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Arada [10]
3 years ago
7

A box contains 5 red and 10 white marbles. If 8 marbles are to be chosen at random (without replacement), determine the probabil

ity that (a) 4 will be red, (b) all will be white, (c) at least one will be red.
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
8 0

Answer:

a) 0.0023

b) 0.007

c) 0.993

Step-by-step explanation:

The total number of marbles are;

5 + 10 = 15

Probability of red = 5/15

Probability of white = 8/15

Probability of 4 being red means, 4 will be white too;

Thus, the probability without replacement will be;

5/15 * 4/14 * 3/13 * 2/12 * 10/11 * 9/10 * 8/9 * 7/8 =

0.002331002331 which is approximately 0.0023

b. All white

Here, we have all the marbles selected being white

Thus the probability without replacement will be;

10/15 * 9/14 * 8/13 * 7/12 * 6/11 * 5/10 * 4/9 * 3/8

= 0.006993006993 which is approximately 0.007

c. At least one will be red

Mathematically, that will be;

1 - p(no red)

p(no red) = p(all white)

P(all white) = 0.007

hence P(no red) = 0.007

P(at least one red) = 1 - 0.007 = 0.993

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A local farm sells produce to a large grocery chain. The grocery store uses a 28% markup on the farms produce. Of the farm sells
kkurt [141]

Answer:

$3.84

Step-by-step explanation

move the decimal back two place - .28, it is a mark up so add a 1 at the beginning - 1.28 - multiply - 3 x 1.28 = 3.84

5 0
3 years ago
Using the distributive property, which of the following expressions is equivalent to 6(3 + 6y)?
labwork [276]
6*3 + 6y*6 = 18+36y The answer is D!
5 0
3 years ago
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In the year 2003 a company made 8.8 million in profits. For each consecutive year after that their profits increased by 6%. How
yaroslaw [1]

Answer:

The company's profit in 2007 was 11.088 millions

Step-by-step explanation:

This is a compound interest problem where the initial amount is 8.8 million, the interest rate is 6% and the time period is 4 years and it gets compounded yearly. So we can use the compound interest formula, that is given by:

A = P*(1 + r/n)^(n*t)

Where A is the final amount, P is the initial amount, r is the rate, t is the total amount of time and n is the number of times it gets compounded in one year. We can now use all the values that were given to us to find out the profit of the company.

A = 8.8*(1 + (0.06))^(4) = 8.8*(1.06)^16

A  = 8.8*1.26 = 11.088 millions

So the company's profit in 2007 was 11.088 millions

6 0
3 years ago
A water tower that is 132 feet tall casts a 48-foot long shadow. If Shannon is 1 point
MariettaO [177]

Answer:

2.03 ft

Step-by-step explanation:

132 divided by 48 is 2.75 and 5.6 divided by 2.75 is 2.03

6 0
3 years ago
NO LINKS!!!<br><br>Make a flowchart to show the two triangles are similar. ​
timama [110]

Answer: The flowchart is shown below.

Explanation:

Each box is a different statement. The reason for the statement is provided below the box. The arrows on the flowchart direct the flow of how the proof is laid out. Typically the flow is left to right, top to bottom, or a mix of both. This is to match the reading order of many western countries. Though I would imagine the flow is reversed for countries that read from right to left.

The structure of any type of proof is to start with what you are given. Then use the previously established, or previously proven, theorems to make your way to what you want to prove.

In this case, we start off with MN and KL being parallel line segments. This is shown by the arrows on MN and KL. Because the segments are parallel, we then can determine these two facts:

  • angle MNJ = angle KLJ
  • angle NMJ = angle LKJ

Both of those will have the reasoning of "corresponding angles theorem"

We have two pairs of angles which are congruent. This then directly leads to the triangles being similar. Refer to the AA (angle angle) similarity theorem for more information.

Feel free to use symbols in place of some words. For example, instead of saying something like "Triangle NMJ is similar to Triangle LKJ", you could write \triangle \text{NMJ} \sim \triangle \text{LKJ}

If you're curious what app I used to make the flowchart, the app is called "LucidChart". They have 3 options: 1 free and the other 2 are paid versions. I went with the free version and it worked just fine. But it's up to you which you prefer most.

5 0
2 years ago
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