Using the binomial distribution, it is found that there is a 0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For each die, there are only two possible outcomes, either a 3 or a 4 is rolled, or it is not. The result of a roll is independent of any other roll, hence, the <em>binomial distribution</em> is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 9 rolls, hence
.
- Of the six sides, 2 are 3 or 4, hence

The desired probability is:

In which:

Then



Then:


0.857 = 85.7% probability that at least 2 of the rolls come up as a 3 or a 4.
For more on the binomial distribution, you can check brainly.com/question/24863377
Answer:
$80, $48
Step-by-step explanation:
The original price was x.
The price is reduced by 40%. The markdown is 40% of x, or 0.4x.
The actual dollar amount of the markdown is $32.
That means that 0.4x must equal $32.
We set up an equation and solve for x, the original price.
0.4x = 32
Divide both sides by 0.4
x = 32/0.4
x = 80
The original price is $80.
The markdown is $32.
$80 - $32 = $48
The marked down price is $48.
Answer: $80, $48
Answer:
Option 4: <u>(2x + 16)° + (x)° = 180°</u>
Step-by-step explanation:
See the attached figure.
For a quadrilateral inscribed in a circle
The opposite angles are supplementary.
So, ∠D + ∠B = 180°
From the figure:
∠B = x° and ∠D = (2x+16)°
∴ <u>(2x + 16)° + (x)° = 180°</u>
Answer: yes, 4/3 can be simplified
Step-by-step explanation:
Since it is an improper fraction, it can be simplified.
three goes into four once, And there is a remainder of one. so the new fraction is: 1 1/3
Answer:
The volume of the metal used is 5277.9 cm³.
Step-by-step explanation:
The volume of a cylinder is given by:

Where:
r: is the radius
h: is the height = 50 cm
The volume of metal (
) can be found by subtracting the internal volume (
) from the external volume (
):

The external radius is given by the sum of the internal radius with the tickness:

Hence, the volume is:

Therefore, the volume of the metal used is 5277.9 cm³.
I hope it helps you!