On a certain hot​ summers day, 685people used the public swimming pool. The daily prices are$1.75 for children and$2.00 for adults. The receipts for admission totaled $1.282.50 How many children and how many adults swam at the public pool that​ day?

An explicit rule for the g(x) will be g(x) = 60,000(1.1)ˣ.

A function is a connection between a number of inputs and a single output. A function is, to put it simply, an association between inputs where each input is linked to exactly one output. For each function, a domain, codomain, or range exists. A function is often represented by the expression f(x), where x represents the input.

Given, Stefany's income at her company, Horizon Logistics begins off evolving at a base income of $60,000.

Since Stefany's salary at Horizon Logistics starts at a base salary of $60,000, we can write:

g(1) = 60,000

g(2) = 66,000 = 60,000 + 6000

g(2) = 60,000 + 60000(0.1)

g(2) = 60,000* (1.1)

g(3) = 72600 = 66,000 + 6600 +

g(2) = 66,000 + 66000(0.1)

g(2) = 66,000* (1.1) = 60,000 (1.1)²

And so on

thus, we can formulate the function for g(x)

such that

g(x) = 60,000(1.1)ˣ

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If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, then none of the statements is false.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

Since a/b = c/d, are proportional then can cross-multiply to get ad = bc.

Now, evaluate each statement -

A. b/a = d/c

Cross-multiplying, it is obtained that bc = ad, which is true based on the original proportion.

Therefore, this statement is true.

B. a/c = b/d

Cross-multiplying, it is obtained ad = bc, which is also true based on the original proportion.

Therefore, this statement is true.

C. b/a = c/d

This is equivalent to the original proportion, so it is true.

D. (a + b)/b = (c + d)/d

Simplify the equation -

d(a + b) = b(c + d)

da + db = bc + bd

da = bc

Cross-multiplying, it is obtained that da = bc, which is true based on the original proportion.

Therefore, this statement is true.

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esta es la respuesta 8 B)

porque si lo restas y sumas da a 8

Answer:

Step-by-step explanation:

In a circle with a radius of 0.1, an arc length of 0.4 is intercepted by an angle. To find the angle in radians, we use the formula:

angle in radians = arc length / radius

Substituting the given values, we have:

angle in radians = 0.4 / 0.1 = 4

So the angle in radians is 4 radians, to the nearest tenth.

$5

$5 is the y intercept, so that would be the delivery fee. Also, each pizza costs $10

volume of a cube = x³

where x the length of the side of the cube

so, the volume = (4.2)³

= 74.088 in³

Value of limit expression

[tex]\lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]  [tex]=\dfrac{5}{9}[/tex]

Value of limit expression

[tex]\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex] [tex]= \dfrac{1}{7}[/tex]

In mathematics, the limit is the value that the function approaches as the input approaches the value. Limits are essential in calculus and mathematical analysis and are used to define continuity, derivatives and integrals  

Given

[tex]a) \lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]

[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{sin6\theta}[/tex]

[tex]sin\theta = \theta - \dfrac{\theta^{3}}{3!} + \dfrac{\theta^{5}}{5!} + .......[/tex]

[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{6\theta - \dfrac{(6\theta)^{3} }{3!} +\dfrac{(6\theta)^{5} }{5!}- ......}[/tex]

[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{(6\theta)(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex][tex]\dfrac{10}{3\times6} \lim_{\theta \to 0} \dfrac{\theta}{(\theta)(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex][tex]\dfrac{10}{3\times6} \lim_{\theta \to 0} \dfrac{1}{(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex]

[tex]\dfrac{10}{3\times6} \times \dfrac{1}{(1 - \dfrac{(0)^{2} }{3!} +\dfrac{(0)^{4} }{5!}- ......)}[/tex]

[tex]=\dfrac{5}{9}[/tex]

[tex]b)\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex]

[tex]\lim_{x \to 1} \dfrac{(x -1) - \dfrac{(x - 1)^{3}}{3!}-\dfrac{(x - 1)^{5}}{5!} - ......}{x^{2} + 6x - x -6}[/tex][tex]\lim_{x \to 1} \dfrac{(x -1) - \dfrac{(x - 1)^{3}}{3!}-\dfrac{(x - 1)^{5}}{5!} - ......}{x(x + 6) - 1(x +6)}[/tex][tex]\lim_{x \to 1} \dfrac{(x - 1)(1 - \dfrac{(x - 1)^{2}}{3!}-\dfrac{(x - 1)^{4}}{5!} - ......)}{(x- 1)(x +6)}[/tex]

[tex]\dfrac{(1 - \dfrac{(1 - 1)^{2}}{3!}-\dfrac{(1 - 1)^{4}}{5!} - ......)}{(1 +6)}[/tex]

[tex]=\dfrac{1}{7}[/tex]

Hence, [tex]\dfrac{5}{9}[/tex] is value of limit expression [tex]\lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]

and [tex]\dfrac{1}{7}[/tex] is value of  expression [tex]\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex]

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Answer:

33 inches

Step-by-step explanation:

Use triangle calculator online

The volume of the open-topped box expressed as the function is V(x) = x(9 - 2x)(12 - 2x)

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

Length = 9

Width = 12

Cut out = x

The volume as a function of x is represented as

V(x) = (Length - 2x) * (Width - 2x) * x

Substitute the known values in the above equation, so, we have the following representation

V(x) = x(9 - 2x)(12 - 2x)

Hence, the function si V(x) = x(9 - 2x)(12 - 2x)

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Let's call the smaller number "x". Since the larger number exceeds the smaller number by 1, we can call the larger number "x + 1".

The problem tells us that the sum of the numbers is 25, so we can set up an equation:

x + (x + 1) = 25

Simplifying and solving for x:

2x + 1 = 25

2x = 24

x = 12

So the smaller number is 12. To find the larger number, we can use x + 1:

x + 1 = 12 + 1 = 13

So the larger number is 13.

Therefore, the two numbers are 12 and 13.

h(-2) = 3

h(0) = 0

h(5) = 3/4

This can be solved by using the concept of function.

In arithmetic, a function from one set to another, X to Y, allocates precisely one element of Y to each element of X. Both of the set X and the set Y usually known as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

A function with the name f is defined by the formula y=f(x). This is understood to mean "y is a function of x." The input value, also known as an independent variable, is represented by the letter X. The outcome value, or dependent variable, is denoted by the letter y, or f(x).

This is a piece wise-defined function:

For h(-2):

h(-2) = 3

For h (0):

h(0) = (x + 1)²- 1

h(0) = (0 + 1)² - 1

h(0) = 1 - 1

h(0) = 0

For h(5):

h(5) = -1/4 x + 2

h(5) = -1/4(5) + 2

h(5) = 3/4

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Now that we know k is 3/2, we can use the formula to find the value of y when x is 14:

y = (3/2)(14) = 21

Therefore, when x = 14, y = 21.

A variable is a number in mathematics that can change depending on the issue. Several statements and equations in mathematics use the generic letters x, y, and z. Or to put it another way, a variable is a symbol that denotes an unknowable numerical value. Assume that x + 5 = 10. The term "x" is used here.

Since y varies directly with x, we know that the ratio of y to x is constant. Let's call this constant k. Then we can write:

y = kx

To find k, we can use the first two rows of the table:

When x = 2, y = 3, so:

3 = k(2)

k = 3/2

When x = 10, y = 15, so:

15 = k(10)

k = 3/2 (which matches the previous calculation)

Now we can use k to find y when x = 14:

y = (3/2)(14) = 21

Therefore, when x = 14, y = 21.

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Circumcenter is term describes point N .

What are circumradius and circumcenter?

The center of a triangle's circumcircle is known as the circumcenter. The radius of that polygon's circumscribed circle is known as the circumradius.

                         A polygon's circumcenter is marked by the circumcenter point of the circumcircle. The circle that encircles a polygon from all of its vertices is known as its circumcircle, and its circumcenter is where that circle begins.

We have been given an image of a triangle KLM  and we are asked to choose the term that describes point N.

We can see that point N is the point where perpendicular bisector of our given triangle are intersecting.

Since the point where the perpendicular bisectors of a triangle intersect is called circumcenter, therefore, point N is the circumcenter of our given triangle KLM .

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Answer:

Step-by-step explanation:

Let's assume that x is the number of boxes that the moving company moves in a certain amount of time (in hours). Then we can write the following equation to represent the relationship between the number of boxes moved and the time taken:

x = 50h

where h is the number of hours taken to move x number of boxes.

This equation means that the number of boxes moved, x, is equal to the product of 50 boxes per hour and the number of hours, h, taken to move those boxes.

For example, if the moving company moves 200 boxes, then we can find the time taken as:

200 = 50h

h = 200/50

h = 4

Therefore, the moving company takes 4 hours to move 200 boxes.

The third expression i.e. a(b) + a(c) is not equivalent to the other expressions. The solution has been obtained by using the algebraic expressions.

What is an algebraic expression?

A mathematical phrase is said to as "algebraic" if it contains variables, constants, and algebraic operations (addition, subtraction, etc.).

We are given three expressions.

The first expression is a + b+ c which represents the sum of the three variables.

The second expression is c + b + a which also represents the sum of the three variables but just the order of adding is different.

The third expression is a(b) + a(c) which represents sum of two variables multiplied with the third variable.

Hence, the third expression i.e. a(b) + a(c) is not equivalent to the other expressions.

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In a case whereby volume of this sphere is 904.32 cubic inches the surface area of this sphere can be expressed as 452.16 in^2

The concept here is using the surface area formula which is

A = Area = (4 π r^2 )  

V= Volume =( 4/3 π r^3)

Then A / V = 3 / r

Also, r = [(3 * V / 4 *  π)^1/3 ]

Then we can substitue the values as

π = 3.14

volume = 904.32 cubic inches

=[ (3 * 904.32 / (4 *  π))^1/3]

= 6 inch

Hence ,  A =( 3 / 6 * V )

= (1/2 * 904.32)

= 452.16 in^2

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Complete question:

The volume of this sphere is 904.32 cubic inches. What is the surface area of this sphere?

Use a 3.14 and round your answer to the nearest hundredth.

16% (percent) of the total planes is made up of Green Planes.

The percentage refers to the ratio of one value or quantity compared to another.

The percentage can be computed as the quotient of the numerator and the denominator multiplied by 100.

Percentage values range from 0% to 100%.

               Car        Plane        Train       Total

Green     120         250           500         870

Blue        150         350           750       1250

Yellow    170         200           450        820

Red       200         300           300        800

Brown   220         450           320        990

Total     860        1550        2320       4730

Green Plane = 250 of 1,550 total planes = 16.13% (250/1,550 x 100)

Green Plane = 250 of 870 Vehicles = 28.74% (250/870 x 100)

Thus, we can conclude that of the 1,550 planes, green planes consist of 16%.

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The sum of interior angles of the polygon is 900 degrees.

A polygon is a two-dimensional geometric figure that has a finite number of sides. Therefore, a polygon is named according to the number of sides. For example we have triangles, hexagon, pentagon, quadrilaterals, heptagons, nonagon, decagons etc.

Therefore, the polygon in the diagram has seven sides. Hence its an heptagon.

The sum of interior angles of a heptagon can be found as follows:

sum of interior angles = 180(n - 2)

where

sum of interior angles = 180(7 - 2)

sum of interior angles = 180(5)

Therefore,

sum of interior angles = 900 degrees

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The sum of the interior angle of the polygon is 900^o.

A polygon is a plane shape which has three or more number of sides. The important thing about polygons is that they are named according to their number of sides. Some common examples are: trigon- 3 sides, pentagon- 5 sides, heptagon - 7 sides etc.

The sum of internal angles of a polygon = (n - 2)180

where n is the number of sides of the polygon

In the given diagram, the polygon has 7 sides, thus it is a heptagon. Thus n is 7, so that;

sum of internal angles of a heptagon = (n - 2)180        

                                            = (7 - 2)180

                                            = 5*180

                                            = 900

Therefore, the sum of the interior angles of the polygon is 900^o.

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a) The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = 0.1406

b) The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 0.4219

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

The number of possible answers = 4

Let the probability that the answer is correct P ( C ) = 1/4

Let the probability that the answer is wrong P ( W ) = 3/4

Now , probability that the first two guesses are wrong and the third is correct is P ( WWC ) = P ( W ) x P ( W ) x P ( C )

On simplifying , we get

The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = ( 3/4 ) x ( 3/4 ) x ( 1/4 )

The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = ( 9/64 ) = 0.1406

And ,

The probability that exactly one correct answer when 3 guesses are made is = P ( WWC ) + P ( WCW ) + P ( CWW )

The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 3 x 0.140625

The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 0.4219

Hence , the probabilities are solved

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The requried Kristen travels 9.5 miles to work. Option D is correct.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
We can use the formula distance = rate x time to solve this problem.

When Kristen is biking, her rate is 10 mph and her time is 1/4 hour. So her distance traveled is:

distance = rate x time

distance = 10 mph x 1/4 hour

distance = 2.5 miles

When Kristen is on the train, her rate is 28 mph and her time is another 1/4 hour. So her distance traveled on the train is:

distance = rate x time

distance = 28 mph x 1/4 hour

distance = 7 miles

Therefore, the total distance Kristen travels to work is the sum of the distances she traveled while biking and on the train:

total distance = distance biked + distance on train

total distance = 2.5 miles + 7 miles

total distance = 9.5 miles

So Kristen travels 9.5 miles to work.

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The reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

Vector, in mathematics, a quantity that has both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.

The reflection of a vector v in a line L can be found by projecting v onto L and then doubling the projection.

To project v onto L, we need to find the projection of v onto a vector that lies on L. Let's call this vector a. We can find a by normalizing the vector [1, -2, 2] to get:

a = [1/3, -2/3, 2/3]

Now, the projection of v onto a is given by the dot product of v and a:

proj_v_a = (v . a) * a = [(81/3) + (5(-2/3)) + (7*2/3)] * [1/3, -2/3, 2/3]

= [13/3, -26/3, 26/3]

To find the reflection of v in L, we need to double the projection and subtract it from v:

ref_v_L = 2 * proj_v_a - v

= 2 * [13/3, -26/3, 26/3] - [8, 5, 7]

= [26/3, -52/3, 52/3] - [8, 5, 7]

= [2/3, -67/3, 31/3]

Therefore, the reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

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The first positive solution is approximately x = 1.011. Therefore, the answer is D. x= 1.011.

An equation is a mathematical statement that expresses the equality between two mathematical expressions or values. It is a concise representation of a relationship between two or more variables, which can be represented using symbols or numbers. An equation usually consists of two sides separated by an equal sign, where each side represents a mathematical expression.

Equations are used in various branches of mathematics, science, engineering, and other fields to describe various phenomena and solve problems. They play a crucial role in understanding and describing real-world phenomena, from the laws of physics to the behavior of financial markets. Equations can help us predict outcomes, design solutions, and solve complex problems.

In mathematics, equations are used to solve problems that involve unknown variables. The unknown variables can be found by manipulating the equation to isolate the variable. Solving equations is a fundamental skill in mathematics, and it is often used in fields like physics, chemistry, and engineering.

Equations can be linear or nonlinear, depending on the degree of the variables involved. Linear equations involve variables raised to the first power only, while nonlinear equations involve variables raised to higher powers or are composed of a combination of functions.

In summary, equations are a fundamental tool in mathematics and other fields, which help us describe and understand the relationships between variables and solve problems involving unknown variables.

To find the first positive time at which the particles have approximately the same velocity, we need to find the derivative of the displacement function for each particle, set them equal to each other, and solve for x.

The derivative of the displacement function for particle 1 is:

f'(x) =[tex]-4e^(4[/tex]cos(x))sin(x)

The derivative of the displacement function for particle 2 is:

g'(x) =[tex]-x^2 - x[/tex]

Setting f'(x) equal to g'(x), we get:

[tex]-4e^(4[/tex]cos(x))sin(x) =[tex]-x^2 - x[/tex]

We can solve this equation numerically using a graphing calculator or computer software. The first positive solution is approximately x = 1.011. Therefore, the answer is D. x= 1.011.

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Answer:

the answer is A. 11 1/4

Step-by-step explanation:

the base times height for the triangle divided by 2 plus the bxh of the rectangle.

3x3/2 + 1 1/2 x 4 1/2

The program to find the divisible values gives the number of multiples of 2 between 3 and 8 inclusive is 3

To check if an integer is divisible by x, you could divide it by x and check if the remainder is 0.

If the remainder is 0, then the integer is divisible by x and therefore is a multiple of x.

We can use this concept to find the number of multiples of x between low and high inclusive.

If low is 3, high is 8, and x is 2, then we can check if each number between 3 and 8 is divisible by 2.

3 is not divisible by 2, so it is not a multiple of 2.

4, however, is divisible by 2, so it is a multiple of 2.

5 is not divisible by 2, so it is not a multiple of 2.

6, however, is divisible by 2, so it is a multiple of 2.

Then 7 is not divisible by 2, so it is not a multiple of 2. 8 is divisible by 2, so it is a multiple of 2.

Therefore, the number of multiples of 2 between 3 and 8 inclusive is 3 (4, 6, and 8).

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Answer:

Step-by-step explanation:

Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.

We know that the 5th term is 729, so:

a * r^4 = 729

10th term is 3, so:

a * r^9 = 3

r^5 = 3/729

r^5 = 1/243

r = (1/243)^(1/5)

r = 1/3

a * (1/3)^4 = 729

a = 3^7

Therefore, the sequence is:

3^7, 3^6, 3^5, 3^4, 3^3, ...

The 12th term is:

3^2 = 9

Yellow makes up approximately 17.32% of the total number of trips.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

To find the percentage of the total that Yellow makes up, divide the total number of Yellow trips by the overall total number of trips, and then multiply by 100 to convert to a percentage -

Yellow total = 820

Overall total = 4730

Yellow percentage = (820/4730) x 100%

Yellow percentage = 0.1734

Yellow percentage = 17.34%

Therefore, Yellow makes up approximately 17.32% of the total number of trips.

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Answer:

[tex]\frac{3}{x+7}[/tex]

Step-by-step explanation:

[tex]\frac{3x-21}{x^{2} -49}[/tex]

We will start with factoring the numerator, by pulling a 3 out of each term:

3(x - 7)

We will then factor the denominator. As the denominator is a difference of perfect squares (in the form [tex]x^{2} -a^{2}[/tex]), we know that it can be factored in the form (x + a)(x - a), a being the square root of the number given. (In this case, a = 7, because the square root of 49 is 7.)

Our denominator is now:

(x + 7)(x - 7)

And our fraction is now:

[tex]\frac{3(x-7)}{(x-7)(x+7)}[/tex]

As both the numerator and denominator have the term (x-7), they will cancel, leaving us with the simplified expression:

[tex]\frac{3}{x+7}[/tex]

Two polygons are similar if and only if all corresponding angles are congruent and all corresponding sides are proportional. The solution has been obtained by using concept of similar quadrilaterals.

What are similar quadrilaterals?

Two quadrilaterals are considered to be similar when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).

Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.

Hence, the corresponding angles need to be congruent.

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Answer:

Step-by-step explanation:

4x-22.2=1.90

22.20-4x=1.90

4x + 1.90 = 22.20

Answer:

[tex]\frac{26}{3}[/tex]

Step-by-step explanation:

Decimal form would be 8.6

The values are

a. h(-2) = 20

b. h(-1) = -4

c. h(-x) =x⁴+3x²-8

d. h(3a) = 243a⁴+27a² -8

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

h(x) =x⁴+3x²-8

therefore f(-2) = (-2)⁴ + 3(-2)²-8

= 16+12-8

= 20

h(-1) = (-1)⁴+ 3(-1)²-8

h(-1) = 1+3-8

= -4

h(-x) = (-x)⁴ + 3(-x)² -8

= x⁴+3x²-8

h(3a) = 3(3a)⁴ + 3(3a)² -8

= 243a⁴+27a² -8

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