Brooke has money in an account that earns 10% interest compounded annually.
She earns $1.47 in 2 years, how much money did Brooke initially invest?

Answer: THE PRODUCT

Step-by-step explanation:

The associative property of multiplication says that the product of three or more numbers remains the same no mater how the numbers are grouped.

example (3x5x2) is the same as ( 5x2x3) both = 30

The measures of center or variability are greater than 5 degrees

This Week's Mean: (4 + 13 + 6 + 9 + 8) / 5 = 40 / 5 = 8

Last Week's Mean: (10 + 9 + 5 + 6 + 5) / 5 = 35 / 5 = 7

Then the ranges

This Week's Range: (13 - 4) = 9

Last Week's Range: (10 - 5) = 5

The MAD for both weeks

|(4 - 8)| + |(13 - 8)| + |(6 - 8)| + |(9 - 8)| + |(8 - 8)|

= 4 + 5 + 2 + 1 + 0 = 12

This Week's MAD: 12 / 5 = 2.4

|(10 - 7)| + |(9 - 7)| + |(5 - 7)| + |(6 - 7)| + |(5 - 7)| = 3 + 2 + 2 + 1 + 2 = 10

Last Week's MAD: 10 / 5 = 2

Hence the measures of center or variability are greater than 5 degrees are:

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Answer:

22

Step-by-step explanation:

length is given by (3--1=4)

width is given by (2--5=7)

perimeter is given by:

P=2l + 2w

P=2(4)+2(7)

P=8+14

P=22

The cost of the utility pole with a radius of 17.8 cm and a height of 700 cm is; $3774.4

From the information given, we have the following parameters;

Density = 5.4 g/cm³

Mass = Ikg = 0.71 kg

Cost per mass = $0. 51

Let's determine the volume of this cylinder:

Volume = mass / density

Substitute the values

Volume = 0.71 /5.4

Volume = 0.131 cm³

Thus, 0.131  cm³ costs $0.71

For the utility pole;

Volume = 2 πr²h

Where:

r is 17.8cm

height is 700cm

Volume = 3. 142 × 17.8 × 17.8 × 700

Volume = 696414.32 cm³

If  0.131  cm³ costs $0.71

Then  696414.32  cm³ will cost:

= 696414.32   × 0.71/ 0.131  

= 3774.4

Thus, the cost of a utility pole is  $3774.4

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The missing number in the ratios of numbers are 16:10     8:20 and 0:30

Ratios are quantitative relationships between two numbers that describe how many times one value can contain another

the given parameters are

Forks         16          8              ----

Spoons       10         ---            30

The numbers are written in ascending order of magnitude

Using AP,

for forks: a = 16, 2nd term = 8

common difference = 8-16 - -8

For spoons a = 10, 3rd term = a + 2d = 30

30 = 10 + 2d

30 -10 = 2d

d= 20/2 = 10

Therefore the 2nd term = 10+10=20

The table reappears as follows

Forks         16          8             0

Spoons       10        20          30

Therefore the equivalent ratios are 16:10     8:20 and 0:30

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The value of the variable x for the triangle base length is derived as 5.

Using the proportionality theorem for evaluating x as follows:

JD/DK = PJ/PK

3x/(4x + 1) = 20/28

3x × 28 = 20(4x + 1) {cross multiplication}

84x = 80x + 20

84x - 80x = 20 {collect like terms}

4x = 20

x = 20/4 {divide through by 4}

x = 5

Therefore, the value of the variable x for the triangle base length is derived as 5.

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All the three locations has been checked below.

Using Pythagoras theorem,

12² = 8² + x²

144 - 64 = x²

x= √80

x=8.9

Now, using Trigonometry

tan F = P/B

tan F= 8/8.9

and, sin F = P/H

      sin F= 8/12 = 2/3

and, cos F = B/H

        cos F= 12/8.9

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The composite numbers between 10 and 20 are: 12, 14, 15, 16 and 18 which have more than 2 factors.

To find a composite number, we find the factors of the given number. The best way to determine a composite number is to do a divisibility test. The divisibility test helps us determine if the number is prime or composite. Divisibility means that one number is divided completely (without remainder) by another number.

Answer:

1,2, and 4

Step-by-step explanation:

vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.

Answer:

640 Oz

Step-by-step explanation:

1 Lb = 16 Oz

40 Lb • 16 Oz = 640 Oz

hope this helps

Mark brainliest , pls

The possible outfits that Casey can make is 30 and  this is shown in the image that is attached.

The tree diagram is known to be one that shows the hierarchical organization of tasks and subtasks that must be done to achieve a goal. The branching diagram start with a single element that divides into two or more, each of which further divides into two or more, and so forth.

Based on the question, Casey has:

5 shirts

3 skirts

2 blazers

Therefore, to make a tree diagram of any possible outfits that Casey can make.​, there are a total of:

5 x 3 x 2

= 30

So, the possible outfits that Casey can make is 30.

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Answer:

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

Each question can be answered either true or false, giving two possible choices for each of the 8 questions.

Therefore, the total number of ways to answer the questions is the product of the number of choices for each question, which is:

The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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Answer:

Step-by-step explanation:

Let P(t) be the fox population t years after 2000. We know that the population has a continuous growth rate of 4% per year, which means that the population increases by a factor of 1.04 each year. Therefore, we can model the population as:

P(t) = 21400 * 1.04^t

Here, we start with the population in the year 2000 (21400) and multiply it by 1.04 raised to the power of the number of years after 2000 (t).

For example, if we want to find the population in the year 2015 (15 years after 2000), we can plug t = 15 into the equation:

P(15) = 21400 * 1.04^15

= 21400 * 1.618

= 34694.8

Therefore, we can expect the fox population to be approximately 34,695 in the year 2015.

The domain and the range of the function are given as follows:

The function in this problem is given as follows:

y = 600 - 75x.

The input variable x represents the number of months, which cannot be negative, hence the lower bound of the domain is given as follows:

x = 0.

Meaning that the upper bound of the range is of y = 600.

The balance remaining cannot be negative, hence:

The problem asks for the domain and the range of the function.

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By calculating the volume of both figures, we will see that 11,160 cubes can be fit in the prism.

Now, So we start with a rectangular prism that measures (7 + 1/2)cm by 12cm by (15 + 1/2) cm.

Hence, The volume is just the product of these 3 values,

so we get:

V = (7 + 1/2)cm × 12cm × (15 + 1/2)cm

V = 1,395 cm³

Now, a cube with an edge length of 1/2 cm has a volume of:

V' = (1/2cm)³

V' = 0.125 cm³

To see how many of the small cubes enter in the prism, we just need to take the quotient between these two volumes, this is:

V/V' = ( 1,395 cm³)/(0.125 cm³) = 11,160

This means that, 11,160 of the cubes can be fit in the prism.

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complete question is,

A rectangular prism measure 7 1/2 by 12 by 15 1/2

Calculate the number of cubes with edge length 1/2 cm that fit in this prism.

What is the volume of the prism in cm? If you are stuck, think about how many cubes with 1/2-cm edge lengths fit into 1 cm.

1. To find the probability that the length of a single trout taken at random from the pond is between 7 and 11 inches long, we need to use the normalcdf command with the given parameters. The formula for normalcdf is normalcdf(lower bound, upper bound, mean, standard deviation).

Thus, normalcdf(7, 11, 10.5, 1.2) = 0.6827.

Therefore, the probability that the length of a single trout taken at random from the pond is between 7 and 11 inches long is 0.6827.

2. To find the probability that the mean length of five trout taken at random is between 7 and 11 inches, we need to use the central limit theorem, which states that the sample mean will also follow a normal distribution with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size (i.e., sigma/sqrt(n)).

Thus, we first need to find the standard deviation of the sample mean, which is sigma/sqrt(n) = 1.2/sqrt(5) = 0.5367.

Then, we can use the normalcdf command with the given parameters. The formula for normalcdf is normalcdf(lower bound, upper bound, mean, standard deviation).

Thus, normalcdf(7, 11, 10.5, 0.5367) = 0.9468.

Therefore, the probability that the mean length of five trout taken at random is between 7 and 11 inches is 0.9468.

The value of the expression is 0.017455065

Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.

The given expression is (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9)

This gives [Tan (π/18 * π/9) ÷ 1/(Tan(π/18 * π/9)

Simplify further to have

Tanπ²/162 * 162/π²)

This gives Tan1 =  0.017455065

This implies that  (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9) = 0.017455065

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The hypothesis is

Scientific investigations employ a crucial concept known as the null hypothesis, which asserts that there is no apparent correlation between analyzed data or variables.

The null tells us that the standard deviation is equal to 2.6

Concurrently, an alternate theory sets forth that an effect does indeed exist within the population being investigated. This differentiation allows researchers to draw meaningful conclusions from carefully collected empirical evidence.

H1: SD < 2.6

There is insufficient data to solve for the test stat

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The composition of f. g derived from the equations in the attached image is:  [tex]\frac{1}{10}(2x + 1)[/tex] and f+g as  √(4x-1))/(5x²+3)

Composition is a mathematical operation that combines two functions to form a new function. From our question, we are given two functions f(x) and g(x).

One of their composition can be represented by f(g(x)).f(g(x)) means function out of g(x) will serve as input x for function f(x). In a more simpler words, f(g(x)) is the function obtained by taking the output of g(x) and using it as the input for f(x).

Using the question given as an example,

For f.g:

Firstly, we have to compute the composition of f and g.

This can be expressed as:

f(g(x))f(g(x)) = f(√(4x-1))= 1/[5(√(4x-1))² + 3]= 1/[5(4x-1) + 3]

= 1/(20x + 10)

= [tex]\frac{1}{10}(2x + 1)[/tex]

For f+g:

To find f+g, we will just add the two functions together as below:

f+g = 1/(5x²+3) + √(4x-1)= (√(4x-1) + (5x²+3)

= √(4x-1))/(5x²+3)

So the answers are;

f.g: = [tex]\frac{1}{10}(2x + 1)[/tex]

f+g =  √(4x-1))/(5x²+3)

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The height of the can in inches is 44.68 inches

From the question, we have the following parameters that can be used in our computation:

Volume = 8 cubic inches

Radius = 3/4 inches

The volume of a cylinder is calculated as

V = πr²h

substitute the known values in the above equation, so, we have the following representation

π * (3/4)²h = 8

So, we have

h = 8π/[(3/4)²]

Evaluate

h = 44.68

Hence, the height of the can in inches is 44.68 inches

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The difference between the median test score in the morning and the afternoon is 12.5

From the question, we are to determine the difference between the median test score in the morning and the afternoon.

From the given diagram, we have box plots.

From the given box plots, we will determine the median test score in the morning and the median test score in the afternoon.

The median test score in the morning = 87.5

The median test score in the afternoon = 75

Thus,

The difference between the median test score in the morning and the afternoon =

Median test score in the morning - Median test score in the afternoon

The difference between the median test score in the morning and the afternoon = 87.5 - 75

The difference between the median test score in the morning and the afternoon = 12.5

Hence,

The difference is 12.5

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The angles formed by the chords and secants of the circle are;

28) m[tex]\widehat{AB}[/tex] = 60°

29) m[tex]\widehat{GH}[/tex] = 52°

30) m[tex]\widehat{DH}[/tex] = 90°

31) m∠1 = 90°

32) m∠2 = 58°

33) m∠3 = 32°

34) m∠5 = 49°

35) m∠6 = 90°

36) m∠7 = 99°

37) m∠8 = 96°

38) m∠9 = 116°

A chord is a segment that joins two distinct points on the circumference of a circle.

The angles formed by the arcs in the circle indicates that we get;

28) m[tex]\widehat{AB}[/tex] = 360° - 56° - 18° - 42° - 180° = 60°

29) m[tex]\widehat{GH}[/tex] = 90° - 38° = 52°

30) m[tex]\widehat{DH}[/tex] = 90°

31) m∠1 = 180°/2 = 90°

32) m∠2 = (56° + 18° + 42°)/2 = 58°

33) m∠3 = 90° - 58° = 32°

34) m∠5 = (1/2) × (38° + 18° + 42°) = 49° (Angles of intersecting chords theorem)

35) m∠6 = 90° (Supplementary angle to a right angle is 90 degrees angle is )

36) m∠7 = 180° - 32° - 49° = 99°

37) m∠8 = (1/2) × (52° + 38° + 60° + 42°) = 96°

38) m∠9 = m∠3 + (180° - m∠8) (External angles theorem and linear pair angles)

m∠9 = 32° + (180° - 96°) = 116°

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Answer: Yes

Step-by-step explanation:

Yes because the angles are both 120 degree's

(I'm not sure if this is right but btw I love your pfp :))

The probability that a randomly

selected point within the circle falls in the

red-shaded square is 63.7%.

A figure is shown, in which a square is inscribed in a circle. To find the probability that a randomly selected point within the circle falls in the red shaded area (Square).

radius  = 7cm

side of square = 7√2 cm

Area of the circle = πr²

                             = 3.14 * 7²

                             = 153.86 cm²

Area of the square = side * side

                               =  7√2 * 7√2

                               = 98 cm²

= Area of square / Area of the circle

= 98 / 153.86

=  63.7%

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Answer:

63.7

Step-by-step explanation:

I entered that and got it right

Answer:

$1.50

Step-by-step explanation:

3÷2=1.50

Answer:

1/20

Step-by-step explanation:

To multiply two fractions, you simply multiply their numerators (top numbers) together and multiply their denominators (bottom numbers) together.

So, for 2/5 x 1/8, we have:

(2/5) x (1/8) = (2 x 1) / (5 x 8) = 2/40 = 1/20

Therefore, 2/5 x 1/8 is equal to 1/20.

Multiplying the numerators and denominators directly is the most straightforward method to solve the multiplication of fractions. However, there is another method called cross-multiplication, which you can use to solve this problem as well.

To use cross-multiplication, you multiply the numerator of the first fraction by the denominator of the second fraction, and then multiply the denominator of the first fraction by the numerator of the second fraction.
Then, you simplify the resulting fraction.

So, for 2/5 x 1/8, we have:

(2/5) x (1/8) = (2 x 1) / (5 x 8)

Cross-multiplying, we get:

(2/5) x (1/8) = (2 x 1) / (5 x 8) = (2 x 1) / (5 x 8) = 2/40

Simplifying the fraction 2/40, we can divide both the numerator and denominator by 2, to get:

2/40 = 1/20

Therefore, using cross-multiplication, we get the same answer as before:

2/5 x 1/8 is equal to 1/20.

The number of children ticket sold is 90 while the number of adult ticket sold is 200.

Math land theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250.

Therefore, let's find the number of each type of ticket sold as follows:

Hence,

Let

Therefore, using equation,

c + a = 290

5c + 9a = 2250

Multiply equation(i) by 5

5c + 5a = 1450

5c + 9a = 2250

subtract the equation

4a = 800

divide both sides by 4

a = 800 / 4

a = 200

Therefore, let's find c

c = 290 - 200

c = 90

Hence,

number of children's ticket = 90

number of adult tickets = 200

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