Topic: Using the rational theorem to find all zeros of a polynomial
Question: 5x^4-26x^3-64x^2+9x-14

Answer:

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

Given measurements:

Bring all to same unit, grams, then compare;

Order them from smallest to largest:

Answer:

The order of the measurements from smallest to largest is:

Step-by-step explanation:

The three given measurements of mass are:

Therefore, to be able to order the three given measurements from smallest to largest, first convert them to the same unit of mass (grams):

⇒ 3,000 g = 3,000 g

⇒ 60,000 mg = 60,000 × 0.001 = 60 g

⇒ 1.5 kg = 1.5 × 1000 = 1,500 g

Therefore, the order of the measurements in grams from smallest to largest is:

So, the order of the measurements in their original units from smallest to largest is:

The inequality showing the maximum number of days he can rent a car is 10d ≤ 75.

The inequality expressions are the mathematical equations related by each other by using the signs of greater than or less than. All the variables and numbers can be used to make the equation of inequality.

Given that Passion has a budget of $75 and wants to rent a car for a trip. A fixed daily fee of 10 is charged.

The product of the number of days and the rent per day should be less than the amount he has.

The inequality mathematically can be written as:-

10t ≤ $75

Therefore, the inequality 10d ≤75 shows how many days he can rent an automobile for the most.

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Answer: 1/m^2n^2

Step-by-step explanation: when dividing powers, we subtract.

so, the top would all cancel out

and we would be left with only m^-2n^-2.

to get rid of the negative we put the number into the denominator.

so m^-2n^-2 would become 1/m^2n^2.

If the gross income per month is $4000 , then the monthly disposable income will be $2920   .

To find the monthly disposable income, we subtract the various taxes from the gross income.

The Federal tax is = 10% of $4000 = $400  ;

The State tax is = 7% of $4000 = $280  ;

The City tax is = 3% of $4000 = $120  ;

and the Social security tax is = 7% of $4000 = $280  ;

So , the Total monthly tax is = $400 + $280 + $120 + $280 = $1080  ;

We know that the Monthly disposable income = Gross income - Total tax ;

⇒ Monthly disposable income = $4000 - $1080  ;

⇒ Monthly disposable income = $2920  .

Therefore, the monthly disposable income after taxes is $2920.

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For the given inequality, the values of u are:

We want to see which ones of the values are solutions of the inequality:

u ≤ 10

So u can be smaller than 10, or equal to 10.

For example, for the irst case u = 8.

8  ≤ 10

This is true, because 8 is smaller than 10.

Then:

u = 8 is a solution.

u = 4 is a solution.

u = 10 is a solution.

u = 13 is not a solution.

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Answer:

Step-by-step explanation:

i9 have no idea sorry

Percentage of the tickets were discount tickets is 36 %, if 144 out of 400 tickets sold were discount tickets.

Percentage is a number or ratio that can be expressed as a fraction of 100. According to the question, at an amusement park, 144 out of 400 tickets sold were discount tickets.

This means total number of tickets = 400

number of discount tickets = 144

we, have to find percentage of the tickets were discount tickets

Let the percentage be x

therefore x% of 400 = 144

              [tex]\frac{x}{100}[/tex] * 400 = 144

               x = 144 ÷ 4

               x = 36

so, percentage of the tickets were discount tickets is 36%

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (3 {m}^{5} )(4m {}^{9} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (3 \times 4)(m {}^{5} \times m {}^{9} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 12m {}^{(5 + 9)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 12m {}^{14} [/tex]

So, The correct choice is B.) 12 m¹⁴

Answer:

= 74cm²

Step-by-step explanation:

Perimeter of a rectangle

[tex] = 2(l) + 2(w)[/tex]

therefore

= 2(18) + 2(19)

= 36 + 38

= 74cm².

a) The probability of being dealt a flush is approximately 0.00198, or about 0.2%.

b) The probability of being dealt one pair is approximately 0.422, or about 42.2%.

a. To find the probability of being dealt a flush, we need to first determine how many possible flush hands there are, and then divide that by the total number of possible hands. There are 4 suits in a deck of cards, so there are 4 ways to choose which suit the flush will be in.

Once we have chosen a suit, there are 13 cards of that suit, and we need to choose 5 of them. The number of ways to choose 5 cards from 13 is given by the combination formula: C(13,5) = 1287. Therefore, there are 4 x 1287 = 5148 possible flush hands.

The total number of possible hands is given by the combination formula for choosing 5 cards from a deck of 52: C(52,5) = 2598960. Therefore, the probability of being dealt a flush is 5148/2598960, which simplifies to approximately 0.00198, or about 0.2%.

b. To find the probability of being dealt one pair, we need to first determine how many possible one pair hands there are, and then divide that by the total number of possible hands. There are 13 denominations in a deck of cards, so there are 13 ways to choose which denomination will form the pair.

Once we have chosen a denomination, there are 4 cards of that denomination, and we need to choose 2 of them. The remaining 3 cards must each be a different denomination from the pair, so there are 12 denominations left to choose from, and 4 cards of each denomination.

We need to choose 3 of these 12 denominations, and then 1 card from each of those 3 denominations. The number of ways to choose 2 cards from 4 is given by the combination formula: C(4,2) = 6. The number of ways to choose 3 denominations from 12 is given by the combination formula: C(12,3) = 220.

The number of ways to choose 1 card from each of 3 denominations is 4 x 4 x 4 = 64. Therefore, the total number of possible one pair hands is 13 x 6 x 220 x 64 = 1,098,240. Dividing this by the total number of possible hands gives us the probability of being dealt one pair, which is 1,098,240/2598960, or approximately 0.422, or about 42.2%.

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Quadrilateral FGHI is a scalene quadrilateral as none of the sides equal to each other from calculated slopes and lengths.

Coordinates of the quadrilateral FGHI are,

F (-1,-8), G(-3,2), H(0,1) and I(2,7)

Slope of side lengths of FGHI are:

Slope FG = ( 2 + 8)/ (-3 + 1)

               = -5

Slope GH = ( 1 -2)/ (0 + 3)

                = -1/3

Slope HI = ( 7 -1)/ ( 2 -0)

              = 3

Slope IF = ( 7 + 8 )/ (2 + 1)

              = 5

Product of slopes of perpendicular lines = -1

FG is perpendicular to IF

GH is perpendicular to HI

Measure of side lengths are:

FG = √(2+8)² + (-3+1)²

     = √104

     = 2√26

GH =√(1-2)² + (0 +3)²

     = √10

HI = √(7-1)² + (2-0)²

    = √40

    =2√10

IF = √(7+8)² + (2+1)²

   = √234

   = 9√26

Therefore, the given quadrilateral is scalene quadrilateral concluded using slopes and lengths.

The above question is incomplete, the complete question is:

The points F (-1,-8), G(-3,2), H(0,1) and I(2,7) form a quadrilateral. Find the desired slopes and lengths, then fill in the words that BEST identifies the type of quadrilateral.

Slope of FG = __                            Length of FG = __

Slope of GH = __                            Length of GH = ___

Slope of HI= __                               Length of HI = ____

Slope of IF = __                               Length of IF = ____

Quadrilateral FGHI is ______

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The number of tots Rew has = X and X∈[0,5] or X(10,∝).

What is a number line?

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Let the number of tots Rew has = X.

It is given that Rew has either no more than 5 tots or more than 10 tots.

This means that the number of tots is either less than 5 or greater than 10.

which mean that X≤5 or X>10.

X∈[0,5] or X(10,∝)

The graph of the number line is attached below.

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The expression that represents that number of items collected by Team A is a=2b+4.

Given that in a hunt, two teams collected a number of items for their teams. Now the items collected by team A is 4 more than the twice of the items collected by the team B. Let the items collected by team A be 'a' and the items collected by team B will be 'b'.

Now, team A collected items are 4 more than the doubled value of team B.

The expression that represents the items collected by the second team, that is Team A is:

a=2b+4

Therefore the expression that represents items collected by team A is a=2b+4.

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The required coordinates of B are (0, 6) for the given parabola.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, is the location or coordinate from where the line crosses.

To determine the coordinates of B, we can use the information given in the problem.

A is an x-intercept, which means that the y-coordinate of A is 0, and it can be found by setting x = 0 in the equation for f(x).

The line AB is g(x) = 3x + 6. This line is a straight line and it is perpendicular to the x-axis at B, which means that the x-coordinate of B is 0.

Therefore, we can set x = 0 in both equations to find the y-coordinate of B.

For f(x), we have:

f(0) = a × 0² + b × 0 + c = c

For g(x), we have:

g(0) = 3 × 0 + 6 = 6

Since the line AB passes through the turning point B, we know that the y-coordinate of B is equal to both f(0) and g(0). Therefore, we have:

c = 6

So, the coordinates of B are (0, 6).

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We can estimate that there is about 1000 joules of kinetic energy in an average size helium balloon.

The amount of kinetic energy in an average size helium balloon can be estimated using the ideal gas law and the equipartition theorem.

Assuming the balloon is filled with helium at room temperature (around 298 K) and atmospheric pressure (around 1 atm), the volume of the balloon can be estimated to be around 0.5 m^3. The number of helium atoms in the balloon can be estimated using Avogadro's number, which is around 6.02 x 10^23.

Using the equipartition theorem, we can estimate the average kinetic energy of each helium atom in the balloon. At room temperature, each atom has an average kinetic energy of (3/2)kT, where k is the Boltzmann constant (1.38 x 10^-23 J/K).

Therefore, the total kinetic energy of the helium atoms in the balloon can be estimated as:

KE = (3/2)kT * N

where N is the number of helium atoms in the balloon.

Plugging in the estimated values, we get:

KE = (3/2) * (1.38 x 10^-23 J/K) * 298 K * 6.02 x 10^23

KE ≈ 9.95 x 10^2 J

Therefore, An average-sized helium balloon contains roughly 1000 joules of kinetic energy, according to our estimation. It's important to note that this is just an estimate, and the actual amount of kinetic energy in a helium balloon can vary depending on a number of factors such as the temperature, pressure, and size of the balloon.

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Answer:

Student A is incorrect. Student b is correct.

Step-by-step explanation:

Yes, both students' evaluations of the expression are correct.

The product of a number by addition is equal to the total of the products of that number by each of the addends, according to the distribution property of multiplication.

Simplify the given expression 17(4 + 15) using the distributive property as:

17(4 + 15) = 17(19) = 323

Student A evaluates the expression by adding the product of 17 and 4 to the product of 17 and 15:

17(4) + 17(15) = 68 + 255 = 323

Thus, student A's evaluation is correct.

Student B evaluates the expression by determining the product of 17 and 19:

17(19) = 323

Thus, student B's evaluation is also correct.

Therefore, both students' evaluations are correct.

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a) "What is your age?" is a quantitative data.

b) "Are you male or female?" is a categorical data.

c) "When did you first start reading the wsj?" is a categorical data.

d) "How long have you been in your present job or position?" is a quantitative data.

e) "What type of vehicle are you considering for your next purchase?" is a categorical data.

(a) "What is your age?" - This question provides quantitative data because age is a numerical value that can be measured and ordered in a meaningful way. Respondents could give an answer such as "25", "45", or "70", for example, which can be used to calculate statistics such as the mean or median age of the survey population.

(b) "Are you male or female?" - This question provides categorical data because the responses fall into discrete, non-numeric categories (in this case, "male" or "female"). It's not possible to order the responses in a meaningful way, since there is no inherent numerical value associated with being male or female.

(c) "When did you first start reading the WSJ?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (high school, college, early career, mid career, late career, or retirement). While it's possible to order the categories in a logical sequence, they don't represent numerical values.

(d) "How long have you been in your present job or position?" - This question provides quantitative data because the responses can be measured as numerical values (for example, "3 years", "10 years", or "25 years"). The data can be used to calculate statistics such as the average length of time that respondents have been in their current position.

(e) "What type of vehicle are you considering for your next purchase?" - This question provides categorical data because the possible responses fall into discrete, non-numeric categories (sedan, sports car, SUV, minivan, etc.). While it's possible to order the categories in a logical sequence based on size, price, or other factors.

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The number of times a variable appears in a data set is Known as Frequency.

Frequency

The frequency of a particular data is the number of times the data value appears. Denote the frequency of a data value by f. For example, if 5 students got an A in science, the frequency of an A score is considered to be 5.

Frequency distributions are used to tabulate the collected data. Data can be scores given by students, temperatures in different cities, scores scored in volleyball matches, and so on. After data is collected, it needs to be presented in a meaningful way for better understanding. Organize your data so that all characteristics are summarized in a table. This is called a frequency distribution.

Types of Frequency distribution:

1. Group frequency distribution: Use group frequency distribution tables to organize large numbers of observations or data. By doing so, we create class intervals to calculate the frequency of data belonging to a particular class interval.

2. Ungrouped Frequency Distribution:  In an ungrouped frequency distribution table, we record the exact frequency of individual data without classifying them.

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The chance of a series of draws can be calculated while drawing from a collection of things (for instance, a deck of cards) without replacing the items after they are drawn.

Calculate the likelihood of the initial draw while accounting for the sample space's abundance of favourable outcomes. The probability of drawing two consecutive red marbles is 4/25.

Probabilities are always in the 0 to 1 range. Probability = Number of favourable outcomes / Total number of outcomes is the general formula for probability. Or. P(A) = f / N.

On the initial draw, there is a 2/5 chance of getting a red marble.

Out of the five marbles, there are two red ones.

On the second draw, there is still a 2/5 chance of drawing a red marble.

Probability of drawing a red marble on the first draw equals the probability of drawing two red marbles (Probability of drawing a red marble on the second draw)

= (2/5) × (2/5)

= 4/25

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Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{-2}~,~\stackrel{y_1}{8})\qquad P(\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 6 -2}{2}~~~ ,~~~ \cfrac{ 2 +8}{2} \right) \implies \left(\cfrac{ 4 }{2}~~~ ,~~~ \cfrac{ 10 }{2} \right)\implies (2~~,~~5)[/tex]

Answer:

x=7/6

Step-by-step explanation:

add 2/3 to both sides

The graph of the piecewise function is given by the image presented at the end of the answer.

A piecewise function is a function that has multiple definitions, according to it's input values.

The two definitions for this problem are given as follows:

For the values until x = 1, we have an increasing linear function, with intercept of y = -2, and finishes at the point (1,-1).

For the values greater than x = 1, the function is a linear function, starting at the point (1,-1), and decaying.

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Answer:

Step-by-step explanation:

y = 2x:

This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.

12 x 12:

This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".

After '2' hours, both Car A and Car B will be '20' miles from McDonald Middle School

What is a graph?

A diagram or pictorial representation that organises the depiction of data or values is known as a graph.

The relationships between two or more items are frequently represented by the points on a graph.

Given that, both the cars are traveling at a constant speed and given a graph showing the distance from The school in Y-axis and Time in X-axis

To find the point where the cars meet, We should look at the point of intersection of both the lines of Car A and Car B

We can see the point of intersection to be (2 hours, 20 miles)

i.e., After 2 hours, Both the cars are 20 miles from the school

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Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup.

Calculate the x and y means in step one.

X's average: (0 + 10) / 2 = 5.

(95 + 88.5) / 2 = 91.75 is the mean of y.

Calculate the variance and covariance in step two.

(-5 6.5) + (5 -2.5) = 32.5 is the covariance.

X's variation is (5 0).

2 + (10 − 0)2 = 125

Calculate the regression coefficients in step three.

x = -32.5 / 125 = -0.26 where a = Covariance / Variance of x

Mean of x = 91.75 (-0.26 5) = 99.97 where b = Mean of y a Mean of x

Step 4: Compose the equation for exponential regression.

y = -0.0063e^0.16x + 99.97

Y = -0.0063e0.16x + 99.97 is the exponential regression equation for the data, where x is the time in minutes and y is the temperature of the soup. We must first determine the means of x and y before we can solve the problem. By summing the first and last values of x and dividing by 2, the mean of x is 5 and the mean of y is 91.75. (calculated by adding the first and last y values and then dividing by 2).

Calculating the covariance and variance comes next. The difference between each x and the mean of x is multiplied with the difference between each y and the mean of y to determine the covariance. By squaring the difference between each x and the mean of x, the variance of x is determined. The regression coefficients a and b can be determined when the covariance and variance have been computed.

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Answer:

y=-2 over 1x+18

Step-by-step explanation:

The value of x the width of the solar panel is 18.5.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have Pythagoras theorem:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We are given that;

Length of base of panel= 40feet

Other length = 12feet

Now,

Applying the pythagoras theorum;

|AC|^2 = |AB|^2 + |BC|^2  

|AC|^2= 12^2 + 14^2

|AC|^2= 144+196

AC= 18.5

Therefore, by Pythagoras theorem x will be equal to 18.5.

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