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3 years ago

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After selling one third of his apple crop, a farmer sold the remainder at the same price per bushel for $600. What was the value

of the crop?
A) $1000
B) $1200
C) $800
E) None of these answers

1 answer:

shtirl [24]3 years ago

5 0

300. if you sold a third. then 2/3 would be left. you can then infer each is 300. Hope This Helps.

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Which is the correct label of the parallel lines?

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Answer:

a ∥ b

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Same applies to line "b", which has 2 points forming segment CD.

Therefore, the correct label if the parallel lines is a ∥ b

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Read 2 more answers

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Answer:

If we compare the p value and the significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.

Step-by-step explanation:

1) Data given and notation

$\bar X=1440$ represent the mean annual premium value for the sample

$s=165$ represent the sample standard deviation for the sample

$n=25$ sample size

$\mu_o =1503$ represent the value that we want to test

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

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean annual premium in Pennsylvania is lower than the national mean annual premium, the system of hypothesis would be:

Null hypothesis: $\mu \geq 1503$

Alternative hypothesis: $\mu < 1503$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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".

Calculate the statistic

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

$t=\frac{1440-1503}{\frac{165}{\sqrt{25}}}=-1.909$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=25-1=24$

Since is a one side left tailed test the p value would be:

$p_v =P(t_{(24)}$

Conclusion

If we compare the p value and the significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can conclude that the mean annual premium in Pennsylvania is significantly lower than the national mean annual premium of 1503 at 5% of significance.

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4 years ago

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3 years ago

Manuel is planting a garden in the shape of a right triangle. The longer leg is 3 ft longer than the shorter leg. The hypotenuse

Gnesinka [82]

Answer:

The length of shorter side of triangle is 9 cm

The length of longer side of triangle is 12 cm

The length of hypotenuse is 15 cm

Step-by-step explanation:

Given as , for the garden in the shape of right triangle :

Let The length of shorter side = B = x ft

So , the length of longer side = P = ( x + 3 ) ft

And The hypotenuse length = H = ( 3 + P ) ft

I.e H = ( 3 + x + 3 ) ft = ( x + 6 ) ft

Now<u> from Right angled Triangle method </u>

Hypotenuse² = Perpendicular² + Base²

Or, ( x + 6 )² = ( x + 3 )² + x²

Or, x² + 12 x + 36 = x² + 6 x + 9 + x²

Or, - x² + 6 x + 27 = 0

Or, - x² + 9 x - 3 x + 27 = 0

Or, - x ( x - 9 ) - 3 ( x - 9 ) = 0

So, ( x - 9 ) ( - x - 3 ) = 0

∴ x = 9 , - 3

So, shorter length = x = 9 cm

The longer length = x + 3 = 9 + 3 = 12 cm

The hypotenuse length = x + 6 = 9 + 6 = 15 cm

Hence The length of shorter side of triangle is 9 cm

The length of longer side of triangle is 12 cm

And The length of hypotenuse is 15 cm . Answer

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3 years ago