MATHEMATICS COLLEGE

A bag contains 4 red marbles, 1 green one, 1 lavender one, 3 yellows, and 2 orange marbles. HINT [See Example 7.] How many sets of five marbles include at most one of the yellow ones?

Answers

Answer 1

Answer:

Answer:

266

Step-by-step explanation:

Red marbles = 4

Green marbles = 1

Lavender marbles = 1

Yellow marbles = 3

Orange marbles = 2

To pick 5 marbles with at most 1 yellow, we can pick 5 non-yellow marbles or (4 non-yellow marble and 1 yellow marble).

Picking 5 non-yellow marbles

There are 4 + 1 + 1 + 2 = 8 non-yellow marbles.

The number of ways of picking any 5 is

$n_1 = \dbinom{8}{5} = 56$

Picking 4 non-yellow marble and 1 yellow marble

The number of ways of picking any 4 non-yellow marbles is

$n_2 = \dbinom{8}{4} = 70$

The number of ways of picking any 1 yellow marble from 3 is

$n_3 = \dbinom{3}{1} = 3$

Number of ways for both = $70*3=210$

Total number of picking 5 marbles with at most 1 yellow

Therefore, total number of ways = 56 + 210 = 266

Related Questions

What is the domain of the function f (x) = StartFraction x + 1 Over x squared minus 6 x + 8 EndFraction?
A 170-lb man carries a 20-lb can of paint up a helical staircase that encircles a silo with radius 30 ft. The silo is 90 ft high and the man makes exactly three complete revolutions. Suppose there is a hole in the can of paint and 8 lb of paint leaks steadily out of the can during the man's ascent. How much work is done by the man against gravity in climbing to the top
kim and courtney share a 20 ounce box of cereal. By the end of the week kim has eat 2/5 of the box and courtney has eaten 1/10 of the box of cereal what fraction of the box is left
Suppose your net income every month is $3.750. In the 20-60-20Model, how much ofyour net income would be in each category?Answer in three complete sentences to explain how much of your income is in each category.
If someone build a house for 50 years how many months did it take to complete

6th grade math look at the pictures

Answers

Answer:

2. 17.624

3. 9.72

4. 14.3

5. 2.11

8. 5,105.16

10. 124.7

Step-by-step explanation:

Answer:

use a calculator.

Step-by-step explanation:

Which graph shows a system with no solutions? Graph A Graph B Graph C y=-3x 5+ y = 2x-1 بل 42y = 4x-2

Answers

Answer:

Graph B

Step-by-step explanation:

Given

Graphs A, B and C

Required

The graph with no solution

Each of the graphs have two parallel lines.

For Graph A

There is a point of intersection between both lines

For Graph B

No visible point of intersection between both lines

For Graph C

Both lines are the same

Since graph B has no point of intersection between the two lines, it has no solution

Given m || n, find the value of x and y.
(3x-4)
(6x-5)

Answers

Answer:

X=21 and Y=121

Step-by-step explanation:

With these types of problems, we need to know our vertical angles and that lines are 180° when two angles on a line are next to each other.

To solve this problem algebraically we want to add (3x-4) and (6x-5) together so that they equal 180. The reason we do this is that they lie on the same line which is 180°. The equation would look like $3x+6x-5-4=180$ . We then want to add like terms which will leave us with $9x-9=180$ . Now we want to get 9x by itself by adding 9 on each side which leaves us with $9x=189$ . To isolate x we need to divide on each side by 9 which finally leaves us with $x=21$

Now that we have the value of x (21) we can now utilize our knowledge of vertical angles (angles that are completely across and equal to one another.) We can find y by doing this equation: $y=6x-5$ and with the value of x found we can plug in the value to get $y=6(21)-5$ which simplifies to $y=126-5$ then to $y=121$ .

It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work in temperatures of 200-500 degrees. In a test of one type of mask, 24 of 55 were found to have their lenses pop out at 325 degrees. Construct and interpret a 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees.

Answers

Answer:

The 93% confidence interval for the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574). This means that we are 93% sure that the true proportion of masks of this type whose lenses would pop out at 325 degrees is (0.3154, 0.5574).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{(\pi(1-\pi))/(n)}$

In which

z is the zscore that has a pvalue of $1 - (\alpha)/(2)$ .

For this problem, we have that:

$n = 55, \pi = (24)/(55) = 0.4364$

93% confidence level

So $\alpha = 0.07$ , z is the value of Z that has a pvalue of $1 - (0.07)/(2) = 0.965$ , so $Z = 1.81$ .

The lower limit of this interval is:

$\pi - z\sqrt{(\pi(1-\pi))/(n)} = 0.4364 - 1.81\sqrt{(0.4364*0.5636)/(55)} = 0.3154$

The upper limit of this interval is:

$\pi + z\sqrt{(\pi(1-\pi))/(n)} = 0.4364 + 1.81\sqrt{(0.4364*0.5636)/(55)} = 0.5574$

How many units long is side w?
A. 14
B. 6.2
C. 22
d. 5.5

Answers

Answer:

d. w is 5.5 units

Step-by-step explanation:

$(11)/(16) = (w)/(8)$

$16w = 88$

$w = 5.5$

So d is correct.

Consider the function f(x) = (3x-7)/2 with a domain of - ∞ < x < ∞what is the range of f^-1(x) [this is the inverse function]

a. - ∞ <_ x <_ ∞
b. - ∞ < x < ∞
c. - ∞ < f^-1(x) < ∞
d. - ∞ <_ f^-1(x) <_ ∞

please help and thank you!!

Answers

Here we have to use the fact that the domain of the function is equal to the range of the inverse function and range of the function is equal to the domain of the inverse function .

In the given question , the domain of the given function is given. So the range of the given option is same as the domain.

Therefore the correct option is c.

Other Questions

HELP LE WITH THE WORKSHEET ITS FOR 6 TH GRADE YALL GOT THIS CMON PLEAE HELPPP ILL GIVE YOU ALL THE POINTS I CAN PLEASE PLEASE PLEASE I BEG

Please help so urgent

Which coordinates represent the plotted point? Check all that apply. (StartRoot 13 EndRoot, 146.3 degrees) (StartRoot 13 EndRoot, 213.7 degrees) (negative StartRoot 13 EndRoot, negative 33.7 degrees) (Negative StartRoot 13 EndRoot, negative 146.3 degrees) (−3, 2) (3, −2) (−2, 3)

Cindy typed 200 words in 5 minutes. At this rate, how many words can she type in 25 minutes?