All categories

3 years ago

Which equation represents a direct proportion? a. y=x+1 b.6y=12x c.6y+4=x d. y=2x-2

Mathematics

1 answer:

Hatshy [7]3 years ago

5 0

Direct proportion would mean that there is no y-intercept. The answer would be answer choice b

You might be interested in

(a) The probability that an automobile being filled with gasoline will also need an oil change is 0.35; the probability that it

cricket20 [7]

Answer:

0.714 ; 0.556 ; (A1 n A2 n A3) = 0

Step-by-step explanation:

Given that :

P(oil) = 0.35

P(filter) = 0.45

P(oil n filter) = 0.25

P(filter | Oil) = P(oil n filter) / P(oil)

P(filter | Oil) = 0.25 / 0.35 = 0.714

11)

P(Oil | filter) = P(oil n filter) / P(filter)

P(Oil | filter ) = 0.25 / 0.45 = 0.556

Number of red aces = 2

Queen or king = 4 + 4 = 8

Number on card greater than 3 and less than 8 = {4,5,6,7} = 4 card ; for 4 suits = 4 * 4 = 16

Total number of cards in deck = 52

Choosing without replacement :

Hence,

A1 = 2 / 52

A2 = 8 / 51

A3 = 16 / 50

(A1 n A2 n A3) ;this means card common to all three events.

However, (A1 n A2 n A3) = 0 because ;

1.) No red ace card is greater than 3 and less than 8.

11.) An ace card can neither be a king nor a queen

3 0

3 years ago

What is the quadric regression equation that fits these data

Angelina_Jolie [31]

Where’s the data?................

6 0

4 years ago

Find the mass and the center of mass of a wire loop in the shape of a helix (measured in cm: x = t, y = 4 cos(t), z = 4 sin(t) f

Sholpan [36]

Answer:

Mass

$\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)$

Center of mass

Coordinate x

$\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Coordinate y

$\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Coordinate z

$\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

Step-by-step explanation:

Let W be the wire. We can consider W=(x(t),y(t),z(t)) as a path given by the parametric functions

x(t) = t

y(t) = 4 cos(t)

z(t) = 4 sin(t)

for 0 ≤ t ≤ 2π

If D(x,y,z) is the density of W at a given point (x,y,z), the mass m would be the curve integral along the path W

$m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt$

The density D(x,y,z) is given by

$D(x,y,z)=x^2+y^2+z^2=t^2+16cos^2(t)+16sin^2(t)=t^2+16$

on the other hand

$||W'(t)||=\sqrt{1^2+(-4sin(t))^2+(4cos(t))^2}=\sqrt{1+16}=\sqrt{17}$

and we have

$m=\displaystyle\int_{W}D(x,y,z)=\displaystyle\int_{0}^{2\pi}D(x(t),y(t),z(t))||W'(t)||dt=\\\\\sqrt{17}\displaystyle\int_{0}^{2\pi}(t^2+16)dt=\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)$

The center of mass is the point $(\bar x,\bar y,\bar z)$

where

$\bar x=\displaystyle\frac{1}{m}\displaystyle\int_{W}xD(x,y,z)\\\\\bar y=\displaystyle\frac{1}{m}\displaystyle\int_{W}yD(x,y,z)\\\\\bar z=\displaystyle\frac{1}{m}\displaystyle\int_{W}zD(x,y,z)$

We have

$\displaystyle\int_{W}xD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}t(t^2+16)dt=\\\\=\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)$

$\bar x=\displaystyle\frac{\sqrt{17}(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{(\displaystyle\frac{(2\pi)^4}{4}+32\pi)}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

$\displaystyle\int_{W}yD(x,y,z)=\sqrt{17}\displaystyle\int_{0}^{2\pi}4cos(t)(t^2+16)dt=\\\\=16\sqrt{17}\pi$

$\bar y=\displaystyle\frac{16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

$\displaystyle\int_{W}zD(x,y,z)=4\sqrt{17}\displaystyle\int_{0}^{2\pi}sin(t)(t^2+16)dt=\\\\=-16\sqrt{17}\pi$

$\bar z=\displaystyle\frac{-16\sqrt{17}\pi}{\sqrt{17}(\displaystyle\frac{8\pi^3}{3}+32\pi)}=\displaystyle\frac{-16\pi}{(\displaystyle\frac{8\pi^3}{3}+32\pi)}$

3 0

3 years ago

Hi I was wondering if I could get help on this please

Lerok [7]

Answer:

Step-by-step explanation:

The equation of line is y=-1/2 x+3 as it takes the form of y=mx+c

From this, the graph having gradient of -1/2 then the line will run from left to right. This eliminates options A and D

The pictures are not clear but we must ensure where the line crosses y intercept, the value of y should be 3 hence the only graph having these properties is option B.

4 0

3 years ago

What is the value of 0.53?

Marrrta [24]

The value of the decimal, 0.53 is $\frac{53}{100}$ or 53%.

Sure hope this helps you

7 0

3 years ago

Read 2 more answers