Answer: D. The polynomial is irreducible.
From the explanation below we do not get polynomial .
Step-by-step explanation:
A.(x+3)(x-6)
= x^2-6x+3x-18
=x^2-3x-18
B.(x-3)(x+6)
=(x^2+6x-3x-18)
=x^2+3x-18
C.(x+3)(x^2-4x+6)
=x^3-4x^2+6x+3x^2-12x+18
=x^2-x^2-6x+18
D.The polynomial is irreducible
the population of a town increased from 3450 in 2006 to 5700 in 2012. find the absolute and relative (percent) increase. absolute increase: relative increase:
Answer:
The absolute difference is 1050
The relative percentage is 32.3076%
Step-by-step explanation:
We are given
The population of a town increased from 3,250 in 2008 to 4,300 in 2010
In 2008:
In 2010:
Absolute difference:
we know that
absolute difference =
absolute difference =
absolute difference is 1050
Relative increase:
we know that
Relative percentage is
now, we can plug values
=32.3076
So, the relative percentage is 32.3076%
2 3/5 times 3 1/3
NEED ASAP
Answer:
Answer is: 8 2/3 but improper is 26/3
multiply the maclaurin series for e z and 1 1 z to obtain the series expansion for e z 1 z up to z 5 . on what disk does it converge?
The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.
The Maclaurin series for e^z is:
e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...
The Maclaurin series for 1/1-z is:
1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...
Multiplying these two series together gives:
e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)
= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...
= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...
This series converges for |z| < 1
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7 The nth term of a sequence is u, = 10 x 3" Write down the first four terms in the sequence.
The first four terms in the sequence are 30, 90, 270 and 810 respectively.
How to determine the termsWe have that the nth term of the sequence is expressed as;
U = 10 × 3 ^n
Where;
n = number of terms
To determine the first terms, let's substitute the value of n as 1, we get;
U = 10 × 3^1
Multiply the values
U₁ = 30
The second terms, n = 2
U₂ = 10 × 3²
U₂ = 10 × 9
Multiply through
U₂ = 90
The third year, n = 3
U₃ = 10 × 3³
Find the cube of the value and multiply the values
U₃ = 270
The fourth year, n = 4
U₄ = 10 × 3^4
U₄ = 10 × 81
Multiply through
U₄ = 810
Thus, the numbers are 30, 90, 270, 810
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Two sailboats are sailing up a river. The relationship between the distance (d ), in miles, from the starting point to the time (t ), in hours, it takes to sail a distance d for each boat is given.
The correct statement regarding the proportional relationships is given as follows:
Boat A travels at a faster rate than Boat B.
What is a proportional relationship?A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:
y = kx
The function for boat A is:
d = 10.5t.
Hence the rate is:
10.5 miles per hour.
From the graph, the rate for boat B is obtained as follows:
k = 90/10 = 9 miles per hour.
A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.
Missing InformationThe problem is given by the image shown at the end of the answer.
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Complete the statement to describe the expression (a+b+c)(d+e+f)(a+b+c)(d+e+f). The expression consists of 3 factors, and each factor contains terms
The statement about the given expression is described below.
What is expression?A math expression consist numbers, variables and operators its operation addition, subtraction, multiplication, and division. The parts of the expression that are connected with addition and subtraction are considered as terms.
According to given data:Expression, (a+b+c)(d+e+f)(a+b+c)(d+e+f) = (a +b+c)^2(d+e+f)^2
It has factors two which consist of 3 termsEach factor has a multiplicity of 2terms in factor (a+b+c) are a, b, cTerms in factor (d+e+f) are d, e, fThus, given expression has two factors which consist 3 terms.
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8x - 4y = 16
8x+4y= 16
Answer:
X = 2, Y = 0
Step-by-step explanation:
Add the two equations together to cancel out -4y and +4y
leaving you with:
8x = 16
8x = 16
divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)
leaving you with:
x = 2
substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):
8(2) - 4 y = 16
8 x 2 = 16
leaving you with:
16 - 4y = 16
subtract 16 from both sides to get 4y on its own
leaving you with:
-4y = 0
so y = 0, and x = 2
The function shown models the depth d (in inches) of snow on the ground during the first 9 hours of a snowstorm, where t is the time (in hours) after the snowstorm begins
d(t)=1/2t+6
What is the domain
What is the range
The domain of the function d(t)=1/2t+6 is (-∞, ∞) and the range of the function is (-∞, ∞).
What are Domain and Range?Similar to how we input different numbers into functions, we also receive new numbers as the outcome. The two main characteristics of functions are domain and range.
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values. Range, Domain, and Function. A is the domain and B is the co-domain if a function f: A → B exists that maps every element of A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R. The set of images is the function's range.
The domain of the function d(t)=1/2t+6 is given by
Domain: (-∞, ∞), {x|x ∈ R}
The range of the function is given by
Domain: (-∞, ∞) , {y|y ∈ R}
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Reese made a deposit into an account that earns 8% simple interest after 8 years Reese had earn $400 how much was Reece's initial deposit?
HELP
The principle investment necessary to obtain a total sum of $400.00 from simple interest at an annual rate of 8% for 8 years is $243.90.
What is arithmetic operation?Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on.
Here,
First, converting R percent to r a decimal
r = R/100 = 8%/100 = 0.08 per year.
Solving our equation:
P = 400 / ( 1 + (0.08 × 8)) = 243.90243902439
P = $243.90
The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 8 years is $243.90.
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the nth term of a gp 145800. if the fist term is 2 and the common ratio is 3. find the sum of the gp
The sum of the geometric progression with the features stated in the text is given as follows:
S = 2.62 x 10^(43).
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The sum of a finite geometric sequence with n terms is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
In this problem, the first term and the common ratio are given as follows:
[tex]a_1 = 2, n = 3[/tex]
Hence the equation is:
[tex]a_n = 2(3)^{n - 1}[/tex]
The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:
[tex]a_n = 2(3)^{n - 1}[/tex]
[tex]1458000 = 2(3)^{n - 1}[/tex]
[tex]3^{n - 1} = 729000[/tex]
[tex]3^{n - 1} = 3^{90}[/tex]
Then:
n - 1 = 90
n = 91.
Thus the sum of the sequence is given as follows:
[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]
[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]
S = 2.62 x 10^(43).
Typing mistakeThe problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.
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Write equivalent fractions for 8/9 and 5/8 using the least common denominator.
Type the fractions, using a slash ( / ) to separate the numerator and denominator.
8/9 =
5/8 =
The equivalent fractions for 8/9 and 5/8 using the least common denominator are 8/9 = 64/72 and 5/8 = 45/72.
What is the Least Common Denominator?
The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD). The smallest number that may be used as the denominator to produce a group of comparable fractions that all have the same denominator is known as the lowest common denominator.
The given fractions are 8/9 and 5/8.
The denominators of these fractions are 8 and 9.
so Least Common Divisor(LCD) of 8 and 9 will be = 8 × 9
= 72.
so the equivalent fraction can be calculated as
for 8/9 = [tex]\frac{8*8}{9*8}[/tex]
= 64/72
and for 5/8 = [tex]\frac{5*9}{8*9}[/tex]
= 45/72
Hence, the equivalent fractions are 64/72 and 45/72.
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During the Christmas season, a store offers a sale. You buy one item for the regular price then you get 60% discount on a second item of equal or less value. You choose to buy two items with regular prices of $30 and $20. In addition, the store charges 9% sales tax of your purchase after the discount. Which of the following is what you actually pay for the items?
The amount you pay for the items is C. $41.42.
How is the amount determined?The amount that the customer pays for the two items is determined by first discounting the second item by 60%.
The result after the discount is added to the cost of the first item before the sales tax is added to get the final cost of the items.
Discount on second item = 60%
The price of the first item purchased = $30
The price of the second item purchased = $20
Discounted price on the second = $8 ($30 x (1 - 60%)
Total cost before sales tax = $38 ($30 + $8)
Sales tax = 9%
Total cost after sales tax = $41.42 ($38 x 1.09)
Thus, after discounting the second item by 60% and adding the sales tax of 9%, the customer will pay $41.42 for the items.
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Answer:
c. 41.42 my teacher told me the answer
Step-by-step explanation:
What is the ordered pair for the reflection of the point (2,-1) over the x~axis
Answer:
(2,1)
Step-by-step explanation:
The x-value stays the same since we are only moving up/down and the y-value becomes the opposite
(x,y)--> (x,-y)
So the point becomes (2,1)
Answer:
(2,-1) hope this helps you understand
I need help asap please now please !!!!!!!!!!!
A men’s basketball coach would like to know if there is a relationship between how tall a player is and how high he can jump. Here is a scatterplot of the data.
A graph has height (inches) on the x-axis and vertical jump distance (inches) on the y-axis. The points form a line with positive slope.
Describe the scatterplot.
The relationship between height and vertical jump distance is
,
, and
.
There are
unusual observations.
The relationship between height and vertical jump is High positive correlation.
What is a correlation?
A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.
Main body:
To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.
If the line doesn't pass through all points it has low positive correlation.
hence this has high positive correlation .
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Answer:
-positive
-linear
-strong
-no.
Step-by-step explanation:
edge 2023
an analog signal received at a detector (measured in micro volts) may be modeled as a gaussian random variable n (200, 256) at a fixed point in time. what is the probability that the signal will exceed 240 micro volts? what is the probability that the signal is larger than 240 micro volts, given that it is larger than 210 micro volts?
Given that the signal gets larger than 210 microvolts, there is a 2.335 % chance that it is also larger than 240 microvolts.
Define the term Gaussian random variable?We consider the Gaussian form whenever we need to describe complex valued random variables for whom the distribution is unknown. The Central Limit Theorem (CLT), which deals with the sum of several random variables, is substantially fundamental for this tendency.As, per the given question.
Gaussian random variable n (200, 256)
Part a: Probability that signal will exceed 240 micro volts.
P(x > 240) = 1 - P(x ≤ 240)
P(x > 240) = 1 - P(240 - 200)/16
P(x > 240) = 1 - P(2.5)
See p value for z = 2.5
P(x > 240) = 0.00621
Thus, Probability that signal will exceed 240 micro volts is 0.00621.
Part b: larger than 210 micro volts.
P(x ≥ 240) | x ≥ 210) = P(x ≥ 240) / P(x ≥ 210)
P(x ≥ 240) | x ≥ 210) = 1 - P(240 - 200)/16 / 1 - P(210 - 200)/16
P(x ≥ 240) | x ≥ 210) = 0.00621 / 0.26599
P(x ≥ 240) | x ≥ 210) = 0.02335
Thus, for the signal gets larger than 210 microvolts, there is a 0.02335 percent chance that it is also larger than 240 microvolts.
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Elliot makes and sells key chains. His profit depends on what price he charges for a
key chain.
He writes the expression (x - 10) (60 - 3x) to represent his profit based on the
price per key chain, x.
Enter Elliot's average change in profit for two different sections of the graph.
When charging $15 for a key chain, it is discovered that his maximum profit is $75 using the vertex of the quadratic function.
The vertex of a quadratic equation,
A quadratic equation is given by, [tex]ax^{2} +bx +c[/tex]
The vertex is given by [tex]A (x_{1} ,y_{1} )[/tex]
[tex]x_{1} = \frac{-b}{2a}\\ \\y_{1} = \frac{-b^{2} +4ac }{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.
If a > 0, it will be a minimum point.
The function given is (x -10 ) (60 -3x)
f(x) = (x -10 ) (60 -3x) = 60x -3[tex]x^{2}[/tex] -600 +30x = -3[tex]x^{2}[/tex] +90x -600
So, here a = -3, b = 90 and c = -600
So,
[tex]x_{1} = \frac{-b}{2a}\\ \\x_{1} = \frac{-90}{2*(-3)} = 15[/tex]
[tex]y_{1} = \frac{-b^{2} +4ac }{4a} = \frac{(-90)^{2} + 4*(-3)*(-600) }{4*(-3)} = 75[/tex]
Hence, He can make up to $75 in profit when he charges $15 for a key chain.
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Please help me please help me
Answer:
the answer Is 6 .........
Expand and simplify (2x + 5)2
Answer: 4x+10
simplified: 2x+5
Step-by-step explanation:
Answer: 4x+10
You multiply 2 by (2x) = 4x
You multiply 2 by (5) = 10
How much of a radioactive kind of bismuth will be left after 8 minutes if the half-life is 2
minutes and you start with 79,360 grams?
grams
Please help I’ll give 30 pts
The area of the figure created by Brianna is [tex]33\frac{3}{4}[/tex] square feet.
Explain area in mathematics.
Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area or, it can be simply defined as the total amount of space occupied by a flat (2-D) surface or an object's shape.
Solution Explained:
A square with a side of 4 1/2 feet and two parallelograms with bases of 4 1/2 feet and heights of 1 1/2 feet make up the figure.
Therefore, the total area of the figure is
Area of Square + 2 X Area of Parallelogram
= (side)^2 + 2(b X h)
= (4 1/2)^2 + 2(4 1/2 X 1 1/2)
= 81/4 + 27/2
= 135/4
= [tex]33\frac{3}{4}[/tex] square feet
Area of the figure is [tex]33\frac{3}{4}[/tex] square feet.
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a survey of 398 children given at a local elementary school showed that 175 like chocolate ice cream 150 like pistachio ice cream, and 123 do not like chocolate or pistachio ice cream. how many children like at least one kind of ice cream mentioned in the survey? a) 225 b) 100 c) 325 d) 275 e) 125 f) none of the above.
The number of student like at least one kind of ice cream is given by (d) 275.
Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.
Now given that, n(C) = 145, n(P) = 150
Also given that, 123 students do not like neither chocolate or pistachio ice cream.
So, n(P' and C') = 123
The required number of student like at least one kind of ice cream is given by,
N = 398 - n(P' and C') = 398-123 = 275
Hence the correct option is (d).
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at a university, the probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12. find the probability that the student takes statistics given that he or she is a business major
The probability that the student takes statistics given that he or she is a business major is 0.04.
Define probability.The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.
Given,
The probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12
Students who have taken both:
P( statistics ∩ business) = 0.036
Only a statistics major:
P( statistics/ business) = 0.9
P( student is business major)
P ( statistics / business) ÷ P( statistics/ business)
0.036/0.9
0.04
The probability that the student takes statistics given that he or she is a business major is 0.04.
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Find g(x) if g(x) is the resulting function from moving f(x) = (x + 2) right 1 unit and up 6 units.
g(x) = (x+2-3) + 4 = (x-1)+4
if f(x) = 2x - 4 find f(3x)
Answer: the answer would be 2
Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.
2x3=6-4=2
Question 2
When G(3,-5) is reflected in the
line y = -2, the image is located at
G'
Reflection in geometry means the type of transformation that flips a shape in a mirror line.
What is reflection ?
Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.
Let us suppose that the triangle with one coordinate [tex](3,-5)[/tex] and the other two are unknown and we do not even want to know them but it would be better if we do know them:-
And we have a graph.
Let us draw a line [tex]y=-2[/tex] on the graph and draw the triangle
Now the coordinates [tex](3,-5)[/tex] are three boxes away from the line [tex]y=-2[/tex], so we plot this coordinate three boxes up from the line [tex]y=-2[/tex] and do the same for other coordinates so [tex](x,y)[/tex] is one box up from the line [tex]y=-2[/tex] so we plot the coordinates one box up from the line [tex]y=-2[/tex]
Hence, the image is located at [tex]G[/tex] is plotted above.
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Round 74.9963 to the nearest 10
The number 74.9963 would round down to 70
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
We need to round 74.9963 to the nearest 10
We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.
The answer would be 70
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the ages of five randomly chose cars in the parking lot are determined to be 7, 9, 3,4, and 6 years old. if we consider these 5 cars in groups of 3, how many groups can be formed?
The number of groups formed is 10 if we consider 5 cars in groups of 3.
Given, 5 cars in groups of 3, we can use the formula,
(5 3) = 5! / 3! × 2!
= 10
Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.
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in a tournament there are six teams that play each other twice. a team earns 3 points for a win, 1 point for a draw, and zero points for a loss. after all the games have been played it turns out that the top three teams earned the same number of total points. what is the greatest possible number of total points for each of the top three teams?
The greatest possible number of total points for each of the top three teams is 24.
Given;
Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.
After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.
Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).
Therefore, this case brings a total of 4 + 18 = 22 points.
Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.
This case brings a total of 18 + 6 = 24 points.
Therefore, we use case (II) since it brings the greater amount of points as 24.
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find the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet and the smallest possible surface area.
The dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3
Rectangular Box with Square base
Volume v = a²b = 12
S = Surface area = 2a² + 4ab
v = a²b = 12
b = 12/a²
S = 2a² + 4ab = 2a² + 4a(12/a²) =2a² + 48/a
S'(a) = 4a -48/a² = 0
4a³ = 48
a = 12^ 1/3
b = 12/a² = 12/12^ 2/3 = 12^ 1/3
Therefore, the dimensions of a rectangular box with a square base which has a volume of 12 cubic feet is a = 12^ 1/3, b = 12^ 1/3
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