How many subsets does the set {Apple, Banana} have?
2
3
4
5
6

The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.

In this case, the angle would be s/r or 4.2/4  which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.

Answer:

Step-by-step explanation:

Length of a circular arc is given by:

S = rФ

where Ф is the angle in radians subtended at the center by the arc.

Ф = S/r = 4.2 / 4 = 1.05 radians = (1.05*180)/π = 60.16° ≅ 60°

Measure of minor arc AB is 60°

Answer:

Therefore the length of aluminum surrounding the pool is 88 feet.

Step-by-step explanation:

Circle:

Given that the circular swimming pool has walls made of aluminum.

To find out the length of the of aluminum, we need to find out the circumference of the pool.

The radius of the circular pool is = 14 feet.

Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]

                                                                       [tex]=2\times \frac{22}{7} \times 14[/tex]  feet

                                                                     =88 feet

Therefore the length of aluminum surrounding the pool is 88 feet.

Answer:

This is the volume of cube V = 729 [tex]in^{3}[/tex]

Step-by-step explanation:

Surface area of cube = 486 [tex]in^{2}[/tex]

Surface area of the cube is given by A = 6 × [tex]a^{2}[/tex]

⇒ 6 × [tex]a^{2}[/tex] = 486

⇒ [tex]a^{2}[/tex] = 81

⇒ a = 9 in

This is the value of side of the cube. so volume of the cube is given by

⇒ V = [tex]a^{3}[/tex]

Put the value of a in above formula w get,

⇒ V = [tex]9^{3}[/tex]

⇒ V = 729 [tex]in^{3}[/tex]

This is the volume of cube

To find the volume of a cube with a surface area of 486 in², calculate the side length using the formula A=6s², leading to a side length of 9 inches, and then calculate the volume as V=s³, resulting in 729 cubic inches.

The volume of a cube with a given surface area using the formula A=6s², where A is the surface area and s is the side length of the cube. First, find the side length by dividing the given surface area by 6, then take the square root. After finding the side length, calculate the volume using the formula V=s³.

Given the surface area A=486 in², the side length s can be found as follows:

Answer:

B. [tex](1,-5)[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.

[tex]y=-7x+2...(1)[/tex]

[tex]y=9x-14...(2)[/tex]

To solve our given system, we will equate both equations as:

[tex]9x-14=-7x+2[/tex]

Combine like terms:

[tex]9x+7x-14+14=-7x+7x+2+14[/tex]

[tex]16x=16[/tex]

[tex]x=\frac{16}{16}=1[/tex]

Upon substituting [tex]x=1[/tex] in equation (1), we will get:

[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]

Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.

Answer:

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14

They bought a movie for $12. The amount that they have left is

14 - 12 = $2

They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is

2/1 = 2

If they split the containers evenly between themselves, then each person would get

2/2 = 1 container of fruit salad

Answer:

(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]

(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]

(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]

Step-by-step explanation:

If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]

Using Pythagoras,

Opposite=5, Hypotenuse =6, Adjacent=?

[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]

In the Second Quadrant,

[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]

(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]

(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]

(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]

[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]

Answer:

 22.19 feet

Step-by-step explanation:

You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

Using these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.

Referring to the attached diagram, we have ...

  CE = 8/sin(63°) ≈ 8.9786

  FC = 6/cos(63°) ≈ 13.2161

Then the total length of the ladder is ...

  FE = CE +FC

  FE = 8.9786 +13.2161 = 22.1947

The length of the ladder is about 22.19 feet.

Step-by-step explanation:

[tex]y = - 2x + 3[/tex]

The slope of the above line = -2

slope of the line perpendicular to the above line = 1/2

If it passes through point (4,-3) , it's equation

[tex] \frac{y - ( - 3)}{x - 4} = \frac{1}{2} [/tex]

[tex] \frac{y + 3}{x - 4} = \frac{1}{2} [/tex]

[tex]2(y + 3) = x - 4[/tex]

[tex]2y + 6 = x - 4[/tex]

[tex]x - 4 - 2y - 6 = 0[/tex]

[tex]x - 2y - 10 = 0[/tex]

A = 1, B = -2 and C = -10

A+B+C= 1+(-2)+(-10)

= 1-2-10

= 1-12

= -11

Answer:

A = 1, B = -2 and C = -10

Step-by-step explanation:

Answer:

36 π square feet

Step-by-step explanation:

so the formula for area of a circle is  πr^2

so the radius is 6, which we can just plug in

π(6)^2

36π

so option 3

Answer:

24p8 - 36p6 + 36p2 = 48p

Step-by-step explanation:

I hope this helps!

Answer: last option.

Step-by-step explanation:

There are several transformations for a function f(x). Some of them are shown below:

1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.

2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.

3. If [tex]f(x+k)[/tex], then the function is translated "k" units left.

4. If [tex]f(x-k)[/tex], then the function is translated "k" units right.

In this case you have the following function:

[tex]h(x)=log_6x[/tex]

And the function m(x) is obtained by transformating the function h(x). This function is:

[tex]m(x)=log_6(x+3)[/tex]

Then, based on the transformatios shown before, you can identify that:

[tex]m(x)=h(x+3)[/tex]

Therefore, you can determine that you could graph the function  [tex]m(x)=log_6(x+3)[/tex] by translating each point of the graph of the function h(x) 3 units left.

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Vertex = (-5, -2)

Point = (-4, 2)

This is a vertical parabola the opens upwards.

The equation is

                             (x - h)² = 4p(y - k)

Substitution

                             (-4 + 5)² = 4p (2 + 2)

Simplification

                                      1² = 4p(4)

                                      1 = 16p

                                      p = 1/16

Equation of the parabola

                          (x + 5)² = 4/16(y + 2)

                          x² + 10x + 25 = 1/4y + 1/2

Conclusion

The coefficient of the squared expression is 1

The flight departing at 3:15 PM MST, after 2 hours and 30 minutes, arrives at an estimated time of 4:45 PM PST considering that PST is one hour behind MST.

The subject of this question revolves around time conversion between different standard global time zones. The departure time is 15:15 or 3:15 PM Mountain Standard Time (MST). A flight taking 2 hours and 30 minutes is added onto this original departure time. Therefore, in MST, the arrival time would be 17:45 or 5:45 PM MST. However, we must consider the time difference to Pacific Standard Time (PST) which is one hour behind MST. This means, to reflect PST, we subtract one hour from the MST arrival time, giving us an estimated arrival time of 16:45 or 4:45 PM PST.

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Answer:

The system

6*x  - 3*y  =  6

8*x  -  9*y  =  - 22

Solution:

x = 4

y = 6

Step-by-step explanation:

We have:

"x" number of points for a goal

"y" number of points for a penalty

Then according to problem statement, we get the two equation system

Clare       6*x  - 3*y  = 6       And

Hoah      8*x  -  9*y  =  - 22

If we are going to solve it, we can:

6*x  - 3*y  =  6      ⇒    2*x  - y  = 2

                              8*x  -  9*y  =  - 22

y = 2*x - 2

8*x  - 9 *( 2*x -2)  =  - 22    ⇒    8*x - 18*x + 18  =  - 22

-10*x = - 40       x = 4

And then  y =  2*x - 2      ⇒   y  =  8 - 2    ⇒  y  = 6

Answer:

0.56

Step-by-step explanation:

There are 14 girls, and a total of 25 students.  So the probability of selecting a girl is P = 14/25 = 0.56.

The probability of calling on a girl will be 0.56. The correct option is C.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.

The probability of calling on a girl can be calculated by dividing the number of girls by the total number of students in the class:

Probability of calling on a girl = Number of girls / Total number of students

Number of girls = 14

Total number of students = 11 + 14 = 25

Therefore, the probability of calling on a girl is:

Probability of calling on a girl = 14 / 25 = 0.56

So, the correct answer is (c) 0.56.

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Answer: 275 cm squared

Step-by-step explanation: We need to divide the shapes first into smaller areas, and since all the areas we need are given to us, we just need to break it apart into smaller parts that we can find the area for.

Length x Width = Area

Answer:

[tex]x > - 3[/tex]

Step-by-step explanation:

[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]

Answer:

Step-by-step explanation:

#using java

Double result;

public Double half(Double number){

return number/2;

}

result=half(number);

Final answer:

The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.

Explanation:

The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.

Example of a half function in C++:

double half(double number) {
   return number / 2.0;
}

This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.

To use this function, you would write the following code in your main program:

double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0

Understanding the code:

When invoked, the function will return half of the input value, effectively operating as number / 2.0.

Answer:

Option B is correct.

Stephanie should add Jim to her health care plan.

Step-by-step explanation:

Let's take the options one by one.

Option 1

If Jim's employers insure him and his wife.

Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries.

It means Jim will pay (0.58 of $378) for himself plus (0.73 of $345) for his wife.

Amount Jim pays = (0.58 × 378) + (0.73 × 345) = $471.09

Option 2

If Stephanie's employers insure both of them.

Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary.

It means Stephanie would pay (0.65 of $298) she'll pay for herself plus (0.70 of $349) she'll pay for her husband minus (10% of $298) that her company wants to pay out of the insurance fee of any of her additional beneficiary.

Amount Stephanie will pay = (0.65 × 298) + (0.70 × 349) - (0.10 × 298) = $408.2

Option 3

If each of them does an insurance plan with their respective employers

Jim’s employer pays 42% of his $378 monthly premium.

Stephanie’s employer pays 35% of her $298 monthly premium

Jim would pay (0.58 × $378) for himself = $219.24

Stephanie would pay (0.65 × $298) for herself = $193.7

Total they would pay in this option = $219.24 + $193.7 = $412.94

Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.

Hope this Helps!!!

Insurance is termed as the process of safeguarding against financial loss. It's a type of risk management that's used mostly to protect against the danger of a speculative or unpredictable loss.

An insurer, an insurance company, an insurance carrier, an underwriter is a business that sells insurance.

The correct answer is option B.  Stephanie should add Jim to her health care plan.

The evaluation of each and every option is as follows:

Option 1

If Jim and his wife are covered by Jim's employer's insurance.

Jim's $378 monthly premium is covered by his company to the tune of 42 percent. Additional beneficiaries will be covered by 23 percent of his insurance plan's $345 cost.

Jim will have to pay 0.58 of $378 for himself and 0.73 of $345 for his wife.

Jim's payment = = $471.09

Option 2

If both of them are protected by Stephanie's company's insurance.

Stephanie's company pays 35% of her $298 monthly premium, but she has the choice of paying a further 10% of her discount for each beneficiary she adds to her plan. For each new beneficiary, her employer would pay 30% of the $349 payment.

Stephanie would pay (0.65 of $298) for herself plus (0.70 of $349) for her husband, minus (10 percent of $298) that her firm wants to pay out of any of her extra recipients' insurance payments.

Stephanie will pay $408.2 by multiplying (0.65 298) by (0.70 349) by (0.10 298).

Option 3

If they both join an insurance plan via their companies, Jim's employer will cover 42 percent of his $378 monthly payment.

Stephanie's $298 monthly charge is compensated by the business to the tune of 35%.

For himself, Jim would pay [tex](0.58 \times \$378)[/tex]= $219.24

Stephanie would pay (0.65 $298) for herself = $193.7 The total cost of this option would be $219.24 + $193.7 = $412.94.

Stephanie ensures herself and Jim with her employers for a total cost of $408.2, against a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they insure each other with their respective jobs.

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Answer: it will take 1.8 hours

Step-by-step explanation:

The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes

t = k/s

The journey takes 1.5 h when the average speed is 54 miles per hour. This means that

1.5 = k/54

k = 54 × 1.5 = 81

The equation becomes

t = 81/s

Therefore, when the average speed is 45 miles per hour, the time taken would be

t = 81/45

t = 1.8

Answer: The answer should be C!

Step-by-step explanation:

I took the quiz

The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).

The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.

In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.

This is so because it doesn't fall under the shaded area.

This is due to the broken horizontal line; y < 3.

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When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.

To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:

So, the result of the subtraction is 12a^2 - 9a - 36.

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Answer:

Each boy will get 25 marbles.

Step-by-step explanation:

Given:

William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.

Now, to write an expression using parentheses to find number of marbles each boy get.

Let the number of marbles each boy get be [tex]x.[/tex]

Total number of boys = 2.

Number of marbles first jar holds = 12.

                          Second jar holds = 21.

                        And third jar holds = 17.

As given, William shares marbles equally with his brother.

Now, we write the expression to find the number of marbles each boy get:

[tex]x=\frac{(12+21+17)}{2}[/tex]

[tex]x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}[/tex]

[tex]x=6+10.5+8.5[/tex]

[tex]x=25.[/tex]

Therefore, each boy will get 25 marbles.

Answer:

26

Step-by-step explanation:

The diameter of the wheel is 29 in.

The circumference of the wheel is 3.14 × 29 in = 91.06 in.

For each revolution, the bike moves forward one circumference.  So the number of revolutions is (200 ft × 12 in/ft) / 91.06 in ≈ 26.

Answer:

Each of these is based on the principle of difference of two squares where:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Step-by-step explanation:

1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]

[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]

2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]

[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]

3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]

[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]

4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]

[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]

Answer: the total cost of this order is $14

Step-by-step explanation:

She sells 3 hot dogs and 2 pretzels for $15.00.

She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is

3h+2p=15 - - - - - - - - - - - -1

5h+p=21.5 - - - - - - - - - - -2

Multiplying equation 1 by 5 and equation 2 by 3, it becomes

15h + 10p = 75

15h + 3p = 64.5

Subtracting, it becomes

7p = 10.5

p = 10.5/7

p = 1.5

Substituting p = 1.5 into equation 1, it becomes

3h + 2 × 1.5 = 15

3h + 3 = 15

3h = 15 - 3 = 12

h = 12/3 = 4

If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be

(4 × 2) + (4 × 1.5)

= 8 + 6 = $14

Sure, what do you need help finding?

Answer:

to find a percentage of a number u multiply/divide 100

Answer: the value of the car will be about $12634

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^ t

Where

A represents the value of the car after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

P = $22000

r = 10.5% = 10.5/100 = 0.105

t = 5 years

Therefore

A = 22000(1 - 0.105)^5

A = 22000(0.895)^5

A = $12634

Answer:

29/100 (Every 100 students, 29 more students like cats than dogs)

Step-by-step explanation:

First we need to put these numbers in fractions

The fraction that represents students that like dogs is 9/25

The fraction that represents students that like cats is 13/20

Now, we just need to subtract the fraction of cats by the fraction of dogs:

13/20 - 9/25

To do that, we need to make the denominators equal. We do that making multiplying the first fraction by 5 and the second by 4, so we have:

13/20 = 65/100

9/25 = 36/100

Then, subtracting then, we have:

65/100 - 36/100 = 29/100

So every 100 students, 29 more students like cats than dogs.