Andrew randomly selects a number from 1-15. What is the probability that the number he selects is an even number?

Answer:

[tex](a)\ g(x) = \frac{2}{3}(x+1)[/tex]

[tex](b)\ h(y) = \frac{1}{3}[1 + 4y][/tex]

[tex](c)[/tex] [tex]P(x>0.5) =\frac{5}{12}[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \left \{ {{\frac{2}{3}(x+2y)\ \ 0\le x \le 1,\ 0\le y\le 1} \right.[/tex]

Solving (a): The marginal density of X

This is calculated as:

[tex]g(x) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dy[/tex]

[tex]g(x) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dy[/tex]

[tex]g(x) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dy[/tex]

Integrate

[tex]g(x) = \frac{2}{3}(xy+y^2)|\limits^{1}_{0}[/tex]

Substitute 1 and 0 for y

[tex]g(x) = \frac{2}{3}[(x*1+1^2) - (x*0 + 0^2)}[/tex]

[tex]g(x) = \frac{2}{3}[(x+1)}[/tex]

Solving (b): The marginal density of Y

This is calculated as:

[tex]h(y) = \int\limits^{\infty}_{-\infty} {f(x,y)} \, dx[/tex]

[tex]h(y) = \int\limits^{1}_{0} {\frac{2}{3}(x + 2y)} \, dx[/tex]

[tex]h(y) = \frac{2}{3}\int\limits^{1}_{0} {(x + 2y)} \, dx[/tex]

Integrate

[tex]h(y) = \frac{2}{3}(\frac{x^2}{2} + 2xy)|\limits^{1}_{0}[/tex]

Substitute 1 and 0 for x

[tex]h(y) = \frac{2}{3}[(\frac{1^2}{2} + 2y*1) - (\frac{0^2}{2} + 2y*0) ][/tex]

[tex]h(y) = \frac{2}{3}[(\frac{1}{2} + 2y)][/tex]

[tex]h(y) = \frac{1}{3}[1 + 4y][/tex]

Solving (c): The probability that the drive-through facility is busy less than one-half of the time.

This is represented as:

[tex]P(x>0.5)[/tex]

The solution is as follows:

[tex]P(x>0.5) = P(0\le x\le 0.5,0\le y\le 1)[/tex]

Represent as an integral

[tex]P(x>0.5) =\int\limits^1_0 \int\limits^{0.5}_0 {\frac{2}{3}(x + 2y)} \, dx dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 \int\limits^{0.5}_0 {(x + 2y)} \, dx dy[/tex]

Integrate w.r.t. x

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (\frac{x^2}{2} + 2xy) |^{0.5}_0\, dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 [(\frac{0.5^2}{2} + 2*0.5y) -(\frac{0^2}{2} + 2*0y)], dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}\int\limits^1_0 (0.125 + y), dy[/tex]

[tex]P(x>0.5) =\frac{2}{3}(0.125y + \frac{y^2}{2})|^{1}_{0}[/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125*1 + \frac{1^2}{2}) - (0.125*0 + \frac{0^2}{2})][/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125 + \frac{1}{2})][/tex]

[tex]P(x>0.5) =\frac{2}{3}[(0.125 + 0.5][/tex]

[tex]P(x>0.5) =\frac{2}{3} * 0.625[/tex]

[tex]P(x>0.5) =\frac{2 * 0.625}{3}[/tex]

[tex]P(x>0.5) =\frac{1.25}{3}[/tex]

Express as a fraction, properly

[tex]P(x>0.5) =\frac{1.25*4}{3*4}[/tex]

[tex]P(x>0.5) =\frac{5}{12}[/tex]

Answer:

16.1

Step-by-step explanation:

Answer:

I believe the answer is x = 16.1

Step-by-step explanation:

Answer:

i think B

Step-by-step explanation:

Answer:

140=(w+4)×w

140=w²+4w

w²+4w-140

w=10

l=w+4

l=14

Divide Total time into two Time Periods. A regular Demand and a High Demand Time Period. Since 75% of the 1,200 calls occur between 9:30 am and 3:30 pm. We multiply .75 x 1,200 to get 900. We get an average of 900 calls every day between the hours of 9:30 am and 3:30 pm – Our net time for this time period is 6 hours.

Therefore, 6 Hours/900 becomes our quotient

Again, since the denominator is larger we invert it to 900 calls/6 Hours

To get a demand of 150 calls per hour.

We need to be able to handle 150 calls per hour.

So how Many Call Representatives are needed?

Again, our historical data tells us that each person can handle 10 calls an hour.

Therefore 150 calls per hour /10 Minutes = 15 Customer Service Representatives are needed during Peak Time!

Now, Subtract the Peak Hours from the 21 Hours Net Time Per day, gives us 15 Non-Peak hours we have to staff.

Answer:

x=4

Step-by-step explanation:

1. Rearrange terms

[tex]2(-3x+3)=-18[/tex]

2. Distribute

[tex]-6x+6=-18[/tex]

3. Subtract 6 from both sides of the equation

[tex]-6x+6-6=-18-6[/tex]

4. Simplify by subtracting the numbers

[tex]-6x + 6-6=-18-6[/tex]

[tex]-6x=-18-6[/tex]

[tex]-6x=-24[/tex]

5. Divide both sides of the equation by the same factor

[tex]\frac{-6x}{-6} = \frac{-24}{-6}[/tex]

6. Simplify

a) Simplify the fraction

[tex]\frac{-6x}{-6} = \frac{-24}{-6}[/tex]

[tex]x = \frac{-24}{-6}[/tex]

b) Divide the numbers

[tex]x=+4[/tex]

7. Remove the postive sign.

[tex]x=4[/tex]

Answer:

136 ft²

Step-by-step explanation:

floor = 7 x 6 = 42 ft²

sides = 2 x 7 x 5 = 70 ft²

ends = 1/2 x 6 x 4 x 2 = 24 ft²

42 + 70 + 24 = 136 ft²

Answer:

C- The size of the initial water sample, in gallons.

Step-by-step explanation:

Answer: 20 mangoes.

Step-by-step explanation: This is a simple subtraction problem. If you take away 8 from 28, you'll have 20.

28 - 8 = 20

Answer:

60 minutes

Step-by-step explanation:

She painted 2/5 of the wall.

She still needs to paint 3/5 of the wall.

3 is 50% more than 2, so 3/5 is 1.5 times 2/5, so it will take her 1.5 times the time it took so far.

1.5 * 40 minutes = 60 minutes.

Answer: 60 minutes

Answer:

i willl help on all three if u help on my chemistry problems

Answer:

t = 0.86 or t = 1.45

Step-by-step explanation:

Answer:

697.5 ft squared

Step-by-step explanation:

Divide into top two squares and rectangle on bottom so...

(10×7.5)+(8×7.5)×(12.5×45)=area

75+60+562.5=697.5 ft squared

Answer: The First Cylinder has more volume

Step-by-step explanation:

1. V = 471.24

2. V = 282.74

Answer:16 is the answer of your question

hope it is helpful to you

Answer:

53

Step-by-step explanation:

106 miles per hour would get him home in 1 hour but it takes 2 hours so you can divide 106 by 2 to 53 miles per hour.

Answer:

6 gallons = 3.785 liters

Answer:

1.5850323141      

Step-by-step explanation:

Answer: 10 miles

Step-by-step explanation:

Given

The length of the road is 1000 miles

Solve

1 : 100 = x : 1000 ⇔ Proportion Set Up

100x = 1000 ⇔ Cross Multiply

100x/100 = 1000/100 ⇔ Divide both sides by 100

x=10 ⇔ Simplify

Hope this helps!! :)

Please let me know if you have any questions

9514 1404 393

Answer:

  D

Step-by-step explanation:

Choices A and D agree in all but one term: row 2 column 3 is (-2)(3) = -6. The term with the correct sign is only found in choice D.

Answer:

g=1

Step-by-step explanation:

6g+3g=-3g+9+3g, add 3g to both sides and you get closer to the answer

Answer:

g=1

Step-by-step explanation:

solved and got the same answer

Answer:

it will look the same, just shifted.

Step-by-step explanation:

The parabola will be the same shape, size, etc., it will simply be in a different location. Instead of the bottom of the parabola being at (0,0), it will be at (3, -8). translated right 3, down 8.

Answer:

(Length x Width x Height)

6x18x12=

I hope this helped! ♡+*

1. You can find what the cheapest and most expensive card is.

2. You could find what percent of the people on your cards are brunettes.

You could also find what the average strikes for a team.

You're welcome

Answer:

64 inches

Step-by-step explanation:

There are 12 inches in a foot

12 x 5 is 60

64 is greater then 60

Answer:

i dunno if this will help any but i think 1/4 and 25% is the same since 100/4=25

Step-by-step explanation:

if it doesn't i'm sorry for waisting ur time-

Step-by-step explanation:

- 35/10(2-15n/10) 145n/10 - 7 - 6n

-70/10 +35*15n/100.145n/10 -7-6n

-7 + 525n/100.145n/10 -7- 6n

-14 +5.25n .14.5n -6n

-14 +76.125n^2 -6n is final answer

Answer:

$800 is the original price

Step-by-step explanation:

15% discount

if 85% = $680

100% =?

100/85 * $680

=$800

Answer:

800

Step-by-step explanation:

Answer:

The possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.

Step-by-step explanation:

From statement we know that [tex]AB = 2\cdot BC[/tex]. By Analytical Geometry, we use the equation of a line segment, which is an application of the Pythagorean Theorem:

[tex]AB = 2\cdot BC[/tex]

[tex]\sqrt{(x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2}} = 2\cdot \sqrt{(x_{C}-x_{B})^{2}+(y_{C}-y_{B})^{2}}[/tex] (1)

Where:

[tex]x_{A}[/tex], [tex]x_{B}[/tex], [tex]x_{C}[/tex] - x-Coordinates of points A, B and C.

[tex]y_{A}, y_{B}, y_{C}[/tex] - y-Coordinates of points A, B and C.

[tex](x_{B}-x_{A})^{2}+(y_{B}-y_{A})^{2} = 4\cdot (x_{C}-x_{B})^{2}+4\cdot (y_{C}-y_{B})^{2}[/tex]

Then, we expand and simplify the expression above:

[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} +x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot (x_{C}^{2}-2\cdot x_{C}\cdot x_{B}+x_{B}^{2})+4\cdot (y_{C}^{2}-2\cdot y_{C}\cdot y_{B}+y_{B}^{2})[/tex]

[tex]x_{B}^{2}-2\cdot x_{A}\cdot x_{B} + x_{A}^{2} +y_{B}^{2}-2\cdot y_{A}\cdot y_{B} + y_{A}^{2} = 4\cdot x_{A}^{2}-8\cdot x_{C}\cdot x_{B}+4\cdot x_{B}^{2}+4\cdot y_{C}^{2}-8\cdot y_{C}\cdot y_{B}+4\cdot y_{B}^{2}[/tex]

If we know that [tex]x_{A} = 5[/tex], [tex]y_{A} = 6[/tex], [tex]x_{B} = 1[/tex], [tex]y_{B} = b[/tex], [tex]x_{C} = 1[/tex] and [tex]y_{C} = -3[/tex], then we have the following expression:

[tex]1 -10 +25 +b^{2} -12\cdot b+36 = 100 -8 +4 +36+24\cdot b +4\cdot b^{2}[/tex]

[tex]b^{2}-12\cdot b +52 = 4\cdot b^{2}+24\cdot b +132[/tex]

[tex]3\cdot b^{2}+36\cdot b +80 = 0[/tex]

This is a second order polynomial, which means the existence of two possible real solutions. By Quadratic Formula, we have the following y-coordinates for point B:

[tex]b_{1} \approx -2.944[/tex], [tex]b_{2} \approx -9.055[/tex]

In consequence, the possible values of [tex]b[/tex] are -2.944 and -9.055, respectively.

Answer:

The probability that their average salary;

standard error

= 10,000/sqrt(16)

=10,000/4

= 2500  

(77,500 - 75000)/2500

2,500/2500

= 1  

p (z > 1) = .1587

So, the probability that their average salary is more than $77,500 is 0.1587

Step-by-step explanation:

Answer: 166 2/3m

Step-by-step explanation:

Area of a rectangle = length times width

Length: 16 2/3

To find the width, multiply it by 3/5.

w = 16 2/3 ·  3/5

w = 10

Then, multiply the length by the width.

a = l · w

a = 16 2/3 · 10

a = 166 2/3m