Compound Interest
When Jack turned 21, he decided to start investing $200 a month every year for nine years. At age 30, he decided to stop investing altogether.

Blake started a little later, investing $200 a month every month starting at age 30, all the way until the ripe old age of 67.

Assuming that they were both amazing at investing and made 11% interest per year, how much money will they both have at age 67?

Answer:

b and c

Step-by-step explanation:

The statements that are true are:

Fractions and ratios cannot have zero in the denominator.

Fractions and ratios can be simplified in the same way.

Fractions and ratios are different names for the same thing.

Options A, B, and C are correct.

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Fraction is written as:

1/2, 3/4, 5/6

Where 1, 3, and 5 are numerators and 2, 4, and 6 are denominators.

The ratio is written in the form a:b.

1:2 = 1/2

4:8 = 4/8 = 1/2

Fractions and ratios cannot have zero in the denominator.

This is true because if we have zero in the denominator the fraction becomes undefined.

Example:

1/0 = ∞

The ratio can not have zero in the denominator because we are comparing two units where neither one unit can be zero.

Fractions and ratios can be simplified in the same way.

This is true.

Example:

Fraction = 2/4 = 1/2

Ratio = 2:4 = 2/4 = 1/2

Fractions and ratios are different names for the same thing.

This is true.

Because ratio can be written as a fraction.

Example: 2:3 = 2/3

Some fractions and ratios can be written as mixed numbers.

This is not true

Fractions can be written as a mixed numbers.

Example:

5/2 = [tex]2\frac{1}{2}[/tex]

Ratios can never be written as a mixed number.

Thus,

The statements that are true are:

Fractions and ratios cannot have zero in the denominator.

Fractions and ratios can be simplified in the same way.

Fractions and ratios are different names for the same thing.

Options A, B, and C are correct.

Learn more about fractions here:

https://brainly.com/question/24370499

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Answer:

D.) Domain: 0≤x≤16

The domain represents the set of all possible inputs - the times when depth was measured

Step-by-step explanation:

Domain of a function is the possible set of inputs which are usually plotted on the x-axis, while range are corresponding outputs plotted on the y-axis.

In this case, the domain is the set of all possible inputs (x-values), which represents the times the depth was measured.

Domain ranges from 0 to 16. Thus:

Domain: 0 ≤ x ≤ 16

Answer:

B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147

Step-by-step explanation:

We are given that

[tex]\angle ABC=85^{\circ}[/tex]

Exterior angle=[tex]147^{\circ}[/tex]

We have to find the value of x.

We know that

Exterior angle=Sum of opposite interior angles of triangle

Using the property

[tex]x+85=147[/tex]

Subtract 85 from both sides we get

[tex]x=147-85[/tex]

[tex]x=62[/tex]

Option B is true.

B. x = 62 because 147 – 85 = 62 and 85 + 62 = 147

Answer:

80

Step-by-step explanation:

Answer: 24

Step-by-step explanation:

144-24=120

64-24=40

40*3=120 three times smaller

Answer:

34% of 480=34/100×480=163.2

3 1/2 of 480=7/2×480=1680

Answer:

15n

Step-by-step explanation:

Since it is 15 samples per day, you just need to multiple 15 by the number of days.

The person above is correct give them brainliest

Answer:

ajjvtjeiqwchiedgvgfeggyryftyyyug ytugttbghg

Answer:

The mean and standard deviation of the sampling distribution for the 36 students will be:

Mean = 18.6

Standard deviation = 6

Step-by-step explanation:

The mean and standard deviation of the sampling distribution is equal to the population mean and standard deviation respectively.  The only difference is that the population mean and standard deviation are parameters or fixed values calculated from every individual in the population, while the sample mean and standard deviation are statistics.  Statistics are calculated from only some of the individuals in a population.  They are meant to represent or approximate the population parameters.

Answer:

9h + 1

Step-by-step explanation:

36h + 4 divided by 4 is 9h + 1

Answer:

m < 4 = 120

Step-by-step explanation:

When two anlges are supplementary, their angle measures add up to 180, apply this knowledge here;

m<3 + m<4 = 180

60 + m<4 = 180

m<4 = 120

Answer:

120

Step-by-step explanation:

m<3 is 60 and 180-60=120

Answer:

Step-by-step explanation:

f(x) + g(x) = x^2 - 2x + x + 12

f(x) + g(x) = x^2 - x + 12

(f + g)( -1) = 1 + 1 + 12 = 14

f(x) - g(x) = x^2 - 2x - x - 12

f(x) - g(x) = x^2 - 3x - 12

(f + g)(-1) = (-1)^2 -(3)(-1) -12

(f + g)(-1) = 1 + 3 - 12

(f + g)(-1) = - 8

Answer:

8ft

Step-by-step explanation:

Use similarity and congruence

AB/ED=AC/EF

3/6=4/X

CROSS MULTIPLICATION

3X=6*4

3X=24

X=8ft

Answer:

Abraham Lincoln was 56 years old when he died.

Step-by-step explanation:

Answer:

I am not sure on the first one but this is what I think:

False

False

True

Step-by-step explanation:

Sorry if it's wrong!!

Answer:

4,000 and 40

Step-by-step explanation:

Answer:

4,201, 4 would be in the thousands place and the 4 in 65,143 would be in the tens place. So it would be 4,000 and 40.

9514 1404 393

Answer:

  18 miles

Step-by-step explanation:

The map distance and ground distance are proportional.

  (distance to school)/(3 in) = (12 miles)/(2 in)

Multiplying by 3 in gives ...

  distance to school = (12 miles)(3/2) = 18 miles

Answer:

f(x) = -0.5x - 2;

At x = 0, f(x) = -2

At x = 1, f(x) = -2.5

At x = 2, f(x) = -3

At x = 3, f(x) = -3.5

At x = 4, f(x) = -4

g(x) = (2^(x - 1)) - 5;

At x = 0, g(x) = -4.5

At x = 1, g(x) = -4

At x = 2, g(x) = -3

At x = 3, g(x) = -1

At x = 4, g(x) = 3

Step-by-step explanation:

First equation;

f(x) = -0.5x - 2

f(0) = -0.5(0) - 2 = -2

f(1) = -0.5(1) - 2 = -2.5

f(2) = -0.5(2) - 2 = -3

f(3) = -0.5(3) - 2 = -3.5

f(4) = -0.5(4) - 2 = -4

For the second equation;

g(x) = (2^(x - 1)) - 5

g(0) = (2^(0 - 1)) - 5 = 2^(-1) - 5 = -4.5

g(1) = (2^(1 - 1)) - 5 = 2^(0) - 5 = -4

g(2) = (2^(2 - 1)) - 5 = 2 - 5 = -3

g(3) = (2^(3 - 1)) - 5 = 4 - 5 = -1

g(4) = (2^(4 - 1)) - 5 = 3

Answer:

c) Percentages

Step-by-step explanation:

Percentages can be used to compare changes from one period to another.

In calculating a percentage change, either a percentage increase or percentage decrease, we must have both the new and old measurement of the specific quantity.

For example, let's find percentage increase of the number of students that joined a book club using the parameters below;

Original number of students = 32

New number of students = 36

We will calculate the increase using;

[tex] Increase = original \; number - new \; number [/tex]

Substituting the values, we have;

Increase = 36 - 32 = 4

[tex] Percentage \; increase = \frac{increase}{original \; number} * 100[/tex]

[tex] Percentage \; increase = \frac{4}{32} * 100[/tex]

[tex] Percentage \; increase = 0.125 * 100[/tex]

Percentage increase = 12.5%

Therefore, the number of students in the school club increased by 12.5%.

Answer:

[tex]\frac{112}{3}[/tex]

Step-by-step explanation:

14 ÷ 3/8 = 14 • 8/3

= 112/3

Answer:

37 1/3

Step-by-step explanation:

use Keep Change Flip when dividing with fractions! :) It's helpful

for example: 14 ÷ 3/8

14 (keep as 14)

* (change to multiplication)

8/3 (flip the fraction)

14 times 8/3= 37 1/3

Answer:

145%.

Step-by-step explanation:

Given that the price of an item yesterday was $120, and today, the price rose to $294, in order to find the percentage increase, the following calculation has to be made:

120 = 100

294 = X

((294 x 100) / 120) = X

29,400 / 120  = X

245 = X

245 - 100 = 145

Therefore, the percentage increase of the product was of 145%.

Answer:

Step-by-step explanation:

We can solve this using a ratio. If there a 2 bottles of cherry in the ratio and there are 34 actual bottles of cherry, then the ratio is

[tex]\frac{ratio}{actual}:\frac{2}{34}[/tex]

In the ratio, we are told that the mix of bottles is 7 parts mango and we want to know how many actual bottles there are of mango. So filling in:

[tex]\frac{ratio}{actual} =\frac{2}{34} =\frac{7}{m}[/tex] and cross multiply to get

2m = 238 and

m = 119. There are 119 bottles of mango juice. And just for the record, there are 17 bottles of fruit juice.

Answer:

m = 119. There are 119 bottles of mango juice. there are 17 bottles of fruit juice.

Answer:

the answer is 2616

hope this helped

Step-by-step explanation:

Given:

Endpoint of segment AB are A(0,2), B(2,3).

Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).

To find:

The scale factor of dilation.

Solution:

If a figure is dilated about the origin with factor k, then

[tex](x,y)\to (kx,ky)[/tex]

Using this rule, we get

[tex]A(0,2)\to A'(k(0),k(2))[/tex]

[tex]A(0,2)\to A'(0,2k)[/tex]

So, the image of A is A'(0,2k).

It is given that image of A is A'(0,4). So,

[tex]A'(0,2k)=A'(0,4)[/tex]

On comparing the y-coordinates from both sides, we get

[tex]2k=4[/tex]

[tex]k=\dfrac{4}{2}[/tex]

[tex]k=2[/tex]

Therefore, the scale factor is 2 and the correct option is B.

Dilation involves changing the size of a line

The scale factor is 2.

From the graph, the coordinates of AB are:

[tex]\mathbf{A = (0,2)}[/tex]

[tex]\mathbf{B = (2,3)}[/tex]

The coordinates of AB are:

[tex]\mathbf{A' = (0,4)}[/tex]

[tex]\mathbf{B' = (4,6)}[/tex]

Divide A' by A or B' by B to calculate the scale ratio (k)

[tex]\mathbf{k = \frac{A'}{A}}[/tex]

So, we have:

[tex]\mathbf{k = \frac{(0,4)}{(0,2)}}[/tex]

Expand

[tex]\mathbf{k = \frac{2(0,2)}{(0,2)}}\\[/tex]

Divide

[tex]\mathbf{k = 2}\\\\\\\\[/tex]

Hence, the scale factor is 2.

Read more about scale factors at:

https://brainly.com/question/16713785

Answer:

first angle be 30°

second angle be 70°

third angle be 80°

Step-by-step explanation:

first angle be x

second angle be y

third angle be z

x+y+z=180

given, y+z = 5x; z=5x-y

also, z=y+10

5x-y = y+10

5x= 10+y+y = 10+2y

x= (10+2y)/5

x+y+z=180

(10+2y)/5 + y + y+10 = 180

(10+2y)/5 = 180 -2y -10

(10+2y)/5 = 170-2y

multiply both sides by 5

10+2y = 5(170-2y)

10+2y= 850-10y

2y+10y = 850-10

12y= 840

y= 840/12 = 70°

z=y+10 =70+10= 80°

5x= (10+2y) = 10+2(70) = 10+140= 150

x = 150/5 = 30°

Answer:

804

Step-by-step explanation:

multiply 402 by 2

12÷2=6

6=402miles

402×2=804

#gamer