A friend proposes a game: Spin the spinner twice and if the sum is even, then you win. Let's say my spinner lands on 2 for the first spin, and then lands on 3 for the second spin.
My calculated sum would then be 5. However, if the sum is odd, then your friend wins. Is this a fair game?

The measure of the central angle θ in degrees and then multiply by 1/(2π). Then that result by πr²

We will use the following points to find the area of the sector;

First of all, the angle that is formed in a full rotation is 2π.

The area of a circle is given by the formula; A = πr²

The central angle is given by the angle symbol θ. Thus, we have to multiply the area of the circle by a factor θ/2π

Thus, the area of a sector is given by the formula;

A = (θ/2π) * πr²

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All measures and angles of sides and angles are:

c = 20

D ≈ 69.2

θ = 37.34°

θ = 120°

c = 11

D = 77.6

θ = 92.87°

c = 13

D = 63.5

θ = 90°

1) We are given;

m<C = 32°

a = 28

b = 13

Since two sides and the opposite angle of an unknown side are given, then we can use law of cosine which is expressed as:

c = √(a² + b² - (2ab*cos C)

Thus;

c = √(18² + 17² - (2*8*17*cos 32°)

c ≈ 19.55

c ≈ 20

2) The length of the longer diagonal of a rhombus is found by the  formula: D = 2a*cos 0.5θ

Where:

D - Length of the larger diagonal.

a - Side length.

θ - Measure of the smaller angle, in degrees.

We are given; a = 36 and θ = 32°. Thus;

D = 2 * 36 * cos (0.5 * 32°)

D ≈ 69.2

3) Using the length of diagonal of rhombus formula as above gives;

D = 2a*cos 0.5θ

We are given;

D = 36 and a = 34

Thus;

36 = 2 * 34 * cos 0.5θ

cos⁻¹36/68 = 0.5θ

18.67 = 0.5θ

θ = 18.67/0.5

θ = 37.34°

4) Applying the law of cosine, we can find the larger angle as;

18² = 10² + 12² - (2 * 10 * 12 * cos θ)

324 = 244 - (240 * cos θ)

244 - 324 = (240 * cos θ)

-120/240 = cos θ

θ = cos⁻¹(-0.5)

θ = 120°

5) By using Law of cosines, we have;

c = √(12² + 14² - (2 * 14 * 12 · cos 38°)

c ≈ 11

6) Still using formula in number 2, we have;

D = 2a*cos 0.5θ

D = 2*40*cos(0.5*28)

77.6

7)  Applying the law of cosine, we can find the larger angle as;

14² = 8² + 12² - (2 * 8 * 12 * cos θ)

196 = 208 - (192 * cos θ)

12 = (240 * cos θ)

12/240 = cos θ

θ = cos⁻¹(-0.05)

θ = 92.87°

8) Still using the using the cosine approach, we have;

We are given;

m<C = 50°

a = 14

b = 15

Since two sides and the opposite angle of an unknown side are given, then we can use law of cosine which is expressed as:

c = √(a² + b² - (2ab*cos C)

Thus;

c = √(14² + 14² - (2*8*17*cos 32°)

c ≈ 12.702

c ≈ 13

9) The length of the longer diagonal of a rhombus is found by the  formula: D = 2a*cos 0.5θ

Where:

D - Length of the larger diagonal.

a - Side length.

θ - Measure of the smaller angle, in degrees.

We are given; a = 34 and θ = 42°. Thus;

D = 2 * 34 * cos (0.5 * 42°)

D ≈ 63.5

10) Applying the law of cosine, we can find the larger angle as;

26² = 22² + 14² - (2 * 22 * 14 * cos θ)

676 = 680 - (616 * cos θ)

4 = (616 * cos θ)

4/616 = cos θ

θ = cos⁻¹(0.065)

θ = 90°

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The equation that is equivalent to the equation 4x + 41 = x + 5 is 3x + 41 = 5

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

/4x+41=x+5

Express the equation properly

So, we have the following representation

4x + 41 = x + 5

Subtract the variable x from both sides of the equation

So, we have the following representation

-x + 4x + 41 = x + 5 - x

Evaluate the difference

So, we have the following representation

3x + 41 = 5

The above equation is equivalent to the equation 4x + 41 = x + 5

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Answer:

Inequality Form: g≤15

Interval Notation: (−∞,15]

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Detailed explanation and solution is available in the photo. I wish you success. If there is something you do not understand, please do not hesitate to ask.

The lowest coMmon denominator of 9, 15, and 21 is 315 (3•3•5•7). These 3 bells ring together every 315 minutes after 5:45 pm.

45 min • 1/60 hr/min = 0.75 hr

5:45 = 5 + 0.75 hr = 5.75 hr

5:45 pm to 10:00 am next day in minutes is:

available time = (12 - 5.75 + 10) hr • 60 min/hr

available time = 16.25 • 60 = 975 min

So as much as 975 min are available for the synchronized or periodic ringings.

Number of simultaneous ringings in 975 min:

975/315 = 3.1

3•315 = 945 min

975 - 945 = 30 mins after 3rd ringing after 5:45 pm.

315 min = 315•1/60 hr/min = 5.25 hr. 5.25 hr between simultaneous rings.

The next 3 ringings after 5:45 pm (5.75 hr) are at 5.75 + 5.25 hr = 11:00 pm, and then 11.0 pm + 1 = 12 am + 4.25 = 4.25 am (4:15 am), and then 4.25 + 5:25 hr = 9:30 am. There are 30 minutes left to 10:00 am (975 mins after 5:45 pm), so a 4th ringing does not have enough time.

ANSWER: Including 5:45 pm, the bells ring together at 11:00 pm, 4:25 am, and 9:30 am — a total of 4 times

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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If the H.C.F of Q and R is 4056,the value of a is 13

HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).

Q = 2³ × 3 × a³ and R = R=2⁴ × 3² × a²

This means that Q = 24a³ and R = 144a²

The common factors between 24 and 144 are: 1,2,4,6,12 and 24.

And the common factors between a³ and a² are : a, a²

Therefore the highest common factors are 24 and a² = 24a²

4056 is given as the H.C.F

therefore 4056 = 24a²

divide both sides by 24

a² = 169

Therefore a = √169 = 13

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Answer:

[tex]c^{9}[/tex][tex]d^{15}[/tex]

Step-by-step explanation:

Answer:9

Step-by-step explanation:

13r-17=21r-89

subtract 13r from 21r so your left with

-17=8r-89

Then add 89 to -17 then you get

72=8r

divide

r=9

Answer:

The first figure, fourth and fifth!

First one has 24.

Second one has 30.

Third has 16.

Fourth has 24.

Fifth has 24.

Step-by-step explanation:

Hope it helps!

(A)  120 is 25% of 500.

(B) 25% of 120 is 30.

(C) 6 is 5 percent of 120

(D) 120 is 500 percent of 25

Percentage is a part of the whole number. It is denoted by % sign.

1 %= 1/100.

(A)

Let 120 is 25 % x,

125 = (25/100) x

x = 500

(B)

Let 25% of 120 is x,

(25/100) x 120  = x

x = 30

(C)

Let 6 is x percent of 120.

6= (x/100) 120

x = 5

(D)

Let 125 is x percent of 25.

125 = 25 (x/100)

x = 500

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If a skateboard originally cost $119.50, what was the final price after all discounts had been taken? $62.74

This refers to the term that is used to describe the deduction of price from the usual price of an item.

Based on the given conditions, formulate:

Calculate the sum or difference: 119.5 x ( 1 - 25% ) x ( 1 - 30%)

Calculate the sum or difference: 119.5 x 0.75 x (1-0.3)

Calculate the product or quotient: 119.5 x 0.75 x 0.7

Calculate the product or quotient: 89.625 x 0.7

Round the number: 62.74

Therefore, the final price after all discounts had been taken is $62.74

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Answer: A rational number is not always an integer, but an integer is ALWAYS an rational number

Step-by-step explanation:

-> A rational number is a number that can be expressed as the ratio of two integers. For example, 1/2, 3/4, and 5/6 are all rational numbers.

However, a rational number is not always an integer. An integer is a whole number, whereas a rational number can be a fraction with a non-zero denominator.

-> For example, 1/2 is a rational number, but it is not an integer because it is a fraction with a non-zero denominator. On the other hand, 1 is a rational number and an integer because it can be expressed as the ratio of two integers (1/1).

So in summary, a rational number is not always an integer, but all integers are rational numbers.

Answer:

18.5 cups

Step-by-step explanation:

There are 2 cups in 1 pint, so 9 1/4 pints is equal to 18.5 cups.

Hope this helps and if you have any more questions just ask in the comments

Jane will have traveled a average of 7 miles, so she will be 5 miles away from her starting point. This can be approximated to 5.00 miles, which can be rounded to the nearest hundredth.

1. Jane has walked north for 3 miles.

2. Jane has turned 45 degrees to the right.

3. Jane has walked 4 miles after turning 45 degrees to the right.

4. Jane is now 5 miles away from her starting point. This can be approximated to 5.00 miles, which can be rounded to the nearest hundredth.

Jane has walked 3 miles north and then turned 45 degrees to the right and walked 4 more miles. This means that she has traveled a total of 7 miles from her starting point. To calculate the exact distance, we use trigonometry. We can approximate the distance to 5.00 miles, which can then be rounded to the nearest hundredth. This means that Jane is 5 miles away from her starting point.

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The statement that is true is that the lowest score in section 2 is higher than the highest score in either of the other sections.

Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15.

To determine this, we can look at the boxplots. In section 1, the lowest score is 15 and the highest score is 27. In section 2, the lowest score is 24 and the highest score is 32. In section 3, the lowest score is 20 and the highest score is 28.

Since the lowest score in section 2 (24) is higher than the highest score in either of the other sections (27 and 28, respectively), this statement is true. Therefore the correct option is b.

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The answer choice which best describes the solution of the given equation as represented above is; The equation has no solution.

It follows from the task content that the answer choice which best reflects the solution of the equation be determined.

As evident in the task content; the given equation is;

-6x = -5 ( x - 1 ) - x

-6x = -5x + 5 - x

Therefore, we have that;

-6x = -6x + 5

Add 6x both sides of the equation so that we have;

-6x + 6x = 5

0 = 5......which does not hold true.

Hence, since 0 ≠ 5; it follows that the given equation has no solution.

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Answer:

a. Yes, you should make the investment.

b. The NPV of the opportunity is $49,719.

c. Yes, you should invest. The NPV of the opportunity with a 10% discount rate is $55,000.

Step-by-step explanation:

The value of expression putting indicated value is -2,4,1.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is [tex]\frac{x}{4}[/tex] .

Now put x=-8 into [tex]\frac{x}{4}[/tex] then,

=> [tex]\frac{-8}{4}[/tex] = -2.

Now put x=16 into [tex]\frac{x}{4}[/tex] then

=>  [tex]\frac{16}{4}[/tex] = 4.

Now put x= 4 into    [tex]\frac{x}{4}[/tex] then

=> [tex]\frac{4}{4}[/tex] = 1.

Hence the value of expression putting indicated value is -2,4,1.

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Answer: Dear User, I have attached my answer in a PNG file because Brainly doesn't let me use the symbols required for this answer.

Step-by-step explanation:

Answer: 1 and 13/15 pounds

Step-by-step explanation:

By adding 1.5 and 0.3 we can see that the worker has 1.8 lbs. Converted to a fraction, this is 1 4/5. This can be multiplied by 3/3 to reach 1 and 12/15. He needs 3 and 10/15. By doing this we can see that the worker needs 1 and 13/15 lbs.

The unit cost of postcard and envelope are given as 6 and 8 cents respectively.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

Suppose the cost of postcard be $x.

Then, the cost of envelope is x + 0.02.

As per the question, the following question can be written for the cost as,

15x + 10(x + 0.02) = 1.70

⇒ 25x = 1.50

⇒ x = 0.06

Thus, the cost of envelope is 0.06 + 0.02 = $0.08.

Which is equivalent to 8 cents.

Hence, the cost of each postcard and the envelope are obtained as 6 and 8 cents respectively.

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Answer:

y=-1/4+1

Step-by-step explanation:

Slope Intercept Form: y=mx+b

the y-intercept is b and is where the line passes through on the y-axis whether it is negative or positive.

In this case, the y-intercept is 1

Plug into the equation

y=-1/4+1

Hope this helps :)

If a slice of chocolate fudge cake contains 7.25 grams of sugar, thr grams of sugar in 2/3 of a slice of chocolate is 4 5/6 grams of sugar

In general, the term proportion refers to a part, share, or amount that is compared to a whole.

Using the definition of proportion, two ratios are in proportion when they are equal.

The number of grams of sugar in the chocolate is calculated using proportions

If a slice of chocolate fudge cake contains 7.25 grams of sugar

1 slice = 7.25 grams of sugar

2/3 slice  = ?

cross multiplying

1 * ? =  2/3 * 7.25

? = 29/6

? = 4 5/6 grams of sugar

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The average annual rate of change in the population density from 2000 to 2009 will be 1.9.

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;

The table shows the population density for the state of Texas in various years.

Now,

Since, Population in year 2000 = 79.6 people per square mile.

Population in year 2009 = 96.7 people per square mile.

Hence, Change in population density between year 2000 and 2009 is:

⇒ 96.7 - 79.6 = 17.1

And, Total number of year between year 2000 and 2009 is:

⇒ 2009 - 2000 = 9

So, Substituting the values in formula, we get;

⇒ Average rate of change = 17.1 / 9

                                         = 1.9

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The types of triangles are -

a) Triangle ABE is a right-angled triangle.

b) Triangle BEC is an isosceles triangle.

c) Triangle DEF is an equilateral triangle.

d) Triangle CDF is a scalene triangle.

In general, triangles fall into one of two categories -

Triangles determined by the measurements of their sides - Scalene Triangle, Isosceles Triangle, Equilateral Triangle

Triangles based on their inner angles - Acute Triangle, Obtuse Triangle, Right Triangle

According to the diagram -

a) Triangle ABE has angle A which is 90°. Angle B and Angle E will be 45° each, since the sum of interior angles of the triangle should result in 180°. So, it can be classified as a right-angled triangle.

b) Line segment EC=EF+FC=5+2=7. Now, the line segment BE is also having the measurement of 7. Since, both the sides of triangle BEC are equal, hence it falls under the category of isosceles triangle.

c) Triangle DEF has all the sides equal. Hence, it is an equilateral triangle.

d) In triangle CDF, only one of the side DF=5 is known and other two sides are unknown. The sides are not marked equal and the three interior angles are also unknown. Therefore, this triangle is a scalene triangle.

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The statement that best describes Juliet's distance from her home from the graph is; C) It is decreasing in the interval 3 < x < 4 hours.

An interval on a graph is defined as a section of the x-axis that is usually examined to see whether or not the graph is increasing or decreasing throughout that section.

Now, a graph is said to be decreasing through an interval if the x-value increases as the y-value decreases. However, the graph is said to be increasing if the x-values increases as the y-values increase.

Now, looking at the given graph, we can say that between the intervals of 3 < x < 4, the graph is decreasing as it will have a negative slope. However between the intervals of 4 < x < 5, the graph is increasing as it will have a positive slope.

Thus, we can conclude that the correct option is Option C.

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Answer:

Step-by-step explanation:

The quarter fall a distance of 22 feet

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

Top of the well = 0 feet

Location of the quarter after the fall = -22 feet.

The distance fell by the quarter is then calculated as

Distance = Top of the well - Location of the quarter after the fall

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

Distance = 0 + 22

Evaluate

Distance = 22

Hence, the distance is 22 feet

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Answer:

there are 4.5 pints in a quart

Step-by-step explanation:

There are 2 pints in a quart so just divide 9 by 2 and you get 4.5

Answer: 9 pints = 4.5 quarts

Step-by-step explanation:

1 pint = 0.5

9 pints = 0.5 x 9 = 4.5