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3 years ago

11

to make fruit punch ,you need 3 cups of grape juice for every 5 cups of apple juice. if you have 15 more cups of apple juice ,ho

w many cups do you have total

1 answer:

zepelin [54]3 years ago

6 0

You'd get a total 24 cups, 3/5=9/15. 9+15=24

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Let Y1 and Y2 have the joint probability density function given by:

Ann [662]

Answer:

a) k=6

b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16

Step-by-step explanation:

a) if

f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1, 0, elsewhere

for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then

P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1

then integrated between

y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1

∫∫f (y1, y2) dy1*dy2 = ∫∫k(1 − y2) dy1*dy2 = k ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)- (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)

then

k/6 = 1 → k=6

b)

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p

then

p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =

6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)= 9/16

therefore

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = 9/16

8 0

3 years ago

1/2x-5=10-3/4x please helpppppp

GarryVolchara [31]

Answer:

x=12

Step-by-step explanation:

1/2x - 5 = 10 - 3/4x ---> move like terms to the same side

1/2x + 3/4x = 10 + 5 ---> calculate

5/4x = 15 ---> multiply both sides by 4/5

x = 12

8 0

2 years ago

If 4+2=26,8+1= 79 and 6+5=111 then what is 7+3

Nastasia [14]

Answer:

its 21 obviously

Step-by-step explanation:

this is because

<em> $8 {6 \times 58964 \sqrt[45 \sqrt{66x3 \times \frac{?}{?} } ]{?} \times \frac{?}{?} }^{2}$ </em>

4 0

3 years ago

Match the information on the left with the appropriate equation on the right.

solmaris [256]

Answer:

Step-by-step explanation:

1). Equation of a line which has slope 'm' and y-intercept as 'b' is,

y = mx + b

If slope 'm' = 1 and y-intercept 'b' = -3

Equation of the line will be,

y = x - 3

x - y = 3

2). Equation of a line having slope 'm' and passing through a point (x', y') is,

y - y' = m(x - x')

If the slope 'm' = 1 and point is (-1, 2),

The the equation of the line will be,

y - 2 = 1(x + 1)

y = x + 1 + 2

y = x + 3

x - y = -3

3). Equation of a line passing through two points $(x_1, y_1)$ and $(x_2,y_2)$ will be,

$y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$

If this line passes through (-2, 3) and (-3, 4),

$y-3=\frac{(4-3)}{(-3+2)}(x+2)$

y - 3 = -1(x + 2)

y = -x - 2 + 3

y = -x + 1

x + y = 1

4 0

3 years ago

The perpendicular bisector of a line segment is a line perpendicular to the segment that passes through its midpoint. What is th

adoni [48]

Answer:

y = 1/3 x.

Step-by-step explanation:

The slope of the given line is

(4 - (-2) / 2 - 4)

= -3.

So the slope of the line perpendicular to it = -1 / (-3) = 1/3.

This line also passes through the point (3, 1) so its equation is ( by the point-slope form):

y - 1 = 1/3(x - 3)

y - 1 = 1/3x - 1

y = 1/3 x (answer).

hope that help you mark me brinilylist

8 0

3 years ago