Answer:
Defintion. A subset W of a vector space V is a subspace if
(1) W is non-empty
(2) For every v, ¯ w¯ ∈ W and a, b ∈ F, av¯ + bw¯ ∈ W.
Expressions like av¯ + bw¯, or more generally
X
k
i=1
aiv¯ + i
are called linear combinations. So a non-empty subset of V is a subspace if it is
closed under linear combinations. Much of today’s class will focus on properties of
subsets and subspaces detected by various conditions on linear combinations.
Theorem. If W is a subspace of V , then W is a vector space over F with operations
coming from those of V .
In particular, since all of those axioms are satisfied for V , then they are for W.
We only have to check closure!
Examples:
Defintion. Let F
n = {(a1, . . . , an)|ai ∈ F} with coordinate-wise addition and scalar
multiplication.
This gives us a few examples. Let W ⊂ F
n be those points which are zero except
in the first coordinate:
W = {(a, 0, . . . , 0)} ⊂ F
n
.
Then W is a subspace, since
a · (α, 0, . . . , 0) + b · (β, 0, . . . , 0) = (aα + bβ, 0, . . . , 0) ∈ W.
If F = R, then W0 = {(a1, . . . , an)|ai ≥ 0} is not a subspace. It’s closed under
addition, but not scalar multiplication.
We have a number of ways to build new subspaces from old.
Proposition. If Wi for i ∈ I is a collection of subspaces of V , then
W =
\
i∈I
Wi = {w¯ ∈ V |w¯ ∈ Wi∀i ∈ I}
is a subspace.
Proof. Let ¯v, w¯ ∈ W. Then for all i ∈ I, ¯v, w¯ ∈ Wi
, by definition. Since each Wi
is
a subspace, we then learn that for all a, b ∈ F,
av¯ + bw¯ ∈ Wi
,
and hence av¯ + bw¯ ∈ W. ¤
Thought question: Why is this never empty?
The union is a little trickier.
Proposition. W1 ∪ W2 is a subspace iff W1 ⊂ W2 or W2 ⊂ W1.
i hope this helped have a nice day/night :)
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 83 months with a variance of 81. If the claim is true, what is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors? Round your answer to four decimal places.
Answer:
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The production manager claims they have a mean life of 83 months with a variance of 81.
This means that [tex]\mu = 83, \sigma = \sqrt{81} = 9[/tex]
Sample of 146:
This means that [tex]n = 146, s = \frac{9}{\sqrt{146}}[/tex]
What is the probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors?
This is 1 subtracted by the p-value of Z when X = 81.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{81.2 - 83}{\frac{9}{\sqrt{146}}}[/tex]
[tex]Z = -2.42[/tex]
[tex]Z = -2.42[/tex] has a p-value of 0.0078.
1 - 0.0078 = 0.9922.
0.9922 = 99.22% probability that the mean monitor life would be greater than 81.2 months in a sample of 146 monitors.
I do not understand this and could use help it needs the work shown
Answer:
a = 9
Step-by-step explanation:
The given trinomial is :
[tex]x^2-6x+\_\_\__[/tex]
let the blank is a.
So, we need to find the value of a so that it results in a perfect square trinomial.
We know that, [tex](m-n)^2=m^2-2mn+n^2[/tex]
So,
[tex]x^2-6x+a=x^2-2(1)(3)+3^2\\=(x-3)^2[/tex]
So, the value of a is 9. If a is 9, then only it would be a perfect square trinomial.
If we add one unit to the length (l) of a rectangle that has width (w), what is its new area (NA) in terms of its old area (A)?
NA = A x w
NA = A + w
NA = A + l
NA = A
NA = A + W
By adding one unit to length, we increase the overall area by the width of the rectangle. This is because the formula for the area of a rectangle is A = l x w. So, NA = (l + 1) x w = (l x w) + w = A + w.
yes it's surprisingly for highschool can someone help I just can't figure it out
22
Step-by-step explanation:
For simplicity, let
x = teary smiley
y = tongue smiley
z = plain smiley
So now our system of equations is
[tex]x + x + x = 12\:\:\:\:\:\:(1)[/tex]
[tex]y + z + x = 18\:\:\:\:\:\:\:(2)[/tex]
[tex]z + z + y = 22\:\:\:\:\:\:\:(3)[/tex]
[tex]z + y + 2x= ??\:\:\:\:\:\:(4)[/tex]
From Eqn(1), we plainly see that
[tex]3x = 12 \Rightarrow x = 4[/tex]
Now subtract Eqn(2) from Eqn(3) to get
[tex](2z + y) - (y + z + x) = 22 - 18[/tex]
[tex]\Rightarrow z - x = 4[/tex]
But we know that [tex]x = 4[/tex], which then gives us [tex]z = 8.[/tex]
Using the values of [tex]x[/tex] and [tex]z[/tex] in Eqn(2), we find that [tex]y = 6.[/tex] Now that we the values of all the variables, use them in Eqn(3) and we'll get
[tex](8) + (6) + 2(4) = 22[/tex]
find the HCF of 72,108 and 180
Answer:
36 is the answer
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
72: 2×2×2×3×3
108: 2×2×3×3×3
180: 2×2×3×3×5
here, common factors are 2,2,3 and 3 ..
so.. HCF: 2×2×3×3
•°•HCF=36 ..
tìm tích phân tổng quát
xy'lny/x=x+ylny/x
Answer:
rhe
ehd
end
Step-by-step explanation:
jsu
uss
su
dj
dje
ej
e
Water boils at 100° Celsius and above. Which inequality describes the temperatures at which water would boil?
Answer:
D.
Step-by-step explanation:
The required inequality is given as x ≥ 100 as the water boils at 100°C and above, Option B is correct.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
As given in the question,
Water boils at 100°C and above,
So let x be the temperature of the water,
And according to the condition,
x ≥ 100° C
Thus, the inequality x ≥ 100 is shown in option B.
Thus, the required inequality is given as x ≥ 100 as the water boils at 100°C and above, and Option B is correct.
Learn more about inequality here:
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59 less than twice Mabel's score
Answer:
Mabel's score = s
2s-59
Step-by-step explanation:
I HOPE MABEL HAS A NICE GRADE
Is it Mabel from Gravity Falls?
lol
Try this 33-33+33×33÷0
Answer:
the answer is
Step-by-step explanation:
1089 first divide then multiply both numbers after that substract the numbers
Answer:
the answer is error
hope it helps
find the area of the triangle and round to the nearest tenth
Answer: 73.5mi²
Step-by-step explanation:
Area of triangle = 1/2×b×h
= 1/2×14×10.5
= 7×10.5
=73.5mi²
please click thanks and mark brainliest if you like :)
The volume of the cylinder is V=1/3r^2h, where r is the radius and h is the height. if the radius of a cylinder is 3 inches and the height is 8 inches, which answer below best estimates it’s volume?
Answer:
75 inches
Step-by-step explanation:
with this we use change of subject
V=1/3
Pie=3.14
radius =3
height =8
so therefore
V=1/3 ×3.14×3×3×8
V=75.36
Factor the following
9t^2-42t+49
Answer:
(3t -7)²
Step-by-step explanation:
We know that the square of a binomial is ...
(a -b)² = a² -2ab +b²
So, when we see the first and last terms are both perfect squares, we suspect that the trinomial is a perfect square trinomial.
9t² = (3t)²
49 = 7²
-42t = -2(3t)(7) . . . . confirming we have a perfect square
The factorization is ...
(3t -7)²
Determine the remaining sides and angles of the triangle ABC.
c=6 mi, B = 38.71°, C = 32.51°
Find the measure of angle A.
A=°
(Type an integer or a decimal.)
Find the length of side a.
а:
mi
(Round to the nearest mile as needed.)
Find the length of side b.
b=mi
(Round to the nearest mile as needed.)
9514 1404 393
Answer:
A = 108.78°
a = 11 mi
b = 7 mi
Step-by-step explanation:
The sum of angles in a triangle is 180°, so the third angle is ...
A = 180° -38.71° -32.51°
A = 108.78°
__
The remaining sides can be found from the law of sines.
a/sin(A) = c/sin(C)
a = sin(A)·c/sin(C) ≈ 0.946762 × 11.163896
a ≈ 11 mi
b = sin(B)·11.163896 ≈ 0.625379 × 11.163896
b ≈ 7 mi
Please answer I’m struggling
Step-by-step explanation:
Question 7.[tex] \frac{{(3 + u)}^{2} }{8} [/tex]
[When u = 5]
[tex] = \frac{{(3 + 5)}^{2} }{8} [/tex]
[tex] = \frac{ {(8)}^{2} }{8} [/tex]
[tex] = \frac{8 \times 8}{8} [/tex]
= 8 (Ans)
Question 8.-2(a - 7)
(Using Distributive property)
= - 2 × a -2 × (-7)
= -2a + 14 (Ans)
Answer:
7. 8
8. -2a+14
Step-by-step explanation:
(Excuse this form of the expression)
7.
u = 5
(3 + u)²
---------
8
Plug in
(3 + 5)²
---------
8
(8)²
---------
8
64
---- = 8
8
8.
-2(a - 7)
Multiply -2 with each number in the parenthesis
-2a + 14
A movie theater has a seating capacity of 187. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1338, How many children, students, and adults attended?
___ children attended.
___ students attended.
___ adults attended.
Answer:
A) children attended=98 b) students attended=60 c)adults attended=49
Step-by-step explanation:
system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29
Simplify and solve the system.
-
a%2B2a%2Bx=207
3a%2Bx=207
x=207-3aandc=2a
-
The revenue equation can be written in terms of just one variable, a.
10a%2B7%28207-3a%29%2B12a=1498
Solve for a;
use it to find x and c.
FURTHER STEPS
-
10a%2B1449-21a%2B12a=1498
a%2B1449=1498
a=98-49
highlight%28a=49 -------adults
-
c=2a
c=2%2A49
highlight%28c=98 -------children
-
x=207-a-c
x=207-49-98
highlight%28x=60 ---------students
Find x on this special right triangle
Answer:
the ans is 45⁰ BC it is a right angle
Step-by-step explanation:
Is this a trigonometry ratio
Please help explanation if possible
Answer:
17.3
Step-by-step explanation:
14.4 x 1.2
= 17.28
= 17.3 ( approximately )
A rational expression is _______ for those values of the variable(s) that make the denominator zero.
9514 1404 393
Answer:
undefined
Step-by-step explanation:
A rational expression is undefined when its denominator is zero.
Một tàu biển trị giá 2.500.000 USD đang chở các lô hàng A, B,C có giá trị lần lượt là 100.000 USD; 300.000USD, 500.000USD và tiền cước chưa thu thuộc chủ tàu là 60.000 USD. Trong hành trình đi từ Indonesia về cảng Sài Gòn tàu bị mắc cạn, vỏ tàu bị thủng, nước tràn vào làm hư hỏng một số hàng hóa. Để cứu tàu và hàng, thuyền trưởng quyết định bịt lỗ thủng bằng các phương tiện trên tàu và vứt một số hàng để tàu nhẹ bớt, đồng thời thuyền trưởng cũng cho máy tàu làm việc vượt công suất nhằm giúp tàu thoát cạn. Sau sự việc, các tổn thất được xác định như sau:
- Vỏ tàu thủng dự kiến phải sửa chữa hết 100.000 USD
- Máy tàu hư do hoạt động quá công suất và dự kiến phải sửa hết 250.000 USD
- Lô hàng B bị nước tràn vào giảm giá trị thương mại 100%.
- Lô Hàng A bị vứt xuống biển toàn bộ.
- Thiệt hại để cứu tàu và chi phí cho thủy thủ trong việc cứu tàu là 10.000 USD.
a. Hãy xác định các tổn thất riêng của các bên
b. Hãy xác định tổng tổn thất chung của các bên
c. Hãy xác định giá trị chịu phân bổ tổn thất chung (giá trị đóng góp của từng chủ thể trên tàu)
d. Hãy xác định các khoản đóng góp vào tổn thất chung của các bên
Answer:
ask in English then I can help
3. What is the length of a rectangle with a width of 1.2 m and an area of 2.4 m2 m ?
Step-by-step explanation:
area=length×width
2.4=x×1.2
1.2x=2.4
x=2.4÷1.2
x=2
therefore width = 2cm
The length of the rectangle is 2 meters.
We have,
Width of rectangle= 1.2m
Area of rectangle = 2.4 m²
To find the length of a rectangle when given its width and area, you can use the formula:
Length = Area / Width
So, the length rectangle
Length = 2.4 m² / 1.2 m
Length = 2 meters
Therefore, the length of the rectangle is 2 meters.
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We are again studying the times required to solve two elementary math problems. Suppose we ask four students to attempt both Problem A and Problem B. Assume the students are independent and all results are normally distributed, but note that a particular student's times on the two questions are likely to be positively correlated. The results are presented below (in seconds).
student Problem A Problem B
1 20 35 2 30 40 2 3 15 20 4 40 50
Again find a two-sided 95% CI for the difference in the means of A and B.
Answer:
(-16.494 ; -3.506)
Step-by-step explanation:
student Prob A Prob B difference, d (A-B)
1 20 35____ - 15
2 30 40 ___ - 10
3 15 20 ___ - 5
4 40 50 __ - 10
Difference, d = -15, -10, -5, -10
Xd = Σd/ n = - 40 / 4 = - 10
Standard deviation of d ; Sd = 4.082
The confidence interval for the difference is given as :
Xd ± Tcritical*(Sd/√n)
Tcritical at 95%; df = n - 1 ; 4 - 1 = 3
Tcritical(0.05, 3)). = 3.182
C.I = -10 ± 3.182(4.082/√4)
C.I = -10 ± 6.494462
C. I = (-16.494 ; -3.506)
How do you multiply 123 x 62?
Answer:
(123)(62)=x
Step 1: Simplify both sides of the equation.
7626=x
Step-by-step explanation:
Have a good day.
Answer:7,626
Step-by-step explanation:The easiest way I do it is by taking the numbers and putting them under each other like this
123
62
then take the number 2 for example and multiply it by 3 then 20 then 100 and do the same with the 6=60 and heres how I solve it
2 x 3=6 2 x 20=40 2 x 100=200 60 x 3=180 60 x 20=1,200 60 x 100=6,000 now take all the numbers and add them
6+40+200=246
180+1,200+6,000=7,380
7,380+246=7,626
(if this helps in anyway feel free to put brainiest but thats your choice) :) happy to help.
Translate and solve: five less than z is 4
z -5 =4
neutralize the left -5 by adding 5 on both sides
z -5 (+5) = 4 (+5)
z = 9
I want to know how to solve this equation
Answer:
B
Step-by-step explanation:
5³.5^×
simply means
5³×5^×
using indices rule,
multiplication is addition
5 is common
so 5(³+×)
hence 5^3+×
What is the sine ratio for
Answer:
the since ratio is 5/4
Step-by-step explanation:
hope this is helpful ask manyUse the following conversions to answer the question.
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
How many minutes are there in a week?
A. 420
B. 1,400
C. 10,080
D. 604,800
Answer:
C. 10,080
Step-by-step explanation:
We can multiply to find how many minutes there are in 1 day.
24 * 60 = 1,440
Now, we can multiply that value by 7 to find out how many minutes there are in 1 week.
1,440 * 7 = 10,080
Best of Luck!
Assume that x and y are both differentiable functions of t. Find dx/dt when x=11 and dy/dt=-4 for the equation xy=99 .
Differentiating both sides of
xy = 99
with respect to t yields
x dy/dt + y dx/dt = 0
When x = 11, we have
11y = 99 ==> y = 9
and we're given that dy/dt = -4 at this point, which means
11 (-4) + 9 dx/dt = 0 ==> dx/dt = 44/9
Which of the following will result in a rational answer? multiplying pi by a fraction. adding the square root of a non perfect square to a whole number. adding the square root of a perfect square to pi. multiplying a fraction by a repeating decimal.
Correct option is "multiplying a fraction by a repeating decimal."
Explanation:
Since multiplying a fraction is a rational and repeating decimal is also rational, therefore, it's result is also rational.
Hope it helps you... pls mark brainliest if it helped you
5/root 7 - root 3 +1/root 7+ root 3
[tex]\\ \sf\longmapsto \frac{5}{ \sqrt{7} - \sqrt{3} } + \frac{1}{ \sqrt{7} + \sqrt{3} } \\ \\ \sf\longmapsto \frac{5( \sqrt{7} + \sqrt{3} ) + 1 (\sqrt{7} - \sqrt{3} )}{( \sqrt{7} - \sqrt{3} )( \sqrt{7} + \sqrt{3} )} \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + 5 \sqrt{3} + \sqrt{7} - \sqrt{3} }{( { \sqrt{7} )}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \sf\longmapsto \frac{5 \sqrt{7} + \sqrt{7} + 5 \sqrt{3} - \sqrt{3} }{7 - 3} \\ \\ \sf\longmapsto \frac{6 \sqrt{7} + 4 \sqrt{3} }{4} [/tex]
write your answer in simplest radical form
Answer:
c = 4√2
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 30
Opposite = 2√2
Hypothenus = c =?
We can obtain the value of c by using the sine ratio as illustrated below:
Sine θ = Opposite / Hypothenus
Sine 30 = 2√2 / c
½ = 2√2 / c
Cross multiply
c = 2 × 2√2
c = 4√2
Therefore, the value of c is 4√2.
