A survey was conducted to determine whether a group of 11th graders and 12th graders preferred to go to the amusement park or to the zoo for a class
trip. The results are shown in the table.
Amusement Park Zoo
11th Graders
32
18
12th Graders
24
26
Based on the table, what is the probability that a student preferred a class trip to the zoo given they are in 11th grade?

We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

What is the tangent of the angle?

The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.

The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.

Here,

We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.

We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

To learn more about the tangent of the angle from the given link

https://brainly.com/question/8846313

#SPJ4

Answer:

The tree is 9.1 meters high.

Step-by-step explanation:

We can use the Pythagorean Theorem to solve this problem. Let T be the height of the tree. We can set up the following equation:

4.2^2 + T^2 = 6.5^2

Solving for T, we get:

T = sqrt(6.5^2 - 4.2^2)

T = sqrt(41.25 - 17.64)

T = sqrt(23.61)

T = 4.878

Since the height of the tree is measured to the nearest tenth, we can round this value to 9.1 meters.

The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

Volume is the measure of the amount of 3-dimensional space occupied by an object or substance. It is usually measured in cubic units, such as cubic centimeters (cm3) or cubic meters (m3). Volume is an important concept in mathematics, physics, chemistry, and engineering, and is used to calculate the amount of material needed for a given project.

The volume of the box can be calculated by multiplying the area of the base with the height of the box. The area of the base is 58 cm² and the height of the box is x - 2 cm. Therefore, the volume of the box can be expressed as:
Volume = 58 cm² x (x - 2 cm)
     = 58 cm³
The volume of the box is 58 cm³. Therefore, the units of the answer are cm³.

To learn more about volume
https://brainly.com/question/23963432
#SPJ1

[tex] \longmapsto \: =25/35 [/tex]

[tex] \longmapsto \: =5/7[/tex]

[tex] \longmapsto \: =5:7[/tex]

Answer:

see explanation

Step-by-step explanation:

A

∠ UVX and ∠ WXV are alternate angles and are congruent , then

∠ UVX = ∠ WXV = 15°

∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°

B

opposite sides of a parallelogram are congruent , then

UV = XW = 36

C

consecutive angles are supplementary , sum to 180° , then

∠ XUV + ∠ WVU = 180° , so

∠ XUV + 39° = 180° ( subtract 39° from both sides )

∠ XUV = 141°

D

diagonals bisect each other , so

YW = UY = 10

Answer:

x=-1 y=2

Step-by-step explanation:

Use Elimination or Substitution (Elimination shown below)

6x+5y=4

6x-7y =-20 <- Multiply by -1

-6x+7y=20

12y = 24

y=2

Plug back into either of the equations and solve for x.

6x + 10= 4

6x = -6

x = -1

Double check work:

-6+10 = 4

The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .

These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.

We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.

To learn more about logical operations

brainly.com/question/13092292

#SPJ4

The requirement of the parallel sides is Alternate interior angles.

The angle formed by the line intersecting two parallel lines is called the alternate interior angle. This two angles are equal in magnitude.

The alternate interior angles require two parallel lines to be formed. Therefore the requirement of the parallel sides is Alternate interior angles.

To know more about alternate interior angles follow

https://brainly.com/question/24839702

#SPJ2

Answer:

The theater has 698 seats.

Step-by-step explanation:

So, the first row has 26 seats, and that's one out of 25 rows.

Let's find the amount in the following rows.

The following rows have an additional 2 seats, so:

28 × 24 = 672

Now, we add the other 26 seats from the first row:

672 + 26 = 698

And there's your answer.

Answer:

2nd graph

Step-by-step explanation:

Given

f(x) = x² + 3x - 4

To find the zeros let f(x) = 0 , that is

x² + 3x - 4 = 0 ← in standard form

(x + 4)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 1 = 0 ⇒ x = 1

The only graph with zeros at x = - 4 and x = 1 is the 2nd graph

Second graph is a required answer

Answer:

True

True

False

y = 0.25x + 50 and y = 0.3x + 40 will be the equation to find the cost to rent a car.

A mathematical formula known as a cost function is used to visualize how manufacturing costs will vary depending on the output level. In other words, given a specified quantity produced, it calculates the entire cost of production.

Costs are the dollar amount spent on materials, labor, services, goods, equipment, and other items for use by a company or other accounting organization.

y = 0.25x + 50

y = 0.3x + 40

The equations will be written as y = mx + b, or slope-intercept form. You must determine what you have in order to determine what belongs where.

They receive $50 per day plus $0.25 per mile from Rent-A-Wreck. This indicates that the $0.25 per mile is the number that changes daily. Thus, y = 0.25x + 50 will be the equation.

They receive $40 per day with $0.30 per mile from Drive-A-Lemon. This indicates that the $0.30 per mile is the number that changes daily. y = 0.3x + 40 will be the formula.

To learn more about cost visit the link:

https://brainly.com/question/25811981

#SPJ1

The number that belongs to both sequences is 26.

The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."

By changing the term number's value, we can create a series that uses the nth term (n).

To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.

We have two sequences, let's call one as A and the other as B.

The n-th term of sequence A is written as:

aₙ = 3*n^2 - 1

the nth term of sequence B is written as:

bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

Then we will heave:

3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

3*n^2 = 31 - x^2

n^2 = (31 - x^2)/3

n = √(  (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √(  (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √(  (31 - 2^2)/3)  = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

Therefore, The number that belongs to both sequences is 26.

To learn more about sequences visit : brainly.com/question/21961097

#SPJ4

Answer:

The answer to this is 14%

Step-by-step explanation:

sorry if im wrong

(hope this helps can i plz have brainlist :D hehe)

Answer:

p + s = 45

s = 2p + 5

Step-by-step explanation:

Let s = number of students.

Let p = number of parents.

p + s = 45

s = 2p + 5

Answer:

The initial fee

Step-by-step explanation:

Thats the fee to sort of set up the membership, the 15 is the monthly cost, and m is the months you use the membership. Make sense?

Answer:I think 1/3

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

The process of each individual getting chosen is a sequence of events, meaning we need to multiply each individual probability separately in order to get the probability of this happening. For the first choice, the probability is 1/3 since there can only be one chosen to go first and there are three options. For the second choic,e the probability is 1/2 because only one can be chosen but there are now only 2 options since someone got chosen to be first. This leaves the last probability which is 1/1 since only one person is left. Therefore, to get the probability of this event happening we need to multiply all of these probabilities together...

1/3 * 1/2 * 1/1 = x

[tex]\frac{1 * 1 * 1}{3 * 2 * 1} =[/tex] [tex]\frac{1}{6}[/tex]

Therefore the probability of Bobby going first, Chandler going second, and Adrian going last is 1/6

Its a solid and a cube

You were wrong with square because a square only has one face while a cube has 6.

You were also wrong with polygon because while polygons are 1-dimensional a cube is 3-dimensional

The following terms correctly describe the given object Square, Solid, Cube, Polygon.

Options A, B, C, D are correct.

A cube is a 3-D solid shape, which has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All the six faces of a cube are squares, a two-dimensional shape.

Square is a figure in which all four sides are equal.

Solid is a three dimensional figure.

A Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Polygon is two dimensional figure with straight lines.

The following terms correctly describe the given object Square, Solid, Cube, Polygon.

Options A, B, C, D are correct.

Find out more information about cube here

https://brainly.com/question/14075440

#SPJ2

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

Let's simplify step-by-step.

3a − 2 ( 8 + 4a )

Distribute:

= 3a + ( −2 ) ( 8 ) + ( −2 ) ( 4a )

= 3a + −16 + −8a

Combine Like Terms:

= 3a + −16 + −8a

= ( 3a + −8a ) + ( −16 )

Answer:

= −5a − 16

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:i need to know what youre trying to find first

Step-by-step explanation:

The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .

The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.

The side lengths of the triangle are given as 4 units , 5 units and 6 units ,

According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]36 = 16 + 25[/tex] ;

[tex]36 \neq 41[/tex]

that means the given side do not form a right triangle .

Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .

Learn more about Right Triangle here

https://brainly.com/question/13054127

#SPJ4

The half-life of caffeine in the body is approximately 5-6 hours, not 666 hours. Given this information, we can calculate the latest time Charlotte can drink a 222-ounce shot of espresso that contains 80mg of caffeine and still have no more than 2020mg of caffeine in her system at 11pm.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

We know that after 5-6 hours, the amount of caffeine in the body decreases by 50%. Therefore, in 11 hours, the amount of caffeine in the body would decrease by approximately 87.5%.

If we let x be the number of hours before 11pm that Charlotte can drink the espresso, then the amount of caffeine in her body at 11pm would be:

80mg * (1 - (87.5% ^ (x/5-6))) = 2020mg

Solving for x, we find that the latest time Charlotte can drink the espresso is approximately 6:30pm.

learn more about percentage

https://brainly.com/question/24304697

#SPJ4

Answer:

(a)  

∠(a) = 105°

(b)  ∠(b) = 75°

(c)  

∠(c) = 105°

Step-by-step explanation:

Complete Question

1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:

(a) Suppose a car is traveling west on 4th Street and turns onto King Avenue heading south. What is the measure of the angle created by the car's turning? Explain your answer.

(b) Suppose a car is traveling southwest on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

(c) Suppose a car is traveling northeast on King Avenue and turns right onto 4th Street. What is the measure of the angle created by the car's turning? Explain your answer

Also find the attachment

Solution

(a)  

∠(a) + 75° = 180°

∠(a) = 180° - 75°

∠(a) = 105°

(b) As we can see the 3rd and 4th street are parallel thus the corresponding angle will be equal  

Thus, ∠(b) = 75°

(c)  

∠(c) + 75° = 180°

∠(c) = 180° - 75°

∠(c) = 105°

Answer:

All real numbers greater than or equal 2.

Step-by-step explanation:

There is a closed circle on the number 2,which means that it is included in the range. The line is increasing, meaning that all real numbers greater than or equal to 2 is the range.

The number of adult tickets purchased is 12.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let no. of adult = x

No. of children = 28 -x

So, 7. 25 * x + (28 - x) *4. 50  = 159

⇒2.75x +126=159

⇒2.75x =33

⇒x=33/2.75

x=12

Hence, the number of adult tickets purchased is 12.

Learn more about arithmetic, by the following link.

https://brainly.com/question/13181427

#SPJ4

Answer:

850 m²

Step-by-step explanation:

There are 3 different pairs of rectangles—the side rectangles, the rectangles on the top and bottom, and the other side rectangles.

10x11=110

110x2=220

15x10=150

150x2=300

15x11=165

165x2=330

330+300+220=850 m².

Answer: A.

Step-by-step explanation: Because a solid can go from a liquid to a gas and if you think of ice, Ice starts as a solid then when it melts it turns into a liquid the when the liquid evaporates it turns to a gas. Hope this helped