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JulijaS [17]
2 years ago
11

Eliza brought 3 pans of homemade fruit bars to school. Her classmates ate 7/12 of each pan. Eliza gave 1 whole pan of the leftov

er fruit bars to the school's secretaries and took the rest home. Explain how to find how much of a pan of fruit bars Eliza took home.
Mathematics
1 answer:
-BARSIC- [3]2 years ago
3 0
To solve this, you have to take 7/12 out of each pan first, so how to do that is to divide each pan into 1/12. So you did that, and all three pans equal 36/12. Great. Eliza has 36/12 fruit bars. 
Now, you see that the classmates at 7/12 out of EACH. To find that out, you just multiply 7/12 by 3 which is 21/12. Subtract 21/12 from 36/12 since the classmates ate 21/12 out of the total and you get 15/12.
Now she gave 1 pan to the secretaries, which is 12/12, so you subtract that from the 15/12 you have left over. That's 3/12.

And she brought 3/12 home. You can simplify that into 1/4.
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How many extraneous solutions does the equation below have? StartFraction 2 m Over 2 m + 3 EndFraction minus StartFraction 2 m O
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Answer:

0

Step-by-step explanation:

We have the fraction \frac{2m}{2m+3} -\frac{2m}{2m-3}

Step 1. Use LCM of the fraction, (2m+3)(2m-3), to simplify the fraction:

\frac{(2m-3)(2m)-(2m+3)(2m)}{(2m+3)(2m-3)} =\frac{2m^2-6m-[2m^2+6m]}{(2m+3)(2m-3)} =\frac{2m^2-6m-2m^2-6m}{(2m+3)(2m-3)} =\frac{-12m}{(2m+3)(2m-3)}

Step 2. Equate the resulting fraction to zero and solve for m:

\frac{-12m}{(2m+3)(2m-3)} =0

-12m=0[(2m+3)(2m-3)]

-12m=0

m=\frac{0}{-12}

m=0

Step 3. Replace the value in the original equation and check if it holds:

\frac{-12m}{(2m+3)(2m-3)} =0

-12m=0

Since m=0,

-12(0)=0

0=0

Since the only solution of the equation holds, the equation bellow doesn't have any extraneous solution

5 0
1 year ago
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A research organization keeps track of what citizens think is the most important problem facing the country today. They randomly
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Answer:

Step-by-step explanation:

From the information given, the population is divided into sub groups. Each group would consist of citizens picking a particular choice as the most important problem facing the country. The choices are the different categories. In this case, the null hypothesis would state that the distribution of proportions for all categories is the same in each population. The alternative hypothesis would state that the distributions is different. Therefore, the correct test to use to determine if the distribution of​ "problem facing this country ​today" is different between the two different​ years is

A) Use a​ chi-square test of homogeneity.

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2 years ago
The National Science Foundation (NSF) offers grants to students who are interested in pursuing a college education. The student
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6 0
1 year ago
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An investigation of a number of automobile accidents revealed the following information:
seropon [69]

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

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3 0
2 years ago
Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3​ inches, with a standard dev
dangina [55]

Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3​ inches, with a standard deviation of 2.5 inches. a baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than 2.5 inches. the heights​ (in inches) of  20 randomly selected players are shown in the table.

72 74 71 72 76

70 77 75 72 72

77 72 75 70 73

74 75 73 74 74

What are the correct hypotheses for this  test?

The null hypothesis is H₀?: ____ 2.5

The alternative hypothesis is H₁?: ____  2.5

Calculate the value of the test statistic.

x² = _____ (Round to three decimal places)

Answer:

Null hypothesis, H₀: σ = 2.5

Alternative hypothesis,  Hₐ: μ<2.5

Test statistic = 12.920

Step-by-step explanation:

Given Data shows that:

men between the ages of 20 and 29 in a general population have a mean height of 69.3​ inches, with a standard deviation of 2.5 inches

We consider a random sample of 20 selected baseball players.

Therefore;

The Null and Alternative hypothesis are as follows:

The Null hypothesis is the standard deviation of the heights of major league baseball players is not less than 2.5 inches.

Null hypothesis, H₀: σ = 2.5

On the other hand: The Alternative hypothesis is the standard deviation of the heights of major league baseball players is less than 2.5 inches.  

Alternative hypothesis,  Hₐ: μ<2.5

The Mean Calculation is:

\bar{x} = \frac{1}{2} \sum x_i

= \frac{1}{20} (72+74+...+74) \\ \\ = \frac{1468}{20} \\ \\ =73.4

The sample standard deviation is:

s = \sqrt{\frac{1}{n-1} \sum (x_1 - \bar{x})^2 }

= \sqrt{\frac{1}{20-1} \sum (72-73.4)^2 + ...+(74-73.4)^2 }  \\ \\ =  \sqrt{4.25}  \\ \\ = 2.06

The test statistics is now determined as :

x^2 = \frac{(n-1)s^2}{\sigma^2} \\ \\ = \frac{(20-1)(2.06)^2}{(2.5)^2}  \\ \\ = \frac{19*4.25}{6.25} \\ \\ = \frac{80.75}{6.25} \\ \\ = 12.920

4 0
2 years ago
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