Applying the Pythagorean Theorem In this activity, you will explain your understanding of mathematical relationships and use the Pythagorean theorem to solve real-world problems. Question 1 In your own words, explain the relationship between the legs and the hypotenuse of a right triangle.

Answer:

Only Z

Step-by-step explanation:

Supplementary angles are angles whose sum up to 180 degrees.

Step-by-step explanation:

The volume of a rectangular box is given by the formula:

Volume = length x breadth x height

In this case, the length is a, the breadth is 2b, and the height is 3c. So, the volume can be calculated as:

Volume = a x 2b x 3c

= 6abc

Therefore, the volume of the rectangular box with a, 2b and 3c as length, breadth and height respectively is 6abc.

Tina and Carl will use 6 and 12 ounces of clay, respectively. Tina uses 3/10 of the 20-ounce bucket and Carl uses 3/5 of the 20-ounce bucket.

To determine how much clay Tina and Carl will use, we need to first find the total amount of clay they will use together.

If 3/10 of the clay is used by Tina and 3/5 of the clay is used by Carl, we can find the total amount of clay used by adding these fractions:

3/10 + 3/5 = (3/10 * 1/2) + (3/5 * 1/2) (we multiply by 1/2 to find the common denominator of 10)

= 3/20 + 6/20

= 9/20

Therefore, Tina and Carl will use a total of 9/20 of the 20-ounce bucket of clay.

To find how much each of them will use, we can multiply the total amount of clay by each person's fraction:

Tina: (3/10) x 20 ounces = 6 ounces

Carl: (3/5) x 20 ounces = 12 ounces

Therefore, Tina will use 6 ounces of clay, while Carl will use 12 ounces of clay.

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Tina and carl share a 20 ounce bucket of clay 3/10 and 3/5, how much of the clay each of them will use?

Answer: We have:

(5i√3)² = (5i)²(√3)² = -25(3) = -75

Therefore, the square of 5i√3 is -75.

Step-by-step explanation:

The square of the complex number of 5i√3 is 75.

A complex number is the sum of a real number and an imaginary number.

To find the square of the complex number, 5i√3, we use the following Steps below

Step1: Square the expression

Step 2: use the law of surd to seperate each of the terms in the expression

Note: In complex number notation,

Therefore,

Hence, square of 5i√3 is 75

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15 is the distance of the equation of a line passing through the points.

What is distance ?

Distance is the separation between two objects. Moreover, it serves as a gauge for the distance between two objects. It is measurable along any route. So even though his position does not change, a person who circles about has moved a certain amount of distance.

the points (4,-3) and (16, 6)

D = √(x₂ - x₁)² + (y₂ - y₁)²

     = √(16 - 4)² + (6 -(-3)²

     = √(12)² + (9)²

      = √144 + 81

       = √225

       = 15

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The method of collecting data that was used in the given scenario is voluntary response.

A voluntary response method of data collection is a research technique that allows participants to decide whether or not they want to be included in the sample.

When participants are allowed to choose whether or not to participate, this is known as self-selection.

This method has a disadvantage in that it could lead to bias in the data because those who respond to the survey may not represent the entire population of interest.

In the given scenario, the COC admissions department put a link on their website so that any students that want to try out the program can. The students can then take a survey and say how well they like the new system. This means that the method of collecting data that was used is voluntary response.

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The completed chart for a one-time investment made in the amount of $9,200 is attached below.

For Annually compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.06)¹⁵

A = $9,200 (1.06)¹⁵

A = $22,048.34

For Semi-Annually compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.03)³⁰

A = $9,200 (1.03)³⁰

A = $21,214.29

For Quarterly compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.015)⁶⁰

A = $9,200 (1.015)⁶⁰

A = $20,947.34

For Monthly compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.005)¹⁸⁰

A = $9,200 (1.005)¹⁸⁰

A = $20,812.09

For Weekly compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.0012)⁷⁸⁰

A = $9,200 (1.0012)⁷⁸⁰

A = $20,756.54

For Daily compounded interest:

A = P (1 + i)ⁿ

A = $9,200 (1 + 0.0002)⁵⁴⁷⁵

A = $9,200 (1.0002)⁵⁴⁷⁵

A = $20,726.55

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Image transcribed:

1. Fill in the chart for the following investment.

A one-time investment is made in the amount of $9,200 for 15 years at an APR of 6%.

Compound Interest: A = P (1 + i)", where A is the final amount, P is the principal invested, i is the interest rate per compounding period, and n is the number of compounding periods.

The area of regular pentagon is 758.7 square in.(rounded to the nearest tenth.)

A pentagon is a specific type of polygon with 5 sides and 5 angles. The word “pentagon” is constructed of two words, namely Penta and Gonia, which defines five angles. So in a simplified way it can be said that pentagon is a polygon having 5 sides.

Here is a regular pentagon with side length 21 in.

Area of regular pentagon (A)= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} a^{2}[/tex]

Here a= 21 in

So Area = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} (21)^{2}[/tex] square in.

             = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} 441[/tex]     "

             ≈758.73053 square in

              = 758.7 square in. ( rounded to the nearest tenth).

Hence the area of regular pentagon is 758.7 square in.

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Answer:

37 hours

Step-by-step explanation:

First, we will find the amount of money that Adrienne makes per hour: 98/8, which equals $12.25.

Now, we can find the number of hours it takes to earn $453.25 by dividing it by $12.25:

$453.25 / $12.25 = 37 hours

Answer: 3.04

Step-by-step explanation:

3.04

Answer: 1. 37.5%,

Step-by-step explanation:

1. we can solve this using a proportion, 10/13.75 = 100/x

a. using cross multiplication we get 10x = 1375

b. when you simplify you get x= 137.5, the percent it was of the whole

c. then subtract the original 137.5-100, and you get 37.5%

The rest of the problems follow a similar fashion

Answer:

2x

Step-by-step explanation:

it is x+x or 2x, since if x>=0, the absolute value of x is just x, then we can say that it is x+x without the absolute value symbols. :)

Let x be the number of weeks it will take Paul to save enough money to buy the skateboard.

In one week, Paul earns $5, so in x weeks he will earn 5x dollars.

Since he already has $25 saved, the total amount of money he will have after x weeks is:

5x + 25

To be able to buy the skateboard that costs $85, Paul needs to save up an additional:

85 - 25 = 60

Therefore, we can set up the following equation to find the number of weeks it will take Paul to save up enough money:

5x + 25 = 60

Simplifying and solving for x:

5x = 35

x = 7

Therefore, it will take Paul 7 weeks to save up enough money to buy the skateboard.

The equation that describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard is:

5w + 25 = 85

Answer:

B. $50,000

Explanation:

4%=.04

50,000 x .04=2000

48000/12=4000

She makes $4000 off of her salary each month.  Then because she only gets 4% of her commissions you multiply the 50000 by .04 and you get 2000.  So she gets $2000 in commissions and $4000 off of her salary.

Answer:

1) 3rd one down   1  7/12 ( the one you've selected well doneee)

2)pretty sure its also the 3rd one down ( don't come for me if its wrong)

Step-by-step explanation:

4 1/6 = 25/6

5  3/4= 23/4

25/6   x4=    100/24

23/4  x 6 = 138/24

138/24  - 100/24  = 38/24

divide by 2:

19/12= 1   7/12

Thus, the two digits are 9 and 11.

Two-variable equations are algebraic equations that involve two variables, typically x and y, and describe a relationship between them.

Let's call the tens digit "T" and the ones digit "O". Based on the problem, we know that:

T = 2 + O

Then substitute this equation in 10T + O = 10O + T + 27 i.e.

10T + O = 10O + T + 27

10T - T = 10O - O + 27

9T = 9O + 27

9(2 + O) = 8O + 27

9(2 + O) = 8O + 27

18 + 9O = 8O +  27

9O - 8O =  27 - 18

O = 9

Then,

T = 2 + 9

T = 2 + 9

T = 11

Thus, the two digits are 9 and 11.

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Unit rate of commercials per hour is 12 commercials per hour based on division in mathematics.

We must divide the number of ads by the number of hours in order to determine the unit rate of commercials per hour.

Wendy watched her favourite television programmes for an hour or an hour and a half. There were 18 advertisements running at this time.

So, the unit rate of commercials per hour can be calculated as:

18 commercials ÷ 1.5 hours = 12 commercials per hour

So, it is possible to compute the number of ads each hour as follows: 18 commercials divided by 1.5 hours equals 12 commercials every hour.

Consequently, 12 commercials are broadcast each hour as the unit rate of commercials.

This indicates that while viewing her favorite television programes, Wendy saw 12 adverts every hour on average.

It's crucial to remember that unit rate come in handy when comparing two quantities that are measured using various units. In this instance, we were comparing two different units of measurement: the quantity of advertising and the amount of time in hours. By providing the rate at which the quantity is changing per unit of time, the unit rate enables us to meaningfully compare them.

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Dark chocolate usually takes longer to melt than milk chocolate, as shown by the fact that the median melting time for dark chocolate is higher than the median melting time for milk chocolate.

Based on the given box plots, it is most likely true that after 64 seconds, about half of the brands of milk chocolate are likely to melt, and none of the brands of dark chocolate are likely to melt.

After 259 seconds, none of the brands of milk chocolate are likely to melt, and about a quarter of the brands of dark chocolate are likely to melt.

This conclusion is based on the fact that the box plot for milk chocolate shows a wider spread of melting times, indicating more variation in melting times among the different brands.

while, the box plot for dark chocolate shows a narrower spread of melting times, indicating less variation in melting times among the different brands.

Therefore, Additionally, the median melting time for dark chocolate is higher than the median melting time for milk chocolate, indicating that dark chocolate generally takes longer to melt.

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The expressions, when written as products , would be:

To factor this expression, let's first rearrange the terms:

(81a² - c²) + (6bc - 9b²)

Now, we can see that the first part is a difference of squares, which can be factored as:

(9a - c)(9a + c)

However, the second part (6bc - 9b²) cannot be factored further as a product of binomials. So the expression can be written as:

(9a - c)(9a + c) + 6bc

1 - 25x² + 10xy - y²

This expression remains:

(1 - 5x + y)(1 + 5x + y)

Using the same rule as above.

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Answer:

Step-by-step explanation:

425 - 59 is 366

:)

Answer:

366.

Step-by-step explanation:

In order to identify all the prime numbers less than 200, a person will have to eliminate the multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13.

What are multiples?

   Multiples are products that result from multiplying any given number by whole numbers. They are obtained by multiplying a whole number by another whole number. Prime numbers are natural numbers that are greater than 1 and have no positive divisors other than 1 and the number itself.

 The number 1 is not considered a prime number. In order to identify all the prime numbers less than 200, the person will have to eliminate the multiples of the following additional numbers: Multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13

      The person will have to eliminate the multiples of all these numbers to complete the task of identifying all the prime numbers less than 200.

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The ratio of false positives to false negatives in this scenario is 3.5.

3.5 is the correct answer. False positives are lightning detector activations when there is no lightning in the area. False negatives are lightning detector not activations when there is lightning in the area. To calculate the ratio of false positives to false negatives, divide the false positives (7%) by the false negatives (2%). 7/2 = 3.5. Therefore, the ratio of false positives to false negatives in this scenario is 3.5.

The ratio of false positives to false negatives in this scenario is 3.5.

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Answer:

i took the test :)

Step-by-step explanation:

3.5

The uniform probability distribution is option (c) The probabilities of drawing any individual card in a deck with one draw

The uniform probability distribution is a probability distribution where all outcomes are equally likely. Out of the options provided, (c) The probabilities of drawing any individual card in a deck with one draw is an example of a uniform probability distribution. This is because each card in a deck is equally likely to be drawn, assuming that the deck is well-shuffled.

The other options are not examples of a uniform probability distribution.

(a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO is not a uniform distribution because the probability of reaching 75F is not the same throughout the year, and is influenced by many factors like seasonal variation, climate changes, etc.

(b) A time period in which it rained 25% of the time and did not rain 75% of the time is not a uniform distribution since the probability of rain is not equally likely across the time period.

(d) Flipping a coin two times and recording whether heads or tails is also not a uniform distribution as the probability of getting heads or tails is not the same, it is 0.5 for each individual flip, but the probability of getting two heads, two tails or one head and one tail are different.

Therefore, the correct option is (c) The probabilities of drawing any individual card in a deck with one draw

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The given question is incomplete, the complete question is:

Which would be a uniform probability distribution? a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO  b) A time period in which it rained 25% of the time and did not rain 75% of the time c) The probabilities of drawing any individual card in a deck with one draw d) Flipping a coin two times and recording whether heads or tails

Assuming that we have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5, we can conclude that neither data set is more spread out than the other.

Suppose you have two data sets A and B, with means of 20 and 30, respectively, and the same standard deviation of 5. To determine which data set is more spread out, we need to compare the variance of the two data sets. Since the variance is the square of the standard deviation, we can compare the variances of the two data sets. Using the formula, Var = s², we can calculate the variances of data set A and B.

[tex]Var(A) = (5)^2 = 25\\Var(B) = (5)^2 = 25[/tex]

Both data sets have the same variance, indicating that they have the same amount of spread, or convergence. Therefore, we can conclude that no data set is more spread out than the other.

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Answer:

2) x = 3√5; y = 6;

3) x = 12√2; y = 12;

4) x = 45∘; y = 45∘;

5) x = 60∘; y = 30∘

Step-by-step explanation:

2) Use trigonometry:

[tex] \cos(60∘) = \frac{3}{y} [/tex]

Use the property of the proportion to find y:

[tex]y = \frac{3}{ \cos(60∘) } = \frac{3}{1} \div \frac{1}{2} = \frac{3}{1} \times \frac{2}{1} = 6[/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {y}^{2} + {3}^{2} = {6}^{2} + {3}^{2} = 36 + 9 = 45[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{45} = 3 \sqrt{5} [/tex]

3) Use trigonometry:

[tex] \sin(45∘) = \frac{12}{x} [/tex]

Use the property of the proportion to find x:

[tex]x = \frac{12}{ \sin(45∘) } = \frac{12}{1} \div \frac{ \sqrt{2} }{2} = \frac{12}{1} \times \frac{2}{ \sqrt{2} } = 12 \sqrt{2} [/tex]

Use trigonometry:

[tex] \tan(45∘) = \frac{12}{y} [/tex]

Use the property of the proportion to find y:

[tex]y = \frac{12}{ \tan(45∘) } = \frac{12}{1} = 12[/tex]

4) Use trigonometry:

[tex] \tan(x∘) = \frac{3}{3} = 1[/tex]

x = 45∘

[tex] \tan(y∘) = \frac{3}{3} = 1[/tex]

y = 45∘

5) Use trigonometry:

[tex] \cos(x∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]

x = 60∘

[tex]x = \sin(y∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]

y = 30∘

The function that represents the total cost f(x) to send a letter that is x ounces can be calculated as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

The total cost to send a letter that is 1 ounce is $0.50, and the total cost to send a letter that is 3 ounces is $0.92. Since the postal service calculates the weight to the whole ounce, if we send a 2-ounce letter, we can consider it as sending two 1-ounce letters.

Therefore, the total cost of sending a 2-ounce letter will be twice the cost of sending a 1-ounce letter.

Let f(x) be the total cost to send a letter that is x ounces.

Then,f(1) = 0.50f(2) = 2f(1) = 2(0.50) = 1.00f(3) = f(2) + 0.42 = 1.00 + 0.42 = 1.42

Hence, we can represent the function as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

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The gallons of gas that Aubrey would need to travel 111.54 miles is 7.8 gallons.

In Mathematics, a direct proportion simply refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.

By applying direct proportion to the given information, we have the following mathematical equation:

15 gallons of gasoline = 214.5 miles

X gallons of gasoline = 111.54 miles

By cross-multiplying, we have the following:

214.5x = 15 × 111.54

x = 1,673.1/214.5

x = 7.8 gallons of gasoline.

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Answer:

95.2 square yards

Step-by-step explanation:

8(3) + 2(1/2)(3)(7.2) + 2(1/2)(8)(6.2)

= 24 + 21.6 + 49.6 = 95.2 square yards

By following these steps, you can use the unit circle to define the trigonometric functions of any angle.

Steps: Draw a unit circle,  place the angle, Identify the point of intersection, Define the trigonometric functions.

To use the unit circle to define the trigonometric functions of any angle, follow these steps:
1. Draw a unit circle: This is a circle with a radius of 1, centered at the origin (0, 0) of the coordinate plane.

2. Place the angle: Position the angle in standard position, which means that the initial side (starting side) of the angle is along the positive x-axis and the terminal side (ending side) is formed by rotating the initial side counterclockwise to a certain position.

3. Identify the point of intersection:

Determine the point where the terminal side of the angle intersects the unit circle.

This point will have coordinates (x, y).
4. Define the trigonometric functions:

Using the coordinates (x, y), define the six trigonometric functions as follows:
  - Sine (sin): sin(angle) = y
  - Cosine (cos): cos(angle) = x
  - Tangent (tan): tan(angle) = y/x
  - Cosecant (csc): csc(angle) = 1/y
  - Secant (sec): sec(angle) = 1/x
  - Cotangent (cot): cot(angle) = x/y.

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Answer: $1820

Step-by-step explanation:

Area = Length*Width

Forst we have to solve for the area.

A = 12 * 12

A = 144 ft^2

Next we have to multiply be the cost per square foot.

144 * 35

= $5040

Solve for the area.

A = 14 * 14

A = 196 ft^2

Multiply by the cost per square foot.

196 * 35

= $6860

Lastly subtract both costs:

6860 - 5040 = 1820

Therefore the difference in cost would be $1820.

Hope this helps :)