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ArbitrLikvidat [17]
3 years ago
8

Which graph can be used to find the solution to the system of equations below? 2x + y = -4 - 3y = 2x + 12 2 -4-3-2-1 -1 1 2 3 5

2. -5 3-2 1 2 1 2 3​

Mathematics
1 answer:
larisa86 [58]3 years ago
7 0

Answer:

F

Step-by-step explanation:

2x+y = -4

put into slope-intercept form: y = -2x - 4

-3y = 2x+12

In slope-intercept form: y = -⅔x - 4

Both equations have a y-intercept of -4. There is only one graph where both lines pass through (0,-4).

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Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pens, and 3 green pens. If X is the number
Flauer [41]

Answer:

a) f(x,y) =\frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}} ;   x = 0, 1 , 2;  y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b) = \frac{9}{14}

Step-by-step explanation:

joint probability is a function that characterizes the distribution of a random variable. If X and Y be two random variables then the joint probability will be P(X = x, Y=y)

Given Data,

X = The number of blue Pens

Y = The number of red Pens

a)

possible outcomes(X, Y) are (0, 0), (0, 1), (1, 0), (1, 1), (0, 2), (2,0)

Please refer fig. also

total number ways of selecting any 2 pens = \binom{8}{2}= \frac{8!}{2! 6!} =28

f(x,y) = \frac{\binom{3}{x}\binom{2}{y}\binom{3}{2-x-y}}{\binom{8}{2}} ;   x = 0, 1 , 2;  y = 0, 1 , 2; 0 ≤ x+y ≥ 2

b)

P(X,Y)∈A = P(X + Y ≤ 1)

= P(0,0) + P(1,0) + P(0,1)

= \frac{3}{28} + \frac{3}{14} + \frac{9}{28}

= \frac{9}{14}

4 0
3 years ago
In direct variation, the variables change by a constant _______________.
jolli1 [7]
Direct variation is of the form y=kx   (inverse variation is of the form y=k/x)
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3 years ago
Let f (x)<br>sinx cosx, then f'(x) =<br>A. Cos2x<br>B. sin2x<br>C. tan 2x<br>D. cos2x - sin2x<br>​
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Answer:

A. Cos2x

Step-by-step explanation:

f(x) = sin(x)cos(x) = (1/2) sin(2x)   using double angle formula.

f'(x) = ( (1/2)sin(2x) )' = 2(1/2)cos(2x) = cos(2x)

8 0
3 years ago
An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) = 85e−0.04t liters per minute. How much
Furkat [3]
Given the rate of water flow is given by:
r(t)=85e^(-0.04t)
thus the amount of water flow in the first hour when t=1, will be:
r(1)=85e^(-0.04*1)
=81.667
thus the amount of water that flowed out will be:
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Answer:

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Step-by-step explanation:

3 0
3 years ago
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