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lara31 [8.8K]
3 years ago
12

In a box there are six envelopes each containing two cards. Three of the envelopes contain two red cards, two of them contain a

red and a black card, and the last one contains two black cards. An envelope is selected at random and a card is withdrawn and found to be red. What is the chance the other card is black?
Mathematics
1 answer:
Sphinxa [80]3 years ago
5 0

Answer:

\frac{2}{5}

Step-by-step explanation:

3 envelopes having 2 red card

2 envelopes having 1 red card and 1 black card

1 envelope having 2 black cards

We are given that . An envelope is selected at random and a card is withdrawn and found to be red.

So, No. of ways of envelope having red card = 3+2 = 5

No. of required ways of envelope having 1 red card and 1 black card = 2

So, probability of getting an envelope having 1 red card and 1 black card = \frac{2}{5}

Hence The chance the other card is black is \frac{2}{5}

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Answer:

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Step-by-step explanation:


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4 years ago
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Rick deposit is $1000 into an investment account which earns 4% interest annually. Sally loans what doesn’t dollars to a friend,
pshichka [43]

Answer:

After 10 years

Rick will have $1,480.24

Sally will have $1,500

Step-by-step explanation:

Data provided in the question:

Principle amount = $1,000

Now,

For Rick

Interest rate by bank, r = 4% = 0.04

Time period, n = 10 years

Now,

Final amount after 10 years with Rick using the compounding formula

Final amount = Principle × (1 + r)ⁿ

= $1,000 × (1 + 0.04 )¹⁰

= $1,480.24

For Sally

Amount paid each year = $50

Therefore,

Total amount paid in 10 years = $50 × 10

= $500

Thus,

Final amount Sally will have after 10 years

= $1,000 + Total amount paid in 10 years

= $1,000 + $500

= $1,500

Hence,

After 10 years

Rick will have $1,480.24

Sally will have $1,500

6 0
4 years ago
You invest $15,000 to start a hot dog stand at the local sports complex. It costs you $.65 to produce each hot dog. How many hot
SCORPION-xisa [38]

Answer:

  • Below is the procedure to find the answer: 30,000 hot dogs.

Explanation:

The <em>average cost </em>is found dividing the total cost by the number of hot dogs:

         Average\text{ }cost=Total\text{ }cost/Number\text{ }of\text{ }hot\text{ }dogs

The total cost is the the sum of amount that you invest plus the product of the cost of producing each hot dog times the number of hot dogs:

Total\text{ }cost=investment+Number\text{ }of\text{ }hot\text{ }dogs\times cost\text{ }to\text{ }produce\text{ }each\text{ }hot\text{ }dog

  • Substitute the values:

           Total\text{ }cost=15,000+0.65x\\ \\ Averate\text{ }cost=(15,000+0.65x)/x=1.15

Where x is the number of hot dogs.

  • Solve for x from the equation:

         (15,000+0.65x)/x=1.15\\ \\ 15,000+0.65x=1.15x\\ \\ 15,000=1.15x-0.65x\\ \\ 15,000=0.5x\\ \\ 15,000/0.5=x\\ \\ 30,000=x\\ \\ x=30,000

Which shows you how you can find that the answer is 30,000 hot dogs.

8 0
3 years ago
For a car moving at a constant speed, the distance traveled varies directly with the time spent driving. If such a car travels 5
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4 years ago
identify the different parts to the word problem. A bowling ball of 35.2kg generates 218kg-m/s units of momentum. what is the ve
Margaret [11]

Answer:

  • mass: 35.2 kg
  • momentum: 218 kg·m/s
  • velocity: ≈ 6.19 m/s

Step-by-step explanation:

The mass and momentum are given in the problem statement. You are expected to know that ...

... momentum = mass × velocity

To find the velocity, you can fill in the given numbers in this relation, then solve.

... 218 kg·m/s = 35.2 kg · velocity

... (218 kg·m/s)/(35.2 kg) = velocity ≈ 6.193182 m/s . . . . . (divide by mass)

Rounded to appropriate precision, ...

... velocity = 6.19 m/s

_____

<em>Comment on word problems</em>

A word problem generally gives you the values of certain quantities, and may give you the relationship between them. It will ask you to make use of the given relationship(s), or one(s) you are expected to know, in order to find the values asked for. Laws of physics (as here), universal constants, geometric relationships, financial relationships, algebraic relationships, and other relationships may be involved. That is why you study these things, learn math and English vocabulary, and pay attention in the real world. (By the time you get to college, you are also expected to be familiar with number facts and the operation of your calculator.)

4 0
4 years ago
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