A theme park sells adult tickets (a) for $159.50 and child tickets (c) for $109.00. The theme park needs to make at least 5.49 million dollars to make a profit each day. Which inequality could the theme park use to determine how many of each ticket must be sold in a day to make a profit?

A. 159.50a + 109c ≤5,490,000


B. 159.50a + 109c ≥5,490,000


C. 159.50a + 109c <5,490,000


D. 159.50a + 109c >5,490,000

Hence, the remainder is [tex]0[/tex] and the quotient is [tex]3x-y[/tex].

What is the polynomial?

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here given polynomial is

[tex]\frac{9x^4+3x^3y-5x^2y^2+xy^3}{3x^3+2x^2y-xy^2}[/tex]

                      [tex]3x-y[/tex]

[tex]\sqrt[3x^3+2x^2y-xy^2]{9x^4+3x^3y-5x^2y^2+xy^3} \\\\[/tex]

                  [tex]9x^4+6x^3y-3x^2y^2+0[/tex]

              -----------------------------------------

                         [tex]-3x^2y-2x^2y^2+y^3x[/tex]

                         [tex]-3yx^3-2y^2x^2+y^3x[/tex]

             ------------------------------------------

                                              [tex]0[/tex]

Hence, the remainder is [tex]0[/tex] and the quotient is [tex]3x-y[/tex].

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There's not enough evidence to refute the publisher's claim.

Here, we are given that a newsletter publisher believes that 29% of their readers own a personal computer.

The testing firm believes this is inaccurate and hence conducts hypothesis testing to verify the claim.

They take a significance level of 0.02 and fail to reject the null hypothesis.

The null hypothesis of the testing firm would be- 29% of the readers own a personal computer because this is what is established by the publisher.

They fail to reject this null hypothesis which means that there is not enough evidence at 0.02 significant level that the percentage is not 29%.

Thus, there's not enough evidence to refute the publisher's claim.

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Answer:

x ≤ -5

Step-by-step explanation:

Treat this EXACTLY like you would an equation:

-3(x+4) ≥ x+8

-3x - 12 ≥ x + 8

-4x - 12 ≥ 8

-4x ≥ 20

Except here (when dividing BOTH sides by a negative):

-4x ≥ 20  ⇒  x ≤ -5

The scale factor of the figure of the two squares is 1.5

The scale factor is determine using division

The formula involve:

let the scale factor be r then we say

area of square A * r = area of square B

8 * 8 * r = 12 * 12

64r = 144

r = 144 / 64

r = 1.5

using the dimensions

8r = 12

r = 12 / 8

r = 1.5

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The type of sampling required for this test is Independent sampling with quantitative data.

Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that samples are independent underlies many statistical analyses.

In the hypothetical situation, independent sampling is required since the researcher needs two distinct samples: one from freshmen and one from sophomores. These samples are independent since there would be no relationship between them.

The information would be quantitative in nature. Student GPAs are the dependent variable in this study. Since GPA is a qualitative indicator, the kind of data being collected is also quantitative.

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The complex numbers will be 3-i and I and the coordinates will be (-1,-3) or C point on the coordinate plane.

Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.

Here,

A=(1,3)

B=(-3,1)

C=(-1,-3)

D=(3,-1)

=(3-i)/i

=-1-3i

The coordinates will be (-1,-3) that is C point on the coordinate plane and the complex numbers be 3-i and i.

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12 People plan to visit the art museum only.

What is Set Theory?

We study sets and their characteristics in the area of mathematical logic known as set theory. A set is a collection of things or a group of things. These things are frequently referred to as elements or members of a set. A set is, for instance, a group of cricket players. A set is a clearly defined collection of things or people, as we already learnt in the introduction. Numerous examples from everyday life, such as the number of rivers in India and the colors in a rainbow, can be used to relate sets.

Given,

Total no of people =116

No of people visiting any of the three places = total - people visiting none of the places

= 116 -14 = 102

No of people visiting only Gateway arch = total people visiting gateway arch - (people visiting all the three +  people visiting Gateway ans museum butnot zoo +people visiting gateway and zoo butnot museum)

= 66 - (18+9+14) = 25

Similarly, people visiting only zoo = 14

Total no of people plan to visit Art Museum only = 102 - (25+14+9+18+10+14) = 112

12 People plan to visit the art museum only.

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Part a: 0.75x + 0.15y = 90 is the equation that indicates how many club pens and pencils the glee club can purchase.

Part B: The maximum number of pens and pencils the club can purchase is 120 and 600 respectively.

The stated values in the questions are-

Cost of one pen = $0.75

Let total number of pens be x.

Cost of one pencil = $0.15

Let total number of pencils be y.

Total cost (pens and pencils) = $90

Total cost = (Cost of one pen) x (Number of pens)  +  (Cost of one pencil)x(Number of pencils)

The equation modelling number of club pens and pencils is:

0.75x  +  0.15y    =   90

For the greatest number of pens ;

0.75x  = 90

x  =  90/0.75

x  =  120

Thus, the greatest number of pens bought by club is 120.

For greatest number of pencils;

0.15y = 90

y  =  90/0.15

y  =  600

Thus, the greatest number of pencils bought by club is 600.

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Answers to both the subparts are as follows:

(A) In order to factor A(t), we obtain A(t) = -cost + 1.

(B) t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.

Two expressions are combined by the equal sign to form a mathematical statement known as an equation.

For instance, a formula might be 3x - 5 = 16.

After solving this equation, we learn that the value of the variable x is 7.

(A) Factorize A(t):

A(t) = 2cost - 3cost + 1

After assembling the cost terms, we have:

A(t) = cost(2 - 3) + 1

A(t) = cost(- 1) + 1

A(t) = -cost + 1

In order to factor A(t), we obtain A(t) = -cost + 1.

(B) Solving equation A(t) = 0 for 0 ≤t≤ 2:

Since A(t) = -cost + 1

When we solve A(t) = 0 for 0 ≤ t ≤ 2, we get:

A(t) = 0

-cost + 1 = 0

-cost = -1

cost = 1

If we take the inverse cosine, we get:

t = cos⁻¹(1)

t = π/2

t = 3.142/2

t = 1.571

t ≅ 1.57

t = 1.57 after solving A(t) = 0 for 0 t 2

Therefore, answers to both the subparts are as follows:

(A) In order to factor A(t), we obtain A(t) = -cost + 1.

(B)  t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.

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Complete question:
Let A (t) = 2 cost-3 cost+1, 0 ≤t ≤ 2

A. Factorize A(t).

B. Hence, solve the equation A(t) = 0 for 0 ≤t≤ 2.

The unit rate per batch of cookies is 2.75 as Lennon uses 5 1/2 cups of flour for every 2 batches of cookies she bakes.

To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.

When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.

Based on the given conditions, formulate:

(5 1/2)/2

We have to find the common denominator and write the numerators above the common denominator.

(((5×2)/2)+(1/2))/2

Now, we have to calculate the product or quotient:

((10/2)+(1/2))/2

Now, write the numerators over common  denominator,

((10+1)/2)/2

Then, calculate the sum or difference:

(11/2)/2

=11/4

=2.75 (or) 2 3/4

Therefore, the unit rate per batch of cookies is 2.75.

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Answer:  9 hours

Step-by-step explanation:

here are a couple of things to notice here. You don’t have a starting temperature, so that will be an unknown. I will call it S.

The next thing to notice is that the current temperature (C) at any given time is just the starting temperature minus 4 times the number of hours (H) that have passed since 1 PM.

C = S – 4*H

We want to solve this for H when the current temperature (C) is -1.

-1 = S – 4*H

You can rearrange this by adding 4*H to both sides and adding 1 to both sides:

4*H = S + 1

Then you divide both sides by 4

H = (S+1)/4

This will tell you the number of hours PAST 1 PM that it takes to get to -1 degrees. Of course, you need to know the starting temperature, S, in order to get a numeric answer.

Let’s check this with an example. If the starting temperature were exactly 4 degrees above -1, then it should take exactly 1 hour. So let S = -1 + 4 = 3. If you plug 3 in for S, you do see that H becomes 1 hour PAST 1 PM (2 PM).

Answer:

n=15

Step-by-step explanation:

Answer: no i need this too :(

Step-by-step explanation:

Answer: 9x - 20

Step-by-step explanation:

You can graph 2(3x - 10) + 3x.

Here is how I would do it:

First, Distribute

2(3x - 10) + 3x (Original)

6x - 20 + 3x (Distribute)

Second, Combine like terms

6x - 20 + 3x

9x - 20

Therefore, the solution to your problem is 9x - 20

When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.

Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.

Hence, When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t

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The solutions are given below.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

lines u and v are parallel,

And ∠ 9 = 80° and ∠ 5 = 68°

(a)

Angle 12 is supplementary angle of angle 9,

Therefore, ∠12 = 180 - 80 = 100

(b)

Angle 1 and angle 9 are corresponding angle and are equal.

∠ 1 = ∠ 9 = 80

(c)

Angle 1 is supplementary angle of angle 4,

Therefore, ∠ 4 = 180 - 80 = 100

(d)

Angle 3 and angle 1 are vertically opposite angles,

Therefore, ∠ 3 = ∠ 1 = 80°

(e)

Angle7 and angle 5 are vertically opposite angles,

Therefore, ∠ 7 = ∠ 5 = 68°

(f)

Angle 16 and 7 are supplementary angles,

Therefore,  ∠16 = 180 - 68 = 112

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Answer:

As a decimal:0.016

As a percentage:1.6%

Step-by-step explanation:

The number of terms that must be added together to achieve this series s is 5000.

Given that,

The remainder of the following convergent series must be less than 10 Superscript negative 5 in magnitude.

We have to calculate the number of terms that must be added together to achieve this.

Given

S= summation n=0 to infinity (-1)ⁿaₙ.

An upper bound for the error of the series Rₙ is aₙ₊₁ so

Rₙ=|s-sₙ|≤aₙ₊₁

In this case we have

1/2n+1≤1/10⁴

10⁴≤2n+1

(10⁴-1)/2≤n

(10⁴-1)/2 is approximately 5000.

Therefore, the number of terms that must be added together to achieve this series s is 5000.

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A sample observation results in a point estimate of 0.53 for the mean value of paint thickness.

The mean value theorem states that there is one point on a curve where the tangent is parallel to the secant running through the two points.

A low-viscosity paint sample with the following thickness is provided to us.

0.810.870.901.051.111.141.301.301.481.481.591.601.661.691.781.84

a) Point estimate of the mean value of coating thickness.

To estimate the mean coating thickness, we use the mean value of the sample.

mean= sum of all observations/total number of observations

mean=8.16/16

mean=0.53

Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. 0.810.870.901.051.111.141.301.30 1.481.481.591.601.661.691.781.84 Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)

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Answer:

ITS A

Step-by-step explanation:

The area of the triangle is 3/4 units.

What is area of the triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.

Suppose

x is the shorter leg of the triangle.

As the longer leg of a right triangle is three times as long as the shorter leg.

⇒ 3x is the longer leg of the triangle.

The hypotenuse of the triangle is, √5.

By using Pythagorean theorem,

[tex]x^2 + (3x)^2 = (\sqrt{5} )^2\\x^2 + 9x^2 = 5\\10x^2 = 5\\x^2 = \frac{5}{10}\\ x^2 = \frac{1}{2} \\x = \frac{1}{\sqrt{2} }[/tex]

⇒ Shorter leg of the triangle is 1/√2.

⇒ Longer leg of the triangle is 3/√2.

Now to find the area of the triangle.

Area of triangle = [tex]\frac{1}{2}(\frac{1}{\sqrt{2} })(\frac{3}{\sqrt{2} } )[/tex]

[tex]A = \frac{3}{4}[/tex]

Hence, the area of the triangle is 3/4 units.

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The value of c should be 20.2 so that 99% of all parcels are at least 1 lb under the surcharge weight (that is, only 1% are beyond c-1 lb).

What is surcharge?

Surcharges are extra fees or taxes, as the name implies. A 10% surcharge on a 30% tax rate effectively increases the total tax burden to 33%. A 10% surcharge is added to the tax obligation for people whose net taxable income exceeds Rs 1 crore. The surcharge is increased to 5% if the net income is greater than Rs 10 crore. If a company's net income surpasses Rs. 1 crore and Rs. 10 crore, they are both provided a margin of relief.

Solution Explained:

Given,

m = 12

d = 3.5

P(z<x) = 0.99 = ¢(Z)

Z = 2.33

Since Z = (x - m)/d

x = dZ + m

x = 3.5*2.33 + 12

x = 20.155 lb approximately

x = 20.2 lb

Therefore, the highest weight for 99% if the parcels is 20.2 lb.

That is, the surcharge weight = 20.2 + 1 = 21.2 lb

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Jay is incorrect in doing addition first.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression as;

3x (3 +12 divided by 3) -4.

To simplify this expression, then must follow PEMDAS.

3x(3+12÷3)

3x(3+4)

3x(7)

21x

Which means that Jay is incorrect in doing addition first.

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Answer: 32 every month or day. if its every month the answer is 384, if its every day it would be 11680

Step-by-step explanation:

Given:

Find the amount of interest:

Find the balance after one year:

The following are the amount each person receive:

a. 6 : 4

Total ratio = 6 + 4

= 10

6/10 × 500

= $300

4/10 × 500

= $200

b. 1 : 4 : 5

Total ratio = 1 + 4 + 5

= 10

1/10 × 500

= $50

4/10 × 500

= $200

5/10 × 500

= $250

c. 1 : 8 : 1

Total ratio = 1 + 8 + 1

= 10

1/10 × 500

= $50

8/10 × 500

= $400

1/10 × 500

= $50

d. 8 : 9 : 8

Total ratio = 8 + 9 + 8

= 25

8/25 × 500

= $160

9/25 × 500

= $180

8/25 × 500

= $160

e. 10 : 5 : 4 : 1

Total ratio = 10 + 5 + 4 + 1

= 20

10/20 × 500

= $250

5/20 × 500

= $125

4/20 × 500

= $100

1/20 × 500

= $25

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The domain and the range of the functions are given by the images at the end of the answer.

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, on the graph, it will be given by the values of x of the graph, the values assumed by the horizontal axis of the graph.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, on the graph, it will be given by the values of y of the graph, the values assumed by the vertical axis of the graph.

The notations are given as follows:

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Answer: specific analyze is as it follows

Step-by-step explanation:

correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children is a. child-adoptive: 0.20; child-biological: 0.40

Children for adoption

Adoption is the social, emotional, and legal process in which children who will not be raised by their birth parents become full and permanent legal members of another family while maintaining genetic and psychological connections to their birth family.

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There are 80 sundaes possible using one flavor of ice cream and three different toppings.

Here, we are given that a club is hosting an ice cream sundae party with four different flavors of ice cream and six different toppings.

For choosing 1 flavor of ice cream from 4, we have 4 ways.

Now, we need to choose 3 different toppings from the given 6.

This can be done in 6C3 ways

6C3 = 6! / (3! × 3!)

= (6 × 5 × 4) / (3 × 2)

= 120/ 6

= 20

Thus, we have 20 ways of choosing 3 different toppings.

Now, the number of ways of making the sundaes would be-

4 × 20

= 80

Thus, there are 80 sundaes possible using one flavor of ice cream and three different toppings.

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The appropriate statistic test should be ANOVA and The degree of freedom is 12.

What are Statistical tests?

An instrument for making quantitative judgments about a process or processes is a statistical test. The goal is to decide whether there is sufficient data to "reject" a theory or hypothesis on the process.

In the given problem the average age of the corporate executives at the three locations is being calculated, it means more than two groups are being compared. hence, The appropriate statistic test would be ANOVA.

In order to calculate the degree of freedom, we must know the no. of observations.

here,  no. of observations are 15 ( 3 × 5 ) and the no. of groups are 3.

∴ Degree of freedom = no. of observations - no. of groups

                                    = 15 - 3 = 12.

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