Answer:
It’s true
Step-by-step explanation:
Proof by induction
Let the four chosen numbers be x_1, … x_4 and, without loss of generality, let x_1 < x_2, … < x_4.
For x_1 = 1, the smallest possible choice, let x_2 = x_1 + 20 = 21 be the smallest possible choice that has a difference larger than 19. Likewise, x_3 = x_2 + 20 = x_1 + 40 = 41. Then x_4 has to be at least x_3 + 20 = x_1 + 60 = 61 which is out of range.
For the induction, suppose that x_4(n) = x_1(n) + 60 > 60 and therefore x_4(n) can’t be chosen for a given x_1(n). Then incrementing x_1(n+1) = x_1(n) + 1 would require x_4(n+1) to be at least x_1(n) + 1 + 60 = x_4(n) + 1 > 61, so this is out of range as well.
For another induction, suppose that x_4(n) = x_2(n) + 40 > 60 and therefore x_4(n) can’t be chosen for a given x_2(n). Then incrementing x_2(n+1) = x_2(n) + 1 would require x_4(n+1) to be at least x_2(n+1) + 40 = x_4(n) + 1 > 61, so this is out of range as well.
Likewise, for the induction, suppose that x_4(n) = x_3(n) + 20 > 60 and therefore x_4(n) can’t be chosen for a given x_3(n). Then incrementing x_3(n+1) = x_3(n) + 1 would require x_4(n+1) to be at least x_3(n+1) + 20 = x_4(n) + 1 > 61, so this is out of range as well.
Therefore all choices of x_1, x_2, x_3 with differences greater than 19 leaves no choice of x_4 within range with x_4 > x_3 + 19.
Help please please answer
Answer:
A
Step-by-step explanation:
x. y = 28
check attachment
When Three friends divide four boxes of baseball trading cards ?evenly, they each get 48 cards. How many cards are in each box?
Answer:
36 cards in each box
Step-by-step explanation:
Let the number of cards in each box be x.
4 * x / 3 = 48 (4 packs of cards, three friends)
x / 3 = 21
x = 36.
Answer:
36 cards in each box
Step-by-step explanation:
Because each friend gets the same amount of cards, there needs to be 48*3 or 144 trading cards in total. There are 4 boxes so in each box there would be 144/4 or 36 cards in total.
Alex and glen share a 30 ounce bucket of clay by the end of the week alex has used 1/10 of the bucket and glen has used 2/5 of the bucket of clay how many ounces are left in the bucket
Answer:
21 ounces
Step-by-step explanation:
Answer:
15 ounces
Step-by-step explanation:
we know that the whole is 30 we know that Alex 1/10 and glen has 2/5 we dont know wht left over :: 1/10 + 2/5 = 1/10 + : 4/10 = 5/10 so 1 - 5/10 = 5/10
We need to find how many ounces of clay are left. Which equation can we use to find how many ounces are in 5/10
of the whole bucket? 5/10 x 30 and 5x 30 10
15 onces
Anyone know the middle question ?
Trapezoid STUV is similar to trapezoid NOPQ. What is the length of OP?
Answer:
F. 4 2/3 centimeters
Step-by-step explanation:
since the trapezoids are similar to each other, that means there is a common ratio between them. so taking into consideration the first trapezoid STUV when we compare that to NOPQ, OP comes out to be 4 and 2/3 centimeters. start by comparing the ratio of ST to NO and then move on to TU and then OP.
. Since the pentagon is a regular pentagon, the measure of each interior angle will be the same.
To find the size of each angle, divide the sum, 540º, by the number of angles in the pentagon.
(which is the same as the number of sides).
540° ÷ 5 = 108° There are 108° in each interior angle of a regular pentagon.
2. 540°
Sum of Interior Angles of a Polygon
A pentagon has five sides, thus the interior angles add up to 540°, and so on.
please help!
thank u!
Answer:
c
Step-by-step explanation:
A line with a slope of 2 passes through the point (5, 8). What is its equation in slope-intercept form? (I will make u brainleist)
Answer:
y= 2x -2
Step-by-step explanation:
Find the solution
4y-x=5+2y
3x+7y=24
Answer:
24
Step-by-step explanation:
Please explain how you got the answer. Don’t just tell me the answer
Answer: (4 3/5) x (3 1/2)
23/5 (3 1/2)
23/5 (7/2)
161/10 =
your answer is 16 1/10
Step By-step explanation:
A baker melts 80 grams of chocolate that contains 40% cocoa and mixes it with 60
grams
of his secret mixture. The result is a chocolate with 55% cocoa. What is the
percent of cocoa in the baker's secret mixture?
Answer:
15%
Step-by-step explanation:
55%-40% = 15% cocoa.
IM GIVING 43 POINTS PLS ANSWER ASAP I MARK BRAINLIEST
Answer:
m = 3Step-by-step explanation:
Get two points and use slope formula
Points
(50, 40) and (60, 70)Find the slope:
m = (y₂ - y₁)/(x₂ - x₁) m = (70 - 40)/(60 - 50) = 30/10 = 3Help with #10 please I’m having trouble understanding
Answer:
u=66(oppodite angles of parallrlogram are equal)
66+3v=180( cointerior angle)
3v=114
V=38
Step-by-step explanation:
plz mske me brainliest
9x + 5 = 4(x + 2) + 5x
solve for X
Answer:
no solution
Step-by-step explanation:
9x + 5 = 4(x+2) + 5x
9x + 5 = 4x + 8 + 5x
9x + 5 = 9x + 8
9x + 5 can never be equal to 9x + 8, so the answer is no solution
Answer:
x=3
Step-by-step explanation:
9x + 5 =4(x+2) + 5x
9x + 5= 4x + 8+ 5x ( do the parenthesis first- mulitiply 4 and x and get 4x and 4 times 2 = 8)
9x + 5 = 9x + 8 ( add the x's together 4x +5x = 9x )
9x = 9x + 3 ( subtract 5 both sides and you get 3 )
=3 ( subtract 9x from both sides
Brainliest if right i need a couple more to move on :)
and if there is a choice no solution :))
What is the measure of angle AEB? Enter your answer as a whole number.
Answer: 89 or 90 degrees.
Step-by-step explanation:
Ryan scored 12 more points than Alex on a video game. If together they scored 214 points, how many points
does each person score?
Answer:
Ryan 113, Alex 101
Step-by-step explanation:
Ryan beats Alex by 12 points
101+101=202
202+12=214
113+101=214
Consider the line - 4x – 3y = 5.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
The slope of the perpendicular line is 1/4
A line parallel to this will have the same gradient of -4.
Need help fast as possible!!!! Pleaseeeee!!!!!!!!
ita 3 fiths x plus three eigths
plz plz plz help ASAP
Answer
B. number five is right
Step-by-step explanation:
Answer:
$5
Step-by-step explanation:
First, subtract the $6 toy from the total of $71.
$71 - $6 = $65
The total of the shirts and pants is $65.
She bought 9 shirts and 4 pants, which would be 13 shirts and pants.
We then divide the total cost of the shirts and pants, $65 by the total shirts and pants, 13.
65 / 13 = 5
So, each shirt or pants costs $5.
I would appreciate brainliest, if not that's ok!
Luego de dormir 6 horas al día a usted le quedan 18, que puede repartir entre estudio y ocio. X representa
las horas dedicadas al ocio y la variable Y las horas de estudio. Represente la relación lineal existente entre
las distintas combinaciones posibles de X e Y.
The linear relationship between the different possible combinations of X and Y is Y= -X + 18.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
We know that after sleeping for 6 hours, there are 18 hours left in a day. These 18 hours can be split between leisure time and study time.
Now,
Let's let X be the number of hours of leisure time, and Y be the number of hours of study time.
Since we know that there are a total of 18 hours,
we can set up the following equation.
X + Y = 18
This equation represents all the possible combinations of X and Y that add up to 18 hours.
Now,
To represent a linear relationship between X and Y.
Y = -X + 18
This equation represents a linear relationship between X and Y.
Where X is the independent variable and Y is the dependent variable.
This is in the form of a slope-intercept form.
y = mx + c
Where m = -1 and c = 18
So,
The slope = -1 and the y-intercept is 18.
Thus,
Y= -X + 18 represents all the different possible combinations of leisure time and study time that adds up to 18 hours.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ5
The complete question.
After sleeping 6 hours a day, you have 18 hours left, which you can divide between study and leisure. X represents the hours dedicated to leisure and the variable Y the hours of study. Represent the linear relationship between the different possible combinations of X and Y.
The rectangle is enlarged by a scale factor of 5. What is the perimeter of
the enlarged rectangle?
Answer:
I believe its 90
Step-by-step explanation:
You multiply each side by 5
5x5=25
double it for the other side
4x5= 20
double it
50+40=90
CAN I GET HELP PLEASE!
Answer:
0.30 of a book / hour or 3/10 of a book per hour.
Step-by-step explanation:
Usually I tell people to put the numbers into decimals. Unfortunately for this question, it won't work. So we have any choice but to do it with fractions.
r = amount / time
amount = 1/4
time = 5/6
r = [tex]\frac{\frac{1}{4} }{\frac{5}{6} }[/tex]
Invert the denominator and multiply
r = [tex]\frac{1}{4} * \frac{6}{5}[/tex]
r = 6 * 1 / (5*4) = 6/20 = 3/10
The answer is 3/10 of a book per hour
5/6 of an hour is almost an hour.
1/4 of a book is 0.25 of a book.
3/10 of a book is 0.30 of a book. So it looks like it is just about right.
HELP meeeeee please
Answer: a = 23, b = 21, c = 136
Step-by-step explanation:
5(wx + yz) =5wx + 5xy
Answer:
Step-by-step explanation:
5wx+5yz=5wx+5xy
5wx-5wx+5yz=5xy
5yz=5xy
can someone solve this?
47z²−25
Step-by-step explanation:
3627272727822881818181
Answer:
130z-3
Step-by-step explanation:
Break down the equation:
(9[tex]z^{2}[/tex]-4)=
9z * 9z= 81z
You can't subtract 4, so I left it at (81z- 4)
(7[tex]z^{2}[/tex]+ 1)=
7z * 7z= 49z
You can't add 1, so I left it at (49z+ 1)
Then Solve:
You can add 81z and 49z.
81z+49z= 130z
-4+1= -3
Hope this helps!
HELP PLS!!! WILL GIVE BRAINLIEST!!!
Answer:
The correct answer is B.2 plz mark as brainliest.
Step-by-step explanation:
is 144 a natural number yes or no
Answer:
is 144 a natural number yes or no
Yes
I'm not sure
Spins a fair spinner numbered 1 - 5 and flips a fair coin. What is the probability of obtaining a factor of 15 and a tail?
Answer:
3/10
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that the fair spinner is numbered 1 - 5, the factors of 15 there are 1, 3 and 5 hence the probability of obtaining a factor of 15
= 3/5
The probability of obtaining a tail from the flip of a coin
= 1/2
Hence the probability of obtaining a factor of 15 and a tail
= 3/5 * 1/2
= 3/10
HELP ASAP ILL GIVE U BRAINLEIST
Answer:
"A number cubed is a power where the base is the variable n and the exponent is 3"
"Increased by 4 means add 4"
"The expression is written as n^3 + 4"
On a map with a scale of 1 cm : 2.5 km two towns are 5 cm apart. What is this distance in real life?
Answer:
12.5 km
Step-by-step explanation:
1cm = 2.5km
2cm = 5km
3cm = 7.5km
4cm = 10km
5cm = 12 5km
The expression logx (ab) is equivalent to
Answer:
logx a + logx b
Step-by-step explanation: