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3 years ago

5

Antonio used 1613 cups of flour to make banana bread. The recipe for one loaf of banana bread calls for 213 cups of flour. What

equation can be used to find the number of loaves of banana bread that Antonio made?

1 answer:

musickatia [10]3 years ago

8 0

1613 divided by 213

Answer: 8 loaves (if rounded)

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The mean weight of an adult is 69 kilograms with a variance of 121. If 31 adults are randomly selected, what is the probability

amid [387]

Answer:

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Also, important to remember that the standard deviation is the square root of the variance.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 69, \sigma = \sqrt{121} = 11, n = 31, s = \frac{11}{\sqrt{31}} = 1.97565$

What is the probability that the sample mean would be greater than 70.5 kilograms?

This is 1 subtracted by the pvalue of Z when X = 70.5. So

$Z = \frac{X - \mu}{\sigma}$

By the Central limit theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{70.5 - 69}{1.97565}$

$Z = 0.76$

$Z = 0.76$ has a pvalue of 0.7764

1 - 0.7764 = 0.2236

0.2236 = 22.36% probability that the sample mean would be greater than 70.5 kilograms.

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3 years ago

PLEASE HELP WITH GEOMETRY!!!

svetoff [14.1K]

Answer:

ok what u need?

Step-by-step explanation:

7 0

3 years ago

One hypotenuse and one leg of a right triangle have lengths 61 and 11. Find the length of the other leg

atroni [7]

If the length is the same as one leg, than all the other legs should be the same exact dimensions, legs can not be different measurements by height. Hope that this help you!

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3 years ago

Suppose the solutions of a homogeneous system of four linear equations in five unknowns are all multiples of one nonzero solutio

Akimi4 [234]

Consider a homogeneous machine of four linear equations in five unknowns are all multiples of 1 non-0 solution. Objective is to give an explanation for the gadget have an answer for each viable preference of constants on the proper facets of the equations.

Yes, it's miles true.

Consider the machine as Ax = 0. in which A is 4x5 matrix.

From given dim Nul A=1. Since, the rank theorem states that

The dimensions of the column space and the row space of a mxn matrix A are equal. This not unusual size, the rank of matrix A, additionally equals the number of pivot positions in A and satisfies the equation

rank A+ dim NulA = n

dim NulA =n- rank A

Rank A = 5 - dim Nul A

Rank A = 4

Thus, the measurement of dim Col A = rank A = five

And since Col A is a subspace of R^4, Col A = R^4.

So, every vector b in R^4 also in Col A, and Ax = b, has an answer for all b. Hence, the structures have an answer for every viable preference of constants on the right aspects of the equations.

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3 years ago

It is believed that 44% of all Americans eat breakfast every day. For a class project, you randomly select Clemson students and

GaryK [48]

Answer:

For this case we want to conduct a test in order to see if the proportion of Clemson students who eat breakfast is different from 0.44 (alternative hypothesis). And the complement would represent the null hypothesis, and the system of hypothesis for this case are:

Null Hypothesis: $p =0.44$

Alternative hypothesis: $p \neq 0.44$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to conduct a test in order to see if the proportion of Clemson students who eat breakfast is different from 0.44 (alternative hypothesis). And the complement would represent the null hypothesis, and the system of hypothesis for this case are:

Null Hypothesis: $p =0.44$

Alternative hypothesis: $p \neq 0.44$

8 0

3 years ago