There are 715 ways to select 9 players for the starting lineup.
Permutation is used whenever there is arrangement or where order is important . denoted by [tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]
n= no of item , r = no of items to be arranged.
Combination is used when there is selection . denoted by[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]
n=no of item , r= no of item to be selected.
Part (a)
In the given question
we have to select 9 players out of 13 player , combination will be used
[tex]C(13,9)=\frac{13!}{9!*(13-9)!}=\frac{13*12*11*10*9!}{9!*4!} =\frac{13*12*11*10}{4*3*2}[/tex]=715 ways.
Part(b)
In this part we have to find how many ways are there to select 9 players for the starting lineup and a batting order for the 9 starters.
Since the batting order is important , permutation will be used.
[tex]P(13,9)=\frac{13!}{4!} =\frac{13*12*11*10*9*8*7*6*5*4!}{4!} =13*12*11*10*9*8*7*6*5[/tex]
=259459200 ways.
Part(c)
In this part we have to do selection of 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
Since order is not important Combination will be used.
To select 3 left handers from total 6 left handers = C(6,3)
& to select 6 positions of left handers from remaining 7 right handers=C(7,6)
No of ways of selection = C(6,3)*C(7,6)
[tex]=\frac{6!}{3!*(6-3)!} *\frac{7!}{6!*(7-6)!} \\ \\= \frac{6!}{3!*3!} *\frac{7!}{6!*1!} \\ \\[/tex]
On solving further we get
[tex]= \frac{7!}{3!*3!} =\frac{7*6*5*4*3!}{3!*3*2*1} =7*5*4=140ways[/tex]
Therefore ,(a)There are 715 ways to select 9 players for the starting lineup.
(b) there are 259459200 ways to to select 9 players for the starting lineup and a batting order for the 9 starters and 140 ways .
(c)there are 140 ways to select 3 left-handed outfielders and have all other 6 positions occupied by right-handed players.
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Directions: Use what you have learned this week in class to answer the question. You should show your work or explain your reasoning in mathematical terms. Be specific. Draw a picture if you need to.
Question:
Evelyn has some paracord with a total length of 5-½ meters. She needs to cut the cord into 12 equal portions. What is the length of each piece written as a fraction? Is this value rational or irrational; why?
Work/Reasoning & Answer:
The above number divided 12 equal parts is given as 0.45833333333. In fraction, this is represented as: 45833333329/99999999990.
Hence it is right to conclude that it is an irrational number.
What is an irrational number?
An irrational number is any real number that cannot be expressed in fraction form.
Non-terminating, non-repeating decimals, such as 0.45445544455544445555..., are included. Irrational numbers are any square roots that are not perfect roots.
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Two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting and then selecting .
The probability of a given event gives a result of 0.00037. It is generated by applying the basic concepts of probability to the assigned problem.
What is probability?
Probability depicts the number of possibilities of how many times an event can occur. The probability of happening of an event invariably lies between 0 and 1. For a sure event, it is always 1. Its formula is given as P(E) = No. of favourable outcomes / Total no. of outcomes
Calculation of finding the probability according to the conditions specified
The entire number of cards in a standard deck = 52
Total number of favourable outcomes = 1
The probability of selecting two cards is given by P(E1) which is equal to 1 / 52
P(E1) = 1 / 52
Another card is selected without replacing the first card, so the total number of cards in the deck becomes 51. The probability of selecting a card from these 51 cards is given by P(E) i.e. (1 / 52) × (1 / 51)
P(E) = 1 / 2652
P(E) = 0.00037
Hence, the required probability is given by 0.00037.
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charlies mom just had a baby. he notices that they use an average of 9 dipers per day. At this rate, how many total dipers will they use during June and july this year?
We get that the total dipers that Charlie's mom will use in the month of June and July will be 549 dipers.
Charlie's mom uses an average of 9 diapers a day.
Average = 9
Average means a number that is calculated by adding quantities together and dividing the total by the number of quantities.
Average = Sum of observations / number of observations
A = S / N
We know that:
June has = 30 days
July has = 31 days.
Total days = 30 days + 31 days = 61 days
N = 61
Let the sum = S be x.
Substituting the values in the formula, we get that:
9 = S / 61
S = 9 × 61
S = 549
Therefore, we get that the total dipers that Charlie's mom will use in the month of June and July will be 549 dipers.
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NEED THIS ASAP PLEASE HELP
Bob's Gift Shop sold 200 cards for Mother's Day. One salesman, Bao, sold 2% of the cards sold for Mother's Day. How many cards did Bao sell?
Someone please help me
The type of reasoning utilized in each of the given sentences are;
1) Inductive reasoning
2) deductive reasoning
3) Inductive reasoning
4) Deductive reasoning
5) Deductive reasoning
What is Inductive and Deductive Reasoning?
Inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory.
1) This statement depicts inductive reasoning because it is trying to develop a theory that that studying for a test earns you good grades.
2) This statement depicts deductive reasoning because you are testing an existing theory that red meat has iron in it to draw a conclusion that the steak on your plate has iron in it.
3) This statement depicts inductive reasoning because you are trying to develop a theory that sum of all angles in a triangle is 180 degrees.
4) This statement depicts deductive reasoning because you are testing an existing theory that parallelograms have two pairs of parallel sides to conclude that rectangles also have two pairs of parallel sides.
5) This is deductive reasoning.
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Which rational number equals 0.5?
solve the inequality 5(a - 5) greater than 25
Answer:
5a-25=bigger than 25
a=bigger than 10
Step-by-step explanation:
Answer:
a>10
Step-by-step explanation:
10-5=5
5 times 5=25
So a must be bigger than 10
Which expression is NOT equivalent to 24+12?
3(8+9)
4(6+2)4(6+2)
4(6+12)4(6+12)
4(6+3)4(6+3)
|n| = 5 brainly help
Answer:
Here is the answer: n = 5 or n = -5
Solve the linear equation x/3-7=-5
Answer:
x = 6
Step-by-step explanation:
[tex]\frac{x}{3} -7=-5[/tex]
→ Add 7 to both sides
[tex]\frac{x}{3} =2[/tex]
→ Multiply both sides by 3
x = 6
translate and solve: 6 fewer than s is no less than −78. (write your solution in interval notation.)
When 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)
Interval notation is a way of writing subsets of the real number line
Given,
6 fewer than s is no less than -78
6-s < -78
Move 6 to right hand side
-s < -78-6
-s < -84
s > 84
Then the interval notation is (84,∞)
Hence, when 6 fewer than s is no less than −78, the solution in interval notation is (84,∞)
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X-3 5X-3X-12-4x + 18X-7
Answer:
Algebraic Expressions- An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc. For example, let us have a look at the expression 2x + 4. Thus, we can say that 2x + 4 is an example of an algebraic expression.
Here are more examples:
• 5x + 4y + 10
• 2x2y - 3xy2
• (-a + 4b)2 + 6ab
To simplify an algebraic expression, we just combine the like terms. Hence, the like variables will be combined together. Now, out of the like variables, the same powers will be combined together
Multiply the numbers
x - 3 . 5x – 3x -12 - 4x + 18x - 7
= x – 15x - 3x – 12 – 4x + 18x – 7
Subtract the numbers
= x – 15x – 3x – 12 – 4x + 18x - 7
= x – 15x – 3x – 19 - 4x + 18x
Combining the like terms
= - 2x – 19
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25 points!
answer possibilities: A, B, C or D?
Answer:
A
Step-by-step explanation:
[tex]\frac{2xy}{-4x^3y^2}[/tex] ( cancel 2 and - 4 by 2 )
= [tex]\frac{xy}{-2x^3y^2}[/tex] ( cancel x on numerator/ denominator )
= [tex]\frac{y}{-2x^2y^2}[/tex] ( cancel y on numerator/ denominator )
= [tex]\frac{1}{-2x^2y}[/tex]
Change the following statement into coordinate points
a)f(-1)=1
b)f(2)=7
c)f(1)=1
d)f(3)=0
Changing [f(-1) = 1] into coordinate points, we get (x₁, y₁) = (-1, 1),
Changing [f(2) = 7] into coordinate points, we get (x₂, y₂) = (2, 7),
Also, changing [f(1) = 1] into coordinate points, we get (x₃, y₃) = (1, 1),
And finally, changing [f(3) = 0] into coordinate points,
We get (x₄, y₄) = (3, 0).
As per question statement, we are provided with Four separate functions, as follows, [f(-1) = 1], [f(2) = 7], [f(1) = 1] and [f(3) = 0].
We are required to convert the above mentioned functions into coordinate points.
To solve this question, we need to know the standard form of conversion of functions into coordinate points, which goes as [y = f(x)], i.e., the ordinate is a function of the abscissa.
Thus comparing [y = f(x)] to [1 = f(-1)], we get (x, y) = (-1, 1).
Similarly, comparing [y = f(x)] to [7 = f(2)], we get (x, y) = (2, 7),
Comparing [y = f(x)] to [1 = f(-1)], we get (x, y) = (-1, 1),
And finally, comparing [y = f(x)] to [0 = f(3)], we get (x, y) = (3, 0).
Function: In Mathematics, a function is an operator which when provided with a input, gives a certain output.Coordinate Points: The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane by using the horizontal and vertical distances from the two reference axes.To learn more about Coordinate Points, click on the link below.
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how do you solve this
Answer:
F(x) =y
Step-by-step explanation:
He ask you what x equal when y=4 it will be 3 inshallah
Given m ∥ n m∥n, find the value of x. m n t (x+9)° (2x+6)°
Evaluate the expression and enter your answer in the box below.
|34|
Answer:
34
Step-by-step explanation:
the absolute value function always gives a positive result , that is
| - a | = | a | = a , then
| 34 | = 34
Find the equation of a straight line passing through the point (2, 3) and makes an angle 60° with the x-axis. Hono
Answer:
Equation of a straight line, y=mx+c
i.e. y=
3
x+3
Therefore, y=
3
x+3 is the required equation of the line
Step-by-step explanation:
Is the inequality x ≤ 6 equivalent to the inequality
x-5≤6-5?
Explain your reasoning
Step-by-step explanation:
two inequalities are equivalent if they have the same set of solution
x - 5 < 6 - 5
x - < 1 Ladd 5 to both sides
x < 6
this is not with the question but the is a _ under all the < it didn't let me do it
What are the x- and y-intercepts of the function f(x) = -² + 4x − 4?
Select all correct answers.
The point (0,2) is an x-intercept of the function.
The point (2,0) is an x-intercept of the function.
The point (0,-4) is a y-intercept of the function.
The point (-2,0) is an x-intercept of the function.
The point (-4,0) is a y-intercept of the function.
Answer:
x-intercept(s): (2,0)
y-intercept(s): (0,-4)
Step-by-step explanation:
Question 3: A family is traveling in their RV all summer. They have several propane tanks on their RV. Propane is safe to use between temperatures of −40° F and 120° F.
Write an inequality to represent the temperatures at which the propane is safe to use.
The inequality to represent the temperatures at which the propane is safe to use is -40 < x < 120.
It is said that it is safe to use Propane between the temperatures of -40°C and 120°C.
We already know the use of an equality. It makes the values on both sides of it equivalent.
An inequality compares the values on both sides of it. It informs us which one is greater than or less than the other or if they are equal. That is, inequality has a possibility for equality too.
Here the minimum temperature at which propane is safe to use = -40°C
The maximum temperature at which Propane is safe to use = 120°C
We take a variable 'x' to denote the safe temperature of Propane.
Then according to the information, the inequality to represent the temperatures at which the propane is safe to use is,
-40 < x < 120
An inequality is written with the bigger value is in the open end of '<' and the lower value at the other end.
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A betta fish tank is in shape of a cube. The volume of the fish tank is 216 cubic inches. What is the edge length, in inches, of the fish tank?
Considering the definition of volume and volume of a cube, the edge length of the fish tank is 6 inches.
Definition of volumeAll matter occupies a space that can vary depending on its size. This space can be defined by volume, which is defined as the extension of an object in its three dimensions. That is, the volume corresponds to the measure of the space that a body occupies.
Volume of a cubeThe cube is a polyhedron or three-dimensional geometric figure, with six equal sides, each of which is a regular polygon, that is, a square. In other words, a cube is a body made up of six faces that are square.
The volume of a cube is equal to the measure of its side to the cube:
Volume = side x side x side = side³
Edge length of the fish tankIn this case, you know that:
The volume of the fish tank is 216 cubic inches.The fish tank is in shape of a cube.Replacing in the definition of volume of a cube:
216 cubic inches = side³
Solving:
∛216 cubic inches= side
6 inches= side
Finally, the edge length of the fish tank is 6 inches.
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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.If two angles are congruent, then they are vertical angles.
The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles
How to determine the truth value of the conditional statement?The conditional statement is given as:
If two angles are congruent, then they are vertical angles.
The above statement is false because not all congruent angles are vertical angles
A counterexample of this statement is a corresponding angle
i.e. corresponding angles are congruent angles, but they are not vertical angles
Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle
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The sum of two numbers is twenty-one. one number is eighteen less than two times the other. find the numbers.
Answer:
The sum of two numbers is twenty-one. one number is eighteen less than two times the other =
8 and 13
Evaluating Functions → Finding the
->
Output
f(x) = 5x + 6
Find f(3)
21 is the value of function f(3) .
What is function?
A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.Four main categories can be used to classify different sorts of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.f(x) = 5x + 6
f(3) = 5(3) + 6 = 15 + 6 = 21
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use the distributive property to find the quotient 628/2
Answer:
314
Step-by-step explanation:
Help me please what is 25,473+13,648+15,306
Answer:
54,427
here's your answer
Solve using PEMDAS
11²-[3. (8-5)*7-19=
Step-by-step explanation:
The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
Answer:
39.
Step-by-step explanation:
I say good try to the first guy, but aye, it's not fully answering the question.
PEMDAS is the order you solve all of this in. Parenthesis (), Exponents (^), Multiplication (*), Division (/), Addition (+), and Subtraction (-).
We would solve (8-5) first for 3, since there is no sign between both three's, this will be multiplication.
Next is the exponent, 11^2 is 11*11, which is equal to 121.
121 - 3 * 3 * 7 - 19
Next up is Multiplication. 3 * 3 = 9, and 9 * 7 is 63.
Now our equation is 121 - 63 - 19. There is no Division or addition symbol, so we skip to Subtraction.
121 - 63 = 58, and 58 - 19 = 39.
Your Answer is 39.
-1/2 x -3/5 this is what i need help with.
Answer:
3/10 or 0.3
Step-by-step explanation:
The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 42 inches. Find the length and width of the rectangle.
Answer:
The length of the rectangle is 11 inches, and the width of the rectangle is 10 inches.
Step-by-step explanation:
Let l be the length of the longer side of the rectangle. Then the width of the rectangle is l-1 inches. Since the perimeter of the rectangle is 42 inches, we have:
2(l + l - 1) = 42
l + l - 1 = 21
2l = 22
l = 11 inches, so l - 1 = 10 inches