The manager of a baseball team has 15 players to choose from for his nine person batting order. How many different ways can he arrange the players in the lineup. A.5005. B.362880. C.3603600. D.1816214400
Answer: D. 1816214400
Step-by-step explanation:
When we select r things from n things in order we apply permutations and the number of ways to select r things = [tex]^nP_r=\dfrac{n!}{(n-r)!}[/tex]
Given : Total player = 15
Required number of players for Batting order = 9
Then the number of different ways to select 9 person batting order so that he arrange the players in the lineup would be [tex]^{15}P_9=\dfrac{15!}{(15-9)!}[/tex]
[tex]=\dfrac{15\times14\times13\times12\times11\times10\times9\times8\times7\times6!}{6!}[/tex]
[tex]=1816214400[/tex]
∴ The number of different ways can he arrange the players in the lineup = 1816214400
Hence, the correct answer is D. 1816214400
Find the difference.
Correct and best explained answer gets brainliest.
A circle has a center of (5,-5) and goes through (6,-2). What is the radius?
What is the midpoint of (4,8) and (3,12)
The product of the roots of 8x² - 2x = 1 is:
Answer:
[tex]\text{Product of its zeros = }\frac{-1}{8}[/tex]
Step-by-step explanation:
The quadratic equation is given to be : 8x² - 2x = 1
We need to find the product of its zeros
First finding the number of zeros :
⇒ 8x² - 2x - 1 = 0
⇒ 8x² - 4x + 2x - 1 = 0
⇒ (4x + 1)(2x - 1) = 0
[tex]\implies x = \frac{-1}{4}\:\:and\:\: x = \frac{1}{2}[/tex]
[tex]\text{Product of its zeros = }\frac{-1}{4}\times\frac{1}{2}=\frac{-1}{8}[/tex]
Your goal is to save at least $240.00 over the next 4 week. How much money must you save each week in order to meet that goal? Write and solve an inequality
The solution is x ≥ $ 60
The value of the inequality equation is x ≥ 60
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Let the minimum money per week to be saved be = x
The number of weeks = 4
The goal is to save at least $240.00 over the next 4 week
So , substituting the values in the equation , we get
x ≥ 240 / number of weeks
x ≥ 240 / 4
On simplifying the equation , we get
x ≥ 60
Therefore , the value of A is x ≥ 60 and should save a minimum of $ 60 per week
Hence , the inequality equation is x ≥ 60
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what is the x-intercept of the graph of the function f(x)=x2-16x+64?
Answer:
x-intercept: (8,0)
Step-by-step explanation:
Given: [tex]f(x)=x^2-16x+64[/tex]
For x-intercept, Put y=0 and solve for x.
x-intercept: It is a point where y-coordinate zero.
[tex]x^2-16x+64=0[/tex]
[tex]x^2-8x-8x+64=0[/tex]
[tex](x-8)(x-8)=0[/tex]
Equate each factor to 0 and solve for x
x-8 = 0 , x-8 = 0
x=8,8
x-intercept: (8,0)
Hence, The x-intercept is 8.
The x-intercept of the function is 8
The equation of the function is given as:
[tex]f(x) = x^2 - 16x + 64[/tex]
Expand the equation
[tex]f(x) = x^2 - 8x - 8x + 64[/tex]
Factorize the above equation
[tex]f(x) = x(x - 8) - 8(x -8)[/tex]
Factor out x - 8
[tex]f(x) = (x - 8) (x -8)[/tex]
Set f(x) to 0, to calculate the x-intercept
[tex](x - 8) (x -8)=0[/tex]
Rewrite as:
[tex](x - 8)^2=0[/tex]
Take the square roots of both sides
[tex]x - 8=0[/tex]
Solve for x
[tex]x = 8[/tex]
Hence, the x-intercept of the function is 8
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he time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions? Image for option 1 Image for option 2 Image for option 3
Answer:
0 0
5 27.5
10 55
15 82.5
Step-by-step explanation:
Line segment
a.a series of points that extend in two directions without end plane
b.two lines that intersect at 90° angles perpendicular lines
c.lines that lie in the same plane and do not intersect line
d.a flat surface that extends infinitely and has no thickness parallel lines
e.part of a line that has two endpoints
Please, would somebody help me solve this math problem? I have no idea how to solve it.
An __________ is used to indicate the repeating part of a repeating decimal.
The relationship between feet and inches is described by the equation y = 12x, where x = a given length in feet and y = the equivalent length in inches. If a table is 7.25 feet long, what is its length in inches? A. 84 inches B. 87 inches C. 81 inches D. 90 inches
The length of the table in inches is 87 inches.
Explanation:To solve this problem, you can use the equation y = 12x to convert the length from feet to inches. Given that the table is 7.25 feet long, you can substitute x = 7.25 into the equation to find y.
y = 12(7.25) = 87
Therefore, the length of the table in inches is 87 inches.
What causes water molecules to stick together in liquid water?
A. Water vapor
B. Carbon dioxide
C. Sun's gravity
D. Hydrogen bonds
(05.01 MC)
The table and the graph each show a different relationship between the same two variables, x and y:
A table with two columns and 5 rows is shown. The column head for the left column is x, and the column head for the right column is y. The row entries in the table are 3,210 and 4,280 and 5,350 and 6,420. On the right of this table is a graph. The x axis values are from 0 to 10 in increments of 2 for each grid line. The y axis values on the graph are from 0 to 550 in increments of 110 for each grid line. A line passing through the ordered pairs 2, 110 and 4, 220 and 6, 330 and 8, 440 is drawn.
How much more would the value of y be in the table than its value on the graph when x = 11?
100
165
395
440
The value of y in the table is 165 more than the value of y in the graph
The points on the table are represented as:
(3,210) and (4,280)So, the equation of the table is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{280 - 210}{4 - 3} (x - 3) + 210[/tex]
[tex]y = 70(x - 3) + 210[/tex]
Expand
[tex]y = 70x - 210 + 210[/tex]
[tex]y = 70x [/tex]
When x = 11,
We have:
[tex]y = 70 \times 11[/tex]
[tex]y = 770[/tex]
The points on the graph are represented as:
(2,110) and (4,220)So, the equation of the graph is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{220 - 110}{4 - 2} (x - 2) + 110[/tex]
[tex]y = 55 (x - 2) + 110[/tex]
Expand
[tex]y = 55x - 110 + 110[/tex]
[tex]y = 55x[/tex]
When x = 11,
We have:
[tex]y = 55 \times 11[/tex]
[tex]y = 605[/tex]
Calculate the difference between the y-values
[tex]y_2 - y_2 =770 - 605[/tex]
[tex]y_2 - y_2 =165[/tex]
Hence, the value of y in the table is 165 more than the value of y in the graph
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Which polynomial is a perfect square trinomial? (1 point) 49x2 − 28x + 16 4a2 − 20a + 25 25b2 − 20b − 16 16x2 − 24x − 9?
Given a group of 8 women and 11 men, how many different ways are there of choosing one man and one woman for a committee?
Final answer:
There are 88 different ways of choosing one man and one woman for a committee.
Explanation:
In order to find the number of different ways of choosing one man and one woman for a committee, we can use the concept of combinations. The number of ways of choosing one item from a group of n items is denoted by n C 1, which is equal to n. So, the number of ways of choosing one man from a group of 11 men is 11, and the number of ways of choosing one woman from a group of 8 women is 8. To find the total number of ways, we multiply these two numbers:
Total number of ways = 11 * 8 = 88
Therefore, there are 88 different ways of choosing one man and one woman for a committee.
For each equation below find y if x=2
There are 20 wild pigs on an island and the number of pigs doubled each year for the past 5 years. The independent variable is
Answer:
The independent variable is time.
Step-by-step explanation:
Given,
The original number of pigs on the island = 20,
Also, the number of pigs doubled each year,
After 1 year the pigs = 20(2),
After 2 years = 20(2)²,
After 3 years = 20(2)³,
......................., so on...
Similarly, the number of pigs after t years would be,
[tex]y=20.2^t[/tex]
⇒ The value of y depends upon t,
⇒ The number of pigs depends upon the time ( in years ),
Since, the variable in which the other variable depends is called independent variable,
Hence, the independent variable must be time.
Andrew makes $6 an hour plus $9 an hour for every hour of overtime. Overtime hours are any hours more than 40 hours for the week. Part A: Create an equation that shows the amount of wages earned, W, for working x hours in a week when there is no overtime. (3 points) Part B: Create an equation that shows the amount of wages earned, S, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 40 hours. (3 points) Part C: Andrew earned $330 in 1 week. How many hours (regular plus overtime) did he work? Show your work. (4 points)
HELP If f(x)=15x+3, then f^-1(x)=?
The inverse of the function f(x) = 15x + 3 is found by swapping x and f(x) in the equation and solving for f^-1(x), which leads to f^-1(x) = (x - 3) / 15.
Explanation:To find the inverse of the function f(x) = 15x + 3, it is necessary to first swap x and f(x) in the function equation. This results in x = 15f^-1(x) + 3. Secondly, solving for f^-1(x) means isolating this on one side of the equation. That results in f^-1(x) = (x - 3) / 15.
So, the inverse function of f(x) = 15x + 3 is f^-1(x) = (x - 3) / 15.
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A choir has 3 spots open for altos, and 8 altos are interested in them. In how many ways can the open spots be filled?
There are total 56 ways to fill the open spot .
What is combination?
A combination is a way for determining the number of possible arrangements in a collection of items where the order of selection does not matter.
Formula for combination[tex]C(n, r) =\frac{n!}{(n - r)!r!}[/tex]
where,
n is the number of items in set.
r is the number of items selected from the set.
According to the question we have,
Number of altos, n = 8
Number of open spots, r = 3
Therefore, the number of ways to fill open spots = C(8, r)
Number of ways = [tex]\frac{8!}{3!(8-3)!}[/tex]
Number of ways = [tex]\frac{8!}{5!3!}[/tex][tex]= \frac{(8)(7)(6)(5!)}{5!3!}[/tex] = [tex]\frac{(8)(7)(6)}{(3)(2)} =8(7) = 56[/tex]
Hence, there are total 56 ways to fill the open spot .
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Why is world population distribution uneven what factors contribute to this uneven distribution?
Luisa knit a rectangular scarf that measures 4 feet by 1 foot. She wants to use the remaining 6 square feet of fabric to create a border around the scarf.
Which equation can she use to find the required width of the border x?
To solve this problem, let us recall that the formula for Area of a rectangle is:
A = l * w
Where,
l = length of one side = 4 ft
w = width of one side = 1 ft
Therefore the original area is:
Ao = 4 ft * 1 ft
Ao = 4 ft^2
Since each border would be increased by x, therefore the new l and w would be:
l = 4 + 2x
w = 1 + 2x
The new area becomes:
A = (4 + 2x) (1 + 2x)
The difference of the two would be the area of the remaining scarf:
A – Ao = 6 square ft
(4 + 2x) (1 + 2x) – 4 = 6 ---> 1
(4 + 2x) (1 + 2x) = 10 ---> 2
The equation to use can be equation 1 or equation 2.
What do the parallel lines shown on segment BD and segment DC represent? _____________________
the 2 parallel lines mean that the lines are equal
SO since BD = 18, DC is also 18
What 12 multiplied by 3
Double-checking my answer.. Given 3^2x = 9^6, what value of x satisfies this equation? (Use Laws of Exponents).
Thanks:)
Please solve for c :3
3c - 2 = 5(c+2)
The function $f : \mathbb{r} \rightarrow \mathbb{r}$ satisfies $f(x) f(y) - f(xy) = x + y$ for all $x$, $y \in \mathbb{r}$. find $f(x)$.
An amusement park charges $9.00 for admission $4.00 per ride. Write an equation that gives the cost in dollars as a function of number of rides
T = total cost
X= number of rides
T=4.00x+9.00
What is the area of the polygon given below?
Answer:
181 square units
Step-by-step explanation: