What is the length of the missing leg?

Answer:

It diverges; it does not have a sum.

Step-by-step explanation:

3, 9, 27, 81, ..

ratio = r = 9/3 = 3

since |r| ≥ 1, it diverges and doesn't have a sum

The solution is, the given series is divergent and it has a sum infinity.

Option (A) is CORRECT. i.e. It diverges; it does not have a sum.

A geometric series is a series in which the division of any consecutive two terms will be the same.

here, we have,

We are given to check whether the following infinite geometric series diverge or converge :

given that,

3 + 9 + 27 +81 +....

We know that

an infinite geometric series diverges if the modulus of the common ratio is greater than 1.

For the given geometric series, the common ratio r is given by

r = 9/3

 = 3

So, we get

r = 3 > 1

Therefore, the given infinite geometric series diverges.

Also, we know that the sum of a divergent infinite geometric series with first term a and common ratio r is given by,

the sum will be infinity.

For the given series,

it does not have a sum.

Therefore, the required sum will be infinity.

Thus, the given series is divergent and it has a sum infinity.

Option (A) is CORRECT. i.e. It diverges; it does not have a sum.

For more about geometric series

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Answer:

Original value of investment = £500 (Approx.)

Step-by-step explanation:

Given:

Rate per year = 4%

Number of year = 3 years

Value of investment after 3 year = £562.43

Find:

Original value of investment

Computation:

A = P[1+r]ⁿ

562.43 = P[1+4%]³

562.43 = P[1+0.04]³

562.43 = P[1.04]³

562.43 = P[1.1248]

Original value of investment = 562.43 / 1.1248

Original value of investment = 500.026

Original value of investment = £500 (Approx.)

Answer:

From 10 a.m. to 2 p.m., the temperature at Sam's house increased by 8 degrees Fahrenheit.

Step-by-step explanation:

Write as a number equation ---->  2 - (-6) = 8

Answer:

Step-by-step explanation:

An easy way to do slope is to know the formula which is (y1-y2)/(x1-x2)

In this case you have two points (2,5) and (0,-1)

2 = x1 (cause it’s the first x)

5 = y1 (cause it’s the first y)

0 = x2 (second x)

-1 = y2 (second y)

So the slope would be

(5-(-1))/2-0= 6/2 = 3

Answer:

3/7(when simplified)

Step-by-step explanation:

there are 6 daisies out of 14 flowers and so the probability would be 6/14. When simplified, the answer would be 3/7

Answer:

Bar graph

Step-by-step explanation:

is the right answer for mine

Answer:

x = 0.2

Step-by-step explanation:

Distribute the 5 to (2 + x) to make it 10 + 5x = 11. You can rewrite it to make it 5x + 10 = 11 to make it easier if you want but you dont have to. Subtract the ten from both sides to make it 5x = 1. Divide both sides by 5 to get 0.2. If you want to double check your answer you can substitute 0.2 in for x in (2 + x)5 = 11 or in 5x + 10 = 11. It doesn't matter which.

Answer:

11/12 should be the correct answer!

Step-by-step explanation:

Let's make the denominator the same!

Lcm of 3 and 4 is 12

sooo... multiply

2/3 x 4/4 = 8/12

1/4 x 3/3 = 3/12

8/12 + 3/12 = 11/12

Answer:its A or C

Step-by-step explanation:i hope this helps

Answer: [tex]337.77\%[/tex]

Step-by-step explanation:

Given

For 70 year old, premium is 79.79 per month

For 80 year old it is 349.30 per month

Percentage increase in premium costs from age 70 to 80 is

[tex]\Rightarrow \%\ \text{increase}=\dfrac{349.30-79.79}{9.79}\times 100\\\\\Rightarrow \%\ \text{increase}=\dfrac{269.51}{79.79}\times 100\\\\\Rightarrow \%\ \text{increase}=337.77\%[/tex]

Answer:  sorry i dont know this

Step-by-step explanation:

Explanation:

Draw out a rectangle and make sure it's not a square. So you could have it be longer than it is tall. Imagine rotating that rectangle 180 degrees. The before and after (preimage and image) will be identical. The same applies if we slanted the sides of this rectangle. This shows that any parallelogram has rotational symmetry.

Side note: any rectangle is a parallelogram, but not the other way around.

Answer:

$9.05

Step-by-step explanation:

x = $adult

y = $kid

2x + 3y = 72.85 (Heather)

2x + 5y = 94.75  (Carl)

subtract the equations to get:

-2y = -21.90

y = 10.95

solve for 'x':

2x + 3(10.95) = 72.85

2x + 32.85 = 72.85

2x = 40

x = 20

Difference between 20 and 10.95 is $9.05

The probability of 3 sunny days in a row is P = 0.512, so the correct option is C.

We know that the probability of rain each day is 20%. Then the probability of a sunny day is 100% - 20% = 80%.

Writing this probability in the decimal form we get 0.8.

Now, to get 3 sunny days in a row, we need to have the probability 0.8 3 times (and remember that the probabilities multiply between them) so the joint probability is:

[tex]P = (0.8)^3 = 0.512[/tex]

To get it in percentage form, we multiply it by 100%.

P = 0.512*100% = 51.2%

So the correct option is C.

If you want to learn more about probability:

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[tex]\huge\bold{To\:find:}[/tex]

✎ The value of [tex]x[/tex].

[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]

[tex]\sf\purple{The\:value\:of\:x\:is\:10°. }[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

Since it is right angle,

[tex]Sum \: of \: angles \: = 90° \\ ⇢ 2x °+ 7x° =90 ° \\ ⇢9x° = 90° \\ ⇢x° = \frac{90°}{9} \\ ⇢x° = 10°[/tex]

[tex]\sf\blue{Therefore,\:the\:value\:of\:x\:is\:10°.}[/tex]

[tex]\huge\bold{To\:verify :}[/tex]

[tex]2x° + 7x° = 90° \\ ➡ \: 2 \times 10° +7 \times 10° = 90° \\ ➡ \: 20° + 70° = 90° \\ ➡ \: 90° = 90° \\ ➡ \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.ඞ}}}}}∘[/tex]

Answer:

C. 9:5

Step-by-step explanation:

I got a 100 on my test

Answer:

y = 3x + 40

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (- 12, 4 ) into the partial equation

4 = - 36 + c ⇒ c = 4 + 36 = 40

y = 3x + 40 ← equation of line

Answer:

The cost of the paint will be $123.75.

Step-by-step explanation:

Since Pranav paints a wall of area 53m ^ 2, and one liter of paint covers an area of 4.5m ^ 2, and paint is sold in 2.5 liter tins, each costing $ 24.75, if Pranav buys the least number of tins to paint this wall, to determine the cost of the paint, the following calculation must be performed:

(53 / 4.5) = liters of paint needed

11.77 = liters of paint needed

11.77 / 2.5 = tins of paint needed

4.71 = tins of paint needed (rounds to 5)

5 x 24.75 = Total cost

123.75 = Total cost

The cost of the paint will be $123.75.

Answer:

7 books

$27

Step-by-step explanation:

3x + 6= 5x - 8

3x - 5x = -14

-2x= -14

x= 7 books

he has (3×7)+6= $27

Let comics be c and mystery be m

Cost be y

c=m

The equations are

Solve for m

He has

3x - 6 = 90

3x - 6 + 6 90 + 6

3x = 96

3x ÷ 3 = 96 ÷ 3

x = 32

Answer:

4kg

Step-by-step explanation:

Mr Sharma packed 42 kg of tea into one big bag and sox small bags each of the same size

The first step is to calculate the quantity in the big bag

= 3/7 × 42

= 3×6

= 18

The amount left in the remaining bags is

= 42-18

= 24

Therefore the kg of tea in the small bags can be calculated as follows

= 24/6

= 4

Hence there are 4kg of tea in the small bags

Answer:

sorry buddy i dont know the answer hope this helps

Step-by-step explanation:

Isn't this what u did to me when i needed help and took my points away.

Answer:

heyy sorry i dont really know what is the 'standard deviation' but as for the mean you go to add all the numebers together and divide them by the amount of numbers there are (7 in this scenario)

Step-by-step explanation:

21 + 29.5 + 38 + 46.5 + 55 + 63.5 + 72 = 325.5

then you divide 325.5 by the number of numbers present in the question

325.5 / 7 = 46.5

hope it helped :)

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Explanation:

1 hour = 60 minutes

2 hours = 120 minutes (multiply both sides by 2)

2 hrs + 20 min = 120 min + 20 min (add 20 min to both sides)

2 hrs, 20 min = 140 min

Juan studied for 140 min

---------------------

Ken studied for 2/3 of an hour, so he studied for (2/3)*60 = 120/3 = 40 min

We see that Juan studied more than Ken, so that must mean Juan's study time as a percentage of Ken's study time is over 100%

This is because

and so on

We divide Juan's time by Ken's time to get: 140/40 = 3.5 = 350%

350% of Ken's study time was Juan's study time.

In other words, if we take 350% of the 40 min figure, then we get 3.5*40 = 140 which represents Juan's study time.

If your teacher asked the reverse of this, and instead asked "what percent of Juan's study time was Ken's?", then the answer would be 40/140 = 0.2857 = 28.57% approximately.

Answer:

B) 9

Step-by-step explanation:

110 + 75 + 11x - 9 + 8x + 13 = 360

19x + 189 = 360

19x (+ 189 - 189) = 360 - 189

19x = 171

19x/19 = 171/19

x = 9

Answer:

3/5

Step-by-step explanation:

Because if you take 3/4 x 4/5 you can cross simplify the 4's in the equation and they cancel eachother out, so then u are left off with 3/1 x 1/5 and then you get 3/5

Answer:

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Explanation:

If the diameter is d = 18, then the radius is half that at r = d/2 = 18/2 = 9

Then that radius is plugged into the circle area formula below

A = pi*r^2

A = pi*9^2

A = pi*81

A = 81pi

If you were to use an approximation like pi = 3.14, then the approximate area would be 81*pi = 81*3.14 = 254.34 mm^2; however, your teacher wants you to write the exact area.

Are you sure about the numbers ( 83 x 52) ? I think there is a mistake