29 years ago, James put some money into a savings account with 8% interest compounded quarterly (4 times a year). He just remembered it and saw that there was now $7328 in it. Find the original amount he invested.

Step-by-step explanation:

sorry for my bad handwriting, hope it helps

[tex]a_2 = ar^{2-1} =ar = 6~~ ...(i)\\\\a_4 = ar^{4-1} = ar^3 = 2186 ~~....(ii)\\\\\\(ii)\div (i):\\\\\dfrac{ar^3}{ar} = \dfrac{2186}6\\\\\implies r^2 = \dfrac{2186}6 = \dfrac{1093}3\\\\\implies r = \pm \sqrt{\dfrac{1093}3}\\\\a= \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}}\\\\\text{nth term} = ar^{n-1} = \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( \pm{ \sqrt{\dfrac{1093}3} \right)^{n-1} = \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( { \sqrt{\dfrac{1093}3} \right)^{n-1} \\\\\\[/tex]

[tex]= 6\left(\dfrac{1093}3 \right)^{\tfrac{n-2}2}[/tex]

Answer:

Step-by-step explanation:

Given:

Equation of nth term of GP:

Substitute for 2nd and 4th terms:

Substitute the value of a₂ into a₄ and find the value of r:

Find the first term:

The equation of nth term is:

Divide everything by half

Since she doubled the recipes, divide all by half.

1 cup of sugar / 2 = 1/2 cup of sugar

3 1/2 cups of flour / 2 = 7/2/2 cups of flour = 7/4 cups of flour or 1 3/4 cups of flour.

Answer:

Sugar: 1/2  Flour: 1 3/4

Step-by-step explanation:

1 cup of sugar

3 1/2 cups of flour

Since the recipe is doubled you'll divide the ingredients by 2.

Sugar: 1÷2=1/2

Flour: 3 1/2÷2=7/4

=1 3/4

Hope this helps :)

Answer:

it is 1.5

Step-by-step explanation:

if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5

Answer:

At present he has x stamps

Every month he adds 6 numbers, for 8 months

So total added 8x6=48

The total will be x+48 which is expected to be twice of x

x+48=2x

Solving x=48

At present he has 48 stamps

Step-by-step explanation:

Answer:

356

Step-by-step explanation:

53 + 36 = 89

89 x 4 = 356

and where is the bar diagram????

Answer:

104 bracelets

Step-by-step explanation:

182 ÷ 1.75 = 104

Answer:

1/20

Step-by-step explanation:

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 8 by 4, and get 32.

Then we multiply 3 by 10, and get 30.

Next we give both terms new denominators -- 10 × 4 = 40.

So now our fractions look like this:

32/40−30/40

Step 2

Since our denominators match, we can subtract the numerators.

32 − 30 = 2

So the answer is:2/40

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

2/40÷ 2 =1/20

Let's try dividing by 2 again...

No good. 2 is larger than 1. So we're done reducing.

There you have it! The final answer is:

1/20

Answer:

It is congruent to M

Step-by-step explanation:

[tex]\boxed{\sf E=Pt}[/tex]

E is energy

P is power

t is time in hours

Cost

Answer:

$0.12

Step-by-step explanation:

Conversions

  1000 watts = 1 kilowatt-hour
  ⇒ 1200 watts = 1.2 kilowatt-hour

  60 minutes = 1 hour
  ⇒ 30 minutes = 0.5 hour

A microwave requiring 1200 watts will use 1.2 kilowatts per hour.

If the microwave is used for a total of 30 minutes, it will use:

⇒ 1.2 × 0.5 =  0.6 kWh

If the cost is $0.20 per kWh, the cost of running the 1200 watt microwave for 30 minutes is:

⇒ 0.6 × $0.20 = $0.12

Answer:

1.12

2.11

3.19

Step-by-step explanation:

Sana nakatutulong

#Carry on learning

Pa brainliest po

Answer:

Step-by-step explanation:

x = 2

Answer:

5+(11 x n)

Step-by-step explanation:

I hope this helps

Answer:

M: (-2,6)

M': (-2,-6)

X coordinate

Answer:

a f

Step-by-step explanation:

(−5, 2) is point lie on a line that passes through the origin with a slope of −2/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the points lie on a line that passes through the origin with a slope of −2/5

The line passes through (0, 0) and (x, y) form a slope of -2/5

-2/5=y/x

So y is 2 and x is 5.

Hence, (−5, 2) is points lie on a line that passes through the origin with a slope of −2/5

To learn more on slope of line click:

https://brainly.com/question/14511992

#SPJ2

After doing some quick calculations, we can determine that X = −35.9

I hope this helps! :)

Answer:

x = -35.9

Step-by-step explanation:

Subtract both sides by 11.2                                                                                                 11.2 - 11.2 equals zero leaving x on one side.

x = - 24.7 - 11.2

A negative minus another negative number is a larger negative number.

x= -24.7 - 11.2 = -35.9

x = -35.9

Answer:

Swap 10 from box A and 15 from box B

Step-by-step explanation:

For calculate the ratio between the boxes we find the mean of the box A and the mean of the box B and divide this two results.

For find the mean of a set you use the next formula  [tex]\bar{x} = \frac{\text{sum numbers}}{\text{total numbers}}[/tex]

[tex]\bar{A} = \frac{4+5+9+10+12}{5} = \frac{40}{5}= 8\\\bar{B} = \frac{6+7+13+15+19}{5} = \frac{60}{5}= 12[/tex]

Then the ratio is equal to [tex]\frac{\bar{A}}{\bar{B}} = \frac{8}{12} = \frac{2}{3}[/tex]

Know the ask us for a ratio of 9:11 then we know two things about the boxes.

If you swap the numbers between them the total of numbers in the mean not change is always 5 and the sum of all the elements in both boxes is always 100. With this we can state the next equation:

The new mean of [tex]\bar{A}[/tex] is 9 then:

[tex]\frac{\text{sum of elements in box A}}{5} = 9[/tex]

[tex]\text{sum of elements in box A} = 45[/tex]

The new mean of [tex]\bar{B}[/tex] is 11 then:

[tex]\frac{\text{sum of elements in box B}}{5} = 11[/tex]

[tex]\text{sum of elements in box B} = 55[/tex]

Now we know what is the sum of the elements in both boxes, but how we find the elements for swap? Well with the next relation.

When you take out a element from the box A this elements is substracted to the total sum of the elements in the box A and get a new sum of total of elements named [tex]c[/tex] (where [tex]a[/tex] is the element taken):

[tex]40 - a = c[/tex]

And when you sum an element to the box A the current sum of total elements in the box change to (where [tex]b[/tex] is the added element):

[tex]b + c = 45[/tex]

So replace [tex]c[/tex] for the first relation and get:

[tex]b + 40 - a = 45\\b - a = 5[/tex]

From the last equation you can deduct that [tex]b[/tex] is greater than [tex]a[/tex] and the different between both values is 5. So the last step is find a number in the box B that substracted to a number from the box A give us 5. These both numbers are 15 and 10 because 15 - 10 = 5.

Answer:

13122

Step-by-step explanation:

Our equation is 2(3)⁸

once its solve we get 13122 as our answer

Answer:

3e-3/2f-3/8

Step-by-step explanation:

You multiply everything in the parenthesis with 1/2. 1/2*6e=3e, 3f*1/2=3/2f, 3/4*1/2=3/8. This would be the answer.

Answer: y = (1/2)x + 3

Step-by-step explanation:

The equation in slope-intercept form  y = (1/2)x+3

To determine how to write an equation from two points, we must determine the value of the slope and the yy-intercept. First, we will calculate the slope. This will be the value of mm in the slope-intercept form equation:

y=mx+b

Let’s answer the question, “What is the slope-intercept form of a line going through the points (1,5)(1,5) and (-4,7)(−4,7)?”

Remember, to calculate the slope we use the equation:

y2-y1/x2-x1

Therefore, the slope of the line is

-2/5

​

We can substitute

-2/5 for m.

To learn more about equation in slope-intercept refer to:

https://brainly.com/question/1884491

Answer:

  No; no sign change of g(x) in that interval

Step-by-step explanation:

The intermediate value theorem tells you there will be at least one zero between any two points where the function changes sign. The table shows sign changes in the intervals [-2, -1], [0, 1], and [1, 2]. So, the three zeros of the cubic lie in those intervals.

There are no additional zeros to be found, and there are no sign changes of g(x) between x=2 and x=3, so there is no zero in the interval [2, 3].

_____

Additional comments

We can only answer this with certainty because we have already found the locations of the three real zeros this cubic has. If there were two that were unaccounted for, then the possibility might exist for the graph to make an excursion across the x-axis and back in the interval [2, 3].

__

First differences of the table values are ...

  -5, +1, +2, -3, 0

Second differences are ...

  6, 1, -5, 3

Third differences are ...

  -5, -6, +8

This table cannot represent a real cubic function. For evenly-spaced x-values, a cubic polynomial must have constant 3rd differences. If the last two values in the table were -1 and -12, the function would be ...

  g(x) = -5/6x^3 +1/2x^2 +7/3x -1

You may want to discuss this question with your teacher.

Answer:

Step-by-step explanation:

Three options for the first position

Two options for the second position

one option for the third position

3•2•1 = 6 ways

their orders could be

1) ABC

2) ACB

3) BAC

4) BCA

5) CAB

6) CBA

Answer:

Would be 6 ways

Step-by-step explanation

3x2=6

Answer:

20, 4

Step-by-step explanation:

Let's assume total number of students registered is n

Last week n/4 people are absent

so people present are n - n/4 = 3n/4

Today after return of Jen  1/5 n are absent

so people present are n - n/5 = 4n/5

which is also equal to last week present people + 1 (Jen)

= 3n/4 + 1

= (3n + 4) / 4

so (3n + 4) / 4 = 4n/5

=> 3n + 4 = 4n/5 * 4

=> (3n + 4) * 5 = 16n

=> 15n + 20 = 16n

=> 20 = n

=> n = 20

So total students registered for class is 20

today no of people absent = n/5 = 20/5 = 4

This expression 40=4+(n-1)3 represents the correct arithmetic progression.

What is an arithmetic progression?

Every term following the first is derived by adding a constant value, known as the common difference, in an arithmetic progression.

We have,

4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 +31 + 34 + 37 + 40

Arithmetic progression formula:

                             [tex]a_{n}=a_{1}+(n-1)d[/tex]

where

[tex]a_{n}[/tex] = the nᵗʰ term in the sequence

[tex]a_{1}[/tex] = the first term in the sequence

[tex]d[/tex] = the common difference between terms

By using arithmetic progression formula we can find last term of an Arithmetic series.

                    [tex]a_{n}=a_{1}+(n-1)d[/tex]

                    [tex]a_{n}[/tex]= 4 + (n-1)3

                    [tex]a_{n}[/tex] = 4 + (13-1)3

                     [tex]a_{n}[/tex]  = 40.

we have calculated the last term by using arithmetic progression formula which is 40.

Hence, This expression 40=4+(n-1)3 represents the correct arithmetic progression.

To learn more about arithmetic progression from the given link,

https://brainly.com/question/24191546

#SPJ1

Answer:

A = 2.37500

B = 8.5

Step-by-step explanation:

Explanation A - 19 divided by 8 is 2.37500

Explanation B - 34 divided by 4 is 8.5