a catering service offers 4 appetizers, 6 main course, and 12 desserts. a banquet chairperson is to select 3 appetizers, 2 main course and 5 desserts or a banquet. in how many ways can this be done

Answers

Answer 1

Answer: If you have 4 appetizers and you need to choose just 3 of them, it would be the same amount of options as just choosing 1 out of the 4; so there are 4 ways to choose the appetizer. For the main course, you are choosing 2 out of 6. So there are 6 ways to choose the first main course, and assuming there is no repeats, there would be 5 ways to choose the next one. However, there will be some overlap, so you need to divide it by 2. So you have $(6*5)/(2) =15$ options for main course. Finally for dessert, you have 12 desserts to choose from and 5 desserts to choose. So you do a similar thing to the main courses. $(12*11*10*9*8)/(5*4*3*2*1)$ would be the equation you would use. Because there are 12 ways to pick the first dessert, 11 ways for the 2nd and so on until you reach 5 desserts. You divide it by 5*4*3*2*1 or 5! (Factorial) because there are overlaps for each of the 5 so you have to account for those. After solving the equation, there are 792 ways to pick desserts So you now know that you have 4 ways of picking the appetizer, 15 ways for the main course and 972 ways to pick desserts. So for options of the full meal, you need to multiply all these values together: $4*15*792=47520$ . Therefore, there are 47,520 possible ways this could be done.

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Solve the following three variable system. 2x + 3y + 4z = 9
-x + 2y - z = 0
-2x + 4y + z = 3

Answers

$1)\ \ \ 2x + 3y + 4z = 9\n2)\ \ \ -x + 2y - z = 0\n3)\ \ \ -2x + 4y + z = 3\n===================================\n3)\ \ \ -2x + 4y + z = 3\ \ \ \Rightarrow\ \ \ z=2x-4y+3\n\n1)\ \ \ 2x + 3y + 4z = 9\ \ \ \Rightarrow\ \ \ 2x + 3y + 4(2x-4y+3) = 9\n2x+3y+8x-16y+12=9\n10x-13y=-3\n\n2)\ \ \ -x + 2y - z = 0\ \ \ \Rightarrow\ \ \ -x+2y-(2x-4y+3)=0\n-x+2y-2x+4y-3=0\n-3x+6y=3\ /:(-3)\nx-2y=-1\ \ \ \Rightarrow\ \ \ x=2y-1\n\n$

$1)\ \ \ 10x-13y=-3 \ \ \ \Rightarrow\ \ \ 10(2y-1)-13y=-3\n20y-10-13y=-3\n7y=7\ /:7\ \ \ \Rightarrow\ \ \ y=1\n\n2)\ \ \ x=2y-1\ \ \ \Rightarrow\ \ \ x=2\cdot2-1=1\n\n3)\ \ \ z=2x-4y+3\ \ \ \Rightarrow\ \ \ z=2\cdot1-4\cdot1+3=2-4+3=1\n\nAns.\ x=y=z=1$

H(t)=-16t^2+24So I have to find how long (in seconds) it will take a tool to fall to the ground from a height of 24 feet. I am using the equation h(t)=-16t^2+24 to find it but I'm not sure how to solve it or where to even get started! Any help would be great thank you!

Answers

when h(t)=0, it hits the ground

solve
0=-16t^2+24
factor out -8
0=-8(2t^2-3)
we know that
0=2t^2-3 since factors have to multiply to 0
add 3 to both sides
3=2t^2
divide both sides by 2
1.5=t^2
sqrt both sides
1.2247=t

after about 1.2247 seconds it will hit the ground

If AB = 4x +10, BC = 2x +3 and AC= 9x - 15 find AC. and show work plzz !!!!

Answers

Answer:

Step-by-step explanation:

AB + BC = AC

4x + 10 + 2x + 3 = 9x - 15

6x + 13 = 9x - 15

6x + 13 + 15 = 9x

6x + 28 = 9x

3x = 28

x = 9 1/3 = 28/3

AC = 9 * 28/3 - 15

AC = 3 * 28 - 15

AC = 84 - 15

AC = 69

Which will result in a perfect square trinomial?(3x – 5)(3x – 5)
(3x – 5)(5 – 3x)
(3x – 5)(3x + 5)
(3x – 5)(–3x – 5)

Answers

Answer:

the answer is a

Step-by-step explanation:

(3x-5)(3x-5) that would be a perfect square because all numbers are squared. I dont know how else to explain...

Answer:

(3x – 5)(3x – 5) I think

Which method used to calculate finance charges is most favorable to the card issuer?a.
adjusted balance
b.
average daily balance
c.
previous balance
d.
usual balance

Answers

Answer: c. previous balance method

The method used by credit card companies to calculate finance charges in which it is most favorable to the card issuer is the previous balance method. This is computed by charging the interest into the new billing period. This is least favorable to cardholder thus, most favorable to card issuer.

Answer:

usual balance

Step-by-step explanation:

The width of a rectangle is 4 less than half the length. If represents the length, which equation could be used to find the width, w?