Ila invested $42,000 into an account earning 4% compounded annually. She makes no other deposits and does not withdraw any money.

What is the balance of Ila's account in 5 years?

Counterexample

A counterexample is an example that meets the mathematical statement's condition but does not lead to the statement's conclusion. It is used to check the validity of an argument.

We have been given the conjecture:-

"For every integer n, [tex]n^3[/tex] is positive."

We have to show that the conjecture is false by finding a counterexample.

Let us take an integer n = - 5

Finding its cube we, get

[tex]n^3[/tex] = -125

We know that,

-125 is not positive, it is negative.

Hence, the conjecture "For every integer n, [tex]n^3[/tex] is positive." is proven wrong by finding a counterexample which states otherwise.

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Answer:

x=10.50

Step-by-step explanation:

14 =  5

________
29.40 = x

cross multiply - 29.40 x 5 = 147

Then u would divide like this

14/14=1      147/14=10.5

[tex]1 \frac{1 \\ }{6} [/tex]

There are 1.17 grams of sugar are in 1 ounce of soda.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

A 12-ounce can of soda contains 14 grams of sugar.

Now,

Since, A 12-ounce can of soda contains 14 grams of sugar.

Hence, The amount of soda for 1 ounce of can = 14/12

                                                                        = 1.17 grams

Thus, There are 1.17 grams of sugar are in 1 ounce of soda.

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The solution for the linear equation is:

a = 1/4.

I believe we have the linear equation:

(a + 2)/3 = 3/4

To solve this, we need to isolate the variable a in one of the sides of the linear equation, to do so, we can start by multiplying both sides by 3.

3*(a + 2)/3 = 3*(3/4)

a + 2= 9/4

Now we can subtract 2 in both sideS:

a + 2 - 2 = 9/4 - 2

a = 9/4 - 8/4 = 1/4

a = 1/4

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Answer:

Answer is 1097.28 cm

Step-by-step explanation:

prove me wrong

Answer:

1097.28

Step-by-step explanation:

There are 91.44 centimeters per yard

12 x 91.44

Answer:

30.375

Step-by-step explanation:

this is a geometric sequence, meaning it has a common growth factor

to find the growth factor, you divide a term by the previous term (example: 9/6)

so for this problem:

9/6 = 1.5

6/4 = 1.5

so 1.5 is the common growth factor

then you just multiply so:

9 • 1.5 = 13.5

13.5 • 1.5 = 20.25

20.25 • 1.5 = 30.375

4, 6, 9, 13.5, 20.25, and 30.375

so 30.375 is your 6th term

hope this helps :)

Question 2a

[tex]x+6+x+3=17 \\ \\ 2x+9=17 \\ \\ 2x=8 \\ \\ x=4[/tex]

Question 3a

[tex]1+2x+31=x+20 \\ \\ 2x+32=x+20 \\ \\ x+32=20 \\ \\ x=-12[/tex]

Four ways to find the slope and y–intercept of straight line equation are;

A straight line equation is of the form, y = m•x + c

Where;

m = The slope of the graph of the equation

c = The point the graph intersects the x–axis.

The process by which the slope–intercept form of a straight line equation can be found from the above ways are as follows;

1. Making use of the graph of the equation

When the graph is given, the y–intercept is found from the point the graph crosses the y–axis

Note the y–intercept

Find two points on the graph where coordinates can be obtained

Find the ratio of the rise to the run to get the slope of the graph

[tex] \displaystyle{ Slope, \: m = \frac{ rise}{run} } = \frac{ \triangle y }{\triangle x} [/tex]

With the slope and y–intercept, the equation of the line can be written as; y = m•x + c

2. Obtaining the coordinates of the x–intercept

Given the slope and the y–intercept, the x–intercept can be found by plugging in the values of the slope, m, and the y–intercept, c, in the equation, y = m•x + c, to get the equation of the line

From the equation, the x–intercept can be found by plugging y = 0, to get;

0 = m•x + c

The x–intercept becomes, [tex] \displaystyle \frac{-c}{m} [/tex]

The graph can then be plotted by drawing a line through the x and y–intercept

3. Finding the y–intercept given the slope and the x–intercept

When the slope and the x–intercept and the slope is known, whole number part of the numerator can be added to the x–value of the x–intercept to obtain the x–coordinates of a second point on the graph

The process is repeated to find the y–coordinate of the second point

The slope is calculated using the two points and the equation for the slope given in the first method

4. When two points are known, the slope is calculated using the equation in method 1

The two are joined with a straight line and the y–intercept is obtained from the point the graph intersects the y–axis

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Angles of a polygon add to 360 degrees. To find the measure of each exterior angle of a regular n-gon. divide 360 by n.

The simplified form of the expression is 2.4 x 10⁻⁶.

Expression:

An expression is the sentence with a minimum of two numbers/variables and at least one math operation in it.

Given,

Here we have the expression

[tex]\frac{7.2\times10^{-8}}{3\times 10^{-2}}[/tex]

Here we need to simplify this expression.

Here we have to divide this expression first,

Then we get,

[tex]= > \frac{7.2}{3}\times\frac{10^{-8}}{10^{-2}}[/tex]

First, we have to divide the numbers term then we get,

=> 7.2/3 = 2.4

Then we have to solve the exponential form,

For that we have to move the denominator value to upper term,

Then we get,

=> 10⁻⁸ x 10²

=> 10⁻⁸⁺²

=> 10⁻⁶

So, the simplified form is, 2.4 x 10⁻⁶.

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5. The value of x = 15

6. The converse that must be used is: C. Same-side exterior ∠s converse.

7. The proof is completed in the explanation part.

8. Slope of AB = 7/4; Slope of CD = -4/7, they are perpendicular.

The same-side exterior angles theorem states that same-side exterior angles that are on the same side of a transversal are supplementary to each other. Its converse states that if same-side interior angles are supplementary, then the lines they lie on are parallel to each other.

5. 10x - 22 + 3x + 7 = 180 [same-side exterior angles theorem]

13x - 15 = 180

13x = 180 + 15

13x = 195

x = 15

6. The converse that must be used to show that lines y and x are parallel to each other is: C. Same-side exterior angles converse.

7.

Statements                                      Reasons                                            

1. ∠6 ≅ ∠8                                       1. Given

2. y║z                                              2. Corresponding ∠s converse

3. ∠2 and ∠3 are supplementary  3. Same Side Interior ∠s

8. Given:

A(-3, 8)

B(1, 15)

C(10, -9)

D(3, -5)

Slope = change in y / change in x

Slope of AB = (8 - 15)/(-3 - 1) = -7/-4 = 7/4

Slope of CD = (-9 -(-5))/(10 - 3) = -4/7

-4/7 is the negative reciprocal of 7/4. Perpendicular lines have slope that are negative reciprocals of each other.

Therefore, CD and AB are perpendicular.

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Answer:

Image result for kumon level C

This award is presented to a student who has completed Level C10 or higher during or before their 1st-grade year. Math Level C covers multiplication and division.

Step-by-step explanation:

The difference in the latitudes of Athens, Greece, Latitude 38° N, and Sydney, Australia, latitude 34° S is 72° .

We have two different coordinates, 38° N and  34° S

We can find the differnce in two different coordinates by following a few steps.

We have to consider South as negative North. So, we can write 34° S as -34° N.

Hence, we can determine the difference in between two coordinates.

Difference in coordinates ≡ 38° N - 34° S  = 38° N - ( - 34° N ) = 38° N + 34° N = 72°  N

So, we can conclude that, the difference is 72°.

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Step-by-step explanation:

1.

200 - 7/21 = (200×21 - 7)/21 = (4200 - 7)/21 =

= 4193/21 = 599/3 = (199×3 + 2)/3 =

= 199 2/3

we could have seen that 7/21 = 1/3.

so, then this problem was

200 - 1/3 = (200×3 - 1)/3 = 599/3 = 199 2/3

(see above)

2.

50 - 4/7 = (50×7 - 4)/7 = (350 - 4)/7 =

= 346/7 = (49×7 + 3)/7 = 49 3/7

3.

24 1/4 - 20 3/5 = (24×4 + 1)/4 - (20×5 + 3)/5 =

= 97/4 - 103/5

to calculate this we need to bring both fractions to the save denominator. the LCM (lowest common multiple) of 4 and 5 is 20.

so,

97/4 - 103/5 = (97×5)/(4×5) - (103×4)/(5×4) =

= 485/20 - 412/20 = 73/20 =

= (3×20 + 13)/20 = 3 13/20

4.

10 5/8 - 6 4/9 = (10×8 + 5)/8 - (6×9 + 4)/9 =

= 85/8 - 58/9

the LCM of 8 and 9 is 72.

85/8 - 58/9 = (85×9)/(8×9) - (58×8)/(9×8) =

= 765/72 - 464/72 = 301/72 =

= (4×72 + 13)/72 = 4 13/72

5.

6 1/2 - 5 3/4 = (6×2 + 1)/2 - (5×4 + 3)/4 =

= 13/2 - 23/4

the LCM of 2 and 4 is 4.

13/2 - 23/4 = (13×2)/(2×2) - 23/4 =

= 26/4 - 23/4 = 3/4

Answer:

Step-by-step explanation:

0.000000005% can be written as a fraction: 0.000000005 / 100

Answer:

7 hours

Step-by-step explanation:

each day she practices 1 hour and there are 7 days in a week so 7 hours by the end of the week

Answer 3c+9d

Step-by-step explanation: add 3c 9d

Answer: False

Step-by-step explanation:

The x-value of 1 maps onto 4 different y values.

The provided sentence "Five less than the quotient of eighteen" is converted into an algebraic expression as 18/x - 5.

Five less than the quotient of eighteen and a number

We must convert the provided sentence into an algebraic expression.

Let "x" represent the number.

Therefore,

Five less than that of the quotient of eighteen and "x"

The term quotient refers to the outcome of division.

Therefore,

18/x - 5

That is, Five less than the quotient of eighteen and x.

As a result, the provided sentence is converted into an algebraic expression.

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Answer:

Box on the right is 6 and the lower box on the left is 840

Step-by-step explanation:

Make a proportion:

[tex]\frac{168}{1008}[/tex] =[tex]\frac{1}{x}[/tex]  cross multiply and solve

168x = 1008  Divide both sides by 168

x = 6

[tex]\frac{168}{x}[/tex] = [tex]\frac{1}{5}[/tex]  Cross multiply and solve

x = 168(5)

x = 840

nswer

First image

Angle ABC covers around the inside and outside of the circle.

Second image

Angle x l

hird image

Angle DBE l

ngle of arc DE l

ngle of arc AC l

ourth angle

ll the angles at U lie inside the circle.

ngle 78° l

ngle 114° l

ope this Helps!!!

Answer:

48

Step-by-step explanation:

Answer:

3 × 5 = 15

Step-by-step explanation:

5 is the common number

Answer:

  22 ft

Step-by-step explanation:

Given a river that has a depth in January of -5 ft, and a depth in July of -27 ft, you want the difference between the depths in January and July.

The difference between two numbers is found by subtracting the second from the first:

  (January depth) - (July depth) = (-5 ft) -(-27 ft)

  = (-5 +27) ft = 22 ft

The difference between depths in January and July is 22 feet.

Answer:

first drop down is, doesn't matter. Second one is, must be the negative reciprocal of the slope of the original line. Third is, must be different from the y intercept of the original line. If the y intercepts are the same, the two lines will intersect as proven by one of the questions asked by the user.

Step-by-step explanation:

Hope this helps! :)

Answer:

56,52

Step-by-step explanation:

take n as 3.14 multiples with 9 and multiples with 2

Using divisibility rules, it is found that there are 165 members in the band.

The number of students in the last row gives the remainder of the division of the total number of members by the number of members in each row.

Hence:

It is also stated that the band has fewer than 200 members.

From the third bullet point, the possible values, that is, values that when divided by 8 have a remainder of 5, are given as follows:

{5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 133, 141, 149, 157, 165, 173, 181, 189, 197}.

The number is 165, because:

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Answer: Question E: The answer is that A(9) is greater.

Step-by-step explanation:

For questions A and C, you can see that the table is exponentially growing. So the equation will use multiplication. You can also see the value of the equation is growing by x2.

So you could say the table starts at a base of 1/2, then grows exponentially at a rate of 2. (Basically saying the value grows x2 per term). The equation will result in y= 1/2(2)^x

For questions B and D, you can see that the graph is growing linearly. So the equation will use multiplication.

By drawing a line between the lines you can easily see the growth of the triangle. You can then tell the 0th term to 1st term goes right 1 and up 10.

Next, you look at the 1st term to the 2nd term. You can tell that it goes right 1 and up 10. So, the rate is 10 per term. (10x) and it starts at 2 (+2). The equation will result in y=10x+2

Question E, solve each equation by substituting the x by 9.

A(9)

y= 1/2(2)^x

y= 1/2(2)^9

y= 1/2(512)

y=256

B(9)

y=10x+2

y= 10(9) +2

y= 90+2

y=92

The answer is that A(9) is greater.

Applying the rules for the constant, logarithm and exponents, the derivative of the given function is of:

f'(x) = 3/x - 6x² - 8/(x^5).

The function is given by:

f(x) = √2^3 + ln(x^3) - 2x^3 - log_3(729) - 2/x^4

The derivative of a sum is the sum of the derivatives, hence:

f'(x) = (√2^3)' + (ln(x^3))' - (2x^3)' - (log_3(729))' - (2/x^4)'

The derivative of a constant is of zero, hence:

Hence:

f'(x) = (ln(x^3))' - (2x^3)' - (2/x^4)'.

The derivative of the logarithm is given by:

ln(h(x))' = (1/h(x)) x h'(x).

Hence:

(ln(x^3))' = 3x²/x³ = 3/x.

The derivative of the power of x is given by:

[x^n]' = nx^(n-1).

Hence:

Hence the derivative of the function is given by:

f'(x) = 3/x - 6x² - 8/(x^5).

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