Answer:
[tex]2x^3-9x^2+7x+6[/tex]
Step-by-step explanation:
The standard form of a polynomial is a method of writing a polynomial such that the terms are organized by degrees. In essence, the first term, or the left-most term has the highest degree or largest exponent. The right-most term or last term has the lowest degree or smallest exponent. One is given an expression in factored form. Distribute, multiply every term by another in the parenthesis, then simplify. Repeat this process until there are no more factored terms. Finally, rewrite the expression in standard form.
[tex](2x+1)(x-3)(x-2)[/tex]
Distribute,
[tex](2x+1)(x-3)(x-2)[/tex]
[tex]((2x)(x)+(-3)(2x)+(1)(x)+(1)(-3))(x-2)[/tex]
Simplify,
[tex]((2x)(x)+(-3)(2x)+(1)(x)+(1)(-3))(x-2)[/tex]
[tex](2x^2-6x+x-3)(x-2)[/tex]
[tex](2x^2-5x-3)(x-2)[/tex]
Distribute,
[tex](2x^2-5x-3)(x-2)[/tex]
[tex](2x^2)(x)+(-5x)(x)+(-3)(x)+(-2)(2x^2)+(-2)(-5x)+(-3)(-2)[/tex]
Simplify,
[tex](2x^2)(x)+(-5x)(x)+(-3)(x)+(-2)(2x^2)+(-2)(-5x)+(-3)(-2)[/tex]
[tex]2x^3-5x^2-3x-4x^2+10x+6[/tex]
[tex]2x^3-9x^2+7x+6[/tex]
This polynomial is already in standard form, thus there is no need to reorganize it. The leading term or the left-most term has the highest degree, three, the succeeding terms are in respective order of decreasing exponents.
The strength of the association rule is known as _____ and is calculated as the ratio of the confidence of an association rule to the benchmark confidence.
Answer:
Lift
Step-by-step explanation:
Finding patterned and relationship between large sets of data can be obtained using the association rule as it finds insights, relationships and trends within sets of data variables. Lift is a parmater of interest whichbus used when performing analysis on association between variables in datasets. The Lift is literally the ratio of confidence to expected confidence. Where, the confidence of association is divided by the expected confidence (benchmark confidence).
Which of the following could be the equation of the graph shown below?
Answer:
According to the proposed interrogate, as well as the graph provided, the correct answers to such are identified as B. Y = -2x + 5 and C. 2x + y = 4.
Step-by-step explanation:
To evaluate such, a comprehension of linear Cartesian data is required:
Slope = rise/run. If there is a negative rise, the direction of the line is proportional to the left-hand side as it exponentially grows or augments in units.
Y-intercept: The peculiar point in which the linear data observed intersects the y-axis.
X-intercept: The peculiar point in which the linear data observed intersects the x-axis.
Since this is a negative linear, all negative slopes apply.
The interrogate states, “Check all that apply.” Thus, there may be more than one correct answer, shall such be disseminated.
A. Cannot be the answer as the line should have been a horizontal line contained within quadrants I and II on the Cartesian Plane.
B. Contains a negative slope, thus is disclosed as a correct answer.
C. This configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:
2x + y = 4
Y = -2x + 4 <== Slope-Intercept Form (Contains a negative slope, thus considered a correct answer.
D. Likewise, this configuration is denoted in “Standard Form” or “General Form”. To convert this to “Slope-Intercept Form” the following must be executed mathematically:
X - y = 9
-y = -x + 9
Y = x - 9 <== Slope-Intercept Form (Cannot be considered as the correct answer, given the positive slope configuration, thus is marked out).
Thus far, as evaluated, the correct answers to the proposed interrogate, as according to the linear data provided in the Cartesian Plane is acknowledged, and henceforth disseminated, as B. Y = -2x + 5 and C. 2x + y = 4.
*I hope this helps.
Find the value of x .
Answer:
Step-by-step explanation:
Set up a proportion
BE/BC = BD/BA
BE = 3
BC = 2 + 3 = 5
BD = x + 2
BA = x + x + 2
BA = 2x + 2
3/5 = (x + 2) / (2x + 2) Cross multiply
3(2x + 2) = 5 (x + 2) Remove the brackets
6x + 6 = 5x + 10 Subtract 6 from both sides
6x = 5x + 4 Subtract 5x from both sides
x = 4
How do I graph y = -x + 4, please explain
An appliance uses 120 W. If this appliance is on for 8 hours a day, how much CO2 will this produce in the month of April?
...
Calculate Energy Cost by Appliance
Multiply the device's wattage by the number of hours the appliance is used per day.Divide by 1000.Multiply by your kWh rate.hope it's helpful for you!!..pls give me brainlist !!....SCALCET8 3.9.026.MI. A trough is 10 ft long and its ends have the shape of isosceles triangles that are 5 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 13 ft3/min, how fast is the water level rising when the water is 5 inches deep
Answer:
The answer is "0.624"
Step-by-step explanation:
[tex]b = 5x\\\\h = x\\\\ l = 10 \\[/tex]
Using formula:
[tex]V = (\frac{1}{2})(b)(h)(l) \\\\[/tex]
[tex]= \frac{1}{2} \times (5x)\times (x) \times (10)\\\\= 5x\times x \times 5\\\\= 25x^2[/tex]
[tex]\frac{dV}{dt} = 50x \ \frac{dx}{dt} \\\\\text{(where x represents the height in feet and}\ \frac{dv}{dt} = 13\ \frac{ft^3}{min})\\\\\frac{dx}{dt} = (\frac{1}{50})(\frac{1}{x}) \ \frac{dV}{dt}\\\\[/tex]
When the water is 5 inches deep then:
[tex]x = (\frac{5}{12})\ ft\\\\13 =50(\frac{5}{12}) \ \frac{dx}{dt}\\\\13 \times 12 =50(5) \ \frac{dx}{dt}\\\\\frac{13 \times 12}{50 \times 5} = \frac{dx}{dt}\\\\\frac{156}{250} = \frac{dx}{dt}\\\\ \frac{dx}{dt}= 0.624[/tex]
find the length of side x
Answer:
x=8
Step-by-step explanation:
Question 1 of 25
Is ARST - AXYZ? If so, name the postulate that applies.
R
S
x
Given
STYZ
2
A. Congruent - SSS
B. Congruent - SAS
C. Congruent - ASA
D. Might not be congruent
The triangles are congruent by SAS theorem
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be represented as ΔRST
Let the second triangle be represented as ΔXYZ
Now , the measure of side RS = measure of side XY
And , the measure of side ST = measure of side YZ
The measure of angle ∠S = measure of angle ∠Y
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Therefore , the triangles ΔRST and ΔXYZ are congruent triangles by the SAS theorem
Hence , they are congruent
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i dont understand questions like these
Answer:
same
Step-by-step explanation:
J+2/3 evaluate when j=1/4
Answer:
11/12
Step-by-step explanation:
J+2/3
1/4 + 2/3
Get a common denominator of 12
1/4 *3/3 + 2/3 *4/4
3/12 + 8/12
11/12
It takes Barry 912 hours to detail a car. If he worked 57 hours during the week, how many cars did he detail?
Answer:
He detailed 16 cars.
912/57=16
Step-by-step explanation:
Work out giving ur answer as a mixed number
Answer:
6 11/12
Step-by-step explanation:
4 1/6 + 2 3/4
Get a common denominator of 12
4 1/6 *2/2 + 2 3/4 *3/3
4 2/12 + 2 9/12
6 11/12
Evaluate the expression 3√64
Answer:
4
Step-by-step explanation:
We want the cubed root of 64
(64)^(1/3)
(4*4*4) ^ (1/3)
4
Unless this is 3 * sqrt(64)
then it would be
3 sqrt(8*8)
3 (8)
24
2(x-4) +3(2-x) +2x +7
Answer:
x+5
Step-by-step explanation:
Answer:
2x-8+6-3x +2x +7
= 2x -3x +2x -8+6+7
=4x-3x-8+13
= 1x+5
i just need the answer no explanation
Applying log rules leaves us with the following equation:
x^2 + 8 = 6x
Change to standard form and solve using factoring.
x^2 - 6x + 8 = 0
(x - 4)(x - 2) = 0
x = 4
x = 2
Hope this helps!
A two-dimensional vector has an x-component of 10.3~\text{meters}10.3 meters and a y-component of 4.30~\text{meters}4.30 meters. Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis.
9514 1404 393
Answer:
23°
Step-by-step explanation:
The angle a vector makes relative to the +x axis is found as ...
α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°
The angle is about 23°.
__
Additional comment
This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)
PLEASE HELP. What are the coordinates of the terminal point for theta= 4pi/3
Answer:
D
Step-by-step explanation:
i simply used the unit circle
An experiment consists of tossing a pair of balanced, six-sided dice. (a) Use the combinatorial theorems to determine the number of sample points in the sample space S. 36 Correct: Your answer is correct. sample points (b) Find the probability that the sum of the numbers appearing on the dice is equal to 6. (Round your answer to four decimal places.)
Answer:
Sample space = 36
P(sum of 6) = 5/36
Step-by-step explanation:
Number of faces on a dice = 6
The sample space, for a toss of 2 dice ; (Number of faces)^number of dice
Sample space = 6^2 = 6*6 = 36
Sum of numbers appearing on the dice = 6
The sum of 6 from the roll of two dice has 5 different outcomes ; Hence, required outcome = 5
Total possible outcomes = sample space = 36
Probability, P = required outcome / Total possible outcomes
P = 5 / 36
Probabilities are used to determine the chances of events
The given parameters are:
[tex]n=6[/tex] --- the faces of a six-sided die
[tex]r = 2[/tex] -- the number of dice
(a) The number of sample points
This is calculated as:
[tex]Sample = n^r[/tex]
So, we have:
[tex]Sample = 6^2[/tex]
Evaluate the exponent
[tex]Sample = 36[/tex]
Hence, the number of sample points is 36
(b) The probability that the sum of 6
See attachment for the sample space of the sum of two dice.
From the sample space, there are 5 outcomes where the sum is 6.
So, the probability is:
[tex]Pr = \frac{5}{36}[/tex] --- where 36 represents the number of sample points
Divide 5 by 36
[tex]Pr = 0.1389[/tex]
Hence, the probability that the sum of the numbers appearing on the dice is equal to 6 is 0.1389
Read more about probabilities at:
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Convert 625 to base twelve
Answer:
441
Step-by-step explanation:
Find the solution to the system of equations.
x + y + z = 25
y+z= 18
Z= 7
Answer:
x=7
y=11
z=7
Step-by-step explanation:
x + y + z = 25
y+z= 18
Z= 7
Substitute the third equation into the second
y+z=18
y+7 = 18
y = 18-7
y = 11
Now substitute y=11 and z=7 into the first
x +y+z = 25
x+11+7 = 25
x+18 = 25
x = 25-18
x=7
What’s 90×90 to the power of 4×82÷8
Answer:
90^41
Step-by-step explanation:
so 4x82/8 = 41
and so 90 x 90 have the same base number
so the answer is 90^41
michael has an average of 68% in his 3 papers but that is below the pass mark of 70%. what must be his least score in the fouth paper to enable him pass?
Answer:
His least score for him in the fourth paper has to be 76.
Step-by-step explanation:
Given that Michael has an average of 68% in his 3 papers but that is below the pass mark of 70%, to determine what must be his least score in the fouth paper to enable him pass the following calculation must be performed:
(70 x 4) - (68 x 3) = X
280 - 204 = X
76 = X
Therefore, his least score for him in the fourth paper has to be 76.
In a certain survey, 513 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?" Among the respondents, 53% said "yes." We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security. Complete parts (a) through (d) below. a. Are any of the three requirements violated? Can a test about a population proportion using the normal approximation method be used?
Answer:
The sample observations are not a randomsample, so a test about a population proportion using the normal approximating method cannot be used.
Step-by-step explanation:
The necessary conditions are
The sample must be random and independently selected from the normally distributed population.
n*p and n*q both must be greater than 5
There must be two outcomes "success" and "failure"
The number of trials must be fixed.
From the given information 2), 3)and 4) conditions are satisfied, but not 1) because we are not given that people are selected randomly.
Answer: The sample observations are not a randomsample, so a test about a population proportion using the normal approximating method cannot be used.
Briefly explain tha meaning of accounting?
Answer:
Answer given below.
Step-by-step explanation:
Accounting as per American Institute of Certified Public Accountants
" Accounting is the art of recording, classifying, summarizing in a significant manner and in terms of money; transactions and events which are, in part atleast, of a financial character, and interpreting the results thereof. "
{I am a grade 11 commerce student. The following answer is as per what I have learnt. Hope it helps.}
Given limit of f(x) = -4 as x approaches c and limit of g(x) =1/5 as x approaches c. What is limit of g(x)/f(x) as x approaches c?
Answer:
-1/20
Step-by-step explanation:
As x approaches c,
g(x) 1/5
------ = ------------ = -1/20 (matches last of the four given possible answers)
f(x) -4
Answer:
[tex]\displaystyle \frac{-1}{20}[/tex]
General Formulas and Concepts:
Calculus
Limit Property [Division]: [tex]\displaystyle \lim_{x \to c} \frac{f(x)}{g(x)} = \frac{ \lim_{x \to c} f(x)}{ \lim_{x \to c} g(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \lim_{x \to c} f(x) = -4[/tex]
[tex]\displaystyle \lim_{x \to c} g(x) = \frac{1}{5}[/tex]
Step 2: Solve
Substitute in limits [Limit Property - Division]: [tex]\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{ \frac{1}{5} }{ -4 }[/tex]Simplify: [tex]\displaystyle \lim_{x \to c} \frac{g(x)}{f(x)} = \frac{-1}{20}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
expand and simplify
i’ll give u brainiest
√5(√10+√2)
Answer:
[tex] \sqrt{50} + \sqrt{10} [/tex]
Step-by-step explanation:
[tex] \sqrt{5} ( \sqrt{10} + \sqrt{2} ) \\ (opening \: the \: bracket) = (\sqrt{10 \times 5} ) + ( \sqrt{5 \times 2} \\ = \sqrt{50} + \sqrt{10} [/tex]
Answer:
√50 + √10 = 5√2 + √10
Please mark brainliest as answered correctly.
Divide 140 into a ratio of 1:6
The required division is 20 to 120
Given the ratio 1:6
Get the total ratio;
Total ratio = 1 + 6 = 7
Amount to be divided = 140
For the ratio of 1;
[tex]= \frac{ratio}{total}* 140\\= \frac{1}{7} * 140\\= 20[/tex]
For the ratio of 6:
[tex]= \frac{ratio}{total}* 140\\= \frac{6}{7} * 140\\= 6 * 20\\= 120[/tex]
Therefore the division is 20 to 120
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I really need help on this question
9514 1404 393
Answer:
f(-∞) → -∞f(∞) → ∞odd degree5 real zerosStep-by-step explanation:
The general shape of "up to the right" tells you this is an odd-degree polynomial with a positive leading coefficient. As such, the value of f(x) will have the same sign as the value of x when x gets large. The end behavior could be described by ...
lim[x → -∞] f(x) → -∞
lim[x → ∞] f(x) → ∞
__
The curve crosses the x-axis 3 times and touches it once without crossing. Each crossing is a real zero. Each touch is a a real zero with an even multiplicity. The shape (flatness) of the touch gives a clue as to the multiplicity. (Flatter means higher multiplicity.) Here the shape indicates the zero has a multiplicity of 2.
So, there are 4 distinct real zeros, one with a multiplicity of 2, for a total of 5 real zeros.
_____
Additional comment
An even-degree polynomial function has a generally U shape. If the leading coefficient is negative, the U is upside down: ∩. An even-degree polynomial will have the limits of f(x) having the same sign, regardless of the sign of x.
A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $279.29. Find a 99% confidence interval for the true mean checking account balance for local customers.
Answer:
The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 14 - 1 = 13
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 3.0123
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.0123\frac{279.29}{\sqrt{14}} = 224.85[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 664.14 - 224.85 = $439.29
The upper end of the interval is the sample mean added to M. So it is 664.14 + 224.85 = $888.99.
The 99% confidence interval for the true mean checking account balance for local customers is ($439.29, $888.99).
Please Help!!! Whoever helps first and gets it correct gets Brainliest!
Answer:
Step-by-step explanation:
You have three data points. Equation of the line passing through (30,2), (45,2.75), and (60,3.50):
y = 0.5x + 0.5
It takes 0.5 hour to clean up.