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2 years ago

11

An election ballot asks voters to se4five city commissioners from a group of fifteen candidates. In how many wsys can this be do

ne

1 answer:

svp [43]2 years ago

8 0

That's "15 choose 5"

$\displaystyle{15 \choose 5} = \dfrac{15! }{5! 10!} = \dfrac{15 \cdot 14 \cdot 13 \cdot 12 \cdot 11}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} = (15/(5(3))(14/2)(13)(12/4)(11)\\\\= 7(13)(3)(11)=231(13)=3003$

Answer: 3003 ways

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A compressed air tank carried by scuba divers has a volume of 8.00 L and a pressure of 141 atm at 22.0°C. What is the volume (in

weqwewe [10]

Answer:

Volume of air in the tank =1,044 Liter

Step-by-step explanation:

Given:

Tank volume = 8 Liter

Pressure = 141 atm

Temperature = 22°C = 273° + 20° = 295° K

Find:

Volume of air in the tank = ?

Computation:

$\frac{Pressure\times Tank\ volume}{Tempreture} =\frac{Pressure\times Air\ volume}{Tempreture}\\\\\frac{141\times 8}{295} =\frac{1\times Air\ volume}{273.15}\\\\\frac{1,128}{295} =\frac{Air\ volume}{273.15}\\\\Air\ volume=1,044.45$

Volume of air in the tank =1,044 Liter

8 0

2 years ago

Evaluate this exponential expression 7 • (6+2)^2 - 3^2=

Lelu [443]

Answer: 441

Step-by-step explanation:

$7*(6+2)^2-3^2$

$7*8^2-3^2$

$7*64-9$

$448-9$

441

3 0

1 year ago

find the third,fifth and seventeenth terms of the sequence described by each explicit formula f(n)=8+3(n-1) and how you got it

alexira [117]

Answer:

Step-by-step explanation:

plug in 3 , 5 and 17 for n

8 + 3(3 -1) = 8 + 6 = 14

8 + 3(5-1) = 8 + 12 = 20

8 + 3(17-1) = 8 + 48 = 56

3 0

2 years ago

Hey could someone please help me with this really hard assignment is taking me forever. Thank you marking brainliest!

rewona [7]

Answer:

Exercise 1: The length of the unknown leg is 4 inches.

Exercise 3: The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4: Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

Step-by-step explanation:

Exercise 1:

Let suppose that triangle represented in the figure is a right triangle, the length of the missing leg is determined by Pythagorean Theorem:

$y = \sqrt{l^{2}-x^{2}}$ (1)

Where:

$l$ - Hypotenuse, in inches.

$x$ - Known leg, in inches.

$y$ - Unknown leg, in inches.

If we know that $l = 11\,in$ and $x = 10\,in$ , then the length of the unknown leg is:

$y = \sqrt{21}$

Since 4 is the least whole number closest to $\sqrt{21}$ , then we conclude that the length of the unknown leg is 4 inches.

Exercise 3:

The range of possible lengths for the missing side of the triangle is represented by the following simultaneous inequality:

$x + y > l > x-y$ (2)

Where:

$x$ - Greater side, in inches.

$y$ - Lesser side, in inches.

$l$ - Missing side, in inches.

If we know that $x = 8\,in$ and $y = 6\,in$ , then we have the following range of missing sides:

$14\,in > l > 2\,in$

The following straws can be used to construct the triangle: b) $3\,in$ , c) $4.5\,in$ , d) $6.5\,in$ , e) $10\,in$ , f) $13.5\,in$

Exercise 4:

Let check each pair to determine possible constructions by means of the inequality used in Exercise 3:

(i) $x = 4\,in, y = 2\,in$

$6\,in>l>2\,in$

Possible choices: 5 inches.

(ii) $x = 5\,in, y = 2\,in$

$7\,in > l > 3\,in$

Possible choices: 4 inches, 6 inches.

(iii) $x = 6\,in, y = 2\,in$

$8\,in > l > 4\,in$

Possible choices: 5 inches, 6 inches.

(iv) $x = 10\,in, y = 2\,in$

$12\,in > l > 8\,in$

Possible choices: None.

(v) $x = 5\,in, y = 4\,in$

$9\,in > l > 1\,in$

Possible choices: 2 inches, 6 inches.

(vi) $x = 6\,in, y = 4\,in$

$10\,in > l > 2\,in$

Possible choices: 5 inches.

(vii) $x = 10\,in, y = 4\,in$

$14\,in > l > 6\,in$

Possible choices: None.

(viii) $x = 6\,in, y = 5\,in$

$11\,in > l > 1\,in$

Possible choices: 2 inches, 4 inches, 10 inches.

(ix) $x = 10\,in, y = 5\,in$

$15\,in > l > 5\,in$

Possible choices: 6 inches.

(x) $x = 10\,in, y = 6\,in$

$16\,in > l > 4\,in$

Possible choices: 5 inches.

Possible options of this exercise: 1) (2, 4, 5), 2) (4, 5, 6), 3) (5, 6, 10), 4) (1, 2, 11), 5) (1, 4, 11), 6) (1, 10, 11)

7 0

2 years ago

Read 2 more answers

What would be an equation and answer to the equation for The product of 6 and 3 more than k is 48

My name is Ann [436]

You know what product means right? (+,-,×,÷)

7 0

2 years ago