On a certain hot​ summer's day, 353 people used the public swimming pool. The daily prices are 1.50 for children and 2.50 for adults. The receipts for admission totaled 709. How many children and how many adults swam at the public pool that​ day?

The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:

The equation is in the form  

dy/dx +P(x)y=Q(x)yⁿ,  where P and Q are functions of x or constants, this is called Bernoulli's equation.

Now, we have to substitution using 

[tex]v = {y}^{1 - n} [/tex]

Differentiating both side with respect to 'x'

[tex]v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'[/tex]

we get,

[tex]= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)[/tex]

Now, by using 

[tex]v' = {y}^{1 - n} [/tex]

The given equation is expressed as:

[tex]v + (1 - n)p(x)v = (1 - n)q(x)[/tex]

or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)

The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.

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The correct answer is the rate of change is 6 over interval 1 ≤ x ≤ 4 and the rate of change is 6 over interval 2 ≤ x ≤ 4  

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. In general, the formula for rate of change is: R = (D2 - D1)/T. where: R = rate of change.

Given that is a table, we need to find the average rate of change for the function,

a = 1, f(a) = 1

b = 2, f(b) = 3

Average rate of change is given by = f(b)-f(a) / b-a

= 3-1 / 2-1

= 2

a = 3, f(a) = 7

b = 4, f(b) = 15

Average rate of change is given by = f(b)-f(a) / b-a

= 15-7 / 4-3

= 8

a = 2, f(a) = 3,

b = 3, f(b) = 7

Average rate of change is given by = f(b)-f(a) / b-a = 4

Hence, the correct answer is the rate of change is 6 over interval 1 ≤ x ≤ 4 and the rate of change is 6 over interval 2 ≤ x ≤ 4  

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8 is the measure if the angle x in the given diagram.

The point where two lines meet is known as an angle. The given diagram is a circle geometry.

Using the theorem, angle at the arc is twice the angle at the vertex, we will have:

80 = 2(4x + 8)

80/2 = 8x + 8

40 = 4x + 8

4x = 40 - 8

4x = 32

x = 32/4

x = 8

Hence the value of x from the diagram given is 8

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The correct statement regarding the continuity of differentiable functions is given as follows:

D. Yes, if f is differentiable at a, then f is continuous at a.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

For a function to be classified as differentiable, the function must be continuous, plus the first derivative of the function must also be continuous.

This means that all differentiable functions are continuous, and thus the correct option is given by option D.

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Answer:

I spent 13.32 at the store the other day...?

Step-by-step explanation:

What is the question.

If functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x)=x² +16x-24 and g(x)=x²-5x-17.

We need to find  (ƒ + g)(x).

From properties we have (ƒ + g)(x)=f(x)+g(x)

(ƒ + g)(x)=x² +16x-24+x²-5x-17.

Add the like terms

(f+g)(x)=2x² +11x-41

Hence, if functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.

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The equation that represents the amount of money saved is S = $100 + $20w

The equation that represents the amount of money saved is a linear equation . A linear equation is an equation that has a single variable raised to the power of 1.

The form of the linear equation is:

Total money saved = amount in the bank + (amount that would be saved each week x number of weeks)

S = $100 + ($20 x w)

S = $100 + $20w

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[tex]\fbox{\textbf{288, 296, and 304}}

[/tex]

Answer: 946 ml

Step-by-step explanation: 1 pint= 473.2

2*

473.2= 946.4

=946 ml

The equation x^2+y^2=100 is not a function

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

x^2 + y^2 = 100

The above equation is a circle equation

As a general rule, we have

Circle equations are not functions and they do not represent a function on a graph

Hence, x^2+y^2=100 is not a function

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A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.

A conditional statement is one that has the form "If P then Q," where P and Q are sentences. P is referred to as the hypothesis in this conditional statement, and Q is referred to as the conclusion. "If P then Q" implies that Q must be true sometimes when P is true.

The type of conditional statements are as follows:

A statement in which a conclusion is true if the conditions of a particular hypothesis are true is called a conditional statement.

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The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.

A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.

Triangular pyramid  is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.

It has 6 edges, 4 faces, 4 vertices.

A regular triangular pyramid has equilateral triangles all four faces

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The volume of the paperweight is 79.3 cm³.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

From the given information, The area of the star-shaped cutout is,

A square has a side length of 2 cm, and four equilateral triangles have a side and a height of 2 cm.

So, The area of the star-shaped cutout is,

= (2×2) + 4×(1/2)×2×2.

= 4 + 8.

= 12 cm.

Now, The volume of the star-shaped cut-out is,

= 12×height,

= 12×3.

= 36 cm³.

And the volume of the cylinder is,

= π(1 + 2 + 0.5)²×3.

= π(3.5)²×3.

= 115.4 cm³

Therefore, The volume of the paperweight is,

= 115.4 - 36 cm³.

= 79.3 cm³.

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The degree of the expression 7c³d² is 2

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

Expression = 7c³d²

The degree of an expression is the highest power in the expression

In this case,

7c³ =  Constant

d² = Variable

The highest power of the variable is 2

Hence, the degree is 2

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Answer:

They plan to spend $24 on rides.

Step-by-step explanation:

Let the amount they spend on food be x.

ride : 2x

amount left= $56-$20

                    = $36

2x+x= 36

x=12

2x= 2(12)

   = 24

Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

The expressions that have a positive value based on the positions of a and b are a + b and a×b. options 2 and 4

Algebraic expressions are defined as expressions that are made up of terms, variables, factors and constants.

These expressions are also composed of mathematical operations such as;

Given the expressions;

a+ b and a×b.

They have the variables both positive

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The equation of line is y = 30x + 75 , where the slope is m = 30 and the y intercept is 75

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 105 )

Let the second point be Q ( 3 , 165 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 165 - 105 ) / ( 3 - 1 )

Slope m = ( 60 / 2 )

Slope m = 30

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 105 = 30 ( x - 1 )

On simplifying the equation , we get

y - 105 = 30x - 30

Adding 105 on both sides of the equation , we get

y = 30x + 75

Hence , the equation of line is y = 30x + 75

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The average increase in first 2 days is 1.5 pennies/day.

Given is a tabular data about Daisy's piggy bank.

The average increase in first 2 days -

{a} = (7 - 4)/(2 - 0)

{a} = 3/2

{a} = 1.5

Therefore, the average increase in first 2 days is 1.5 pennies/day.

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Answer:

Angle 4 = 140

Angle 3= 40

Angle 5=140

angle 6=40

angle 7=40

Step-by-step explanation:

Adjacent angles are congruent. Thats how I can tell angle 4 is 140. And also how i can tell angle 3 is 40. Any questions?

im not explaining the rest im too tired

btw I also do 8th math lol it stinks.

The equivalent simplified expression is 1.02n.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Given that, Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour.

The expression n +0.02n is one way to represent Arturo's pay per hour after the raise.

Here, the equivalent expression is n +0.02n= 1.02n

Therefore, the equivalent simplified expression is 1.02n.

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The probability of landing on the head side of coin and rolling a 3 on the die is found as 1/12.

Sample space for tossing a coin: (H,T)

P(head) = 1/2

Sample space for tossing a dice : (1, 2, 3, 4, 5, 6)

P(3) = 1/6

So,

Probability of head with 3 on the die = 1/ 2* 1/6 = 1/ 12

Thus, the probability of landing on the head side of the coin and rolling a 3 on the die is found as 1/12.

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The correct question is-

A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.

Enter your answer as a fraction in the form a/b (for example 2/3, 5/7) or as an integer.

If you're making 60 servings of bread and using 540 oz of flour, then the number of ounces of yeast you need is 3 oz.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, to make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180.

If you're making 30 servings of bread and using 0.25 oz of yeast, then

0.25/Flour = 1/200

Flour = 50 oz

If you're making 60 servings of bread and using 540 oz of flour, then

Yeast/540 = 1/180

Yeast = 3 oz

Therefore, if you're making 30 servings of bread and using 0.25 oz of yeast, then the number of ounces of flour you need is 50 oz.

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The connection string for SQL Server using Windows Authentication is as follows:

Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;

Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.

Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.

Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.

Use semicolons (;) to separate the different parts of the connection string.

Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.

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As per the concept of polygon,

a) The sum of the interior angles is 10,440° then the number of sides is 58

b) The value of each interior angle is 171°, then the number of sides is 36

A polygon is a two-dimensional geometric shape made up of straight lines and angles. The number of sides a polygon has is directly related to the sum of its interior angles.

a), we can use the formula for the sum of the interior angles of a polygon, which is (n-2) times 180 degrees, where n is the number of sides. To find n, we can rearrange the formula to

=> n = (sum of interior angles / 180) + 2.

Plugging in the value of 10,440 degrees for the sum of interior angles, we get

=> n = (10440 / 180) + 2 = 58.

Therefore, the polygon in item a) has 58 sides.

For item b), we can use the formula for the value of each interior angle of a regular polygon, we get

=> n = (180(n-2)) / 171 = (180n - 360) / 171.

Solving for n, we find that the polygon in item b) has 36 sides.

In conclusion, polygons with the angle values shown in items a) and b) have 58 and 36 sides respectively. These formulas can be applied to any polygon to find the number of sides based on its interior angle values.

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The equivalent equations are 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n.

Two or more expressions with an Equal sign is called as Equation.

To determine which equations are equivalent to each other, we can simplify and manipulate each equation to see if they have the same solution(s).

52 = 8n + 4 can be simplified by subtracting 4 from both sides:

48 = 8n

n=6

Now 4(2n + 1) = 52

8n+4=52

8n=48

n=6

So the 52 = 8n + 4 and 4(2n + 1) = 52 are equivalent equations.

Now 4 = 52 – 8n

8n=52-4 is also equivalent equation.

4n=48 and n=6 are also equal but they are not in the same form as above equations.

Hence, 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n are equivalent equations.

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To write Euler's number in Symbolab, you can simply use the notation "e". For example, if you want to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.

Euler's number, denoted as "e", is a mathematical constant that is approximately equal to 2.71828. To write Euler's number in Symbolab, you can simply use the letter "e" in lowercase. For example, to evaluate the exponential function with a base of e raised to the power of 2, you can enter "e^2" in Symbolab.

Alternatively, if you want to use the built-in function for Euler's number in Symbolab, you can use the "exp(x)" notation, where x is the exponent. For example, to evaluate e raised to the power of 2, you can enter "exp(2)" in Symbolab. Symbolab supports various mathematical functions and constants, including trigonometric functions, logarithmic functions, and mathematical constants, which can be used to solve various mathematical problems.

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Answer:

  77.7 g

Step-by-step explanation:

You want the mass of a cylindrical scoop of radius 2 cm and height 5 cm when it is filled with water at 1 g/cm³, and has an empty mass of 14.9 g.

The mass of the water will be the product of its volume and its density. The volume is that of a cylinder with radius 2 cm and height 5 cm. That volume is given by the formula ...

  V = πr²h = π(2 cm)²(5 cm) ≈ 62.83 cm³

The mass of the water is then ...

  (62.83 cm³) × (1 g/cm³) = 62.83 g

The total mass of the water-filled scoop is the sum of its empty mass and the mass of the water:

  scoop + water = 14.9 g + 62.8 g = 77.7 g

The mass of the scoop and water is 77.7 grams.