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3 years ago

2. If x is directly proportional to y^3 and x=32 when y=2, i) Find an equation

Mathematics

1 answer:

svp [43]3 years ago

3 0

Answer:

(i)

$x \alpha y {3} \\ \frac{x}{y {3} } = k$

(ii)

$\frac{x}{y {3}^{} } = \frac{x}{y {3}^{} } \\ \frac{32}{ {2}^{3} } = \frac{x}{6 {}^{3} } \\ \frac{32}{8} = \frac{x}{216} \\ x = 864$

(iii)

$\frac{32}{8} = \frac{108}{y {}^{3} } \\ {y}^{3 } = 27 \\ y = \sqrt[3]{27 } \\ y = 3$

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The difference between the observed value of the dependent variable and the value predicted using the estimated regression equat

Elenna [48]

Answer:

For this case we define the dependent variable as Y and the independent variable X. We assume that we have n observations and that means the following pairs:

$(x_1, y_1) ,....,(x_n,y_n)$

For this case we assume that we want to find a linear regression model given by:

$\hat y = \hat m x +\hat b$

Where:

$\hat m$ represent the estimated slope for the model

$\hat b$ represent the estimated intercept for the model

And for any estimation of the dependent variable $\hat y_i , i=1,...,n$ is given by this model.

The difference between the observed value of the dependnet variable and the value predicted using the estimated regression equation is known as residual, and the residual is given by this formula:

$e_i = y_i -\hat y_i , i=1,...,n$

So the best option for this case is:

d. residual

Step-by-step explanation:

For this case we define the dependent variable as Y and the independent variable X. We assume that we have n observations and that means the following pairs:

$(x_1, y_1) ,....,(x_n,y_n)$

For this case we assume that we want to find a linear regression model given by:

$\hat y = \hat m x +\hat b$

Where:

$\hat m$ represent the estimated slope for the model

$\hat b$ represent the estimated intercept for the model

And for any estimation of the dependent variable $\hat y_i , i=1,...,n$ is given by this model.

$e_i = y_i -\hat y_i , i=1,...,n$

So the best option for this case is:

d. residual

7 0

3 years ago

(5n−5)(2+2n) standard form

mash [69]

Answer:

10n -10

Step-by-step explanation:

5n * 2n = 10n

-5 * 2 = -10

-10 + 10n = 10n - 10

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3 years ago

Read 2 more answers

At Andrew Jackson High School, students are only allowed to enroll in AP U.S. History if they have already taken AP World Histor

o-na [289]

Answer:

About 0.22

Explanation:

There are two sets:

Set W of incoming seniors who took AP World History, and

Set E of incoming seniors who took AP European History

And there is a subset, which is the intersection of those two sets:

Subset W ∩ E of senior students who took both.

The incoming seniors who are allowed to enroll in AP U.S. History, call them the subset S, is the set of those students that belong to W or E or both W ∩E.

By property of sets:

S = W + E - W∩E = 175 + 36 - 33 = 178

Then, 178 out of 825 incoming seniors took one or both courses, and the desired probability of a randomly selected incoming senior is allowed to enroll in AP U.S. History is: