Which value is a solution to w∕18 ≥ –1?

Answer:

Step-by-step explanation:

Hello, we want to prove that a proposition depending on n, that we can note P(n), is true for any n positive integer greater than 1. We need to follow several steps.

Step 1 - prove P(1)

For n = 1, n(2n+1)=1*3 =3 so we have

3 = 3, which is obviously true.

First step done!

Step 2 - for [tex]k\geq 1[/tex] we assume P(k) and we need to prove P(k+1)

We assume that 3+7+11+...+(4k-1)=k(2k+1)

so we can write that

3+7+11+...+(4k-1)+(4(k+1)-1)=k(2k+1)+(4k+4-1)=k(2k+1)+4k+3

[tex]=2k^2+k+4k+3\\\\=2k^2+5k+3[/tex]

and

(k+1)(2(k+1)+1)=(k+1)(2k+3)

[tex]=k(2k+3)+2k+3\\\\=2k^2+3k+2k+3\\\\=2k^3+5k+3[/tex]

These two expressions are the same so it means that P(k+1) is true, meaning that

3+7+11+...+(4k-1)+(4(k+1)-1)=(k+1)(2(k+1)+1)

Step 3 - The conclusion

Finally, we have just proved that

3+7+11+...+(4n-1)=n(2n+1) for any n positive integer > 0

Thank you

The given sum of arithmetic progression series 3+7+11+... (4n-1) = n(2n+1) is true.

The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).

The arithmetic progression has wider use in mathematics for example sum of natural numbers.

Natural number = 1,2,3,4,5,6,7,8...

Now it has the same difference between any two consecutive terms d =2-1 = 3-2.

The Sum of n terms of an AP is given by,

S= n/2[2a + (n-1)d ] where a is first term and d is common difference.

In our series 3+7+11+... (4n-1)

First term (a) = 3

Common difference (d) = 7 - 3 = 4

So the sum will be

S = n/2[2(3) + (n-1)4]

S = n[3 + 2(n - 1)]

S = n (2n + 1 ) = Right hand side.

Hence "The given sum of arithmetic progression series 3+7+11+... (4n-1) = n(2n+1) is true".

For more about Arithmetic progression,

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Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

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Answer:

The answer is

Step-by-step explanation:

First factor (x+1)² out of the expression

That's

[tex] \frac{ ({x + 1})^{2} (6 \cos( \frac{\pi}{3} )) {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) }{ ({x + 1})^{2} } [/tex]

Reduce the expression by (x + 1)²

We have

[tex]6 \cos( \frac{\pi}{3} ) \times {x}^{2} - {x}^{3} \times 2 \sin( \frac{\pi}{2} ) [/tex]

Using trigonometric values table

[tex] \cos( \frac{\pi}{3} ) = \frac{1}{2} [/tex]

[tex] \sin( \frac{\pi}{2} ) = 1[/tex]

So we have

[tex]6 \times \frac{1}{2} \times {x}^{2} - {x}^{3} \times 2 \times 1[/tex]

Simplify

We have the final answer as

[tex] {3x}^{2} - 2 {x}^{3} [/tex]

Hope this helps you

Answer:

54°

Step-by-step explanation:

Let ∠CYX=x

AB║CD

∠AXE=∠CYX  (corresponding angles)

∠AXE=3∠CYX-108

x=3x-108

3x-x=108

2x=108

x=108/2=54°

∠AXE=∠CYX=x=54°

∠BXY=∠AXE=54° (Vertically opposite angles)

Answer:

I'm guessing the right answer should be B

Step-by-step explanation:

whaatttttttttttttttt

Answer:

number of games each player has played

the average number of points each player's team scores per

Step-by-step explanation:

number of games each player has played

the average number of points each player's team scores per

Answer:

a)2/7

b)1/2

c)9/14

d)6/7

Step-by-step explanation:

The jar contains 4 red marbles, numbered 1 to 4 which means

Red marbles = (R1) , (R2) , (R3) , (R4)

It also contains 10 blue marbles numbered 1 to 10 which means

Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .

We can calculate total marbles = 4red +10 blues

=14marbled

Therefore, total marbles= 14

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7

Total number of Blue marbles = 10

Blue and even marbles = 5

(a) The marble is red

P(The marble is red)=total number of red marbles/Total number of marbles

=4/14

=2/7

(b) The marble is odd-numbered

Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,

Red marbles with odd number = (R1) , (R3)

Number of odd numbered =(5+2)=7

P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles

P(marble is odd-numbered )=7/14

=1/2

(C) The marble is red or odd-numbered?

Total number of red marbles = 14

Number of red and odd marbles = 2

The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7

n(red or even )= n(red) + n(odd)- n(red and odd)

=4+7-2

=9

P(red or odd numbered)= (number of red or odd)/(total number of the marble)

= 9/14

(d) The marble is blue or even-numbered?

Number of Blue and even marbles = 5

Total number of Blue marbles = 10

Number of blue that are even= 5

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)

=7

n(Blue or even )= n(Blue) + n(even)- n(Blue and even)

= 10+7-5 =12

Now , the probability the marble is blue or even numbered can be calculated as

P(blue or even numbered)= (number of Blue or even)/(total number of the marble)

= 12/14

= 6/7

Answer:

4/5

Step-by-step explanation:

237/1185 = .2 = 1/5

meaning there's 4/5 left

Answer:

Step-by-step explanation:

Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }

To prove that REPEAT [tex]_{TM[/tex]  is undecidable.

Let  REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}

Then, we form a TM  u for L by applying TM v as a subroutine.

Assume Repeat   is decidable

Let M be the algorithm that  TM which decides the REPEATU = on input "s" simulate the M

Accept; if M ever enters the accept state

Reject; if M ever enters the reject state

U does not decide the REPEAT as it may loop over s

so REPEAT is undecidable

Answer:18

Step-by-step explanation:

because 36 is divided by 2 equals 18cm

Answer:

6cm x 6cm

Step-by-step explanation:

It's a square so the dimensions have to be the same (6x6 = 36). Even though 18 is a factor of 36, 18cm by 2cm would make a rectangle.

Answer:

149 degrees

Step-by-step explanation:

This shape is a cyclic, so opposite angles add up to 180 degrees.

180-31 = 149

Answer:

-3/8

Step-by-step explanation:

Hey there!

Well to find the slope with 2 points “(0,-3) and (3,-11)”, we’ll use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

Plug in the given points.

[tex]\frac{-11 - - 3}{3-0}[/tex]

-11 + 3 = -8

3 - 0 = 3

Slope = -8/3

Hope this helps :)

Answer: 20 sq. units .

Step-by-step explanation:

Let A(0, -2), B(3,2), C(8,2), and D(5, -2) are the points for the parallelogram.

First we plot these points on coordinate plane, we get parallelogram ABCD.

By comparing the y-coordinate of B and C with A and D , we get

height = 2+2 = 4 units

Also by comparing the x coordinates of A and D, we get base = 5-0= 5 units  

Area of parallelogram = Base x height

= 5 x 4 = 20 sq. units

Hence, the area of a parallelogram ABCD is 20 sq. units .

Answer:

x=20

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2

21 ^2 + x^2 = 29^2

441+x^2 =841

Subtract 441 from each side

x^2 = 841-441

x^2 = 400

Take the square root of each side

sqrt(x^2) = sqrt(400)

x = 20

Answer:

[tex]\boxed{x = 20}[/tex]

Step-by-step explanation:

Hey there!

Well to find x we need to use the Pythagorean Theorem, which is.

[tex]a^2 + b^2 = c^2[/tex]

We have a which is 21 and 29 which is c.

[tex](21)^2 + x^2 = (29)^2[/tex]

[tex]441 + x^2 = 841[/tex]

[tex]-441[/tex]

[tex]x^2 = 400[/tex]

[tex]x = 20[/tex]

So the missing side "x" is 20.

Hope this helps :)

Answer:

9.5

Step-by-step explanation:

Monday: [tex]4\frac{1}{4}[/tex]

Tuesday: [tex]2\frac{2}{3}[/tex]

Wednesday: [tex]4\frac{1}{4} - 1\frac{1}{3}[/tex]

Total: [tex]4\frac{1}{4} + 2\frac{2}{3} + (4\frac{1}{4} - 1\frac{1}{3})[/tex]

Start by subtracting [tex]4\frac{1}{4} and[/tex] [tex]1\frac{1}{3}:[/tex] [tex]\frac{35}{12}[/tex]

Now, add them all up: [tex]4\frac{1}{4} + 2\frac{2}{3} + \frac{35}{12} = 9.5[/tex]

Therefore, Micah drove 9.5 miles in total.

Answer:

1. B. False

2. B. Evidence suggests a small difference in promotion rates favoring males.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

Answer:

Hey there!

A is correct. The +2 means shifted up two units, 1/2 means compressed by a factor of 1/2, and the -3 means to the left of three units.

Let me know if this helps :)

Answer:  60°

Step-by-step explanation:

∠UQR = 180°

∠UQR = ∠UQ + ∠QR

  180° =  115° + ∠QR

   65° = ∠QR

∠QRT = 180°

∠QRT = ∠QR + ∠RS + ∠ST

  180° =  65° + ∠RS  +  55°

  180° = 120° + ∠RS

   60° = ∠RS

Answer:

please mark my answer brainliest

Step-by-step explanation:

question is unclear to give u correct answer

Answer:

16

Step-by-step explanation:

The sequence is 1, 4,...,64, 256, 1024

Notice that:

● 1 = 2^0

● 4 = 2^2

● 64 = 2^6

● 256 = 2^8

● 1024 = 2^10

Notice that we add 2 each time to the exponent so the missing number is:

● 2^(2+2) = 2^4 = 16

Answer:

or,x2-x=6

or,x2-x-6=0

or,x2-3x+2x-6=0

or,x(x-3)+2(x-3)=0

or,(x-3)(x+2)=0

so either x=3

or x=-2

17 is the answer

(Mark me brainliest)

Answer:

Step-by-step explanation:

Semester Costs = 8*2858 =                     22864

Books / semester= 8 * 391 =                        3128

Total                                                            25992

If he wants to repay all this in six years the answer would be

45000 + 25992/6 = 45000 + 4332 = 49332

Answer:

49332

Step-by-step explanation:

Hi

35/100= 140/ X

X = 100*140 /35

X= 14000/35

X= 400

There are 400 computer in the compagny.

Answer:

5x^3-2

[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]

Explanation:

The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.

We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.

The coefficient is the number to the left of the variable.

The degree is the largest exponent, which helps form the leading term.

The third degree polynomial written above is considered a cubic binomial. "Cubic"  refers to the third degree, while "binomial" means there are 2 terms.

We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.

Answer:

-15

Step-by-step explanation:

If it fell 3 deg every hour for 5 hours so the equation is 3*5 plus a - sign because it dropped degrees

Answer:

The variance is  [tex]\sigma ^2 =25[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  21

     The sum of squares is [tex]SS = 500[/tex]

Generally the variance is mathematically represented as

           [tex]\sigma ^2 = \frac{SS}{n- 1}[/tex]

substituting values

          [tex]\sigma ^2 = \frac{ 500}{21- 1}[/tex]

          [tex]\sigma ^2 =25[/tex]