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Answer: 28

Step-by-step explanation:

The first part of the second step to prove the sequence is to prove that Sn is valid for n = k + 1, Option D is correct.

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

The sum of geometric sequence is given as,

[tex]s_n=\dfrac{r^n-1}{r-1}[/tex]

Here, a is the first term of the sequence, n is total terms and r is the common ratio.

The given equation which need to be proved is,

[tex]S_n= 1 + 2 + 4 +. ...+ 2n - 1 = 2n - 1[/tex]

This can be proved by induction method. This can be done by induction method with two steps:

Thus, the first part of the second step to prove the sequence is to prove that Sn is valid for n = k + 1, Option D is correct.

Learn more about the geometric sequence here;

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Answer:

8

Step-by-step explanation:

5 - (-3) is like adding 5 + 3 which is 8

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Answer:

8

Step-by-step explanation:

Applying the law of cosine, b² = a² + c² - 2ac(cos B), the length of AC of the marsh, to one decimal place, is: 522.1 meters

The Law of Cosine is given as, b² = a² + c² - 2ac(cos B).

From the diagram given, we have the following:

Plug in the values into the law of cosine formula:

b² = 220² + 420² - 2(220)(420)(cos 105)

b² = 272,629.8

b = √272,629.8

b = 522.1 meters. (Length of AC of the marsh)

Learn more about the law of cosine on:

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28/2= 14 42/2= 21 35/7= 5

14/ 2= 7 21/3= 7

28= 2^2 × 7

42= 2 × 3 × 7

35= 7 × 5

LCM= 420

48/2= 24. 72/2= 36. 96/3= 32

24/2= 12. 36/3= 12. 32/2= 16

12/3= 4. 12/3= 4. 16/2= 8

4/2= 2. 4/2= 2. 8/2= 4

4/2= 2

48= 2^4 × 3

72= 2^3 × 3^2

96= 2^5 × 3

LCM= 288

36/3= 12. 44/2= 22

12/3= 4. 22/2= 11

4/2= 2

36= 3^2 × 2^2

44= 2^2 × 11

LCM= 396

Answer:

The answer is in the attachment

Step-by-step explanation:

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Answer:

y = -5x + 7

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

First of all, remember what the equation of a line is:

Where:

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-3,8), point #1, so the x and y numbers given will be called x₁ and y₁. Or x₁ = -3 and y₁ = 8.

Also, let's call the second point you gave, (-2,3), point #2, so the x and y numbers here will be called x₂ and y₂. Or, x₂ = -2 and y₂ = 3.

Now, just plug the numbers into the formula for m above, like this:

[tex]m=\frac{3-8}{-2--3}[/tex]

or...

[tex]m=\frac{-5}{1}[/tex]

or...

[tex]m=-5[/tex]

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

[tex]y=-5x+b[/tex]

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=-5x+b. b is what we want, the -5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-3,8) and (-2,3).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!

You can use either (x,y) point you want..the answer will be the same:

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(-3,8) and (-2,3)

is

y=-5x-7

Answer:

  (a) 2.27 lb/$

  (b) 0.10 mi/min

Step-by-step explanation:

Pounds per dollar is found by dividing pounds by dollars:

  (25 lb)/($11.00) ≈ 2.272727... lb/dollar

The digit in the thousandths place is less than 5, so that digit and all digits to its right are dropped when rounding to hundredths.

  2.27 pounds per dollar

__

Speed in miles per minute is found by dividing miles by minutes:

  (6 mi)/(58 min) ≈ 0.103448... mi/min

Rounding to hundredths is done the same way as above.

  0.10 miles per minute

_____

If the digit to the right of the place you're rounding to is 5 or more, then 1 is added in the place you're rounding to when digits to its right are dropped.

Y = 2.9

Or

X= 2.9, y= - 0.9

Hope this helps!

Answer:

-25 is the simplest form

Answer:   3 2/9

Step-by-step explanation:

It would be the numbers exact form. Not totally sure but it would be my best guess.

Answer:

A. 45°

Step-by-step explanation:

When we are given two measurements of interior angles we add both of those angles together.

Also know that a triangle equals 180 degrees

So when we write out this expression     [tex]80+55+x=180[/tex]

[tex]135+x=180\\-135=-135\\x=45[/tex]

Hope this helps

Divide the restocking fee by the price of the item:

12/200 = 0.06

9/150 = 0.06

Multiply by 100 to get the percent:

0.06 x 100 = 6%

Answer: 6%

Answer:

2

Step-by-step explanation:

log 4 +log 25

Since these two equations have the same base and are being added, we can multiply the arguments

it would be: log 100

which is 2

Answer:

2

Step-by-step explanation: In logs, the opposite of addition is multiplication. Also, there needs to be only 1 log when you're condensing. So you'll multiply 4*25=100. And just plug in your calculator log(100) which is 2.

Hope this helps.

Answer:

90.93%

Step-by-step explanation:

It is clear that the table is a linear function. That is, every hour, the amount of corn increases by the same amount. You can find the slope of the linear function by using the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

In your case, the number comes out to be 825. So the number of corn will be 825*10 = 8250 cu ft.

Now, we know that the volume is area times height. So if the area is pi * r * r, then the volume of the shape is 2888*pi.

Therefore, the answer is 8250/2888*pi or 90.93%.

Answer:

Factors of 56: 1, 2, 4, 7, 8, 14, 28 and 56

Prime Factorization of 56: 56 = 23 × 7

Step-by-step explanation:

Answer:

4x + 2y = 2

Step-by-step explanation:

8x + 4y = 2 ( divide each term by 2 )

4x + 2y = 1 → (1)

we require a situation where the left side cannot possibly equal the right side.

using 4x + 2y = 2 → (2)

subtract (1) from (2) term by term

(4x - 4x) + (2y - 2y) = 2 - 1 , that is

0 + 0 = 1

0 = 1 ← not possible

thus the system has no solution

Answer:

The answer is X equals 12

Step-by-step explanation:

I hope you get it right!

Answer:

81.1 in

Step-by-step explanation:

To find the surface area of a triangular prism:

Find the base area and the remaining 3 rectangles and add them all together.

1.5*2=3 (base of the shape)

2*13=26

1.5*13=19.6

2.5*13=32.5

3+26+19.6+32.5=81.1

answer:

the probability of choosing a gray button is 3/5

after putting it back the probability remains the same, so 3/5 for both answers

Answer:

[tex]\sf \dfrac{3}{10}[/tex] = 0.3 - 30%

Step-by-step explanation:

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Given:

[tex]\sf P(gray) = \dfrac35[/tex]

If the button is not replaced, there are now:

[tex]\sf P(gray) = \dfrac24=\dfrac12[/tex]

Therefore,

[tex]\sf P(gray)\:AND\:P(gray)= \dfrac35 \times \dfrac12=\dfrac{3}{10}[/tex]

Answer:

D is the correct answer.

Step-by-step explanation:

[tex]3 {x}^{2} + 7x - {(x + 4})^{2} - 9 [/tex]

[tex]3 {x}^{2} + 7x - ( {x}^{2} + 8x + 16) - 9[/tex]

[tex]3 {x}^{2} + 7x - {x}^{2} - 8x - 16 - 9[/tex]

[tex]2 {x}^{2} - x - 25[/tex]

Answer:

x=29.3 degrees

Step-by-step explanation:

Vertical angles are congruent therefore the angle with the dot in it is 60.7 degrees and the combination of the dot and w is 90 degrees. 90-60.7=29.3

Answer:

400

Step-by-step explanation:

8% of 5000 is 400. Math:

5000 x 0.08 = 400

Answer:

1/2x + 1/3

Step-by-step explanation:

1/2x + 1/3

Answer:

0.067

Step-by-step explanation:

We just move 0.67's decimal point to the right by one since we are dividing by 10.

0.67 / 10 = 0.067

Give (✿◕‿◕✿)

Answer:

Let's find the number of arrangements with mother and father together, say N & then subtract it from total number of arrangements.

Total arrangements = 6! = 720.

Now, as mother & father are together, let's treat mother and father as a single person. Now, there're 5 persons.

Number of arrangements in this way = 5! = 120.

But mother and father can change their places in 2! = 2 ways.

N = 120 × 2 = 240.

Ans. = 720-240 = 480.

Step-by-step explanation:

Answer:

c = 9

Step-by-step explanation:

Given equation:

[tex]\sf 6(c-1)=48[/tex]

Divide both sides by 6:

[tex]\implies \sf \dfrac{6(c-1)}{6}=\dfrac{48}{6}[/tex]

[tex]\implies \sf c-1=8[/tex]

Add 1 to both sides:

[tex]\implies \sf c-1+1=8+1[/tex]

[tex]\implies \sf c=9[/tex]

Answer:

9

Step-by-step explanation:

There are now 48 total cookies shared by the 6 plates after he takes 1 cookie (6 cookies)

48+6 is 54/6 is 9

Answer:

Explanation: This is the answer

Answer:

[tex]h = 9\ cm[/tex]

Step-by-step explanation:

Step 1:  Determine what h is

[tex]Area = \frac{h * b}{2}[/tex]

[tex]45\ cm^2 = \frac{h * 10\ cm}{2}[/tex]

[tex]45\ cm^2 *2 =\frac{h * 10\ cm}{2}*2[/tex]

[tex]90\ cm^2 = h * 10\ cm[/tex]

[tex]\frac{90\ cm^2}{10\ cm}= \frac{h*10\ cm}{10\ cm}[/tex]

[tex]9\ cm = h[/tex]

Answer: [tex]h = 9\ cm[/tex]