I need help with this question

Answers

Answer 1

Probability that first three price winners are omar, kira and elsa is [tex]\frac{1}{84}[/tex]

Probability that omar is first prize winner and kira is second prize winner and elsa is third price winner is [tex]\frac{1}{504}[/tex]

What is permutation and combination ?

When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.

(i)First 3 prizes must be given to 3 persons regardless of order

Hence they can also be arranged in 3! ways.

est 6 can be arranged in 6! ways.

positions ___ ___ ___ ___ ___ ___ ___ ___ ___

number of ways 3 2 1 6 5 4 3 2 1

total number of ways to arrange 9 people = 9!

[tex]P(A)= \frac{(3)(2)(1)(6)(5)(4)(3)(2)}{(9).(8).(7).(6).(5).(4).(3).(2))}[/tex][tex]P(A)=\frac{6}{9.8.7}[/tex][tex]P(A)= \frac{1}{84}[/tex]

(ii)Event A

In event A three positions are fixed .

Omar -1 Kira -2 Elsa -3

Therefore there is only 1 way to fill the 1st,2nd and 3rd position

Permutations can only be made among the other positions.

Positions - ___ ___ ___ ___ ___ ___ ___ ___ ___

Number of ways- 1 1 1 6 5 4 3 2 1

Total number of ways of arranging 9 people =9×8×7×6×5×4×3×2×1

Number of ways to satisfy event A =1×1×1×6×5×4×3×2×1

P(A)= [tex]\frac{(6)(5)(4)(3)(2)(1)}{(9)(8)(7)(6)(5)(4)(3)(2)(1)}[/tex]

P(A)= [tex]\frac{1}{504}[/tex]

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Related Questions

Evalúe the limit. Show steps

Answers

After evaluating the limit we have came to find that the limit of [tex]\lim_{x\rightarrow 2 }\frac{\sqrt{x-1} -1}{x-2}[/tex]as x approaches 2 is 0.5

What is limit?

As an input or as an index approaches a specific value in mathematics, a limit is the value that the function, sequence, or index approaches. The definitions of continuity, derivatives, and integrals all require limits, which are fundamental to calculus and mathematical analysis.

In addition to having a connection to the category theory concepts of limit and direct limit, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit we will use L'Hôpital's Rule

Find the derivative

⇒ [tex]\lim_{x\rightarrow 2 }\frac{\sqrt{x-1} -1}{x-2}[/tex]

⇒ [tex]\lim_{x\rightarrow 2 } \frac{1/2(x-1)^{-1/2}}{1}[/tex]

⇒ [tex]\lim_{x\rightarrow 2 } \frac{1}{2\sqrt{x-1} }[/tex]

Evalúe 2 as x

⇒ [tex]\frac{1}{2\sqrt{(2)-1} }[/tex]

⇒ [tex]\frac{1}{2\sqrt{1} }[/tex]

⇒ [tex]\frac{1}{2}[/tex]

⇒ 0.5

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Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual
mean of 53.2 degrees.
Low Temperature (o F)
Frequency
40-44 45-49 50-54 55-59
1
6
9
6
The mean of the frequency distribution is
(Round to the nearest tenth as needed.)
degrees.
...
60-64
3

Answers

Answer:

7777777777777777777777770

Step-by-step explanation:

7777777777777777777777770

go fast if you are smart.

see attachment beloww.

Answers

[tex]3x + x + (x + 12) = 152[/tex]

<AOD =<COB(VERTICAL OPPOSITE ANGLES)

[tex]3x + x + x = 152 - 12 \\ 5x = 140 \\ \frac{5x}{5} = \frac{140}{5} \\ x = 28[/tex]

x=28°

be reminded that <COB IS MADE OF ALOT OF BRANCH ANGLES THAT WE HAD TO ADD TO GET IT

i.e <COE,<EOF AND <FOB

Answer:x=28°

Step-by-step explanation:

152=3x+x+x+12

152=5x+12

140=5x

x=28

A submarine at -20 feet descends 30 feet. What is the submarine's current location after the descent

Answers

The current location of the submarine would be -50 feet.

How to find the level of descent of the submarine

The questions says that the submarine was at -20 feet already.

Now it says that it descended 30 feet. Remember that the descent refers to a fall. Hence the way that it would be represented would be through the use of a negative sign.

This would be -30

The current location of the descent of the submarine would be

-20 - 30

= -50 feet

Therefore the current location of the submarine would be -50 feet.

Answers

Answer: 0.6

Step-by-step explanation: To find the decimal you seek, you put 12 over 20, 12/20. That means you divide it, so 12 divided by 20 is 0.6, or 60%.

HELP! 100 POINTS!!!
A baking company has developed two new cookie recipes, however, they only have the resources to add one item to their product line. They decide to randomly sample three groups of 100 people to determine which cookie recipe, A or B, is preferred. The results are shown in the following table.

Recipe A Recipe B
Sample #1 26 67
Sample #2 48 89
Sample #3 22 56

A. Based on the collected data, which recipe should the baking company add to their product line? How confident should the company be in their decision? Explain your reasoning using complete sentences.

B. Using the mean of the data for Recipe A, approximately what percentage of people would you expect to prefer Recipe A over Recipe B?

Answers

Answer:

Question A: They should add product B because it has a 69% rate of approval. They can be 69% confident that the addition of product B will be successful.

Question B: 31% of people would prefer cookie A over cookie B

Step-by-step explanation:

What is the sum of the first 7 terms for the geometric sequence with first term 3, seventh
term 46,875, and common ratio 5?

A. 58,593
B. 19,531
C. 35,154

Answers

The sum of the first 7 terms for the geometric sequence with first term 3, seventh term 46,875, and common ratio 5 is 58,583.

A geometric progression is a sequence where each and every succeeding term is formed by multiplying the preceding term by a constant number. That constant number is called common ratio.

The common ratio is provided to be 5. While the first term is 3.

The seventh term is 46875.

The formula for sum of n terms of a GP is,

Sn = a(rⁿ-1)/(r-1)

We have to find sum of seven terms,

Sn = a(r⁶.r - 1)/(r-1)

Putting,

a = 3

r = 5

n =6

Sn = 3(5⁶.5 - 1)/(5-1)

Sn = (3.5⁶.5 - 3)/4

Sn = (46875×5 - 3)/4

Sn = (234375-3)/4

Sn = 234372/4

Sn = 58593.

The sum is 58593.

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please answer correctly 50 points

Answers

Answer:3

Step-by-step explanation:

the original price of an article was 240.00. The price is increased by 12½%. The new price of the article is?

Answers

Answer:

The new price of the article is $270

Step-by-step explanation:

270-240/240

x 100% = 12.5%

12.5x240/100

= 30

Which complex number has an absolute value of 5?

Answers

Answer is
-3+4i
Hope this helps

What is an equation in slope-intercept form for the line
perpendicular to y = 3x + 9 that
contains (-6, 3)?

Answers

An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.

What is slope-intercept form?

The most "popular" type of a straight line is one with a slope-intercept. Due to its simplicity, this is helpful to a lot of students. The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.

The equation for a line written in slope-intercept form

y = mx + b

Where,

m is the slope, and b is the y-intercept.

We know that the slope of a line perpendicular to given equation becomes reciprocal with opposite sign.

So, here slope is 3 and in perpendicular line it will become -1/3.

Now we will go with slope-intercept form and put the values (-6, 3) as x and y in y = mx + b

⇒ 3 = -1/3(-6) + b

Lets solve for b

⇒ b = 3 - ( -1/3(-6))

= 3 - (2)

= 1

Now we have the desired equation

3 = -1/3(-6) + 1

Thus, An equation in slope-intercept form for the line perpendicular to y = 3x + 9 that contains (-6, 3) is 3 = -1/3(-6) + 1.

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Leroi is using coordinate geometry to prove this theorem.
Theorem: The diagonals of a parallelogram bisect one another.
Given: AD//BC; AB//CD; AC and BD intersect at M.
Prove: M bisects AC and BD.
Which of these is the BEST strategy for this proof?
A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD
B) Use the equations of line AC and line BD to find the coordinates of M, then use the Distance Formula to verify that AC= BD
C) Use the equations of line AC and line BD to find the coordinates of M, then use the midpoint Formula to verify that M is the midpoint of both AC and BD
D) Use the Distance Formula to find the coordinates of M, then use the Midpoint Formula to verify that M is the midpoint of both AC and BD

Answers

The BEST strategy for this proof is (A) Use the Midpoint Formula to find the coordinates of M, then use the Distance Formula to verify that AC= BD

How to determine the best strategy for the proof?

The theorem is given as

Theorem: The diagonals of a parallelogram bisect one another.

Also, we have the following given parameters

AD//BC; AB//CD;

AC and BD intersect at M.

The above means that:

Lines AD and BC are parallel lines, and AB and CD are parallel lines

The statement AC and BD intersect at M implies that

AM = MC and BM = MD.

The above means that we need to calculate the lengths of the above segments, and then make comparison

The lengths of the segments can be calculated using the distance formula

Other than that, the coordinate of the point M needs to be calculated

The option that satisfies the above conditions is (a)

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The numbers of trading cards owned by 9 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
352, 409, 424, 471, 497, 503, 515, 525, 561
Send data to calculator
Suppose that the number 561 from this list changes to 768. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
OOO
It decreases by
It increases by
It stays the same.
It decreases by .
0.
It increases by 0.
It stays the same.
X
S

Answers

The mean increases by 23 and the median stays the same.

What are the mean and median?

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the middle value.

Given the data set: 352, 409, 424, 471, 497, 503, 515, 525, 561

(a) Mean = [tex]\frac{352+409+424+471+497+503+515+525+561}{9}[/tex]

Mean = [tex]\frac{4257}{9}[/tex]

= 473

The number 561 from this list changes to 768.

New mean = [tex]\frac{352+409+424+471+497+503+515+525+768}{9}[/tex]

= [tex]\frac{4464}{9}[/tex]

= 496

Thus, the mean increases by 496 - 473 = 23.

(b) Median = mid value

= 497

When the number 561 changes to 768, still the mid value will remain the same i.e. the median remains the same.

Therefore, the mean increases by 23 and the median stays the same.

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If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is
given by y = 88t - 16t².
When does the ball reach its maximum height? (Round to two decimal places)

Answers

If a ball is thrown directly upward with a velocity of 88 ft/s, its height (in feet) after t seconds is given by y = 88t - 16t².The ball will reach its maximum height at 121 feet.

Maximum height

Given equation:

y = 88t - 16t²

Maximum height dy/dt = 0

88-32t = 0

32t = 88

t = 88/32sec

t = 2.75sec

Hence,

Maximum height attained by the ball :

Maximum height attained by the ball = 88(2.75)-16(2.75)²

Maximum height attained by the ball = 242 - 121

Maximum height attained by the ball = 121 feet

Therefore the maximum height is 121 feet.

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let y=ln(x^2+y^2) determine y prime at the point -(e^4-16)^1/2

Answers

dy/dx = -2√e⁴ - 16/e⁴ - 8 is differential equation .

The meaning of a differential equation?

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics.

y = In( x² + y² )

now doing implicit differentiation

dy/dx = d/dx In( x² + y² )

dy/dx = 1/(x² + y² ) × d/dx ( x² + y² )

dy/dx = 1/x² + y² × ( 2x + 2y dy/dx)

(x² + y² )dy/dx = 2x + 2y dy/dx

dy/dx (x² + y² - 2y) = 2x

dy/dx = 2x/(x² + y² - 2y)

we need to calculate dy/dx at ( - √e⁴ - 16 , 4 )

dy/dx = [tex]\frac{2 * ( - \sqrt{e^{4} - 16} }{-\sqrt{(e^{4 - 16)^{2} }+ ( 4)^{2} - 2 * 4 } }[/tex]

dy/dx = - 2√e⁴ - 16/e⁴ - 16 + 16 - 8

dy/dx = -2√e⁴ - 16/e⁴ - 8

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Find the value of (-3/8) x (+8/15)

A. -1/5
B. -1/3
C. 11/15
D. 11/23

Answers

Answer: [tex]\Large\boxed{A. -\dfrac{1}{ 5}}[/tex]

Step-by-step explanation:

Given expression

[tex]-\dfrac{3}{8} \times \dfrac{8}{15}[/tex]

Combine the fractions

[tex]=\dfrac{-3\times 8}{8 \times 15}[/tex]

Cancel out the 8 on both the numerator and denominator

[tex]=\dfrac{-3}{ 15}[/tex]

Divide 3 on both the numerator and denominator

[tex]=\dfrac{-3\div 3}{ 15\div 3}[/tex]

[tex]=\Large\boxed{-\dfrac{1}{ 5}}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer is A. -1/5

Step by step

Multiply across and simplify

-3/8 x 8/15

-3 x 8 = -24 over 120

Simplified to -1/5

[tex]3-\sqrt{x} 5[/tex]

Answers

The value of the expression given as 3 - √x⁵ is 3 - x^2√x

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3 - √x⁵

Express 5 as the sum of 4 and 1