(6th grade math)
adrian has 50$ she spent 12.45 at the movies and 10.19 at the bowling alley. how much money does she have left?

The line represented by the table is:

y = 2x + 40

A general linear relationship is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two pairs:

(6, 52) and (9, 58)

Then we will get:

a = (58 - 52)/(9 - 6)

a = 6/3 = 2

y = 2x + b

To find the value of b, we replace the values of one of the points, if we use the first one (6, 52), then we will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b

40 = b

The line is:

y = 2x + 40

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The minimum sample size for the given event to have a normal approximation has to be 13 people.

For normal approximation,

np or n(1-p) should be greater than 10

where,

n = the sample size

p = probability for the occurrence of the event

Here, 20% of ohio residents support the legalization of marijuana

p = 20% or, 2/10

Hence,

1 - p = 1 - 2/10

= 8/10

Therefore, for normal approximation to be used

either n X 2/10 > 10    or,      n X 8/10 > 10

Therefore,

n X 2 > 10 X 10            or,      n X 8 > 10 X 10

hence,

n > 100/2                      or,               n > 100/8

n >  50                          or,               n > 12.5

Since we need to find the minimum no. of sample size to be required we will consider

n > 12.5

The sample size has to be a whole number hence,

n = 13

Therefore, the minimum sample size for the given event to have a normal approximation has to be 13 people.

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Answer: Probably negative 69

Answer: A

Step-by-step explanation:

The statement given is false. The reason for this is that the convergence of a function does not necessarily imply anything about the value of its derivative. To disprove the statement, we can consider the function f(x) = x^2, which converges for all x, but its third derivative f'''(x) = 0, which means that f'''(0) is also equal to 0. Hence, f′′′(0) is not equal to 2.

In general, it is important to note that the convergence of a function does not provide any information about the behavior of its derivatives. Moreover, a function may converge at some points and diverge at others, and this can be determined by analyzing the behavior of its terms or by using convergence tests. In this case, it is necessary to compute f′′′(0) directly using the definition of the derivative or by applying differentiation rules.

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Answer:

2 * x = 12

Step-by-step explanation:

Answer:

2x = 12

Step-by-step explanation:

let the number be x then 2 times the number is 2x. so

2x = 12 ← in equation form

The value of both domain and range of this exponential function is (−∞,∞).

y = 2x-9

The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).

The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).

Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).

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Answer: (D)

Step-by-step explanation:

Let 8/9=x/12

9*x=12*8

9x=96

x=10.7

Answer:

-3 1/3 , - 1 , -1/2 , 0 , 1 , 4 , 5 , 6 , 21/5

The caffeine level in the bloodstream after 18 hours (3 intervals of 6 hours) is 20 mg.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can include variables, constants, operations, and functions. It consists of one or more terms that are combined using arithmetic operations such as addition, subtraction, multiplication, and division.

The caffeine levels in the bloodstream of the freshman after n number of six-hour intervals:

C(n) = 160 / (\(n^{2}\))

Here, C(n) represents the caffeine level (in mg) after n six-hour intervals, 160 is the initial caffeine amount (in mg) in the freshman's body, and 2 ^ n represents 2 raised to the power of n, which corresponds to the number of times the caffeine amount is halved after n intervals of 6 hours.

To use this mathematical expression, you can simply substitute the value of n to calculate the caffeine level in the bloodstream at that particular time. For example, to calculate the caffeine level after 3 intervals of 6 hours, you can substitute n = 3 into the equation:

C(3) = 160 / (\(2^{3}\)) = 160 / 8 = 20

Therefore, the caffeine level in the bloodstream after 18 hours (3 intervals of 6 hours) is 20 mg.

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Answer:

$8036.784

Step-by-step explanation:

It is easy

The area of carpet is 13.4×24=321.6sq meter

Now, for 1 sq. meter the cost is $24.99

So for 321.6sq.meters, 321.6×24.99

=$8036.784

It will cost amount of $8036.784 to carpet a rectangular room.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

Where W is the width of the rectangle and L is the length of the rectangle

To carpet a rectangular room that measures 13.4 meters by 24 meters, it would area:

13.4 x 24 = 321.6 square meters

Since one square meter, the cost is $24.99

So for 321.6 square meters, 321.6×24.99

= $8036.784

Thus, it will cost amount of $8036.784 to carpet a rectangular room.

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Answer:

Find x

The angles are corresponding.

We have

x+35°+90°=180 (angles in a triangle)

x= 55°

Please give Brainliest

Answer:

x = 20 degrees

Step-by-step explanation:

I cannot give a thorough explanation but I will show my workings and reasoning.

Reasoning:

Vertically opposite angles are equal

Angles in a triangle add up to 180 degrees

Workings:

35 multiplied by 2 is 70

70 add 90 is 160

180 minus 160 is 20

x = 20

Answer:

2) 10.1

Step-by-step explanation:

Answer:

78.42

Step-by-step explanation:

Area of 360 - 80 degree region.

You need to find out the region of the major arc where the circle is almost complete. The area left over will be calculated later

Angle = 360 -80

Angle = 280 degrees.

Area = \(\frac{angle*3.14*r^2}{360}\)

Area = \(\frac{280*3.14*5^2}{360}\)

Area = 23800/360

Area = 66.11

Area of the Triangle with sides of 5 cm each

Here's where I get into a bit of trouble. I have to assume you know some trig.

Find the height

Cos(40) = The height / the hypotenuse

Cos(40) =  h/5

0.7760 = h/5

h = 0.7760*5

h = 3.830

Find 1/2 the base (the chord of the circle)

Sin(40) = 1/2 base / hypotenuse

Sin(40) =  1/2 b / 5                          Multiply both sides by 5

1/2 b = 5*sin(40)                              Find the sin(40)

1/2 b = 5*.6428                               Combine the right

1/2 b = 3.139                                    multiply by 2

b = 6.4278

Find the area of the triangle

Area = 1/2 b * h

b = 6.4278

h = 3.830

Area = 1/2 * 6.4278*3.830

Area = 12.31 cm^2

Total Area

12.31 + 66.11 = 78.42

Answer:

73.6

Step-by-step explanation:

Answer:

x=77°

Step-by-step explanation:

angles in triangle add to 180°

180°-43°-60°=x°

77°=x°

Answer:

24p^2q^2?

Step-by-step explanation:

Not enough info, so this is what I could get...

Answer:

26

Step-by-step explanation:

26

In the object-oriented programming paradigm, a class invariant is a property that must always be true for any instance of a class. It is a condition or a set of conditions that must be maintained by all member functions for the proper functioning of a class.

A class invariant, therefore, is a formal statement of the rules that dictate how the member variables of a class are used. All member functions (with the exception of constructors) can depend on the invariant being valid when the function is called. Each function is also responsible for ensuring that the invariant is valid when the function finishes.

The invariant represents an important constraint that must be maintained in a class. As a result, a well-defined class invariant is important for the stability and reliability of the class.

The class invariant may be a single condition or a set of conditions that need to be maintained for the class to operate correctly. These conditions may be explicitly stated in the class documentation or in the form of assert statements in the class implementation. The invariant may be as simple as a range constraint or as complex as a logical relationship between multiple variables.

In any case, the invariant must be maintained by all the member functions of the class. the invariant of a class is a set of rules that govern how the member variables of a class are used. It is a condition that must always be true for any instance of a class. The invariant is important for the stability and reliability of a class, and each member function is responsible for ensuring that the invariant is valid when the function finishes.

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(a) The IP model aims to maximize profit by determining the optimal number of each type of plane to purchase, considering budget constraints and resource availability.

(b) The BIP formulation transforms the IP model into a binary representation, allowing for an efficient solution by determining whether to purchase a plane of a specific type or not.

The IP model for this problem involves formulating an optimization problem to maximize profit by determining the number of long-range, medium-range, and short-range planes to be purchased. The decision variables represent the quantities of each type of plane, and the objective is to maximize the net annual profit.

The constraints include the budget limit set by the board and the availability of trained pilots and maintenance facilities. By solving this IP model, management can determine the optimal allocation of planes to achieve the highest possible profit within the given constraints.

The BIP formulation of the IP model involves reformulating the problem as a Binary Integer Programming problem. This is achieved by representing the decision variables as binary variables, where a value of 1 indicates the purchase of a plane of a particular type, and 0 indicates no purchase.

The objective function and constraints are adjusted to accommodate the binary representation. By using binary variables, the BIP formulation allows for a more efficient solution approach, as binary variables have a well-defined and discrete nature. Solving the BIP problem will provide the management with the optimal combination of plane purchases that maximizes profit while adhering to the budget and resource constraints.

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Answer:

I am assuming the 8:15 was a typo and was actually supposed to be a 8:14. Anyways, they are equivalent because they all make 4:7 when simplified.

Step-by-step explanation:

4:7 = itself at this point, as they don't have numbers that can simplify each other on both sides, unless you are looking for a decimal answer.

8:14 = 4:7 <- You can divide the 8 and 14 by two. 8 divided by 2 is four, and 14 divided by 2 is 7.

16:28 = 4:7 <- You can divide the 16 and the 28 by four. 16 divided by 4 is 4, and 28 divided by 4 is 7.

20:35 = 4:7 <- You can divide both sides by 5. 20 divided by 5 is 4, and 35 divided by 5 is 7.

a) The values of X and Y that maximize the utility are X = 250 and Y = 125.

b) T he values of X and Y that maximize the utility using the Lagrangean method are X = 250 and Y = 125.

a) To find the values of X and Y that maximize the utility using the substitution method, we can start by substituting the budget constraint into the utility function.

Since the budget constraint is given by 2X + 4Y = 1000 (kr), we can rearrange it to solve for X: X = (1000 - 4Y)/2 = 500 - 2Y.

Now substitute this expression for X in the utility function: U(Y) = 100(500 - 2Y)Y + (500 - 2Y) + 2Y.

Expand and simplify the expression: U(Y) = 50000Y - 200Y^2 + 500 - 2Y + 2Y.

Combine like terms: U(Y) = -200Y^2 + 50000Y + 500.

To maximize the utility, we need to find the critical points. Take the derivative of U(Y) with respect to Y and set it equal to zero:

dU(Y)/dY = -400Y + 50000 = 0.

Solve for Y: Y = 50000/400 = 125.

Now substitute this value of Y back into the budget constraint to find the corresponding value of X:

2X + 4(125) = 1000,
2X + 500 = 1000,
2X = 500,
X = 250.



b) To find the values of X and Y that maximize the utility using the Lagrangean method, we need to set up the following equation:

L(X,Y,λ) = U(X,Y) - λ(2X + 4Y - 1000),

where λ is the Lagrange multiplier.

Taking the partial derivatives of L with respect to X, Y, and λ, we have:

dL/dX = 100Y + 1 - 2λ,
dL/dY = 100X + 2 - 4λ,
dL/dλ = -(2X + 4Y - 1000).

Setting these derivatives equal to zero, we have the following system of equations:

100Y + 1 - 2λ = 0,
100X + 2 - 4λ = 0,
2X + 4Y - 1000 = 0.

Solving this system of equations, we find:

λ = 1/2,
X = 250,
Y = 125.

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Step-by-step explanation:

Let's use the number represented x

x + 9 because 9 more than the x

(x+9)/-4 because it is divided by -4

(x+9)/-4 <= -2 (maximum of -2 means smaller than -2, but it also did not tell not to use -2)

The difference in the number of miles ran by Kiki during practice is 186 miles.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Given that Kiki runs 437 miles during the first week of track practice and she runs 623 miles during the second week of track practice.

The difference in miles will be:

= 623 - 437

= 186 miles.

Therefore, the miles difference is 186 miles.

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Complete question

Kiki runs 437 miles during the first week of track practice. She runs 623 miles during the second week of track practice. What is the difference in the number of miles?

Answer: Outsourcing

Step-by-step explanation: I just took a test.

The use of workers that use networked computers to work at lower rates of pay than American workers is called outsourcing.

The term outsourcing has to do with a situation in which workers from outside the company are contrated to do the work of the company. This could be done remotely most times by the use of a computer.

In this case, the American companies that contracted European and Asian companies, where well educated workers could do jobs on networked computers at lower rates of pay than American workers is called outsourcing.

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★ Now Let's solve given equation :-

Hope it helps!

The fulcrum is in the center and equidistant from both ends of the seesaw.

To find the location of the fulcrum when the seesaw is balanced, we need to consider the torques acting on the seesaw.

The torque (τ) of an object is given by the equation:

τ = F * r * sin(θ)

where F is the force applied, r is the distance from the pivot point (fulcrum), and θ is the angle between the force vector and the lever arm.

In this case, the torque due to the weight on one side of the seesaw should be equal to the torque due to the weight on the other side when the seesaw is balanced.

Let's calculate the torques for each side of the seesaw:

Torque on the left side:

τ_left = (30 kg * 9.8 m/s²) * 1.5 ft = 441 ft·kg

Torque on the right side:

τ_right = (30 kg * 9.8 m/s²) * 1.5 ft = 441 ft·kg

Since the torques on both sides are equal, the fulcrum must be located at the center of the seesaw.

Therefore, the fulcrum is in the center and equidistant from both ends of the seesaw.

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Four 30 kg children are balancing on a 50 kg seesaw, each 1.5 feet from each other and the ends of the seesaw. When the seesaw is balanced, the fulcrum will be at the Center of Mass. Where is the fulcrum when it is balanced?

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Step-by-step explanation:

it is simple - there is a rule you have to burn into your memory for life (together with Pythagoras) :

the sum of all angles in a triangle is always (truly always) 180°.

so,

180 = 79 + (x + 48) + (x + 65)

180 = 79 + x + 48 + x + 65 = 2x + 192

-12 = 2x

x = -6

that means

A = x + 48 = -6 + 48 = 42°

so, the first answer option is correct.

the other angle is x + 65 = -6 + 65 = 59°

and to check

79 + 59 + 42 = 180°

all ok.

Answer:

Angle A = 42

Step-by-step explanation:

In a triangle angles always add up to 180 :

So 79 + (x+48) + (x+65) = 180

Collect like terms :

2x + 192 = 180

Subtract 192 from both sides :

2x = -12

Divide both sides by 2 :

x = -6

Now angle A = x+48

Angle A = -6+48

Angle A = 42

Hope this helped and have a good day

t = 180 - 66 - 57 = 57°