Mathematics, 25.02.2020 05:00 pankajyadav7402

Garcia's Grill offers 77 side dishes, 55 types of steak, and 88 toppings. How many different smothered steak dinners can be made if a smothered steak dinner consists of the customer's choice of steak served with 33 different toppings and 44 different side dishes?

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Answer from: YSGabino2991

Therefore the total number of ways that the customer can order the smothered steak dinner is 9800.

Step-by-step explanation:

There are 7 side dishes, and types of stake and 8 toppings.

The customer will have a smothered steak dinner.

The smothered steak dinner will consist of steak and 3 different toppings and 4 $\binom{8}{3} = \frac{8!}{3! \times 5!} = 56$ different side dishes.

The number of ways steak can be selected is = $\binom{5}{1} = \frac{5!}{1! 4!} =5$

The number of ways toppings can be chosen is = $\binom{8}{3} = \frac{8!}{3! 5!} = 56$

The number of ways side dishes can be chosen = $\binom{7}{4} = \frac{7!}{4!3!} = 35.$

Therefore the total number of ways that the customer can order the smothered steak dinner is

= 5 × 56 × 35 = 9800.

Answer from: Quest

$y> \frac{1}{3}x$ and y≤ -x +4 .

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be = $\frac{1-0}{3-0} = \frac{1}{3}$ .

y-intercept of dotted line is y=0 only.

plugging slope m= $\frac{1}{3}$ and b=0 in slope-intercept form y=mx+b, we get

$y=\frac{1}{3}x$ .

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

$y> \frac{1}{3}x$ .

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be = $\frac{4-1}{0-3} = \frac{3}{-3}=-1$ .

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y≤ -x +4 .
Write a system of inequalities to represent the shaded portion of the graph.

Answer from: Quest

i think the answer would be c

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