We can use both regular and strong induction.
The Fundamentals of Inductive Mathematics (i.e., Regular Induction). If any of the following statements involving a positive number, n, are accurate: The claim is true if and only if n is 1. If the assertion is true for n=k, then it must also be true for n=k+1(x).
In a variation of induction known as strong induction, we make the assumption that the assertion is true for all values before k. This provides us with more information with which to work.
Regular Induction form
N>6 = n=7 in basic case
3n = 37 = 2187
N! = 7! = 5040
For n= 7 3n<n! is true
Induction hypothesis
Let for n= k and k>6
Assume 3k<k! is true
We prove that for k = k+1 the assumption holds true then the assumption must be true for k
K = k+1
3k+1 < (k+1)!
3k. 3 < (k+1) k!
3k < (k+1)/3.k!
For k>6
(k+1)/3 >1 and let (k+1)/3 = p
3k < P.k!
But we assumed that 3k < k! for k > 6 then 3k must be less than p.k1 since P>1
Therefore 3k<k! for k>6
3n < n! for all integers n greater than 6.
Therefore we can use both regular and strong induction
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Mr.Hollis determines that he gives away 800each month if he gives away 16 of his budget then how much is his overall budget
The overall budget the Mr Hollis has is $12800.
What is fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Mr.Hollis determines that he gives away 800 each month and the fraction is 1/6 of his budget.
The value of the overall budget will be illustrated as x.
Therefore 1/16 × x = 800
x / 16 = 800
x = 16 × 800
x = 12800
Hollis has $12800 as budget.
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For a snack, Miss Johnson gives her class graham crackers. She has a package of 30
graham crackers to share equally among twelve students.
How many graham crackers should each student receive?
Dividing
?
graham crackers among
Each student gets
crackers.
students can be found by solving
Answer:
each student get 2.5 of graham crackers
Step-by-step explanation:
[tex]total \: students \: = 12 \\ graham \: crackers \: = 30 \\ 30 \div 12 \\ = 2.5[/tex]
8+ (-3) + (-8)
NEED HELP
Answer:
[tex]-3[/tex]
Step-by-step:
[tex]8+ (-3) + (-8)[/tex]
1 ) Combine like terms...
[tex]=5 - 8[/tex]
2 ) Solve...
[tex]= - 3[/tex]
Hope this helps! :)
The sum of two numbers is 12. The difference of the same two numbers is -4. Wht is the smaller number?
Answer:
The smaller number is 4.
Step-by-step explanation:
X and Y are the two numbers
x+y=12
x-y=-4
Subtract these two equations
(x+y=12)
-(x-y=-4)
—————-
2y=16
y=8
Plug it in to any equation:
x+y=12
x+8=12
x=4
/what is y-5x=3 solve for Y
Answer:
y=3+5x
Step-by-step explanation:
Add 5x to both sides.
A window in the room has an actual width of 2. 5 feet. What is the width of the window in the blueprint? (same scale 3 in:5 ft)
The window width in the blueprint is 1.5 in.
Define the meaning of the term scale factor?A scale factor is a designation for figures with similar appearances but differing scales or measures.Assume two circles appear identical but have different radii. The scale factor specifies how much larger or smaller a figure is compared to the original figure.As per the given question-
A window in the room measures 2. 5 feet in width.
The given scale is-
Blue print (inches) : original (feet)
3 in : 5 ft
Divide both side by 2
1.5 in : 2.5 ft
Window's width in Blue print (inches) = 1.5 in.
As a result, the window width in the blueprint is 1.5 in.
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1. which of these variables are discrete and which are continuous random variables? (a) the number of new accounts established by a salesperson in a year. (b) the time between customer arrivals at a bank atm. (c) the number of customers at big nick's barber shop. (d) the amount of fuel in your car's gas tank. (e) the number of minorities on a jury. (f) the outside temperature today.
The discrete and continuous random variables are-
a) Discrete; (b) Continuous; (c) Discrete; (d) Continuous; (e) Discrete; (f) Continuous
Define the term discrete and continuous random variables?Discrete variables are those whose values may be measured through counting. Contrarily, random variables which it reflect something are designated continuous variables.(a) So because number of new accounts is counted, (a) discrete (like, non-negative integers).
(b) Continuous, given that the interval between customer arrivals may have decimal values (like 2.9 minutes or 27.75 seconds).
(c) Because the quantity of clients is counted, (c) discrete (like, non-negative integers).
(d) Continuous, as the fuel consumption can have decimal values (like 15.5 gallons).
(e) Since this number of minorities is counted, (e) discrete (like, non-negative integers).
(f) Continuous since the outdoor temperature can be expressed in decimal degrees (e.g., 7.78 C).
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The bids in an online auction are represented by the arithmetic sequence shown below. Write an explicit formula to represent the bids as an arithmetic sequence. What is the twelfth bid?
195, 205, 215, 225,...
A(n) =
A(12) =
(Type an expression using n for the variable.)
(Simplify your answer.)
(a) The nth term of the sequence is given by A(n)=195 + (n - 1)10.
(b) The 12th term of the sequence is A(12) = 305.
What is an arithmetic sequence?One arithmetic progression with a common difference of 2 is the sequence 5, 7, 9, 11, 13, 15,...
The term "finite arithmetic progression" or "arithmetic progression" refers to a limited segment of an arithmetic progression.
A mathematical sequence has the following structure: a, a+d, a+2d, a+3d, etc., up to n terms. The initial term is a, the shared distinction is d, and n is the total number of words. Find the AP, the first term, the number of terms, and the common difference for the computation using the arithmetic sequence formulae. To determine the nth term, sum, or common difference of a given arithmetic sequence, many formulae related to arithmetic series are utilized.
A(n)=195+(n-1)10
The given arithmetic sequence is 195, 205, 215, 225,.....
The first term a =195
The common difference d= 205-195
d =215-205
d =225-215
So, d = 10
(a) The nth term is given by
A(n)=a+(n-1)d
A(n)=195+(n-1)10
(b) For n=12, the 12th term is given by
A(12)=195+11(10)
A(12)=305
Therefore, A(n)=195+(n-1)10
And A(12)=305
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Nigel is selling candy bars for his outdoor club. He is averaging 4 bars every 3 days. If he continues at this rate, how many days will it take to sell his box of 35? Answer in whole number form and round up to the next whole number.
The number of days that it will take to sell his box of 35 is 21 days.
What is a ratio?Ratio simply demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
In this case, Nigel is selling candy bars for his outdoor club and he is averaging 4 bars every 3 days.
Let the number of days be x.
This will be:
3/x = 4/35
Cross multiply
4x = 3 × 35
x = (3 × 35)/4
x = 105 / 4
x = 21
It will take 21 days
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Peni needs $1.20 daily for bus
fares, 50 cents daily to spend at the school canteen and $1.00 per day for newspaper.
Answer:
Peni will need a total of $17.90
Step-by-step explanation:
$1.20 x 7 = $8.40
$0.50 x 5 = $2.50
$1.00 x 7 = $7.00
$8.40 + $2.50 + $7.00 = $17.90
Corinne and Deanna decide to race from one corner of an open field to the other. The field is rectangular in shape, 60 meters long and 80 meters wide. Since Corinne is older and faster, she's going to run along the outside of the field, and Deanna will take the diagonal route. If Deanna can run at a rate of 5 meters per second, how fast will Corinne have to run to get there at the same time as Deanna?
Answer:
Corinna will have to run at 7 meters per second to get there at the same time as Deanna.
Step-by-step explanation:
So to find the distance of Deanna's route, you can use the Pythagorean theorem.
a^2 + b^2 = c^2
60^2 + 80^2 = 10000
c^2 = 10000
Take the square root of both sides.
c = 100
So Deanna runs 100 meters at 5 meters per second.
100/5 = 20
She runs for 20 seconds.
To find Corinne's distance, we add 60 and 80, which is 140.
To find how fast she need to run to get there in 20 seconds, you divide 140 by 20, which gets 7 (meters per second). You can also think of it like this: to run 140 meters in 20 seconds, she has to run at 140 meters per 20 seconds, which you can simplify (like a fraction) to 7/1, or just 7
Which statement best analyzes the role this event plays in the plot?
In "The Necklace" Mathilde realizes too late that the necklace is a fake.
The statement that best analyzes the role this event plays in The Necklace plot is A. It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.
How to illustrate the information?There are both planned and unplanned events, and the start and end times may be noted. Event types include accidents, celebrations, natural disasters, and rallies. The event is the occurrence of the event.
Loisel is well-liked and adored by all. As she walks away, she searches for the pendant and discovers it has gone missing. After days of searching, she and her husband decide to replace it with something similar. It takes her ten decades to pay for the successor, which costs the same as your salary.
In this case, it best analyzes the role this event plays in leading to the resolution where Mathilde learns a lesson about the downfall that can come from vanity and greed The plot of The Necklace.
Therefore, the correct option is A.
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Complete question
Which statement best analyzes the role this event plays in The Necklace plot?
“Oh, my poor Mathilde! Why, my necklace was paste! It was worth at most only five hundred francs!”
It leads to the resolution where Mathilde learns (a little too late) a lesson about the downfall that can come from vanity and greed.
It is the climax of the story since the reader is most excited at this point.
It serves as a complicating incident because Mathilde will have to suffer the consequences of her actions.
It serves as the falling action because it shows that Mathilde will have to get used to her place in life.
Please help now asap !!! Due tomorrow
Answer:
Step-by-step explanation:
it help by showinbng thta
How many triangles are in the figure below?
- 5
- 6
- 7 < answer
- 8
This question isn't possible, so I missed it and checked afterwards. Here's the answer for anyone else who may cross it's path. If possible, I'd love to know why 7 is the answer. I really have no idea.
Answer:
7 is correct.
There are 4 small triangles, 2 medium-sized triangles, and 1 large triangle.
You're putting 81 feet of molding
along the walls around a rectangular
room that's 12 feet wide; what is the
area of that room (if you subtracted
3 feet for the width of the door)?
Answer:
360 sq feet
Step-by-step explanation:
The width of the room is given in the question, 12 feet.
We don't know the length. Let's call the length x.
x = length
We were also given the perimeter, 81, that's the distance around the sides...
all the sides added up.
Use x for the long wall.
Use x-3 for the wall with the door in it.
x + 12 + x-3 + 12 = 81
combine like terms
2x + 21 = 81
subtract 21
2x = 60
divide by 2
x = 30
The room is 30 feet long by 12 feet wide.
Area =
length × width
= 30 × 12
= 360
The area of the room is 360sq feet.
A 132 -inch is cut into two pieces. One piece is times the length of the other. Find the length of the shorter piece.
The length of the shorter piece is 33 inches.
According to the question,
We have the following information:
A 132 -inch is cut into two pieces. One piece is three times the length of the other.
Now, let's take the length of the shorter piece to be x inches and the length of another piece will be 3x inches.
Now, we have the following expression:
x+3x = 132
4x = 132
4 is in multiplication on the left hand side. So, it will be in the division on the right hand side.
x = 132/4
x = 33 inches
Hence, the length of the shorter piece is 33 inches.
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the table below gives the annual sales (in millions) of a product. year 1998 1999 2000 2001 2002 2003 2004 2005 2006 sales 273 327 369 399 417 423 417 399 369 what was the average rate of change of annual sales a) between 2001 and 2002 millions of dollars/year b) between 2001 and 2006 millions of dollars/year
Main answer:
a) 18 millions of dollars/year
b) 6 millions of dollars/year
Step-by-step explanation:
a) the average rate of change of annual sales between 2001 and 2002 millions of dollars/year
Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)
= (417 - 399) / (2001 - 2002)
= 18 / 1
= 18 millions of dollars/year
b) the average rate of change of annual sales between 2001 and 2006 millions of dollars/year
Average rate = (Final year - Initial year) / (Sales on Final year - Sales on Initial year)
= (369 - 399) / (2006 - 2001)
= 30 / 5
= 6 millions of dollars/year
The average rate of change of annual sales between 2001 and 2002 is 18 millions of dollars/year , between 2001 and 2006 is 6 millions of dollars/year
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The polynomial f(x) = 2x ^ 3 + a * x ^ 2 + bx + 6 is exactly divisible by 2x - 3 and has the remainder -28 when divided by (x + 3) a) find the values of a and b. b) solve the equation f(x) = 0
The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9
To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).
The given polynomial is:
f(x) = 2x³ + ax² + bx + 6
- The polynomial is exactly divisible by (2x-3) means:
f(3/2) = 0
2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0
27 + 9a + 6b + 24 = 0
9a + 6b = - 51 (equation 1)
- f(x) divided by (x+3) has remainder -28
f(-3) = -28
2. (-3)³ + a(-3)² + b(-3) + 6 = -28
9a - 3b = 20 (equation 2)
Substract equation 2 from equation 1
9a + 6b = -51
9a - 3b = 20 _
9b = -71
b = -71/9
9a - 3(-71/9) = 20
9a = 131/3
a = 131/27
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Pls help asap
Number 3
Answer:
No
Step-by-step explanation:
The value that corresponds with the other value on a data (34 to 2, 51 to 3, 68 to 5 etc.) needs to have the same quotient (or ratio) when you compare them.
34/2 = 51/3 ? Yes (but you can't stop here because you need to test ALL the values, what I mean is ALL the values UNTIL you found one that is not equal to each other, if all of them are equal, then the data are proportional.
34/2 = 68/5 ? No (Now you can stop here and say it's not proportional because we already found one pair that are not equal).
2 Dora has solved the equation 4(x - 1) = 11
4(x - 1) = 11
4x41 = 11
4x = 52
x = 13
Dora is incorrect. Explain her mistake.
Dora put the x es
and did 4x11
11 and
Find the correct solution to 4(x − 1) = 11
I mark
Dora solved the equation.
She multiplies 4 inside the bracket. But she fails to know that 4× -1 = -4. Instead she multiplied that 4×-1 = -41. This is her first mistake.
In the second step, she shifted -41 to the right side in order to find the value of x. As -41 gets shifted to right side , -41 becomes +41 and added with +11 to get 52. which is totally a wrong method.
Step-by-step explanation:
Here is the exact method of solvation.
[tex]{ \blue{ \bold{4(x - 1) = 11}}}[/tex]
[tex]{ \blue{ \bold{4x - 4 = 11}}}[/tex]
[tex]{ \blue{ \bold{4x = 11 + 4}}}[/tex]
[tex]{ \blue{ \bold{4x = 15}}}[/tex]
[tex]{ \blue{ \boxed{ \red{ \sf{x = \frac{15}{4}}}}}} [/tex]
can someone help its easy but im lazy plssss
The equation which represents the price of the ticket after the discount is y = 0.25x.
What is a linear equation?A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Given that the movie theatre is giving a discount of 75% the original cost of the ticket is x and discounted cost is represented by the variable y.
The equation for the cost of the ticket will be written as,
y = x - 0.75x
y = 0.25x
The graph of the linear equation is attached with the answer below.
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Write an equation of a line that passes through (-1,2) and is parallel to a line with x-intercept (3,0) and y-intercept (0,1).
The Equation of line is y= -1/3x + 5/3
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
x-intercept = (3,0) and y-intercept = (0,1).
slope, m= 0-1/ 3-0= -1/3
so, The slope-intercept form of the equation of a line is
y= mx + b
y= -1/3x +b
Now, the passes through (-1, 2) we get
2= -1/3(-1) + b
2- 1/3= b
b= 5/3
So, the Equation of line is y= -1/3x + 5/3
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Zachary is applying biomechanics to develop a specialized bat for a professional player. What does he compar
the hitter to?
Oa machine
O a computerized model
O another professional player
O a 3-D diagram
Answer:
Another Professional Player
A company orders 11 boxed lunches from a deli for $84.15. If each boxed lunch costs the same amount, how much do 14 boxed lunches cost?
The cost for 14 boxed lunches is $107.10.
How to calculate the price?From the information, the company orders 11 boxed lunches from a deli for $84.15. Therefore, we need to calculate the unit price and this will be:
= Total amount / Number of orders
= $84.15 / 11
= $7.65
Therefore, the value for 14 boxes will be:
= Unit price × Number of orders
= $7.65 × 14
= $107.1
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Use the rules of measurement to divide
Answer:
[tex] \frac{ {m}^3{} }{25} [/tex]
Step-by-step explanation:
that is the answer
Which statement is true?
This table does not show a probability distribution.
This table shows a probability distribution.
After using the probability distribution table, the given table does not show a probability distribution. The statement 1 is correct.
In the given question, we have to check which statement is correct regarding to the given option.
The given statements are:
(1) This table does not show a probability distribution.
(2) This table shows a probability distribution.
Before checking the statement we learn about a probability distribution table.
In a probability distribution table every result of a statistical experiment is connected to the likelihood that the result will actually occur. An experiment's result is recorded as a random variable, which is typically written with a capital letter.
As we can see that there is given the probability of having the blue, green, yellow and red color.
So the given table does not show a probability distribution.
So the statement 1 is correct.
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the profit y (in dollars) for a business from selling x games is represented by y=33x graph the equation
THIS IS URGENT!!! SOMEONE PLEASE RESPOND!!!!
ty!
Answer: check the image attached
Step-by-step explanation:
Hope this helps
Answer:
Just point the graph on Y=33x+0
Step-by-step explanation:
There's no B or starting point, so you would just plant the point on 0,33
Can anyone state the vertex of the graph?
The graph has no vertex
The transformations from the parent function are
Vertical shift down 2Horizontal shift left 4How to determine the vertex?The graph represents the given parameter
As a general rule, the maximum or the minimum of a graph is the vertex
However, the graph has no maximum or minimum
This means that there is absence of a vertex in the graph
The transformationHere, we have:
The graph is translated 4 units to the left of the origin The graph is translated 2 units below the originThis transformation can be represented as (x - 4, y - 2)
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16. Points X, Y, and Z are collinear, and Y is
the midpoint of XZ. Find the value of b.
Answer:
12=b
Step-by-step explanation:
2b+7=3b-4 is what your gonna do ti solve the problem because both segments have the same length. Then you solve for b by -2b from each side. Then it will become 7=b-4. Add 4 to the seven to get 12=b
Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer: 0.86 pounds of fruit
Step-by-step explanation:
8.3-7.44=0.86