2

Hamburger Hut sells regular hamburgers as well as a larger burger. Either type can include cheese, relish, lettuce, tomato, must

Studentka2010 [4]

Answer:

a) 40 different hamburgers can be ordered with exactly three extras

b) 20 different regular hamburgers can be ordered with exactly three extras

c) 7 different regular hamburgers can be ordered with at least five extras

Step-by-step explanation:

The order in which the extras are ordered is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this problem:

2 options of hamburger(regular or larger)

6 options of extras(cheese, relish, lettuce, tomato, mustard, or catsup.).

(a) How many different hamburgers can be ordered with exactly three extras?

1 hamburger type, from a set of 2.

3 extras, from a set of 6. So

$C_{2,1}*C_{6,3} = \frac{2!}{1!(2-1)!}*\frac{6!}{3!(6-3)!} = 2*20 = 40$

40 different hamburgers can be ordered with exactly three extras

(b) How many different regular hamburgers can be ordered with exactly three extras?

3 extras, from a set of 6. So

$C_{6,3} = \frac{6!}{3!(6-3)!} = 20$

20 different regular hamburgers can be ordered with exactly three extras

(c) How many different regular hamburgers can be ordered with at least five extras?

Five extras:

5 extras, from a set of 6. So

$C_{6,5} = \frac{6!}{5!(6-5)!} = 6$

Six extras:

6 extras, from a set of 6. So

$C_{6,6} = \frac{6!}{6!(6-6)!} = 1$

6 + 1 = 7

7 different regular hamburgers can be ordered with at least five extras

8 0

3 years ago

Jemima receives £5 pocket money

Lorico [155]

Answer:

51% of the money was spent, that is, 51/100. In conclusion, Jemina still has 49/100 of the money available.

Step-by-step explanation:

Since Jemima received $ 5 in pocket money, and spent $ 1.75 on a magazine and $ 0.80 on a drink, to determine the proportion of money he spent and the proportion he has left, the following calculation must be performed:

5 - (1.75 + 0.80) = X

5 - 2.55 = X

2.45 = X

5 = 100

2.55 = X

(2.55 x 100) / 5 = X

255/5 = X

51 = X

Therefore, 51% of the money was spent, that is, 51/100. In conclusion, Jemina still has 49/100 of the money available.

7 0

3 years ago

What are the coordinates of the vertex of the function f(x)=x2+10x-3?

Vlad1618 [11]

Answer:

(- 5, - 28 )

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² + 10x

f(x) = x² + 2(5)x + 25 - 25 - 3

= (x + 5)² - 28 ← in vertex form

with (h, k) = (- 5, - 28)

Vertex = (- 5, - 28 )

5 0

3 years ago

Suppose the graph of a cubic polynomial function

fiasKO [112]

Answer:

Use the zeroes to determine the roots.

Write the polynomial as a product of the leading coefficient, a, and the factors, where each factor is x minus a root.

Use the y-intercept (0, –5) to solve for the leading coefficient.

Substitute the leading coefficient into the polynomial function for a and simplify.

Step-by-step explanation:

6 0

3 years ago

Which point on the number line represent the product of (-4)(-2)(-1)<br>

Slav-nsk [51]

-4 times -2 equals 8.

8 times -1 equals -8.

Therefore, the point on your number line that is on -8 is your answer!

7 0

4 years ago

Read 2 more answers