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3 years ago

Find the area 12 6 5 14

Mathematics

1 answer:

oee [108]3 years ago

4 0

Answer:

Step-by-step explanation:

In this shape we have to use the formula: A= 1/2xbxh

So we use this formula. 1/2 X (5 X 14)= 35

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The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 15c

Alexus [3.1K]

Answer:

a) 5.13% probability that all of the offices are filled by members of the debate team

b) 2.56% probability that none of the offices are filled by members of the debate team

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the people are chosen is important, since the first person is the president, the second is the vice president and so on... So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

(a) What is the probability that all of the offices are filled by members of the debate team?

Desired outcomes:

4(president, vice president, secretary, and treasurer) offices from a set of 8(candidates of the members debate team).

$D = P_{(8,4)} = \frac{8!}{(8-4)!} = 1680$

Total outcomes:

4 offices from a set of 15 candidates.

$T = P_{(15,4)} = \frac{15!}{(15-4)!} = 32760$

Probability:

$P = \frac{D}{T} = \frac{1680}{32760} = 0.0513$

5.13% probability that all of the offices are filled by members of the debate team

(b) What is the probability that none of the offices are filled by members of the debate team?

Desired outcomes:

4(president, vice president, secretary, and treasurer) offices from a set of 7(candidates who are not of the members debate team).

$D = P_{(7,4)} = \frac{7!}{(7-4)!} = 840$

Total outcomes:

4 offices from a set of 15 candidates.

$T = P_{(15,4)} = \frac{15!}{(15-4)!} = 32760$

Probability:

$P = \frac{D}{T} = \frac{840}{32760} = 0.0256$

2.56% probability that none of the offices are filled by members of the debate team

7 0

3 years ago

Find the equation of the line containing the point (-3,5) and having slope: 4

alina1380 [7]

Answer: d) y=4x+17

remember y=mx+b

good luck

5 0

2 years ago

How do I simplify this expression

sergij07 [2.7K]

You have to put 2 to the power of five. than multiply both exponents by 5 so 3x5 then 2x5. So your answer should be 32 exponent of 15 than x with an exponent of 10.

3 0

2 years ago

Andre's band is made up of 6 members. Thete are 3 guitar players, 1 drummer, and 2 singers. What id the ratio od drummers to sin

gogolik [260]

Answer:

C. 1/2

Step-by-step explanation:

Since there is 1 drummer and 2 singers, the ratio is 1 to 2.

5 0

2 years ago

1. Find all values of $x$ such that the fraction x/(x - 5) = the fraction 4/(x - 4)

Ksju [112]

1. x/(x - 5) = 4/(x - 4)

x (x - 4) / ((x - 5) (x - 4)) = 4 (x - 5) / ((x - 5) (x - 4))

x (x - 4) = 4 (x - 5)

x² - 4x = 4x - 20

x² - 8x = -20

Solving for x by completing the square gives

x² - 8x + 16 = -4

(x - 4)² = -4

x - 4 = ± 2i

x = 4 + 2i or x = 4 - 2i

2. Since -7 + 2i and -7 - 2i are roots of the given quadratic, we have

z² + bz + c = (z - (-7 + 2i)) (z - (-7 - 2i))

z² + bz + c = (z + (7 - 2i)) (z + (7 + 2i))

z² + bz + c = z² + ((7 - 2i) + (7 + 2i)) z + (7 - 2i) (7 + 2i)

z² + bz + c = z² + 14z + 53

so that b = 14 and c = 53, which makes b + c = 67.

3. If x + y = 4, then

x³ + y³ = 100

x³ + (4 - x)³ = 100

x³ + (64 - 48x + 12x² - x³) = 100

12x² - 48x + 64 = 100

12x² - 48x = 36

x² - 4x = 3

and by completing the square,

x² - 4x + 4 = 7

(x - 2)² = 7

x - 2 = ± 7

x = 2 + 7 or x = 2 - 7

x = 9 or x = -5

If x = 9, then y = -5, so one pair of solutions would be (x, y) = (9, -5).

4 0

1 year ago