/1.5
= 2
j = 2
Substitute j = 2 into (3)
4j + r =12
4(2) + r =12
8 + r = 12
r= 12-8
r= 4
Substitute j=2 and r= 4 into (1)
g + j + r=12
g + 2 + 4 = 12
g + 6 = 12
g = 12-6
=6
g=6
g= 6
j = 2
r= 4
Answer:
The correct option is: b) the test would also be statistically significant at level alpha = 0.10
Step-by-step explanation:
Consider the provided information.
Suppose a medical researcher conducts a statistical test of hypotheses and finds there is statistically significant evidence for the alternative hypothesis at a significance level alpha = 0.05.
It means that the test would be statically significant at level alpha = 0.10
As we know that if alternative hypothesis is true then the value of p must be less than α.
That means if the p-value is less than 0.05 then it must be less than 0.10.
Hence, the correct option is: b) the test would also be statistically significant at level alpha = 0.10
Answer:
p= 0.15<em>m</em>+750
Step-by-step explanation:
Using the binomial distribution, it is found that there is a 0.0008 = 0.08% probability that she will get a passing score.
For each question, there are only two possible outcomes, either she answers it correctly, or she does not. The probability of answering a question correctly is independent of any other question, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- 18 questions, thus
- Guess one of three correct options, thus .
A passing score is <u>at least 13 correct</u>, thus, the probability is:
Then
The others, until P(X = 18), will be approximately 0, thus:
0.0008 = 0.08% probability that she will get a passing score.
A similar problem is given at brainly.com/question/24863377