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The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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Answer:

A.0.059 , B.0.063

Step-by-step explanation:

1. There are 13 clubs in a pack of 52 cards;

Hence the probability of picking the first club is 13/52;

The probability of picking the second is 12/ 51( remember one card has been removed already so the total number of cards decreases).

Probability of picking two clubs in succession is ;

13/52 × 12/51 = 0.0588 = 0.059( to the nearest thousandth).

2. The probability of drawing a club followed by a club with replacement is;

13/52 × 13 /52 = 0.0625 = 0.063( to the nearest thousandth)

Answer:

The next number is 13.

This sequence consists of numbers which are sum of digits of 2^n.

For example: when n= 1, 2^n is 2 which is the first number of sequence.

When n=6, 2^6=64. So,6+4=10 which is sixth number of sequence.

So, when n=8, 2^8=256,So, 2+5+6=13 which will be the eighth number of sequence.

Hope this helps :)

Step-by-step explanation:

The mean is 27.3. and the median is 24.5.

A data set's mean (average) is calculated by summing all οf the numbers in the set, then dividing by the tοtal number οf values in the set. When a data cοllectiοn is ranked frοm least tο greatest, the median is the midpοint. The number that appears mοst frequently in a data set is called the mοde.

Part A:

Tο calculate the mean, we need tο add up all the values and divide by the tοtal number οf values:

15 + 20 + 22 + 24 + 25 + 26 + 30 + 35 + 36 + 60 = 273

273 / 10 = 27.3

Therefοre, the mean is 27.3.

Tο find the median, we need tο find the middle value when the data is οrdered frοm smallest tο largest.

Median = (24 + 25) / 2 = 24.5

Therefοre, the median is 24.5.

Part B:

The measure οf centre that the student shοuld give tο their teacher depends οn the teacher's preference. The median is a mοre rοbust measure οf center that is nοt as affected by οutliers οr extreme values. The median alsο gives a better sense οf the typical value in the data.

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Answer:

you will add $1.53 to every bracelet you make

Step-by-step explanation:

figure out what 85 percent of 1.80 is and then add that to 1.80 for the total price

85% x 1.8 = 1.53 (markup ammount)

1.80 + 1.53 = 3.33 (total cost)

Answer:

F(2) = 3

Step-by-step explanation:

Given the function, F(x) = 5 - x:

Substitute 2 as a value of x in the given function:

F(2) = 5 - 2 =  3.

Therefore, F(2) = 3.

Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

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Answer: 17,160 feet

Step-by-step explanation:

Because I mile = 5280 feet, 3 and 1/4 miles = 3.25 x 5280 = 17160 feet

a)

i) The mean number of refunds given in the summer is 21.

ii) The mean number of refunds given in the winter is 20.

b) The answer to part a) does NOT support the hypothesis.

To calculate   the mean number of refunds given in the summer and winter,we need to find the average of the  values for each season over the given years. Let's calculate  -

a) Mean number of refunds given in the summer  -

(20 + 15 + 10 + 15 + 32 + 34) / 6

= 126 / 6

 = 21

b) Mean number of refunds given in the winter   -

(24 + 10 + 15 + 18 + 26 + 27) / 6

= 120 / 6

= 20

The mean   number of refunds given in thesummer is 21, and the mean number of refunds given in the winter is 20.

b) Based on the calculated means, the answer to part a) does NOT support the hypothesis.

The mean number   of refunds given in the summer (21) is greater than the mean number of refunds given in thewinter (20), indicating that more refunds are   given in the summer than in the winter, contrary to the hypothesis.

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Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

This function gives the same result as the previous function we derived, but it expresses the calculation as a composition of the two separate functions that represent each raise separately.

A function is a set of instructions or statements that perform a specific task or computation and returns a value or result. In programming, a function is typically defined using a specific syntax and can be called or invoked by other parts of the program to carry out a particular operation.

Functions are used in programming to break down complex tasks into smaller, more manageable pieces of code, which can then be reused in multiple parts of the program. They can also help to improve the organization, readability, and maintainability of code.

by the question.

let the worker's original hourly wage be represented by the variable x. Then the function for the worker's new hourly wage when the 20% raise is applied before the $2 raise can be expressed as follows:

\(f(x) = (1.20x) + 2\)

In this function, the expression (1.20x) represents the worker's hourly wage after the 20% raise is applied, and the additional $2 raise is added to this amount to determine the final hourly wage.

We can also express this function using function composition notation. Let g(x) represent the function that applies the 20% raise to the worker's hourly wage and let h(x) represent the function that adds the $2 raise to the resulting hourly wage. Then we have:

\(g(x) = 1.20x\)

\(h(x) = x + 2\)

Using function composition, we can write the function for the worker's new hourly wage as:

\(f(x) = h(g(x)) = h(1.20x) = 1.20x + 2\)

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The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is the sum of the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied.

The final amount momentum of the t-shirt is 17.5 kg⋅m/s, which is calculated by summing the initial momentum of the t-shirt (2 kg⋅m/s) and the change in momentum (15.5 kg⋅m/s) due to the force applied. Momentum is a vector quantity which is equal to the product of the mass and velocity of an object. In this case, the t-shirt has a mass of 4 kg and a velocity of 4 m/s. The force of 15 N applied to the t-shirt for 3 seconds causes the t-shirt to accelerate, increasing its velocity from 4 m/s to 8 m/s. This increase in velocity results in an increase in the momentum of the t-shirt from 2 kg⋅m/s to 17.5 kg⋅m/s. Thus, by calculating the change in momentum due to the applied force, we can determine the final momentum of the t-shirt.

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Answer:

B and E

Step-by-step explanation:

the graph (Justine) shows the line

y = 2x

the line for Velma is

y = 4x

now we need to remember that the slope (inclination) of a line is the factor of x (so, 2 and 4 in the two line equations).

a slope is expressed as y/x and indicates how many units y changes when x changes a certain amount of units (like 1).

as described (and also confirmed by the graph) the x units are minutes, and the y units are meters.

so, as per her slope, Velma moves 4 meters in 1 minute.

and Justine moves 2 meters in 1 meter.

so, Justine is half as fast as Velma.

and therefore, Justine moves a shorter distance than Velma each minute.

Answer:

Step-by-step explanation:

B and E

It is important the order we write the vertices of a triangle in a congruent statement as

B. The order tells us what sides are congruent.

D. The order tells us what angles are congruent.

A vertex (plural vertices) in geometry is the intersection of two straight lines. Three line segments come together to form a triangle. The ends of a triangle's three sides meet at three separate points in a plane to form the triangle, which has three sides with two endpoints each. The vertices of a triangle are the three distinct intersecting points or corners.

Congruent triangles are triangles that are precisely the same size and shape. The word congruent has the sign. When the three sides and three angles of one triangle match the same dimensions as the three sides and three angles of another triangle, two triangles are said to be congruent.

The vertices of a triangle in a congruent statement are important for the ordering. In conclusion, the correct options are B and D.

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Answer:

  (x -14)² +(y -7)² = 1²

Step-by-step explanation:

You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...

  (x -14)² +(y -7)² = 1²

The equation of the line that passes through the given points is            y= -4x+23.

A line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

From the stardard form equation:

Solving the system for equations 1 and 2.

3=5a+b

-13=9a+b * (-1)

3=5a+b

13=-9a-b * (-1)

16= -4a

4= -a

a= -4

If a= -4 from equation 1, you have

3= 5 * (-4)+b

3= -20+b

b=23

Therefore, the line equation is y= -4x+23.

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Answer:

The circle's circumference is approximately 106.81 centimeters.

Explanation:

The formula for the circumference of a circle is C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the circle.

So, for a circle with a radius of 17 centimeters, its circumference can be found by:

C = 2πr

C = 2 x 3.14 x 17

C ≈ 106.81 cm

Therefore, the circumference of the circle is approximately 106.81 centimeters.

Answer:

Area = 240 cm²

Perimeter = 80 cm

Step-by-step explanation:

✔️ Area of the triangle = ½*base*height

base of the triangle = 24 cm

height = 20 cm

Plug in the known values

Area = ½*24*20

= 12*20

Area = 240 cm²

✔️Perimeter of the triangle = sum of all the three sides that make up the triangle

Perimeter = 22 + 24 + 34

= 80 cm

The number of pounds of grapes that can be purchased are 2.45, 2.4, 2.39.

The total amount Lauren's mother can spend has to be less than $15. This is why the inequality sign used is the less than sign - <.

Given this equation: 0.89g + 12.79 < 15.00 , in order to determine the pounds of grapes that can be used, take the following steps:

Combine similar terms

0.89g < 15 - 12.79

Add similar terms

0.89g < 2.21

Divide both sides of the equation by 0.89

g < 2.48g

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The statement that best describes who is correct regarding the rational number 1/12 is given as follows:

A. Jesse is correct, as the rational equivalent is 0.08333, in which the 3 repeats.

The rational numbers are composed by the set of all numbers that can be represented by fractions, such as whole numbers, terminating decimals, or repeating decimals.

The irrational numbers, conversely, are composed by the set of numbers that cannot be represented by fractions, such as non-exact roots and non-terminating decimals.

The fraction in this problem is given as follows:

1/12.

The decimal equivalent is obtained with the division of the numerator 1 by the denominator 12, hence:

1/12 = 0.08333... (3 repeats).

The repeating 3 means that the number is non-terminating, thus Jesse is correct and option A is the correct option.

The problem is given by the image shown at the end of the answer.

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Step-by-step explanation:

speed = distance / time

distance = speed × time

they both have the same speed.

distanceB = distanceA + 4

so,

distanceA = speed × 25 min

distanceB = distanceA + 4 = speed × 35 min

distanceA = speed × 35 - 4

both distanceA expressions must be equal :

speed × 25 = speed × 35 - 4

subtract 25speed from both sides

0 = speed × 10 - 4

add 4 to both sides

4 = speed×10 min

divide both sides by 10 min

4 miles / 10 min = speed

to get the usual miles per hour, we need to multiply numerator and denominator by the same number, so that the denominator is 1 hour = 60 minutes.

as we cab see, we need to multiply by 6/6 :

4/10 × 6/6 = 24/60 = 24 miles per hour.

Answer:

Step-by-step explanation:

Answer:

3:1

Step-by-step explanation:

&%6#46+4636$7$-&&%$44

Answer:

36 green marbles

Step-by-step explanation:

If 60% of the 60 marbles in the bag are green, then the number of green marbles can be calculated as:

Green marbles = 60% x 60 marbles

To simplify this calculation, we can convert 60% to a decimal by dividing by 100:

Green marbles = 0.60 x 60 marbles

Green marbles = 36 marbles

Therefore, Rudy received 36 green marbles.

Answer: 36

Step-by-step explanation:

60 is 6/10 of 100 so if you are taking a percent of 60 just multiply the percentage by 6/10. 6/10 of 60 is 36

The diamond rule creates a system of equation for variables m and n

The possible values of m and n are 8 and 4 or 4 and 8

The question is incomplete; so I will make use of the attached figure

When the diamond rule is applied to the figure, we have the following equations

\(mn = 32\)

\(m + n = 12\)

Make n the subject, in the second equation

\(n = 12 - m\)

The first equation becomes

\((12 - m)m = 32\)

Expand

\(12m - m^2 = 32\)

Rewrite as:

\(-m^2 + 12m - 32 = 0\)

Multiply through by -1

\(m^2 - 12m + 32 = 0\)

Expand

\(m^2 - 4m - 8m + 32 = 0\)

Factorize

\(m(m - 4) - 8(m - 4) = 0\)

Factorize

\((m - 8)(m - 4) = 0\)

Solve for m

m = 8 or m = 4

Recall that:

\(n = 12 - m\)

So, we have:

n = 12 - 8 or n = 12 - 4

Solve

n = 4 or n = 8

Hence, the possible values of m and n are 8 and 4 or 4 and 8 (using the attached figure)

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Answer:  The correct answer is:  " 40 mg ".
____
There are 40 mg ["40 milligrams" of fluoxetine in 10 mL of the solution given.

Explanation:

10 mL * (20 mg/ 5 mL)  =  __?__mg??

Solve for "?" ; our answer:
____

Given:  the concentration:  "20 mg/ 5 mL" ;

we can reduce this "fraction" ratio ; as a "unit rate" ;

that is:  "milligrams per single unit of mL" ;

    by dividing each side of the ratio/fraction by "5":
____

20 mg / 5 mL =  (20 ÷ 5) mg / (5 ÷ 5) mL
                       =   4 mg / mL ;

Now, with this "newly written" form of concentration:

We are asked: How many milligrams (mg) in 10 mL ?

→   10 mL (4 mg / 1 mL) ;  
    →  The units of "mL" cancel out to "1" ; [since:  "mL ÷ mL = 1 "] ;
And we have:
    10 * 4 mg ;

      = (10 * 4) mg ;

     =  40 mg .

____
The answer is:  " 40 mg " .

____
Hope this is helpful to you.  Best wishes!

____

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

(3, -7)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

y = -2x - 1

y = 3x - 16

Step 2: Solve for x

Substitution

Step 3: Solve for y

Step 4: Graph Systems

We can check the solution set to the systems of equations.

Where the 2 lines intersect is the solution set to the systems of equations.

The 2 lines and our algebraically solved solution sets are the same.