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.
Make h the subject
G=5h-2f÷3
Answer:
I think H=5g-2f÷3 ( I'm not sure at all sorry )
A school Buys 3 boxes of pencils. each box has an equal number of pencils. There are 4272 pencil altogether. How many pencils are in two boxes.
Answer:
Each box contains 1424 pencils;
There would be 2848 total pencils in two boxes.
Step-by-step explanation:
1424 x 2 = 2848 pencils
Equivalent factored form for 10x^2+15x-9=2x^2+x-14
15 out of 60 markers are blue. What percent of the markers are blue?
How will we solve this problem?
Answer:
Step-by-step explanation:
if 15 out of 60 markers are blue
the percentage is 15/60=1/4
0.25*100=25%
Titus and Theresa have collected money and are buying food for a dog shelter. Titus buys 2 bags and 5 cans of dog food, spending $17.50. Theresa buys 6 bags and 2 cans of dog food for $40.80. Let x represent the price of a bag of dog food and y represent the price of a can of dog food. Write a system of equations and use the elimination method to find a reasonable price for a can of dog food.
A)$0.90
B)$1.70
C)$6.30
D)$6.50
solve the equation P=b+c+a solve for b
Answer:
b = P - c - a
Step-by-step explanation:
Norma and Albert both clean pools. Each charges a flat fee to clean a pool. Norma cleans 12 pools in 8 hours and earns $270. Albert cleans 9 pools in 7.5 hours and earns $195.75.
Answer:
Step-by-step explanation:
Noma cleans 12 pools in 8 hours
How many pools in how many minutes?
8 x 60= 480
He cleans 12 pools in 480 minutes
How many minutes does he take to clean a pool?
480/12 = 40
He cleans a pool in 40 minutes.
How much does he earn to clean a pool?
since he cleans 12 pools to earns $270
then 270/12 =22.5
Therefore, he charges $22.5 to clean a pool in 40 minutes.
Albert 9 pools in 7.5 hours
How many pools in how many minutes?
7.5 x 60= 450
He cleans 9 pools in 450 minutes
How many minutes does he take to clean a pool?
450/9 = 50
He cleans a pool in 50 minutes.
How much does he earn to clean a pool?
since he cleans 9 pools to earns $195.75
then 195.75/9 =21.75
Therefore, he charges $21.75 to clean a pool in 50 minutes.
A net of a rectangular pyramid is shown. The rectangular base has length 26 cm and width 24 cm. The net of the pyramid
has length 74.8 cm and width 71.8 cm. Find the surface area of the pyramid.
The surface area is
cm2 help
Answer:
kk
Step-by-step explanation:
no pic
Work out the perimeter of an equilateral triangle with side length 2.7mm
Answer:
, so easy
Step-by-step explanation:
3×2.7mm=8.1mm
Answer:
8.1mm
Step-by-step explanation:
equilateral triangle all sides are equal.
If 1 side is 2.7mm what will be the total of three sides. 2.7+2.7+2.7=8.1mm
Determine the area of the triangle when tana=1 the image is in the picture above
Answer:
The area will be:
[tex]A=18(1+\sqrt{3}) \: u^{2}[/tex] or [tex]A=49.18 \: u^{2}[/tex].
Step-by-step explanation:
Using the definition of tangent, we have:
[tex]tan(\alpha)=\frac{6}{\vec{AB}}[/tex]
We know that tan(α) = 1, then we can find AB
[tex]1=\frac{6}{\vec{AB}}[/tex]
[tex]\bar{AB}=6\: u[/tex]
u means any unit.
Now, we need to find the distance BC. If the angle ∠D is 60°, then ∠C must be 30°. Using the tangent definition in the triangle BCD we have:
[tex]tan(30)=\frac{6}{\bar{BC}}[/tex]
[tex]\bar{BC}=\frac{6}{tan(30)}[/tex]
[tex]\bar{BC}=\frac{6}{1/\sqrt{3}}[/tex]
[tex]\bar{BC}=6\sqrt{3} \: u[/tex]
So, the base of the triangle will be:
[tex]b=\bar{AB}+\bar{BC}=6+6\sqrt{3}=6(1+\sqrt{3}) \: u[/tex]
The area of a triangle is given by the following equation:
[tex]A=\frac{b*h}{2}[/tex]
b is the base ([tex]b=6(1+\sqrt{3})\: u[/tex])h is the height (h=6 u)[tex]A=\frac{6(1+\sqrt{3})*6}{2}[/tex]
[tex]A=18(1+\sqrt{3})[/tex]
Therefore, the area will be [tex]A=49.18 \: u^{2}[/tex].
I hope it helps you!
Any help? Still learning this so it’s not of a problem. Thanks!
at the party Adrian will serve each guest 1/8 of a cake he has 3 cake what is the greatest number of guests can Adrian serve
HELPPPP: From the top of a light house 50 meters high, the angle of depression of a boat out at sea has a measure of 15°. Find to the nearest meter the distance from the boat to the foot of the light house, which is at sea level.
Answer:
13m
Step-by-step explanation:
[tex]d=50tan(15)=13m[/tex]
The required distance from the boat to the foot of the light house, which is at sea level is 13meter
Given that,
The top of a light house 50 meters high,
The angle of depression of a boat out at sea has a measure of 15°.
We have to determine,
To the nearest meter the distance from the boat to the foot of the light house, which is at sea level.
According to the question,
The angle of depression may be found by using this formula = opposite/adjacent.
The opposite side in this case is usually the height of the observer or height in terms of location.
Therefore, angle of depression = 15degree
Height of the light house = 50m
The distance from the boat of the light house is denoted by d.
Then the distance from the boat of the light house is given as.
[tex]tan15 = \frac{d}{50} \\\\d = 50 \times tan15\\\\d = 50\times0.26\\\\d = 13[/tex]
Hence, The required distance from the boat to the foot of the light house, which is at sea level is 13meter
For more information about Trigonometry click the link given below.
https://brainly.com/question/2773823
Find the area of the polygon pls
Given:
The figure of a polygon.
To find:
The area of the polygon.
Solution:
Area of a triangle is
[tex]Area=\dfrac{1}{2}\times Base\times Height[/tex]
Area of trapezoid is
[tex]Area=\dfrac{1}{2}(a+b)h[/tex]
Where, a, b are bases and h is the height.
The area of the triangle with base 6 cm and height 8 cm is
[tex]A_1=\dfrac{1}{2}\times 6\times 8[/tex]
[tex]A_1=24[/tex]
Height of the trapezoid is [tex]13-8=5\ \text{cm}[/tex] and the bases are 6 cm, 12 cm. So, the area of the trapezoid is
[tex]A_2=\dfrac{1}{2}(6+12)(5)[/tex]
[tex]A_2=\dfrac{1}{2}(18)(5)[/tex]
[tex]A_2=(9)(5)[/tex]
[tex]A_2=45[/tex]
Now, the total area of the polygon is
[tex]A=A_1+A_2[/tex]
[tex]A=24+45[/tex]
[tex]A=69[/tex]
Therefore, the area of the polygon is 69 sq. cm.
please help, will be grateful and give brainliest!
Answer:
x=216°
Step-by-step explanation:
100%=360°
To find 10% divide by 10
10%=36°
x4
40%=144°
in a full circle thered 360°
360-144=216°
x=216°
The formula to convert Celsius to Fahrenheit is FC +32. Convert 87°F to
Celsius. Round to the nearest degree.
Answer:
31°
Step-by-step explanation:
To convert Fahrenheit to Celsius is C= (F-32) * 5/9
So first do parenthesis 87-32= 55
Next multiply that number by 5/9 which is 30.55555555
Then round your answer = 31°
What is the solution?
Answer:
(1,-1)
Step-by-step explanation:
the solution is where the two lines meet up at and they meet up at (1,-1)
Evaluate the expression (13 - 2) ^ 2 ÷ 11
What is the value expression?
Answer:
11
Step-by-step explanation:
(13-2)^2/11
11^2=121
121/11=11
Calculate the quotient.
A. 3/4 divided by 5 1/5 is? B. 3/7 divided by 2 1/2 is? C. 5/8 divided by 6 5/6 is? D. 8 3/10 divided by 5/8 is?
What are the answers?
A) 3/4 ÷ 5 1/5.
Answer:
[tex] \frac{15}{104} [/tex]
B) 3/7 ÷ 2 1/2.
Answer:
[tex] \frac{6}{35} [/tex]
C) 5/8 ÷ 6 5/6.
Answer:
[tex] \frac{15}{164} [/tex]
D) 8 3/10 ÷ 5/8.
Answer:
[tex]13 \frac{7}{25} [/tex]
3. Select all the situations that can be represented by an exponential function.
1. Jim deposits $1,000 in an account that doubles in value every 7 years.
2. Brian deposits $30 in a savings account. Then he deposits $2 each month for the next 9 months.
3. Leon runs a mile in 8 minutes. Then he runs a mile each day for the next 4 days, reducing his time by 1.5% each day.
3.Cynthia runs a mile in 9 minutes. Then she runs a mile each day for the next 4 days, reducing her time by 6 seconds each
5.Marie deposits $30 in a savings account. Then she makes a deposit each month for the next 9 months, putting in $2 more
deposit
I think the answer is A, B, and E. I'm not sure if it is 100% correct.
Anyone know the middle question ?
Which equation yields the solutions x=−2 and x=−10?
Options:
A. −x2−2x+35=0
B. 5x2+40x+60=0
C. −4x2+24x−20=0
D. x2+12x+20=0
Answer: its not B
sorry it only let me choose once ttm2021
The length of a diagonal of a square is 10 square root of 2 inches. Find the length of one side of the square.
Answer:
10inches
Step-by-step explanation:
Let the length of one side of the square be a
If the diagonal of a square is 10√2 inches
According to pythagoras theorem
a²+a² = (10√2)²
2a² = 100(2)
2a² = 200
a² = 200/2
a² = 100
a = √100
a = 10
Hence the length of one side of the square is 10inches
Three-quarters of a pound of candy cost 66 cents. Find the cost of one pound
of candy.
Answer:
$0.88 per pound
Step-by-step explanation:
you want to divide the 3/4 pounds by 3, and when you do that, you also have to divide the 66 cents by 3 as well, then multiply the 1/4 you get from dividing 3/4 by 3, and multiply it by 4 to get 1 pound, but when you do that, you have to do the same thing with the 22 cents you get from dividing 66 cents by 3, which will give you 88 cents per pound
Amelia calls people at random to conduct a survey. So far, 20 calls have been answered and 30 calls have not been answered. What is the approximate probability that someone answers the next call she makes?
A.
40%
B.
67%
C.
0.6
D.
2/3
Answer: 40%
Step-by-step explanation:
I guessed on this but i got it right
Answer:
40%
Step-by-step explanation:
Mel uses one fourth of a yard of ribbon to make a hair bow how many hair bows can mel make with 1 yard of ribbon
Answer:
4
Step-by-step explanation:
If its 1/4 then you can use it 4 times to equal a whole yard
n
Which equation represents the line that passes through (-6, 7) and (-3, 6)?
O y=-x+9
y=-*x+5
y=-3x - 11y
y=-3x + 25
Answer:
Y=-3x-11y
Step-by-step explanation:
Not sure but I am pretty sure it is this
A new bank customer with $3,500 wants to open a money market account. The bank is offering a
simple interest rate of 1.1%.
a. How much interest will the customer earn in 10 years?
b. What will the account balance be after 10 years?
Answer:
A. they will earn 385 dollars in interest in ten years
B. the accounts balance will be $3,885 after 10 years
Step-by-step explanation:
for part A, there are 2 possible answers, depending on what your looking for, if your looking for the percentage interest, then its 11%, but if your looking for how much they will make off of interest in 10 years, then the answer would be $385.
please help!!!!!! emergency
lena purchased a prepaid phone card for $20. long distance call cost 18 cents a minute using this card. Lena used her cared only once to make a libg distance call. if the remaining credit on her card is $13.34, how many minutes did her call last?
Answer:
37 minutes
Step-by-step explanation:
We start by finding the difference between the original amount and what is left
Mathematically, that will be;
20-13.34 = 6.66
To
cents that will be 6.66 * 100 = 666 cents
We now divide by the amount per minute
The amount per minute is 18 cents
Thus, the number of minutes will
be 666/18 = 37