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2 years ago

What is the following simplified product? Assume x greater-than-or-equal-to 0

Mathematics

2 answers:

andreev551 [17]2 years ago

8 0

Answer:

Option C is correct.

Step-by-step explanation:

We have to simplify the product of

(StartRoot 6 x squared EndRoot + 4 StartRoot 8 x cubed EndRoot) (StartRoot 9 x EndRoot minus x StartRoot 5 x Superscript 5 Baseline)

= $(\sqrt{6x^{2}} + 4\sqrt{8x^{3}})(\sqrt{9x} - x\sqrt{5x^{5}})$

= $(\sqrt{6x^{2}} + \sqrt{128x^{3}})(\sqrt{9x} - \sqrt{5x^{7}})$

= $\sqrt{54x^{3}} - \sqrt{30x^{9}} + \sqrt{1152x^{4}} - \sqrt{640x^{10}}$

= $3x\sqrt{6x} - x^{4}\sqrt{30x} + 24x^{2}\sqrt{2} - 8x^{5}\sqrt{10}$

= 3 x StartRoot 6 x EndRoot minus x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x squared StartRoot 2 EndRoot minus 8 x Superscript 5 Baseline StartRoot 10 EndRoot

Therefore, option C is correct. (Answer)

Lisa [10]2 years ago

5 0

Answer:

this is incorrect, option A is the correct answer. i just took it.

Step-by-step explanation:

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A whisper room is a room that allows two people to stand on opposite sides of an elliptically shaped room and hear each other’s

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2 years ago

What is the error due to using linear interpolation to estimate the value of sinxsin⁡x at x = \pi/3? your answer should have at

Serhud [2]

<h3>Answer:</h3>

using y = x, the error is about 0.1812
using y = (x -π/4 +1)/√2, the error is about 0.02620

<h3>Step-by-step explanation:</h3>

The actual value of sin(π/3) is (√3)/2 ≈ 0.86602540.

If the sine function is approximated by y=x (no error at x = 0), then the error at x=π/3 is ...

... x -sin(x) @ x=π/3

... π/3 -(√3)/2 ≈ 0.18117215 ≈ 0.1812

You know right away this is a bad approximation, because the approximate value is π/3 ≈ 1.04719755, a value greater than 1. The range of the sine function is [-1, 1] so there will be no values greater than 1.

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If the sine function is approximated by y=(x+1-π/4)/√2 (no error at x=π/4), then the error at x=π/3 is ...

... (x+1-π/4)/√2 -sin(x) @ x=π/3

... (π/12 +1)/√2 -(√3)/2 ≈ 0.026201500 ≈ 0.02620

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2 years ago

A printer can print 12 pages in 9 seconds. What is the closest estimate of the

ExtremeBDS [4]

Answer:

Step-by-step explanation:

there are 60 seconds in a minute so about 6 9 seconds in a minute. then there is 12 pages per 9 seconds and since there is 6 9 seconds then you can just multiply 6 by 9 to get the answer 72

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2 years ago

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Amy and two of her friends eat lunch at a restaurant. Their bill, including tax, comes to $27.63. They decide to split the bill

Art [367]

Answer:

Step-by-step explanation:

$27.63 / 2 = $13.82

$13.82 * 0.20 = $2.76

$13.82 + $2.76 = $16.58

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2 years ago

A researcher gathers data on the length of essays (number of lines) and the SAT scores received for a sample of students enrol

LenaWriter [7]

Answer:

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

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: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other wouds we want to check is our slope is significant.

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

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

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

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