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3 years ago

To make five apple pie’s you need about 2 pounds of apples. How many pounds of apples do you need to make 20 apple pies

Mathematics

2 answers:

DedPeter [7]3 years ago

7 0

20 apples / 5 apple pies = 4

4 * 2 pounds = 8 pounds

Hope this helps!

Vsevolod [243]3 years ago

3 0

To solve this problem, we should set up a proportion. Let's let the unknown number of pounds of apples we need be represented by the variable x. Our proportion should be:

2 pounds of apples/5 apple pies = x pounds of apples/20 apple pies

Because our units are the same on both sides of the equation, we can eliminate them and keep the numbers only.

2/5 = x/20

Next, we can begin to solve this equation by cross multiplication. To cross-multiply, you multiply the numerator of one fraction by the denominator of the other fraction and set it equal to the product of the other numerator and denominator. This is modeled below:

2 * 20 = 5 * x

To simplify, we begin by performing the multiplication on both sides of the equation.

40 = 5x

Next, we should divide both sides of the equation by 5, so that we can get the variable x alone on the right side of the equation.

x = 8

Therefore, your answer is that you need 8 pounds of apples to make 20 apple pies.

Hope this helps!

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For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.

For part b the $p_v>\alpha$ so then we FAIL to reject the null hypothesis at this significance level.

For part c the $p_v>\alpha$ so again we FAIL to reject the null hypothesis at this significance level.

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3 years ago

What is the solution to the system of equations? y = 2x – 3.5 x – 2y = –14

iogann1982 [59]

Answer:

Step-by-step explanation:

Substitution then simplify

8 0

3 years ago

What is the perimeter of a rectangle with a length of (x^2+x) and a width of (2x^2+3x)

Mazyrski [523]

Answer:

Perimeter = 6x² + 8x

Step-by-step explanation:

Perimeter = 2(length + width)

perimeter = 2((x²+x)+(2x²+3x))

perimeter = 2(x²+2x² + x+3x)

perimeter = 2(3x² + 4x)

perimeter = 2*3x² + 2*4x

perimeter = 6x² + 8x

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3 years ago

Out of 100 people sampled, 42 had kids. Based on this, construct a 99% confidence interval for the true population proportion of

maksim [4K]

Answer:

The 99% confidence interval for the true population proportion of people with kids is (0.293, 0.547).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.