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MrMuchimi
1 year ago
6

Two new drugs are to be tested using a group of 60 laboratory mice, each tagged with a number for identification purposes. Drug

A is to be given to 21 mice, drug B is to be given to another 21 mice, and the remaining 18 mice are to be used as controls. How many ways can the assignment of treatments to mice be made? (A single assignment involves specifying the treatment for each mouse—whether drug A, drug B, or no drug.) (Enter the exact number or an equivalent algebraic expression.)
Mathematics
1 answer:
lakkis [162]1 year ago
8 0

Answer:

4.979044478499338 × 10²⁶

Step-by-step explanation:

Combination can be used to determine the number of ways the mice can be selected for the drugs (A, B) and the control group.

Combination factorial is define by  ⁿCr = \frac{n!}{(n-r)!r!}

21 group of mice receiving Drug A  can be selected in ⁶⁰C₂₁ = \frac{60!}{21!39!}

(60 - 21 = 39 ) mice remained for selection of 21 mice for the second drug

Drug B 21 mice can be chosen with ³⁹C₂₁ = \frac{39!}{21!18!}

( 39 - 21 = 18)  remained for control with ¹⁸C₁₈ = \frac{18!}{18!0!}

The number of ways the mice can be chosen for drug A, drug B and the control = ⁶⁰C₂₁ × ³⁹C₂₁ × ¹⁸C₁₈ = \frac{60!}{21!39!} × \frac{39!}{21!18!} × \frac{18!}{18!0!} = 4.979044478499338 × 10²⁶

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A summer camp cookout is planned for the campers and their families. There is room for 525 people. Each adult costs $9, and each
zaharov [31]

x+y≤525 and 9x+5y≤1200 represents the scenario.

Step-by-step explanation:

Given,

Room for people at summer camp = 525 people

Maximum budget = $1200

Cost per adult = $9

Cost per camper = $5

It means that there cannot be spent more than $1200.

x represents the number of adults.

y represents the number of campers.

x+y≤525      

9x+5y≤1200

x+y≤525 and 9x+5y≤1200 represents the scenario.

Keywords: inequality, budget

Learn more about inequalities at:

  • brainly.com/question/1517760
  • brainly.com/question/1522572

#LearnwithBrainly

6 0
1 year ago
A construction crew is lengthening a road. The road started with a length of 54 miles, and the crew is adding 3 miles to the roa
patriot [66]
53+3(D) = L

53 + 3(38) =L

53 +114 = L

167=L
6 0
1 year ago
Two planes, A and B, start from the same place and move in different directions, making an angle of 50º between them. The speed
cluponka [151]

Answer: The distance between them is 230.65 miles.

Step-by-step explanation:

Since we have given that

Speed of plane A (b) = 200 miles per hour

Speed of plane B (c) = 300 miles per hour

Angle between them = 50°

So,

We will use the "Cosine formula", we get

a^2=b^2+c^2-2bc\cos A\\\\a^2=200^2+300^2-2\times 200\times 300\cos 50\textdegree\\\\a^2=40000+90000-120000\cos 50\textdegree\\\\a^2=130000-120000\times 0.64\\\\a^2=130000-76800\\\\a^2=53200\\\\a=\sqrt{53200}\\\\a=230.65\ miles\ per\ hour

So, distance between the two planes after one hour will be

Distance=\frac{Speed}{time}=\frac{230.65}{1}=230.65\ miles

So, the distance between them is 230.65 miles.

6 0
2 years ago
Read 2 more answers
How many units of a 10% solution are needed to prepare 500 units of a 2% solution?
Akimi4 [234]
First find how many units of solution there is:

500* 2% = 500(.02) = 10 units

You need 10 units of solution in 'x' units of a 10% solution.

x*10% = 0.1x = 10 units   ----->  x = 10/0.1 = 100

100 units are needed
8 0
2 years ago
A grapefruit has a peel that is 1cm thick and a total diameter of 12cm. What percentage of volume of the grapefruit is the peel?
ira [324]

Answer:

0.3056 or 30.56%

Step-by-step explanation:

The volume of the grapefruit with the peel is:

V_p=\frac{4 \pi (d/2)^2}{3}\\V_p=\frac{4 \pi (12/2)^2}{3}\\V_p=48 \pi

When removing the peel, the grapefruit diameter becomes 10 cm (take out 1 cm of peel from each side). The volume of the grapefruit without the peel is:

V_n=\frac{4 \pi (d/2)^2}{3}\\V_n=\frac{4 \pi (10/2)^2}{3}\\V_n=33.333 \pi

The percentage of the volume correspondent to the peel is given by the difference between both volumes, divided by the total volume:

\%P = \frac{48\pi - 33.333\pi}{48\pi}\\ \%P =0.3056 = 30.56\%

30.56% of volume of the grapefruit is the peel.

4 0
2 years ago
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