In an ordinary annuity, when does the interest on a yearly investment start building interest?

Answer:

3n^2

Step-by-step explanation:

3, 12, 27, 48, 75

List the differences between terms:-

9, 15, 21, 27

Now find the second differences:-

6, 6, 6

The sequence in the question is  quadratic and the first coefficient ( that of n^2) = 6/2  = 3.  The first term in the nth term formula is 3n^2.

Now we write out the original sequence and the  3n^2 values  as follows:-

3  12  27  48  75

3  12  27  48  75

They are the same so the formula for the nth term is 3n^2.

The nth term of the given sequence is 3n².

A sequence's series is the total number of terms in the sequence.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Given the series,

3,12,27,48,75

Since all terms are multiplied of 3

3 × 1 = 3

3 × 4 = 12

3 × 9 = 27

3 × 16 = 48

3 × 25 = 75

It is clear that it is forming a series by 3 and the product of the square root of a natural number.

So, it will be 3n².

Hence "The nth term of the given sequence is 3n²".

For more information about the series,

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Answer: .0459

Step-by-step explanation:

It takes 11 seconds to scan one person. So we have this ratio to start with

11 seconds: 1 person

Divide both sides by 11 to get this new ratio

1 second: 1/11 person

1 second: 0.0909 person

So in 1 second, 0.0909 of a person can be scanned. This statement seems silly because we can't have a fraction of a person, but it helps with the next part as shown below. The next step is to multiply both sides by 1800 to get....

1 second: 0.0909 person

1800*1 second: 1800*0.0909 person

1800 seconds: 163.62 persons

In a span of 1800 seconds (equivalent to 30 minutes), about 163 people's lunches can be scanned. Unfortunately, none of the answer choices are 163. The closest thing is 180, but that is an overestimate. So I would ask your teacher if there is a typo somewhere.

Note: if it took exactly 10 seconds for each student (instead of 11), then the answer would be 1800*(1/10) = 1800*0.10 = 180.

I'll do the first one to get you started.

Start at point A as that is the first letter of the sequence ABC. The second letter is B so we'll record the length of segment AB, which is 4 units long.

Note how we have a segment that is also 4 units long in the other triangle; however, we won't use that one just yet. Instead, we'll go for the 2 unit segment. As it turns out, every piece of the triangle on the right side is half that of the left side triangle.

Segment ED is 2 units long. So AB and ED pair up

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

BC is 8 units long; DF is 4 units long (half of BC). So BC and DF pair up

I started at A, went to B, then to C in that exact order marking the side lengths of 4 and 8 respectively. At the same time for the other triangle, I started at E, moved to D, then to F recording the side lengths 2 and 4

So A pairs up with E, B pairs with D, and C pairs with F

Therefore, triangle ABC is similar to triangle EDF. The order is very important so that the points line up and correspond in the proper manner.

I used the SSS (side side side) similarity theorem to prove the triangles similar. This theorem says that if the sides are in proportion to one another, then the triangles are similar.

Answer:

3 3/5 lbs

Step-by-step explanation:

We will multiply the pounds of berries by the faction she used to see how much she used for the pie

4 4/5 * 3/4 = amount used in pie

We need to convert the mixed number to an improper fraction

4 4/5 = (5*4+4)/5 = 24/5

24/5 * 3/4 =

I will change the order to make the math easier

24/4 * 3/5

6 * 3/5 =

18/5

Now we need to change it back to a mixed number

5 goes into 18   3 times with 3 left over

3 3/5 lbs

She used 3 3/5 lbs

Answer:

x = [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

The fraction [tex]\frac{4}{4}[/tex] is equal to 1, so putting this into the equation:

1x = [tex]\frac{4}{32}[/tex]

So x = [tex]\frac{4}{32}[/tex]

Or simplified down by dividing the fraction by 4:

x = [tex]\frac{1}{8}[/tex]

Answer:

1/8

Step-by-step explanation:

for this problem, you just have to think about how many times 4 goes into 32, so what times 4 equals 32? the answer is 8. so by simplifying the 4 and 32, you get 1/8

The ratio of Ella’s balloons to Taylor’s balloons is 5:7. Then the correct option is B.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Ella has 5 balloons. Taylor had 7 balloons.

Then the ratio of Ella’s balloons to Taylor’s balloons is given by the division of the numbers 5 and 7. Then we have

Ratio = 5 / 7

The ratio of Ella’s balloons to Taylor’s balloons is 5:7. Then the correct option is B.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

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The correct solution: 4x^2 -27x +167 - 996/(x+6)

Step-by-step explanation:

Answer:

0.124

Step-by-step explanation:

[tex]\frac{7.19}{58}[/tex]

To divide the numbers, we need to remove the decimal point

To remove decimal point , we multiply top and bottom by 100

[tex]\frac{719}{5800}[/tex]

Use long division. After using decimal point at the top we can include any number of zeros with 719

                            . 1 2 3 9

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

        5800         7190

                          5800

                     ------------------------(subtract)

                          13900

                          11600

                       ---------------------------(subtract)

                           2300 0

                           1740 0

                       --------------------------(subtract)

                            56000

                            52200

                       ---------------------------(subtract)

                             3800 0

Division goes on ............

Estimate the quotient to 3 decimal places

Quotient = 0.124

Answer:

30:75:60

Step-by-step explanation:

I'm not sure if this is how you're supposed to solve it, but I'll give it my best shot.

1. Think of the 2:5:4 as "chunks". 2 Chunks:5 Chunks:4 Chunks. 2+5+4 is 11. We obviously have to use all of the 165 perimeter units, and we know the ratio already.

2. We need to take 165, and divide it by 11. This will give us what one "chunk" is. It equals 15.

3. Now that we know what one chunk is equal to, we can simply multiply.

2 Chunks * 15 Per Chunk = 30

5*15=75

4*15=60

So, our final answer is 30:75:60

--

Checking, 30+75+60=165, so we used the whole perimeter.

The measure of sides of the triangle be 30, 75 and 60 unit.

Given,

the ratio of the measures three sides of triangles is 2:5:4.

The perimeter of triangle is 165 units.

Let the sides of triangle be 2x, 5x and 4x respectively.

We know that perimeter of triangle is sum of all sides, So

[tex]\rm P= 2x+5x+4x[/tex]

[tex]165=11x[/tex]

[tex]x=\dfrac{165}{11} \\\\[/tex]

[tex]x=15\\[/tex]

So the sides of triangle will be [tex]2\times15=30[/tex], [tex]5\times 15=75[/tex] and [tex]4\times15=60[/tex] units respectively.

Thus the sides of triangle are 30, 75 and 60 units.

For more details on perimeter of triangle follow the link:

https://brainly.com/question/24388271

The anwser is ten because the number i saw is 14 estimate is ten.

Answer:

x=1 , y=6

Step-by-step explanation:

7x+3y = 25

-2x-y = -8

Multiply the second equation by 3 so we can eliminate y

3(-2x-y )= -8*3

-6x -3y = -24

Add this equation to the first equation

-6x -3y = -24

7x+3y = 25

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

x = 1

But we still need to find y by substituting x =1

-2x -y = -8

-2(1) -y = -8

-2-y = -8

Add 2 to each side

-2+2 = -8+2

-y = -6

Multiply by  -1

y = 6

Answer:

d=-2

Step-by-step explanation:

We have

[tex]10(d+3)-(-9d-4)=d-5+3[/tex]

now we remove parenthesis and use distribution property

[tex]10d+30+9d+4=d-5+3[/tex]

now we combine like terms

[tex]10d+9d+30+4=d-2[/tex]

[tex]19d+34=d-2[/tex]

[tex]19d-d+34=-2[/tex]     (subtract d from both side )

[tex]18d=-2-34[/tex]  ( subtract 34 from both side )

[tex]18d=-36[/tex]

[tex]d=\frac{-36}{18}[/tex]    ( divide both side by 18)

[tex]d=-2[/tex]

Answer:

The answer is 8696

Step-by-step explanation:

This answer is obtained by multiplying the speed per second by 8

Answer:

8696 feet

Step-by-step explanation:

We are given that the sound travels at a speed of nearly 1087 feet per second when the temperature is 32 F. And we are supposed to find the distance the sound travels in 8 seconds.

We know the formula of the speed:

[tex]Speed = \frac{distance}{time}[/tex]

Putting in the values to find the distance:

[tex]1087=\frac{distance}{8}[/tex]

[tex]distance = 1087*8\\\\distance=8696[/tex]

Therefore, the speed travels for 8696 feet in 8 seconds.

The slope-intercept form:

y = mx + b

m - slope

b - y-intercept

The parallel lines have the same slope.

We have y = -3x + 7 → m = -3. Therefore y = -3x + b.

Put the coordinates of the point (2, -4) to the equation of a line:

[tex]-4=-3(2)+b[/tex]

[tex]-4=-6+b[/tex]            add 6 to both sides

[tex]2=b\to b=2[/tex]

Answer

the answer is P=7.8

Step-by-step explanation:

P=14.7e           -0.21x

X=14.7e      (-0.63)

take the natrual log of both sides

1n(P)=1n(14.7e(-.63)

1n(P)=1n(14.7)-.63

(because ln(e^a) = a)

1n(P)=2.688 - .63

1n(P)=2.058

P=e       2.058

P=7.8

Final answer:

To find the average atmospheric pressure at an altitude of 2.3 miles, substitute x = 2.3 into the given formula and solve, resulting in approximately 9.1 pounds per square inch.

Explanation:

The average atmospheric pressure for an altitude of 2.3 miles can be found by substituting x = 2.3 into the given formula: [tex]p = 14.7e^{-0.21x[/tex]

Substitute x = 2.3 into the formula:

p = [tex]14.7e^{-0.21(2.3)[/tex]

p ≈ [tex]14.7e^{-0.483[/tex]

p ≈ 14.7⁩ × 0.617 ≈ 9.1 pounds per square inch (rounded to the nearest tenth)

Answer:

SSS

Step-by-step explanation:

For the triangle to be considered similar, 2 sides and an angle must be similar or two angles and a side or three  angle or the three sides are similar.

For the case above the three are similar and this makes triangle ABC similar to DEF.  

Answer:

Third option SSS is the correct answer.

Step-by-step explanation:

It is given the BC/EF = 1/2  

Consider Two triangle ABC and DEF

To find the ratio of sides

From the given data, we get

AC/DF = 3/6 = 1/2 and AB/DE = 12/24 =1/2

The ratio of sides are equal  then the triangles are similar.

Based on the given data we can conclude that triangle ABC and  DEF are similar.

Answer:

one solution, i.e x = 1 and y = -2

Step-by-step explanation:

Given two equations :

x+3y = -5   -------(1)

4x - y =6   ---------(2)

Using elimination method,

Multiply equation (2) by 3 and add it to equation (1)

We get,

x + 3y + {(4x - y)×3} = -5 +(6×3)

x + 12x + 3y - 3y = -5 + 18

13x = 13

x = 13/13  = 1

And corresponding y will be:

x + 3y = -5   , Plug x =1  to get y

1 + 3y = -5

3y = -5 - 1

y = -6/3 = -2

Hence we got only one solution, i.e x =1 and y = -2

Answer:

6 apples

Step-by-step explanation:

20 - 5 = 15

15 + 2 = 17

17 - 7 = 10

10 - (2 x 2) = 6

Your answer is 6 apples

Yum yum!!

Answer:

A = -1.5

Step-by-step explanation:

Ax+3y=48

Plug in  (-18,7)

A(-18) +3(7)=48

-18A + 21 = 48

-18A = 27

A = - 27/18

A = - 3/2

A = -1.5

[tex]Domain:\ x\neq-2\\\\\dfrac{x+2}{x-4}<0\iff(x+2)(x-4) < 0\\\\x+2=0\to x=-2\\x-4=0\to x=4\\\\(x+2)(x-4)=x^2-4x+2x-8\\\\\text{parabola op}\text{en up}\\\\\text{Look at the picture}\\\\Answer:\ \dfrac{x+2}{x-4}<0\ for\ x\in(-2,\ 4)\to\boxed{B)\ -2 < x < 4}[/tex]

Other method:

[tex]\dfrac{x+2}{x-4}<0[/tex]

zeros of numerator and denominator are x = -2 and x = 4.

Look at the second picture.

for x < -2 → x + 2 < 0 and x - 4 < 0

therefore [tex]\dfrac{x + 2}{x - 4}=\dfrac{(-)}{(-)}>0[/tex]

for -2 < x < 4 → x + 2 > 0 and x - 4 < 0

therefore [tex]\dfrac{x+2}{x-4}=\dfrac{(+)}{(-)} < 0[/tex]

for x > 4 → x + 2 > 0 and x - 4 > 0

therefore [tex]\dfrac{x+2}{x-4}=\dfrac{(+)}{(+)} > 0[/tex]

Answer:

-2 < x < 4

Step-by-step explanation:

Lisa has 5 limes left on her tree after harvesting half. So, the correct answer is option 5) 5.

Let's break down the problem step by step:

1. Katie's orange tree has 30 oranges.

2. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes.

3. Let's denote the number of limes Lisa originally had as  x .

4. After Lisa harvested half of her limes, she was left with [tex]\( \frac{x}{2} \)[/tex] limes.

5. Since Katie's tree has three times as many fruits as Lisa's tree originally had, the total number of fruits on Katie's tree is  3x .

6. The problem states that Katie's tree has 30 oranges, so  3x = 30 .

7. Solving for  x , we find [tex]\( x = \frac{30}{3} = 10 \).[/tex]

So, Lisa originally had 10 limes on her tree. After harvesting half of them, Lisa is left with [tex]\( \frac{10}{2} = 5 \)[/tex] limes.

Therefore, the correct answer is option 5) 5.

The Correct question is:

Katie's orange tree has 30 oranges. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her limes on the tree. How many limes does Lisa have on her tree now?

1)10

2)45

3)90

4)15

5)5

Lisa initially had 10 limes on her tree. After harvesting half, she has 5 limes remaining. Therefore, Lisa now has five limes on her tree.

To find out how many limes Lisa has on her tree now, we need to break down the problem step-by-step:  

Katie's tree has three times as many fruits as Lisa's:  30 = 3x

Solving for x:  x = 10  

So, Lisa originally had 10 limes on her tree.

Next, we calculate how many limes Lisa has after harvesting half:

Therefore, Lisa has five limes on her tree now.

Answer:

C. (5,0)

Step-by-step explanation:

you can check the graph at the point where those two lines meet

or

solve the simultaneous equation

you will solve for x=5 and y=0 if you use elimination/substitution

Answer:

(5,0)

Step-by-step explanation:

we have two equations with two unknown variables

equation 1 :    3x -2y =15

equation 2:    4x  -  y =20

we can multiply the equation 2  for  two in order to add the equations and  eliminate a term

(-2)*(equation 2)= -2(4 x- y) =-2*20

-8x +2y=-40     equation 3

now, let´s add the equation 3 to equation 1

-8x +2y = -40

3x  -2y =  15

___________

-5x  +0     =-25

[tex]x=\frac{-25}{-5} \\x=5[/tex]

and leaving y from equation 2

4 x - y =20

4x -20 =y

y=4(5)-20

y=20-20=0

y = 0

the only coordinate that satisfies the equation is  (5,0)

have a great day

36 is 12.5% of 288

I hope this helps!

Answer:

Step-by-step explanation:

4x=2z+5/y

X= 1/4(2z+5/y)

Answer:

see explanation

Step-by-step explanation:

(a)

Since lines AB and CD are parallel then their slopes are equal

y = - [tex]\frac{1}{2}[/tex] x + 14 is in slope- intercept form ( y = mx + c )

with slope m = - [tex]\frac{1}{2}[/tex]

Hence slope of CD = - [tex]\frac{1}{2}[/tex]

D is the point (0, 7) ⇒ c = 7

y = - [tex]\frac{1}{2}[/tex] x + 7 ← equation of CD

(b)

to find the x- intercept let y = 0, in the equation and solve for x

- [tex]\frac{1}{2}[/tex] x + 7 = 0 ( multiply through by 2 )

- x + 14 = 0 ⇒ - x = - 14 ⇒ x = 14 ← x- intercept of CD