Answer:
(a) 1,411,200.
(b) 302,400.
(c) 100,800.
(d) 1,008,000.
Step-by-step explanation:
Permutation is the number of ways to select k items from n distinct items in a specific order.
The formula to compute the permutation or arrangement of k items is:
[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]
(a)
Compute the total number of schedules as follows:
[tex]\text{Total Number of Schedules}=\ ^{8}P_{4}\times \ ^{7}P_{4}[/tex]
[tex]=\frac{8!}{(8-4)!}\times \frac{7!}{(7-4)!}\\\\=\frac{8\times 7\times 6\times 5\times 4!}{4!}\times \frac{ 7\times 6\times 5\times 4\times 3!}{3!}\\\\=(8\times 7\times 6\times 5)\times (7\times 6\times 5\times 4)\\\\=1411200[/tex]
Thus, the total number of schedules are, 1,411,200.
(b)
Compute the number of schedules that includes neither sister as follows:
If neither of sister are included in the schedule then the number of players from the team are 7 and 6 respectively.
[tex]\text{Number of Schedules without the sisters}=\ ^{7}P_{4}\times \ ^{6}P_{4}[/tex]
[tex]=\frac{7!}{(7-4)!}\times \frac{6!}{(6-4)!}\\\\=\frac{ 7\times 6\times 5\times 4\times 3!}{3!}\times \frac{ 6\times 5\times 4\times 3\times 2!}{2!}\\\\=(7\times 6\times 5\times 4)\times (6\times 5\times 4\times 3)\\\\=302400[/tex]
Thus, the number of schedules that includes neither sister is 302,400.
(c)
Compute the number of schedules including both sisters and have them playing against each other as follows:
If both the sisters are playing against each other then there will be three more places to be filled in both the teams.
And the two sisters can play in any of the 4 matches.
[tex]\text{number of schedules including} \\\text{both sisters against each other}=(\ ^{7}P_{3}\times \ ^{6}P_{3})\times 4[/tex]
[tex]=[\frac{7!}{(7-3)!}\times \frac{6!}{(6-3)!}]\times 4\\\\=[\frac{ 7\times 6\times 5\times 4!}{4!}\times \frac{ 6\times 5\times 4\times 3!}{3!}]\times 4\\\\=[(7\times 6\times 5)\times (6\times 5\times 4)]\times 4\\\\=100800[/tex]
Thus, the number of schedules including both sisters and have them playing against each other is 100,800.
(d)
Compute the number of schedules including both sisters as follows:
[tex]\# \text {Schedules with the Sisters}=\text{Total}\ \#\ \text{Schedules }-\ \# \text {Schedules without the Sisters}[/tex] [tex]=1411200-302400\\=1108800[/tex]
Now compute the number of schedules having the sisters playing in different matches as follows:
[tex]\text{Playing in Different Matches}=\# \text {Schedules with the Sisters}-\text{Playing together}[/tex]
[tex]=1108800-100800\\=1008000[/tex]
Thus, the number of schedules including both sisters, but have them playing in different matches is 1,008,000.
20 POINTS IF ANSWERED
△ABC and △CDE similar right triangles. The coordinates of all the vertices are integers.
A: The relationship between the slope of AC¯¯¯¯¯ and the slope of CE¯¯¯¯¯ cannot be determined, because the triangles are congruent.
B:The slope of AC¯¯¯¯¯ is equal to the slope of CE¯¯¯¯¯ . This this because ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC¯¯¯¯¯ as for CE¯¯¯¯¯
C:The slope of AC¯¯¯¯¯ is greater than the slope of CE¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for AC¯¯¯¯¯ than for CE¯¯¯¯¯ .
D:The slope of AC¯¯¯¯¯ is less than the slope of CE¯¯¯¯¯ . This is because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for AC¯¯¯¯¯ than for CE¯¯¯¯¯ .
Answer:
Option B.
Step-by-step explanation:
Slope of the line AC = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{\text{AB}}{\text{BC}}[/tex]
= [tex]\frac{4}{6}[/tex]
= [tex]\frac{2}{3}[/tex]
Slope of the line CE = [tex]\frac{\text{DC}}{\text{DE}}[/tex]
= [tex]\frac{2}{3}[/tex]
Therefore, slope of the line AC = Slope of the line AC
And this is because ratio of change in y-values of the endpoints to the change in x-values of the endpoints is the same for AC as for CE.
Option B. is the answer.
Which of the following is an example of an improper fraction?
A. 3
B. 9/5
C. 5/9
D. 1 1/2
−7x − 7y = −14 2x +7y = 19
Answer:
(-1, 3)
I hope this helps
if you could, feel free to mark me Brainliest it would be much appreciated :D
is 1,569 divisible by 9
Answer:
Yes the answer is 179 remainder 3
Answer:
no
Step-by-step explanation:
hope this helped!
p.s it would be cool if you gave me brainliest.
a bag of a certain type of sand weighs 42 pounds and has a volume of 0.5 cubic feet. a sandbox has a volume of 16 cubic feet. approximately how many pounds of sand will it take to fill the sandbox
Answer:32
Step-by-step explanation:I divided 16 by 0.5
The average person takes in 900 breaths per hour. How many breaths does an average person take in 6 hours?
A 1,500 breaths1,500 breaths
B 4,500 breaths4,500 breaths
C 5,400 breaths5,400 breaths
D 54,000 breaths54,000 breaths
Answer:
C 5,400 breaths
Step-by-step explanation:
900 breaths per hour x 6 hours = 5,400 breaths in 6 hours
-24+to the power of 3
Answer:
-13824
Step-by-step explanation:
Are the following lines parallel, Perpendicular OR neither
A. 4x - 2y = -12
B. 3x + 6y = 24
Answer:
Neither I am sure because if to the equation the answer is same
Henry is playing a new game app where he needs to navigate through a maze without touching the walls. each player stars with 1,000 points, and 5 points are deducted each time a wall is touched.
What type of relationship most appropriately models this situation?
A. Exponential Decay
B. Linear Decrease
C. Exponential Growth
D. Linear Decrease
Answer:
Step-by-step explanation:
Linear decrease
A tennis racket normally costs $70. The tennis racket is on sale for 30% off. What is the sale price of the tennis racket?
Which prime number do the prime factorization of 130 and 165 have in common?
Answer:
They both have the #5 and they both have 3 #'s that are prime?
Step-by-step explanation:
prove that the following lines are parallel to each other.
3x+4y-7=0 and 6x+8y-11=0
(plzz do in process )
Answer:
Yes, they are paralle.
Step-by-step explanation:
Step-by-step explanation:
Hey there!
Here;
The equations are:
3x + 4y - 7 = 0.............(I)
6x + 8y -11 = 0.........(ii)
Let's simply work with this.
From equation (I)
[tex]slope(m) = \frac{ - coeff.of \: x}{coeff.of \: y} [/tex]
[tex]m1 = \frac{ - 3}{4} [/tex]
From equation (ii)
[tex]slope(m2) = \frac{ - coeff. \: of \: x}{coeff. \: of \: y} [/tex]
[tex]m2 = \frac{ - 6}{8} [/tex]
[tex]m2 = \frac{ - 3}{4} [/tex]
As per the condition of parallel lines;
M1 = M2
-3/4 = -3/4. (true)
Therefore, the lines are parallel to eachother.
Hope it helps...
How many degrees is the measurement of the missing angle? (Only numeric answer, no words or symbols at all)
Answer:
The answer is 135
Step-by-step explanation:
all angles in a triangle equal to 180.
so, 25+22= 45
then, 180-45= 135
the missing angles measure is 135 degrees
hope this helps!
Write - 2.17 as a fraction
Answer:
2 17/100
Step-by-step explanation:
not sure if that is a negative sign before, if so, add the negative
Solve 2/3x= 20
Please help i’ll give 30 points for it
Answer:
the answer is 30
Step-by-step explanation:
hope it helps
Peter is saving money to buy an MP3 Player. After one month, he has $50. After two months he has $85. After three months, he has $120. He plans to keep saving at the same rate. How long will it take Peter to save enough money to buy an MP3 Player that costs $295?
Answer:
9 months
Step-by-step explanation:
peter is saving 35 dollars per month.
295=35x
295/35=8.42 which is less than 295
9 is an approximate answer
35*9 equals 315, which is enough to pay 295 and have 20 dollars left over
Jeremy's boss increased his salary from $8 per hour to $12 per hour. By
what percent did his hourly wages increase?
Answer:
1.5 percent
Step-by-step explanation:
HELP.!!!!
The area of a rectangular yard is given by the trinomial 2x^2 + x - 36. What are the possible dimensions of the yard?
A
(2x + 9) and (x-4)
B
(-2x + 9) and (-x + 4)
С
(2x - 2) and (x-4)
D
(2x - 4) and (x + 4)
Answer:
A . (2x + 9) and (x-4)
Explanation:
Given parameters:
Given trinomial;
2x² + x - 36
Possible dimensions of the yard = ?
Solution:
To solve this apply the quadratic factorization;
2x² + x - 36 = 0
2x² -8x + 9x - 36 = 0
2x(x - 4) + 9(x -4) = 0
(2x + 9) (x -4) = 0
The possible dimensions of the rectangular yard is (2x + 9) and (x -4)
I will give you branilest!
To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets of information is given by b = 1500p where p represents the number of packets and b represents the number of bytes of information.
c. Each byte contains 8 bits of information. Write an equation to represent the relationship between the number of packets p and the number of bits s.
s =
if freya makes 2 of her 5 free throws in a basketball game what is her free throw shooting percentage ?
a. 20%
b. 40%
c. 80%
d. 90%
Answer:
40
Step-by-step explanation:
100 /5 = 20
20*2= 40
40%
Divide and write the answer in the simplest form:
110
1
10
÷ 512
5
12
=
124
1
24
311
3
11
625
6
25
120
Answer:
What?
Step-by-step explanation
now I'm confused
write it regularly
what is 2x3 - 5x2 - 4x - 25
divided by X - 4
Answer:
2x² + 3x + 8 + 7/x-4
Step-by-step explanation:
For this problem, we can use synthetic division.
4 | 2 -5 -4 -25
| 8 12 32
|_________
2 3 8 7/x-4
This means the quotient is 2x² + 3x + 8 + 7/x-4.
Please help if u care pls
1/4x+5/2x-2=4-1/4x
What is the value of x
Answer: The correct answer is: [A]:
__________________________________________________
" Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
__________________________________________________
Step-by-step explanation:
__________________________________________________
Note that the "unit rate" is the term that refers to:
a "quantity" / or "quantitative value" ;
→ of some type of "countable units"
{e.g. "currency" — [such as: dollars, cents, pounds] ; "distance/length/ width/ height" — [such as: miles, kilometers, meters, centimeters, yards, feet, inches] ; pieces of fruits — [such as: number of apples; cans of soda, number of red dresses] ;
__________________________________________________
per "single unit" of something — {e.g. per hour; per minute; per mile; per ounce; per hour; per dollar, per kilometer, per day, per week.
{e.g.
→ " 3 apples eaten per [single] apricot eaten" ;
→ " 46 miles per hour.
→ " 8.3 cents per oz." ;
→ " 5 Liters of soda per dollar " ;
→ " 2.3 grams per mole " ;
→ " 4.6 mg solute / kg of solvent " ;
→ " 5 km / hr " ; {that is: " 5 km per hr " } .
→ " 3 yds. per [single] square inch."
→ " 35 parts per hundred" ; {that is: " 35 percent" ; or: " 35 % " . } .
→ " ... The cilantro is on sale for 33 cents per bundle ...} ."
→ ... to provide a few examples.
__________________________________________________
On on Cartesian plane graph, the "x-axis" is located on the "horizontal axis" that represents the "independent variable" (or, at times, the "experimental value" — which can be manipulated — or "controlled" —or be subjected to being "manipulated" / "controlled" / or, "selected".
The "y-axis" is located on the "vertical axis" that represents the "dependent variable" (or, at times, the "control value") that cannot be "manipulated" / controlled/ or "selected" / since it represents the "y-value" of the corresponding coordinate to which the "x-value" happens to corresponds to at the given value for "x" .
So, if the "unit rate" represents the "single unit rate" ; we look at "x = 1 " ; since we are "choosing" this particular "single" rate of per "single" (i.e. "1" ) ; so we do not have a choice in what "y-value" of the particular graph to select. We can control the fact that we are "choosing" to find the "unit" rate, so we select the "independent variable" , "x = 1 " . We then examine the "corresponding y-value" that happens to exist when "x = 1 " .
{Note that we have "no control" over what that "y-value" is ; at the: "[point which: " x = 1 .] . "
_________________________________________________
→ As such, that "y-value" [insert that numeric "y-value" ; followed by the units represented by the "y-axis" ] ;
per " 1 " [insert "single unit" represented by the "x-axis" ] ;
_________________________________________________
→ is the: "unit rate" .
__________________________________________________
So:
The correct answer is: [A]:
__________________________________________________
" Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1 . That value is the unit rate. "
Answer:
Step-by-stbhubhbhnhnkjnkjnep explanation:
Resplendent quetzal (Pharomachrus mocinno) is a beautiful bird species that lives in the tropical forests of Central America. Assuming that you started a breeding program and you would like to breed resplendent quetzal to produce longer tails. You measured 50 resplendent quetzals and obtained a mean tail length of 85.4 cm. You selected 10 resplendent quetzals with longest tails as breeders. The mean tail length of the breeders is 91.2 cm. After mating, offspring of the resplendent quetzal breeders have a mean tail length of 87.7 cm. What is the heritability of tail length in this resplendent quetzal population
Answer:
The value is [tex]H =0.3966[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 50
The mean tail is [tex]\= x = 85.4 \cm[/tex]
The number of resplendent quetzals selected as breeders is [tex]k = 10[/tex]
The mean tail breeders is [tex]\= x_1 = 91.2 \ cm[/tex]
The mean tail of the breeders after mating [tex]\= x_2 = 87.7 \ cm[/tex]
Generally the selection differential is mathematically represented as
[tex]D = \= x_1 - \= x [/tex]
=> [tex]D = 91.2- 85.4 [/tex]
=> [tex]D = 5.8 \ cm [/tex]
Generally the selection response is mathematically represented as
[tex]S = \= x_2 - \= x[/tex]
=> [tex]S = 87.7 - 85.4[/tex]
=> [tex]S =2.3 \ cm [/tex]
Generally the heritability of tail length in this resplendent quetzal population is mathematically represented as
[tex]H = h^2 = \frac{S}{D} [/tex]
=> [tex]H = h^2 = \frac{2.3}{5.8} [/tex]
=> [tex]H = h^2 = \frac{2.3}{5.8} [/tex]
=> [tex]H = h^2 = 0.3966/tex]
Enter the value of 7 + (-3) - 3 - 7
Answer:
-6
Step-by-step explanation:
Simplify: 7 - 3 - 3 - 77 - 3 - 3 - 7 = -6I hope this helps!
Answer:
-3
Step-by-step explanation:
I
What is the sale price of a stereo that normally sells for $250.00 and is on sale for 10% off?
Answer:
$225.00
Step-by-step explanation
First, take the percentage and switch it to a decimal. 10%= 0.10
Next, take $250.00 and multiply that by 0.10. 250x0.10=25
Lastly, subtract 25 from 250. 250-25= 225.
So you’re final answer is $225.00 Hope this helped!
Answer:
$225
Step-by-step explanation:
To find the sale price you convert 10% to decimals so that is equal to .10. Then you multiply the .10 by the original price, and that equals $25. After you have to subtract the found price by original price (250-25) then that should give you $225.
Multiple Choice
Evaluate.
1. -59 - 6 for g=-2 (1 point)
A.4
B.16
C.10
D.-13
Domain and range of a graph please helppppp
Answer:
Domain : (-∞,∞)
Range : (-∞,∞)
Step-by-step explanation:
Domain is how many x-values the graph touches and Range is how many y-values the graph touches. And this graph has no point on which it stops nor any asymptotes, so both domain and range are all real numbers.
Answer:
if FB gxjxjdjdjhgdjjdidjqjdjjdid
Which expressions have a quotient of 4/5
a. 5/2 ÷ 1/2
b.6/9 ÷ 5/6
c. 3/6 ÷ 2/5
d.7 1/2 ÷ 6
e.1 1/3 ÷ 1 2/3
Answer:
b and eStep-by-step explanation:
a. 5/2 ÷ 1/2 =
5/2*2 =5b. 6/9 ÷ 5/6
2/3*6/5 =2*2/5 = 4/5c. 3/6 ÷ 2/5
1/2 * 5/2 =5/4d. 7 1/2 ÷ 6 =
15/2*1/6 =5/(2*3) =5/6e. 1 1/3 ÷ 1 2/3=
4/3 ÷ 5/3 =4/3 * 3/5 =4/5Answer:
Trick answer none of them do.
Step-by-step explanation:
