Part B
Assume the statement is true for n=k. Prove that it must be true for n=k+1, therefore proving it true for all natural
numbers, n.
Hint: Since the total number of dots increases by n each time, prove that d (k) + (k+1)=d(k+1).
BIUX¹ X₂ 15px
AVE
V

Answers

Answer 1

We have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

Mathematical Induction : For each and every natural number n, mathematical induction is a method of demonstrating a statement, theorem, or formula that is presumed to be true.

It is given that the statement is true for n = k

Explanation:

According to the principle of Mathematical Induction,

Let d(n) be a statement involving Natural Number n such that

d(1) is true

d(m) is true

d(m+1) is true

So ,  the statement d(n) is true for all the n natural numbers.

According to the second principle of Mathematical Induction

Let d(n) be a statement involving Natural number n such that

d(1) is true

d(m) is true when d(n) is true for all n where 1 ≤ n ≤m .

Then the statement d(n) is true for all the values of n ( natural number)

Therefore , we have proved below that d( k+1) is only true when d(k) is true , also d(1) should also be true using Mathematical Induction.

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Related Questions

Notes:
For semiannual premiums, use 51% of the annual rate.
For quarterly premiums, use 26% of the annual rate.
For monthly premiums, use 9% of the annual rate.
For females, use the age of a male three years younger.
Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value of $50,000. What will his annual premium be, if his age for insurance purposes is thirty-one?

(Use a thousands comma where applicable.)

Answers

The annual insurance premium that Will C. Lowe will be paying is $ 766.5

What is insurance premium?

Insurance premium is annual, quarterly, semi annual or monthly payments that has to be paid accordingly to keep our insurance policy active.

Annual insurance premium can be calculated by multiplying the face value per $1000 of the policy by the rate of the insurance of policy.

Given is that Will C. Lowe is 31 year old male who wants to buy a ordinary whole life insurance policy with a face value of $50,000.

From the table we can see that rate of insurance for a 31 year old male for a ordinary whole life insurance policy  is 15.33

Then annual premium = (face value per $1000)*(rate of insurance)

                                     = $ (50,000/1000)*(15.33) = $766.5

Therefore, the annual insurance premium that Will C. Lowe will be paying is $766.5

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Please help!!
Solve for a:
b(a + f) = M

Answers

Answer: a = (M/b) - f

help plss

Answers

okay i will help u out ok!!

Which values, when substituted for x in the expression _/x , will result in an irrational number? Select all that apply.

Answers

The values, which when substituted for x in the expression √x , would result in an irrational number are:

x = 168x = 2x = 8x = 21x = π

The types of numbers.

In Mathematics, there are six (6) common types of numbers and these include the following:

Natural (counting) numbersWhole numbersRational numbersIrrational numbersReal numbersIntegers

What is an irrational number?

An irrational number can be defined a type of number which comprises non-terminating or non-repeating decimals such as the square root of 168, 2, 8, 21, π, 11.

In conclusion, when a perfect square or 4 is substituted for x in the expression √x, the result is not an irrational number because it is neither a terminating nor a repeating decimal.

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Complete Question:

Which values, when substituted for x in the expression √x, will result in an irrational number? Select all that apply.

x = 168

x = 2

x = 8

x = 21

x = π

x = 4

when x is a perfect square.


What are the solution(s) of 2(x+3)²/₃=8 ?

Answers

The solution is 5

Rewriting the expression -

2(x+3)²/₃=8

Divide Left Hand Side and Right Hand Side of the equation -

(2(x+3)²/₃)÷2 = 8÷2

Performing division to find the solution

(x+3)²/₃ = 4

Taking cube on both sides of the equation

((x+3)²/₃)³ = 4³

The exponent on Left Hand Side will be multiplied cancelling 3, as it is common in both numerator and denominator

(x + 3)² = 64

Now, taking square root on both sides of equation

√(x + 3)² = √64

Solving the square root on both sides of equation

x + 3 = 8

Shifting 3 to Right Hand Side of the equation

x = 8 - 3

Performing subtraction

x = 5

Hence, the solution of equation is 5

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Find 6y + 10z - 2yz, use y=2 and z=3​

Answers

Answer:

30

Step-by-step explanation:

6(2) + 10(3) - 2(2)(3)
12 + 30 - 2(6)
42 - 12
30

The value of the expression 6y + 10z - 2yz when y = 2 and z = 3 is 30.

What is the value of the expression when y=2 and z=3​?

Given the expression in the question:

6y + 10z - 2yz

y = 2

z = 3

To determine the value of the expression 6y + 10z - 2yz, we simply substitute y = 2 and z = 3 into the expression and then simplify.

6y + 10z - 2yz

Plug in y = 2:

6( 2 ) + 10z - 2(2)z

Plug in z = 3:

6( 2 ) + 10( 3 ) - 2(2)(3)

Simplifying, we get:

12 + 30 - 12

Add 12 and 30:

42 - 12

Subtract 12 from 42:

30

Therefore, the value of the expression is 30.

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Michael is doing an underwater handstand. His feet are sticking up 0.5 meters above the surface
hands are 1.8 meters directly below his feet.
of the water. Michael's
What is the position of Michael's hands relative to the surface of the water?

Answers

Answer:

Step-by-step explanation:

Answer:

michael is doing an underwater handstand . His feet are sticking up 0.5 meter above the surface handsare 1.8 meters directly below his feet of the water

michael handsrelative to the surface of the water

Step-by-step explanation:

8 over 3 / 3 simplified

Answers

Answer:

8

Step-by-step explanation:

if you mean 8/ (3/3), Then you get 8 because 3/3 = 1 and 8/1 is 8. Also if you put that equation into a calculator then you get 8

Is it possible to have a Triangle with
3cm , 6cm , 7cm ?

Answers

Answer:

yes

Step-by-step explanation:

Is it possible to have a Triangle with

3cm , 6cm , 7cm ?

the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. so your answer is YES (obtuse Triangle)

If there are 30 dogs and 36 cats at a pet daycare, fill out all of the possible ratios of
dogs to cats that could be made.
There are 30 dogs for every 36 cats (30:36 ratio)
There are
dogs for every cats try
Type in an equivalent ratio of dogs and cats.
8
(14)
19 (20)
(25) (26)
13
15
6
10 11 (12)
(16
(18)
23 (24)
28 (29) (30
17
(18)
(19) (20) (21) (22) (23) (24
(25)
(31)
(22)
(30)
(35) (36)

Answers

Answer:

1:2

Step-by-step explanation:

Kaylee deposits $500 into a savings account with a 3% intrest rate what will her balance be in 3 years

Answers

Answer: $576.99 in 3 years

Step-by-step explanation:

Answer:

546.36

Step-by-step explanation:

Interest rate calculator

Pls help! Slope Question

Answers

The slope between points C and D is 12/7 = 1.71

How to find the slope between points C and D?

We know that the slope between two points with coordinates (x₁, y₁) and (x₂, y₂) is given by:

s = (y₂ - y₁)/(x₂ - x₁)

In this case, the coordinates of point C are (0, 0)

The coordinates of point D are (7, 12)

Then the slope on that interval is:

s = (12 - 0)/(7 - 0) = 1.71

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pls help.. A bird is flying at an average altitude of 10 meters above the ground. After 3 seconds, it settles on a branch that is 3 meters above the ground. Interpret the quotient to describe the rate of change in the bird’s altitude. Give your answer to the nearest hundredth.

Answers

The bird settles on the branch at the rate of 2.33 meters per second.

What is the rate of change?

The rate of change refers to the traveling speed of the bird when perching on the branch.

The rate of change (which is speed) is the distance (altitude) divided by time.

Data and Calculations:

The bird's flying altitude above ground = 10 meters

Time in seconds to settle on a branch = 3 seconds

The altitude above ground after settling on the branch = 3 meters

The change in altitude = 7 meters (10 - 3)

Rate of change = 2.33 meters per second (7/3)

Thus, the rate of change that the bird used to settle on the branch is 2.33 meters per second.

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Answer:

-2.33

Step-by-step explanation:

Identify the like terms in the list.
16y ^6, 2y^ 5, 4y ^2, 10y, 16y^ 2

Answers

Answer:

4y^2

16y^2

Step-by-step explanation:

16 y^6 matches nothing. The powers on the letter must be the same to have like terms.

2y^5 has the same comment.

4y^2 and 16y^2 are similar terms. Both have y^2

10y matches nothing

mr. fullingham has 75 geese and 125 turkeys. what is the ratio of te number of geese to the total number of birds in simplest terms

Answers

The total number of birds will be 75 geese + 125 turkeys = 200.

So the ratio of geese to birds is 75:200

Which of these are examples of deductive reasoning? Select the correct answer. Milk costs $2.99 per gallon at the first three grocery stores that Gema visited. She concludes that milk costs costs $2.99 per gallon everywhere. Most tulips grow to between 6 and 24 inches tall. Janelia concludes that the flowers in her garden will be shorter than 24 inches. Felix knows that everything that fits in his bookbag will fit in his suitcase. His laptop fits in his bookbag, so he concludes that the laptop will fit in his suitcase. Everytime Matthew has left for school at 7 am, he has been on time. Matthew concludes that if he leaves the house at 7 am today, he will be on time. The school's schedule states that lunch period is from 12 p.m. to 1 p.m. Eric concludes that it is after 12:00 p.m. because it is currently the lunch period. Sammy notices that the ants around his house all have 6 legs. He concludes that all ants must have 6 legs.​

Answers

An example of deductive reasoning is Most tulips grow to between 6 and 24 inches tall. Janelia concludes that the flowers in her garden will be shorter than 24 inches.

What is a deductive reasoning?

Deductive reasoning  can be described as the  mental process  that involves the  the act of drawing deductive inferences.

It should be noted that this inference can be valid in the case whereby   the  conclusion is seen to be in line with logic from its premises, hence option B is correct because it follows a logical sequesnce before amking a conclusion.

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Answer:

Step-by-step explanation:

It's C and E

Felix and The school's schedule

can someone please tell me what 383.0 divided by 90 is?????????

Answers

Sure!!!

The answer is 4.25555!

Hope this helps! Have a great day! :D :)

Answer:

The answer is 4.2555555556

if an airplane's speed is 625 miles per hour what is its speed in feet per second? round your answer to the nearest whole number. there are 5,280 feet in a mile
A. 426 ft per second
B.917 ft per second
C.55,000 ft per second
D.1,188,000 ft per second

Answers

The speed with which the airplane is flying in feet per second is 917 ft per second.

The speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

It is given that,

The speed with which the airplane is flying is = 625 mile per hour

We need to find the speed of the airplane in feet per second

Number of seconds in 1 hour = 60 x 60 = 3600s

Number of feet in 1 mile = 5280 feet

Number of feet in 625 mile = 5280 x 625 = 33,00,000 feet

Speed of airplane in feet per second = [tex]\frac{33,00,000}{3,600}[/tex]

= 916.66 feet per second

~917 feet per second

Hence, the speed with which the airplane is flying in feet per second is 917 ft per second.

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Which table represents a linear function?

Answers

b because they will go at an angle

Justin borrowed money from a credit union for 2 years and was charged simple interest at an annual rate of 7%. The total interest that he paid was $840. How much money did he borrow?

Answers

Justin borrow $6,000 from a credit union for 2 years.

What is Principal amount?

The amount of money initially borrowed from the lender, and as the loan is repaid, it can also refer to the amount of money still owed, is called Principal amount.

Given that;

Simple interest = $840

Time = 2 years

Annual rate = 7%

Now, The formula for calculate the principal amount is,

Simple interest = Principal amount × Rate × time / 100

Principal amount = Simple interest × 100 / Rate × time

Hence,

Principal amount = 840 × 100 / 7 × 2

Principal amount = 84,000 / 14

Principal amount = $6000

So, Justin borrow $6,000 from a credit union for 2 years.

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If z=30 when x=3 and y=2 , write the function that models the relationship.
z varies directly with x and inversely with y .

Answers

z = 20 x/y is the variation of equation.

How to write the function that models the relationship?

A relationship between a set of values for one variable and a set of values for other variables is known as a variation.

One of the most fundamental concepts in mathematics is the idea of a function, in part because functions are a useful tool for describing and illuminating patterns.

given that

z=30 when x=3 and y=2

z varies directly with x that means z is directly proportional to x.

z = kx .................(1)

z varies inversely with y means z is inversely proportional to y.

z = k 1/y ................(2)

both equation 1 and 2

z = k x/y

k = zy/x

now, find the value of k using given information.

k = 30(2)/3

k = 60/3

k = 20

now,

z = k x/y

z = 20 x/y

This is the variation of equation.

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Pleas look at screenshot

Answers

/9/=9
/-10/=10

The absolute value of both of them would be positive , cause the absolute value of a number is never negative .

If the point (x, y) is in Quadrant III, which of the following must be true?
x < 0 and y>0
x < 0 andy<0
Submit
x > 0 and y>0
x > 0 and y < 0

Answers

Answer: x < 0 and y < 0

Step-by-step explanation:

quadrant three is here

                      |

        II            |        I

                      |

--------------------|-------------------

                      |

        III           |        IV

                      |

    here /\

so, the x is to the left which is negative, and the y is down which is negative. x is less than zero, and y is less than zero

I which of the numbers
are solutions to the
equation x² = 100? Select all that apply.


-10,000
-50
-10
0
10
50
10,000

Answers

The numbers that fits into the equation X² = 100 are -10 and 10.

How to illustrate the information?

It should be noted that squares simply means multiplying a number by itself.

In this case, X² = 100.

Therefore, the numbers that fits X will be:

X² = 100

Square root both sides

X = ✓100

X = 10

Also, it should be noted that (-10)² = 100

Therefore, the numbers that fits into the equation X² = 100 are -10 and 10.

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Calculate (7.15 x 10^9) - (4.56 x 10^8).

2.59 x 10^1
2.59 x 10^9
6.694 x 10^8
6.694 x 10^9

Answers

Answer:

D. 6.694 * 10^9

Step-by-step explanation:

The exponent is 9 because the result of the first equation had 9 digits. It is positive because the decimal moves to the right.

1. Solve for x:
1/3x = -26

Answers

1/3x = -26

To solve for this, we can divide both sides by 1/3 since it is the coefficient. This would look like:

1/3 / 1/3 = 1
-26 / 1/3 = -78

x = -78

The blue dot is at what value on the number line -16 to -10

Answers

Tbh I truly don’t know I’m srry for wasting your time but I gotta get this homework done ASAP

3xy+5x+2+3y+x+4 answer

Answers

The equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x  + 3y  + 6

What are expressions?

Expressions are mathematical statements that are represented by variables, coefficients and operators

How to evaluate the expression?

The expression is given as

3xy + 5x + 2 + 3y + x + 4

Collect the like terms in the above expression

So, we have

3xy + 5x + 2 + 3y + x + 4 = 3xy + 5x + x  + 3y  + 4+ 2

Evaluate the like terms in the above expression

So, we have

3xy + 5x + 2 + 3y + x + 4 = 3xy + 6x  + 3y  + 6

Hence, the equivalent expression of the expression given as 3xy + 5x + 2 + 3y + x + 4 is 3xy + 6x  + 3y  + 6

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In the figure, AC=86. Find BC.

Answers

Bc would equal too 12cm


Which expression is NOT equivalent to ⁶√16 ²?
(A) (16 r²)¹/₆ (B) 4 r¹/₃ (C) (4 r)¹/₃ (D) ∛4 r}

Answers

The correct option is (B) [tex]4 r^\frac{1}{3}[/tex]

The exponential expression  [tex]4 r^\frac{1}{3}[/tex] is not equivalent to ⁶√16r².

What is exponential expression ?

In, mathematics a exponential function or exponential expression is inverse of logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The basic form of the exponential function can be written as  [tex]a^x[/tex] .Or we can say that there is always has something power something rule in case of exponents.

where, a is the base expression of function

          x = exponent of expression

According to question,

the expression,[tex]\sqrt[6]{16r^2}[/tex]  can be written in following ways:

Case 1 : if we simplify the expression using fractional method ,

            then, [tex]\sqrt[6]{16r^2}[/tex] = [tex]({16r^2})^{\frac{1}{6}} = (4r)^\frac{2}{6 } = (4r)^\frac{1}{3 }[/tex]

            i.e. option (A) and (C) are satisfying the expression

Case 2 : if we simplify the equation exponentially ,

             then, [tex]\sqrt[6]{16r^2} = 3\sqrt{4r}[/tex]

             i.e. option (D) is satisfying the expression

Hence, the expression is not equivalent to ⁶√16r² is option B.

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