If 24 pencils cost $1.20 then how much does one pencil cost?

Answer:

4/10

Step-by-step expla

Answer:

To find the first four terms of the series, we can substitute the values of n from 1 to 4 in the given formula and simplify:

n=1: -4(2/3)^0 = -4(1) = -4

n=2: -4(2/3)^1 = -4(2/3) = -8/3

n=3: -4(2/3)^2 = -4(4/9) = -16/9

n=4: -4(2/3)^3 = -4(8/27) = -32/27

So the first four terms of the series are -4, -8/3, -16/9, -32/27.

To determine if the series converges or diverges, we need to find the common ratio r, which is the ratio of any term to its preceding term:

r = (-4(2/3)^n) / (-4(2/3)^(n-1)) = 2/3

Since the absolute value of the common ratio is less than 1, the series converges.

To find the sum of the series, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where a is the first term and r is the common ratio. Substituting the values we found:

S = -4 / (1 - 2/3) = -4 / (1/3) = -12

So the sum of the infinite geometric series is -12.

Answer:

a)  The first four terms of the series are:

    -4, -8/3, -16/9, -32/27

b)  The series converges.

c)  The sum of the infinite geometric series is -12.

Step-by-step explanation:

Given infinite geometric series:

\(\displaystyle \sum^{\infty}_{n=1} -4 \left(\dfrac{2}{3}\right)^{n-1}\)

Therefore, the formula for the nth term of the sequence is:

\(a_n=-4 \left(\dfrac{2}{3}\right)^{n-1}\)

where:

Calculate the first four terms of the series by substituting the n-values 1 through 4 into the nth term formula.

\(a_1 = -4 \left(\dfrac{2}{3}\right)^{1-1} = -4 \left(\dfrac{2}{3}\right)^{0}=-4\)

\(a_2 = -4 \left(\dfrac{2}{3}\right)^{2-1}= -4 \left(\dfrac{2}{3}\right)^{1}=-\dfrac{8}{3}\)

\(a_3 = -4 \left(\dfrac{2}{3}\right)^{3-1}= -4 \left(\dfrac{2}{3}\right)^{2}=-4 \left(\dfrac{4}{9}\right)=-\dfrac{16}{9}\)

\(a_4 = -4 \left(\dfrac{2}{3}\right)^{4-1}= -4 \left(\dfrac{2}{3}\right)^{3}= -4 \left(\dfrac{8}{27}\right)=-\dfrac{32}{27}\)

A geometric series converges if the absolute value of its common ratio is less than 1. As r = 2/3 and |2/3| < 1, the series converges.

Use the infinite geometric series sum formula to find sum of the infinite series.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\;\;for\;$|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}\)

Substitute a = -4 and r = 2/3 into the formula to find the sum of the infinite series:

\(\begin{aligned}\implies S_{\infty}&=\dfrac{-4}{1-\frac{2}{3}}\\\\ &=\dfrac{-4}{\frac{1}{3}}\\\\&=-4 \cdot \dfrac{3}{1}\\\\&=-\dfrac{12}{1}\\\\&=-12\end{aligned}\)

Therefore, the sum of the given infinite geometric series is -12.

Answer:

t=1

Step-by-step explanation:

Answer:

t=1

Step-by-step explanation:

Answer:

(3/2 m)^2 -(5n)^2^

Step-by-step explanation:

Answer: 9m^2 / 4  -  25n^2

Step-by-step explanation:

Use the identity: (a-b)(a+b)=a^2 - b^2
substitute values of a and b, where a=3/2m and b=5n.
The following simplifies to (3/2m)^2 - (5n)^2.

Answer: True

Step-by-step explanation:

Plug 4 in for m

Left side is 7 less than the right side 20 which means that the given statement is true

Answer:

Step-by-step explanation:

B, Mrs web

Answer:

B)  60%

Step-by-step explanation:

Percentage formula

\(\sf Percentage=\left(\dfrac{Value}{Total\:value}\right) \times 100\)

To find what percent of 200 is 120, substitute the values into the percentage formula:

\(\begin{aligned}\implies \sf Percentage & = \dfrac{120}{200} \times 100\\\\&=\dfrac{120 \times 100}{200}\\\\&=\dfrac{12000}{200}\\\\&=\dfrac{120}{2}\\\\&=60\%\end{aligned}\)

Therefore, 120 is 60% of 200.

Answer:

Step-by-step explanation:

Answer:

Explanation:

Answer:

Explanation:

Answer:

Explanation:

Answer:

Explanation:

Answer: YOUR MOM

Step-by-step explanation:

Answer:

Step-by-step explanation:

18 quarts

Answer:

A

Step-by-step explanation:

We can solve for H by isolating it on one side of the equation, as follows:

J/H - I/H = G

Taking H as the common denominator:

(J - I)/H = G

Multiplying both sides by H:

J - I = GH

Adding I to both sides:

J = GH + I

Dividing both sides by G:

H = (J - I)/G

So the answer is

(A)

H = (J - I)/G.

Answer:   A

Step-by-step explanation:

\(\frac{J}{H} = G + \frac{I}{H}\)                >Since you are solving for H bring I/H to the other side

                                   by subtracting I/H from both sides

\(\frac{J}{H}- \frac{I}{H} = G\)               >There is a common denominator so you can

                                   combine the fractions

\(\frac{J-I}{H} = G\)                   >Multiply both sides by H or cross multiply whichever

                                  way your mind things about how to get H on top

\(J-I = G(H)\)           >Divide both sides by G

\(\frac{J-I}{G} = H\)                   >Answer is A

Answer:

The constant of proportionality is divide by 3

Example equation:

9 ÷ 3 = 3

Y = 3

Answer:

Step-by-step explanation:

The equation of a proportional relationship is ...

  y = kx

where k is the constant of proportionality. Solving for k, we find ...

  k = y/x

It is convenient to calculate this using the smallest whole-number values of x and y that the table provides:

  k = 1/3 . . . . the constant of proportionality

Then the equation is ...

  y = (1/3)x

Answer: the answer would be D

Step-by-step explanation:

and hope this helps tell me if you get it right an don't mind to BRAINLIESTTT

Answer:

24 root 6

Step-by-step explanation:

To calculate the percent increase in annual usage of cell phones, we can use the following formula:

Percent increase = [(new value - original value) / original value] x 100

where the new value is the current year’s usage and the original value is last year’s usage.

In this case, Nick found that residents used their cell phones for 217,470 minutes last year and 434,940 minutes this year. So we can plug these values into the formula:

Percent increase = [(434940 - 217470) / 217470] x 100

Percent increase = 100%

Therefore, there was a 100% increase in annual usage of cell phones.

I hope that helps! Let me know if you have any other questions.

Answer:

6670 divided by 2=3335 SOOOO the answer is  :3335

Step-by-step explanation:

If they used 50 percent of their phone time, they're using half of it. Therefore, 1/2 of 6670 is 3335.   YW

Answer:

We can start by using the formula:

time = distance / speed

Let t be the time (in hours) for Tom and Katherine to meet.

Tom's distance = Tom's speed x time = 14t

Katherine's distance = Katherine's speed x time = 10t

Since they are riding towards each other, the total distance they cover is the sum of their distances:

Tom's distance + Katherine's distance = 42 miles

14t + 10t = 42

Simplifying:

24t = 42

t = 42 / 24

t = 1.75 hours

Therefore, Tom and Katherine will meet after 1.75 hours of riding.

Answer:The last one

Step-by-step explanation:

Answer:

i think its A .

Step-by-step explanation:

Answer:-5 it is point slope form and it is asking for m which is -5

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

Step-by-step explanation:

Here you just have to assume values for x and plug them to find f(x).

4) f(x) = 6x - 4

   we will assume for each equation 4 values of x: -1, 0, 1, and 2.

x = -1 --> f(-1) = 6(-1) - 4 = -10

x = 0 --> f(0) = 6(0) - 4 = -4

x = 0 --> f(1) = 6(1) - 4 = 2

x = 0 --> f(2) = 6(2) - 4 = 8

5) f(x) = 5 - 2x

   Again, we will assume for each equation 4 values of x: -1, 0, 1, and 2.

x = -1 --> f(-1) = 5 - 2(-1) = 7

x = 0 --> f(0) = 5 - 2(0) = 5

x = 0 --> f(1) = 5 - 2(1) = 3

x = 0 --> f(2) = 5 - 2(2) = 1

6) f(x) = 7 + 3x

    Again, we will assume for each equation 4 values of x: -1, 0, 1, and 2.

x = -1 --> f(-1) = 7 + 3(-1)  = 4

x = 0 --> f(0) = 7 + 3(0) = 7

x = 0 --> f(1) = 7 + 3(1) = 10

x = 0 --> f(2) = 7 + 3(2) = 13

Answer:

get better at work and pay attentionn you'll know!!!!!!!!!!!!!!

Step-by-step explanation:

p=29°

56°+q=180° <linear pair>

q=180°-56°

q=124°

Again

124°+27°+q=180° <sum of angles In a triangle>

p=180°-151°

p=29°

Answer:

Step-by-step explanation:

29 it wouldn't let me tell you why so here we are.

Answer:

D is the right choice and no you cannot fit the pizza inside the box.

Step-by-step explanation:

D is the answer because to turn 2/3 into a decimal you would divide 2 by 3 and the answer you would get would be 0.66666666666...You would then add 12 to the answer and get 12.6666... Once you get this answer you would round it to the hundredths to get 12.67 but since that is not an option you could use D, 12.66 inches.

Answer:

I believe the answer is D.

Step-by-step explanation:

GOOGLE

Answer:

402.12 + 804.24 = 1206.36

Answer:

?

Step-by-step explanation:

Answer:

1 3/4, 1 1/2, 5/6, 1/4

with a common denominator, it looks like this

21/12 = 1 3/4, 18/12 = 1 1/2  10/12 = 5/6   3/12 = 1/4

The order of the fraction from largest number to smallest number is 1 3/4, 1 1/2, 5/6, and 1/4.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data given in the question,

1 1/2 = 3/2 = 1.5

1/4 = 0.25

1 3/4 = 7/4 = 1.75

5/6 = 0.83

So, the order from largest to smallest number is:

1 3/4, 1 1/2, 5/6, and 1/4.

Now, with a common denominator it will be:

21/12 = 1 3/4, 18/12 = 1 1/2 10/12 = 5/6   3/12 = 1/4

To know more about arithmetic operations:

https://brainly.com/question/25277954

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