Find the difference. Simplify completely. Please show work.1. 7/9 - 3/8 2. 5 4/5 - 2 1/4

Mathematics

1 answer:

fenix001 [56]4 years ago

4 0

1. 7/9 - 3/8 = (7·8 - 9·3)/(9·8) = (56 -27)/72 = 29/72

2. (5 4/5) - (2 1/4) = (5 - 2) + (4/5 - 1/4) = 3 + (4·4 -5·1)/(5·4) = 3 11/20

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(a/b) -(c/d) = (ad -bc)/(bd) . . . . a useful formula to remember when working problems like this. It is equivalent to multiplying the first fraction by d/d and the second one by b/b to get a common denominator of bd. Of course if the second fraction is added instead of subtracted, the sign changes in both places.

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The equation 4s = 33.4 models a constant rate situation. Drag and drop the value of 2s in the box. a 16.7

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The answer to the equation you posted The equation 4s = 33.4 models a constant rate situation. what is <span>the value of 2s is:
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A researcher planned a study in which a crucial step was offering participants a food reward. It was important that three food r

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Answer:

Step-by-step explanation:

Hello!

A pilot study was conducted to test if three food rewards are equally appealing to the participants.

Of 60 participants surveyed:

16 preferred cupcakes (CC)

26 preferred candy bars (CB)

18 preferred dried apricots (DA)

If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3

The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. $X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}$ Where k= number of categories of the variable.

For this example the statistical hypotheses are:

H₀: P(CC)=P(CB)=P(DA)= 1/3

H₁: At least one of the proportions isn't equal to the others.

To calculate the expected frequencies for each category you have to use the formula: $E_i= n* P_i$ where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.

$E_{CC}= n* P(CC)= 60*1/3= 20$

$E_{CB}= n*P(CB)= 60*1/3= 20$

$E_{DA}= n* P(DA)= 60* 1/3= 20$

The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:

Assuming α: 0.05

$X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378$

The rejection region is then X²₂ ≥ 7.378

$X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8$