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3 years ago

A line with slope -2 and x-intercept (4,0)

Mathematics

1 answer:

Luden [163]3 years ago

7 0

Answer: y = -2x + 4

Step-by-step explanation:

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The ten students in a club are lined up in a row for a group photograph. How many different arrangements are possible if the clu

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It's 10!/3! so its 604, 800.

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2 years ago

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There are 8 brooms and 6 mops in a janitor's closet. What is the ratio of the number of mops to the total number of brooms and m

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B 3:7

If there are 6 mops, and 14 mops and brooms, you get 6:14, which simplifies to 3:7.

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This Venn diagram shows the pizza topping preferences for 9 students. Let event A = The student likes pepperoni. Let event B = T

Lelechka [254]

Answer:

$P(A\ or\ B)=\frac{7}{9}$

Step-by-step explanation:

We need to use the formula to calculate the probability of (A or B) where

A=Probability a student likes pepperoni

B=Probability a student likes olive

A and B =Probability a student likes both toppings in a pizza

A or B =Probability a student likes pepperoni or olive (and maybe both), a non-exclusive or

The formula is

$P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$

Since 6 students like pepperoni out of 9:

$P(A) = \frac{6}{9}$

Since 4 students like olive out of 9:

$P(B) = \frac{4}{9}$

Since 3 students like both toppings out of 9

$P(A\ and\ B) = \frac{3}{9}$

Then we have

$P(A\ or\ B)=\frac{6}{9}+\frac{4}{9}-\frac{3}{9}$

$P(A\ or\ B)=\frac{7}{9}$

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2 years ago

Consider the differential equation <img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%3D6%20y%5E%7

Nutka1998 [239]

As a Bernoulli equation:

$x^2\dfrac{\mathrm dy}{\mathrm dx}=6y^2+6xy\iff x^2y^{-2}\dfrac{\mathrm dy}{\mathrm dx}-6xy^{-1}=6$

Let $z=y^{-1}\implies\dfrac{\mathrm dz}{\mathrm dx}=-y^{-2}\dfrac{\mathrm dy}{\mathrm dx}$ . The ODE becomes

$-x^2\dfrac{\mathrm dz}{\mathrm dx}-6xz=6$
$x^6\dfrac{\mathrm dz}{\mathrm dx}+6x^5z=-6x^4$
$\dfrac{\mathrm d}{\mathrm dx}[x^6z]=-6x^4$
$x^6z=-6\displaystyle\int x^4\,\mathrm dx$
$x^6z=-\dfrac65x^5+C$
$z=-\dfrac6{5x}+\dfrac C{x^6}$
$y^{-1}=-\dfrac6{5x}+\dfrac C{x^6}$
$y=\dfrac1{\frac C{x^6}-\frac6{5x}}$
$y=\dfrac{5x^6}{C-6x^5}$

With $y(3)=6$ , we get

$6=\dfrac{5(3)^6}{C-6(3)^5}\implies C=\dfrac{4131}2$

so the solution is

$y=\dfrac{5x^6}{\frac{4131}2-6x^5}=\dfrac{10x^6}{4131-12x^5}$

which is valid as long as the denominator is not zero, which is the case for all $x\neq\sqrt[5]{\dfrac{4131}{12}}$ .

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3 years ago

What type of sequence fits with linear mathematical models?

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3 years ago

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