Not sure how this works as a fraction to place the dot in the right place

Answer:

[tex]-a-\frac{a^2}{2}-\frac{a^3}{3}-\frac{a^4}{4}-...-\frac{a^n}{n}-...[/tex]

Step-by-step explanation:

1) the rule is:

[tex]ln(1+a)=a-\frac{a^2}{2}+\frac{a^3}{3}-\frac{a^4}{4}+...+(-1)^{n-1}\frac{a^n}{n}+...[/tex]

2) according to the rule above:

[tex]ln(1+(-a))=(-a)-\frac{(-a)^2}{2}+\frac{(-a)^3}{3}-\frac{(-a)^4}{4}+...+(-1)^{n-1}\frac{(-a)^n}{n}+...[/tex]

finally,

[tex]ln(1-a)=-a-\frac{a^2}{2}-\frac{a^3}{3}-\frac{a^4}{4}-...-\frac{a^n}{n}-...[/tex]

[tex]\begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} 0&-5\\ 1&-1\\ 2&3\\ 3&7\\ \cline{1-2} \end{array} \begin{array}{llll}\\[-0.5em] \leftarrow \textit{let's use this point}\\\\\\ \leftarrow \textit{and this point} \end{array}\qquad \qquad (\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{7})[/tex]

[tex]\stackrel{slope}{m}\implies\cfrac{\stackrel{rise}{\stackrel{y_2}{7}-\stackrel{y1}{(-5)}}}{\underset{run}{\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{7+5}{3}\implies \cfrac{12}{3}\implies 4[/tex]

Step-by-step explanation:

of course, we have to use Pythagoras.

c² = a² + b²

c is the Hypotenuse = the side opposite of the 90° angle.

and here is the problem : are 9 and 12 the legs. or is one of them the Hypotenuse ?

I don't know from the description.

let's see what we get one way or the other :

assumption : the known sides are the "legs".

c² = 9² + 12² = 81 + 144 = 225

c = 15 ft

that is a nice number. so, it looks like that was the intention.

just to be sure, here also the other options :

9² = 12² + side²

81 = 144 + side² that makes side² negative, so, not valid.

12² = 9² + side²

144 = 81 + side²

63 = side²

side = sqrt(63) this is not a nice round number, so, we go with the first option.

therefore, the 3 sides are

9 ft, 12 ft, 15 ft

perimeter = 9+12+15 = 36 ft

area = baseline×height/2

since this is a right-angled triangle, the "legs" with the enclosed 90° angle serve as baseline and height.

area = 9×12/2 = 9×6 = 54 ft²

Answer:

2.4

Step-by-step explanation:

The constant of proportionality is y=kx which should 2.4

Answer:

48

Step-by-step explanation:

There are various multiples of 6 that are greater than 40, but less than 90. Including 42, 48, 54, 60, 66, 72, 78, and 84. :)

Answer: 301.44 cubic inches.

Step-by-step explanation:

The formula for the volume of a cone is [tex]V = \pi r^2 \frac{h}{3}[/tex], so by plugging in the radius (6) and height (8), and using 3.14 as pi, you can get 301.44 as the total volume.

Since it is volume, it is in inches cubed, Therefore, the final answer is 301.44 cubic inches.

I hope this helps! :)

Answer:

99th term is 51

Step-by-step explanation:

Arithmetic sequence equation

a1= first term = 2

d= common difference = 0.5 or 1/2

2, 5/2 = 5/2 - 2 = 0.5 or 1/2

3 - 5/2 = 1/2

7/2 - 3 = 1/2

an = a1 + (n - 1)d

a99 = 2 + (99-1) 1/2

a99= 2 + 98 (1/2)

a99 = 2 + 49

a99 = 51

The length of the shorter string is 18 inch while that of the longer string is 30 inch.

An equation is an expression used to show the relationship between two or more variables and numbers.

Let s represent the length of the shorter string.

One piece is 12 inches longer than the other

Length of longer string = s + 12

Since a 48-inch piece of string is cut into two pieces. Hence:

s + (s + 12) = 48

2s + 12 = 48

2s = 36

s = 18

Length of longer string = 18 + 12 = 30

The length of the shorter string is 18 inch while that of the longer string is 30 inch.

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Answer:

17

Step-by-step explanation:

-2 - 19 x -1

-2 + 19(because two negatives make a positive)

17

Answer:

17 is the answer.

Step-by-step explanation:

Given:

Let's substitute.

=> -2 - 19t

=> -2 - 19(-1)

=> -2 - (-19)

=> -2 + 19

=> 17

Therefore, 17 is the answer.

Hoped this helped.

Answer:

Step-by-step explanation:

Not near enough information to know.

I ASSUME that the pool is surrounded by a walkway of constant width (w = 2 ft, from comments)

The pool shape is important as well. No mention of  the shape

If the pool is circular and the walkway is 3 ft wide

the fence encloses a diameter of 110/π = 35 ft

so the diameter of the pool would be 35 - 2(3) = 29 ft.

POOL IS RECTANGULAR from comments

If the pool is square and the walkway is 2 ft wide, each side of the fence is

110 / 4 = 27.5 ft and the pool would be 27.5 - 2(2) = 23.5 ft on a side.

There are an infinite number of rectangular width and length dimensions and walkway dimensions which would result in a fence length of 110 ft.

Edit from comments

Still an infinite number of rectangular length an width dimensions for a pool with a 2 ft wide walkway around it.

Let's say that we are told the pool is 12 ft wide with 2 ft walkway.

Let L be the pool length

110 = 2(12 + 2(2)) + 2(L + 2(2))

110 = 32 + 2L + 8

70 = 2L

L = 35 ft

Answer:

zero point zero three six

Answer:

8 512 =8 X 8 X 8

Step-by-step explanation:

Answer:

maybe it's 12 but i don't know...

Answer:

True

Step-by-step explanation:

Eg. Republican party nominates a candidate to be considered by the people [hopefully voted] into office. If they win the election, they control a part of government in office.

Answer:

The median goes up 0.5

Step-by-step explanation:

Before the number 10.

Mean x¯¯¯ 10.111111111111

Median x˜ 7

Mode 2

Range 22

Minimum 2

Maximum 24

Count n 9

Sum 91

Quartiles Quartiles:

Q1 --> 3

Q2 --> 7

Q3 --> 19

Interquartile

Range IQR 16

Outliers none

After 10 is added.

Mean x¯¯¯ 10.1

Median x˜ 7.5

Mode 2

Range 22

Minimum 2

Maximum 24

Count n 10

Sum 101

Quartiles Quartiles:

Q1 --> 4

Q2 --> 7.5

Q3 --> 18

Interquartile

Range IQR 14

Outliers none

It goes up .5.

Answer:

12 students

Step-by-step explanation:

30×0.4=12.

The compound interest is applied to the remaining balance in the account

each subsequent year.

Reasons:

The given compound interest rate, r = 6.25% = 0.0625

The balance in the account after 2 years, A = $700

Required:

The required deposit, P, that gives the given account balance after 2 years.

Solution:

The following is the compound interest formula to use;

Where;

t = 2 years

We get;

[tex]\displaystyle P = \mathbf{ \frac{A}{(1 + r)^t}}[/tex]

Which gives;

[tex]\displaystyle P = \frac{700}{(1 + 0.0625)^2} \approx \mathbf{620.07}[/tex]

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Answer:

70⁰ + 30⁰ + x = 180 ( angle sum property (

100⁰ + x = 180

x = 80⁰

Answer:

7 = 7 * 10 = 70

Step-by-step explanation:

Answer:

• 1080

Step-by-step explanation:

How to Calculate Rounding to the Nearest Tens Whole Number?

If the ones digit (first number after decimal point) of the number is greater than or equal to 5 we add 1 to tens of number, If the ones digit of the number is less than 5 we change ones digit to 0.

Example:

[tex] \: [/tex]

Answer:

Do PRT: 5009.31

Step-by-step explanation:

Princable: 5000

Rate: 2.5

Time: 10

Answer:

Answer:

16

Step-by-step explanation:

x+y=30  solve for x   x=30-y

substitute x with 30-y and solve

11.25x+22.4y=515.9

11.25(30-y)+22.4y=515.9

337.5+11.15y=515.9

11.15y=178.4

y=16

since we're solving for just large candles it's 16

if need small cangle number 30-16=14

Answer:

check online for more information

Answer:

yes i love this app , this app so good

1. Value=206

2. Value=205

3. Value= 208

4. Value=207

Answer:

[tex]The \: fraction \: \frac{15}{4} \: is \: equivalent \: to \: 3 \frac{3}{4 } .[/tex]

This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denomintor (4). So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction [tex]3 \frac{3}{4} [/tex]

The fraction [tex] \frac{15}{4} [/tex]

is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.

The fraction 15/4 is equivalent to 3 3/4.

Here, we have,

To simplify the fraction 15/4, you need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (4) and divide both the numerator and denominator by the GCD.

The GCD of 15 and 4 is 1 since there are no common factors other than 1.

Dividing both the numerator and denominator by 1, we get:

(15 ÷ 1) / (4 ÷ 1) = 15/4

This fraction is a improper fraction once the absolute value of the top number or numerator (15) is greater than the absolute value of the bottom number or denominator (4).

So, the equivalent fraction is a mixed number which is made up of a whole number (3) and a proper fraction 3 3/4.

The fraction 15/4 is also equal to 15÷4 and can also be expressed as a decimal as 3.75 and expressed as a percentage as 375%.

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Answer:

It is 3 2/3 away from zero or 3.7 (3.66666666667) away from zero.

Step-by-step explanation:

It is 3 2/3 away from zero or 3.7 (3.66666666667) away from zero.

Answer:

A

Step-by-step explanation:

The square root of 50 is less than the square root of 78.

Answer:

1.  n=10

2. n=35

3. n=6

4. n=0 ? not sure for this one. two variables in the proportion

5. n=36

Step-by-step explanation:

set each set of proportion equal to each other and do cross multiplication

hope this helps !

how are you ?

Answer:

Step-by-step explanation:

Please take a look of the attached photo for the solution.