Answer and Step-by-step explanation:
Let f(x) = x4 + x3 + x2 +x + 1 Є Z2[x]. Prove that f(x) is irreducible over Z2[x] or not?
Proof:-
Let f(x) = x4 + x3 + x2+ x+1 Є Z2[X].
Then f (0) = 1 = f(1), so f(x) has no roots, By Factor theorem, which states that polynomial f(x) has a factor(x-a) if and only if f(a)=0. Hence, f(x) has no linear factor. If f(x) is reducible, it must have factors of degree 2 and degree 3. But f(x) has no degree 2 factors.
We know that only irreducible quadratic in Z2[X] is x2 + x +1. When we divide f(x) by x2 + x +1 we get a remainder of 1, so x2 + x +1 is not a factor of f(x) therefore f(x) is irreducible.
How to simplify this problem: (4c^4)^3
Answer:
64c^12
Step-by-step explanation:
(4c^4)^3 distribute exponents
{(4)^3 (C^12)} simplify
64c^12
Find the derivative F(x)=(5x+3)(2x^2+1)
Answer:
10x^3 + 6x^2 + 5x + 3
Step-by-step explanation:
F(x)=(5x+3)(2x^2+1)
= 5x*2x^2 + 5x*1 + 3*2x^2 + 3*1
= 10x^3 + 5x + 6x^2 + 3
= 10x^3 + 6x^2 + 5x + 3
What is the solution to the equation 1/4x+2= -5/8x-5?
Answer:
x=( -8)
Step-by-step explanation:
hope it helps.^-^
What is the length of an arc given that the measure of the central angle is 30 degree and the radius is 7 cm?
La longitud del arco (s) en una circunferencia, conociendo el radio (r) y el ángulo (θ) que forman los dos radios, es:
s = r∙θ
Con el ángulo en radianes
F V7 w7 :
PLEASE HELP meeeeeeee
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{4 \sqrt{15k} + 3 \sqrt{5k} }}}}}[/tex]
Option B is the correct option.
Step-by-step explanation:
[tex] \sf{ \sqrt{15k} (4 + \sqrt{3} )}[/tex]
Distribute √ 15 k through the parentheses
[tex] \dashrightarrow{ \sf{4 \sqrt{15k} + \sqrt{15k \times 3}}} [/tex]
[tex] \dashrightarrow{ \sf{4 \sqrt{15k} + \sqrt{45k} }}[/tex]
[tex] \dashrightarrow{ \sf{4 \sqrt{15k} + 3 \sqrt{5k} }}[/tex]
Hope I helped!
Best regards! :D
10 The table below shows the results of a swimming race.
Time (sec)
Name
Paula
47.983
Marci
50
Kelli
47.972
Susan
47.21
Carla
46
10
Brenda
46.97
Which of the following gives the first four finishers in order from 1st to 4th place
F Brenda, Carla, Marci, Paula
G Carla, Brenda, Marci, Susan
H Carla, Marci, Brenda, Susan
J Susan Marci Brenda. Carla
Answer:
G. Carla, Brenda, Marci, Susan
Step-by-step explanation:
The time given for all participants are in decimals except for that of Marci and Carla which are given in the form of mixed fractions.
Convert the mixed fractions into decimals, then compare the figures together to do the ranking.
Marci = [tex] 46\frac{49}{50} = \frac{2,349}{50} = 46.98 [/tex]
Carla = [tex] 46\frac{9}{10} = \frac{469}{10} = 46.9 [/tex]
The first four finishers from the 1st to the 4th are:
1. Carla - 46.9
2. Brenda - 46.97
3. Marci - 46.98
4. Susan - 47.21
Solve the formula h=54t+12at2 h = 54 t + 1 2 a t 2 for a.
The data below is your data set for your mini lab. For this assignment, you are the researcher. You gave the facial recognition lab to 40 students, 20 males and 20 females. The data set below contains the number of correct hits for each subject. Complete the calculations below based on the data provided.Males 5 5 8 5 6 7 4 5 3 4 8 5 10 6 5 5 8 7 5 6Females 9 8 7 7 9 8 8 8 9 10 7 9 8 9 7 9 8 7 9 7 .Calculate the mean number of correct responses (hits) for male subjects. Round to the nearest hundreths place2. Calculate the Standard Deviation (SD) of the correct reponses for male subjects. Round to the nearest hundreths place3. Calculate the Standard Error of Mean (SEM) of correct responses for male subjects. Round to the nearest hundreths place.4. Calculate the mean number of correct responses (hits) for female subjects. Round to the nearest hundreths place5. Calculate the Standard Deviation (SD) of the correct reponses for female subjects. Round to the nearest hundreths place6. Calculate the Standard Error of Mean (SEM) of correct responses for female subjects. Round to the nearest hundreths place.7. Use a statistical software program or your favorite stats website and find the t value for an unpaired 2 sample t test using the data from the 2 groups, the males and females.8. What is the degree of freedom associated with this t test.9. The p value associated with the t value isa. less than .05b. greater than .05c. I have no idea10. Based on your calculations, would you reject the null hypothes that there is no difference between males and females on this recognition task?a. Yes, I would reject the null hypothesis.b. No, I would not reject the null hypothesis.c. I have no idea.
Answer:
Reject the null hypothesis that there is no difference between males and females on the recognition task.
Step-by-step explanation:
Use MS-Excel to compute the required values.
Consider the data for male subjects first:
Mean = [tex]\frac{1}{20}\sum X_{m}}=5.85[/tex] SD = [tex]\sqrt{\frac{1}{20-1}\sum (X_{m}-\bar X_{m})^{2}}=1.69[/tex] SEM = [tex]\frac{SD}{\sqrt{20}}=0.38[/tex]Consider the data for female subjects:
Mean = [tex]\frac{1}{20}\sum X_{f}}=8.15[/tex] SD = [tex]\sqrt{\frac{1}{20-1}\sum (X_{f}-\bar X_{f})^{2}}=0.93[/tex] SEM = [tex]\frac{SD}{\sqrt{20}}=0.21[/tex]Use the Data Analysis tool in Excel to perform the hypothesis test.
The hypothesis can be defined as follows:
H₀: There is no difference between the two responses, i.e.[tex]\mu_{m}-\mu_{f}=0[/tex] .
Hₐ: There is a significant difference between the two responses, i.e.[tex]\mu_{m}-\mu_{f}\neq 0[/tex] .
Consider the Excel output for the hypothesis test.
The test statistic value is:
t = -5.32
The degrees of freedom is:
df = 38
The p value associated with the t value is:
p-value = 4.91025E-06 < 0.05
As the p-value is less than the significance level the null hypothesis will be rejected.
Conclusion:
Reject the null hypothesis that there is no difference between males and females on the recognition task.
Solve |f−6| = |f+8| Can someone please help me with this question? I'm stuck.
Answer:
no solution
Step-by-step explanation:
|f-6| = |f+8|
solve absolute values
f-6 = f+8
add 6 to 8
f = f+14
subtract f from f
0=14
not true; no solution
Katie has a collection of nickels dimes and quarters with a total value of $4.60. there are 6 more dimes than nickels and 8 more quarters than nickels. How many of each coins does she have?
Answer:
920
Step-by-step explanation:
$4.60×6-8
$4.60×2dimes
=920
please help!! will make branliest!!
Ryan is moving, and he is packing a box with plates and bowls. The box can only hold 12 pounds. Each plate weighs 1.2
pounds, and Ryan has already packed 4 plates in the box. Each bowl weighs 0.9 pounds. Which Inequality could be used to
find b, the number of bowls that can be added to the box?
OA. 4(1.2) + 0.90 <12
OB. 4(1.2 +0.9b) 12
OC. 4(1.2) + 0.96 > 12
OD. 4(1.2 + 0.9b) 12
Answer:
yay ryan is getting rid of his kitchen plates!!!
Step-by-step explanation:
Answer:
I think it's A
Step-by-step explanation:
For which values of the parameter B the following system admits a unique solution [ 1 b 1-b 2 2 0 2–2B 4 0] [x y z] = [1 2 0]
Answer: β ≠ ±1
Step-by-step explanation: For a system of equations to have an unique solution, its determinant must be different from 0: det |A| ≠ 0. So,
det [tex]\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right][/tex] ≠ 0
Determinant of a 3x3 matrix is calculated by:
det [tex]\left[\begin{array}{ccc}1&\beta&1-\beta\\2&2&0\\2-2\beta&4&0\end{array}\right]\left[\begin{array}{ccc}1&\beta\\2&2\\2-2\beta&4\end{array}\right][/tex]
[tex]8(1-\beta)-[2(2-2\beta)(1-\beta)][/tex]
[tex]8-8\beta-4+8\beta-4\beta^{2}[/tex]
[tex]-4\beta^{2}+4\neq 0[/tex]
[tex]\beta^{2}\neq 1[/tex]
[tex]\beta \neq \sqrt{1}[/tex]
β ≠ ±1
For the system to have only one solution, β ≠ 1 or β ≠ -1.
The angle of elevation of a ladder leaning against a wall is 60 degrees and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is ___ m.
Answer:
8
Step-by-step explanation:
Kyle wants to buy a new laptop that has an original price of $540. The store is having a sale, so the laptop is 10 percent off, which amounts to a discount of $54. If sales tax is 8 percent on the final price of the laptop, how much tax will he need to pay?
Answer:
A. 38.88
Step-by-step explanation:
$540-54 is 486
486(0.08) or 486(8%) is 38.88
Answer:
$38.88
I took the test, trust me
1. Solve the shape equation puzzle?
Answer:
circle = 5, triangle = 2, square = 6
Step-by-step explanation:
If we look at the first and second equations, we see that circle + triangle + square = 13. Because triangle + square = 8, we can substitute this into the first equation, therefore, circle + 8 = 13 and circle = 5. Next, looking at the third equation, we see that circle + triangle = 7 and since circle = 5 we know that 5 + triangle = 7, therefore, triangle = 2. Finally, we can substitute triangle = 2 into the second equation which gives us 2 + square = 8, therefore, square = 6.
3u+5u=64
What is the simplify of this
What does u
Answer:
u = 8
Step-by-step explanation:
3u + 5u = 64
8u = 64
8u/8 = 64/8
u = 8
Jeff can walk comfortably at 2.25 miles per hour. Find a linear equation that represents the total distance Jeff can walk in t hours, assuming he doesn't take any breaks.
The linear equation that represents the total distance Jeff can walk in t hours is d = 2.25t
How to find a linear equation that represents the total distance Jeff can walk in t hours?The given parameters are
Speed = 2.25 miles per hour
The linear equation that represents the total distance (d) Jeff can walk in t hours is calculated as:
d = Speed * t
This gives
d = 2.25 * t
Evaluate
d = 2.25t
Hence, the linear equation that represents the total distance Jeff can walk in t hours is d = 2.25t
Read more about linear equations at:
https://brainly.com/question/13763238
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a local hamburger shop soda combined order of 497 hamburgers and cheeseburgers on Friday there was 53 fewer cheeseburgers sold than hamburgers how many hamburgers were sold on Friday
Answer:
you need a answer I can see 425
Which fraction has a repeating decimal as its decimal expantion
Chang Industries has bonds outstanding with a par value of $210,400 and a carrying value of $218,600. If the company calls these bonds at a price of $214,000, the gain or loss on retirement is:
Answer:
The loss is $4600.
Step-by-step explanation:
The par value of the bonds = $210400
The carrying value of the bonds or the actual value of bonds = $218600
The company calls the bonds at the price = $214000
Now have to find the gain or loss from the given information. Thus, below is the calculation to find the gain or loss.
Loss or gain on retirement = $214,000 - $218,600 = -$4,600
Thus the loss on retirement is $4600.
Which phrase best describes f(x), graphed on the coordinate plane below?
answer.next time out the graph
Step-by-step explanation:
Answer:
It's A, an odd function
4(3x - 2) - x = 3x - 4x
Answer:
2/3
Step-by-step explanation:
Step 1:
4 ( 3x - 2 ) - x = 3x - 4x
Step 2:
12x - 8 - x = - x
Step 3:
11x - 8 = - x
Step 4:
11x = - x + 8
Step 5:
12x = 8
Answer:
x = 2/3
Hope This Helps :)
Answer:
[tex]\displaystyle{x=\frac{2}{3}}[/tex]
Step-by-step explanation:
[tex]4(3x-2)-x=3x-4x\\(12x-8)-x=3x-4x\\12x-x-8=3x-4x\\11x-8=3x-4x\\11x-8=-x\\11x=-x+8\\12x=8[/tex]
[tex]\displaystyle{x=\frac{8}{12}}[/tex]
[tex]\displaystyle{x=\frac{2}{3}}[/tex]
F(x) = 3x - 7 and g(x) = -2x - 6. Find (f o g)(4)
Answer:
(f o g)(4) = - 49Step-by-step explanation:
F(x) = 3x - 7
g(x) = -2x - 6
To find (f o g)(4) we must first find (f o g)(x)
To find (f o g)(x) substitute g(x) into f(x) that's for every x in f (x) replace it with
g (x).
We have
(f o g)(x) = 3( - 2x - 6) - 7
= - 6x - 18 - 7
We have
(f o g)(x) = - 6x - 25
To find (f o g)(4), substitute the value of x that's 4 into (f o g)(x)
We have
(f o g)(4) = - 6(4) - 25
= - 24 - 25
We have the final answer as
(f o g)(4) = - 49Hope this helps you
Find the absolute value and solve the problem
|-23| + |-15|
Answer:
38
Step-by-step explanation:
|-23| + |-15|
First find the absolute values, which are the non negative values
23 +15
Then add
38
4a-2b+40 when a=2 and b=7
Answer:
34
Step-by-step explanation:
4(2)-2(7)+40
8-14+40
-6+40=34
4a-2b+40
4x2-2x7+40
8-14+40
-6+40
34 is the answer.
Sanna has 38 homework problems to finish she finishes the 14 problems in 25 minutes. How long will it take her to finish the rest of the assignment, if she continues at the same pace?
Answer:
45
Step-by-step explanation:
What is 12.325 + 8.274
Answer:
20.599
Step-by-step explanation:
Answer:
12.325 + 8.274 = 20.599
The number line represents −412+314. What is the sum?
Answer:
the answer is -98
Step-by-step explanation:
i hope it is write
Answer: The number line represents −4 1/2 +3 1/4.
4*2+1 / 2 =8.5 + 3*4+1 /4 =3.25
-8.5 + 3.25 =-5.25
What is the sum? -5.25
C). -1 1/4
Step-by-step explanation:
Find the lengths of the sides of the triangle PQR. P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) a. |PQ| = b. |QR| = c. |RP| =
Given :
Three points , P(4, 3, 4), Q(2, 1, 3), R(2, 7, 0) .
To Find :
The length of sides .
Given :
We know , length of two points P(x,y ,z) and Q(a,b,c) is given by :
[tex]L=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}[/tex]
Length of PQ :
[tex]PQ=\sqrt{(4-2)^2+(3-1)^2+(4-3)^2}\\\\PQ=\sqrt{4+4+1}=\sqrt{9}\\\\PQ=3[/tex]
Length of QR :
[tex]QR=\sqrt{(2-2)^2+(1-7)^2+(3-0)^2}\\\\QR=\sqrt{0+6^2+3^2}\\\\QR=\sqrt{36+9}\\\\QR=\sqrt{45}\\\\QR=3\sqrt{5}[/tex] :
Length of RP :
[tex]RP=\sqrt{(2-4)^2+(7-3)^2+(0-4)^2}\\\\RP=\sqrt{2^2+4^2+4^2}\\\\RP=\sqrt{4+16+16}\\\\RP=\sqrt{36}\\\\RP=6[/tex]
Hence , this is the required solution .