Determine whether the following subsets are subspaces of the given vector spaces or not.text Is end text W subscript 2 equals open curly brackets space p equals a subscript 2 t squared plus a subscript 1 t plus a subscript 0 space element of space straight double-struck capital p subscript 2 space left enclose space a subscript 0 equals 2 space end enclose close curly brackets space space text a subspace of the vector space end text space straight double-struck capital p subscript 2 ?(Note: space straight double-struck capital p subscript 2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.)Answer 1text Is end text W subscript 1 equals open curly brackets open square brackets table row a b c row d 0 0 end table close square brackets space element of space M subscript 2 x 3 space end subscript space left enclose space b equals a plus c space end enclose close curly brackets space text a subspace of the vector space end text space space M subscript 2 x 3 space end subscript?(Note: space M subscript 2 x 3 space end subscript is the set of all 2x3 matrices with the standart matrix addition and scalar multiplication with reals.)

The main answer is that the infinite number of types of matter arises from the unique combinations of elements and their arrangements in terms of composition and geometry.

While the number of elements is limited, their combinations and arrangements allow for an infinite number of types of matter. Elements can combine in different ratios and configurations, forming various compounds and structures with distinct properties.

Additionally, the arrangement of atoms within a molecule or the spatial arrangement of molecules within a material can create different types of matter. These factors, along with the possibility of isotopes and different states of matter, contribute to the vast diversity and infinite types of matter despite the limited number of elements.

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Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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Answer:

R=22% , T=8yrs , P=$250

I=PRT/100

I=250×22×8/100

I=$440.00

The Interest that's earned will be $440.

The formula for calculating simple Interest will be:

= PRT/100

where,

P = $250

R = 22%

T = 8 years

Therefore, the simple interest will be:

= (250 × 22 × 8) / 100

= 44000/100

= 440

Therefore, the simple interest is $440.

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This is a proposition. It is a statement that can be evaluated for its truth. In this case, the statement is always true, as it is a universally accepted fact that it always rains on Tuesdays.

This proposition can be evaluated using the laws of logic, and is a valid argument.

We can use the law of modus ponens to assess this statement. Modus ponens states that if “If P, then Q” is true, and “P” is true, then “Q” is also true.

In this case, the statement “If it is Tuesday, then it rains” is a valid statement, and if it is Tuesday, then it follows that it must be raining.

The law of contradiction can also be used to assess this statement. This law states that a statement cannot be both true and false at the same time.

In this case, the statement “It always rains on Tuesdays” cannot be false, as it is a universally accepted fact that it rains on Tuesdays. Therefore, this statement is true.

To sum up, the statement “It always rains on Tuesdays” is a valid proposition and is true.

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The about withheld for the FIT tax, considering the given table, is of:

B. 8.

The table gives the fixed amount withheld by the FIT tax, considering the weekly pay and the number of allowances claimed.

For Gabriel McKernan, the amount of tax paid is obtained as follows:

Hence the amount of taxes paid by Gabriel McKernan is found looking at the fifth column of the last row of the table, and is of 8.

Thus the correct option regarding how much he pays for the FIT tax is given by option B.

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Answer: The answer is 4

Step-by-step explanation: Firstly you want to convert the whole number into a fraction, the fraction will be 24/1. Then you multiply 1/6 by 24/1 or 1x24/6x1 which equals 26/6. This fractio can be simplified, by finding the greatest common factor. The GCF of 24 and 6 is 6.

24/6 = 4

6/6 = 1

So our full answer is 4/1 which simplifies to 4

Answer:

4

Step-by-step explanation:

take 24 divided by 6 you'll get

Answer:

15

Step-by-step explanation:

The ratio of the weight of a semi-truck trailer tire compared to the weight of a mobile home will be 51: 52.

The utilization of two or more additional numbers that compares is known as the ratio.

The weight of the semi-truck trailer tire is 102 pounds.

The weight of the mobile home is 104 pounds.

The ratio of the weight of a semi-truck trailer tire to a mobile home is given as.

Ratio = 102 / 104

Ratio = 51 / 52

Ratio = 51: 52

The ratio of the weight of a semi-truck trailer tire to a mobile home will be 51: 52.

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Answer:

3.

Step-by-step explanation:

Difference means subtract. So your question is 7 - 4 and that is 3.

Answer:

3

Step-by-step explanation:

Let the number be x

7-x=4

-x=4-7

-x = -3

x=3

Answer:

Answer is b . Hope you like answer

The likelihood of selecting a single value randomly that is below $976 is around 52.78% or approximately 0.5278.

To find the probability that a single randomly selected value is less than $976, we can use the z-score formula and standard normal distribution.

The z-score formula is given by:

z = (x - μ) / σ

Where:

x = the value we want to find the probability for ($976 in this case)

μ = the mean ($960)

σ = the standard deviation ($231)

Calculating the z-score:

z = (976 - 960) / 231

z = 16 / 231

z ≈ 0.0691

Next, we need to find the probability corresponding to this z-score using a standard normal distribution table or calculator.

Using the z-table or calculator, we can find that the probability of a z-score of 0.0691 or less is approximately 0.5278.

Therefore, the probability that a single randomly selected value is less than $976 is approximately 0.5278 or 52.78%.

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Answer:

10.4

Step-by-step explanation:

8 + 4 x 3/5

4/1 x 3/5 + 12/5

8 + 2.4 = 10.4

The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.

There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.

A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.

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Step-by-step explanation:

There are no exponents or division? as is, all of these are linear because there are no exponents, division by a variable, or square roots. did you miss something writing this? these are all changing at a constant rate.

Answer:

Its b

Step-by-step explanation:

The point-slope form of the equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

From the graph, we can see that the line passes through the points (-4, 4) and (1, -1). To find the slope of the line, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (-1 - 4) / (1 - (-4)) = -5 / 5 = -1

Therefore, the slope of the line is -1.

The point (-2, -2) is already given in the form (x1, y1). Therefore, we can use this point to write the equation in point-slope form.

Using the point-slope form of the equation and the information we found above, we get:

y - (-2) = -1(x - (-2))

Simplifying, we get:

y + 2 = -x - 2

Subtracting 2 from both sides, we get:

y = -x - 4

Therefore, the equation of the line in point-slope form is y - (-2) = -1(x - (-2)), and in slope-intercept form is y = -x - 4.

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Mountain Mack can carve 60 fishing lures and 50 duck decoys in a week.

Let's denote the number of fishing lures carved by Mountain Mack as "L" and the number of duck decoys carved as "D". Based on the given information, we can set up a system of equations: When Mountain Mack spends all his time carving fishing lures, he can  carve 60 lures in a week:

L = 60

When Mountain Mack spends all his time carving duck decoys, he can carve 50 decoys in a week:

D = 50

For every 10 duck decoys carved, Mountain Mack must give up 12 fishing lures:

12 * (D / 10) = L

Now, let's solve the system of equations to find the values of L and D.

From equation (3), we can simplify it as:

12 * (D / 10) = L

12D/10 = L

6D/5 = L

Substituting L = 60 into the equation above:

6D/5 = 60

Solving for D:

6D = 5 * 60

D = 300/6

D = 50

So, we find that D = 50, which matches the information given.

Now, substituting D = 50 into equation (2):

L = 6D/5 = 6 * 50/5 = 60

Therefore, L = 60, which also matches the information given. Hence, the values of L and D satisfy all the given conditions.

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Answer: (x - 2)^2 + (y + 3)^2 = 18 3(2^(1/2)) (2,-3)

Step-by-step explanation:

7x^2 - 28x + 7y^2 + 42y - 35 = 0

divide 7 out

x^2 - 4x + y^2 + 6y - 5 = 0

add 5 to other side

x^2 - 4x + y^2 + 6y = 5

solve by completing the square

take b values divide them by 2  square and add to both sides

-4/2 = -2

-2^2 = 4

6/2 = 3

3^2 = 9

X^2 - 4x + 4 + y^2 + 6y +9 = 4 + 9 +5

(x - 2)^2 + (y + 3)^2 = 18

(x - k)^2 + (y - h)^2 = r^2

r^2 = 18

r = \(\sqrt{18}\) = 3\(\sqrt{2}\) = 3(2^(1/2))

center of circle = (2,-3)

Adrian would need to buy 13 tins of red paint to paint the area of the first wall of the community centre.

The wall of the community center is divided into 11 stripes, and Adrian needs to paint the stripes with red and pink shades. The first stripe is red, and the rest is in the shades of pink made by mixing the red and white paint in different ratios. The last stripe is white.The total area of the wall to be painted is the sum of areas of all the stripes. The area of a stripe is the product of the width of the stripe and the height of the wall. Hence, the area of a stripe is 10 m × 6 m = 60 m².The total area of the wall is the product of the height of the wall and the sum of widths of all the stripes. Hence, the total area of the wall is 6 m × (10 + 9 + 8 + ... + 1) m = 6 m × 55 m = 330 m².The area painted with red paint is 10 m × 6 m = 60 m². The area painted with the first shade of pink is (9/10) × 60 m² = 54 m². The area painted with the second shade of pink is (8/10) × 60 m² = 48 m². Hence, the areas painted with shades of pink decrease by 6 m² for each stripe.The total area painted with shades of pink is the sum of areas painted with all the shades of pink. Hence, the total area painted with shades of pink is 54 m² + 48 m² + ... + 6 m² = (9 + 8 + 7 + ... + 1) × 6 m² = 6 m² × 45 = 270 m².The total area painted with red paint and the shades of pink is 60 m² + 270 m² = 330 m², which is the total area of the wall. Hence, Adrian would not need to paint any area with white paint, and all the paint would be red or pink.The area covered by 1 litre of paint is 12 m². Hence, Adrian would need (330 m²)/(12 m²/litre) ≈ 27.5 litres of paint.Adrian would mix red and white paint in different ratios to make pink shades. Hence, Adrian would need to buy only red paint. The total area painted with red paint is 60 m². Hence, Adrian would need (60 m²)/(12 m²/litre) = 5 litres of red paint. Since Adrian would buy all the paint in 1-litre tins, Adrian would need to buy 5 tins of red paint.

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Answer:

1/16

Step-by-step explanation:

To find probiblity all you have to do is divide the number of events by the number of possible outcomes

There are 16 possible outcomes

and there is only 1` way that the student can get all 4 questions right

so the answer is: 1/16

Answer:

1/16

Step-by-step explanation:

Number of possible outcomes = 16

Only one set will be the correct option

P(getting all four questions correct) = 1/16

Answer:

acute

Step-by-step explanation:

Answer:

Complementary angle pair is here working

Answer:

9.3 ft

Step-by-step explanation:

Answer:

160°

Step-by-step explanation:

Take notice that m∠1 and m∠2 are supplementary angles, meaning their angle measures will add up to 180°.

Since we know m∠2, we can find m∠1 easily.

180-20=160°

Hope this helped!

Answer:

2x-y+2= 0

Step-by-step explanation:

(-5,-2)=(x1, y1)

(3, 14) =(x2, y2)

now,

slope(m)= y2-y1 / x2-x1

=14+2 / 3+5

= 16 /8

=2 units

passing point = (-5,-2) = x1,y1

now,

eqn of the line can be represented as,

y -y1 = m (x-x1)

y +2 = 2 (x +5)

y+2 = 2x +10

y = 2x+10-8

0 = 2x+2-y

2x-y+2 =0 is the required eqn

Answer:

licker 90000000000000000

Answer:

1/7

Step-by-step explanation:

There are seven people in all on person will arrive at a different time than others. Every single one of them arrives at different times so it's 1/7

1) The amplitude c+ is c+l

2) The expectation value is 0

3) The uncertainty ΔSX is √(3/7) c+.

Now, we know that any wave function can be written as a linear combination of two spin states (up and down), which can be written as:

Ψ = c+ |+> + c- |->

where c+ and c- are complex constants, and |+> and |-> are the two orthogonal spin states such that Sx|+> = +1/2|+> and Sx|-> = -1/2|->.

Hence, we can write the given wave function as:Ψ = c+|+> + i/√7|->

Now, we know that the given wave function has been defined in Sx basis, and not in the basis of |+> and |->.

Therefore, we need to write |+> and |-> in terms of |l> and |r> (where |l> and |r> are two orthogonal spin states such that Sy|l> = i/2|l> and Sy|r> = -i/2|r>).

Now, |+> can be written as:|+> = 1/√2(|l> + |r>)

Similarly, |-> can be written as:|-> = 1/√2(|l> - |r>)

Therefore, the given wave function can be written as:Ψ = (c+/√2)(|l> + |r>) + i/(√7√2)(|l> - |r>)

Therefore, we can write:c+|l> + i/(√7)|r> = (c+/√2)|+> + i/(√7√2)|->

Comparing the coefficients of |+> and |-> on both sides of the above equation, we get:

c+/√2 = c+l/√2 + i/(√7√2)

Therefore, c+ = c+l

The amplitude c+ is a real number and is equal to c+l

The expectation value of the operator Sx is given by: = <Ψ|Sx|Ψ>

Now, Sx|l> = 1/2|r> and Sx|r> = -1/2|l>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= -i/√7(c+l*) + i/√7(c+l)= 2i/√7 Im(c+)

As c+ is a real number, Im(c+) = 0

Therefore, = 0

The uncertainty ΔSX in the state |Ψ> is given by:

ΔSX = √( - 2)

where = <Ψ|Sx2|Ψ>and2 = (<Ψ|Sx|Ψ>)2

Now, Sx2|l> = 1/4|l> and Sx2|r> = 1/4|r>

Hence, = (c+l*) + (c+l) + (i/√7) - (i/√7)(c+l*)= 1/4(c+l* + c+l) + 1/4(c+l + c+l*) + i/(2√7)(c+l* - c+l) - i/(2√7)(c+l - c+l*)= = 1/4(c+l + c+l*)

Now,2 = (2i/√7)2= 4/7ΔSX = √( - 2)= √(1/4(c+l + c+l*) - 4/7)= √(3/14(c+l + c+l*))= √(3/14 * 2c+)= √(3/7) c+

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The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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The three (3) statements which are true include the following:

A. The radius of the circle is 3 units.

B. The center of the circle lies on the x-axis.

D. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²   ....equation 1.

Where:

h and k represents the coordinates at the center of a circle.

r represents the radius of a circle.

From the information provided, we have the following equation of a circle:

x² + y² – 2x – 8 = 0      ......equation 2.

In order to determine the true statements, we would rewrite the equation in standard form and then factorize by using completing the square method:

x² – 2x + y² = 8 = 0

x² – 2x + (2/2)² + y² = 8 + (2/2)²

x² – 2x + 1 + y² = 8 + 1

(x – 1)² + (y - 0)² = 9         .......equation 3.

Comparing equation 1 and equation 3, we have the following:

Center (h, k) = (1, 0)

Radius, r = 3

Additionally, this line and the circle's center lies on the x-axis because the y-value is equal to zero (0).

(x – 0)² + (y - 0)² = 3²

x² + y² = 9.

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Answer:

Y-intercept is 0

Step-by-step explanation:

\(f(x)=x^2(2x+10)(x+2)^2(x-4)\\f(0)=0^2(2(0)+10)(0+2)^2(0-4)\\f(0)=0\)