9514 1404 393
Answer:
a) 3003
b) 1419
Step-by-step explanation:
a) With no restrictions, the problem amounts to counting the number of combinations of 14 people taken 6 at a time. That is ...
14!/(6!(14-6)!) = 3003 . . . teams with no restrictions
__
b) With the restrictions, there are two cases:
(i) all 6 people are taken from the 12 that exclude the couple. That number of combinations is ...
12!/(6!(12-6)!) = 924
(ii) 4 people are taken from the 12 that exclude the couple, and the couple fills the last two team slots. That number is ...
12!/(4!(12-4)!) = 495
The sum of the counts of these two cases is ...
924 +495 = 1419 . . . teams with inseparable couple
if you dont mind, i just need to know what is the final answer in standard form of the equation. please!
Answer:
I'm pretty sure it's (x-1)*(5x+8)*(3x^4-2x^2+4x-8)
Step-by-step explanation:
what are the missing reasons in the proof. im having an hard time with this.
Answer:
Please see below
Step-by-step explanation:
Step 3: Definition of parallelogram
Step 4: Alternate internal angles between parallel lines AB // CD
Step 5: Reflexive property of congruence
Step 6: ASA theorem
A train travel 20 miles in 15 minutes 40 miles in 30 minutes and 60 miles in 45 minutes which equation represents the speed of the train in miles per hour
Answer:
y = 80x
Step-by-step explanation:
In 30 minutes the train went 40 ml so in an hr the train would be at 80 ml
Which shaded region is larger? Explain your reasoning..
Answer:
It's B because If you cover the blue you will see space that looks like a triangle. Do the same to A. You see how in B the Triangle looking thing is lower than A because A triangle thing is like more up and wider so it has space. Also B has a little space than A
Step-by-step explanation:
A gardening company sells clay flower pots and plastic flower pots. There must be at least 2 pots in each shipment, but there cannot be more than 8 in a shipment. Additionally, the shipment must weigh less than 100 lbs. Each shipment container weighs 20 lbs., and there is 1 lb. of packing material. A clay flower pot weighs 15 lbs., whereas a plastic flower pot weighs 7.5 lbs.
(A) Write a system of inequalities that represent the constraints on the number of pots that can be included in one shipment.
The system of inequalities can be obtained from the given information
on the allowable weights and number of pots.
The correct responses:
The system of inequalities that represent the constraint on the number
of pots that can be included in one shipment are;
2 ≤ x + y ≤ 815·x + 7.5·y ≤ 79 lbs.Methods used to find the system of inequalitiesThe inequality that represents the number total number of clay, T, in each shipment is 2 ≤ T ≤ 8
The inequality that represents weight of each shipment is w < 100 lbs
The weight of each shipment container = 20 lbs
The weight of the packing material = 1 lb
Therefore;
The maximum weight of the flower pots = 100 lbs - 21 lbs = 79 lbsThe weight of each clay flower pot = 15 lbs
The weight of each plastic flower pot = 7.5 lbs
Let "x" represent the number of clay flower pot included in one shipment
and let "y" represent the number of plastic flower pot included in one
shipment, we have;
The system of inequalities that represent the constraint on the number of pots that can be included in one shipment are as follows;
2 ≤ x + y ≤ 815·x + 7.5·y ≤ 79 lbs.Learn more about inequalities here:
https://brainly.com/question/10868639
We will find the system of inequalities:
C*15 lb + P*7.5lb < 79 lb
2 ≤ P + C ≤ 8
How to write a system of inequalities?
First, we need to define the variables that we will be using, these are:
C = number of clay pots.P = number of plastic pots.From the first restriction, we have that:
2 ≤ P + C ≤ 8
The other restriction says that the weight must be less than 100lbs:
W < 100lbs
Where the weight is:
W = C*15 lb + P*7.5lb + 20lb + 1lb
Where 20lb is the weight of the container and 1lb is the weight of the packing material, then we have:
C*15 lb + P*7.5lb + 20lb + 1lb < 100lb
We can subtract 21 lb in both sides to get:
C*15 lb + P*7.5lb < 100 lb - 21 lb
C*15 lb + P*7.5lb < 79 lb
So we got our two inequalities, then the system is:
C*15 lb + P*7.5lb < 79 lb
2 ≤ P + C ≤ 8
If you want to learn more about systems of inequalities, you can read:
https://brainly.com/question/9774970
Please give me the correct answer
Answer:
(-3,-2)
Step-by-step explanation:
If you draw a line across from Point A to -3, and a line down from Point P to -2, you get the point (-3,-2) and a right triangle.
A pair of linear equations is shown below: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points) On a graph, find the point of intersection of two lines, the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1. On a graph, find the point of intersection of two lines, the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2. On a graph, find the point of intersection of two lines, the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1. On a graph, find the point of intersection of two lines, the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.
Answer:
On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
- sorry I answered late! but I just did the test and got a 100 :)
Can someone pls help me
2 1/4 cups of pretzels
Annalise withdraws $22.50 each day from her account for a week. How can you represent the change in her account after 2 weeks?
Answer: She would have $315
Because there are 7 days in a week so you multiply 22.50 by 7 and you get 157.5, Then because she does it for two weeks you multiply 157.5 by 2 and you get 315
Hope this helps
Answer:
By subtracting
Step-by-step explanation: If you subtract 22.50 by 2 your answer will get lowerFind the slope and y-intercept of 5x – y = 7. Reduce all fractions.
slope = - Ô =
y-intercept =
B
Answer:
slope= ( 5,1 ) Y-intercept= ( 0,-7 )
Step-by-step explanation:
I need this answer ASAP
Answer:
i think the area is 60 i added it up
Jeremiah plans on building a 5 meter long garden walkway that is paved with square stones that measure 5/6 meters on each side. There will be no spaces between the stones. How many stones will be needed to complete the garden walkway? (whoever answers the question first correctly will get brainiest.)
Answer:
Figure it out yourself I just told you how to do it
Step-by-step explanation:
Search are my plans on building you find me along garden walkway this is paid with square stone that is mushroom 5 / 6 meters on each side but if there is no spaces between the stones than that means it 5A few times 5 meters and 6 / 5 you will get your answer on how long the stalls will be needed to complete the garden walkway
find a number n when decreased by 9 equals 17
Answer:
26-9=17 26 is the answer
Step-by-step explanation:
Answer:
The number n is 26
Step-by-step explanation:
Decreased means subtract
n-9 = 17
Add 9 to each side
n-9+9 = 17+9
n = 26
The number n is 26
There were 20 questions on an exam. You answered 40% of them incorrectly. How many did you answer incorrectly?
Answer: 4
Step-by-step explanation: 20-10=10 which is %50. 20-16=4
Find the gcf of 12,18 and 24( must be a factor of all numbers)
The lengths of the sides of a triangle are in the extended ratio 4 : 7 : 8. The perimeter of the triangle is 95 cm. What are the lengths of the sides?
Answer:
20 cm, 35 cm, 40 cm
Step-by-step explanation:
sum the parts of the ratio, 4 + 7 + 8 = 19 parts
Divide the perimeter by 19 to find the value of one part of the ratio.
95 cm ÷ 19 = 5 cm, then
4 parts = 4 × 5 cm = 20 cm
7 parts = 7 × 5 cm = 35 cm
8 parts = 8 × 5 cm = 40 cm
Thus the 3 sides are 20 cm, 35 cm and 40 cm
Answer:
The measure of the sides of a triangle will be:
4x = 4(5) = 20 cm
7x = 7(5) = 35 cm
8x = 8(5) = 40 cm
Step-by-step explanation:
Given that the lengths of the sides of a triangle are in the extended ratio 4 : 7 : 8.
Also given that the perimeter of the triangle is 95 cm.
We know that the Perimeter of a triangle is the sum of all the sides of a triangle.
As the lengths of the sides of a triangle are in the proportion 4 : 7 : 8. Thus, the measure of the sides will have the same scale factor x.
Therefore,
4x + 7x + 8x = 95
Add similar elements: 4x + 7x + 8x = 19x
19x = 95
Divide both sides by 19
19x/19 = 95/19
x = 5
Therefore, the measure of the sides of a triangle will be:
4x = 4(5) = 20 cm
7x = 7(5) = 35 cm
8x = 8(5) = 40 cm
Verification:
20 + 35 + 40 = 95
95 = 95
Find the slope of the line that passes through the points (2,4) and (6,12)?
Answer:
2 hurry!
Step-by-step explanation:
Answer:
m=2
Step-by-step explanation:
y2-y1/x2-x1
12-4/6-2
=8/4=2
m=2
: How many 3/2's are in 5?
Answer:
3 1/3
Step-by-step explanation:
5/3/2 = 10/3 = 3 1/3
help please... definition and an example of a quadratic function
Answer:
Step-by-step explanation:
Quadratic function is a function that can be described by an equation of the form fx = ax2 + bx + c, where a ≠ 0.
Example:
1. Use the graph of y = x2 + x - 6 to solve x2 + x - 6 = 0.
2. Use the graph of y = -x2 + 4 to solve -x2 + 4 = 0.
3. Use the graph of y = x2 -2x + 1 to solve x2 -2x + 1.
Colin buys a tv for £740. It depreciates at a rate of 4% per year. How much will it be worth in 5 years? Give your answer to the nearest penny where appropriate.
Given :
Colin buys a tv for £740. It depreciates at a rate of 4% per year.
To Find :
How much will it be worth in 5 years.
Solution :
Decrease in price in 1 year is :
[tex]P = P_o- P_o\times 0.04\\\\P = 0.96P_o[/tex]
So, decrease in price after x years is :
[tex]P = (0.96)^x P_o[/tex]
Putting value of x and [tex]P_o[/tex] in above equation, we get :
[tex]P = 0.96^5\times 740\\\\P = \£\ 603.38[/tex]
Therefore, the worth of T.V after 5 years is £603.38 .
yoooyoyooyoyoyoyoyoyoyooyo help
Answer:
Step-by-step explanation:
according the the pythogryamthreme the distance between 30 degress and 40 would vary since the length of 40 would change there by multipling 2 to 40 and 30 then times that by pie then divide it by 2 you should get the value for x, but for y it is more complex you see you much find the slope and plabora of the value x and 40 then using the 2 numbers times it by 30 after divide both numbers to each other resulting in the answer
49x + 9 = 49x + 83
PLEASE quickkkk i need a specific explanation on how to do this
Answer:
Step-by-step explanation:
49x + 9 = 49x +83
-49x -9
---------------------------
74
Dominique's age is 4 years less than twice brother's age b. Dominique is 12 years old. How old is her brother? Write an equation and solve using the replacement set of (6,7,8)
Answer:
8
Step-by-step explanation:
Dominique - 12
Brother- 12 / 6 * 4
12 / 6 is 2 then 2 * 4 is 8.
So her brother is 8 years old.
To prove this multiply 8 by 2 givig you 16. then 16 - 4 giving you 12. This means the answer is correct because dominique is supposed to be 4 years less than TWICE THE AGE OF HER BROTHER.
IF YOU DON'T UNDERSTAND PLEASE ASK AND I'LL GIVE YOU MORE CLARIFICATION :)
HOPE THIS HELPED
Answer:
Step-by-step explanation:
yeah 4-12x=2
so 16
Need answers for #3 please hep
Help!!”A 41-foot rope is stretched from the top of a 40-foot flagpole to the ground. How far is the base of the flagpole from the end of the rope.”
Answer:
9 feet away
Step-by-step explanation:
40²+b²=41²
1600+b²=1681
b²=81
b=9
The base of the flagpole from the end of the rope is 9 feet.
What is the Pythagorean theorem?Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We have,
Hypotenuse = 41 foot
Base = x
Height = 40 foot
Applying the Pythagorean theorem.
41² = x² + 40²
1681 = x² + 1600
x² = 1681 - 1600
x² = 81
x = 9
Thus,
The base of the flagpole from the end of the rope is 9 feet.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/14930619
#SPJ2
Quantities x and y are in a proportional relationship.
Answer:
yes they are
Step-by-step explanation:
Answer:
yes.
Step-by-step explanation:
they are.
For the diagram below, set up an equation and solve for all missing variables, find x. Plz help
Answer:
x=20
Step-by-step explanation:
what is the answer to 5(2x-4)
Answer:
-10x
Step-by-step explanation:
Answer:
6x
Step-by-step explanation:
?
Solve for X
9x + 8 = -1
Answer:
x = -1
Step-by-step explanation:
9x + 8 = -1
Subtract 8 from each side
9x + 8-8 = -1-8
9x = -9
Divide each side by 9
9x/9 = -9/9
x = -1
56 bananas Is what percent of
80 bananas?
Answer:
70%
Step-by-step explanation:
Branlist please!
Answer:
56 bananas Is what percent of
80 bananas?
56/80x100
=70%