1507 are the different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
Solution:
Given that,
5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players
This is a combination problem
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter
The formula is given as:
[tex]n C_{r}=\frac{n !}{r !(n-r) !}[/tex]
Where n represents the total number of items, and r represents the number of items being chosen at a time
Let us first calculate 5 baseball players from 12 baseball players
Here, n = 12 and r = 5
[tex]\begin{array}{l}{12 C_{5}=\frac{12 !}{5 !(12-5) !}} \\\\{12 C_{5}=\frac{12 !}{5 ! \times 7 !}}\end{array}[/tex]
For a number n, the factorial of n can be written as:
[tex]n !=n \times(n-1) \times(n-2) \times \ldots . \times 2 \times 1[/tex]
Therefore,
[tex]\begin{aligned}12 C_{5} &=\frac{12 \times 11 \times 10 \times \ldots \ldots \times 2 \times 1}{5 \times 4 \times 3 \times 2 \times 1 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \\\\12 C_{5} &=\frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2} \\\\12 C_{5} &=792\end{aligned}[/tex]
Similarly, 4 basketball players be selected 13 basketball players
n = 13 and r = 4
Similarly we get,
[tex]\begin{aligned}&13 C_{4}=\frac{13 !}{4 !(13-4) !}\\\\&13 C_{4}=\frac{13 !}{4 ! \times 9 !}\end{aligned}[/tex]
[tex]13C_4 = 715[/tex]
Thus total number of ways are:
[tex]12C_5 + 13C_4 = 792 + 715 = 1507[/tex]
Thus there are 1507 different ways
To determine the number of ways to select 5 baseball players from 12, and 4 basketball players from 13, we use the combination formula for both and multiply the results, applying the Counting Principle.
Explanation:The question asks how many different ways can 5 baseball players and 4 basketball players be selected from 12 baseball players and 13 basketball players. This is a problem of combinatorics, specifically the use of combinations, since the order of selection does not matter.
To find the number of ways to select the baseball players, we use the combination formula C(n, k) = n! / (k! * (n-k)!), where 'n' is the total number to choose from, 'k' is the number to choose, and '!' denotes factorial. For the 5 baseball players from 12, it is C(12, 5).
For the basketball players, it's C(13, 4), as we are choosing 4 out of 13. To find the total number of ways to form the group, we multiply these two values together, because each combination of baseball players can be paired with each combination of basketball players, which is an example of the Counting Principle.
So, the calculation is C(12, 5) * C(13, 4).
urgent please be my saint VX is a midsegment of △WYZ. If YZ=t+95 and VX=10t, what is the value of t?
Answer:
[tex]t = 5[/tex]
Step-by-step explanation:
By the mid-segment theorem of triangles,
[tex]VX= \frac{1}{2} YZ[/tex]
We substitute the expressions in terms of t.
[tex]10t = \frac{1}{2} (t + 95)[/tex]
We multiply through by 2 to get:
[tex]20t = t + 95[/tex]
Subtract t from both sides:
[tex]20t - t = 95[/tex]
[tex]19t = 95[/tex]
Divide both sides by 19:
[tex]t = \frac{95}{19} [/tex]
[tex]t = 5[/tex]
When you isolate the variable,the goal is to get the variable
Answer: you isolate the variable so you can get a equation of y= 10x or something like that
Step-by-step explanation:
Borrowed 8000 at a rate of 12% compound monthly, no payments how much will be owed after 7 years?
Answer:
[tex]\$18,453.78[/tex]
Step-by-step explanation:
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final amount owed
P is the amount borrowed
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=7\ years\\ P=\$8,000\\ r=12\%=12/100=0.12\\n=12[/tex]
substitute in the formula above
[tex]A=8,000(1+\frac{0.12}{12})^{12*7}[/tex]
[tex]A=8,000(1.01)^{84}[/tex]
[tex]A=\$18,453.78[/tex]
Ben is 4 times as old as I Ishaan and is also 6years older than ishaan
Answer:
24
Step-by-step explanation:
4 times 6 =24
Answer:
Ishaan is 2 years old and Ben is 8
Step-by-step explanation:
Ben is 4 x (2) = 8
Ben is 6 + (2) = 8
44 decreased by twice a number
use the variable "n" to represent an unknown number
Answer:
44-2n
Step-by-step explanation:
Hope it helps!
Final answer:
The expression '44 decreased by twice a number' can be represented as 44 - 2n, where n is the unknown number.
Explanation:
The question involves expressing a given mathematical relationship using a variable. Here, the relationship is '44 decreased by twice a number.' To represent this situation with the variable n, we use the expression 44 - 2n. To simplify further, just substitute the variable 'n' with the unknown number. This represents the original number 44 being reduced by two times the value of some unknown number n.
If inflation from last year to this year was 2% and a pair of designer jeans sold for $75 last year, what would you expect to pay for them this year?
Answer:
$76.5
Step-by-step explanation:
We have been given that inflation from last year to this year was 2% and a pair of designer jeans sold for $75 last year. We are asked to find the price of pair of designer jeans this year.
An inflation of 2% will increase the price of pair of jeans by 2%, so price of pair of jeans this year would be $75 plus 2% of $75.
[tex]\text{Price of pair of jeans this year}=\$75+\$75\times\frac{2}{100}[/tex]
[tex]\text{Price of pair of jeans this year}=\$75+\$75\times0.02[/tex]
[tex]\text{Price of pair of jeans this year}=\$75+\$1.5[/tex]
[tex]\text{Price of pair of jeans this year}=\$76.5[/tex]
Therefore, the price of pair of jeans would be $76.5 this year.
A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. There were twice as many balcony tickets sold as gallery tickets, and 225 more main floor tickets than balcony tickets. If g represents the number of gallery tickets sold, which expressions represents this situation?
Answer:
Let the number of balcony seats be b
Let the number of gallery tickets be g
Let the number of main floor tickets be m
b + g + m = 1020
b = 2g
m = b + 225
The number of balcony tickets = 318
The number of gallery tickets = 159
The number of main floor tickets = 543
Step-by-step explanation:
Let the number of balcony seats be b
Let the number of gallery tickets be g
Let the number of main floor tickets be m
i) Therefore we can write b + g + m = 1020
ii) there were twice as many balcony tickets sold as gallery tickets
therefore b = 2g [tex]\Rightarrow[/tex] g = 0.5b
iii) there were 225 more main floor tickets than balcony tickets
therefore m = b + 225
iv) using equation ii) and equation iii) in equation i) we can write
b + g + m = b + 0.5b + b + 225 = 1020 [tex]\Rightarrow[/tex] 2.5b = 795 [tex]\Rightarrow[/tex] b = 318
v) g = 0.5 b = 0.5 [tex]\times[/tex] 318 = 159
vi) m = b + 225 = 318 + 225 = 543
Answer:
D. Gallery: g
Balcony: 2g
Main Floor: 2g+225
Step-by-step explanation:
Gallery is g
Balcony had 2 times as many tickets than Gallery so 2•g (2•gallery)
Main floor had 225 more tickets than Balcony so Balcony’s equation plus 225 tickets. 2g + 225
doug has 45 coins worth $9.00. The coins are all quarters or dimes. How many of each type of coin dose doug have?
Doug have 30 quarters and 15 dimes.
Step-by-step explanation:
Given,
Number of coins = 45
Worth of coins = $9.00 = 9.00*100 = 900 cents
Each quarter = 25 cents
Each dime = 10 cents
Let,
x be the number of quarters
y be the number of dimes
According to given statement;
x+y=45 Eqn 1
25x+10y=900 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=45)\\10x+10y=450\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2
[tex](25x+10y)-(10x+10y)=900-450\\25x+10y-10x-10y=450\\15x=450[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}=\frac{450}{15}\\x=30[/tex]
Putting x=30 in Eqn 1
[tex]30+y=45\\y=45-30\\y=15[/tex]
Doug have 30 quarters and 15 dimes.
Keywords: linear equation, elimination method
Learn more about elimination method at:
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Doug has 30 quarters and 15 dimes.
Let
x = number of quarters
y = number of dimes
The total number of coins is 45. Therefore,
Total number of coins:x + y = 45Total amount of the coins is $9. Therefore,
Total cost of the coins:0.25x + 0.1y = 9Therefore,
x + y = 45
0.25x + 0.1y = 9
0.1x + 0.1y = 4.5
0.25x + 0.1y = 9
0.15x = 4.5
x = 4.5 / 0.15
x = 30
y = 45 - 30
y = 15
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Given that ABCD is a rhombus, what is the value of x?
(3x - 26)
Answer:its 29
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
3x to the power of the 4th - x to the second power - x to the second power-5x to the power of 4 +3
Answer:
3x^4-x^2-x^2-5x^4+3
-2x^4-2x^2+3 is the answer
To simplify the given expression, combine like terms by adding or subtracting the coefficients of the same powers of x.
Explanation:The given expression is 3x4 - x2 - x2 - 5x4 + 3.
To simplify this expression, combine like terms by adding or subtracting the coefficients of the same powers of x.
Combining like terms, we have: -2x2 - 2x4 + 3.
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can you solve this equation for me?
simplify the expression 6-2x+5+4x
Answer:
11 + 2x
Step-by-step explanation:
First you will want to separate like variables, so (6, 5) and then (-2x, 4x)
Then you will use the signs to do the math. You can move everything to help visualize the solution easier.
6+5+4x-2x
6+5 = 11
4x-2x = 2x
Because you cannot add or subtract a variable with a non variable, and both numbers are positive you end up with
11 + 2x
The expression 6-2x+5+4x simplifies to 11 + 2x by combining like terms: the constants (6+5=11) and the variables (-2x+4x=2x).
To simplify the expression 6-2x+5+4x, we start by combining like terms. Combining the constant terms (6 and 5) and the variable terms (-2x and 4x), we get:
Constant terms: 6 + 5 = 11
Variable terms: -2x + 4x = 2x
Thus, the simplified expression is 11 + 2x.
Share £40 in the ratio 1:4
Answer:
8:32
Step-by-step explanation:
1x+4x=40
5x=40
x=8
1*8:4*8
8:32
make g the subject of x=3g+2
Answer:
look at picture shown.
Solve for the intersection point
2x+3y=-6
-2x+3y=-18
Answer:
(3,-4)
Step-by-step explanation:
Please help me calculate the proper number of significant figures, I would like to check my answers to see if this is correct based on the significant figure rules
A.) 320.80−(6101.3/1.8)320.80−(6101.3/1.8)=
B.) [(286.4×105)−(1.300×103)]×2.8951=
C.) (0.0041×26000.0)+(2811×15)=
D.) 863×[1251−(3.11×109)]=
Final answer:
To determine the proper number of significant figures in a calculation, follow the rules for addition/subtraction and multiplication/division, and round the final answer to the proper number of significant figures.
Explanation:
To determine the proper number of significant figures in a calculation, follow these rules:
Addition and subtraction: The result should have the same number of decimal places as the number with the fewest decimal places.Multiplication and division: The result should have the same number of significant figures as the number with the fewest significant figures.Rounding: Round the final answer to the proper number of significant figures.Using these rules, the proper number of significant figures for the given calculations are:
A.) 320.80 - (6101.3 / 1.8) = 300
B.) [(286.4 x 105) - (1.300 x 103)] x 2.8951 = 839000
C.) (0.0041 x 26000.0) + (2811 x 15) = 40000
D.) 863 x [1251 - (3.11 x 109)] = -1.7742e12
What is the measure of angle X? 56° 41°
Question:
What is the measure of angle X?
The image of the measurements is attached below:
Answer:
The measure of angle x is 83°
Explanation:
Since, Vertical angles have equal measure,
Let us consider that the angle opposite to 41° is ∠y and they are equal.
i.e, ∠y = 41°
Since, the angles in a straight line add up to 180°, we have,
∠x + ∠y + 56° = 180°
Substituting the value ∠y = 41°, we have,
∠x + 41° + 56° = 180°
Adding the terms, we get,
∠x + 97° = 180°
Subtracting both sides by 97°, we get,
∠x = 83°
Thus, the measure of ∠x is 83°
Answer:
83 degrees
Step-by-step explanation:
I took the test
The perimeter of the rectangle is 14x + 4, the length of the rectangle is 2x. What is the width of the rectangle?
Answer:
5x+2
Step-by-step explanation:
P=2L+2W
14x+4=2(2x)+2W
14x+4=4x+2W
14x+4-4x=2W
14x-4x+4=2W
10x+4=2W
(10x+4)/2=W
5x+2=W
Find the area of shaded region. Round the answer to 2 decimal places if necessary
[tex]\boxed{A=50units^2}[/tex]
Explanation:Hello! Remember you have to write complete questions in order to get good and exact answers. Here you haven't provided any regions so I'll help you assuming a system of inequalities that leads to a shaded region that is a right triangle as shown in the figure below. The system is the following:
[tex]\left\{ \begin{array}{c}x>0\\y>0\\y<-x+10\end{array}\right.[/tex]
From the figure below, the shaded region is a right triangle with base 10 units and height 10 units. So:
[tex]A=\frac{b\times h}{2} \\ \\ \\ A:Area \ of \ the \ triangle \\ \\ b:base \ of \ the \ triangle \\ \\ h:height \ of \ the \ triangle[/tex]
So:
[tex]A=\frac{10\times 10}{2} \\ \\ A=\frac{100}{2} \\ \\ \boxed{A=50units^2}[/tex]
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Arthur earned $136 in three weeks. He goes back to school in one more week. He needs at least $189 to buy the coat that he wants for school. How much must Arthur earn in the next week?
Which number has the smallest number? -5 or -15?
Answer:
-15
Step-by-step explanation:
this is the negative scale, so the bigger the smaller
Answer:-15
Step-by-step explanation:
-15 is 15 away from 0 while -5 is only 5 away from 0
Write the expression "N is the same as 6 reduced by 2" as a number sentence.
Answer:
N = 6 - 2
Step-by-step explanation:
Take each part of the word expression and translate it:
"N" => N ("N" is a variable that represents a number you don't know)
"is the same as" => = ("the same" means equals)
"6 reduced by 2" => 6 - 2 ("reduced" means use subtraction "-")
Put the sentence back together in the same order.
N = 6 - 2
If you wanted to find "N", you can simplify by doing 6 - 2.
N = 4
$300 at 4 percent for 3 years
A: Find the interest earned
B: Find the balance of the account
Kim says that multiply 1/4×12 is the same as dividing 12 x 4 do you agree with him explain your answer
Answer: No
Step-by-step explanation: 12 x 4 is 48. 12 x 1/4 is the same as dividing 12 by 4, which gives you 3. 3 is not equal to 48.
The correct statement is that the number 3 is not equal to 48.
I do not agree with him.
What is simplification?Simplification is to make something easier to do or understand and to make something less complicated.
Given
Kim says that multiplying 1/4×12 is the same as dividing 12 x 4
How to find the solution?The multiplication of 12×4 = 48.
1/4×12 is the same as dividing 12 by 4, which gives you 3.
Therefore, 3 is not equal to 48.
I do not agree with him.
More about the simplification link is given below.
https://brainly.com/question/12616840
#15 You earned 89 out of
100 points on your math
quiz. What percent of the
points did you earn?
#16 Outc
are in bar
of studen
Answer:
89%
Step-by-step explanation:
Percent is a number out of 100.
If you got 89 out of 100, you got 89%
there were 20 members in thr running club in september. the membership increased to 25 in october. the membership decreased back to 20 in november. what was the percent decrease from october to november?
There was a decrease of 20% in membership from October to November.
Step-by-step explanation:
Step 1; To find the percent by which the running clubs membership decreased we must find the difference between the number of members in October and the number of members in November. The number of members in the club in October was 25 whereas it reduced to 20 in the month of November.
Difference in members = Number of members in October -Number of members in November = 25 - 20 = 5
Step 2; To find the percent decrease in number of members in the running club, we divide the difference in number of members by the number of members in November . We multiply this value by 100 to get it in terms of percentage.
Percent decrease in number of members =(Difference in members / number of members in November) *100
= (5/25) * 100 = 0.20 * 100 = 20%
So number of members in the club decreased by 20% from October to November.
Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is
450 kilograms (\text{kg}kgstart text, k, g, end text), but Renna and her load of identical packages mass a total of 620\,\text{kg}620kg620, start text, k, g, end text. Each package has a mass of 37.4\,\text{kg}37.4kg37, point, 4, start text, k, g, end text.
Answer:
Whats the full question ?
Step-by-step explanation:
Answer:
37.4p ≥ 170
5 packages
Step-by-step explanation:
The inequality is:
37.4p ≥ 170
Renna needs to remove a minimum of 555 packages from the elevator to meet the mass requirement.
Also the answer above is not ok to do.
Saying random things just for the points is wrong.
Instead you can say it where it says comment under the question
Hope this helps ;)
What is the answer to (7+4)2+(14/7)
Answer:
24
Step-by-step explanation:
HWEEEPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
P = 105°
QR = 11.6
M = 45°
LN = 8.5
Step-by-step explanation:
when reading the order of what is given LMN = PRQ the order DOES matter
so whe looking at what is being asked....
P will equal whatever its place is in the opposite equation. In this case that is L. This means that P = L. Since L = 105° then so does P.
You can do this with the rest of the letters. What ever letter is in it's place in the opposite equation that is what it equals.
Allie bought a roll of wrapping paper that is 8 1/2 feet long. She is wrapping gifts for her staff and needs 1 3/4 feet of wrapping paper for each gift. If Allie wraps as many gifts as possible with one roll, how many feet of wrapping paper will she have left over?
Answer:
1 1/2 feet
Step-by-step explanation:
We know that she needs 1 3/4 feet of wrapping paper per gift and she has a total of 8 1/2 feet.
The number of gifts she can wrap is:
[tex]8.5/1.75=4.86[/tex]
She can wrap four gifts
Therefore:
[tex]4\cdot{1.75}=7[/tex]
She will use 7 feet of wrapping paper and she has:
[tex]8.5-7=1.5[/tex]
She has 1 1/2 feet of wrapping paper left
Answer:
11/2
Step-by-step explanation:
A rectangular window in a door is 30 inches tall. If the area of the window is 300 square inches, how wide is the window?
10 inches
(300 square inches devided by 30 inches)
it is 10 inches wide!
explanation:
300/30=10