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3 years ago

Which equation has a constant of proportionality equal to 1? A. y=10/11x B. y= 7/8x C. y= 3/15x D. y=x

Mathematics

1 answer:

shtirl [24]3 years ago

8 0

An equation is said to have a constant of proportionality if 'x' is a multiple of 'y' or 'y' is a multiple of 'x'.

Now, we have to determine an equation with constant of proportionality as '1'.

1. $y = \frac{10}{11}x$

This equation has constant of proportionality as ' $\frac{10}{11}$ '.

2. $y = \frac{7}{8}x$

This equation has constant of proportionality as ' $\frac{7}{8}$ '.

3. $y = \frac{3}{15}x$

This equation has constant of proportionality as ' $\frac{3}{15}$ '.

4. $y = x$

This equation has constant of proportionality as '1'.

Option D is the correct answer.

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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 .

7 0

3 years ago

Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.

-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

$3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)$

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

$4^n+17$ is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so $4^k+17$ is divisible by 3

and we check what happens for k+1

$4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17$

$3\cdot 4^k$ is divisible by 3 and

$4^k+17$ is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that $4^n+17$ is divisible by 3 for all positive integers n.

Thanks

4 0

3 years ago

VGravel is being dumped from a conveyor belt at a rate of 50 ft3/min. It forms a pile in the shape of a right circular cone whos

kupik [55]

Answer:

0.325 ft/min

Step-by-step explanation:

To solve we must follow the following steps:

First, the volume of a cone is given by the equation:

Vc = (1/3) * Pi * (r ^ 2) * h

where r is the radius and h is the height.

they tell us that the height is equal to twice the radius, therefore

h = 2r; r = h / 2

replacing r in the volume of the cone:

Vc = (1/3) * Pi * ((h / 2) ^ 2) * h

solving we have:

Vc = (1/3) * Pi * (1/4) * (h ^ 2) * h

Vc = (1/12) * Pi * h ^ 3

They give us the change in volume with respect to time, that is, dV / dt = 50

It can also be expressed in the following way:

dV / dt = (dV / dh) * (dh / dt)

We know V, so we can derive with respect to h, we are like this:

dV / dh = 3 * (1/12) * Pi * h ^ 2

dV / dh = (1/4) * Pi * h ^ 2

we know that h is equal to 14, therefore:

dV / dh = (1/4) * Pi * 14 ^ 2

dV / dh = (1/4) * 3.14 * 196 = 153.86

Now if we replace

dV / dt = (dV / dh) * (dh / dt)

50 = 153.86 * (dh / dt)

(dh / dt) = 50/158.36

(dh / dt) = 0.3249

This means that the change in height with respect to time is 0.325 feet per minutes.

4 0

3 years ago

Read 2 more answers

Given log Subscript 3 Baseline 2 almost-equals 0. 631 and log Subscript 3 Baseline 7 almost-equals 1. 771, what is log Subscript

kari74 [83]

You can use the properties of logarithm to get to the solution.

The approximate value for given term is given by

$log_3(14) \approx 2.402$

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

$a^b = c$

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

$b = log_a(c)$

Some properties of logarithm are:

$log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})$

<h3>Using the above properties</h3>

$log_3(2) + log_3(7) = log_3(2 \times 7) = log_3(14)\\\\0.631 + 1.771 = log_3(14)\\\\log_3(14) = 2.402$

Thus,

The approximate value for given term is given by

$log_3(14) \approx 2.402$

Learn more about logarithm here:

brainly.com/question/20835449

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2 years ago

Read 2 more answers

Box A contains 2 red and 2 green balls and box B contains 1 red and 2 green balls. A box is selected at random and then a ball i

serious [3.7K]

The answer is 1/2. I think that since the question is about Box B , only boxes will be taken into consideration. Since the total number of boxes are two and box b is one ,the probability of the box being B is 1/2.

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3 years ago