Generate the next three terms of each geometric sequence
below.
f(n) = f(n-1).-2 and f(1) = 5

Answer:

(a) The population in the year 2033 is 18630.

(b) After nearly 36years from the starting population of 11500 we will get our population tripled.

Step-by-step explanation:

In 2017, the population of a city is 11500, and is increasing exponentially at a rate of 3.1% per year

This can be formulated with the compound interest formula, also we can think the given situation as we have 11500 rupees which increases at the rate of 3.1% per year.

we can formulate the given situation using the compound interest formula.

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

A is the final population

P is the initial population = 11500

r is the rate at which the population increases = 3.1A =% = 0.031

n denotes the number of times the population increases per year = 1

t is the time or year = 1

A = [tex]11500( 1 + 0.031)[/tex]^1*t

(a) The number of years to reach the year 2033 from 2017 is 16years.

so we have the value of t = 16

 so the final population in the year 2033 will be

A = 11500(1+0.031)^1*16

   = 11500(1.031)^16

   = 11500*1.63

A = 18630

Therefore the population size in the year 2033 will be 18630.

(b) We need to find the year in which the population gets tripled. we will triple our population from the population which was in 2017

 so the our equation will be

 11500*3 = 11500(1+0.031)^1*t

  3 = (1.031)^t

upon taking logarithm both sides we get

log(3) = t*log(1.031)    ( using the property log(a^b) = blog(a)

0.477 = t*0.133

t = 0.477/0.0133

t = 35.86years

upon taking approximation we will get 36 years.

Therefore after nearly 36years from the starting population of 11500 we will get our population tripled.

Answer:

Alice started with $196.54 in her account.

Step-by-step explanation:

161.23 + 35.31 = 196.54

Step-by-step explanation:

P(x)

= (x - 2)Q¹(x) + 5

= (x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5.

Since x³ - 8 = (x - 2)(x² + 2x + 4),

(x - 2)[(x² + 2x + 4)Q²(x) + 2x - 3] + 5

= (x - 2)(x² + 2x + 4)Q²(x) + (x - 2)(2x - 3) + 5

= (x³ - 8)Q²(x) + (2x² - 7x + 11).

Hence when P(x) is divided by (x³ - 8),

the remainder is 2x² - 7x + 11.

Answer:

(-2 , 2)

Step-by-step explanation:

y=x+4

y=-2x-2

x+4=-2x-2

3x=-6

x=-2

y=2

graph attached

[tex]\large\boxed{\boxed{\pink{\bf \leadsto (-2,2) \ is \ the \ solution \ of \ the \ given \ linear \ equations .}}}[/tex]

Given to equations to us are ,

[tex]\qquad \red{\bullet} \: y = x + 4 \\\\\qquad \red{\bullet} \: y = -2x - 2 [/tex]

And we need to find the solution using graphical method.

So , after plotting the graph of both equations the point where both lines intersect will be the solution of the graph.

And , for plotting we need at least two points .

For equation (1) :-

[tex]\implies y = x + 4 [/tex]

When x = (-4) .

[tex]\implies y = -4+4\\\\\bf\implies y = 0 [/tex]

When x = (-3)

[tex]\implies y = -3+4\\\\\bf\implies y = -1 [/tex]

[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-4) & (-3) \\\cline{1-3} \bf y & 0 & 1 \\\cline{1-3}\end{tabular}}[/tex]

For equation 2 :-

[tex]\implies y = -2x - 2 [/tex]

When x = (-1) .

[tex]\implies y = -2(-1)-2\\\\\bf\implies y = 0 [/tex]

When x = (0)

[tex]\implies y = 0-2\\\\\bf\implies y = -2 [/tex]

[tex]\large\boxed{\begin{tabular}{|c|c|c|} \cline{1-3} \bf x & (-1) & 0 \\\cline{1-3} \bf y & 0 & -2 \\\cline{1-3}\end{tabular}}[/tex]

Now , let's plot their graphs. Graph is in attachment. Hence on plotting the graph we see that both the lines Intersect on (-2,2) . Hence x = -2 and y = 2 is the solution of the given linear equation.

Answer:

a and d

Step-by-step explanation:

Answer:

I think it might be y= x+2

Step-by-step explanation: because it is going up times 2 every time

OWO

Answer:

Answers 3 ((3x4)x2) and 6 (3x(4x2)) are equal to eachother.

Step-by-step explanation:

1. 3(4+2)=18

2. 3+(4x2)=11

3. (3x4)x2=24

4. (3x4)+2=14

5. (3+4)+2=9

6. 3x(4x2)=24

3. and 6. are the only two answers that have the same outcome, therefore equaling eachother.

Answer:

-4

Step-by-step explanation:

Answer:

Different Amount

Step-by-step explanation:

4 is more than 2 and there would need to be 2 sandwiches in family a in order for them to be equal

hi can you send me the formula...let me teach you

Answer:

Step-by-step explanation:

ABCD is a square.

BD and AC are diagonals and they have equal length.

We have AC = 7x + 18 and BD = 10x - 3

Since AC = BD, we substitute their values and solve for x:

Then find the length of BD:

Correct option is B.  BD = 67

Answer:

a=9

Step-by-step explanation:

2/3 (a-18)=-6

a−18=−6×( 3/2)

a−18=−6×3/2

a−18= −18/2

a−18=−9

a=−9+18  

a=9

​

Answer:

A=9

Step-by-step explanation:

Simplify both sides of the equation.

2/3(a−18)=−6

(2/3)(a)+(2/3)(−18)=−6(Distribute)

2/3a+-12=-6

2/3a-12=-6

Add 12 to both sides.

2/3a−12+12=−6+12

2/3a=6

Multiply both sides by 3/2

(3/2)* (2/3a)= (3/2)* (6)

A=9

Answer:

The missing value y=12.5 and we have (5,12.5)

Step-by-step explanation:

The formula used for direct variation is:

[tex]y\: \alpha \:x\\y=kx[/tex]

We need to find missing value (2,5)(5,y)

First we will find k, and then y

We have x=2, y=5

Find k:

[tex]y=kx\\5=k(2)\\k=\frac{5}{2}\\k=2.5[/tex]

Now, we cam find missing value in (5,y)

We have x=5, k=2.5 and y=?

[tex]y=kx\\y=2.5(5)\\y=12.5[/tex]

So, the missing value y=12.5 and we have (5,12.5)

Answer:

54 groups of 1, 27 groups of 2, 18 groups of 3, 9 groups of 6, and repeat vice versa (6 groups of 9, etc).

Step-by-step explanation:

Total number of ways are 8 to arrange the balloon,

Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,

Given that,

Total number of balloon Sabrina has = 54,

The number of ways Sabrina can arrange the balloon are:

1 group of 54 balloons,

2 groups of 27 balloons,

3 groups of 18 balloons,

6 groups of 9 balloons,

9 groups of 6 balloons,

18 groups of 3 balloons,

27 groups of 2 balloons,

54 groups of 1 balloon,

There are total 8 different ways Sabrina can arrange the balloons.

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Answer:

[0.184, 0.266]

Step-by-step explanation:

Given:

Number of survey n =280

Number of veterans = 63

Confidence interval = 90%

Computation:

Probability of veterans = 63/280

Probability of veterans =0.225

a=0.1

Z(0.05) = 1.645 (from distribution table)

Confidence interval = 90%

So,

p ± Z*√[p(1-p)/n]

0.225 ± 1.645√(0.225(1-0.225)/280)

[0.184, 0.266]

Answer:

C. y = -5/2x +8

Step-by-step explanation:

To solve first find the slope using the slope formula which is m=[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. To find the slope simply plug in the points, [tex]\frac{-2-3}{4-2}[/tex] which equals -5/2. Next, put the equation into slope-point form, which is [tex]y-y_{1} = m(x-x_{1})[/tex]. I will use the point (2,3). y-3=-5/2(x-2), then solve for y which equals y=-5/2+8.

Answer:

5 is the correct answer.............

Answer:

90

Step-by-step explanation:

Any two lines coming from the two edges of a diameter when they meet it gives 90

Answer:

45%

Step-by-step explanation:

90/200 = 0.45

0.45 = 45%

noob

Answer:

Try finding some place with cheap screen fixing prices. If you can't, ask a friend if they know how to do this type of stuff.

Step-by-step explanation:

Answer:

B. the slope is 1/4

the y-intercept is (0,3)

Step-by-step explanation:

(-8,1)(0,3)

rise/run

Answer:

2.25

Step-by-step explanation:

i think though

Each colored marker costs $1.75.

The amount of one quantity in another single quantity is termed as the unit rate of that quantity.

For example, speed is a unit rate in terms of distance and speed.

Number of colored markers Jason bought = 8

Cash that Jason gives the cashier = $15

Cash that cashier gives back = $1

Price of 8 colored markers = 15 - 1

                                             = $14

We have to find the unit rate of the colored marker, that is the price of one colored marker.

Let x be the cost of the one colored marker.

Using proportion,

8 : 14 = 1 : x

8/14 = 1/x

Doing cross multiplication,

8x = 14

x = 14/8

x = 1.75

Hence the unit rate of the colored marker or the cost of one colored marker is $1.75.

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Answer:

undefined

Step-by-step explanation:

when x has the same number is undefined

but when y has the same is zero

Answer:

Haven't found the answer but in the comments above me someone said it was D and it was def not D so try anything other than that, I just took the test on Edg2020

Step-by-step explanation:

Answer:

solution

-V=17-2

-V=15

Answer:

y = -1.25x + 3

Step-by-step explanation:

To see if the coordinate pairs are on this line, plug x into the equation above.

y = -5 + 3

y = -2, so (4, -2) is on that line.

y = -1.25(8) + 3

y = -10 + 3

y = -7, so (8, -7) is also on that line.

Answer:

y = -1.25x + 3

Step-by-step explanation:

i got it right

Answer:

second option

Step-by-step explanation:

Answer:

we know that the probability of drawing black card is 26/52. Probability of drawing a king is 4/52

Step-by-step explanation:

Answer:

x = -6

y = 2

Step-by-step explanation:

1. Approach

x - 3y = -12

4x + 6y = -12

In this problem, it would likely be easier to use elimination, but since the problem specifically says that one must use substitution, substitution will be used. Substitution is when one solves one of the equations for a variable, similar to solving a literal equation. The one will substitute in the value of the variable into the other equation and solve for the other varibale. Then one will finally back substitute in that value of the other variable to find the value of the first variable, hence solving the equation.

2. Solve equation 1

x - 3y = -12

Solve the literal equation with inverse operations;

x - 3y = -12

   +3y    + 3y

x = 3y - 12

3. Substitute the answer into the second equation

4x + 6y = -12

x = 3y - 12

4 ( 3y - 12 ) + 6y = -12

Distribute;

12y - 48 + 6y = -12

Simplify;

12y - 48 + 6y = -12

18y - 48 = -12

Inverse operations;

18y - 48 = -12

     +48     +48

18y = 36

/18   /18

y = 2

4. Backsolve for x

Substitute the value for y back into the equation for x and solve

x = 3y - 12

y = 2

x = 3(2) - 12

x = 6 - 12

x = -6