A proof by mathematical induction is supposed to show that a given property is true for every integer greater than or equal to an initial value. In order for it to be valid, the property must be true for the initial value, and the argument in the inductive step must be correct for every integer greater than or equal to the initial value. Consider the following statement. For every integer n ≥ 1, 3n − 2 is even. The following is a proposed proof by mathematical induction for the statement. Since the property is true for n = 1, the basis step is true. Suppose the property is true for an integer k, where k ≥ 1. That is, suppose that 3k − 2 is even. We must show that 3k + 1 − 2 is even. Observe that 3k + 1 − 2 = 3k · 3 − 2 = 3k(1 + 2) − 2 = (3k − 2) + 3k · 2. Now 3k − 2 is even by inductive hypothesis, and 3k · 2 is even by inspection. Hence the sum of the two quantities is even by (Theorem 4.1.1). It follows that 3k + 1 − 2 is even, which is what we needed to show. Identify the error(s) in the proof. (Select all that apply.) The inductive hypothesis is assumed to be true. (3k − 2) + 3k · 2 ≠ 3k(1 + 2) − 2 The property is not true for n = 1. 3k + 1 − 2 ≠ (3k − 2) + 3k · 2 3k − 2 is odd by the inductive hypothesis.

Answer:

4)120

5)13

6)70

7)115

Step-by-step explanation:

Answer: 4. 120 degrees 5. 13 degrees 6. 70 degrees 7. 115 degrees

Answer: v=85/11

Step-by-step explanation: Cross multiply to get 11v=85, divide both sides by 11, and you get v=85/11.

Hope that this helped! Have a great day!!

Answer:2

8

2

+

2

8

Step-by-step explanation:

Answer:

84x

Step-by-step explanation:

If you have any questions feel free to ask in the comments.

Answer:

-3.5 will be answer he he he he he he he he

Answer:

In the first one you are missing (x - 3) so it will be 4(x - 3) and if you factor it out it will be 4x - 12

In the second one you are missing a (x -5)which means 9x(x -5) or when you factor it out it will be 9x^2 - 45x

Step-by-step explanation:

3x^2 -23x + 40 = (3x - 8) (x - 5)

3x^2 -17x + 24 = (3x -8) ( x - 3)

Answer:

6.48

please mark me as brainliest

Answer: b

Step-by-step explanation:

The range is the set of y-values of the function.

Answer:

I can help!

Step-by-step explanation:

Each line on the plot is 1. It keeps adding by 1. All you have to do is put a dot on the right line every time you see a number. Some may have none.

Answer:

X=5times (root2)/2

Step-by-step explanation:

Sin45=x/5

x=5sin45

x=5 times root2/2

Answer:

the answer is 0 to 1 and 3 to 4

9514 1404 393

Answer:

  55,637.8 square inches

Step-by-step explanation:

We can find side n using the Law of Sines:

  n/sin(N) = p/sin(P)

  n = p(sin(N)/sin(P)) = 600·sin(64°)/sin(96°)

  n ≈ 542.246913 . . . . inches

The angle O is ...

  O = 180° -N -P = 180° -64° -96° = 20°

Then the area is ...

  A = 1/2·np·sin(O)

  A = (1/2)(542.246913 in)(600 in)·sin(20°) ≈ 55,637.81008 in²

The area of ∆NOP is about 55,637.8 in².

Answer:Area

≈

55637.81

≈

55637.8

Area≈55637.81≈55637.8

Step-by-step explanation:

Step-by-step explanation:

Total sections= 8

Yellow sections=2

So,

2/8

In second black write

1/4 ( by reducing 2/8)

hope it helps

Answer:

The differnce is 3 and 1/2 as 9/2 - 1 = 3 and 1/2 according to the points plotted above the diagram meaning 5 and 0 are excluded values which do not have any place within the diagram.

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

it

is

the

answer

C

Answer:

The 90% confidence interval for the true mean lifespan of this product is between 13.1 and 16.9 years.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 50 - 1 = 49

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.6766

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.6766\frac{8}{\sqrt{50}} = 1.9[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 15 - 1.9 = 13.1 years

The upper end of the interval is the sample mean added to M. So it is 15 + 1.9 = 16.9 years

The 90% confidence interval for the true mean lifespan of this product is between 13.1 and 16.9 years.

Answer:

Option 2

Step-by-step explanation:

The problem given is saying this for example 24 ÷ (2+4)

The problem you picked would be saying (2+4) ÷ 24

Option 2 is saying 24 ÷ (4+2)

Nothing is changing except the order of the numbers in the parantheses, no matter which way you put them it's still the same answer

Option (A) Political organization C is correct if four candidates in an election are each supported by a different political organization.

Skepticism often referred to simply as skepticism, is a skeptical attitude or doubt against a or more alleged instances of knowing that are claimed to be simply belief or dogma. Skepticism is a philosophical issue of interest, notably in epistemology.

We have four candidates in an election each supported by a different political organization.

If a report is issued that speaks highly of Bruce Walton and is backed by the political organization A.

Because the study talks favorably of Bruce Walton, and Bruce Walton is sponsored by the political organization A, the political organization that produced the report should generate the most distrust. Bruce Walton will despise other organizations.

Thus, option (A) Political organization C is correct if four candidates in an election are each supported by a different political organization.

Learn more about the skepticism here:

https://brainly.com/question/2555146

#SPJ2

Answer to your question is Political organization C :)

Answer:

B) 4

Step-by-step explanation:

(x-1+2)^2=(x-1)^2+(2x-4)^2

(x+1)^2=(x-1)^2+(2x-4)^2

x^2+2x+1=x^2-x+1+4x^2-16x+16

0= 4x^2-18x+17-2x-1

4x^2-20x+16=0/4

x^2-5x+4=0

(x-4)(x-1)=0

x-4=0

x=4

hope it helps..

have a great day!!

Answer:

3 cups or 1.5 pints

Answer:

A

because i think it is

Answer:you will end up with 350.00 dollars left

Step-by-step explanation: you are spending money on the thing that you are buying

Answer:

5

Step-by-step explanation:

Answer: - 9/8

Step-by-step explanation:

Answer:

y is the total the pens produced at the factory   each week

Step-by-step explanation:

total pens produced at the factory each week   = y   (=52,000)

3/4 of the total are red ( 39,000)

9514 1404 393

Answer:

  45.6°

Step-by-step explanation:

The attached result was found by typing "arccos(7/10) in degrees" into a web browser search box.

Your calculator can give you the same result. The inverse cosine function often shares a key with the cosine function. It is often marked as cos⁻¹. Be sure that the angle mode is set to degrees, not radians.

Answer:

308

Step-by-step explanation:

Answer:

I recoment using the formula because its different ways its taught

Step-by-step explanation:

maybe look up different formula's

Answer:

The answer is D

Step-by-step explanation:

The y values are going up by 2

For linear equations you follow y = mx + b

M = 2

B would be 1 since that is what y is when x is 0

So it must be D

Answer:

2) The number is 4, 3) The number is 36, 4) The number is 16, 5) The number is 32, 6) The consecutive numbers are 14 and 15, 7) The solution of this system is: [tex]x = 17[/tex], [tex]y = 13[/tex], 8) The solution of this system is: [tex]x = 58[/tex], [tex]y = 60[/tex].

Step-by-step explanation:

Now we proceed to solve arithmetically on each statement:

2) Statement is incorrect, correct form is: Find [tex]x[/tex] if the product of [tex]x[/tex] by 12 is 48.

Mathematically speaking, we have the following formula:

[tex]12\cdot x = 48[/tex]

[tex]x = 4[/tex]

The number is 4.

3) Mathematically speaking, we have the following formula:

[tex]\frac{3\cdot x}{6} = 18[/tex]

[tex]\frac{x}{2} = 18[/tex]

[tex]x = 36[/tex]

The number is 36.

4) Mathematically speaking, we have the following formula:

[tex]\frac{5\cdot x}{4} = 20[/tex]

[tex]x = 16[/tex]

The number is 16.

5) Mathematically speaking, we have the following formula:

[tex]\frac{x}{2} = 16[/tex]

[tex]x = 32[/tex]

The number is 32.

6) Let be [tex]n[/tex] and [tex]n + 1[/tex], whose sum equals 29. Mathematically speaking, we have the following formula:

[tex]n + (n +1) = 29[/tex]

[tex]2\cdot n + 1 = 29[/tex]

[tex]n = 14[/tex]

The consecutive numbers are 14 and 15.

7) Let be [tex]x[/tex] and [tex]y[/tex] the quantities of pink and yellow roses. Mathematically speaking, we have the following system of linear equations:

[tex]x - y = 4[/tex] (1)

[tex]x + y = 30[/tex] (2)

The solution of this system is: [tex]x = 17[/tex], [tex]y = 13[/tex]

8) Let be [tex]x[/tex] and [tex]y[/tex] the numbers of grade 6 and grade 3. Mathematically speaking, we have the following system of linear equations:

[tex]x-y = -2[/tex] (3)

[tex]y = 60[/tex] (4)

The solution of this system is: [tex]x = 58[/tex], [tex]y = 60[/tex]