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VladimirAG [237]
3 years ago
12

Is 5/4 times 6, 11/8 times 6, and 3/8 times 6 products greater than 6?

Mathematics
2 answers:
weeeeeb [17]3 years ago
7 0

Here were are dealing only with positive numbers and positive fractions whose numerators and denominators are positive integers.

If you multiply a number by 1, you get that number.

For example, 1 * 5 = 5; 1 * 8 = 8

If you multiply a number by a positive number less than one, the result is smaller than the number you started with.

For example, 1/2 * 6 = 3. Since 1/2 is less than 1, multiplying 1/2 by 6 gives a result smaller than 6. 3 is smaller than 6.

If you multiply a number by a number greater than 1, the result is greater than the number you started with.

For example, 2 * 6 = 12. Since you multiplied 6 by a number greater than 1, which 2 is, you get 12 which is greater than 6.  5/4 * 20 = 25. Since 20 was multiplied by 5/4, and 5/4 is greater than 1, the result, 25, is greater than 20.

It's easy to tell if a fraction is greater than or less than 1. If the numerator is less than the denominator, the fraction is less than 1.

Examples of fractions less then 1: 1/3, 1/6, 5/6, 11/12, 18/121. In every case to the left, the numerator is less than the denominator, so all fractions are lees than 1.

If the numerator is greater than the denominator, then the fraction is greater than 1.

Examples of fractions that are greater than 1: 4/3, 11/8, 3/2, 121/100, 17/18.

5/4 is greater than 1, so 5/4 * 6 is greater than 6.

11/8 is greater than 1, so 11/8 * 6 is greater than 6.

3/8 is less than 1, so 3/8 * 6 is less than 6.

enyata [817]3 years ago
7 0

Answer:

5/4 is greater than 1, so 5/4 * 6 is greater than 6.

11/8 is greater than 1, so 11/8 * 6 is greater than 6.

3/8 is less than 1, so 3/8 * 6 is less than 6.

Step-by-step explanation:

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Kruka [31]

Answer:

a) The profit will be: Profit=y^2-99500

b) Since the profit is -9500 (negative) so, company will not gain any profit if they produce 300 bicycles.

Step-by-step explanation:

Cost of Bicycles= y^2+10y+100,000

Revenue generated = 2y^2+10y+500

Find a polynomial that represent profits

The formula used for finding profit is:

Profit = Total \ Revenue - Total \ Cost\\Profit=  2y^2+10y+500 - (y^2+10y+100,000)\\Profit=  2y^2+10y+500 - y^2-10y-100,000\\Profit=2y^2-y^2+10y-10y+500-100,000\\Profit=y^2-99500

So, the profit will be: Profit=y^2-99500

If the company can produce bicycles y= 300

The profit will be:

Profit=y^2-99500\\Profit=(300)^2-99500\\Profit=90000-99500\\Profit=-9500

Since the profit is -9500 (negative) so, company will not gain any profit if they produce 300 bicycles.

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3 years ago
Suppose you are interested in the effect of skipping lectures (in days missed) on college grades. You also have ACT scores and h
DIA [1.3K]

Answer:

a) For this case the intercept of 2.52 represent a common effect of measure for any student without taking in count the other variables analyzed, and we know that if HSGPA=0, ACT= 0 and skip =0 we got colGPA=2.52

b) This value represent the effect into the ACT scores in the GPA, we know that:

\hat \beta_{ACT} = 0.015

So then for every unit increase in the ACT score we expect and increase of 0.015 in the GPA or the predicted variable

c) If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: \beta_i = 0

Alternative hypothesis: \beta_i \neq 0

Or in other wouds we want to check if an specific slope is significant.

The significance level assumed for this case is \alpha=0.05

Th degrees of freedom for a linear regression is given by df=n-p-1 = 45-3-1 = 41, where p =3 the number of variables used to estimate the dependent variable.

In order to test the hypothesis the statistic is given by:

t=\frac{\hat \beta_i}{SE_{\beta_i}}

And replacing we got:

t = \frac{-0.5}{0.0001}=-5000

And for this case we see that if we find the p value for this case we will get a value very near to 0, so then we can conclude that this coefficient would be significant for the regression model .

Step-by-step explanation:

For this case we have the following multiple regression model calculated:

colGPA =2.52+0.38*HSGPA+0.015*ACT-0.5*skip

Part a

(a) Interpret the intercept in this model.

For this case the intercept of 2.52 represent a common effect of measure for any student without taking in count the other variables analyzed, and we know that if HSGPA=0, ACT= 0 and skip =0 we got colGPA=2.52

(b) Interpret \hat \beta_{ACT} from this model.

This value represent the effect into the ACT scores in the GPA, we know that:

\hat \beta_{ACT} = 0.015

So then for every unit increase in the ACT score we expect and increase of 0.015 in the GPA or the predicted variable

(c) What is the predicted college GPA for someone who scored a 25 on the ACT, had a 3.2 high school GPA and missed 4 lectures. Show your work.

For this case we can use the regression model and we got:

colGPA =2.52 +0.38*3.2 +0.015*25 - 0.5*4 = 26.751

(d) Is the estimate of skipping class statistically significant? How do you know? Is the estimate of skipping class economically significant? How do you know? (Hint: Suppose there are 45 lectures in a typical semester long class).

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: \beta_i = 0

Alternative hypothesis: \beta_i \neq 0

Or in other wouds we want to check if an specific slope is significant.

The significance level assumed for this case is \alpha=0.05

Th degrees of freedom for a linear regression is given by df=n-p-1 = 45-3-1 = 41, where p =3 the number of variables used to estimate the dependent variable.

In order to test the hypothesis the statistic is given by:

t=\frac{\hat \beta_i}{SE_{\beta_i}}

And replacing we got:

t = \frac{-0.5}{0.0001}=-5000

And for this case we see that if we find the p value for this case we will get a value very near to 0, so then we can conclude that this coefficient would be significant for the regression model .

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