Answer:
a)
Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.
Proof by Contrapositive:
Assumed statement: Suppose that integers x and y do not have opposite parity.
Proven Statement: x and y are not a pair of consecutive integers.
Proof -
x = 2u₁ , y = 2u₂
Then
(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)
If y = 2u₁ + 1
Not possible
⇒x and y are not a pair of consecutive integers.
Hence proved.
Proof by Contradiction:
Assumed statement: Suppose x and y are not a pair of consecutive integers.
Proven Statement: Suppose x and y do not have opposite parity.
Proof -
If x and y are not a pair of consecutive integers.
⇒ either x and y are odd or even
If x and y are odd
⇒x and y have same parity
Contradiction
If x and y are even
⇒x and y have same parity
Contradiction
(b)
Proof by Contrapositive:
Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)
Proven Statement: n² is not odd (i.e n² is even)
Proof -
Let n is even
⇒n = 2m
⇒n² = (2m)² = 4m²
⇒n² is even
Hence proved.
Proof by Contradiction:
Assumed statement: Let n be an integer such that n² be odd.
Proven Statement: suppose that n is not odd (i.e n is even)
Proof -
Let n² is odd
⇒n² is even
⇒n² = 2m
⇒2 | n²
⇒2 | n
⇒n = 2x
⇒ n is even
Contradiction
What is the probability that a value picked at random from the standard normal distribution will be between -1.96 and 1.96?
Answer:
P( -1.96 ≤ Z≤ 1.96) = 0.95
Step-by-step explanation:
Explanation:-
Given that the z -scores -1.96 and 1.96
we have to find P( -1.96 ≤ Z≤ 1.96)
P( -1.96 ≤ Z≤ 1.96) = |A(1.96)+A(-1.96)|
= |A(1.96)+A(-1.96| (∵A(-Z) = A(Z))
= 0.4750+0.4750
= 2×0.4750
= 0.95
The probability lies between -1.96 to 1.96
P( -1.96 ≤ Z≤ 1.96) = 0.95
10.In an experiment , the approximate population P of a bacteria colony is given by P = 15t ^ (5/3) , where t is the number of days start of the experiment . Find the population of the colony on the 8th day .
Answer:
Step-by-step explanation:
15×8^(5/3) = 15×∛8^5 = 15×2^5 = 15×32 = 480
Population after 8 days is 480
Population after 8 days is 480.
What is exponential function?The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
here, we have,
given that,
the approximate population P of a bacteria colony is given by
P = 15t ^ (5/3)
where t is the number of days start of the experiment .
now,
the population of the colony on the 8th day is,
15×8^(5/3)
= 15×∛8^5 ]
= 15×2^5
= 15×32
= 480
hence, Population after 8 days is 480.
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One number is 10 less than 5 times the second number. Their sum is 26. Find the numbers.
The two numbers are 6 and 20 respectively.
What are word problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given is that one number is 10 less than 5 times the second number. Their sum is 26.
Let the numbers be [x] and [y] repsectively. Then, we can write that -
x + y = 26 ..... Eq[1]
x = 5y - 10 ..... Eq[2]
We can write -
x + y = 26
5y - 10 + y = 26
6y = 36
y = 6
Then, we can write [x] as -
x = 5 x 6 - 10 = 30 - 10 = 20
x = 20
Therefore, the two numbers are 6 and 20 respectively.
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Which of the following sets does NOT represent a function.
O {(1,9), (-1,-9),(2,9), (-2, -9) }
O {(1,-9), (2,-5), (-1,9), (-2,5)}
O {(1,9) (-1,5), (2, -9), (-2,-5) }
O {(1,9), (1,-9), (2,5),(2,-5) }
Answer:
last one, the same X cant have more than one Y.
Solve for x please help
Step-by-step explanation:
4x + 2 + 3x + 3 = 180 (straight angle)
4x + 3x + 2 + 3 = 180
7x + 5 = 180
7x = 175
x = 25°
HELP!!! Bill paid $45in tax on a laptop that cost $500. What percent sales tax did Bill pay?
Answer:
He paid 9% in sales tax
Step-by-step explanation:
Which figure is a pyramid? A cone. B cylinder. C rectangular prism. D pyramid.
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Please answer :)
( Will give brainlst)
Answer:
thank you for give me some time
800 liralık bir telefonun fiya-
tina %6 zam yapılıyor.
Yeni satış fiyatı kaç lira
olur?
Answer:
8ile 6 yı çarp sonucu 800 ile topla 48+800= 848
-4x = 8
what is it??
Answer: if your solving for x it’s -2
Step-by-step explanation:
Answer:
x is -2
Step-by-step explanation:
because -4 x -2 is 8
5. A baker had 2 pans of corn bread. He served 1 1/4 pans. What fraction of a pan was left?
Answer:
3/4
Step-by-step explanation:
2- 1 1/4= 3/4
Answer:
3/4
Step-by-step explanation:
Sarah is a news anchor. She works 55 hours a week, but she is only on-air about 17% of those hours. Approximately how many hours is Sarah on-air each week?
Find the value of z in parallelogram CDEF
Answer:
z = 13
Step-by-step explanation:
Opposite sides of a parallelogram are equal. Therefore:
3z = z + 26
Subtracf z from each side
3z - z = 26
2z = 26
z = 26/2
z = 13
help now pls bby pls
Answer:
Cities around the country are changing. Faded boards, dull concrete, and old bricks are coming to life. Communities are are turning walls of their buildings, roads, and bridges into colorful murals. Painters might show local scenes, honor a hero or celebrate a culture. Murals can also be great projects for schools. They encourage teamwork, school spirit, and creativity. What would you paint? Your mural could inspire people to recycle, be a volunteer or cheer for a team.
Step-by-step explanation:
there are commas where they are supposed to be
Answer:
yes
Step-by-step explanation:
lil fun for yall
what is the answer to this step by step?
Answer:
194332.125 is the amount of interest
Step-by-step explanation:
In a video game, Clare scored 50% more points than Tyler. If Tyler scored 60 points on the video game, how many
points did Clare score?
60
70
80
90
100
Which one
Answer:
90
Step-by-step explanation:
She scored 50% more so scored 1.5x tyler
1.5 * 60 = 90
Answer:
90
Step-by-step explanation:
so for this, all we have to do is add %50 of the first score to the second one, first lets find out what %50 of that score is
%50 of 60 = 30 (because %50 is half of something)
next, we add that new amount to the first score
60 + 30 = 90
so 90 is %50 more then 60, or 90 is %150 of 60
This month the animal shelter had 50 puppies.
Some puppies were adopted. Now there are 40
puppies. What is the percent of change?
Answer:
5 percent change
Step-by-step explanation:
please help me thank you in advance!
Answer:
First option: (x+9)^2=81
Step-by-step explanation:
It has the same solution
help me
Give the approximate measurement of the following objects by using the appropriate
measuring tool:
1) Length of the blackboard
2) Weight of a pineapple
3) Weight of 5 notebooks
4) Length of the door
5) Volume of used mineral water
Answer:
Step-by-step explanation:
I used SI system for units
1)meter
2)kilogram
3)kilogram
4)meter
5)Litre
Two points are located on a graph, Point A is (-1, 10), and Point B is (4,3). What is the
distance between Point A and Point B?
A) 8.6
B)13.3
C) 10
D)3
Answer:
10
Step-by-step explanation:
write a real-world problem given the equation 2/3x = 12. Then solve the equation.
Answer:
You want to buy long pieces of paper at Dollar Tree for 66 cents. You have $12. How many long pieces of paper can you buy
Step-by-step explanation:
please helppp
Simplify.
(-2)^-3
Answer:
-1/8 <----- FRACTION
Step-by-step explanation:
What is the y-intercept of the Function
Answer:
(0, 3)
General Formulas and Concepts:
Algebra I
Reading a Cartesian planeCoordinates (x, y)The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis.Step-by-step explanation:
According to the graph, when x = 0, we see that y = 3. Therefore, our y-intercept is (0, 3).
factor 1/8 out of 1/8x-49/8
Answer:
1/8(x - 49)
Step-by-step explanation:
When we factor out something, we are basically finding common factors from multiple terms to take out. Example:
ab + ac; factored out: a(b + c)
If we want to factor out 1/8 from 1/8x - 49/8, we simply divide the two terms by 1/8.
[tex]\frac{1/8}{1/8x}[/tex] The 1/8 cancel out giving us x so:
1/8(x - __)
The next term,
[tex]\frac{49/8}{1/8}[/tex]
When two fractions divide, you flip the bottom one and multiply them both,
[tex]\frac{49}{8} *\frac{8}{1}[/tex]
giving us 49.
The answer is: 1/8(x - 49)
Match the following.
1. equilateral triangle
2. rectangle
3. circle circumference
4. trapezoid
5. parallelogram
6. triangle
7. regular polygon
8. circle area
1. A = 1/4s squared, square root of 3
2. A = bh
3. A = pi(r) squared
4. A = 1/2 h (b1+ b2)
5. C = pi(d)
6. A = base x altitude
7. A = 1/2(ap)
8. A = 1/2(bh)
- regular polygon
- trapezoid
- rectangle
- parallelogram
- circle circumference
- equilateral triangle
- circle area
Answer:
Answers are below.
Step-by-step explanation:
1. Equilateral triangle - A = 1/4 s^2 √3
2. Rectangle - A = bh
3. Circle circumference - C = πd
4. Trapezoid - A = 1/2 h (b1 + b2)
5. Parallelogram - A = base x altitude
6. Triangle - A = 1/2 bh
7. Regular polygon - A = 1/2 ap
8. Circle area - A = πr^2
Hope this helps.
Complete the last row for a different batch size that hasn’t been used so far in the table. Explain or show your reasoning.
help :( submit in simplest radical form :(
Answer:
y and x equal
[tex] \sqrt{5 } [/tex]
6. Sheila simplified an expression using the following steps. Which property justifies Step 3?
Step 1: 5x + 4(3 + 2x)
Step 2: 5x + 12 + 8x
Step 3: 5x + 8x + 12
Step 4: 13x + 12
O A. Identity Property
O B. Associative Property
O C. Distributive Property
D. Commutative Property
Answer:
answer is Commutative Property
Step-by-step explanation:
Answer:D
Step-by-step explanation:Don't have one
Valerie and Seth are measuring the outside walls of a house using two different instruments. They want to find the house's perimeter. Valeria measured the north and east sides while Seth measured the west and south sides. Their results are listed in the table.
Part A
Use decimal numbers to write an expression that represents the length of the walls that Valerie measured.
Part B
Now use decimal numbers to write an expression that represents the length of the wall that Seth measured.
Part C
Write an expression for the perimeter of the house. Use the work you completed in part A & B to guide you.
Part D
Simplify the expression from part C to find the perimeter of the house in feet.
Part E
Suppose that you evaluate the expression for Valerie's wall and the expression for Seth's wall separately. Then you add the two expressions together. Will you get the same answer that you arrived at in part D? Why or why not? Show your work to prove your case.
PLEASE PLEASE PLEASE HELP I REALLY NEED HELP IN THIS WORK, THANK YOU.
Answer:
A)
Valerie measured 4 walls at 2 1/2 feet. In decimal form, each wall is 2.5 feet long. So, the total length of the 4 walls is (2.5 × 4) feet.
Valerie measured 3 walls at 21 1/4 feet. In decimal form, each wall is 21.25 feet long. So, the total length of the 3 walls is (21.25 × 3) feet.
Valerie measured 1 wall at 32 feet.
The expression that gives the total length of the walls that Valerie measured is (2.5 × 4) + (21.25 × 3) + 32.
B)
Seth measured 1 wall at 3.5 feet.
Seth measured 2 walls at 22.75 feet. So, the total length of the 2 walls is (22.75 × 2) feet.
Seth measured 1 wall at 58 feet.
The expression that gives the total length of the walls that Seth measured is 3.5 + (22.75 × 2) + 58.
C)
The total length of Valerie’s walls is (2.5 × 4) + (21.25 × 3) + 32.
The total length of Seth’s walls is 3.5 + (22.75 × 2) + 58.
To find the expression for the perimeter of the house, add Valerie’s expression to Seth’s:
(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58.
D)
(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58
= 10 + 63.75 + 32 + 3.5 + 45.5 + 58
= 212.75
The perimeter of the house is 212.75 feet.
E)
The total length of Valerie’s walls is 105.75 feet:
(2.5 × 4) + (21.25 × 3) + 32 = 10 + 63.75 + 32 = 105.75 feet.
The total length of Seth’s walls is 107 feet:
3.5 + (22.75 × 2) + 58 = 3.5 + 45.5 + 58 = 107 feet.
The sum of 105.75 feet and 107 feet is 212.75 feet. The Commutative Property allows me to add numbers in any order. This is why the answers in parts D and E match.
edmentum answers :)
Where would the shape be located after a translation of 5 units to the right?
A. Quadrant 3
B. Quadrant 2
C. Quadrant 1
Answer:
It the shape would be in quadrant 1
Answer: Quadrant 1 I think
Step-by-step explanation:
