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Reika [66]
3 years ago
15

If two standard six-sided dice are tossed, what is the probability that a 5 is rolled on at least one of the two dice? express y

our answer as a common fraction.
Mathematics
1 answer:
zaharov [31]3 years ago
6 0
We define the probability of a particular event occurring as:
\frac{number\ of \ desired\ outcomes}{number\ of\ possible\ outcomes}

What are the total number of possible outcomes for the rolling of two dice? The rolls - though performed at the same time - are <em>independent</em>, which means one roll has no effect on the other. There are six possible outcomes for the first die, and for <em>each </em>of those, there are six possible outcomes for the second, for a total of 6 x 6 = 36 possible rolls.

Now that we've found the number of possible outcomes, we need to find the number of <em>desired</em> outcomes. What are our desired outcomes in this problem? They are asking for all outcomes where there is <em>at least one 5 rolled</em>. It turns out, there are only 3:

(1) D1 - 5, D2 - Anything else, (2), D1 - Anything else, D2 - 5, and (3) D1 - 5, D2 - 5

So, we have \frac{3}{36} = \frac{1}{12} probability of rolling at least one 5.
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Does anyone have an answer?
Yuki888 [10]
A and B, because the producer would be producing some of each product. Not C, because he wouldn't be maximizing his full production potential. Not D, because it is outside its possible range of production. And not E, because he would be producing only rice and no potatoes.
8 0
3 years ago
A bakery offers a sale price of $3.50 for 4 muffins. What is the price per dozen?
Levart [38]

Answer:

$10.5 per dozen.

Step-by-step explanation:

$3.50 x 3 = $10.5

4 = 3.50 4 x 3 = 12 = $10.5

8 0
3 years ago
Two solutions of salt water contain 0.06% and 0.26% salt respectively. A lab technician wants to make 1 liter of solution which
Valentin [98]

Answer:

The volume for the 0.26% is 250 ml and the volume for the 0.06% is 750 ml.

Step-by-step explanation:

In the solution the techinician wants to create there's a total of:

salt = 1*0.11/100 = 0.0011

So the sum of the salt from the other two solutions must be equal to that, since the quantity of salt in each is given by:

salt1 = volume1*0.06/100 = volume1*0.0006

salt2 = volume2*0.26/100 = volume2*0.0026

The sum of the from the two solutions must be equal to the final one:

salt = salt1 + salt2

0.0011 = 0.0006*volume1 + 0.0026*volume2

while the volume of the solutions must be equal to 1 liter:

volume1 + volume2 = 1

If we isolate volume1 on the second equation and replace that on the first one we have:

volume1 = 1 - volume2

0.0006*(1 - volume2) + 0.0026*volume2 = 0.0011

0.0006 - 0.0006*volume2 + 0.0026*volume2 = 0.0011

0.002*volume2 = 0.0011-0.0006

0.002*volume2 = 0.0005

volume2 = 0.0005/0.002 = 0.25 liters = 250 ml

volume1 = 1 - 0.25 = 0.75 liters = 750 ml

The volume for the 0.26% is 250 ml and the volume for the 0.06% is 750 ml.

3 0
3 years ago
Six times the sum of a number and negative four is twelve. Find the number. Round your answer to the nearest integer, if necessa
GuDViN [60]
If we call the number x, we can write an equation to solve:

6(x - 4) = 12
6 × x = 6x
6 × -4 = -24

So you get 6x - 24 = 12

6x - 24 = 12
+ 24
6x = 12
÷ 6
x = 2

And your final answer is 2, I hope this helps!
3 0
3 years ago
Find the balance of $7,000 deposited at 4% compounded semi-annually for 2 years
Rufina [12.5K]

Answer:

The balance will be $7,577.03.

Step-by-step explanation:

The compound interest formula is given by:

A = P(1 + \frac{r}{n})^{nt}

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

P = 7000, r = 0.04

Semianually means twice a year, so n = 2

We want to find A when t = 2.

So

A = P(1 + \frac{r}{n})^{nt}

A = 7000(1 + \frac{0.04}{2})^{2*2}

A = 7577.03

The balance will be $7,577.03.

5 0
3 years ago
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