MATHEMATICS COLLEGE

Jessica is playing a game where there are 4 blue markers and 6 red markers in a box. She is going to pick 3markers without replacement.
If she picks all 3 red markers, she will win a total of $500. If the first marker she picks is red but not all 3 markers
are red, she will win a total of $100. Under any other outcome, she will win $0.
What is the expected value of Jessica's winnings?
Round your answer to the nearest cent.

Answers

Answer 1

Answer:

Answer:

The probability of Jessica picking 3 consecutive red markers is: (1/6)

The probability of Jessica's first marker being red, but not picking 3 consecutive red markers is:

(3/5)−(1/6)=(13/30)

So i am bit stuck here

what i think is it shouldn't be that complex it should be as simple as chance of Jessica's first marker being red=chance of getting red 1 time i.e P(First marker being red)=(6/10) can any explain me the probability of Jessica's first marker being red=(13/30)?

Step-by-step explanation:

Answer 2

Answer:

Answer:

$126.67

Step-by-step explanation:

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Rylen hiked 3/4 of a mile in 2/3 of an hour . What was his hiking speed in miles per hour?1/8 miles per hour

1 1/8 miles per hour

8/9 miles per hour

1 5/12 miles per hour

Answers

Answer:

The hiking speed in miles per hour is 1 1/8.

Step-by-step explanation:

This can be solved by a simple rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

In this problem, the measures are the time spent hiking and the distance hiked. As the the time spent hiking increases, so will the distance hiked. So their relationship is direct.

So:

3/4 - 2/3 hour

x miles - 1 hour

$(2x)/(3) = (3)/(4)$

$x = (9)/(8)$

x can also be written in this format

$x = (9)/(8) = (8)/(8) + (1)/(8) = 1 + (1)/(8)$

So the hiking speed in miles per hour is 1 1/8.

Find the equation of a line through (1,1) whichisperpendicular to a line through (1,3) and (2,5).

Answers

Answer:

$y=(-1)/(2)x+(3)/(2)$

Step-by-step explanation:

Point on a line is (1,3) and (2,5).

$slope=(y_2-y_1)/(x_2-x_1) =(5-3)/(2-1) =2$

slope of given line is 2

slope of perpendicular lines are negative reciprocal of one another

slope of perpendicular line is -1/2

slope = -1/2 (1,1)

$y-y_1=m(x-x_1)$

$y-1=(-1)/(2)(x-1)$

$y-1=(-1)/(2)x+(1)/(2))$

add 1 on both sides

$y=(-1)/(2)x+(3)/(2)$

Let C be the unit circle in the xy-plane, oriented counterclockwise as seen from above. The divergence of the vector field F~ = (z, x, y) is zero, and as a result the flux through every surface with boundary C should be the same. Confirm that this is the case with the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane

Answers

Upper half of the unit sphere (call it $S_1$ ): parameterize by

$\vec s(u,v)=(\cos u\sin v,\sin u\sin v,\cos v)$

with $0\le u\le2\pi$ and $0\le v\le\frac\pi2$ . Take the normal vector to be

$(\partial\vec s)/(\partial v)*(\partial\vec s)/(\partial u)=(\cos u\sin^2v,\sin u\sin^2v,\cos v\sin v)$

Then the flux of $\vec F$ over this surface is

$\displaystyle\iint_(S_1)\vec F\cdot\mathrm d\vec S=\int_0^(\pi/2)\int_0^(2\pi)(\cos v,\cos u\sin v,\sin u\sin v)\cdot(\cos u\sin^2v,\sin u\sin^2v,\cos v\sin v)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^(\pi/2)\int_0^(2\pi)\cos u\sin^2v\cos v+\cos u\sin u\sin^3v+\sin u\cos v\sin^2v=\boxed{0}$

Lower half of the sphere (call it $S_2$ ): all the details remain the same as above, but with $\frac\pi2\le v\le\pi$ . The flux is again $\boxed{0}$ .

Unit disk (call it $D$ ): parameterize the disk by

$\vec s(u,v)=(u\cos v,u\sin v,0)$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to be

$(\partial\vec s)/(\partial u)*(\partial\vec s)/(\partial v)=(0,0,u)$

Then the flux across $D$ is

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^(2\pi)\int_0^1(0,u\cos v,u\sin v)\cdot(0,0,u)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^(2\pi)\int_0^1u^2\sin v\,\mathrm du\,\mathrm dv=\boxed{0}$

Final answer:

The flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same and it is zero.

Explanation:

The divergence of the vector field F~ = (z, x, y) is zero. Therefore, the flux through every surface with boundary C, such as the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane, should be the same.

This can be confirmed by considering that the electric flux through a closed surface is zero if there are no sources of electric field inside the enclosed volume. Since there are no charges inside the surfaces mentioned, the flux through each surface is zero.

Therefore, the flux through the upper half of the unit sphere, the lower half of the unit sphere, and the unit disk in the xy-plane is the same, and it is zero.

Learn more about Electric Flux here:

brainly.com/question/38239959

#SPJ3

Jeremy sprinted for 123 seconds and rested. Then he sprinted for 157 seconds, rested, and sprinted again for 195 seconds. Estimate the combined time he sprinted by rounding to the nearest ten and then adding the rounded numbers.

Answers

480 aproxmately if you round the numbers then add them up

How many 3/4 inch strips for caulk to cover 10 1/2 inches

Answers

The Number of 3/4 inch strips required to cover 10 1/2 inches of caulk will be 14

The total inches of caulk to be covered = 10 1/2 inches

The fraction of inch strip to be used = 3/4 inches

To obtain the number of 3/4 inch strop required ;

We divide the total inches of caulk by 3/4

Hence,

10 1/2 ÷ 3/4

21/2 ÷ 3/4

Change the sign to × and take the reciprocal of 3/4 ;

21/2 × 4/3

(21 × 4) / (2 × 3) = 84 / 6

84 / 6 = 14

Hence, the number of 3/4 inch strip required is 14

Learn more : brainly.com/question/2610134

Answer:

Step-by-step explanation:

So let's think smart. If you look at the image I made a diagram. The 3 squares I colored in represent 3/4. It takes 14 3/4 strips to cover 10 1/2 inches.

What is the circumference of the circle?1) 2 by 6 rectangle is inscribed in circle

2) 5 by 5 square is inscribed in circle

3) 5 by 6 rectangle is inscribed in circle

4)2 by 15 rectangle is inscribed in circle

5) 1 by 12 rectangle is inscribed in circle

Answers

I think it is 2 hope this helped you

Answer:

1. 6 pi

2. 7 pi

3. 8 pi

4. 15 pi

5. 12 pi

Step-by-step explanation: Just took the USATestprep test and got them all correct, sorry I dont have a proper answer on how I got them.

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