Tamika opened a money market account that has a 4.25% annual interest rate, compounded annually. She deposits $1,750 into the account each year. How much interest will the account earn after 15 years?

$9,449.40
$33,949.40
$35,699.40
$71,398.40

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".

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[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:

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

Step-by-step explanation:

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.

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Answer:

22.5

Step-by-step explanation:

To find the rate of speed per hour, you need to divide the kilometer (90) by the hours (4).

90/4=

22.5

The submarine's rate of speed is found by dividing the distance traveled (90 kilometers) by the travel time (4 hours), resulting in a rate of 22.5 kilometers per hour.

You need to use the formula for speed which is speed = distance ÷ time. In this case, the submarine travels 90 kilometers in 4 hours.

To calculate the rate of speed, divide the distance by the time:

Speed = 90 kilometers ÷ 4 hours = 22.5 kilometers per hour.

This means the submarine's rate of speed is 22.5 kilometers per hour.

Answer:

y = 7/2x+5

Step-by-step explanation:

To find the slope we need two points

(-2,-2) and (0,5)

We can find the slope from the formula

m = (y2-y1)/(x2-x1)

m = (5--2)/(0--2)

m = (5+2)/(0+2)

m = 7/2

The slope is 7/2

The y intercept, or where it crosses the y axis, is 5

Using the slope intercept formula for a line

y= mx+b

y = 7/2x+5

36 is 12.5% of 288

I hope this helps!

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:

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:

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

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.

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:

37.5 minutes

Step-by-step explanation:

48/12 = 4 (for every 1 minute, 4 minutes of movie is downloaded.

change 2.5 hours to minutes = 60+60+30 = 150 minutes

150/4 = 37.5 minutes to download the 2.5 hour movie

Answer: .0459

Step-by-step explanation:

Answer:

He should be using distributive property

Sorry if im wrong

Step-by-step explanation:

Answer:

Michael used distributive property

Step-by-step explanation: I got it correct on my test and I'm also in K12

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

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

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.

Answer:

i think c.

Step-by-step explanation:

The numbers are equal (choice A)

This is because 100% of something is that entire thing, not changed at all. It is not added to, or subtracted from. Example: 100% of 78 is 78. If you had 78 people in a room, and selected 100% of them, then you selected all 78 people.

Answer:

D

Step-by-step explanation:

[tex]\frac{7}{3}[/tex] is 7 ÷ 3

Answer:

D. 7 divided by 3

Step-by-step explanation:

A.7 divided by 1/3  

7 ÷ 1/3  Copy dot flip   7 * 3/1 = 21   No

B. 3 divided by 7

3 ÷7 = 3/7   No

C.1/7 of3

1/7 * 3  = 3/7    No

D. 7 divided by 3

7÷ 3 = 7/3   Yes

To determine the number of each type of ticket sold, a system of linear equations is set up and solved using the substitution method. The answer is 600 covered pavilion seats and 800 lawn seats were sold.

To solve this problem, we can set up a system of linear equations based on the given information. Let x be the number of covered pavilion seats sold and y the number of lawn seats sold. We have two equations:

Now we can solve this system of equations using either substitution or elimination method. For simplicity, let's use the substitution method:

From equation 1, we can express x as:

x = 1400 - y

Now substitute x in equation 2:

20(1400 - y) + 15y = 24000

Simplify and solve for y:

28000 - 20y + 15y = 24000

-5y = -4000

y = 800

Since we know y, we can find x by substituting the value of y in x = 1400 - y:

x = 1400 - 800

x = 600

So, the number of covered pavilion seats sold was 600 and the number of lawn seats sold was 800.

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

Answer:

3

Step-by-step explanation:

to do this you need to figure out 5 percent of 60

in order to do this you need to find 95 percent of 60 and subtract it from 60

.95x60=57

60-57=3

they sold 3 discount tickets

3/60=5%

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:

If I am correct It is Commutative  Property

Hope That Helps!

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:

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.

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