In a class of students, the following data table summarizes how many students passed a test and complete the homework due the day of the test. What is the probability that a student chosen randomly from the class passed the test? Passed the test Failed the test Completed the homework 16 3 Did not complete the homework 4 6

Therefore , the solution of the given problem of circle comes out to be arc length 3.93 feet.

Every area of the plane that is separated by a specific amount from this additional point makes a circle (center). As a result, it is a curve made up of spots that are separated from one another on the surface. Additionally, it rotates similarly about the centre at every angle. Every collection of endpoints in the confined, two-dimensional sphere of a circle is uniformly spaced apart from the "centre."

Here,

A circle with a radius of 3 feet is equal to its diameter as follows:

=> C = 2πr = 2π(3) = 6π feet

Since there are 360° of angles in a circle's centre, the angle for a 75° curve is:

5/24 of a complete circle is 75/360.

Therefore, the 75° arc's extent is

5/24 × 6π = 5π/4 ≈ 3.93 feet

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Answer:

-14

Explanation:

3 x -3 - 5 = -14

Answer:

-14, -5, 4, and 13

Step-by-step explanation:

For each x value, substitute it for x in the equation.

For the first one where x = -3,

y = 3(-3) - 5

y = -9 - 5

y = -14

So the first one is -14. The next x value is 0

y = 3(0) - 5

y = 0 - 5

y = -5

Second one is -5. The next x value is 3

y = 3(3) - 5

y = 9 - 5

y = 4

Third is 4. The next x value is 6

y = 3(6) - 5

y = 18 - 5

y = 13

So the last one is 13.

Answer:

x = 3

Step-by-step explanation:

15x + 8 and 9x + 26 are corresponding angles and are congruent , then

15x + 8 = 9x + 26 ( subtract 9x from both sides )

6x + 8 = 26 ( subtract 8 from both sides )

6x = 18 ( divide both sides by 6 )

x = 3

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

See below!

Step-by-step explanation:

254, 202, 284, 269, 151, 258, 202

Mean of the data:

\(\displaystyle Mean= \frac{Sum \ of \ data}{number \ of \ data} \\\\Mean = \frac{254+202+284+269+151+258+202}{7} \\\\Mean=\frac{1620}{7} \\\\\boxed{Mean = 231.4}\)

Median of data:

Arrange the data in increasing order.

151, 202, 202, 254, 258, 269, 284

The middle value = 254

So,

Mode in data:

The mode, here, is 202. (occurring 2 times.)

So,

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.

Answer:

million

Step-by-step explanation:

If the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

In this question, we have been that the top 2% of athletes will go pro.

We are required to find the Z-Score that is required to be the top 2%.

Because only 2% of the top is pro then it will be a two tailed test.

The required percentage will be 2/2=1%

The value which we will require to catch up from table = 0.01

Z value = 0.0438

Therefore, if the top 2% of athletes will go pro, then the Z-Score that is required to be 0.0438.

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Answer:

t = (log200)/4 hours

Step-by-step explanation:

10,000 = 50(10)^(4t)

Divide both sides by 50

200 = 10^(4t)

Take the log of both sides

log200 = 4t

Divide both sides by 4

(log200)/4 = t

t = (log200)/4    (exact answer)

t ≈ 0.575257498915995 (numeric approximation)

Answer:

thank for points

Step-by-step explanation:

Answer:

37/60

Step-by-step explanation:

Because 5/12+1/5=37/60

Answer:

C. 1/4

hopes this helped

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{-8}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{(-8)}}} \implies \cfrac{3 +1}{8 +8} \implies \cfrac{ 4 }{ 16 } \implies \cfrac{1 }{ 4 }\)

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

The possible price for the items if the store sells $600 is (c) $40

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

The supply-demand graph

If the store sells $600, then there is a supply worth of $600

The equation of the supply line is calculated as

y = mx + c

Where

c = y = 0

i.e. c = 100

So, we have

y = mx + 100

Using another point on the graph, we have

30m + 10 = 400

So, we have

m = 13

This means that

y = 13x + 100

For a supply of 600, we have

13x + 100 = 600

So, we have

13x = 500

Divide by 13

x = 38.4

Approximate

x = 40

Hence, the possible price for the items is (c) $40

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Answer:

6,561

that's a good number

0 thru 9 is 10 numbers.

Each digit can be 1 of 10 numbers:

Total combinations = 10 x 10 x 10 x 10 = 10,000

Answer: 10,000

Answer:

we see it in our left side of the road

The exact solutions of the given equation in the interval are;

A: x = 0, π/2, π, ³/₂π

We are given the equation as;

sin 4x = –2sin 2x

Writing the equation in standard form gives;

sin 4x + 2sin 2x = 0

Using trigonometric Identity, substitute (sin 4x) with (2sin 2x.cos 2x) to get;

2sin 2x cos 2x + 2sin 2x = 0

Factorize to get;

2sin 2x(cos 2x + 1) = 0

A. sin 2x = 0

The unit circle will give us 3 solutions for 2x as follows;

2x = 0

Thus; x = 0

2x = π

Thus; x = π/2

2x = 2π

Thus; x = π

B. cos 2x = - 1

The unit circle gives 2 solutions for 2x as;

2x = π

Thus; x = π/2

2x = 3π

Thus; x = ³/₂π

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Complete question is;

How do you find the exact solutions of the equation sin4x = −2sin2x in the interval [0, 2π)?

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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The second differences for the relation is -2 which is option A.

To find the second differences, we need to calculate the difference between consecutive differences of the 'y' values in the given relation.

First, let's calculate the first differences:

-9 - (-4) = -5

-4 - (-1) = -3

-1 - 0 = -1

0 - (-1) = 1

-1 - (-4) = 3

-4 - (-9) = 5

Now, let's calculate the second differences:

-5 - (-3) = -2

-3 - (-1) = -2

-1 - 1 = -2

1 - 3 = -2

3 - 5 = -2

The second differences for the given relation are all -2.

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Approximately 456.3 feet of fence to surround the entire circular yard.

Now, For the amount of fencing needed to surround a circular yard, we have to calculate the circumference of the circle, which is the distance around the circle.

Since, The circumference of a circle is,

⇒ C = πd,

where, C is circumference, d is diameter,

Here, the diameter of the circular yard is 145 feet,

So the radius is half of that,

r = 145/2 = 72.5 feet.

So, Using the formula, we can calculate the circumference as:

C = πd

C = 3.14 x 145

C = 456.3 feet

Therefore, Approximately 456.3 feet of fence to surround the entire circular yard.

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The answer is - 17

here, we have to apply BODMAS rule

given ,- 22 + (10) = 15

            = - 22 - 10 + 15

           = -32 + 15

           = - 17

BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions.

B=Brackets

O=Off

D=Division

M=Multiplication

A=Addition

S=Subtraction

The four basic Mathematical rules are addition, subtraction, multiplication, and division.

Basic math skills are those that involve making calculations of amounts, sizes or other measurements. Core concepts like addition, subtraction, multiplication and division provide a foundation for learning and using more advanced math concepts.

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9514 1404 393

Answer:

  gross pay: $1131.97

Step-by-step explanation:

Greg's total time for the week is ...

  9 +8.25 +9.25 +11 +9.75 = 47.25 . . . . hours

Assuming hours over 40 are overtime hours, this represents ...

  47.25 -40 = 7.25 . . . overtime hours

Greg's regular pay is ...

  $22.25/h × 40 h = $890 . . . regular pay

Greg's overtime pay is ...

  $22.25 × 1.5 × 7.25 = $241.96875 ≈ $241.97 . . . overtime pay

Greg's gross pay is the sum of his regular pay and overtime pay:

  gross pay = $890 +241.97 = $1131.97

_____

Alternate solutions

Once we find that Greg's total hours are 47.25, of which 7.25 are overtime hours, we can add half the overtime hours to get 47.25 +(1/2)(7.25) = 50.875. Greg's gross pay will be equivalent to straight-time pay for this number of hours: $22.25 × 50.875 = 1131.96875 ≈ 1131.97.

Yet another way to solve this is to multiply total hours by the overtime pay rate and subtract an amount to make up for the fact that 40 hours are not paid at that rate. If the OT rate is pre-computed, this only takes two mathematical operations: one multiplication and one subtraction.

  OT rate = 1.5 × 22.25 = 33.375

  gross pay = (47.25 h)×($33.375/h) -445 = $1131.97

Answer is A. 101°

Step-by-step explanation:

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

Probability cured of cervical cancer =  18C0 (0.30)⁰(0.70)¹⁸ +  18C1(0.30)(0.70)¹⁷

Step-by-step explanation:

Given:

Patients cured = 30% = 0.30

Number of patients (n) = 18

Probability cured of cervical cancer = P(X≤1)

Probability cured of cervical cancer  = P(X=0) + P(X=1)

Probability cured of cervical cancer =  18C0 (0.30)⁰(0.70)¹⁸ +  18C1(0.30)(0.70)¹⁷

Answer:

1. -5a

Step-by-step explanation:

The definition of combining like terms is adding their coefficients, for example: 2x + 3x = (2+3)x = 5x.

So for this one, -21a+16a = (-21+16)a = -5a.

Answer:

Let C = cost to rent each chairLet T = cost to rent each table 4C + 8T = 732C + 3T = 28 Multiply the 2nd equation by (-2) and then add the equations together   4C + 8T = 73-4C - 6T = -56 2T = 17T = 17/2 = 8.5 Plug this in to the 1st equation to solve for C 4C + 8(17/2) = 734C + 68 = 734C = 5C = 5/4 = 1.25 So the cost to rent each chair is $1.25 and the cost to rent each table is $8.50

Step-by-step explanation:

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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