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2 years ago

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Sonya plans to spend at least 15$ on berries to make pies. Strawberries are on sale for 3$ per pint, and blueberries are on sale

for 1$ per pint. SHe plans to buy at least 8 pints of berries.
Which system of inequalities can be used to determine the number of pints of strawberries, x, and the number of pints of blueberries, y, that Sonya should buy.
A=(3x+y≥15)
(x+y≥8)
B=(15≥3x+y)
(8≥x+y)
c=(15≥3x+y)
(x+y≥8)
D=(3x+y≥15)
(8≥x+y)

1 answer:

bekas [8.4K]2 years ago

3 0

Answer:

B)

15 ≥ 3x + y

8 ≥ x + y

Step-by-step explanation:

Strawberries= 3x

Blueberries= y

At least symbol= ≥

15 ≥ 3x + y (Plans to spend AT LEAST $15 so this has to be 15 ≥)

8 ≥ x + y (Plans to spend AT LEAST 8 pints so this has to be 8 ≥)

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<u>Step-by-step explanation:</u>

We have A rectangular pool is surrounded by a walk 3 meters wide. The pool is 4 meters longer than its width. If the total area of the pool walk is 372 square meters more than the area of the pool.

Let the width of the pool = x

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The heights of 1/4 sheet cakes baked by a bakery have been normally distributed with a mean of μ = 2.05 inches and a standard de

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Answer:

1. Null hypothesis: $\mu = 2.05$

Alternative hypothesis: $\mu \neq 2.05$

2. $P(Z>a)=0.025, P(Z$

And the value of a that satisfy this is a=1.96. So our critical regions are: $(-\infty,-1.96), (1.96,\infty)$

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4. If we compare the p value and a significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the heights is NOT significant different than 2.05. Using the critical region founded on part 2 we agree with the decision obtained with the p value since -1 is not on the critical zones, so we FAIL to reject the null hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=2.01$ represent the sample mean

$\sigma=0.12$ represent the standard deviation for the population

$n=9$ sample size

$\mu_o =2.05$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

1) The null and alternative hypotheses should be ?

We need to conduct a hypothesis in order to determine if the mean change from 2.05, the system of hypothesis would be:

Null hypothesis: $\mu = 2.05$

Alternative hypothesis: $\mu \neq 2.05$

2. Using the critical value to set up the decision rule, the decision rule should be?

For this case we need two critical values since we are conducting a two tailed test. We have this equality:

$P(Z>a)=0.025, P(Z$

And the value of a that satisfy this is a=1.96. So our critical regions are: $(-\infty,-1.96), (1.96,\infty)$

3. The test statistic of this test is?

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

We can replace in formula (1) the info given like this:

$z=\frac{2.01-2.05}{\frac{0.12}{\sqrt{9}}}=-1$

4. The conclusion of this test should be

Since is a two tailed test the p value would be:

$p_v =2*P(Z$

Conclusion

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To learn more about distance refer to:

brainly.com/question/23848540

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