Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?

Answer:

  A.  1/4 gal/scoop

  B.  w = 1/4s

  C.  line through the origin with slope 1/4; s-, w- axes labeled "scoops" and "gallons"

  D.  3 gallons

Step-by-step explanation:

Given 2 scoops of  powdered drink mix needs 1/2 gallon of water, you want (A) the constant of proportionality, (B) the equation for the relationship, (C) a description of the graph, (D) gallons for 12 scoops.

A proportional relationship between gallons of water (w) and scoops of drink mix (s) can be written as ...

  w = ks

where k is the constant of proportionality.

Solving the equation for k, we get ...

  k = w/s

Using the given values, we find k to be ...

  k = (1/2 gal)/(2 scoops) = 1/4 gal/scoop

The constant of proportionality is 1/4 gallon per scoop.

We show the equation in part A. Filling in the value of k gives ...

  w = 1/4s . . . . . . . where s is number of scoops, and w is gallons of water

The attached shows a graph. A line starts at the origin with slope 1/4; s-, w- axes are labeled "scoops" and "gallons". The practical domain is s ≥ 0, so no part of the graph is in the 3rd quadrant.

The equation tells you that 12 scoops will require ...

  w = 1/4·12 = 3 . . . . gallons

3 gallons of water are needed for 12 scoops of drink mix.

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Events A and B dependent as occurrence of one event does not affect the chances of the occurrence of the other event.

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

To understand this branch, it is extremely important to know its most basic definitions, such as the formula for calculating probabilities in equiprobable sample spaces, probability of the union of two events, probability of the complementary event, etc.

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).

Since we have given that;

A be the event that a store sells all of their ground hamburger for the week

P(A)=0.75

B be the event that that the store sells all of it's steak for the week is

P(B)=0.68

The probability that the store sells all of both of the meats for the week is 0.62.

P(A|B)=0.62

but for A and B to be independent ,

P(A).P(B)= P(A and B)

0.75×0.68=0.51

but,

[tex]P(A|B) = \frac{P(AnB)}{P(B)}[/tex]

P(AnB) = 0.62 x 0.68

P(AnB) = 0.4216

So, P(A∩B) does not satisfy the condition.

Hence, A and B are not independent events.

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Answer: 792 Combinations

The (two-way) wave equation is a second-order partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions.

This article mostly focuses on the scalar wave equation describing waves in scalars by scalar functions u = u (x1, x2, ..., xn; t) of a time variable t (a variable representing time) and one or more spatial variables x₁, x₂, ..., xₙ (variables representing a position in a space under discussion) while there are vector wave equations describing waves in vectors such as waves for electrical field, magnetic field, and magnetic vector potential and elastic waves. By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x-component for the x-axis) of a vector wave without sources of waves in the considered domain (i.e., a space and time). For example, in the Cartesian coordinate system, for Eₓ , Eₐ and Eₙ the representation of an electric vector field wave E in the absence of wave sources, each coordinate axis component

Ei (  i = x , a , n) must satisfy the scalar wave equation. Other scalar wave equation solutions u are for physical quantities in scalars such as pressure in a liquid or gas, or the displacement, along some specific direction, of particles of a vibrating solid away from their resting (equilibrium) positions.

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On dot plot we take no. of successes out of 10. Hence it having 0 to 10 numbering.

What is dot plots in statistics?

For relatively small data sets with values falling into a handful of discrete bins, a dot plot, also known as a dot chart, is a sort of straightforward histogram-like display used in statistics.

                       To create a dot plot, count the data points that fall into each bin and then draw a stack of dots that is that many dots high for each bin.

Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.

On X axis, we take no. of successes out of 10. Hence it having 0 to 10 numbering.

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Answer: 9x

Step-by-step explanation:

-4x+y=5x

solve for x

y=9x

Answer:

344

Step-by-step explanation:

6 percent of 530 is 31.8

530-31.8=498.2 or 498

6 percent of 498=29.88

498-30=468

6 percent of 468=28.08

468-28=440

6 percent of 440=26

440-26=414

6 percent of 414=24.84

414-25=389

6 percent of 389=23.34

389-23=366

6 percent of 366=21.96

366-22=344

Thus, our answer is 344

Answer:

reflection across the line y=x

Step-by-step explanation: the point (-2,1) would turn into (1,-2) which the other figure shows

Rate of change of y =[tex]\frac{5}{4}x +1[/tex]  is 5/4.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y =[tex]\frac{5}{4}x +1[/tex] .

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y =  is 5/4.

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Answer:

–3 4/15

or

3 4/15

Step-by-step explanation:

the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.

What is Diagonalizable matrix?

If there is an invertible matrix P and a diagonal matrix D such that

P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.

If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.

The given statement is false.

If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.

Hence, the given statement is false.

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Answer:135.375[tex]\pi[/tex] ft³

Step-by-step explanation:

The formula for the volume of a right circular cone is [tex]\frac{1}{3}[/tex][tex]\pi[/tex]r²h.

We are given height, and we can find r by dividing diameter by 2, which is 9.5 ft.

Plugging these values into the equation give us [tex]\frac{1}{3} \pi (9.5)^{2} (4.5)[/tex].

This equation equals 135.375[tex]\pi[/tex] ft³

She may sell five of them each week for $21,000. She needs to ask for $20,000 for each unit if she wants to sell six. The marginal revenue of selling the sixth motor home is -$5000. Here option A is the correct answer.

If demand is price inelastic, then raising the price will decrease income. If price increases elastic, lowering the price will boost earnings.

Demand is considered to be elastic if an increase in price results in a loss in overall income because the quantity required is significantly impacted by the price rise. Depending on whether they are requirements or wants, the marketplace. in other words, may have varying elasticities (accessories).

Thus, a fall in revenue because of a rise in price

= (20,000 - $21,000) × (5)

= -$5000

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It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.

the range of variation that is conceivable or the boundaries between it: pricing for various grades of steel; a variety of designs. a thing's operation or action's reach or extent: accessible to the eye. a projectile's range is how far a weapon can or will shoot it.

here the explanation

We can say that our range is any real number value between -infinity and infinity, or (,), if our range is any real number value. The range is all real numbers, but we can express this more succinctly by using the symbol R.

a position where the value of a function is highest. It is an absolute maximum if the value is larger than or equal to all other function values.

It is occasionally accurate to say that the range of an even function is (-∞o, max), where max is the function's maximum.

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The solution set is for the given inequality is (-∞, -2.25]

Here we want to solve the following inequality:

-11 - 8k ≥ 23 - (7 - 4k)

To solve this, we need to isolate the variable k in one side of the equation.

First we can expand the right side so we get:

-11 - 8k ≥ 23 - (7 - 4k)

-11 - 8k ≥ 23 - 7 + 4k

Group like terms:

-11 - 23 + 7  ≥ 4k + 8k

-34 + 7 ≥  12k

-27 ≥  12k

-27/12 ≥  k

-2.25 ≥  k

Then the solution is the set of all values smaller than or equal to -2.25, then the solution set is (-∞, -2.25]

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Answer:

y value also increases

Step-by-step explanation:

As the X value (also known as the independent variable) of the equation y = 2x + 80 increases, the Y value (also known as the dependent variable) will also increase. This is because the coefficient of the X term (2) is positive, which means that for every increase in the X value, the Y value will also increase by an amount equal to twice the increase in the X value.

For example, if the X value increases from 2 to 3, the Y value will increase from 84 (which is calculated as 22 + 80) to 86 (which is calculated as 23 + 80). Similarly, if the X value increases from 3 to 4, the Y value will increase from 86 to 88, and so on.

The number of tennis matches that she could have won before the weekend began is 0.

Before the weekend, the player had a win ratio of 0.500, which indicates that she had won exactly as many games as she had lost. Call this number x for now. She has so lost x matches in addition to the x matches she won before to the weekend.

She competes in three matches during the course of the weekend and loses one, bringing her overall win total (after the weekend) to x + 3 and her overall loss total (after the weekend) to x + 1. Consequently, her weekend victory ratio is

[tex]\frac{(x + 3)}{(x + 1)}[/tex]

= [tex]\frac{(3x + 3)}{(x + 1) }[/tex]

= [tex]\frac{3x }{x + 1 }[/tex]

= [tex]\frac{3}{\frac{1}{x+1} }[/tex]

given that this value is greater than 0.503,

Thus,

[tex]\frac{3}{\frac{1}{x+1} }[/tex] > 0.503

Simplifying,

[tex]\frac{3}{\frac{1}{x+1} }[/tex]> 0.503 - 1

= -0.497

Further,

[tex]\frac{3}{\frac{1}{x+1} }[/tex] > -0.497

[tex]\frac{3}{\frac{1}{x+1} }[/tex] is equivalent to 3x

This inequality can be written as

3x > -0.497

3x is positive, dividing on both sides by 3 we get

x > -0.497 / 3

Simplifying,

x > -0.166

The least value of x that meets this inequality is 0, as x, the number of matches won, must be a positive integer. Thus, the maximum number of games the player might have won prior to the start of the weekend is x = 0, and the response is 0.

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Answer:

164

Step-by-step explanation:

Let n be the number of matches she won, and m be the number of matches she played. Then, n/m = 1/2 and (n + 3) / (m + 4) > 0.503. By the first equation, 2n = m. Substituting m = 2n into the second equation/inequality, we get (n + 3) / (2n + 4) > 0.503. Because n cannot be negative in this context, we can multiply both sides by (2n + 4). We get n + 3 > 0.503 (2n + 4). Distributing the right-hand side, we get n + 3 > 1.006n + 2.012. Solving this inequality gives us 0.006n < 0.988, or n < 164.666667. n must be a whole number, so the greatest n you can achieve is 164.

On an actual test, you can also check using answer choices if given them. 164 gives around 0.50301, so it is 164, or cannot be determined. Then it is a 50/50 guess, and 164 is most likely the correct answer, which in this case, is the correct answer.

Answer:

greater than

Paperclip = 3 matches

Pencil = 6 paperclips

22×3 = 66

66×3 = 198

hope you like it

The probability to choose a group of four tiles with each tile worth one point is 0.200.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let there are total 25 tiles.

From this 20 tiles having one point each and 5 tiles having more than one point.

We have to choose a group of four tiles with each tile worth one point.

So,

probability = 4/20 = 0.200

Hence, the probability to choose a group of four tiles with each tile worth one point is 0.200.

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No, he wanted a park developed within 5 miles of his residence, yet this park is 8.30 miles away.

The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate.

Here,

let the house be (0,0).

coordinate of park=(3,7)

distance=√3²+7²

=√21+49

=√69

=8.30 miles.

No, He wanted a park to be built within 5 miles of his house while this park is 8.30 miles from his house.

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The solution is

a) ∠1 ≅ ∠5 by Corresponding Angles

b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles

c) ∠6 ≅ ∠4 by Alternate Interior Angles

d) ∠2 ≅ ∠8 by Alternate Exterior Angles

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

From the figure , we can see that

The Corresponding angles are

Angle 1 and Angle 5

Angle 2 and Angle 6

Angle 4 and Angle 8

Angle 3 and Angle 7

The Alternate Interior angles are

Angle 4 and Angle 6

Angle 3 and Angle 5

The Co-Interior angles are

Angle 4 and Angle 5

Angle 3 and Angle 6

The Alternate exterior angles are

Angle 1 and Angle 7

Angle 2 and Angle 8

Hence , the angles from the figure that are true are

a) ∠1 ≅ ∠5 by Corresponding Angles

b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles

c) ∠6 ≅ ∠4 by Alternate Interior Angles

d) ∠2 ≅ ∠8 by Alternate Exterior Angles

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The angle measures in this problem are given as follows:

7 - m < ADC = 82º.

8 - m < ADC = 44º.

In item 7, the angle measure is found obtained the angle addition postulate, meaning that the measures are obtained as follows:

m<ADB = m < BDC + m < ADC.

Then the equation to find the value of x is obtained as follows:

144 = 7x + 34 + 9x + 46

16x = 64

x = 64/16

x = 4.

Then the angle ADC is obtained as follows:

m < ADC = 9(4) + 46 = 82º.

In item 8, the bisection means that the two angle measures are equal, hence the value of x is obtained as follows:

7x - 19 = 9x - 37

2x = 18

x = 18/2

x = 9.

m < ADC = 9(9) - 37 = 44º.

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The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

The probability of drawing an even-numbered blue marble.

= Number of even blue marble / Total number of marbles

The probability of drawing an even-numbered blue marble is 3/11.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 5

Number of blue marbles = 6

Number of even blue marbles = 3

Total number of marbles = 5 + 6 = 11

The probability of drawing an even-numbered blue marble.

= Number of even blue marble / Total number of marbles

= 3/11

Thus,

The probability of drawing an even-numbered blue marble is 3/11.

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Jane must therefore deposit her savings in the four rivers bank.

Interest that is added to a loan and deposit sum is known as compound interest. In our everyday lives, it is the notion that is employed the most frequently. Compound interest is calculated as a sum using the interest and principal accrued over time. Compound interest versus simple interest differ primarily in this way.

As per the data provided in the question,

Rate, r = 12%

After five years, the total amount, if Jane had saved at Mystic Bank,if Jane had saved at Mystic Bank would be:

[tex]A = P(1+\frac{r}{100} )^n[/tex]

For compounded quarterly,

n = 5 × 4

n = 20

A = 40000(1 + 12/(4 × 100))²⁰

A = 72244.44     (i)

If Jane placed her savings with the Four Rivers, then,

A = 40000(1 + 14/(2 × 100))¹⁰

A = 40000 × 1.9671

A = 78686.054  (ii)

Therefore, it is evident that case (ii) is higher than case (i). Jane must therefore deposit her savings in the four rivers bank.

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The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

What is meant by absolute maximum and absolute minimum values?

A function's absolute maximum point is the point at which it can reach its highest value. A similar absolute minimum point is where the function's least possible value is obtained.

Given: [tex]f(x)=xe^{\frac{-x2}{32} }[/tex]

Differentiate the function,

[tex]f'(x)=e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }[/tex]

[tex]e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=0[/tex]

[tex]\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=e^{\frac{-x^{2} }{32} }[/tex]

[tex]\frac{x^{2} }{16} =1[/tex]

[tex]x^{2} =16[/tex]

[tex]x=[/tex] ±[tex]4[/tex]

The interval is given as: [-2,8]

This means that the value of x = -4, is out of the interval.

So, we have the following critical points:

x = (-2, 4, 8)

⇒ f(x) at x = -2

[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-(-2)^{2} }{32} }[/tex]

[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-4}{32} }[/tex]

[tex]f(-2)=-1.765[/tex]

⇒ f(x) at x = 4

[tex]f(4)=4[/tex] × [tex]e^{\frac{-(4)^{2} }{32} }[/tex]

[tex]f(4)=4[/tex] × [tex]e^{\frac{-16}{32} }[/tex]

[tex]f(4)=2.426[/tex]

⇒ f(x) at x = 8

[tex]f(8)=8[/tex] × [tex]e^{\frac{-(8)^{2} }{32} }[/tex]

[tex]f(8)=8[/tex] × [tex]e^{\frac{-64}{32} }[/tex]

[tex]f(8)=1.083[/tex]

Hence, by comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.

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Answer:

Below

Step-by-step explanation:

At  B   (  40 mins)  and  D (30 mins)   he is not moving....visiting .

The width of A is the time it took to get to first house = 20 mins

The width of C is t the time to get to second house = 60 to 70 = 10 mins

Riding toward home at C and E  ( the distance...the y-value....is getting less)

He is fastest where the line has greatest slope...where it is steepest =  C

He was away from home the width of the graph = 115 mins

In 480 ways people can be seated in a row so that no two software engineers are together.

We have given that there are 8 people participating in a focus group, 3 of them are software engineers, 2 of them are nurses, 1 is doctor and 2 are technicians.

So the 3 software engineers can sit in 3! ways,

2 nurses can sit in 2! ways,

doctor can sit in 1! way and

2 technicians can sit in 2! ways.

We have to find that how many ways they can sit such that no two software can sit together.

So we first place 5 people in a row and software engineers has to sit between them so no two software engineers are to be sited together.

We get that in 6 places they can sit in 6C3 ways

i.e 6C3 = 20           (by formula of combination)

Therefore total ways are,

6 × 2 × 1 ×2 × 20 = 480.

Hence in 480 ways people can be seated in a row so that no two engineers are together.

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The value of chi-square statistic is;

In the contingency table, "O" stands for the observed value, "E" for the predicted value, and "I" for the "ith" position.

Given,

Chi- Square test;-

A statistical technique called the chi-square test is used to compare actual outcomes with predictions. The goal of this test is to establish whether a discrepancy between observed and expected data is the result of chance or a correlation between the variables you are researching.

We have to find the value of chi- square statistic;

The chi-squared statistic is a single figure that indicates the degree to which the counts you saw deviate from the counts you would anticipate if there were no association at all in the population. If I is the "ith" position in the contingency table, "O" is the observed value, "E" is the anticipated value, and "O" is the observed value.

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The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.

What is standard form of an equation ?

The standard form of such an equation is Ax + By + C = 0 or Ax + By = C.

If you rewrite this equation in a different way, you'll obtain y by itself on the left side, it then forms y = mx +b.

An assertion of equality between two expressions containing variables and/or numbers is called an equation.

In essence, equations are questions, and attempts to discover systematic answers to those questions have spurred the development of mathematics.

Linear equations can be written in three different ways: point-slope form, standard form, and slope-intercept form.

General Procedure:

Equation in slope intercept form has the basic structure

y = mx + b

y - mx = (mx - mx ) + b

y - mx = b

y - mx - b = b - b

y - mx - b = 0

-mx + y - b = 0−mx+y−b=0

If m is an integer, then B will equal 1.

-A/Bx + y - b = 0−

x+y−b=0

-Ax + By - Bb = 0−Ax+By−Bb=0

-Ax + By - C = 0−Ax+By−C=0

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