An angle of 2. 5 radians is subtended by an arc of a circle with a radius of 10cm. What is the length, in cm, of the arc? ​

If there are 5 girls, 6 boys and some adults in a classroom and probability that a girl is chosen is 1/3 , then the probability of an adult being chosen is  4/15 .  

The number of adults in unknown .

So let "n" denote the number of adults.

the number of girls in the room is = 5 girls ;

the number of boys in the group is = 6 boys ;

So , the total number of people to choose from will be =  5 + 6 + n  ;

= 11 + n ;

The probability of picking the girl from this group will be = 5/(11+n) ;

the probability of girl being selected is = 1/3,

Equating both the probabilities ,

we get ; 5/(11+n) = 1/3

On Cross multiplying we have :  11 + n = 15

which means ⇒ n = 4 and number of adults is = 4 ;

So ,the total number of people is = 11 + 4 = 15.

So , The probability of picking adult is = 4/15.

The given question is incomplete , the complete question is

There are 5 girls, 6 boys and some adults in a classroom. The probability that a girl is chosen is 1/3. What is the probability of an adult being chosen ?

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1. The probability of getting heads on the first two and then a tail on the third is 1/8.

2. The probability of not getting a clay pot or a cactus is  1/2.

3. The probability of getting the same number twice is 1/36.

4. The probability of getting at least two heads is

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

1. The probability of getting a head P(H) = 1/2 and the probability of getting a tail P(T) = 1/2.

Therefore, The probability of getting heads on the first two and then a tail on the third is,

= (1/2)×(1/2)×(1/2).

= 1/8.

2. The probability of getting a clay pot is 1/4 and the probability of getting a cactus is 1/4.

So, The probability of getting a clay pot or a cactus is 1/4 + 1/4.

= 2/4.

= 1/2.

Therefore, The probability of not getting a clay pot or a cactus is,

= 1 - 1/2.

= 1/2.

3. Suppose we get a number 1 on the first throw and we know its probability is 1/6,

Therefore, The probability of getting 1 again is also 1/6.

So, The probability of getting the same number twice is,

= (1/6)×(1/6).

= 1/36.

4. The probability of getting at least two heads is,

P(HHT) + P(HHH).

= (1/2)×(1/2)×(1/2) + (1/2)×(1/2)×(1/2).

= 1/8 + 1/8.

= 2/8.

= 1/4.

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The equivalent expression is (a)  1 + √5

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

√5 + 1

The additive property of equality states that

a + b = b + a

using the above as a guide, we have the following:

√5 + 1 = 1 + √5

This means that the equivalent of √5 + 1 is 1 + √5

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Complete question

Which of the following is equivalent to √5 + 1

O A 1 + √5

OB. 1-√√5

O C. √5-1

OD √5-2

The linear speed of the tip of this second hand as it passes around the clock face is 0.84 cm/ seconds

It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).

The formula and procedure we will use to solve this exercise is:

Where:

Information about the problem:

As the distance in the problem will be the circumference of the circle that second-hand makes in one complete revolution, we have:

Length of a circle = 2*pi*r

Length of a circle = 2*3.14*8

Length of a circle = 50.24 cm

The time it takes to complete one full revolution by second hand is 60 seconds, so applying the velocity formula with this time, we get:

speed = x /t

speed  = 50.24 cm/ 60 seconds

speed  =  0.84 cm/ seconds

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Answer: 3 dogs

Step-by-step explanation:

Each dog eats 1/6 cans of food

Stanley uses a total of 1/2 cans of food

[tex]\frac{1}{2}[/tex]  / [tex]\frac{1}{6}[/tex] = 1/2 * 6

= 3 dogs

Answer:

x = 200

Step-by-step explanation:

[tex]\frac{x}{5} = \frac{120}{3}[/tex]

so you cross multiply

5 × 120 = 600

x × 3 = 3x

so

3x = 600

x = 200

She will lay sod over area of 925.02 square feet of 3/4 of circle and triangle.

What is a circle?

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident. A circle is also termed as the locus of the points drawn at an equidistant from the center. The distance from the center of the circle to the outer line is its radius. Diameter is the line which divides the circle into two equal parts and is also equal to twice of the radius.

The equation of circle in the plane is given as:

(x-h)^2 + (y-k)^2 = r^2

where (x, y) are the coordinate points

(h, k) is the coordinate of the center of a circle

and r is the radius of a circle.

and Area of circle = πr²

Now,

Sod will be laid over=3/4*circle + on triangle

=3/4*πr^2+1/2*base*height

=3/4*3.14*18*18+1/2*18*18

=763.02+162

=925.02 square feet

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Answer:

Step-by-step explanation:

Prime factorization is the process of expressing a number as the product of its prime factors. To find the prime factorization of a number, you can use the following steps:Divide the number by the smallest prime factor (2) and write the result.Divide the quotient from step 1 by the next smallest prime factor (3) and write the result.Repeat step 2 with each successive prime factor until the quotient is 1.For example, to find the prime factorization of 60:60 / 2 = 30 -> 2

30 / 2 = 15 -> 2 * 2 = 4

15 / 3 = 5 -> 4 * 3 = 12

5 / 5 = 1 -> 12 * 5 = 60The prime factorization of 60 is 2 * 2 * 3 * 5To find the greatest common factor (GCF) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the GCF as the product of the prime factors that are common to both numbers, each raised to the lowest power that occurs in both factorizations.For example, to find the GCF of 24 and 40:Prime factorization of 24 = 2^3 * 3

Prime factorization of 40 = 2^3 * 5The GCF is 2^3 = 8To find the least common multiple (LCM) of two numbers, you can use the following steps:Write the prime factorization of each number.Write the LCM as the product of the prime factors of each number, each raised to the highest power that occurs in either factorization.For example, to find the LCM of 24 and 40:Prime factorization of 24 = 2^3 * 3

Prime factorization of 40 = 2^3 * 5The LCM is 2^3 * 3 * 5 = 120Alternatively, you can use the formula LCM(a, b) = (a * b) / GCF(a, b)Please note that this is a method for finding the prime factorization and GCF/LCM of small numbers. For larger numbers, it is more efficient to use a specific algorithm or software.

Answer:The mathematical expression -4(-3t-10t-7)-t can be simplified to -4( -13t - 7 ) - t . This can be simplified even further by combining like terms to -4( -13t - 7) - 1t .

Step-by-step explanation:

She buys 15 bags of candy.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be one degree.

Given that the number of bags of taffy was 5 more than the number of bags of caramels.

The Taffy bags weigh 8 ounces each, and the caramel bags weigh 16 ounces each.

The total weight of the bags of candy was 400 ounces.

Consider c be the total number of Carmel candy bags and t the total number of taffy bags that Ariel bought.

t = 5 + c

Then, we have:

8t + 16c = 400

8(5 + c) + 16c = 400

40 + 8c + 16c = 400

24c = 360

c = 15.

Hence, she buys 15 bags of candy.

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Answer: Solving a compound inequality in compact form is similar to solving a simple inequality in the sense that both involve isolating the variable on one side of the inequality and then using the same rules of inequality to find the solution set. Both compound and simple inequalities can be graphed as a line on a number line or coordinate plane, with the solution set being either all the numbers less than, greater than, or between two values, depending on the inequality sign.

However, solving a compound inequality in compact form is different from solving a simple inequality in that a compound inequality has two or more inequality statements combined using "and" or "or" connectors. When solving a compound inequality, we have to consider both inequalities together to find the final solution set. For example, when solving the inequality 3 < x < 5, we have to consider both 3 < x and x < 5, to find the range of x that satisfies both inequalities. And when we have a compound inequality with "or" connector like 3<x<5 or 6<x<8, we need to find the solution set for each inequality separately and then combine them.

So, the difference between solving a compound inequality and a simple inequality is that a compound inequality has multiple inequality statements that must be considered together to find the final solution set, while a simple inequality has only one inequality statement.

Step-by-step explanation:

The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

The following figure accurately depicts the table.

Experimental probability is the likelihood of a future event based on past happenings.

Experimental probability is equal to the ratio of good results to all possible results.

To calculate the likelihood that the Texas Sharpshooters will score precisely

Next hockey game: 1 goal

As displayed in the table:

a successful outcome is repeated four times.

So, positive results equal 4

8 total results

likelihood = 4/8 = 0.5

So, The probability that the Texas Sharpshooters score exactly 1 goal next hockey game is 0.5

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Answer:

0.50 (Choice C)

Step-by-step explanation:

Khan Academy told me.

This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.

What is an algebraic manipulation?

Algebraic manipulation is the process of rearranging mathematical expressions in order to solve equations or to make them easier to understand. It involves the use of mathematical operations and properties such as addition, subtraction, multiplication, division, and the commutative, associative, and distributive properties.

To determine if sending teachers to the summer training on mentor groups is a good decision, the committee needs to calculate the break-even point. This is the point at which the cost of sending the teachers is equal to the cost of not sending them. The break-even point can be calculated by dividing the advanced payment by the difference between the cost at registration and the advanced payment.

In this case, the break-even point is: $1,250 ÷ ($175 - $1,250) = $1,250 ÷ -$1,075 = 7 teachers.

Hence, This means that if 7 or more teachers attend the training, it will be a good decision, as the cost of sending them will be less than the cost of not sending them.

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Answer:

see below

Step-by-step explanation:

5000

60% = 3000 in stocks

year 1 gain 9% = 3000*1.09 =3270

year 2 loss 4% = 3270*(1-4%) =3139.2

40% = 2000 in savings

year 1 earn 4.9% = 2000*1.049 = 2098

year 2 earn 4.9% = 2098*1.049=2200.8

TOTAL in 2 years = 3139.2+2200.8 = 5340

so gain = 5340-5000 =340

if all only in savings:

5000*(1.049)² = 5502

Answer: He can buy 4 pants for $120 and 4 shirts for $80

Answer: Roger wants to buy at least 6 items, so he needs to buy at least 6 pants or 6 shirts or a combination of both.

Step-by-step explanation:

The cost of 6 pants is $30 x 6 = $180.

The cost of 6 shirts is $20 x 6 = $120.

If Roger wants to buy both pants and shirts, he can buy 3 pants and 6 shirts for a total cost of $90 + $120 = $210.

Another option would be 4 pants and 5 shirts for a total cost of $120 + $100 = $220.

Thus, Roger can buy either 6 pants, 6 shirts or a combination of 3 pants and 6 shirts or 4 pants and 5 shirts with his $200.

A line of symmetry is the reflections map the figure onto itself.

A line of symmetry is, in other words, a line that splits a figure into two mirror representations. This line's reflection maps the figure onto itself. While some figures lack symmetry, others do feature one or more lines of symmetry. An example of a form having reflection symmetry is a rectangle.

The symmetry axes are shown and given the letters m and n. The figure will map to itself when reflected across either (or both) of the symmetry axes. It seems like you want to call those reflections...

Ra, where

a = m, and

Rb, where

b = n

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The solution to the equation in the given interval is 2.365

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

3sin(2x - 4) = 2

Divide both sides of the equation by 3

So, we have the following representation

sin(2x - 4) = 2/3

Take the arcsin of both sides

This gives

2x - 4 = 0.73

Evaluate the like terms

2x = 4.73

Divide by 2

x = 2.365

Hence, the value of x is 2.365

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Robel's age will be 15 and Father's age will be 45, which is three times as old as Robel.

Robel's current age = x

Father's current age = 4x

After 5 years,

Robel's age = x + 5

Father's age = 4x + 5

After 5 years, father will be three times a old a Robel

4x + 5 = 3(x + 5)

4x + 5 = 3x + 15

x = 10

Therefore, Robel's current age is 10 years and father's current age is 40 years.

Let x represent the current age of Robel and 4x represent the current age of Robel's father.

We can use the formula 4x + 5 = 3(x + 5) to solve for x.

We rearrange the equation to get x = 10.

Robel's current age is 10 years and father's current age is 40 years.

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Relative frequencies are calculated by dividing the count by the total count in the column or row.

Joint relative frequencies show the proportion of individuals in a specific category of two variables.

They are calculated by dividing the count of individuals in a specific category by the total number of individuals surveyed.

In a two-way table, they are represented by the cells and give a sense of how the two variables are related to each other.

For example, in the given table, the joint relative frequency of males who plan to go to college is 0.35, which means 35% of the surveyed males plan to go to college.

Joint relative frequencies can be used to identify patterns and relationships between two variables, such as how gender and college plans are related.

joint relative frequencies:

Yes No Total

M 0.35 0.23 0.58

F 0.33 0.19 0.52

1

Marginal relative frequencies:

Yes No Total

M 0.58 0.42 1

F 0.52 0.48 1

1

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The points G and H is the center of dilation from the points E, F, G, or H

What is Center of Dilation ?

The middle of a dilation is a hard and fast point inside the aircraft about which all points are increased or reduced in size. The middle is the handiest invariant (now not changing) factor below a dilation (k ≠1), and may be positioned inside, outdoor, or on a parent.

Given ,

In the Quadrilateral ABCD and its dilated image A′B′C′D′ are shown in the figure.

The points E, F, G, or H.

So, The center of dilation could be G and H .

Therefore, The points G and H is the center of dilation from the points E, F, G, or H

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The probability that  randomly selected costume needs both shortened and taken in is 9/33

There are a total of n(T) = 33 costumes. Of these n(A) = 17 require alteration. The two sorts of change are shortening and taking in. n(S) = 15 costumes require shortening, and n(I) = 11 costumers require being taken in.

We are to determine the probability that a randomly selected costume requires both shortening and taken in.

The following is the formula for the union of sets.

P(S ∪ I) = P(S) + P(I) - P(S ∩ I)

∴ S ∪ I = A

∴ P(A) = P(S) + P(I) - P(S ∩ I)

∴ [tex]\frac{n(A)}{n(T)} = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - P(S \cap I)[/tex]

∴ [tex]P(S \cap I) = \frac{n(S)}{n(T)} + \frac{n(I)}{n(T)} - \frac{n(A)}{n(T)}[/tex]

Substituting the values:

∴ [tex]P(S \cap I) = \frac{15}{33} + \frac{11}{33} - \frac{17}{33}[/tex]

∴ [tex]\frac{26}{33} - \frac{17}{33}[/tex]

∴ [tex]\frac{9}{33}[/tex]

Therefore the probability that randomly selected costume needs both shortened and taken in is 9/33

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The lateral surface area of the cylinder is 357.96[tex]cm^2[/tex]

Now, According to the question:

In two-dimensional geometry, a cylinder has two circles as its bases so that both the bases are parallel and congruent.

In a cylinder, there is a lateral surface that is between the bases.

Let us suppose d is the diameter of the base of a cylinder, and h is the height of the cylinder then:

Radius of the cylinder (r) = [tex]\frac{d}{2}[/tex]

Lateral surface area of the cylinder(S) = [tex]2\pi rh[/tex]

Total surface area(A) = lateral area + total area of the bases

Given that the diameter of the above cylinder is 12cm, and the height of the cylinder is 3.5cm.

d = 12cm

and,

h = 3.5cm

Now the radius of the cylinder:

(r) = [tex]\frac{d}{2}[/tex] = 12/2 = 6cm

Now the total surface area of the cylinder:

A = [tex]2\pi r(h +r)[/tex]

A = [tex]2\pi (6)(3.5+6)[/tex]

A = [tex]12\pi (9.5)[/tex]

A = 114[tex]\pi[/tex]

We use [tex]\pi[/tex] = 3.14

A = 114(3.14)

A = 357.96[tex]cm^2[/tex]

Hence, the lateral surface area of the cylinder is 357.96[tex]cm^2[/tex]

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1225 J is the Kinetic Energy of the football as it was traveling down the

field.

Calculate the Kinetic Energy (KE) of the football.

KE = 0.5 x 5 kg x (25 m/s)^2

Calculate the Kinetic Energy of the football in Joules (J).

KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2

Calculate the Kinetic Energy of the football in Joules (J).

KE = 0.5 x 5 kg x (25 m/s)^2 x 9.8 m/s^2 = 1225 J

The energy an object has as a result of motion is known as kinetic energy in physics. It is described as the effort required to move a mass-determined body from rest to the indicated velocity.

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Answer: 90200

Step-by-step explanation:

9020 x 10 = 90200.

Just add one more zero when multiplying by ten.

The original price of the house is 156,000

From the question,

The house was increased by 30% which leads to an increase to 156000

To get the original price of the house

Let the value of the house be x

We then multiply the original price of the house(x) by 30%

we have 0.30*x

0.30x = 156000

Divide both sides by 0.30

x = 520,000

Hence, 520000 is the original price of the house

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The price for a children's ticket is $2.50

Now, According to the question:

A fundraising dinner was held on two consecutive nights.

Let the number of children's tickets be x.

Let the number of adults' tickets be y.

The total number of tickets sold is 937.50

On the first night, 100 adult tickets and 175 children's tickets

Therefore,

100x + 175y = $937.50

On the second night, 200 adult tickets and 316 children's tickets were sold for a total of $1790.

200x + 316y = $1790

Now, we have two simultaneous equations:

100x + 175y = $937.50 ----(1)

200x + 316y = $1790----(2)

Divide by 2 equation (2)

100x + 158y = $895----(3)

From the first equation, make y the subject of the formula:

100x = 937.50 - 175y

Put the value of 100x in equation (3)

937.50 -175y + 158y = $895

937.50 - 17y = $895

-17y = -42.5

y = 2.50

Hence, the price for a children's ticket is $2.50

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Plans for what to do after high school and three ways to protect yourself from the effects of inflation are mentioned below.

To take into account a recovering economy with scarce jobs and low salaries when making plans for after high school, one could consider the following:

To protect oneself from the effects of inflation, one could consider the following:

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The equation can be written as 6 + (-6y) = -6y - 1 + (7).

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given is an equation with missing parts.

The left hand side of the equation does not contain a term with variable, but the right hand side contains it.

Adding that term in the left hand side, we get, 6 + (-6y) in the left hand side.

So the right hand side must be equal.

So the expression in the right hand side is -6y - 1 + (7).

Hence the expressions are 6 + (-6y) on the left hand side and  -6y - 1 + (7) on the right hand side.

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