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
To learn more about regular induction visit
https://brainly.com/question/14642442
#SPJ4
one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. what is the area of the parallelogram? express your answer in simplest radical form.
The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
Here,
A parallelogram has adjacent angles that add up to 180 degrees.
Since one angle of parallelogram is 120°.
240+2x=360
2x=120
x=60
The other will be 60°
The area of parallelogram= lh
l=15 inch
h=b(sin 60°)
=8*√3/2
h=4√3 inch
area of parallelogram= 15*4√3
= 60√3 inch²
The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."
To know more about parallelogram,
https://brainly.com/question/1563728?referrer=searchResults
#SPJ4
Caroline can make eleven lassis out of two mangoes. How many lassis can she make out of twelve mangoes?
Answer
Step-By-Step-Explanation
2 mangoes=eleven lassis
×6 ×6
12 mangoes=66 lassis
Answer=66 lassis
Which postulate can be used to prove the two triangles are congruent?
Answer:
SAS
Step-by-step explanation:
If two sides and the included and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. The included angle is the angle formed by the two sides.
EF = BC
∠ F = ∠ C
DF = AC
then the two triangles are congruent by the SAS postulate.
Answer:
SAS
Step-by-step explanation:
On triangle one and two, they both start by having a congruent side, then a congruent angle, then another congruent side, thus making these triangles congruent by Side Angle Side.
It can't be AAS because there is only one angle, we know is congruent.
It can't be SSS because there are only two sides, we know are congruent.
It can't be HL because there is no right angle, meaning these aren't right triangles.
Use the distributive property to remove the parentheses.
3c³(7c8 +8c+7)
Simplify your answer as much as possible.
Answer: 21 c^16 + 24c^9+ 21 c^8
Step-by-step explanation: To multiply exponents with the same base, add them.
Answer:
3c^3(7c^8+8c+7)
=(3c^3)(7c^8+8c+7)
=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)
=21c^11 + 24c^4 + 21c^3
Step-by-step explanation:
Remember.... ^ is for power
i will literally do ANYTHING for doordash mcdonalds literally Anything for 20 dollars
Answer: Nice
Step-by-step explanation:
A balloon was originally filled to a volume of 4,400 cubic centimeters. air inside the balloon leaks out over time. write an inequality that describes v, the volume of the balloon in cubic centimeters as air leaks out.
Answer:
V<4400
Step-by-step explanation:
Answer:
the answer is V<4,400
if you are using khan academy, do not add the comma for 4,400, otherwise it will not work.
khan academy answer: V<4400
Step-by-step explanation:
if the air leaked out, which is V, that means V would be less than 4,400 because 4,400 is what we have started with.
Therefore, the inequality would be V<4,400 or for khan academy, V=4400
LOTS OF POINTS coordinate proof explaining how the midsegment of a triangle forms a triangle with 1/4 of area
The coordinate geometry, the midsegment theorem shows that the midsegment of a triangle is 1/4 area of the triangle.
How to show that the midsegment of a triangle is 1/4 area?
The midsegment if a triangle is defined as a line that joins two midpoints of two opposite sides of a triangle.
The midsegment theory of a triangle states that in a triangle, the midsegments of 2 sides is parallel to, and half the length of the 3rd side.
The 3 midsegments of a triangle forms a small triangle within the larger triangle.
This therefore, forms 4 triangles.
Area of a triangle =base x height
Hence 4 triangles are formed,
The area of the larger triangle is [tex]\frac{bh}{4}[/tex] =1/4(bh)
Therefore; Area =1/4 of area.
Learn more about midsegment on brainly.com/question/2273557
#SPJ1
Este gráfico circular resume las especializaciones de los 450 miembros de una sororidad universitaria. El ángulo central el sector correspondiente a la especialización de ingeniería mide 50.4°. ¿Qué porcentaje de los miembros de la sororidad se especializan en ingeniería? No redondear.
Los miembros de la sororidad tiene un porcentaje de 14 % de estudiantes procedentes de la especialización de ingeniería.
¿Cuál es el porcentaje de estudiantes de la sororidad que pertenecen a la especialización de ingeniería?
El enunciado describe las características de un diagrama circula, en donde el 100 % de los miembros de la sororidad representan a los 360° del ángulo central del círculo, esto es, una revolución completa del círculo.
El porcentaje de los miembros que se especializan en ingeniería mediante la siguiente fórmula:
e = (E / 360°) × 100 %
Donde E es el ángulo asociado a la cantidad de estudiantes de la especialización de ingeniería, en grados sexagesimales.
e = (50.4° / 360°) × 100 %
e = 14 %
Los estudiantes que especializan en ingeniería corresponden a un porcentaje de 14 % de los miembros de la sororidad.
Para aprender más sobre porcentajes: https://brainly.com/question/10114228
#SPJ1
The toy store created a display of s shelves of remote control cars. Each shelf contains 16 cars. Write an expression that shows how many cars are on the display.
The expression that shows number of remote control cars on the display self is 16s.
Mathematical expressions are formed using at least two numbers, variables, and there must be one arithmetic operation, and a statement. If there are x items are given in one self and there are n number of self and we have to find total number of items in all self, then we have to multiply x by n.
Here, there are 16 remote control cars on a display self. The number of display shelves is s.
So, the total number of cars will be 16 times of s.
Number of cars on display = 16s
Therefore, the expression that shows the number of cars on display is 16s.
To learn more about the equations and expressions visit here:
https://brainly.com/question/4344214
#SPJ1
Answer:
It is 16s
Step-by-step explanation:
Randy and two of his friends have rectangular desks of the exact same size. The sum of the perimeters of the 3 desks is 324 inches.
If the width of each of the desks is 30 inches, what is the length of each desk?
The length of each desk when the width of each of the desks is 30 inches is A. 24 inches.
How to calculate the length?From the information, Randy and two of his friends have rectangular desks of the exact same size and the sum of the perimeters of the 3 desks is 324 inches.
The perimeter for each desk will be:
= 324 / 3
= 108
The perimeter is calculated as:
= 2(length + width)
This will be
2(length + width) = 108
2(length + 30) = 108
2l + 60 = 108
Collect like terms
2l = 108 - 60
2l = 48
Divide
l = 48/2
l = 24
The length is 24 inches.
Learn more about perimeter on:
brainly.com/question/19819849
#SPJ1
Which inequality has like variable terms on each side of the inequality symbol?
Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
As given in the question,
Inequality which have like variables term on each side of the given inequality symbol is :
a. 15c + 25 ≤ 115
In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.
Not correct option.
b. 0.75r - 6.25 > 10
In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.
Not correct option.
c. 16 - 2x > x + 16
In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.
Correct option.
d. 12.25h -175 < 5,000
In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.
Not correct option.
Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
Learn more about inequality here
brainly.com/question/28823603
#SPJ1
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equation that can be used to find the price of one tire patch is 22.20 - 4x = 1.90 and 4x + 1.90 = 22.20
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Rhyan paid using a gift card that had $22.20 on it.
Let x represent the cost of each tire patch needed for the mountain biking trip. Rhyan bought four tire patches and had $1.90 remaining. Hence:
22.20 - 4x = 1.90
4x + 1.90 = 22.20
The equation is 22.20 - 4x = 1.90
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
What are the missing segment lengths shown in the image?
The length of the missing ,line segments show in the image are AC = CD = 10√2 and AB = BC = 10 .
In the question ,
a figure is given , we have to find the length of the missing line segments .
From the given figure
the Δ ACD is a right triangle ,
given that ∠A and ∠D are equal
so , their corresponding length AC and CD will be equal , that is AC = CD
So , By Pythagoras Theorem
AC² + CD² = AD²
2*AC² = AD²
2*AC² = (20)²
2*AC² = 400
AC² = 400/2 = 200
AC = √200
AC = CD = 10√2
The triangle ABC is also right triangle
and ∠A and ∠C are equal
so , their corresponding length AB and BC will be equal , that is AB = BC
So , By Pythagoras Theorem
AB + BC = AC
2*AB² = AC²
2*AB² = (10√2)²
2*AB² = 200
AB² = 200/2 = 100
AB = √100
AB = 10 = BC
Therefore , The length of the missing line segments show in the image are AC = CD = 10√2 and AB = BC = 10 .
Learn more about Triangles here
https://brainly.com/question/21926466
#SPJ1
The ratio of the number of beads collected by Jane to the number of beads collected by Jill is 7: 3. Jane gave some beads to Jill. Is it possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill? Explain why you think so
yes , it is possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill and The number of beads Jane has is 7t/4 and Jill has 3t/4 bead's
The ratio of Jane's beads to Jill's beads is 7: 3
Let x be the number of beads Jane has
y be the number of beads Jill has
x/y = 7/3
When Jane's gives t of her beads away both will have the same number of beads so
x - t = y
substituting in the first equation
x/ ( x- t) =7/3
3x= 7x-7t
4x= 7t
x= 7t/4
y= 7t/4 -t
= 3t/4
learn more about of ratio here
https://brainly.com/question/2409850
#SPJ4
The shaded area of the square above is what fraction of the entire square?
The fraction of the entire square that is shaded is 2/5.
What fraction of the entire square is shaded?A square is a two dimensional object that four sides that are of equal length. This means that the dimensions of the length and the width have the same value. A square has two diagonals that bisect each other at 90°.
A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.
Fraction = number of shaded squares / total number of squares
16 / 40
When expressed in its simplest form, the fraction becomes 2/5.
To learn about squares, please check: https://brainly.com/question/9030544
#SPJ1
. suppose the sides of a rectangle are changing with respect to time. the first side is changing at a rate of 2 in./sec whereas the second side is changing at the rate of 4 in/sec. how fast is the diagonal of the rectangle changing when the first side measures 16 in. and the second side measures 20 in.? (round answer to three decimal places.)
Diagonal of rectangle is changing by the rate of 4.373 in. /sec.
What is rate of change ?Rate of change (ROC) is the rate at which a variable changes over a particular period of time
To find the average rate of change, divide the change in the y-values by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values such as average speed or average velocity.
A ratio is a special ratio in which the two terms have different units.
Calculationthe calculation part is shown in the below picture attached .
so after seeing the solution we come to an answer of = 4.373 in./sec
therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec
learn more about rate of change here :
brainly.com/question/12786410
#SPJ13
Write an absolute value equation representing all numbers x whose distance 7 is 3 units
Answer:
|x-7|=3
Step-by-step explanation:
x is 3 units away from 7
x-3=7
x-7=3
x+3=7
3=7-x
|x-7|=3
7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings
Which of the following would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years? Question content area bottom Part 1 Select all that apply. A. $80 at 75% for 18 months B. $200 at 5% for 8 years C. $225 at 10% for 4 years D. $300 at 2% for 2 years E. $250 at 10% for 2 years
The option that would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years include:
A. $80 at 75% for 18 months
C. $225 at 10% for 4 years
How to calculate the interest?It's important to note that the simple interest can be calculated thus:
= Principal × Rate × Time
Therefore, the amount of interest as a $600 principal with 2.5% interest for 6 years will be:
= PRT
= (600 × 0.025 × 6)
= $90
The interest on $80 at 75% for 18 months will be:
= $80 × 0.75 × 1.5
= $90
The interest on $225 at 10% for 4 years will be:
= $225 × 0.1 × 4
= $90
Learn more about interest on:
brainly.com/question/25793394
#SPJ1
WILL GIVE BRAINLIST TO BEST ANSWER! EASY POINTS
write the point slope form of the equation of the line through the given points.
through (-1, -5) and (-5, 3)
The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (Choose from: shift up, shift down, shift right, shift left). Part B: Solve for k in each type of transformation. (This means tell me how many units you are shifting for each transformation you picked in part A). Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (This would be f(x) + k, f(x) - k, f(x -k), or f(x+k) but replace k with the values from part B).
A. The translations used in the transformation of f(x) to g(x) can be given as follows:
Left 6 units.Up 18 units.B. The solutions for k are given as follows:
Left 6 units: k = 6.Up 18 units: k = 18.C. The rules are given as follows:
Left 6 units: g(x) = f(x + 6).Up 18 units: g(x) = f(x) + 18.What are the translations to an image?There are four cases for the translation of an image, and they can be represented as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.From the graph of the linear functions shown at the end of the answer, two translations are possible, listed as follows:
Left 6 units: As the x-intercept of g(x) is of -6 and the x-intercept of f(x) is of x = 0.Up 18 units, as the y-intercept of g(x) is of 17 and of f(x) is of -1, 17 - (-1) = 18.The values of k are equivalent to the values of a in the bullet points listing the translations above, and the equations were also built from those bullet points.
Missing InformationThe lines are shown by the image at the end of the answer.
More can be learned about translations at brainly.com/question/28174785
#SPJ1
Ahmad decided to increase his homework time of 8 hours per week by 15%,
Calculate his new homework time.
Give your answer in hours and minutes.
Answer:
it's a answer done bro
what if n is negative what is the value of the equation below n(2)+8 divided by 4 = 11
If n is negative the value of the equation that we have below would be -18
How to solve the equationWe have to rewrite the equation in a way that it would be easier to understand first.
[tex]\frac{-2n+8}{4} =11[/tex]
Next we would have to cross multiply
this would give us
-2n + 8 = 11 * 4
-2n + 8 = 44
take the like terms
-2n = 44 - 8
-2n = 36
divide through by -2 from the above
-2n / -2 = 36 / -2
n = - 18
Therefore given that we have that the value of the equation after n is negative is -18.
Read more on equations here: https://brainly.com/question/22688504
#SPJ1
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
Tanks are used to deliver liquid fuel to a factory. each tank holds 22.5 cubic yards of fuel. the weight of 1 cubic yard of fuel is 0.74 tons. the fuel will be stored in containers that each holds 7.4 tons of fuel. how many containers of this size are needed to hold all the fuel from 12 tanks?
27 containers are needed to hold all the fuel from 12 tanks.
How do you prove that?We are given that each tank holds 22.5 cubic yard of fuel, the weight of 1 yd³ (cubic yard) of fuel is equal to .74 tons, and each container holds 7.4 tons of fuel. Solving this problem would involve converting units.
In order to find out how many containers of the size are needed to hold all the fuel from 12 tanks, first we need to find how much fuel is delivered by 12 tanks. Since 12 x 22.5 = 270, 12 tanks are used to deliver 270 yd³ of fuel.
Next we convert it to tons. Recall that 1 yd³ of fuel is equal to .74 tons. Therefore, 270 yd³ = 270 x .74 = 199.8 tons.
A container holds 7.4 tons of fuel. 199.8 ÷ 7.4 = 27, hence 27 containers are needed to hold all the fuel.
Learn more about converting units here: https://brainly.com/question/174910
#SPJ4
need help on this !!!!!!!!!!!
Using the Triangle Inequality Theorem we can state that the range of z is 4 < z < 20.
What is the Triangle Inequality Theorem?The above theorem states that The length of any two sides of a triangle must sum to more than the length of the third side. That is:
12 + 8 > z.............1
12 + z > 8;.............2
8 + z > 12.............3
Solving for (1)
20 > z...............4
Solving for (2)
we have- 12 + z > 8
remove 8 from both sides and we have
4 + z > 0 or z > -4 ...............5
Solving for (3) we have
8 + z > 12
remove 8 from both sides
z > 4 .....................6
Since we can't have a negative value on a triangle, we must deal with expressions 4 and 6 which state:
20 > z; and
z > 4
Another way to write this is:
20 > z > 4; or
4 < z < 20
Hence the range of the unknown side that will form a triangle is:
4 < z < 20
Learn more about Triangle Inequality Theorem:
https://brainly.com/question/1163433
#SPJ1
An aabbccddeeff individual is crossed with an individual with the genotype aabbccddeeff. What is the probability that their offspring will have the genotype aabbccddeeff?.
When an aabbccddeeff individual is crossed with an individual with the genotype aabbccddeeff, the probability that their offspring will have the genotype aabbccddeeff would be 1/64.
The genotype of an organism refers to the complete set of genetic material. An offspring's genotype is the result of the combination of genes from their parents. In order to obtain the overall probability, individual probabilities for each locus will be multiplied. The Parent cross would be AABbccDdEeFF x AaBBCCDdEeff and offspring would be AaBbCcddEEFf.
The A locus cross is AA x Aa, half of the offspring will be AA and half of the offspring will be Aa. Hence, the probability of Aa would be ½.The B locus cross is Bb x BB, half of the offspring will be BB and half of the offspring will be Bb. Hence, the probability of Bb is ½. The C locus cross is cc x CC. All of the offspring will be Cc. Hence, the probability of Cc is 1.The D locus cross is Dd x Dd. One-fourth of the offspring will be DD, one half of the offspring will be Dd, and one-fourth of the offspring will be dd. Hence, the probability of dd is ¼.The E locus cross is Ee x Ee. One-fourth of the offspring will be EE, half of the offspring will be Ee, and one-fourth of the offspring will be ee. Hence, the probability of EE is ¼.The F locus cross is FF x ff. All of the offspring will be Ff. Hence, the probability of Ff is 1.Multiplying all the probability:
½ * ½ * 1 * ¼ * ¼ * 1 = 1/64
Learn more about Genotype:
https://brainly.com/question/902712
#SPJ4
Kelly grows potatoes.
She has 2500 kg of potatoes, correct to the nearest 10kg.
Kelly is going to put the potatoes into sacks.
Each sack will contain 12. 5 kg of potatoes.
Kelly assumes that 12. 5 kg is measured correct to the nearest 0. 1 kg.
(a) Does Kelly definitely have enough potatoes to fill 200 sacks?
You must show how you get your answer
Kelly fill 200 sacks with the weight of 2000 kg potatoes and in each sack, she can fill up to 12.5 kg of potatoes.
What is weight?The gravitational attraction of an item near the Earth or another celestial body toward the center of the body. The weight of an item is determined by its mass and the strength of the gravitational force. We use the following generic formula to compute weight: W = mg. Where 'W' is the object's weight,'m' is the object's mass, and 'g' is the acceleration due to gravity. The value of g on Earth is 9.8 m/s2. The most frequent definition of weight is the force imposed by gravity on a body.
Here,
weight of potatoes she has=2500 kg
weight of each sack that contain the potatoes=12.5 kg
with this, she can fill,
=2500/12.5
=200 sacks
Kelly fills 200 sacks with 2000 kg of potatoes, and each sack can hold up to 12.5 kg of potatoes.
To know more about weights,
https://brainly.com/question/28021669
#SPJ4
If the area of the rectangle is 42 square units, what is the area of the shaded part?
Answer: 16
Step-by-step explanation:
The first triangle has an area of [tex]\frac{1}{2}(7)(2)=7[/tex].
The second triangle has an area of [tex]\frac{1}{2}(6)(3)=9[/tex].
Adding these areas together yields an area of 16.
a box contains tiles. each tile has certain properties: each tile is made of wood or plastic. each tile is red, yellow, or blue. each tile is a triangle, square, pentagon, or circle. there is exactly one tile for each combination of properties. for example, there is one red circle that is made of wood. steve chooses one tile, and ellen chooses a different tile. what is the probability that the two chosen tiles differ with respect to all three properties?
1/24 is the probability that the two chosen tiles differ with respect to all three properties
1/2 chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.
learn more about probability here:
https://brainly.com/question/14210034
#SPJ4
