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nikdorinn [45]
3 years ago
10

There are 16 entrees available at a restaurant. From these, Archie is to choose 6 for his party. How many groups of 6 entrees ca

n he choose, assuming that the order of the entrees chosen does not matter? )If necessary, consult a list of formulas.)
Mathematics
1 answer:
Vikki [24]3 years ago
3 0

Answer:

8008

Step-by-step explanation:

This is the selection of 6 elements out of 16 elements. Applying the combination formula, the total number of selections is nCr with n =16 and r =6.

16C6 = 8008

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A ship is anchored off a long straight shoreline that runs north and south. From two observation points 16 miles apart on shore,
ELEN [110]
D - the shortest distance from the ship to the shore.
d / ( 17 - x ) = tan 32° = 0.62487
d / x = tan 53° = 1.32704
d = 0.62487 ( 17 - x )
d = 1.32704 x
0.62487 ( 17 - x ) = 1.32704 x
10.62279 - 0.62487 x = 1.32704 x
x = 10.62279 : 1.95191
x = 5.44226 miles
d = 5.44226 · 1.32704
Answer:
d = 7.222  miles
6 0
3 years ago
Please help! question is in the pic
steposvetlana [31]

Answer: 2 + 1 = 3      2 x 1 =2

Step-by-step explanation: + 7 = 7

5 0
3 years ago
A model of a 39 foot tall building was made by using the scale 1 in : 4.5 feet. What is the height of the model? Round your answ
Gnom [1K]
1 / 4.5 = x / 39....1 inch to 4.5 ft = x inches to 39 ft
cross multiply
(4.5)(x) = (1)(39)
4.5x = 39
x = 39 / 4.5
x = 8.7 inches <==

7 0
3 years ago
The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the tota
Dafna1 [17]

Answer:

a. The biomass weighs 2.30 * 10^7 kg after a year

b. It'll take 2.56 years to get to 4*10^7kg

Step-by-step explanation:

a.

k = 0.78,K = 6E7 kg

Given

dy/dt = ky(1- y/K)

Make ky dt the subject of formula

ky dt = dy/(1-y/K) --- make k dt the subject of formula

k dt = dy/(y(1-y/K))

k dt = K dy / y(K-y)

k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides

kt + c = ln(y/(K-y))

Ce^(kt) = y/(K-y)

Substitute the values of k and K

Ce^(0.78t) = y/(6*10^7 - y) ----- (1)

Given that y(0) = 2 * 10^7kg

(1) becomes

Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)

Ce° = (2*10^7)/(4*10^7

C = 2/7

Substitute 2/7 for C in (1)

2/7e^0.78t = y/(6*10^7 - y) ---(2)

We're to find the biomass a year later

So, t = 1

2/7e^0.78 = y/(6*10^7 - y)

0.62 = y/(6*10^7 - y)

y = 0.62(6*10^7 - y)

y = 0.62*6*10^7 - 0.62y

y + 0.62y = 0.62*6*10^7

1.62y = 0.62*6*10^7

1.62y = 3.72 * 10^7

y = 2.30 * 10^7kg.

Hence, the biomass weighs 2.30 * 10^7 kg after a year

b.

Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg

Substitute 4*10^7 for y in (2)

2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)

2/7e^0.78t = 4*10^7/2*10^7

2/7e^0.78t = 2

e^0.78t = (2*7)/2

e^0.78t = 2

t = 2 * 1/0.78

t = 2.56 years

Hence, it'll take 2.56 years to get to 4*10^7kg

8 0
3 years ago
Find the area of efg
butalik [34]
The area of EFG is 12 ft
6 0
3 years ago
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