research recommends that teachers use the following pedagogical tool to support the development of students' understanding that fractions are numbers and that they expand the number system beyond whole numbers. (meaning, they help students understand the value of fractions and how the size of these numbers relates to the whole numbers that students already know.)

An explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

What is the explicit description of a null space matrix?

To find an explicit description of the null space of matrix A, we can find a spanning set of vectors that span the null space.

The null space of matrix A, denoted Nul A, is the set of all vectors x that satisfy the equation Ax = 0. In other words, the null space consists of all vectors that are mapped to the zero vector by the matrix A.

To find a spanning set for Nul A, we can use the following steps:

Row reduces the matrix A to a reduced row-echelon form using elementary row operations.

Identify the free variables in the row-reduced matrix.

For each free variable, create a vector with a 1 in the position corresponding to the free variable and 0's in all other positions.

The set of vectors created in step 3 form a spanning set for Nul A.

For example, consider the matrix A = [1, 2, 3, 0; 0, 0, 1, 0]. To find a spanning set for Nul A, we can row reduce the matrix to reduced row-echelon form:

[1, 2, 3, 0] -> [1, 2, 3, 0]

[0, 0, 1, 0] -> [0, 0, 1, 0]

The matrix is already in reduced row-echelon form, so there are no more elementary row operations to perform. The free variables in this matrix are the third and fourth columns, which correspond to the variables x3 and x4, respectively. Therefore, we can create the following vectors:

x3 = [0, 0, 1, 0]

x4 = [0, 0, 0, 1]

These vectors form a spanning set for Nul A, as they are linearly independent and span the null space.

Hence, an explicit description of Nul A is given by the set of vectors {[0, 0, 1, 0], [0, 0, 0, 1]}.

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Answer:

y = 650

Step-by-step explanation:

0.9y = 585

y = 650

Answer:

[tex]y = 650[/tex]

Step-by-step explanation:

[tex]1.25y-0.35y=585[/tex]

[tex]0.9y=585[/tex]

[tex]y = \frac{585}{0.9}[/tex]

[tex]y = 650[/tex]

Yes, it is significant evidence of a difference between the age distribution of jurors and the countrywide age distribution.

No, there is no age bias in the selection of jurors.

P             Oi       Ei        ( Oi-Ei) ^2/Ei

0.421     399     421     1.149643705

0.229     231     229     0.017467249

0.157     158     157     0.006369427

0.193     193     193     1.870466321

  1         1000  1000    3.043946702

The above can be represented in graphs.

Now,

Ei = n × pi

TS = 3.04394672

From TS < value

Value (7.81472)

We fail to reject the null hypothesis at 5% value of significance

No, there is no age bias in the selection of jurors.

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Answer:

8 [tex]\frac{9}{10}[/tex]

Step-by-step explanation:

substitute x = [tex]\frac{2}{3}[/tex] into the expression

(6 × [tex]\frac{2}{3}[/tex] ) + 4 [tex]\frac{9}{10}[/tex]

= (2 × 2) + 4 [tex]\frac{9}{10}[/tex]

= 4 + 4 [tex]\frac{9}{10}[/tex] ( add the whole numbers )

= 8 [tex]\frac{9}{10}[/tex]

The Valley of Ashes symbolizes the emotional turmoil and feelings of the characters the working class who enable the lifestyles of the wealthy the negative economic impact of prohibition laws Gatsby's fears organized crime

On the north shore of Long Island, the valley of ashes was a two to three thousand acre marshland that encircled the Flushing River mouth. This small river primarily serves as an inlet into Flushing Bay, which is an arm of the East River, with tidal water flowing through it rather than fresh water.

It is a metaphor for the moral and societal decay brought on by the unrestrained pursuit of wealth, as the wealthy indulge in only their own pleasure. The emotional turmoil and feelings of the characters from the working class that support the lifestyles of the wealthy are symbolized by The Valley of Ashes. the damaging effects of prohibition laws on the economy Gatsby worries about organized crime.

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Answer:

-15

Step-by-step explanation:

Answer:

The graph

Step-by-step explanation:

The graph has a slope of 4, the equation has a slope of 3, the table has a slope of 2.

The integral for the work required to pump the water out of a spout that rises 2 m above the tank is

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

Integral

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).

Given that:

r = 2m

l = 5m

sinθ = [tex]\frac{x}{r}[/tex]

dv = 2l  [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

Let p be the density of water and g be the acceleration due to gravity.

dm = p dv

dw = dmg (h + r - x)

dw = pg (h + r - x) dx

dw = 2l pg  (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

w = ∫dw

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

Therefore, the integral for the work required to pump the water out of a spout that rises 2 m above the tank is

w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex]  dx

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When two system of linear equations solved by Sara represents the lines parallel to each other then the equations have no solution.

Step by Step explanation:

Given system of two linear equations :

Let us consider system of two linear equation with Sara has :

y =  3x + 7

y = 3x + 9

Here both the lines have same slope = 3

Lines are parallel to each other.

Solve the equation by elimination method :

y =  3x + 7

y = 3x + 9

0 = 0x - 2

⇒ -2 = 0 which is not possible and has no solution.

Therefore, when the system of linear equations with Sara has no solution it represents lines are parallel to each other.

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Note that:

For 1) To compute the average rate (AR), divide the change in y-values by the change in x-values. That is:

AR = (5-2)/5-4)

= 3/1

= 3ft/sec.

For 2) we must use the same formula above:
(2-5)/(10-7)

= -1 ft/sec.

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Full Question:

See attached graph

Answer: [tex]6^{\frac{1}{12} }[/tex]

Step-by-step explanation:

The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....

Given that,

We have to get the first four nonzero terms of the series for f(x), centering at the specified value of a, use the definition of a Taylor series. (Separate your responses into a list using commas.)

f(x)=5/1+x and a=2

We know that,

Take

f(x)=5/1+x and a=2

f(2)=5/1+2=5/3

f'(x)=-5/(1+x)²         f'(2)=-5/(1+2)²=-5/9                  (differentiating)

f''(x)=10/(1+x)³        f''(2)=10/(1+2)³=10/27

f'''(x)=-30/(1+x)⁴     f'''(2)=-30/(1+2)⁴=-30/81=-10/27

Using the taylor series

F(x)=f(a)-(x-a)f'(a)+(x-a)²/2!f''(a)-(x-a)³/3!f'''(a)+....

F(x)=f(2)-(x-2)f'(2)+(x-2)²/2f''(2)-(x-2)³/3!f'''(2)+....

F(x)=5/3-(x-2)(5/9)+(x-2)²/2(10/27)-(x-2)³/6(-10/27)+....

F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....

Therefore, The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....

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Answer:

Below

Step-by-step explanation:

For the boxes:

   the sum of all three angles = 180     for a triangle

     soooo :      28 +    x-4    + 2x = 180

then x = 52   via  algebra

Answer: 0, 1, 5, -2 ,-4

Step-by-step explanation: hope it helps

Answer:    [tex]\displaystyle \frac{10}{3}\left(\frac{1}{3}\right)^{n-1}[/tex]

======================================================

Explanation:

a = 10/3 is the first term

r = 1/3 is the common ratio

Multiply each term by r = 1/3 to get the next term.

Example:

(10/3)*(1/3) = 10/9

We then plug those two items into the formula

[tex]a_n = a(r)^{n-1}[/tex]

to end up with the answer shown above.

The value of n is a positive integer.

Answer:

------------------------------------

Use trigonometry.

Since all three sides are known, you may choose either sine, cosine or tangent.

We'll use sine here:

The minimum sample size required to estimate the mean duration time of TR classes is t distribution confidence interval.

The confidence interval is 75.0694 and 76.9306.

Given that

(a) This is t-distribution confidence interval because sample standard deviation is given and also sample size is less than 30.

(b)

CI for 95%

n 28

mean 76

value of 95% CI and df = 27 (using  table) 2.0518

std. dev. 2.4

SE = standard deviation/n² 0.45356

ME = t*SE 0.93062

Lower Limit = Mean - ME 75.06938

Upper Limit = Mean + ME 76.93062

95% CI (75.0694 , 76.9306 )

95% CI=75.0694 , 76.9306

(c)The 95% confidence interval estimate of the population mean is within 75.0694 and 76.9306 (lower bound and upper bound)

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If a<0, then there is no x-null lines, the system has no equilibrium points.

If a=0, it has only one equilibrium points.

If a>0, the system has two equilibrium points.

Points are (-√a,0) and (√a,0)

The system changes from no fixed points to two fixed points when it increases through a=0.

a is a bifurcation point.

The Jawbian matrix,

                        J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]

Now,

      J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0

      J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a

If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.

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Answer:

x = 5

Step-by-step explanation:

assuming you mean the slope of the line id undefined and passes through (5, 0 )

A line with an undefined slope is a vertical line parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through (5, 0 ) with x- coordinate 5 , then

x = 5 ← equation of line

A figure in the flag has rotational symmetry if the figure can be mapped onto itself by a rotation between 0° and 360° about the center of the figure.

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The multiplication that will give a value of 12✓6 from the numbers will be:

3✓2 × 4✓3

3 × 4✓6

It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, it should be noted that:

3✓2 × 4✓3 = 12✓6

3 × 4✓6 = 12✓6

It should be noted both scenarios highlight the given value of 12✓6.

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Yes, the inverse of the matrix exist and a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2

The inverse of matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity.

The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.

According to the question,

The matrix given is [tex]\left[\begin{array}{cc}2&5\\5&13\end{array}\right][/tex]

Let Matrix be A

To check if its inverse exist , We have to find out the determinant

|A| = 13(2) - 5(5)

=> 26 - 25

=> 1

Determinant is non zero

Hence , Inverse exist

(b) To find the inverse , we have to find the adjoint of A

adj A = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]

Inverse is ratio of adj A and determinant A

A⁻¹ = adj A / |A|

=>  [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex] / 1

=> A⁻¹ = [tex]\left[\begin{array}{cc}13&-5\\-5&2\end{array}\right][/tex]

a11 = 13 , a12 = -5 , a21 = -5 and a22 = 2

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None of the Options are true both the given functions are parabolic functions.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given function are,  f(x)=-15x²+32 and g(x)= -17x²+5x+32,
Zeros for the functions are,
x = ± 1.461 and x = -1.233 and 1.527,
Where g(x) has a higher maximum than f(x), the Intercept of f(x) is greater than g(x). As shown in the graph.

Thus, none of the options are true because both of the supplied functions are parabolic.

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The manny must do his signature on the deposit ticket in order to get deposited the cashback ticket.

What is cashback?

Cashback is a type of reward program offered by some retailers and online merchants that gives customers money back for making purchases. It is a way for retailers to reward customers for their loyalty and encourage them to keep coming back to their store. Cashback can be offered in the form of a fixed amount, a percentage of the purchase price, or a combination of both. Cashback rewards may be paid in cash or as credits to the customer's account, and they may be used to purchase additional items from the store or to offset future purchases.

When teller sees the deposit ticket he must have seen that it is not signed by manny hence he returned this to manny now manny just have to do one work that to sign that deposit ticket after that teller will accept that deposit ticket and manny will get his required cashback easily in his bank account

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Answer:

a edge

Step-by-step explanation:

The three side lengths; 9m, 12m, 15m as given in the task content would form a right triangle.

It follows from the task content that the type of triangle formed by the side lengths given is to be determined.

On this note, recall that given three side lengths, a, b and c where c is the longest of all three side-lengths;

if; c² > a² + b² .....Obtuse triangle.

if; c² < a² + b².......Acute triangle.

if; c² = a² + b²........Right triangle.

On this note, since;

15² = 12² + 9²

225 = 144 + 81

225 = 225.

The three side lengths in discuss would form a right triangle.

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Treatment remains the same. Do not Reject.

Test Statistics:

[tex]f = \frac{\text{treatment}}{\text{error}} = 5.37[/tex]

Reject Null Hypothesis if [tex]f > f(a, a-1, N-a)[/tex]

Critical Value [tex]f(0.01, 3, 15) = 5.42 \text{ (From F Table)}[/tex]

[tex]\because 5.37 < 5.417[/tex]

We fail to Reject [tex]H0[/tex]

[tex]\therefore[/tex] Do not Reject.

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The anwer of number of cups of raisins required for 12 recipes needing 223 cups of raisins each are 2676.

Multiplication operation will be required to find the number of cups of raisins. The expression to be formed for calculation is-

Total number of cups = number of recipes × number of cups for one recipe

Keep the values in formula to find the total number of cups

Total number of cups = 12 × 223

Performing multiplication on Right Hand Side of the equation

Total number of cups = 2676

Thus, 2676 cups are required for recipe.

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