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2 years ago

A sub sandwich shop offers 22 toppings to choose from. How many ways could a person choose a 4-topping sandwich?

Mathematics

1 answer:

ddd [48]2 years ago

4 0

There are 7,315 different combinations, thus, the correct option is c

<h3>How many combinations are there?</h3>

If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:

$C(N, K) = \frac{N!}{(N - K)!K!}$

In this case we have K = 4 and N = 22, replacing that, we get:

$C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315$

So there are 7,315 different combinations, thus, the correct option is c.

If you want to learn more about combinations:

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The leopard population in an African wildlife area is currently 17. Due to a new conservation effort, conservationists hope the

kykrilka [37]

Answer:

$a{_n} = 17 + (n - 1)4$ for n = 1, 2, . . . , 20.

Step-by-step explanation:

This is an arithmetic sequence, because the population is said to increase by 4 animals yearly. The formula for the nth term in an arithmetic sequence is given by:

$a{_n} = a{_1} + (n - 1)d$ where $a_n$ is the nth term, [/tex]a_1[/tex] is the first term, n = 1, 2, . . . and d is the common difference.

Since they are currently 17, this implies that the first number in the population sequence will be 17. In order words, the first term is 17.

Since they increase by 4 yearly, then the common difference is 4.

Since it's for 20years, the n = 1, 2, . . ., 20. The explicit formula is therefore:

$a{_n} = 17 + (n - 1)4$ for n = 1, 2, . . . , 20.

8 0

2 years ago

Sue Brown is a salesperson at a car dealership. She earned a gross pay of $8000 for the month of June. Her state tax rate is 3.5

Neporo4naja [7]

Sue Brown owes $280.00 in state taxes for the month.

Step-by-step explanation:

Given,

Gross pay of Sue in June = $8000

Tax rate = 3.5%

As full amount is taxable; therefore

Amount of tax to be paid = 3.5% of pay of June

Amount of tax to be paid = $\frac{3.5}{100}*8000$

Amount of tax to be paid = 0.035*8000

Amount of tax to be paid = $280.00

Sue Brown owes $280.00 in state taxes for the month.

Keywords: percentage, multiplication

Learn more about percentage at:

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4 0

3 years ago

Which of these functions has an inverse function? Select all that apply.

OLEGan [10]

Y=x^2 is the inverse function

8 0

3 years ago

Find the missing leg of a triangle with legs of 7 and a hypotenuse of 10<br> Help please

ahrayia [7]

Answer:

i believe its 24 in for the other leg

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

In 2012 your car was worth $10,000. In 2014 your car was worth $8,850. Suppose the value of your car decreased at a constant rat

monitta

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

$f(t) = 10000(0.9407)^t$

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

$f(t) = f(0)(1-r)^t$

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that $f(0) = 10000$ , thus:

$f(t) = 10000(1-r)^t$

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

$f(2) = 8850$

We use this to find 1 - r.

$f(t) = 10000(1-r)^t$

$8850 = 10000(1-r)^2$

$(1-r)^2 = \frac{8850}{10000}$

$(1-r)^2 = 0.885$

$\sqrt{(1-r)^2} = \sqrt{0.885}$

$1 - r = 0.9407$

Thus

$f(t) = 10000(1-r)^t$

$f(t) = 10000(0.9407)^t$

7 0

3 years ago