Let M = {a ∈ R: a > 1}. Then M is a vector space under standard addition and scalar
multiplication of real numbers.
False
True

Main answer: An orthogonal basis for the given span H is {x1, x2-x1, x3 - (x1 + x2 - x1)} which simplifies to {x1, x2-x1, x3-x2}.

Supporting explanation: Given, x₁ = 0, x₂ = 1, x₃ = √3The span of H is the set of all linear combinations of x1, x2 and x3.So, we have to find an orthogonal basis for H using the Gram-Schmidt process. Let's start with the first vector x1 = [0, 0, 0]The second vector x2 is the projection of x2 onto the subspace perpendicular to x1. x2 is already perpendicular to x1 so x2-x1 = x2. So, the second vector is x2 = [0, 1, 0].The third vector x3 is the projection of x3 onto the subspace perpendicular to x1 and x2. x3 is not perpendicular to x1 and x2, so we subtract the projections of x3 onto x1 and x2 from x3. Projection of x3 onto x1:projx₁(x₃) = x₁ [(x₁ . x₃)/(x₁ . x₁)] = [0, 0, 0]Projection of x3 onto x2:projx₂(x₃) = x₂ [(x₂ . x₃)/(x₂ . x₂)] = [0, √3/3, 0]Therefore, x3 - projx₁(x₃) - projx₂(x₃) = [0, √3/3, √3]So, the orthogonal basis for H is {x1, x2-x1, x3 - (x1 + x2 - x1)} which simplifies to {x1, x2-x1, x3-x2}.

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Correct Question:

He counts 18 female students, 16 male students, and 6 teachers. There are

720 people in the auditorium. Consider the probability of selecting one person

at random from the auditorium.

Which of these statements are true?

Choose all that apply.

A:  The probability of selecting a teacher is 6%.

B : The probability of selecting a student is 85%.

C : The probability of selecting a male student is 32%.

D : The probability of selecting a female student is 45%.

Step-by-step explanation:

Option B  and D are correct because

The total number of people in one cross section = 18 + 16 + 6 = 40.

A = The probability of selecting a teacher is = (6/40)x100 = 15 % not equal to 6 %

B = The probability of selecting a male student is = (34/40)x100 = 85%

C = The probability of selecting a male student is = (16/40)x100 = 40 % not equal to 32 %

D : The probability of selecting a female student is = (18/40)x100= 45%

Answer:

here,hope this helps : )

Step-by-step explanation:

Answer: A= 32

a (Base) 6

b (Base) 10

h (Height) 4

Step-by-step explanation: A=a+b

2h=6+10

2·4=32    I really hoped this helped

Answer:

Dominos is the better deal.

Question:

A population consists  1, 2, 4, 5, 8. Draw all possible samples of size 2  without replacement from this population.

Verify that the sample mean is an unbiased estimate of the population mean.  

Answer:

[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]

[tex]\hat p = \frac{3}{5}[/tex] --- proportion of evens

The sample mean is an unbiased estimate of the population mean.

Step-by-step explanation:

Given

[tex]Numbers: 1, 2, 4, 5, 8[/tex]

Solving (a): All possible samples of 2 (W.O.R)

W.O.R means without replacement

So, we have:

[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]

Solving (b): The sampling distribution of the proportion of even numbers

This is calculated as:

[tex]\hat p = \frac{n(Even)}{Total}[/tex]

The even samples are:

[tex]Even = \{2,4,8\}[/tex]

[tex]n(Even) = 3[/tex]

So, we have:

[tex]\hat p = \frac{3}{5}[/tex]

Solving (c): To verify

[tex]Samples: \{(1,2),(1,4),(1,5),(1,8),(2,4),(2,5),(2,8),(4,5),(4,8),(5,8)\}[/tex]

Calculate the mean of each samples

[tex]Sample\ means = \{1.5,2.5,3,4.5,3,3.5,5,4.5,6,6.5\}[/tex]

Calculate the mean of the sample means

[tex]\bar x = \frac{1.5 + 2.5 +3 + 4.5 + 4 + 3.5 + 5 + 4.5 + 6 + 6.5}{10}[/tex]

[tex]\bar x = \frac{40}{10}[/tex]

[tex]\bar x = 4[/tex]

Calculate the population mean:

[tex]Numbers: 1, 2, 4, 5, 8[/tex]

[tex]\mu = \frac{1 +2+4+5+8}{5}[/tex]

[tex]\mu = \frac{20}{5}[/tex]

[tex]\mu = 4[/tex]

[tex]\bar x = \mu = 4[/tex]

This implies that [tex]\bar x[/tex] is an unbiased estimate of the [tex]\mu[/tex]

Answer:

[tex](g*f)(x) = 34[/tex]

Step-by-step explanation:

For sake of clarity, [tex](g * f)(x) = g(f(x))[/tex]

First, find [tex]f(1)[/tex]

[tex]f(1) = 2(1)^2 - 2(1) - 4\\f(1) = 2-2-4 \\f(1)=-4[/tex]

Then, take what you got for [tex]f(1)[/tex] and plug that into [tex]g(x)[/tex].  In this case, [tex]f(1) = -4[/tex]

[tex]g(-4) = -5(-4) + 14\\g(-4)= 20 + 14\\g(-4) = 34[/tex]

Please make sure to mark brainliest if this satisfies your

Answer:

YOU DO IT X 2

Step-by-step explanation:

Answer:

389.19 m²

Step-by-step explanation:

The surface area of the box = area of the two equal triangles + area of the 3 different rectangles

✔️Area of the two equal triangles:

Area = 2(½*base*height)

base = 7 m

height = 8 m

Area of the two triangles = 2(½*7*8) = 56 m²

✔️Area of rectangle 1:

Area = Length*Width

L = 13 m

W = 7 m

Area of rectangle 1 = 13*7 = 91 m²

✔️Area of rectangle 2:

L = 13 m

W = 8 m

Area of rectangle 2 = 13*8 = 104 m²

✔️Area of rectangle 3:

L = 13 m

W = 10.63 m

Area of rectangle 3 = 13*10.63 = 138.19 m²

✅Surface Area of the box = 56 + 91 + 104 + 138.19 = 389.19 m²

The probability that the selected individual has children in public schools AND favors the school tax is 0.32

The probability that the selected individual favors the school tax AND has children in public schools is 0.32.

The probability that the selected individual favors the school tax AND does NOT have children in public schools is 0.2.

The probability that the selected individual favors the school tax AND is over 56 years old is 0.15.

The probability that the selected individual favors the school tax AND is 18-25 years old is 0.45.

Based on the given information, the probability of event F (the selected individual favors the school tax) is 0.54, as 54% of the respondents are in favor of the tax. The probability of event C (the selected individual has children in public schools) is 0.59, as the approval rating rises to 59% for those with children in public schools. The probability of event O (the selected individual is over 56 years old) is 0.37, as only 37% of those over age 56 said they would vote for the tax. The probability of event Y (the selected individual is 18-25 years old) is 0.71, as 71% of 18- to 25-year-olds said they would vote for the tax.

Using these probabilities, we can estimate the values of the following probabilities:

(1) P(CF) is the probability that the selected individual has children in public schools AND favors the school tax. Based on the given information, we can multiply the probabilities of events C and F: P(CF) = 0.59 * 0.54 = 0.318, or approximately 0.32.

(ii) P(FIC) is the probability that the selected individual favors the school tax AND has children in public schools. This is the same as P(CF), so P(FIC) = 0.32.

(iii) P(FIN) is the probability that the selected individual favors the school tax AND does NOT have children in public schools. To calculate this, we can use the fact that the approval rating falls to 44% for those with no children in public schools. So, P(FIN) = 0.44 * (1 - 0.59) = 0.18, or approximately 0.2.

(iv) P(FTO) is the probability that the selected individual favors the school tax AND is over 56 years old. To calculate this, we can use the fact that the approval rating for those over 56 years old is only 37%. So, P(FTO) = 0.37 * (1 - 0.59) = 0.1523, or approximately 0.15.

(v) P(FY) is the probability that the selected individual favors the school tax AND is 18-25 years old. To calculate this, we can use the fact that the approval rating for those 18-25 years old is 71%. So, P(FY) = 0.71 * (1 - 0.37) = 0.4477, or approximately 0.45.

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Step-by-step explanation:

D. In 2 _ In

maaf kalo salah

After 100 years, the long-term distribution of population in the city and suburbs of New York state can be calculated based on the given migration rates. The population in the city and suburbs will stabilize at approximately 3.96 million and 16.04 million, respectively. The population distribution can be visualized using a graph that shows the population of the city and suburbs over the 100-year period.

To calculate the long-term population distribution, we can use the concept of equilibrium. Let C represent the population in the city and S represent the population in the suburbs. The equilibrium equations can be written as follows:

C = C - 0.035C + 0.017S

S = S + 0.035C - 0.017S

Simplifying these equations, we have:

C = 0.965C + 0.017S

S = 0.035C + 0.983S

Solving these equations simultaneously, we find that C stabilizes at approximately 3.96 million and S stabilizes at approximately 16.04 million.

To plot the population of the city and suburbs over the 100-year period, you can use the following MATLAB code:

Copy code

years = 0:100;

C = zeros(1, 101);

S = zeros(1, 101);

C(1) = 8.4;

S(1) = 20 - C(1);

for i = 2:101

   C(i) = 0.965*C(i-1) + 0.017*S(i-1);

   S(i) = 0.035*C(i-1) + 0.983*S(i-1);

end

plot(years, C, 'b', 'LineWidth', 2);

hold on;

plot(years, S, 'r', 'LineWidth', 2);

xlabel('Years');

ylabel('Population');

legend('City', 'Suburbs');

title('Population of City and Suburbs Over 100 Years');

This MATLAB code calculates and plots the population of the city (in blue) and suburbs (in red) over the 100-year period.

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After considering the given data we conclude that the new point generated is (2,3), under the condition that g(x) is transformed by [tex]-g[4(x+2)][/tex].

To evaluate the new point after the transformation of point (2,-3) by -g[4(x+2)], we can stage x=2 and g(x)=-3 into the expression [tex]-g[4(x+2)][/tex]and apply  simplification to get the new y-coordinate. Then, we can combine the new x-coordinate x=2 with the new y-coordinate to get the new point.
Stage x=2 and g(x)=-3 into [tex]-g[4(x+2)]:[/tex]
[tex]-g[4(2+2)] = -g = -(-3) = 3[/tex]
The new y-coordinate is 3.
The new point is (2,3).
Hence, the new point after the transformation of point (2,-3) by [tex]-g[4(x+2)][/tex] is (2,3).
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Given that a circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm. We need to find the probability that a randomly selected point inside the trapezoid lies on the circle.

The isosceles trapezoid is shown below: [asy] draw((0,0)--(8,0)--(3,5)--(1,5)--cycle); draw((1,5)--(1,0)); draw((3,5)--(3,0)); draw((0,0)--(1,5)); draw((8,0)--(3,5)); draw(circle((2.88,2.38),2.38)); label("$8$",(4,0),S); label("$2$",(1.5,5),N); [/asy]Let ABCD be the isosceles trapezoid,

where AB = 8 cm, DC = 2 cm, and AD = BC.

Since the circle is inscribed in the trapezoid, we can use the following formula:2s = AB + DC = 8 + 2 = 10 cm

Where s is the semi-perimeter of the trapezoid. Also, let O be the center of the circle. We can draw lines OA, OB, OC, and OD as shown below: [asy] draw((0,0)--(8,0)--(3,5)--(1,5)--cycle); draw((1,5)--(1,0)); draw((3,5)--(3,0)); draw((0,0)--(1,5)); draw((8,0)--(3,5)); draw(circle((2.88,2.38),2.38)); label("$A$",(0,0),SW); label("$B$",(8,0),SE); label("$C$",(3,5),N); label("$D$",(1,5),N); label("$O$",(2.88,2.38),N); label("$8$",(4,0),S); label("$2$",(1.5,5),N); draw((0,0)--(2.88,2.38)--(8,0)--cycle); label("$s$",(3,0),S); label("$s$",(1.44,2.38),E); [/asy]Since O is the center of the circle, we have:OA = OB = OC = OD = rwhere r is the radius of the circle.

Also, we have:s = OA + OB + AB/2 + DC/2s = 2r + 2s/2s = r + 5 cmWe can solve for r:r + 5 cm = 10 cmr = 5 cmNow that we know the radius of the circle, we can find the area of the trapezoid and the area of the circle.

Then, we can find the probability that a randomly selected point inside the trapezoid lies on the circle as follows:Area of trapezoid = (AB + DC)/2 × height= (8 + 2)/2 × 5= 25 cm²Area of circle = πr²= π(5)²= 25π cm²Therefore, the probability that a randomly selected point inside the trapezoid lies on the circle is:

Area of circle/Area of trapezoid= 25π/25= π/1= π

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The probability that a randomly selected point inside the trapezoid lies on the circle is 0.399 or 39.9%. Therefore, option (A) is the correct answer.

The circle is inscribed in an isosceles trapezoid with bases of 8 cm and 2 cm.

Inscribed Circle of an Isosceles Trapezoid

Therefore, the length of the parallel sides (AB and CD) is equal.

Let the length of the parallel sides be ‘a’. Then, OB = OD = r (let)

It is also given that the lengths of the parallel sides of the trapezoid are 8 cm and 2 cm.

Then, its height is given by:

h = AB - CD / 2 = (8 - 2) / 2 = 3 cm

Therefore, the length of the base BC of the right-angled triangle is equal to ‘3’.

Then, the length of the other side (AC) can be given as:

AC = sqrt((AB - BC)² + h²) = sqrt((8 - 3)² + 3²) = sqrt(34) cm

The area of the trapezoid can be calculated as follows:

Area of the trapezoid = 1/2 (sum of the parallel sides) x (height)A = 1/2 (8 + 2) x 3A = 15 sq. cm.

The area of the circle can be given by:

Area of the circle = πr²πr² = A / 2πr² = 15 / (2 x π)

Therefore, r² = 2.39

r = sqrt(2.39) sq. cm.

Now, the probability that a randomly selected point inside the trapezoid lies on the circle can be calculated by dividing the area of the circle by the area of the trapezoid:

P (point inside the trapezoid lies on the circle) = Area of the circle / Area of the trapezoid

P = πr² / 15

P = π (2.39) / 15

P = 0.399 or 39.9%

The probability that a randomly selected point inside the trapezoid lies on the circle is 0.399 or 39.9%.

Therefore, option (A) is the correct answer.

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Answer:

$30.99

Step-by-step explanation:

The formula for simple interest is I = PRT where I = interest earned, P = principal amount borrowed/deposited, R = rate as a decimal, and T = time in years.

I = (30)(0.033)(1)

I = 0.99

Then add that to the amount deposited ($30) and you're done.

30 + 0.99 = $30.99

Please let me know if you have questions.

The answer is $29.01

Answer: You want to calculate the interest on $380 at 5.3% interest per year after .5 year(s).

The formula we'll use for this is the simple interest formula, or:

Where:

P is the principal amount, $380.00.

r is the interest rate, 5.3% per year, or in decimal form, 5.3/100=0.053.

t is the time involved, 0.5....year(s) time periods.

So, t is 0.5....year time periods.

To find the simple interest, we multiply 380 × 0.053 × 0.5 to get your answer.

Step-by-step explanation:

Answer:

150 cm squared

Step-by-step explanation:

I guess that's the answer if I'm wrong you can tell me right away so that I can try another method thank you.

Answer:

the graph has two vertical asymptotes, line q intersects the line at -8 and is the more important one.

Step-by-step explanation:

This is visible based off of the picture.

Answer:

none of these

Step-by-step explanation:

There are 3 boys walking

There are a total of 20 people

3/20 = 0.15

That is 15 percent, therefore none of these answers.

Step-by-step explanation:

any has at least one mode

Answer:

Yield per share = 7.68% (Approx.)

Step-by-step explanation:

Given:

Dividend paid = $4.15

Price per dividend = $54

Find:

Yield per share

Computation:

Yield per share = [Dividend paid / Price per dividend]100

Yield per share = [4.15 / 54]100

Yield per share = [0.0768]100

Yield per share = 7.68% (Approx.)

Answer:

She saved 1.20

Step-by-step explanation:

Purchase Price:

$12

Discount:

(12 x 10)/100 = $1.20

Final Price:

12 - 1.20 = $10.80

Answer:  Complementary     x=15

Step-by-step explanation:

Complementary angles add up to 90°, supplementary angles add up to 180°.

We know they add up to 90 so...

3x+45=90

3x=45

x=15

Answer:

25

Step-by-step explanation:

First, plug -5 in for a, -(-5)^2. We treat the negative on the outside of the paranthese as a -1 so we do -1 times -5 and we get 5. Then we square 5 and get 25.

Answer:

 Forgot picture?

Step-by-step explanation:

Answer:

You can get your grade up by studying, getting a tutor, paying attention in class, taking good notes, asking questions, and cheating (i don't recommend this one :/)

Yes, there is a uniformly most powerful (UMP) test at level a for testing for the given density function.

The test is based on the likelihood ratio, where the critical region is (θ_o, ∞) and the test statistic is (nθ_o^3)/Y(n), where Y(n) is the largest observation in the sample.

To obtain the UMP test at level a for testing H_0: θ ≤ θ_o vs. H_1: θ > θ_o, we need to find the likelihood ratio test with the largest power for all possible alternatives. The likelihood ratio test is constructed as the ratio of the likelihood function under H_0 to the likelihood function under H_1. By algebraic manipulation, we obtain the likelihood ratio test statistic as (nθ_o^3)/Y(n), where Y(n) is the largest observation in the sample.

Under H_0, this test statistic has a chi-squared distribution with one degree of freedom. Therefore, the critical region for rejecting H_0 at level a is the right tail of the chi-squared distribution with one degree of freedom, which is (θ_o, ∞).

This test is UMP because it has the highest power for all possible alternatives. This is because the distribution of Y(n) is stochastically increasing in θ, which means that for a given sample size n, the probability of obtaining an observation larger than a threshold value increases as θ increases.

Therefore, the likelihood ratio test statistic decreases as θ increases, which means that the rejection region (θ_o, ∞) has the highest power for all possible alternatives. Hence, the test based on the likelihood ratio is the UMP test at level a for testing H_0: θ ≤ θ_o vs. H_1: θ > θ_o for the given density function

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Answer: ±√2

Step-by-step explanation: A fraction is undefined when its denominator is =0 or undefined. so we need to get 2/3x²-6=0 or undefined. so we can also do 3x^2-6=0. Solving yields ±√2!

X/2= 87.2

to find X:

87.2 X 2= 174.4

therefore X is 174.4

Answer:

m ÷ 7

Step-by-step explanation:

"Quotient" means you're dividing, so this just means you're dividing m by 7.