The area of a sector is 135π and the arc measure is 216°. What is the radius of the circle?

The number of different ways of distributing the scholarships is 32,760.


consider the situation: fifteen students are competing for 4 Rotary scholarships.
consider each scholarship  is to be a position In which a student assigned.
This is a permutation problem as:
   

A) each student selected from the same set.  
b) No students can be selected twice.
c) The order in which students are assigned to three scholarships.  

Four students  are assigned in 4 activities For scholarships.

Activity A1: select a student from the set of 15 students for giving away the first scholarship.

Activity A2: select a student from remaining 14 students for giving away the second scholarship.

Activity A3: select a  student from remaining 13 students for giving away the third scholarship.

Activity A4: Select a student from remaining 12 students for giving away the forth scholarship.

According to multiplication rule of accounting the number of different arrangements is  A1 X A2 X A3 X A4  
15 X 14 X 13 X 12=32760  

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It's equation in point-slope from is -1/6x+5/2.

An equation is a formula that is express the equality of two equation.

Based on the given condition the formula

M= -1/6

Substitute {m -1/6

                        { X= 9

                        {Y = 1

(Into y= mx+b)

1=-1/6×9+b

Reduce the expression into the Lowest term

1=-1/2×3+b

Write as a single fraction

1=-3/2+b

Rearrange variables to the left side of the equation.

-b= -3/2-1

Now we have to find the denominator and write the numerators above common denominator

-b=-3-2/2

Calculate the sum or difference

-b=-5/2

b=5/2

Substitute {m=-1/6 b=5/2 into y mx+b

Y=-1/6x+5/2

Rewrite the equation of the line

Y= -1/6x+5/2 in point-slope

Y-1 = -x-9/6

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Answer:

Step-by-step explanation:

Step-by-step explanation:

length = 3x

breadth= 7x

area = 1029m2

area = length × breadth

(3x) × (7x)= 1029

now,

3×7=21

7×7=49

(verification 21×49=1029)

so length = 21

breadth = 49

now perimeter = 2(l+b)

=2(21+49)

=2(70)

= 140

so perimeter = 140m

Answer:

The numbers that when multiplied give 15 and when added give -12 are -3 and 5. Multiplying -3 by 5 gives -15, and adding -3 and 5 gives -8.

Explanation:

To find the numbers that when multiplied give 15 and when added give -12, we need to find two numbers that multiply to give -15 and add to give -12. One pair of numbers that satisfy these conditions is -3 and 5. When multiplied, -3 and 5 give -15, and when added, -3 and 5 give -8.

Answer:

Read Below:

12 or 40/9

Unclear, please comment to clarify.

Step-by-step explanation:

Quotient: x, when: [tex]\frac{a}{b} = x[/tex], answer to a division problem.

This could be interpreted 2 ways:

[tex]\frac{(\frac{3}{1/3} )}{3/4}[/tex]

[tex]\frac{9}{3/4}[/tex]

12

or

3 1/3 = 10/3

[tex]\frac{10/3}{3/4}[/tex]

10/3 * 4/3

40/9

The solution of the three variable system will be (- 8, 4, - 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The system of equation are,

⇒ - 5x + y - 4z = 60

⇒ 2x + 4y + 3z = - 12

⇒ 6x - 3y - 2z = - 52

Now,

Since, The system of equation are,

⇒ - 5x + y - 4z = 60

⇒ 2x + 4y + 3z = - 12

⇒ 6x - 3y - 2z = - 52

From option c;

⇒ (x, y, z) = (- 8, 4, - 4)

So, Put x = - 8, y = 4 and z = - 4

We get;

⇒ - 5x + y - 4z = 60

⇒ - 5 × - 8 + 4 - 4 × - 4 = 60

⇒ 40 + 4 + 16 = 60

⇒ 60 = 60

And, ⇒ 2x + 4y + 3z = - 12

⇒ 2 × - 8 + 4 × 4 + 3 × - 4 = - 12

⇒ - 16 + 16 - 12 = - 12

⇒ - 12 = - 12

⇒ 6x - 3y - 2z = - 52

⇒ 6 × - 8 - 3 × 4 - 2 × -4 = - 52

⇒ - 48 - 12 + 8 = - 52

⇒ - 52 = - 52

Thus, The solution of the three variable system = (- 8, 4, - 4).

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Answer:

second option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Red line

using (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (2, 8) ← 2 points on the line

m = [tex]\frac{8-0}{2-0}[/tex] = [tex]\frac{8}{2}[/tex] = 4 , then

y = 4x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (0, 0 ) then

0 = 4(0) + c

0 = 0 + c

0 = c

y = 4x + 0 , that is y = 4x ← equation of red line

Black line

using (x₁, y₁ ) = (0, 10) and (x₂, y₂ ) = (2, 8) ← 2 points on the line

m = [tex]\frac{8-10}{2-0}[/tex] = [tex]\frac{-2}{2}[/tex] = - 1

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = - x + 10 ← equation of black line

A city's citizens cast ballots on whether or not to increase property taxes. There were 8 yes votes and 5 nay votes, in that order. if there were 4955 no votes,The total number of votes was 6,940.

The ratio of yes votes to no votes was 8 to 5, meaning for every 8 yes votes there were 5 no votes.

This ratio can be expressed as a fraction: 8/5.

To calculate the total number of votes, we need to know only the number of no votes, which we know is 4955.

We can then multiply this number by the fraction 8/5. This gives us a total of 6,940 votes.

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Answer:

There are 78 plums and 42 peaches.

Step-by-step explanation:

Let p = number of plums.

Let e = number of peaches.

The value of the plums is 2p.

The value of the peaches is 3e.

"total cost of plims was 30$ more than the cost of peaches"

2p = 3e + 30

"there are 120 fruits some are plums [...] others are peaches"

p + e = 120

We have a system of simultaneous equations.

2p = 3e + 30

p + e = 120

2p = 3e + 30

p = -e + 120

     2p = 3e + 30

+   3p = -3e + 360

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

     5p =         390

p = 78

p + e = 120

78 + e = 120

e = 42

Answer: There are 78 plums and 42 peaches.

Check:

78 plums cost 78 × $2 = $156

42 peaches cost 42 × $3 = 126

$156 - $126 = $30

The plums do cost $30 more than the peaches.

78 + 42 = 120

The total is indeed 120.

The answer above is correct.

Answer: 1

Step-by-step explanation: look at the image attached to show which quadrant is what.

when the x coord is +, it's on the right half of the graph, so by this, quadrants 1 and 4 are possible answers.

when the y coord is +, it's on the top half of the graph, this makes quadrants 1 and 2 possible answers.

look for the consistency, in this case since 1 is the only possible answer between both, the answer is 1

The value of y in the equation 14.25y = 99.75 is C. 7.00.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, the equation is given as:

14.25y = 99.75

Divide through by 14.25

y = 99.75 / 14.25

y = 7

The value of y is 7.

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Answer:

6i-4

Step-by-step explanation:

To simplify the expression 4i+(8-3i) - 12+√-25, you can start by combining like terms.

First, you can combine the terms 4i and -3i to get 1i. You can also combine the constants 8 and -12 to get -4.

So, the expression becomes 1i - 4 + √-25.

Next, you can simplify the square root. √-25 is the same as √(-25) which is the same as √(5*-5), which is the same as 5√(-1). √(-1) is equal to i, so 5√(-1) is equal to 5i.

Therefore, the final simplified form of the expression is 1i - 4 + 5i, which is equal to 6i - 4.

A triangle is closed, with a 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

A triangle is a three-sided polygon that consists of three edges and three vertices.

The labels of the vertices of the triangle, which are generally used in capital letters, are used to name a triangle and we can call the triangle ABC since A, B, and C are vertices of the triangle.

Parts of a Triangle:

A triangle has 3 sides, which consist of ABC, the sides are AB, BC, and CA. The angle formed by any two sides of a triangle is the angle of the triangle, denoted by the symbol ∠.

A triangle has three angles, whose angles of triangle ABC are ∠ABC, ∠BCA, and ∠CAB. These angles are also called ∠B, ∠C, and ∠A.

The point of intersection of any two sides of a triangle is known as a vertex. A triangle has three vertices. In triangle ABC, the vertices are A, B, and C.

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Answer: 52,000

Step-by-step explanation: Because we are rounding to the nearest hundred, we only need to focus on the #'s 4, 3, and 7 in 52,437. So, 3 is less than 5, so we have to round down to 3 (stays the same) and 4 is less than 5 so, we round down to 4 (also stays the same), and since 7 is greater than 5, we can round up to 440. But, 440 is still less than 500, so your final answer should be 52,000.

Answer:

Step-by-step explanation:

81.64

Answer:

Slope is (6/7)

Step-by-step explanation:

6-0= -6

7-0= -7

-6/-7= 6/7

Answer:

Marker = $0.50

Pencil = $0.15

Step-by-step explanation:

The cost of 3 markers and 2 pencils can be represented as 3M + 2P = $1.80.

The cost of 4 markers and 6 pencils can be represented as 4M + 6P = $2.90.

Now that we have our two equations, we can solve for M and P. To do this, we can eliminate one of the variables by multiplying one equation by a constant and adding the two equations together.

For example, if we multiply the first equation by 4 and the second equation by -3, we get:

12M + 8P = $7.20

-12M - 18P = -$8.70

Adding these two equations together, we get:

-10P = -$1.50

Dividing both sides by -10, we get:

P = $0.15

Now that we have found the value of P, we can substitute it back into one of our original equations to find the value of M. If we substitute P = $0.15 into the first equation, we get:

3M + 2($0.15) = $1.80

3M + $0.30 = $1.80

3M = $1.50

M = $0.50

So, the cost of 1 marker is $0.50, and the cost of 1 pencil is $0.15.

The most sensible average to use in this case would be the mode, which is the value that appears most frequently in the data set. In this case, the mode is 2, which appears 9 times in the data set. This means that the most common number of children in a family in the class is 2.

In this case, the most sensible average to use would be the mode, which is the number that appears most frequently in the data set. This is because the mode represents the most common number of children in the families of the children in the class, which is likely to be a more accurate representation of the typical family size in the class than the mean or median.

To find the mode, we first need to count how many times each number appears in the data set. In this case, the numbers 1, 2, 3, and 4 appear in the data set as follows:

1: 7 times

2: 11 times

3: 3 times

4: 1 time

We can see that the number 2 appears most frequently, with a count of 11. Therefore, the mode in this case is 2, and this is the most sensible average to use in this situation.

Answer:

0.5

Step-by-step explanation:

A coefficient is a number that multiplies an unknown

The solution to the equation eˣ + 1 = 2ˣ + 2 is x = 1.2

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

eˣ + 1 = 2ˣ + 2

Split to system of equations

This gives

y = eˣ + 1

y = 2ˣ + 2

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the curves intersect at (1.2, 4.3)

This means that

x = 1.2 (approximated)

Hence, the solution is x = 1.2

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The area of centroid of the region in the first quadrant bounded by the given curves. y = x6, x = y6 is 17 units.

The centroid can be found if we will integrate the result obtained by subtracting the given two functions .

∫ f(x) - g(x) dx

The limits will be a and b where a = 0 and b =1.

f(x )= x⁶

g(x) =y⁶

= ∫ x⁶ -  y⁶dx

=∫ x⁶dx -  ∫  y⁶dx

= 1/7 x⁷ -  1/7 x⁷  

Now since limits are 0 and 1 ,

1/7 1⁷ -  1/7 0⁷  

=17 units

The central point of any geometric figure is known as centroid.

Different figure have different centroid and the all have unique properties.

Integration is a branch of calculus which means to add things up to form a whole.

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Answer:

3/5

Step-by-step explanation:

AB = AC · cos A

18 = 30 · cos A

cos A = 18/30

cos A = 3/5

The charge on the 150 nF capacitor is 3200 nF, the charge on the 120 nF capacitor is 3200 nF, the total energy stored in the network is [tex]76.8 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 150 nF capacitor is [tex]34.1 \times 10^{-6} \mathrm{~J}[/tex], the energy stored in the 120 nF capacitor is [tex]42.67 \times 10^{-6} \mathrm{~J}[/tex], the potential difference across the 120 nF and 150 nF capacitor is 21.33V, 26.67 V.

The equivalent capacitance when the capacitors are connected in series is,

[tex]$$C_{\text {eq }}=\left(\frac{1}{C_1}+\frac{1}{C_2}\right)^{-1}=\left(\frac{1}{150 \mathrm{nF}}+\frac{1}{120 \mathrm{nF}}\right)^{-1}=66.67 \mathrm{nF}$$[/tex]

the charge on each capacitor remains the same because they connected in series. Hence, the charge on each capacitor is,

Q=C V=(66.67 nF) (48 V)=3200 nC

the charge on the 150 nF capacitor is  [tex]Q_{150}[/tex]=3200 nC

the charge on the 120 nF capacitor is [tex]Q_{120}[/tex]=3200 nC

the total energy stored in the network is,

[tex]$$$U=\frac{Q^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(66.67 \times 10^{-9} \mathrm{~F}\right)}=76.8 \times 10^{-6} \mathrm{~J}$$[/tex]

the energy stored in the 150 nF capacitor is,

[tex]$U=\frac{Q_{150}{ }^2}{2 C}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(150 \times 10^{-9} \mathrm{~F}\right)}=34.1 \times 10^{-6} \mathrm{~J}$$[/tex]

the energy stored in the 120 nF capacitor is,

[tex]$U=\frac{Q_{150}{ }^2}{2 \mathrm{C}}=\frac{\left(3200 \times 10^{-9} \mathrm{C}\right)^2}{2\left(120 \times 10^{-9} \mathrm{~F}\right)}=42.67 \times 10^{-6} \mathrm{~J}$$[/tex]

the potential difference across the 150 nF capacitor is,

[tex]$$V_{150}=\frac{Q_{150}}{C_{150}}=\frac{3200 \times 10^{-9} \mathrm{C}}{150 \times 10^{-9} \mathrm{~F}}=21.33 \mathrm{~V}$$[/tex]

the potential difference across the 120 nF capacitor is,

[tex]$$V_{120}=\frac{Q_{100}}{C_{120}}=\frac{3200 \times 10^{-9} \mathrm{C}}{120 \times 10^{-9} \mathrm{~F}}=26.67 \mathrm{~V}$$[/tex]

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QN:-- For the capacitor network shown in (Figure 1) , the potential difference across ab is 48 V .

Find the charge on the 150 nF capacitor.

Find the charge on the 120 nF capacitor.

Find the total energy stored in the network.

Find the energy stored in the 150nF capacitor.

Find the energy stored in the 120nF capacitor.

Find the potential difference across the 150 nF capacitor.

Find the potential difference across the 120 nF capacitor.

When 12 / (y -x) is a denominator of x - y the numerator will be

The problem involves division of fractions

The fractions is a number type that has two major divisions,

the numerator : the number at the top

the denominator: the number below or at the bottom

The division of the fraction: In this case the denominator is the divisor

= (x - y) ÷ 12 / (y -x)

inverting the divisor of the fraction

= (x - y) *  (y -x)/12

= { (x - y) * (y -x) } / 12

the numerator is (x - y)(y -x)

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Null Hypothesis - H0: There is no linear relationship between the weight of pinknits and the number of gogles.

Alternative Hypothesis - Ha: There is a linear relationship between the weight of pinknits and the number of gogles.

To explain the concept behind this question we first need to know about the principle of correlation.

Correlation - It is a measure of comparison of two quantities by which we compute that which two quantities are linearly equal means that if we change one quantity the other will also change at a constant rate.

This principle simply makes a relationship without causing any effect on the quantities.

Now according to the question, we can see that,

Therefore, from the data that scientists predicted, we can conclude that,

Null Hypothesis - H0: There is no linear relationship between the weight of pinknits and the number of gogles.

Alternative Hypothesis - Ha: There is a linear relationship between the weight of pinknits and the number of gogles.

Option 4 is correct.

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A group of scientists discovered a small creature at the bottom of the ocean that they called a "piknit". When this interesting creature dies, it explodes itself into a number of baby piknits called gogles. The scientists randomly selected 20 piknits from the sea-floor and measured their respective weights in grams. After the piknits died they counted the number of gogles that each piknit produced. They wanted to know if the weight of the piknits can be used to predict the number of gogles.

What are the appropriate null and alternative hypotheses?

Group of answer choices

H0: There is no linear relationship between the weight of piknits and the number of gogles

Ha: There is a negative linear relationship between the weight of piknits and the number of gogles

H0: Weight of piknits is a useful predictor for the number of gogles

Ha: Weight of piknits is not a useful predictor for the number of gogles H0: There is a linear relationship between the weight of piknits and the number of gogles

Ha: There is no linear relationship between the weight of piknits and the number of gogles

H0: There is no linear relationship between the weight of piknits and the number of gogles

Ha: There is a linear relationship between the weight of piknits and the number of gogles

The probability that the hotel receives at least one of the defective sets is 0.571 or 57.1%.

The probability of receiving at least one of the defective sets is calculated using the formula for the binomial distribution. The formula has 3 variables: the number of trials (n) being 8, the probability of success (p) being 0.286 (4 defective sets divided by 14 total sets) and the number of successes (k) being 1. We calculate the probability by plugging the variables into the formula and summing the probabilities of all the k values from 1 to 8. This gives us a probability of 0.571 or 57.1%.

P(k≥1) = Σ P(X=k)

       = P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8)

       = 0.286^1.0 x 0.714^7.0 + 0.286^2.0 x 0.714^6.0 + 0.286^3.0 x 0.714^5.0 + 0.286^4.0 x 0.714^4.0 + 0.286^5.0 x 0.714^3.0 + 0.286^6.0 x 0.714^2.0 + 0.286^7.0 x 0.714^1.0 + 0.286^8.0 x 0.714^0.0

       = 0.571 or 57.1%

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The complete table is

Length of fencing(feet)   1             3          6            9            10

cost($)                               9         27         54          81           90

What is fencing of a wall?

A fence is a building used to enclose a space, usually outdoors. It is often made of posts joined by boards, wire, rails, or nets. In contrast to a wall, a fence lacks a firm basis over its whole length.

The cost of fencing 3 feet is $27.

Applying unitary method:

The cost of fencing 1 feet is $27/3 = $9.

The  cost of fencing 6 feet is $(6×9) = $54

The  cost of fencing 10 feet is $(10×9) = $90.

$27 needs to make a fencing with length 3 feet.

$1 needs to make a fencing with length 3/27 feet = 1/9

$9 needs to make a fencing with length (1/9)× 9 = 1 feet.

$81 needs to make a fencing with length (1/9)× 81 = 9 feet.

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In 35mm single-lens camera the images produce negative that can be used as backups instead of using a digital camera.

A single-lens reflex camera (SLR) is a type of camera that typically employs a mirror and prism system (hence the word "reflex" from the reflection of the mirror) and allows the photographer to look through the lens to preview the exact scene that will be photographed.

Most SLR cameras have a mirror that swings out of the way of the light when the shutter button is depressed, allowing light to reach the light receptor and capturing the image.

The roof pentaprism found in the optical path between the reflex mirror and viewfinder of most SLR cameras enables upright and laterally accurate vision.

A camera's manual focus adjustment or an autofocus system's automated focus adjustment are both options.

The images produce negative that can be used as backups in 35mm single-lens camera instead of using a digital camera.

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4000 N  is the work done .

In math, what is a distance?

The length of the segment of the line that connects the supplied two points determines the distance between them. The length of the shortest line segment connecting a point to a line represents the distance between them.

                               Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending point, distance can be defined as the amount of ground it has traveled.

m = 80 kg

d = 5m

g = 10 m/s²

work done = force × distance

                   = mgh

                    =  80 × 10 × 5

                    =  4000 N

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