In 2013 the most expensive cocktail (made with 1858 ‘Cuvee Leonie’ cognac) was sold in Australia for $12,000. What would have be
1 answer:
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Let x be the number of bags of Nature's Recipe Venison Meal & Rice Canine 20 percent protein, y be the number of bags of Nutro Max Natural Dog Food 27 percent protein and z be the number of bags of PetSmart Premier Oven Baked Lamb 25 percent protein a dog breeder buys. He wants to make 300 pounds of a mix. Then
20x+17.5y+30z=300.
Now
- in 20x pounds of Nature's Recipe Venison Meal & Rice Canine 20 percent protein is 0.2·20x=4x pounds of protein;
- in 17.5y pounds of Nutro Max Natural Dog Food 27 percent protein is 0.27·17.5y=4.725y pounds of protein;
- in 30z pounds of PetSmart Premier Oven Baked Lamb 25 percent protein is 0.25·30z=7.5z pounds of protein;
- in 300 pounds of mix containing 22 percent protein is 0.22·300=66 pounds of protein.
Then 4x+4.725y+7.5z=66.
You get a system
From the first equation Substitute it into the second equation:
Simplify it:
y must be divided by 20, then
- y=0, x=9, z=10-6=4;
- y=20, x=16, z is not a whole number;
- y=40, x=23, z is not a whole number;
- y=60, x=30, z=10-20-35<0;
- thus, all other possible z will be <0.
Answer: 9 bags with 1st mix, 0 bags with 2nd mix and 4 bags with 3rd mix.
Answer:
Yes, we have sufficient evidence at the 0.02 level to support the company's claim.
Step-by-step explanation:
We are given that a sample of 1500 computer chips revealed that 32% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that above 29% do not fail in the first 1000 hours of their use.
Let Null Hypothesis, : p
0.29 {means that less than or equal to 29% do not fail in the first 1000 hours of their use}
Alternate Hypothesis, : p > 0.29 {means that more than 29% do not fail in the first 1000 hours of their use}
The test statics that will be used here is One-sample proportions test;
T.S. = ~ N(0,1)
where, = proportion of chips that do not fail in the first 1000 hours of their use = 32%
n = sample of chips = 1500
So, <u>test statistics</u> =
= 2.491
<em>Now, at 0.02 level of significance the z table gives critical value of 2.054. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject null hypothesis as it fall in the rejection region.</em>
Therefore, we conclude that more than 29% do not fail in the first 1000 hours of their use which means we have sufficient evidence at the 0.02 level to support the company's claim.