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3 years ago

Which row of the input/output table is incorrect?

Mathematics

1 answer:

zaharov [31]3 years ago

8 0

Row A: x = 3

y = 2x - 3

y = 2(3) - 3 = 3 This is correct

Row B: x = 5

y = 2x - 3

y = 2(5) - 3 = 7 This is correct

Row C: x = 7

y = 2x - 3

y = 2(7) - 3 = 11 this is correct

Row D: x = 10

y = 2x - 3

y = 2(10) - 3 = 17 THIS IS INCORRECT, SO ROW D

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when tom simplified the expression -2.6 + (-5.4), he got 2.8 what mistake did tom likely make? pls help me

olga_2 [115]

Answer:

2.6 and 5.4 are both the same sign, he should add them and then take that negative sign from (-5.4), so the answer would be -8.0.

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3 years ago

Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

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2 years ago

A researcher was studying how the weights of horseshoe crabs along the East Coast vary between northern and southern habitats. I

Ronch [10]

Answer:

Option D (the weight of crab) would be the correct choice.

Step-by-step explanation:

In mathematics, the sum being analyzed depending on a variety of parameters, which have been calculated as explanatory variables, has become a response variable.
It is analogous with the utilization of the definition of variables of the study. A variable with an order to respond is categorized as either a dependent variable.

Some other preferences are not connected with the sustaining. So choice D is the right one.

6 0

3 years ago

How to solve this. I am very confused.

sergiy2304 [10]

To solve, we will need to plug in -5 for x in both instances.

|-5 + 2| / -5 + 2

|-3| / -3

Now, these absolute value bars may be a bit puzzling. What we have to do is take the absolute value of the number inside of the brackets. Meaning, that if the number is negative, we make it positive, and if the number is positive, then it stays positive.

3 / -3

-1

Hope this helps!! :)

6 0

2 years ago

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The following data pairs represent the average temperature x (in degrees Fahrenheit) and electricity

elena55 [62]

Answer:

<u>The correct answer is C. r = 0 because is most likely the closest to the correlation coefficient of the data.</u>

Step-by-step explanation:

Using Excel, we captured the data provided for the 12 different homes for calculating the correlation coefficient manually, this way:

n = 12

∑x = 904

∑y = 2,169

∑xy = 167,532

∑x² = 69,552

∑y² = 404,615

r = [n *∑xy - (∑x * ∑y)]/[√(n * ∑x² - (∑x)²) * (n * ∑y² - (∑y)²)]

Replacing with the real values, we have:

r = [12 * 167,532 - (904 * 2,169)]/[√(12 * 69,552 - 904²) * (12 * 404,615 - 2,169²)]

r = [2'010,384 -1'960,776]/[√(834,624 - 817,216) * (4'855,380 - 4'704,561]

r = 49,608/√17,408 * 150,819

r = 49,608/ 51'239.215

r = 0.00097

<u>The correct answer is C. r = 0 because is most likely the closest to the correlation coefficient of the data.</u>

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2 years ago

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