Answer:
1) W₁ is a subspace of Pₙ (R)
2) W₂ is not a subspace of Pₙ (R)
4) W₃ is a subspace of Pₙ (R)
Step-by-step explanation:
Given that;
1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R
2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R
3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R
so
1)
let W₁ = { at² ║ a∈ R }
let ∝ = a₁t² and β = a₂t² ∈W₁
let c₁, c₂ be two scalars
c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)
= c₁a₁t² + c²a₂t²
= (c₁a₁ + c²a₂)t² ∈ W₁
Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁ and scalars c₁, c₂
Thus, W₁ is a subspace of Pₙ (R)
2)
let W₂ = { t² + a ║ a∈ R }
the zero polynomial 0t² + 0 ∉ W₂
because the coefficient of t² is 0 but not 1
Thus W₂ is not a subspace of Pₙ (R)
3)
let W₃ = { at² + a ║ a∈ R }
let ∝ = a₁t² +a₁t and β = a₂t² + a₂t ∈ W₃
let c₁, c₂ be two scalars
c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)
= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t
= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃
Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂
Thus, W₃ is a subspace of Pₙ (R)
The height of a building, measured in feet, is an example of:_______.
a. qualitative data
b. either qualitative or quantitative data
c. feet data
d. quantitative data
Answer:
Option d (quantitative data) is the correct choice.
Step-by-step explanation:
Quantitative data seems to be a collection or kind of data which is concerned regarding quantitative information or methods. That indicates its value, as well as the condition, could be represented arithmetically. All evidence that can be quantified, checked, and suitable for statistical analysis categorizes as quantitative methods.The remaining three options do not apply to the specified scenario. Therefore the description made will serve as an example of quantitative data.
PLEASE HELP ME !!!! What is the value of |-25| ?
Answer: 25
Step-by-step explanation: The absolute value is the distance between a number and zero. The distance between − 25 and 0 is 25
Answer:
[tex]\Huge \boxed{25}[/tex]
Step-by-step explanation:
[tex]|-25|[/tex]
The absolute value of a number is the distance of that number from zero.
Applying absolute value rule : [tex]|-a|=a[/tex]
[tex]|-25|=25[/tex]
PLEASE HELP IMMEDIATELY!!!
5x + 11 = 4x + 18 and describe the steps!!!
Answer:
x = 7
Step-by-step explanation:
First, put the x values on one side by subtracting 4x from each side:
5x + 11 = 4x + 18
x + 11 = 18
Subtract 11 from both sides to solve for x:
x = 7
Answer: The value of x is 7.
Step-by-step explanation:
Here's how I got my answer:
5x + 11 = 4x + 18
Isolate variables and combine like terms:
5x - 4x = 18 - 11
Simplify:
x = 7
That is the final answer.
A circle is defined by x^2+y^2+2gx+2fy-15=0. The gradient of the tangent to the circle at the point (3,2) is -1/2. Find the value of g and f
Answer:
(g, f) = (-1, 2)
Step-by-step explanation:
The equation can be put into standard form:
(x^2 +2gx) +(y^2 +2fy) = 15
(x^2 +2gx +g^2) +(y^2 +2fy +f^2) = 15 +g^2 +f^2
(x +g)^2 +(y +f)^2 = 15 +g^2 +f^2 . . . . equation in standard form
The point (3, 2) is on the circle, so one of the equations we have is ...
(3+g)^2 +(2 +f)^2 = 15 +g^2 +f^2
9 +6g +g^2 +4 +4f +f^2 = 15 +g^2 +f^2
6g +4f = 2 . . . . . . . subtract g^2 +f^2 +13
3g +2f = 1 . . . . . . . divide by 2
__
A line through the center of the circle is perpendicular to the tangent at the point of tangency. That line will have a slope that is the negative reciprocal of the tangent's slope: m = -1/(-1/2) = 2. Then in point-slope form the equation of the line through the center is ...
y -2 = 2(x -3)
2x -y = 4 . . . . rearrange to standard form
The point at the center of the circle, (-g, -f), satisfies this equation, so we have another relation for f and g:
2(-g) -(-f) = 4
2g -f = -4 . . . . . . multiply by -1
Adding twice this equation to the one above, we have ...
2(2g -f) +(3g +2f) = 2(-4) +(1)
7g = -7 . . . . . . . . . simplify
g = -1 . . . . . . . . . . divide by 7
f = 2g +4 = 2(-1) +4 = 2 . . . find the corresponding value of f
The values of f and g are: f = 2 and g = -1.
what is 3 2/3 as a fraction
Answer:
[tex]\frac{11}{3}[/tex]
Step-by-step explanation:
[tex]3\frac{2}{3}[/tex]
3 * 3 = 9
So we add 9 to the top which is 2
9+2 = 11
ta da
11/3
Hope this helps!!! :)
pls mark brainliest
Answer:
3 2/3= 11/3
Step-by-step explanation:
Work to prove it:
Step 1
Multiply the denominator by the whole number
3 × 3 = 9
Step 2
Add the answer from Step 1 to the numerator
9 + 2 = 11
Step 3
Write answer from Step 2 over the denominator
11/3
If this helps please mark me the brainiest
Parabola,,Could you help me please??
Answer:
[tex]\large \boxed{\sf \bf \sqrt{\dfrac{10}{3}}}[/tex]
Dimension of the rectangle is
[tex]2\times\sqrt{\dfrac{10}{3}}\\ \\10-\dfrac{10}{3}=\dfrac{20}{3}[/tex]
Step-by-step explanation:
Hello,
[tex]\text{The area is }2x(1-x^2) \\ \\\text{The derivative is }2(10-x^2)+2x(-2x)=2(10-3x^2)\\\\\text{The derivative is }0\text{ for} 10-3x^2=0 \\\text{so for } x=\sqrt{\dfrac{10}{3}}[/tex]
Thanks
What is 5.264 x 2.3? Please show work on how you got the answer
[tex]5.264 \times 2.3[/tex]
Answer:
12.1072
Step-by-step explanation:
5.264
x take 3 multiply with 5264 = 15792
2.3 then take 2 multiply with 5264 = 10528
15792 add column by column as drop 2 down, then 9 + 8
10528 then 7+2, 5+5, 1+0, 1. then count how many numbers total
121072 behind the point .264= 3 numbers + .3 is 1 number= 4#s
then count backward the result 4 numbers 2701 put the
dot there you will get 12.1072
Solve the equation below.
6(-2w - 3) = -4(3w + 7) + 10
Answer: all real numbers
Explanation:
Let's solve your equation step-by-step.
6(−2w−3)=−4(3w+7)+10
Step 1: Simplify both sides of the equation.
6(−2w−3)=−4(3w+7)+10
(6)(−2w)+(6)(−3)=(−4)(3w)+(−4)(7)+10(Distribute)
−12w+−18=−12w+−28+10
−12w−18=(−12w)+(−28+10)(Combine Like Terms)
−12w−18=−12w+−18
−12w−18=−12w−18
Step 2: Add 12w to both sides.
−12w−18+12w=−12w−18+12w
−18=−18
Step 3: Add 18 to both sides.
−18+18=−18+18
0=0
Amanda has a recipe that requires 3 1/2 cups of milk. If she is only making 2/3 of the recipe, how many cups of milk will she need?
Answer:
2 1/3
Step-by-step explanation:
She will need 2/3 of 3 1/2:
(2/3)(3 1/2) = (2/3)(3) +(2/3)(1/2) = 2 + 1/3
Amanda will need 2 1/3 cups of milk.
Find the area of the triangle below. Be sure to include the correct unit in your answer.
Answer:
54cm²
Step-by-step explanation:
Area=1/2bh
=1/2(18)(6)
=54cm²
you are making lemonade to sell at the trck meet. according to the recipe, you need 12 ounces of lemon juice for every 240 ounces of sugar water. You have 16 ounces of lemon juice. How many ounces of sugar water do you need?
2+2995442974346496329869631467646547624672463777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
Answer:
2.9954429743464962e+168
Step-by-step explanation:
solve for x : 8 (2-x) +3x= -4
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]8(2-x)+3x=-4[/tex]
Distribute the first term:
[tex]16-8x+3x=-14[/tex]
Combine like terms:
[tex]16-5x=-4[/tex]
Subtract 16 from both sides:
[tex]-5x=-20[/tex]
Divide both sides by -5:
[tex]x=4[/tex]
So, the value of x is 4 :)
What equation do you obtain when you solve the formula A = 1/2bh for h?ASAP PLEASE
Answer:
2Ab=h
Step-by-step explanation:
A=1/2bh
2A=bh
2Ab=h
Suppose that the height s of a ball (in feet) at time t (in seconds) is given by the formula s(t) = 64 - 16(t - 1)^2. This function is graphed below on the interval 0 ≤ t ≤ 3. Which labeled point (A-G) corresponds to the release of the ball? How high (in feet) was the ball when it was released? Which labeled point corresponds to the highest point of the ball? When (in seconds after being released) did the ball reach its highest point? Which labeled point corresponds to the ball hitting the ground? How long (in seconds) after being released did the ball hit the ground?
Answer:
Kindly check explanation
Step-by-step explanation:
Suppose that the height s of a ball (in feet) at time t (in seconds) is given by the formula
s(t) = 64 - 16(t - 1)^2
t interval = 0 ≤ t ≤ 3
1) point A (from the graph)
11) Height of ball when it was released
Ball was released at t = 0
s(0) = 64 - 16(0 - 1)^2
= 64 - 16(-1)^2
= 64 - 16(1)
= 64 - 16
= 48 feets
111) point C ( from the graph)
IV) highest point of the ball is 64
Hence,
s(t) = 64 - 16(t - 1)^2
64= 64 - 16(t - 1)^2
16(t - 1)^2 = 64 - 64
16(t - 1)^2 = 0
16t^2 - 32t + 16 = 0
t^2 - 2t + 1 = 0
(t-1) = 0 (t-1) = 0
t = 1
V) Point G (from graph)
V1)
height = 0
s(t) = 64 - 16(t - 1)^2
0 = 64 - 16(t - 1)^2
16(t - 1)^2 = 64
(t - 1)^2 = 64/16
(t - 1)^2 = 4
(t - 1)² = 2²
t - 1 = 2
t = 2 + 1
t = 3
Triangle△ABC is rotated -120 about point P to create △ABC
11. Emma has been offered a job that pays $36.950 for working a 52-week year
training software users. What average amount does the job pay per month? per
week?
2.84 per month, 0.71 per week
Step-by-step explanation:
52/4 =13 months
36.95/15=2.84
31.95/52 = 0.71
Twenty points :) plz help. The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary: Earth-151.13 Neptune- 4.4764
Answer:
53357.1428571 hours
Step-by-step explanation:
1.494 billion km from Saturn to earth, divided by 28,000
Question
The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. Show your work. Convert your answer into scientific notation if necessary: Earth-151.13 Neptune- 4.4764
Answer
53357.1428571 hours
Which shows all the factors for 36?
1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 3, 4, 9, 12, 18, 36
2, 3, 4, 6, 9, 12, 18
1, 2, 3, 4, 8, 12, 18, 36
Answer:
1, 2, 3, 4, 6, 9, 12, 18, 36
Hope it helps.
Please mark it as Brainliest.
Write an equation to solve for x, then solve for x. The whole question is in the picture.
Answer:
12x = 60 x = 5
Step-by-step explanation:
2 (2x + 4x) = 2 (6x) = 12x
the perimeter is 12x and 60 is the perimeters value so you divide 60 by 12 and get 5
8. Solve for y. **THINK! a) what type of angles do you have? b) what is their
relationship (add up to 90, add up to 180, or congruent)? c) set up an equation
and solve *
Answer:
a. Linear pair (supplementary)
b. Add up to 180°
c. [tex] y = 20 [/tex]
Step-by-step explanation:
78° and (5y + 2)° are a linear pair. They are supplementary, and add up to 180°.
Therefore, the following equation expresses their relationship:
[tex] 78 + (5y + 2) = 180 [/tex]
Solve for y
[tex] 78 + 5y + 2 = 180 [/tex]
[tex] 78 + 2 + 5y = 180 [/tex]
[tex] 80 + 5y = 180 [/tex]
Subtract 80 from both sides
[tex] 80 + 5y - 80 = 180 - 80 [/tex]
[tex] 5y = 100 [/tex]
Divide both sides by 5
[tex] \frac{5y}{5} = \frac{100}{5} [/tex]
[tex] y = 20 [/tex]
Is the value of the 8 in 12.984 the same as the value of the 8 in 7.38? Justify your response.
Answer:
hundredths’ value in 12.984
hundredths’ value in 7.38
My response: In arithmetic, a hundredth is a single part of something that has been divided equally into a hundred parts. For example, a hundredth of 675 is 6.75. In this manner it is used with the prefix "centi" such as in centimeter. A hundredth is the reciprocal of 100.
Please help me out thank you
Answer:
(-0.0008)^0 =11291^1 =1(1/3)^0 = 1Step-by-step explanation:
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^0=1,\:\\\\(-0.0008)^0 = 1\\\\1291^0 =1\\\\-(-3141)^0 = -1\\\\-(\frac{5}{8} )^0 =-1\\\\0^1 = 0\\\\(\frac{1}{3} )^0 = 1\\[/tex]
Calculate the average rate of change for the given function, from x = -1 to x = 2.
Answer:
it moved 3 spots
Step-by-step explanation:
solve this question 2√8+√8
A. 3√8
B.24
C.16√8
D.2√8
Answer:
Simplify each radical, then combine.
3√8
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
6 √ 2 = 3√8
An experimenter wants to estimate the average water consumption per family in a city. Discuss the relative merits of choosing individual families, dwelling units (single-family houses, apartment buildings, and so on), and city blocks as sampling units. What would you use as a frame in each case?
Answer:
Solution: an Experimenter whats to estimate the average water consumption per family in the city
if individual families are used as the sampling united, a frame could be using censes data or atelephone book
if dwelling are used as the sampli units, aframe could be using Address book or city directory
If city blocks are used as the sampling units, aframe could been using is city directory
Step-by-step explanation:
g In a one-tail hypothesis test where you reject H0 only in the lower tail, what is the p-value if Z STAT
Answer:
The P-value is 0.0166.
Step-by-step explanation:
The complete question is: In a one-tail hypothesis test where you reject H0 only in the lower tail, what is the p-value if ZSTAT = -2.13.
We are given that the z-statistics value is -2.13 and we have to find the p-value.
Now, the p-value of the test statistics is given by the following condition;
P-value = P(Z < -2.13) = 1 - P(Z [tex]\leq[/tex] 2.13)
= 1 - 0.9834 = 0.0166
Assuming that the level of significance is 0.10 or 10%.
The decision rule for rejecting the null hypothesis based on p-value is given by;
If the P-value of the test statistics is less than the level of significance, then we have sufficient evidence to reject the null hypothesis.If the P-value of the test statistics is more than the level of significance, then we have insufficient evidence to reject the null hypothesis.Here, the P-value is more than the level of significance as 0.0166 > 0.10, so we have insufficient evidence to reject the null hypothesis, so we fail to reject the null hypothesis.
A health and fitness club surveys 40 randomly selected members and found that the average weight of those questioned is 157 lb. Is this average an example of a statistic or a parameter?
A) Parameter
B) Statistic
Answer:
B. Statistic
Step-by-step explanation:
The average weight of those questioned which is 157 lb. from the survey of 40 randomly selected member of a health and fitness club is an example of a statistic.
It is a calculated numerical value that characterises some aspects of a sample set of data.
Statistic refers to a numerical piece of information that uses quantified models, representations and synopses for a given set of a study. Statistic is used to to estimate the true value of a parameter in a population.
Translate and solve: 518% of what number is 3885?
Answer:The answer is 750
Step-by-step explanation:3885 of 750 can be written as:
3885/ 750
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
3885/750 × 100/100= (3885 × 100) over 750) × 1 over 100= 518/100
Therefore, the answer is 518%
If you are using a calculator, simply enter 3885÷750×100 which will give you 518 as the answer.
Look at the sets below.
{1, 2, 3, 4, 5} {2, 4, 6, 8, 10}
Which of the following shows the union of the sets?
A.
{1, 2, 3, 4, 5}
B.
{2, 4, 6, 8, 10}
C.
{2, 4}
D.
{1, 2, 3, 4, 5, 6, 8, 10}
Answer:
[tex] \boxed{\bold{\boxed{ \sf{1 \: , \: 2 \: , \: 3\: ,4 \: , \: 5 \: , \: 6 \: , \: 8 \: , \: 10 \: }}}}[/tex]
Option D is the correct option
Step-by-step explanation:
Let the sets be A and B.
A = { 1 , 2 , 3 , 4 , 5 }
B = { 2 , 4 , 6 , 8 , 10 }
Finding A union B ( A ∪ B )
The union of sets A and B is the set of all elements which belongs either A or B or both A and B
So, list them :
A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 8 , 10 }
Hope I helped!
Best regards! :D