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3 years ago

17. Evaluate a. 6! b. 8P5 c. 12C4

1 answer:

7 0

The factorial ! just means we multiply by every natural number less that the value so
6! =6×5×4×3×2×1= 720

for permutations we use the formula n!/(n-r)!
so we have 8!/(8-5)!=8!/3!=8×7×6×5×4

for combinations s we have n!/(n-r)!r!
so we have 12!/(12-4)!4!=12!/8!4!=12×11×10×9/4×3×2=11×10×9/2=99×5

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An actor, Bob, wants to gain weight to look the part for his role as an overweight truck driver in an upcoming movie. He decides

Anastaziya [24]

Answer:

$C = 1000S + 500B$

Step-by-step explanation:

Given

$S = Banana\ Splits$

$B=Bacon\ Rolls$

Reading through the question, we have:

Number of calories per serving:

$S \to 1000$

$B \to 500$

Let

$x = Cholesterol$

$y =Sugar$

So, we have:

Each serving of S

$x \to 1S$

$y \to 3S$

Each serving of B

$x \to 4B$

$y \to 1B$

Recommendation

$x \to \le 10$ - i.e. not more than 10 units of cholesterol

$y \to \ge 2 \& \le 9$ i.e. At least 2units but not more than 9 units of sugar

So, the constraints are:

$S + 4B \le 10$

$3S + B \ge 2$

$3S + B \le 9$

Recall that the calories per serving is:

$S \to 1000$

$B \to 500$

Hence, the objective function is:

$C = 1000S + 500B$

5 0

3 years ago

Flying with the wind a plane went 386 km/h. Flying into the same wind the plane only went 318 km/h. find the speed of the plane

zysi [14]

Answer:

Speed of plane in air is 352 km/hr and speed of wind is 34 km/hr

Step-by-step explanation:

Average speed of plane in with wind = 386 km/h

Average speed of plane against wind = 318 km/hr

Consider the speed of plane in wind be x km/hr and speed of plane against wind be y km/hr

As such speed of plane in wind would be x + y km/hr and speed of plane against wind would be x - y km/hr. i.e

x+y = 386

x-y = 318

by solving these two equation, we get

2x=704

x= 352 km/hr

y=386 - 352

y= 34 km/hr

Hence, Speed of plane in air is 352 km/hr and speed of wind is 34 km/hr

5 0

4 years ago

What are the number factors for 81

choli [55]

1,3,9,27,81 are the number factor of 81.

5 0

4 years ago

Lucy has 1/5 of a pound of chocolates. She would like to make 4 gift bags with chocolates for her teachers.

Lapatulllka [165]

Answer:

0.05 pound of chocolate per gift bag or 1/20 pound of chocolate per gift bag

Step-by-step explanation:

1/5 divided by 4

=0.05 pound of chocolate per gift bag or 1/20 pound of chocolate per gift bag

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<h3><em><u>Hope this helped!! </u></em></h3>

3 0

3 years ago

Plz i need this asap, if you do not know all of them, plz do not answer

Lelechka [254]

1. sqrt 52 = 7.211 rounds to 7

2. irrational number

3. sqrt 441 = 21....rational

4. 12^2 + 3^2 = h^2
144 + 9 = h^2
153 = h^2
sqrt 153 = h
12.4 = h <===

5. 6^2 + b^2 = 18^2
36 + b^2 = 324
b^2 = 324 - 36
b^2 = 288
b = sqrt 288
b = 16.97 rounds to 17 <==

6. 39^2 + 52^2 = c^2
1521 + 2704 = c^2
4225 = c^2
sqrt 4225 = c
65 = c
(39 + 52) - 65 = 91 - 65 = 26 miles shorter <==

7. 4^2 + b^2 = 16^2
16 + b^2 = 256
b^2 = 256 - 16
b^2 = 240
b = sqrt 240
b = 15.49 rounds to 15.5 <==

8. ?

8 0

4 years ago