After considering the given data we conclude the x term of h(x) is [tex]44 + 5*2 = 26.[/tex]We can continue this process for the [tex]x^2[/tex] term, the [tex]x^3[/tex] term, and the [tex]x^4[/tex] term, using the appropriate terms from f(x) and g(x) and adding up the products and the quotient q(x) is [tex]x^2 - x,[/tex] and the remainder r(x) is [tex]3x^2 + 8x + 5,[/tex]
To evaluate the product h(x) of the two polynomials f(x) and g(x) manually, we can apply a table [tex]T_3[/tex] to show line by line how each term is computed.
The table possess columns for the term from f(x), the term from g(x), and the product of the two terms. The rows of the table will correspond to the different powers of x, starting from [tex]x^0[/tex].
For instance , to compute the constant term of h(x), we need to multiply the constant terms of f(x) and g(x). The constant term of f(x) is 5, and the constant term of g(x) is 4, so the constant term of h(x) is 54 = 20.
Similarly, to compute the x term of h(x), we need to multiply the x term of f(x) (which is 4) by the constant term of g(x) (which is 4), and add it to the constant term of f(x) (which is 5) multiplied by the x term of g(x) (which is 2).
Therefore, the x term of h(x) is [tex]44 + 5*2 = 26.[/tex]We can continue this process for the [tex]x^2[/tex] term, the [tex]x^3[/tex] term, and the [tex]x^4[/tex] term, using the appropriate terms from f(x) and g(x) and adding up the products.
To evaluate the quotient q(x) and remainder r(x) when f(x) is divided by g(x), we can use polynomial long division.
We apply division the highest degree term of f(x) by the highest degree term of g(x) to get the first term of q(x).
Then we multiply g(x) by this term of q(x) and subtract the result from f(x) to get the first remainder. We repeat this process with the next highest degree term of the remainder until the degree of the remainder is less than the degree of g(x).
The coefficients of the terms in q(x) are the quotients obtained in each step of the division, and the coefficients of the terms in the remainder are the final remainder obtained after all the steps of the division.
For instance , to compute the quotient q(x) and remainder r(x) when [tex]f(x) = x^4 + 2x^3 + 3x^2 + 4x + 5[/tex] is divided by [tex]g(x) = x^2 + 2x + 4,[/tex]
we first divide [tex]x^4[/tex] by [tex]x^2[/tex] to get [tex]x^2[/tex] as the first term of q(x).
We then multiply g(x) by [tex]x^2[/tex] to get [tex]x^4 + 2x^3 + 4x^2,[/tex] and subtract this from f(x) to get[tex]-x^3 - x^2 + 4x + 5[/tex] as the first remainder.
We then divide [tex]-x^3[/tex] by [tex]x^2[/tex] to get -x as the second term of q(x).
We multiply g(x) by -x to get[tex]-x^3 - 2x^2 - 4x[/tex], and subtract this from the first remainder to get [tex]3x^2 + 8x + 5[/tex]as the final remainder.
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A manufacturer has cube shaped cardboard boxes with an exact volume of 12000 cubic inches. What is the volum of the largest sphere that can be packed inside the cube shaped box? Give you answer rounded to the nearest whole cubic inch
Answer:
6283 in³
Step-by-step explanation:
The largest sphere that can fit into the cardboard box must have its diameter, d equal to the length, L of the cardboard box.
Since the cardboard box is in the shape of a cube, its volume V = L³
So, L = ∛V
Since V = 12000 in³,
L = ∛(12000 in³)
L= 22.89 in
So, the volume of the sphere, V' = 4πr³/3 where r = radius of cube = L/2
So, V = 4π(L/2)³/3
= 4πL³/8 × 3
= πL³/2 × 3
= πL³/6
= πV/6
= π12000/6
= 2000π
= 6283.19 in³
≅ 6283.2 in³
= 6283 in³ to the nearest whole cubic inch
Jump to level 1 Suppose the mean height in inches of all 9th grade students at one high school is estimated. The population standard deviation is 3 inches. The heights of 6 randomly selected students are 63, 72, 65, 73, 60 and 62. ≈ = 65.5 # Margin of error at 99% confidence level = Ex: 1.23 99% confidence interval [Ex: 12.34 Ex: 12.34] - [smaller value, larger value] Check Try again 18 Feedback?
The required answer is [61.77, 69.23].
Given: Mean height of all 9th grade students at one high school is estimated as ≈65.5 Population standard deviation is σ = 3 inches. Number of samples n = 6Margin of error at 99% confidence level = 1.23Margin of error = E = z(σ/√n)Now, z = inv Norm(0.995) (as it is 99% confidence interval, α=0.01 and 1-α=0.99)⇒ inv Norm(0.995) = 2.58∴ E = 2.58(3/√6) = 3.73∴ The margin of error at the 99% confidence level is 3.73 inches .
Confidence interval = [sample mean - E, sample mean + E]=[65.5 - 3.73, 65.5 + 3.73] = [61.77, 69.23]
∴ The 99% confidence interval for the population mean height of all 9th-grade students at that high school is [61.77, 69.23].
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Determine if given expression is a function. If so, find out if it is one to one, onto or bijection.
(a) Given f: Z → Z+, f(x) = |x − 2| + 1.
(b) Given f: Z → Z+, f(x) = −3x + 2.
(c) Given f: R→ R, f(x) = x² − 2x + 1.
(a) The function f(x) = |x − 2| + 1 is a one-to-one function and onto, but not a bijection. (b) The function f(x) = −3x + 2 is a one-to-one function but not onto and not a bijection. (c) The function f(x) = x² − 2x + 1 is a one-to-one function, onto, and a bijection.
Let's evaluate each given expression to determine if it is a function and, if so, determine its characteristics:
(a) Given f: Z → Z+, f(x) = |x − 2| + 1.
This expression represents a function. A function is a relation between two sets where each input value (x) maps to a unique output value (f(x)). In this case, for any integer input x, the function f(x) returns the absolute value of the difference between x and 2, plus 1. Since each input has a unique corresponding output, this function is one-to-one.
To determine if the function is onto or a bijection, we need to examine the range of the function. The range of f(x) is the set of all possible output values. In this case, the function returns only positive integers (Z+). Therefore, the function is onto since it covers the entire range of positive integers. However, it is not a bijection since the domain (Z) and the codomain (Z+) have different cardinalities.
(b) Given f: Z → Z+, f(x) = −3x + 2.
This expression also represents a function. It is a linear function that takes an integer input x and returns the value obtained by multiplying x by -3 and then adding 2. Since each input value maps to a unique output value, the function is one-to-one.
To determine if the function is onto or a bijection, we examine the range of f(x). The function f(x) returns positive integers (Z+). However, it does not cover the entire range of positive integers. Specifically, it only produces negative or zero values when x is positive. Therefore, the function is not onto, and it is not a bijection.
(c) Given f: R → R, f(x) = x² − 2x + 1.
This expression represents a function. It is a quadratic function that takes a real number input x and returns the value obtained by substituting x into the equation x² - 2x + 1. Since each input value maps to a unique output value, the function is one-to-one.
To determine if the function is onto or a bijection, we again examine the range of f(x). The quadratic function f(x) is a parabola opening upward, and its vertex is located at (1, 0). This indicates that the lowest point on the graph is at y = 0, and the range of f(x) includes all real numbers greater than or equal to 0. Therefore, the function is onto, and it is a bijection.
In summary:
(a) The function f(x) = |x − 2| + 1 is a one-to-one function and onto, but not a bijection.
(b) The function f(x) = −3x + 2 is a one-to-one function but not onto and not a bijection.
(c) The function f(x) = x² − 2x + 1 is a one-to-one function, onto, and a bijection.
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m - 12 = 11
A. -23
B. -1
C. 1
D. 23
Answer:
D. 23
Step-by-step explanation:
m-12-(11)=0
m-23 = 0
m = 23
Please answer correctly! I will mark you as Brainliest!
Answer:
C
Step-by-step explanation:
trust me if you really need this done
Answer:
Angelo needs to use the formula V = [tex]\frac{4}{3} \pi (8.5)^3[/tex].
Step-by-step explanation:
The formula for finding the volume of a sphere is [tex]V=\frac{4}{3} \pi r^3[/tex], wherein the variable, r, is the radius. Diameter is one half of the radius; thus, it would be 17/2 = 8.5. Substitute the values into the equation (i.e. V = [tex]\frac{4}{3} \pi (8.5)^3[/tex]).
FIND THE DIFFERENCE:(5a -7c)-(2a + 5c)
7a - 2c
3a - 12c
7a + 12c
Answer:
3a-12c
Step-by-step explanation:
(5a-7c)-(2a+5c)
5a-7c-2a-5c
(5a-2a)+(-7c-5c)
3a-12c
Answer:
3a - 12c
Step-by-step explanation:
Circle A has a radius of 16 inches. What is the circumference?
Answer:
100.571inches
Step-by-step explanation:
Perimeter. =2πr
Perimeter. =2×22÷7×16
Perimeter. =704÷7
Perimeter. =100.571inches
PLEASE GIVE BRAINLIEST
1. Your house is 50 feet below sea level and you hike up 125 feet. What is your current elevation
Answer:
it's 75 feet above sea level
Answer:
75 feet
take 125
minus
50
which give you 75.
Please help me with the question
Answer:
3
Step-by-step explanation:
Since it's at the same time of the day, the ratio between the height of the person and the shadow they cast will stay the same. So the man's height to shadow ratio is 6:8 = 3:4. The son's height to shadow ratio would be the same so x:4 = 3:4 therefore his height is 3 feet.
i need help with algebra 2 stuff. if anyone wanna help me out greatly appreciate it :)
Answer:
Step-by-step explanation:
I will try my best to help you with algebra what is the question
Please help I'm begging a ACE OR GENES To help me please please help please please ASAP please please help please please ASAP please please help
Answer:
2/3
Step-by-step explanation:
the ratio of base1 ABCD to base 1 of WXYZ is
8 to 12
8/12 = 2/3
Plz help I’ll give brainliest
Answer:
1. y = 2x + 5
2. (-5) + 3 + (-8) = 3 - 5 - 8 = 3 - 13 = -10
3. given: 1/2, 3/4, 7/8, 0.55, 0.1
1/2, 3/4, 7/8 = 4/8, 6/8, 7/8
4/8 < 6/8 < 7/8
1/2 < 3/4 < 7/8
0.55 = 55/100 = 11/20
0.1 = 1/10 = 2/20
2/20 < 11/20
0.1 < 0.55
1/2 = 10/20
2/20 < 10/20 < 11/20
0.1 < 1/2 < 0.55
3/4 = 15/20
11/20 < 15/20
0.55 < 3/4
thus
0.1 < 1/2 < 0.55 < 3/4 < 7/8
HELP WILL GIVE BRAINLEASIT
Step-by-step explanation:
try to do 180 - 135 organise a 45-degree that is the first answer of a and b you're taking 180 - 144 you got the answer also 28 degrees
How many students choose strawberry kiwi
Need help with the answer please
NO LINKS!!!
Answer:
15 students. 30%
Step-by-step explanation:
Which statement is true?
A. A number subtracted from itself is a natural number.
B. All rational numbers are integers.
C. All irrational numbers are real numbers. W
D. Every whole number is a natural number.
A number system is a system for the presentation of numbers into groups or categories
The true statement is the option;
C. All irrational numbers are real numbers
Reason:
The number system is composed of two types of numbers, which are;
Real numbers Imaginary numbersImaginary Numbers;
The imaginary numbers are the numbers that have the value √(-1), within them
Real Numbers:
There are two types of real numbers which are;
Rational numbers; Numbers that can be written in the form [tex]\dfrac{a}{b}[/tex], where a, and b, are integers
Irrational numbers; Numbers that cannot be expressed in the form [tex]\dfrac{a}{b}[/tex], such as π, √2, e
Therefore;
All irrational numbers are real numbers
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A circular patio has a diameter of 16 feet . how many square feet of tile will it take to cover the patio
Answer:
201.1 square feet
Step-by-step explanation:
The radius (r) of the patio is 16/2 = 8
Area of a circle is π[tex]r^{2}[/tex] so [tex]8^{2}[/tex]π = 201.0619298 or 64π
Answer:
It will take 113.10 ft² of tiles to cover the patio.
Step-by-step explanation:
area of a circle formula: A = πr²
The diameter is twice the length of the radius. To find the radius, divide the diameter by 2:
16/2 = 8
To find the area of the circular patio, apply the radius to the formula A = πr²:
A = π6²
A = 113.10 ft²
Ally has taken 5 quizzes this year. Her mean quiz score is 8 out of 10. She takes another quiz and gets a perfect score of 10. What happens to her mean score?
Answer:
It goes up
Step-by-step explanation:
envision a totem pole, Estimate the height of the totem pole in the front. How did you go about deciding how to estimate its own height.
Answer:
(5.1×10^15)×(8.1×10^5
A distribution is positively skewed if which of these statements is true about
the dot plot that represents it?
A. The left tail is longer than the right.
B. The left side is a mirror reflection of the right side.
C. The right tail is longer than the left.
D. The left tail is equal in length to the right tail.
Answer:
c the right tail is longer than the left
Step-by-step explanation:
These numbers tell how many books five different students read in the past six months. 8, 11, 15, 22, and 6 a) Create a different set of five pieces of data with a greater mean, but with at least two values less than the values in the set of data above. b) Create a different set of five pieces of data with a lower mean, but with at least two values greater than the values in the set of data above. How did you make it work? c) Create a different set of five pieces of data with a lower mean, but with a higher median than the original set.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Origibal data set
8, 11, 15, 22, 6
Rearranging The value :
x : 6, 8, 11, 15,22
Mean = Σx / n
n = sample size =5
Mean = (6+8+11+15+22) = 62
Mean = 62 / 5 = 12.4
Median = 1/2(n+1)th term
Median = 1/2(6)th term = 6/2 = 3rd term = 11
A.)
X = 4, 5, 15, 23, 19
MEAN = (4 +5 + 15 + 23 + 19) / 5 = 13.2
B.)
X = 2, 6, 5, 23, 34
Mean = (2+6+5+23+24) / 5
Mean = 60 / 2 = 12
C.)
X = 3, 7, 12, 21, 13
X = 3, 7, 12, 13, 21
Mean = (3+7+12+13+21) /5 = 11.2
Median = 1/2(6)th term = 6/2 = 3rd term = 12
assume that the weight loss for the first month of a diet program varies between 6 and 12 pounds
The probability of the weight loss falling between 8 pounds and 11 pounds is 1/2
Variation of weight = Between 6 to 12.
It is required to ascertain the percentage of the overall range that corresponds to that interval in order to calculate the chance that the weight reduction will fall between 8 pounds and 11 pounds.
Calculating the total range of weight -
Range = Higher weight - Lower weight
= 12 - 6
= 6
Similarly, calculating the total range of weight for 8 pounds and 11 pounds
Range = Higher weight - Lower weight
= 11 - 8
Calculating the probability -
Probability = Range of interest / Total range
= 3 / 6
= 1/2.
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Complete Question:
Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost between 8 pounds and 11 pounds
a. 1/2
b. 1/4
c. 2/3
d. 1/3
Each unit on the grid represents 2 kilometers. Find thedistance between Gabe's house and the library?
Answer:
8km
Step-by-step explanation:
there are 4 unit between Gabe's house and the library so distance is 4×2=8km
Use the points (0,60) and (4,90) from the line on the scatter plot What is the equation of the linear modal?
100
90
80
Test Score
70
60
0
0 1 2 3 4 5
Time Studying (hours)
Reflex angle of 95 degrees
Step-by-step explanation:
a a reflex angle is more than 180° but less than 360° so in this case the reference angle of 95 degrees we are going to take 360° - 95 degrees to get255°
Evaluate the expression 6 + 5 × 32 - 8.
43
11
6
91
(and its not 32 its just the 2 is suppose to be up)
(dont steal my points)
Answer:
43
Step-by-step explanation:
A is the answer
Answer:
Ima steal your points
Step-by-step explanation:
Find the inverse Laplace transform f(t) = --!{F(s)} of the function F(s): = 4s $2 – 81 ft= (6) - c-- {} - {22} - = 4s 81 = L وی + help (formulas) 2ی S 9 (1 point) Find the inverse Laplace transform f(t) = (-1{F(s)} of the function F(s) = = 7 52 9 + s-1' 7 f(t) = 2-1 50== -{+} = = help (formulas) S2 S - 1
(a) Inverse Laplace transform of F(s) = 4s/(s² - 81) is
[tex]f(t) = 2e^{(9t)} + 2e^{(-9t).[/tex]
We can rewrite F(s) as F(s) = 4s/[(s - 9)(s + 9)].
Using partial fraction decomposition, we can express F(s) as F(s) = A/(s - 9) + B/(s + 9), where A and B are constants.
Multiplying both sides by (s - 9)(s + 9), we get 4s = A(s + 9) + B(s - 9).
Expanding and equating coefficients, we have 4s = (A + B)s + 9A - 9B.
Equating coefficients of s on both sides, we get A + B = 4.
Equating constants on both sides, we get 9A - 9B = 0, which gives A = B.
From A + B = 4, we have 2A = 4, so A = B = 2.
Therefore, F(s) can be written as F(s) = 2/(s - 9) + 2/(s + 9).
Now, using the inverse Laplace transform formulas:
[tex]L{e^{at}} = 1/(s - a),\\L{e^{(-at)}} = 1/(s + a),[/tex]
we can find the inverse Laplace transform of F(s):
[tex]f(t) = L^{(-1)}{F(s)} = 2L^{(-1)}{1/(s - 9)} + 2L^{(-1)}{1/(s + 9)}\\= 2e^{(9t) }+ 2e^{(-9t).[/tex]
Therefore, the inverse Laplace transform of F(s) = 4s/(s² - 81) is f(t) = 2e^(9t) + 2e^(-9t).
(b) Inverse Laplace transform of F(s) = (7s + 52)/(s² + s - 1):
We can rewrite F(s) as F(s) = (7s + 52)/[(s - 1)(s + 1)].
Using partial fraction decomposition, we can express F(s) as F(s) = A/(s - 1) + B/(s + 1), where A and B are constants.
Multiplying both sides by (s - 1)(s + 1), we get (7s + 52) = A(s + 1) + B(s - 1).
Expanding and equating coefficients, we have 7s + 52 = (A + B)s + (A - B).
Equating coefficients of s on both sides, we get A + B = 7.
Equating constants on both sides, we get A - B = 52.
Solving these equations, we find A = 29 and B = -22.
Therefore, F(s) can be written as F(s) = 29/(s - 1) - 22/(s + 1).
Using the inverse Laplace transform formulas:
[tex]L{e^{at} = 1/(s - a),\\L{e^{(-at)} = 1/(s + a),[/tex]
we can find the inverse Laplace transform of F(s):
[tex]f(t) = L^{(-1)}{F(s)} = 29L^{(-1)}{1/(s - 1)} - 22L^{(-1)}{1/(s + 1)}\\= 29e^t - 22e[/tex]
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Gavin divided his notebook into 8 equal parts. He plans to use 3 parts to take notes for math and 2 parts for reading. He has school from 8:30 A.M to 3:30 P.M. what fraction of his notebook does he have left?
Pls help I well mark you a brainliest...
Answer:
Gavin has 3 parts left.
Step-by-step explanation:
8-3-2=3. The time was not important.
Karita had $138.72 in her checking account. She wrote check to take out $45.23 and $18.00, and then made a deposit of $75.85 into her account. How much dose Karita have in her account now?
AD is tangent to circle B at point C. What is the measure of BCA? O 40° O 50° O 90° O 180°
Answer:
C
90
Step-by-step explanation:
B is likely the center, I think. You can't do it otherwise.
The tangent and a radius of a circle meet at 90o
therefore the answer is 90.
All of this could be confirmed with a diagram.
let be the set of vectors in with the following definition of addition and scalar multiplication: addition: scalar multiplication: determine which of the vector space axioms are satisfied.
The given set of vectors in R with the defined addition and scalar multiplication operations does not satisfy the closure properties, violating the vector space axioms.
In the first part, the set of vectors with the given operations does not satisfy all of the vector space axioms.
In the second part, let's examine the vector space axioms to determine which ones are not satisfied.
Closure under addition: The axiom states that for any vectors u and v in the set, the sum u + v must also be in the set. If we consider the vectors (1, 0) and (0, 1), their sum is (1, 1), which is not in the given set. Therefore, closure under addition is not satisfied.
Closure under scalar multiplication: The axiom states that for any scalar c and vector u in the set, the scalar multiple c * u must be in the set. If we consider the vector (1, 1) from the previous example, multiplying it by a scalar c will result in the vector (c, c). However, for certain values of c, such as c = 2, the resulting vector (2, 2) is not in the given set. Hence, closure under scalar multiplication is not satisfied.
Since the set does not satisfy closure under addition and closure under scalar multiplication, it does not satisfy the vector space axioms.
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