Use the method of mathematical induction to prove that for each integer n≥1, 5+9+13+⋯+(4n+1)=2n^2+3n

Answers

Answer 1

Answer:

Step-by-step explanation: 834^2n>4n


Related Questions

solve each equation 4(a+5)=10+4a

Answers

Answer:

10 = a

Step-by-step explanation:

To find this answer, first you need to distribute 4 times a and 4 times 5, since this is in parenthesis. You should get 4a + 20 = 10 + 4a. From there, you can subtract 4a from both sides of the equal sign, which will cancel out one of the 4a's. You should be left with 20 = 10 + a. Finally, you can subtract 10 from both sides of the equal sign and get 10 = a.

Put these numbers in order from least to greatest.-10, 4/25, -2/8

Answers

The answer is

-10, -2/8, 4/25

-10,-2/8,4/25. That is the order!

If g(x)=2/3(x-4)^2, find x when g(x)=8

Answers

8 = 2/3(x - 4)^2

Take the sqrt of both sides

Sqrt(8) = 2/3(x - 4)

Divide each side by 2/3

(3 * sqrt(2)) = x - 4

Add 4 to both sides

(3 * sqrt(2)) + 4 = x

Simplify the cube root in simplest radical form.
9x374
Please help

Answers

Answer:

D. [tex]xy\sqrt[3]{9y}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{9x^3y^4}[/tex]

[tex]\sqrt[3]{9}\sqrt[3]{x^3}\sqrt[3]{y^4}[/tex]

The [tex]\sqrt[3]{x^3}[/tex] cancels out to become x:

[tex]\sqrt[3]{9}x\sqrt[3]{y^4}[/tex]

Split the [tex]y^4=y*y^3[/tex]

[tex]\sqrt[3]{9}x\sqrt[3]{y^3}\sqrt[3]{y^1}[/tex]

[tex]\sqrt[3]{y^3} =y[/tex]

[tex]xy\sqrt[3]{9} \sqrt[3]{y}[/tex]

Put the cube root of y and cube root of 9 together:

[tex]xy\sqrt[3]{9y}[/tex]

a machinist can produce 114 parts in 6 minutes. at this rate, how many parts can the machinist produce in 15 minutes ​

Answers

Answer:

285!

Step-by-step explanation:

First you have to find out how may parts are produced in a single minute.

We know that 114 parts are produced in 6 minutes so to find how may parts are made in one minute divide 114 by 6 and get an answer of 19

114÷6=19

Now to find how may parts are produced in 15 minutes multiply 19 (number of parts produdced in one minute) by 15 and get an answer of 285!

19×15=285

Hope this helped! :)

(5 points) A random sample of adult drivers was obtained where 50% were men and 49% were women. Note that everyone is not classified as a man or a woman. A survey showed that 77% of the drivers rely on GPS systems. 38% of the drivers are men and use GPS while 38% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected. (0.5 pts.) a) Suppose the person selected is a man. What is the probability that he relies on a GPS system

Answers

Answer:

the probabiility that the selected man relies on a GPS system is 0.494

Step-by-step explanation:

From the given information:

Let X be the event that selected person is a man

Let Y be the event that selected person is a woman

Let Z be the event that selected relies or use GPS system.

So;

the following probabilities are:

P(X) = 0.50

P(Y) = 0.49

P(Z) = 0.77

P(X ∩ Z) = 0.38

P(Y ∩ Z) = 0.38

Now;

if the selected person is a man, the probability that he relies on a GPS system can be determined as follows:

[tex]P(Z|X) = \dfrac{P(X \cap Z)}{P(Z)}[/tex]

[tex]P(Z|X) = \dfrac{0.38}{0.77}[/tex]

[tex]\mathbf{P(Z|X) =0.494}[/tex]

Thus, the probabiility that the selected man relies on a GPS system is 0.494

14. Joe has 3 more than half the number of pets his
friend does. Joe has 4 pets. He represented this
situation with the following equation: 4 = 3+x.
2
1
To figure out how many pets his friend has, Joe wants
to subtract a number from four. He will then multiply the
result by a number to determine how many pets his
friend has
What number should Joe subtract?
What number should Joe multiply by?

Answers

Answer:

He should subtract 3 from 4 and then multiply by 2.

Step-by-step explanation:

4 = 3 + 1/2x

1 = 1/2 x

2 = x

How to calculate a 15% tip?

Answers

If you want to leave a 15% tip, use the fact that 15% = 10% + 5%. Calculate 10% of the bill by moving the decimal point one position to the left. Then, take that number, divide it in half, and add the new amount to the original 10%
Hi I need help with my work can you help me please

Subtract 42.5 – 7.32

Answers

Answer:35.18

Step-by-step explanation:

Did this 7 years ago

The required value of 42.5 – 7.32 is 35.18.

Subtraction of 7.32 from 42.5 to be determined

What is subtraction?

Subtraction is defined as the value that should be reduced to the subtraction value.

Here, subtraction of 7.32 from 42.5,
⇒ 42.5 - 7.32
= 35.18

Thus, the required value of 42.5 – 7.32 is 35.18.

Learn more about subtraction here:
https://brainly.com/question/13619104

#SPJ2


Chelsea wants to buy a new iPhone that costs $324. She
has already saved $56. If she can save $20 a week, how
many weeks will it take for her to be able to purchase the
iPhone?

Answers

Answer:

14 full weeks.

Step-by-step explanation:

The phone costs $324 and she saved $56, so we subtract $56 from $324.

$324 - $56 = $268

She saves $20 each week so we divide $268 by $20 to get the number of weeks.

$268/20 = 13.4

It will take 13.4 weeks, but we have to round up because at 13 weeks she won't have enough saved. So 14 full weeks.

Which exponential expression is equivalent to the one below?

Answers

Answer:

The answer is A.

Step-by-step explanation:

You have to elaborate it :

[tex] {(54 \times ( - 13))}^{66} [/tex]

[tex] = {(54)}^{66} \times {( - 13)}^{66} [/tex]

PLEASE HELP!

What percent of the circle is shaded?
Can you also explain how to get the answer?

Answers

Answer:

C

Step-by-step explanation:

The answer is 30% because 2/5 of the circle is shaded.

a circle has a circumference of 6cm. find the diameter of the circle​

Answers

Answer:

1.9 or 2

Step-by-step explanation:

To find diameter you do,

d= C/pi

C is circumference

so, d=6/3.14

=1.910... or 2

Hope this helps :)

5. How can you get the variable alone in the equation x + 37 = 94?
a. Undo subtracting 37 by adding 37 to both sides
b. Undo subtracting x by adding x to both sides
c. Undo adding x by subtracting x from both sides
d. Undo adding 37 by subtracting 37 from both sides

Answers

The answer is d.because you have to subtract from both side

3. Five kissing cousins met at a family reunion.

Each cousin kissed each of the other cousins

just once. How many kisses were given in all?

Answers

Answer: 20 kisses

Step-by-step explanation:

given data:

number of cousins at the family reunion = 5

each cousing kissing each other just once.

if one cousin kisses everybody round that would be

= 1 * 4

= 4 kisses.

4 kisses from each cousins * number of cousins at the family reunion.

= 4 * 5

= 20 kisses.

in total there were 20 kisses at family reunion

Using the principle of combination, the number of kisses given in all by the five cousins is 10

Number of cousins, n = 5

Using the relation :

[n(n-1)] ÷ 2

Substituting the values into the relation :

[n(n-1)] ÷ 2

[5(5-1)] ÷ 2

(5 × 4) ÷ 2

20 ÷ 2

= 10 kisses

Hence, the Number of kisses exchanged in all is 10.

Learn more : https://brainly.com/question/14375199

2. Give recursive definitions for the following sets. a. The set of all strings over {a, b} containing at least one "a". b. The set of odd-length binary strings that end with 00.

Answers

Answer:

Two definition of sets of all strings and sets of odd length binary are given

Step-by-step explanation:

A.) Suppose A is the string of contain at least one a:A = a

B will be same as it is b:B = b

Sets of the union of the AB  and BA in which A followed B and corresponding B will follow A. Set = will (AB) (BA) = (*a*, *b*) (*b*, *a* )….

B.) There is the regular expression is compared with two 00 which is surrounded by the 0+1 that accepted at least two 0s.

Where would the plane STV intersect plane Z?

Answers

Answer:

Plane Z or plane VTX.

Step-by-step explanation:

From the picture attached,

ST pierces the plane at a point T.

That means line ST is perpendicular to the horizontal plane Z or plane VTX.

Since, S is a point lying on line ST it will not lie on the vertical plane VTX Or plane Z.

Therefore, point S is not contained in the plane Z.

Week (x) 1 2 3 4 5 Number of Customers (y) 30 42 56 72 90 A new business began tracking how many customers entered the store each week. The store owner realized the relationship between the week and the number of customers was quadratic. If the trend continues, during which week will 156 customers enter the store? A) week 7
B) week 8
C) week 16
D) week 17

Answers

Answer:

b

Step-by-step explanation:

What is the correct definition of the word bias? a. particular point of view b. a personal or unreasoned judgment c. to study in detail, or examine critically d. the capability of being believed; trustworthiness​

Answers

Answer:

b. a personal or unreasoned judgment

Step-by-step explanation:

The answer is B because bias is basically something or someone that you favor over anything or anyone else. Or what you belving in your own opion.

As an example, our strong bias in favor for the idea, or a test biased towards people who are excellent at math.

Answer:

D

Step-by-step explanation:

if you don't believe me look up the definition

When x = 4, the y-coordinate is
When x = 8, the y-coordinate is
When simplified, the constant of proportionality, k, is x 2

Answers

Answer:

X2=8/4

X=1

and thats whats it equal too.

Solve the equation 34 - (x + 8) = 6x-2​

Answers

Answer:

x = 4

Step-by-step explanation:

To solve the equation, we would have to solve for the variable x.

34 - (x + 8) = 6x - 2

Remove the parentheses.

34 - x - 8 = 6x - 2

Add 2 to both sides and combine like terms.

28 - x = 6x

Add x to both sides.

28 = 7x

Swap sides.

7x = 28

Divide both sides by 7.

x = 4

So the solution to the equation would be x = 4

I hope you find my answer and explanation to be helpful. Happy studying. :)

The real answer is x=4

1. Let n be the number (in thousands) of fans who attend a Foo Fighiers concert. What does n = 25 mean in this situation?​

Answers

Answer: 25,000 fans attend a Foo Fighters concert

Step-by-step explanation:

25 x 1000 = 25000

it means that 25,000 people attended the foo fighters concert.

A circle has a radius of 7 inches. What is the area of the circle? Use 3.14 for p. (Area of a circle = pr2​

Answers

Answer:

153.94

Step-by-step explanation:

13 5 6 3 2. If g(x) = 16 for the function g(x) = 3x - 2, solve for the value of x.
need help solving please step by step ​

Answers

Replace g(x) with 16:

16 = 3x-2

Add 2 to both sides:

18 = 3x

Divide both sides by 3:

X = 18/3

X = 6

Sep 27,
The midpoint of AB is M(-5,0). If the coordinates of A are (-8,5), what are the
coordinates of B?

Answers

Answer:

Step-by-step explanation:

(x-8)/2 = -5

x - 8 = -10

x = -2

(y+5)/2=0

y + 5 = 0

y = -5

(-2, -5)

If your expression contains square roots, during which step of PEMDAS do you solve them? A parentheses B exponents C multiplication D division

Answers

Answer:

B

Step-by-step explanation:

Roots can also be represented as indicies (exponents) and thus should be treated like them. For example, square root could also be written as exponent 1/2.

When dealing with square roots in a equation, PEMDAS calls for this to be solved when you do B. Exponents

The root of a number is that number expressed exponentially by the root in inverted form. In other words, when you take something to its square root, you would be taking it to the inverse of 2 which is 1/2.

For instance:

√4 = 2 = 4¹/²

This means that you can then solve the square root when you deal with exponents which is the second step.

In conclusion, if you see an expression with square roots, PEMDAS allows you to solve it as an exponent.

Find out more at https://brainly.com/question/20687401.

Pablo wants to get a grade of at least 95 in math this semesterSo far he has test scores of 89 98, 97 and 92. He will take his last test on Friday What is the lowest grade he can get on the test and still get a 95 this semester?

Answers

Answer:

the answer is 97 if you're rounding but 99 if you want exactly 95

Step-by-step explanation:

if you add all the previous grades up it'll add up to 376 and then when you add 97 and then divide it by 5 (the total amount of assignments) it'll add up to 94.6 which rounds up to a 95 unless you want it a 95 exactly which would probably be 99

Answer:

  99

Step-by-step explanation:

Relative to his desired average, Pablo's scores are ...

  -6, +3, +2, -3

In order for his average grade to be 95, the sum of all of these deviations and the one on his last test must be zero

  -6 +3 +2 -3 +x = 0

  x = 4

Pablo must get a 95+4 = 99 on his last test to have a 95 average.

Bernice rectangle workbook is 2/3 foot width and 5/6 foot long.what is the area of the page in her workbook.

Answers

Answer:

As a:

Fraction: 11/20

Decimal: 0.55

Percentage: 55%

Step-by-step explanation:

Write 3.79 as a mixed number.

Answers

Answer:

379/100

Step-by-step explanation:

IS THIS IT???

First convert 3.79 to a whole number. Move the decimal 2 times to the right so the denominator would be 100
Convert it into a fraction 379/100
Now simplify
so it would be 3 79/100

What is the area
this trapezoid?
6 m
1 m
3 m
5 m
o
A. 14 m2
O
B. 18 m2
O
C. 21 m2
O
D. 35 m2

Answers

Answer:

Area of the trapezoid = 18 m²

Step-by-step explanation:

Formula to calculate the area of a trapezoid is,

Area of a trapezoid = [tex]\frac{1}{2}(b_1+b_2)h[/tex]

Where [tex]b_1[/tex] and [tex]b_2[/tex] are the parallel sides of the trapezoid

And h = distance between the parallel sides

From the figure attached,

[tex]b_1[/tex] = 5 m

[tex]b_2[/tex] = (6 + 1) = 7 m

h = 3 m

By substituting these values in the formula,

Area of a trapezoid = [tex]\frac{1}{2}(5+7)3[/tex]

                                 = 6 × 3

                                 = 18 m²

Therefore, area of the given trapezoid is 18 m².

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