What are the two properties of showing the graph of polynomial function?.

The distance of the given point P from the plane would be [tex]\frac{-1}{\sqrt{6}}, \frac{-5}{\sqrt{6}},and, \frac{2}{\sqrt{6}}.[/tex]

What is a plane?

A plane is a two-dimensional Euclidean surface that extends indefinitely in mathematics. A plane is a two-dimensional equivalent of a point, a line, and a three-dimensional space.

The given point P is P(-2, -1, 1) and the plane coordinates are [4, -1, 6].

Then the distance will be

                                [tex]= \frac{-2.4+(-1*-1)+1.6}{\sqrt{(-2)^2+(-1)^2+1^2}}\\\\ =\frac{-1}{\sqrt{6} }[/tex]

Now the distance of a point P from the plane t[1, 6, 3]

                                  [tex]= \frac{-2.1+(-1*6)+1.3}{\sqrt{(-2)^2+(-1)^2+1^2}}\\\\ =\frac{-5}{\sqrt{6} }[/tex]

Now the distance of a point P from the plane [-2, 3, 1]

                                   [tex]= \frac{-2.-2+(-1*3)+1.1}{\sqrt{(-2)^2+(-1)^2+1^2}}\\\\ =\frac{2}{\sqrt{6} }[/tex]

hence, the distance would be [tex]\frac{-1}{\sqrt{6}}, \frac{-5}{\sqrt{6}},and, \frac{2}{\sqrt{6}}.[/tex]

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To find which side of the line on the graph of a linear inequality to shade. Follow the steps-

In order to know which area to shade, first pick a point on the side of the line in your graph. then substitute the x and y values into the inequality. once you get the values, check if the inequality is true at that point. If yes, then you shade that side where the point is in. If not, then you shade the other side.

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Answer:

No Correlation

Step-by-step explanation:

The points are scattered randomly and there is no pattern so there is no correlation.

The set of whole numbers is closed under addition.

A set is the mathematical model for a collection of different things.

The addition of any two whole numbers always produces another whole number. Therefore, the set of whole numbers is closed under addition.

Hence, The set of whole numbers is closed under addition.

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1. The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

2. The probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.

P(M 169.3 cm 168.3 cm) = 0.7724

Given that,

In this question we have 2 question.

1. Steel rods are produced by a firm. The lengths of the steel rods have a mean of 125.2 cm and a standard deviation of 2.3 cm, and they are regularly distributed. 25 steel rods are packaged together for shipping.

We have to determine the probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5-cm) =

We know that,

Mean =μ= 125.2

Standard deviation=σ=2.3

n=25

P(M<124.5)= P[(M-μ)/σ< 124.5-125.2/0.46]

=P(z<-1.522)

Using the z-table,

=0.0603

Therefore, The probability that the average length of a bundle of steel rods chosen at random is less than 124.5 cm.

P(M < 124.5) = 0.0603.

2. Steel rods are produced by a firm. Steel rod lengths have a mean of 168.5 cm and a standard deviation of 1.2 cm, and they are regularly distributed. 24 steel rods are packaged together for shipping.

We have to determine the probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.

P(M 169.3 cm 168.3 cm) =

We know that,

Mean =μ= 168.5

Standard deviation=σ=1.2

n=24

P(168.3<M<169)= P[168.3-168.5/0.2449<(M-μ)/σ< 169-168.5/0.2449]

=P(-0.817<z<2.042)

=P(z<2.042)-P(z<-0.817)

Using the z-table,

=0.9794-0.2070

=0.7724

Therefore, the probability that a bundle of steel rods chosen at random has an average length that falls between 168.3 cm and 169 cm.

P(M 169.3 cm 168.3 cm) = 0.7724

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The following statements are correct :

Property A(Stan):

Security Deposit is not part of Rental Income if it is returned at the end of lease period = $0

In cash basis, any amount received as rent will be taxable regardless if it is earned in that period or not = $1400

$15400

If your tenant pays any of your expenses, those payments are rental income. You may also deduct the expenses if they're considered deductible expenses = $0                                                            

Property B(Dani):

$18000

If security deposit is used for paying rent, then it is part of rental income = $1500

$1600

If your tenant pays any of your expenses, those payments are rental income. You may also deduct the expenses if they're considered deductible expenses = $0

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The scatterplot that shows a strong association between two variables even if the correlation is near zero is graph C.

Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables.

Zero correlation is when there is no linear relationship between the variables been studied. When it is shown on a graph, zero correlation would have no clear linear trend either positive or negative. A linear trend is roughly a straight line. A linear trend is positive if it slopes upward and negative if it slopes downward.

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By performing a change of units from feet to yards, we will see that the backyard measures 31 yards.

We know that Ricardo measured his backyard and he found that it measured 93 feet, but we want to find this measure in yards, so we need to perform a change of units.

To do it, we will use the relation:

1 yard = 3 feet

Then we can write:

1 = (1 yard)/(3 feet).

Now we have the measure:

93 ft

And we can multiply it by (1 yard)/(3 feet), that is equal to 1, so it does not change the measure, only the units:

93 ft = 93ft*(1 yd/3ft) = 31 ft

The backyard measures 31 ft.

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72 = 3x + 6 equation represents if each pie was then cut into six pieces and sold. There were a total of 72 pieces to sell.

In mathematics, an equation is an expression or a statement that consists of two algebraic expressions that have the same value and are separated from one another by the equal symbol. It is an otherwise stated proposition that has been mathematically quantified. There are numerous possible equation types. To equate two expressions, we employ equations.

Given,

The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating three pies to the club.

Each pie was then cut into six pieces and sold.

There were a total of 72 pieces to sell.

Equation representing this equation is:

72 = 3x + 6

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Answer: Line A Is the answer

Answer:

35%

Step-by-step explanation:

Find the number of men:

40-26= 14

Find the ratio of men out of the 40 people

14/40 = 0.35

0.35 * 100% = 35%

The correct option d. decision variables; is used to find the the graphical solution to a linear programming problem.

An uncertain in an optimization method is a choice variable. It has a domain, that is an condensed representation of the entire set of the variable's potential values.

Thus, a linear programming problem's graphical solution is found using decision variables.

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Part A: Equation representing the relationship between cost (y) and number of calls (x) is 25 = y - 2x.

Part B: The number of phone calls in January is 15.

Part C: Total bill for March is $ 35.

Part D: Graph for the equation is attached below.

A statement that states the equality of two expressions formulated by applying an algebraic equation, an algebraic operation—addition, subtraction, multiplication, division, power, square root—to a set of variables. Examples are x³ + 1 and (y⁴x² + 2xy – y)/(x – 1) = 12.

Part A: Equation representing the relationship between cost (y) and number of calls (x).

y = 2x + 25

25 = y - 2x

Part B: For the number of phone calls in January

55 = 25 + 2x

30 = 2x

x = ³⁰/₂

x = 15

Part C: Total bill for March

y = 25 + 2(5)

y = 35

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The 95% confidence interval would be given by (60.554;81.446)  

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population means that sits between an upper and lower interval is frequently stated as a percentage.

Here, we have

Given Data: 92 34 40  105 83 55  56 49 40  76 48 96  93 74 73  78 93 100  53 82

We can calculate the mean and the deviation from these data with the following formulas:

X = ∑ᵃ 1ⁿxₐn

s = √∑ᵃ = 1ⁿ(xₐ - X)²n -1

X = 71  represents the sample mean for the sample  

s=22.35 represent the sample standard deviation

n=20 represents the sample size  

The confidence interval for the mean is given by the following formula:

X ± tα/2 - √n...(1)

In order to calculate the critical value tα/2  we need to find first the degrees of freedom, given by:

df = n - 1 = 20 -1 = 19

Since the Confidence is 0.95 or 95%, the value of α = 0.05 and α/2 = 0.025

and we can use excel, a calculator, or a table to find the critical value. The excel command would be:

tα/2 = 2.09

Now we have everything in order to replace into formula (1):

71 - 2.09- 2.35√20 = 60.554

71 + 2.09- 2.35√20 = 81.446

Hence, the 95% confidence interval would be given by (60.554;81.446).

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Answer:

Step-by-step explanation:

for (i = 0; i < dataPoints.size(); ++i) {

     if (dataPoints.at(i) > maxVal) {

        dataPoints.at(i) = dataPoints.at(i) - 4;

     }

  }

Phenotypic ratio helps us to predict gene expression in the future generations of organisms. In phenotypic ratio calculations, we map out specific parental alleles and predict the probability of how they will be expressed in their offspring.

Phonotypic ratio is a term that describes probability of finding the patterns and frequency of genetic trait outcomes in the offspring of organisms.

Phenotypic ratio is showing physical expression while the genotypic ratio shows genetic makeup. In complete dominance, the progeny shows the intermediate character of both the parents.

A cross of two hybrid F1 hybrids, heterogeneous for a single trait that displays incomplete dominance is predicted to give a 1:2:1 ratio among both the genotypes and phenotypes of the offspring.  

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x=4,-0.4714i and 0.4714i are the zeroes of polynomial 9x³-36x²+2x-8  

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Given polynomial is 9x³-36x²+2x-8

We have to find roots or zeroes of polynomial.

Nine times of x cube minus thirty six x square plus two times of x minus eight.

(((9(x³)) -  (2²3²x²)) +  2x) -  8  = 0

((3²x³ -  (2²3²x²)) +  2x) -  8  = 0

9x³-36x²+2x-8  is not a perfect cube

9x³-36x²+2x-8  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  2x-8= 2(x-4)

Group 2:  -36x²+9x³=9x²(x-4)

Add up the two groups :

(x-4) (9x²+2)

x=4

x=0.0000-0.4714i

x=0.0000+0.4714i

Hence x=4,-0.4714i and 0.4714i are the zeroes of polynomial 9x³-36x²+2x-8  

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The water that was lost between 9 and 11 am is 52 liters by using integration.

An integral in mathematics assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that come from merging infinitesimal data. The process of determining integrals is known as integration. Along with differentiation, integration is a fundamental, essential operation of calculus and is used to answer issues in mathematics and physics involving the area of an arbitrary form, the length of a curve, and the volume of a solid, among others.

The integrals listed below are definite integrals, which can be defined as the signed area of the plane region circumscribed by the graph of a given function between two points on the real line.

Rate of leaking R'(t)=2+8t

Here t is the number of hours.

Total water lost from 9 and 11 am

=[tex]\int\limits^8_2[/tex] (2+8t)dt

=(2t+(8t²/2))⁴₂

=(8+64)-(4+16)

=72-20

=52 liters.

The water that was lost between 9 and 11 am is 52 liters.

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Answer:

(1/2*6e)-(1/2*3f)-(1/2*3/4)

Step-by-step explanation:

[tex]\Large \boxed{\sf 3e-\frac{3}{2}f -\frac{3}{8} }\\\\\\\displaystyle \sf Applying\ the\ distributive\ property \\\\\\\frac{1}{2} \times 6e+\frac{1}{2} \times -3f +\frac{1}{2} \times \frac{-3}{4} \\\\\\ \frac{6e}{2}+\frac{-3f}{2} +\frac{-3}{2 \times 4} \\\\\\ 3e+\frac{-3f}{2} +\frac{-3}{8}[/tex]

The number of different ways for all 4 conditions is 5040 ways, 3603600 ways, 32760 ways, and 604800 ways respectively.

What are permutation and combination?

A permutation is an orderly arrangement of objects or numbers. 

Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.

First condition,

The number of ways to take turns for 7 children is:

= Permutation of 8 children

= 7!

= 5040 ways

Second condition,

The number of ways to select 6 from 15 and in order is computed as the number of permutations of 15 books taken 6 at a time

= 15*14*13*12*11*10

= 3603600 ways

Third condition,

The number of ways to choose 4 different positions from 15 students is:

= Number of permutation of 15 students taken 4 at a time

= 15*14*13*12

= 32760 ways

Last condition,

The numbers cannot be repeated here, the number of permutations of 10 digits taken 7 at a time is:

= 10*9*8*7*6*5*4

= 604800 ways

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The best description of the sample selected by the administrator is Stratified Random Sample that is option D is correct.

Stratified Random Sampling is the method of sampling in which data of population or any other demographic study is divided into smaller subgroups or subdivisions and then measurements are carried out. These subdivisions are known as Strata. The subdivisions are made on the basis of the attributes of the people of the population such as their income statement or their educational qualifications. This type of sampling technique is also known as random or quota random sampling technique. This sampling technique is also used in determining the life expectancy data. It allows researchers to develop a sample of a small area that represents the entire area.

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Complete Question:

as part of a demographic study, a college administrator needed to survey a sample of students from the college. from each major offered at the college, the administrator randomly selected 5 percent of the students with that major to participate in the survey. which of the following is the best description of the type of sample selected by the administrator?

a)cluster sample

b)convenience sample

c)simple random sample

d)stratified random sample

e)systematic random sample

The value of the expression given as 2 - (80/4) - 14 when evaluated is -32

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

2--80/4-14

To start with, we need to represent the expressions properly

This can be done with the use of brackets

So, we have the following representation

2 - (80/4) - 14

Solving further, we need to evaluate the expression in the bracket

This gives

2 - (80/4) - 14 = 2 - (20) - 14

Next, we remove the bracket

So, we have the following representation

2 - (80/4) - 14 = 2 - 20 - 14

Evaluate the difference

So, the expression becomes

2 - (80/4) - 14 = -18 - 14

Evaluate the last difference

So, the expression becomes

2 - (80/4) - 14 = -32

Hence, the solution is -32

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The perimeter is 29' and the area is 30 square units

The perimeter

This is the sum of the side lengths

From the question, the side lengths are

Side lengths = 9', 4', 11' and 5'

When these side lengths are added, we have

Perimeter = 9 + 4 + 11 + 5

Evaluate the sum

Perimeter = 29

So, the perimeter is 29'

The area

This is calculated as

Area = 1/2 * Sum of parallel sides * Height

So, we have

Area = 1/2 * (9 + 11) * 3

Evaluate

Area = 30

So, the area is 30 square units

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The dimensions for which the printed area is maximized are 16.432 × 10.954 in².

let the height of the poster = x inches

area of the poster = 180 in²

thus, its width is 180/x inches.

The printed area has a height of x - 3 inches due to the 1-inch bottom margin and 2-inch top margin.

The sides have a margin of 1 inch, so the width of the printed area is:

180/x - 2

the area of printed area A is given by the formula of a rectangle,

A = height × width

A = (x-3)(180/x - 2)

A = 180 - 2x - 540/x + 6

the maximized area is when dA/dx = 0

dA/dx = - 2 - 540(- 1/x²) = 0

540/x² = 2

x = √270

hence height = √270 = 16.432 inches,

and width = 180/√270 = 10.954 inches.

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The amount 20% more than 1500 is 1800.

The amount 20% of 1500 is

=20/100 × 1500

=300

NOW,

The amount 20% more than 1500 is

=300 + 1500

=1800

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The Correct answer is 27

Odd number are the numbers that are not multiple 2 and cannot be divided into two parts equally.

For examples: 3 , 5 , 7, 9,11 . . . . .

According to the question,

If the third odd number is greater than 6, multiply 9 by 3; if it is less than 5, divide 18 by 3.

Sequence of the number is 1, 5, 4, 7, 3, 7, 9, 2

where  1 , 5 , 7 , 7 ,9 are odd numbers

The third odd number is 7 which is greater than 6

according to question we have to multiple 9 by 3

= 9 × 3

= 27

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The probability of an outcome that lies within 99.7% of the mean is a good indicator that it lies in which standard deviation is B. There is a probability that the outcome is within 3 standard deviations of the mean.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.

It should be noted that 68% of the population is within 1 standard deviation of the mean. 95% of the population is within 2 standard deviation of the mean. 99.7% of the population is within 3 standard deviation of the mean

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The equations that can be used to solve for the length (y) of the rectangular room are:

y(y - 5) = 750

y² - 5y = 750

(y + 25)(y - 30) = 0

The area of a rectangular shape = (length)(width).

Given the following:

Area of rectangular room = 750 square feet.

Length of the room = y

Width of the rectangular room = y - 5 feet

Using the area formula, the equation that we can use to find the value of y would be expressed as follows:

y(y - 5) = 750

Expand

y² - 5y = 750

y² - 5y - 750 = 0

Factorize

(y + 25)(y - 30) = 0

Therefore, the possible equations are:

y(y - 5) = 750

y² - 5y = 750

(y + 25)(y - 30) = 0

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The graph of the exponential function f(x) = 3ˣ is attached below and comparing the graphs with the options available, the answer is option D

An exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.

In the given function

f(x) = 3)ˣ

Applying the values from the table of function, a graph can be drawn to represent the function.

we can use a graphing calculator to plot the graph while applying the values from the table of function

Comparing the graph plotted and the options given, the answer is option D

Kindly find the attached graph below

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