The blue dot is at what value on the number line?

How many different ways are there to choose a dozen donuts from the 4 varities at a donut shop so that you get atleast one donut

Leno4ka [110]

There are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop. (at least one donut of every variety must be selected)

<h3>How to calculate the number of ways to select items?</h3>

There are 'r' items from 'n' different varieties (repetition allowed). Then, the number of ways to select items is given by

The number of ways = $_{n+r-1}C_r$

Where the combination $_{n}C_r$ is calculated as

$_{n}C_r=\frac{n!}{r!(n-r)!}$

<h3 /><h3>Calculation:</h3>

It is given that there are 4 varieties of donuts in a shop. I.e., n = 4

Number of donuts to be selected r = 12 (one dozen)

And also given that at least one donut of every variety has to be selected.

Since there are 4 varieties, at least one from each of these means the count is 4.

So, the remaining number of donuts to be selected is 12 - 4 = 8.

So, r becomes 8 i.e., r = 8

On substituting,

the number of ways of selecting the remaining 8 donuts = $_{4+8-1}C_4$

⇒ $_{11}C_4$

⇒ $\frac{11!}{4!(11-4)!}$

⇒ $\frac{11!}{(4!)(7!)}$

⇒ 330

Therefore, there are 330 different ways for choosing a dozen donuts from the 4 varieties at a donut shop.

Learn more about combinations here:

brainly.com/question/11732255

#SPJ4

5 0

2 years ago

The maximum weight of a shipping container is 125 pounds. What is the maximum weight in kilograms? Round to the nearest kilogram

Helga [31]

Step-by-step explanation:

56 kilograms I know kilograms and pounds, but basically 125 doubles because "2.2" so it's 56 kil

3 0

2 years ago

Find tanX if cotX =2

Tom [10]

Answer:

1/2

Step-by-step explanation:

Let's define these trigonometric functions:

- tangent (tan): opposite / adjacent

- cotangent (cot): adjacent / opposite

Basically, tangent and cotangent are reciprocals of each other.

We know that cot(x) = 2. The reciprocal of 2 is 1/2, which means that tan(x) = 1/2.

Thus, the answer is 1/2.

<em>~ an aesthetics lover</em>

3 0

3 years ago

Julie and mark are selling wrapping paper for a school fundraiser. Julie sold 13 rolls of plain wrapping paper and 8 rolls of ho

patriot [66]

Answer:

Cost of one roll of plain wrapping paper is $12 and Cost of one roll of holiday paper is $17.

Step-by-step explanation:

Solution,

Let the cost of 1 plain wrapping paper be x.

And the cost of 1 holiday paper be y.

Julie sold 13 rolls of plain wrapping paper and 8 rolls of holiday paper and earns $292.

Total Money earned by Julie is equal to sum of number of wrapping paper multiplied with cost of wrapping paper and number of holiday paper multiplied with cost of holiday paper.

So we can frame it in equation form as;

$13x+8y=292\ \ \ \ \ equation\ 1$

Now, Mark sold 7 rolls of plain wrapping paper and 2 rolls of holiday paper and earns $118.

Total Money earned by Mark is equal to sum of number of wrapping paper multiplied with cost of wrapping paper and number of holiday paper multiplied with cost of holiday paper.

So we can frame it in equation form as;

$7x+2y=118\ \ \ \ \ equation\ 2$