Fill in the chart with another piece of evidence that supports the
author's point
Students know
their needs in
elementary school.
K
Evidence
Point
Elementary school
is the time to teach
money skills
Students begin to
understand how to
use money in
elementary school
Students want to
help with
emergencies in
elementary school,
Evidence
?
Students develop
good hobits when
they are in
elementary school
Students buy fancy
sneakers in
elementary school.
1 ?

The rectangle's dimensions are 9 yards in width and 14 yards in length.

Let's assume the width of the rectangle is "x" yards. According to the given information, the length of the rectangle is more than twice the width. Thus, the length can be expressed as 2x + y, where y represents the additional length.

The area of a rectangle is calculated by multiplying its length and width. In this case, we have the equation: (2x + y) * x = 63 yd².

Expanding the equation, we get: 2x² + xy = 63.

Since we know the area is 63 yd², we can find two factors that multiply to give 63 and solve for x. The factors of 63 are 1 and 63, 3 and 21, and 7 and 9. Since the length is more than twice the width, the factor pair that satisfies this condition is 7 and 9.

Therefore, x = 7 and 2x + y = 9. Solving for y, we find that y = 2.

Thus, the dimensions of the rectangle are 7 yards in width and 9 yards in length.

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By answering the above question, we may state that As a result, the arc's  expressions PB length is around 20.45 cm.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Area of sector OAP = (1/12) x r2 x (30/360)

OAP's area is equal to (1/2) x OA, PA, and sin (AOP)

Knowing that OA = PA = r and that AOP = 30°, we can calculate the area of the triangle OAP as (1/2) x r x r x sin(30°) = (1/4) x r2.

As a result, the darkened region's area is:

Area of the darkened zone is equal to (1/12) x r2 - (1/4) x r2 (462 cm2).

When we simplify this equation, we obtain:

\((\pi/3 - 1) x r^2 = 1848\)

The result of dividing both sides by (/3 - 1) is:

\(r^2 = 1848 / (π/3 - 1) = 378.9\)

When we square the two sides, we obtain:

\(r ≈ 19.47\\PB = (1/6) x 2r = (1/3) x r = 20.45 cm\), where

As a result, the arc's PB length is around 20.45 cm.

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Answer:

x^2 - 10x + 25

Step-by-step explanation:

I'm hoping that the 2 means squared.

x^2 - 10x + 25

Answer:

x^2 -10x+25

Step-by-step explanation:

(x-5)^2

(x-5)(x-5)

FOIL

first = x*x = x^2

outer:-5x

inner: -5x

last: -5*-5 = 25

Add them together

x^2 -5x-5x+25

Combine like terms

x^2 -10x+25

Standard form is ax^2 +bx +c so this is standard form

Step-by-step explanation:

I suspect this to be a trick question.

because 2 statements are correct :

B and C.

according to the definition, two triangles are similar if their corresponding angles are congruent (identical) and corresponding sides are proportional (the ratio between the length of corresponding sides is equal for all pairs of corresponding sides, or, in other words, there is one scale factor for all 3 pairs of corresponding sides).

in fact, each criteria alone is sufficient.

if all 3 corresponding angles are identical between both triangles, the corresponding pairs of sides will be proportional.

if all 3 pairs of corresponding sides are proportional, then the corresponding angles are identical.

and the triangles are similar.

The percentage of students that use the internet for more than 402 minutes =  16%

Percentage

Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.

calculate the percentage-

The empirical rule states that

68% of the population lies within 1 standard deviation of the mean

95% of the population lies within 2 standard deviations of the mean

99.7% of the population lies within 3 standard deviations of the mean

Standard Deviation

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The percentage will be illustrated in this:

P(X > 402) = P(X > 30 + 1 × 102)

= (1-0.68) / 2

= 0.32/2

= 16%

The percentage of students that use the internet for more than 402 minutes =  16%.

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Answer:

...

Step-by-step explanation:

The calculated length of the segment AD is 14

From the question, we have the following parameters that can be used in our computation:

B is the midpoint of AC

BD = 9 and BC = 5

Using the above as a guide, we have the following:

AB = BC = 5

CD = BD - BC

So, we have

CD = 9 - 5

Evaluate

CD = 4

So, we have

AD = AB + BC + CD

substitute the known values in the above equation, so, we have the following representation

AD = 5 + 5 + 4

Evaluate

AD = 14

Hence, the length of the segment AD is 14

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The derivative of the function y = x(6x + 1)⁵ is: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴

To find the derivative of the given function, we can apply the rules of differentiation. Using the product rule, we differentiate each term separately and then add them together.

For the first term x, the derivative is simply 1.

For the second term (6x + 1)⁵, we apply the chain rule. The derivative of (6x + 1)⁵ with respect to x is 5(6x + 1)⁴ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get (6x + 1)⁵ * 6 = 6(6x + 1)⁵.

For the third term x(6x + 1)⁴, we again apply the product rule. The derivative of x is 1, and the derivative of (6x + 1)⁴ is 4(6x + 1)³ multiplied by the derivative of the inner function 6x + 1, which is 6.

Multiplying these derivatives together, we get x * 4(6x + 1)³ * 6 = 24x(6x + 1)³.

Finally, we add the derivatives of each term to get the derivative of the entire function: dy/dx = (6x + 1)⁵ + 30x(6x + 1)⁴.

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Complete question:

Use the rules of differentiation to find the derivative of the function y= x(6x + 1)⁵

(6x + 1)⁵ + 30x(6x + 1)⁴

(6x + 1)⁴ (36x + 1)

x-1/6

No correct answer provided.

To solve the expression 3-21 using the rectangular components of vectors a and b with the unit vectors i and j, we can decompose the vectors into their respective components and perform the subtraction operation.

Let's decompose vectors a and b into their rectangular components using the unit vectors i and j. Suppose vector a has components (a1, a2) and vector b has components (b1, b2). To solve the expression 3-21 using the rectangular components, we subtract the corresponding components of the vectors.

So, (3-21) can be written as (3i + 0j) - (21i + 0j). By subtracting the components, we get (3-21)i + (0-0)j, which simplifies to -18i + 0j or simply -18i.

Therefore, using the rectangular components of vectors a and b with the unit vectors i and j, the expression 3-21 evaluates to -18i.

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Answer:a)6,7,8

d)8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30

Step-by-step explanation:

Answer:

Step-by-step explanation:

co-ordinates = (6,-2) (5,-4)

slope = (y² - y¹) / (x² - x¹)

slope = (-4 - 6) / (5 - (-2))

slope = (-10) / (5+2)

slope = (-10) / 7

slope = -10 / 7

Answer:

10/7

Step-by-step explanation:

Answer:

ASA

Step-by-step explanation:

The general solution of the differential equation is given by: \($$y=c_1 x^0 +c_2 x^1 +\sum_{n=0}^\infty \frac{2(n+r)-2}{(n+2)(n+1)}a_n x^{n+2}$$\)

Given: \(\[ x^{2} \frac{d^{2} y}{d x^{2}}-2 x \frac{d y}{d x}+2 y=x^{3} \]\)

We have to find the general solution of the above differential equation.

Here, we need to convert this into standard differential equation of the form of: \(\[ay^{\prime \prime} +by^{\prime}+cy=d(x)\]\)

For this, we need to divide both sides by \($x^2\). This yields: \($$y^{\prime \prime} -\frac{2}{x}y^{\prime} +\frac{2}{x^2}y=x$$\)

Now, we set up the homogeneous equation: \($$y^{\prime \prime} -\frac{2}{x}y^{\prime} +\frac{2}{x^2}y=0$$\)

Using the power series method, we assume a solution of the form: \($$y=\sum_{n=0}^\infty a_nx^{n+r}$$\)

Substituting this into the above equation, we obtain:

\($$\begin{aligned} & \sum_{n=2}^\infty a_nn(n-1)x^{n+r-2}-2\sum_{n=1}^\infty a_nn(x^{n+r-1}+r x^{n+r-1})+2\sum_{n=0}^\infty a_n(x^{n+r-2}) \\ =&\sum_{n=0}^\infty a_n x^{n+r-2} \end{aligned}$$\)

Separating out the terms and setting \($n=0$\), we obtain the indicial equation: \($$r(r-1)a_0=0$$\)

Thus,\($r=0$\)or \($r=1$\).

We use the first value of \($r$\).

Thus, the series becomes: \($$y_1=a_0 +a_1 x$$\)

Now, we use the second value of \($r$\).

Thus, the series becomes: \($$\begin{aligned} y_2 &=a_0 x +a_1 x^2 +a_2 x^3 + \dots \\ &=y_1(x)+x^2 \sum_{n=0}^\infty a_{n+2}x^n \end{aligned}$Substituting $y_2$\)

into the homogeneous equation, we obtain:

\($$\sum_{n=2}^\infty a_{n+2}(n+2)(n+1)x^{n+r}-2\sum_{n=1}^\infty a_{n+1}(n+r)x^{n+r}+2\sum_{n=0}^\infty a_n x^{n+r-2} +x^3 \sum_{n=0}^\infty a_n x^n=0$$\)

Equating the coefficients of each power, we obtain the following system of equations:\($$\begin{aligned} & a_2(2)(1) +a_0 =0 \\ & (n+2)(n+1)a_{n+2} -2(n+r)a_{n+1} +2a_n =0, \ n\geq 1 \\ & a_{n+2}=0, \ n\geq 0, \ n\neq -1,-2 \end{aligned}$$\)

Solving these equations, we obtain:

\($$\begin{aligned} a_0 &=c_1 \\ a_1 &=c_2+c_1 \ln x \\ a_{n+2} &=\frac{2(n+r)-2}{(n+2)(n+1)}a_n, \ n\geq 0, \ n\neq -1,-2 \end{aligned}$$\)

Using the power series method, we find the homogeneous equation of the differential equation: $\(y'' - \frac{2}{x} y' + \frac{2}{x^2} y = 0$\)

We assume that \($y = \sum_{n=0}^{\infty} a_n x^{n+r}$\) is a solution of the homogeneous equation. We then separate out the terms and solve for the coefficients using the indicial equation. We find that \(r = 0$ and $r = 1$\)are solutions of the indicial equation. We then solve for \(y_1$ and $y_2$\) and substitute into the homogeneous equation to solve for the coefficients. We obtain the general solution.

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Answer:

V(5, 1)

Step-by-step explanation:

Given:

M(3, 2)

U(1, 3)

From midpoint to U:

(x, y) → (x - 2, y + 1)

To get from midpoint to V, we inverse the formula:

(x, y) → (x - 2, y + 1)

(x, y) → (x + 2, y - 1)

To find V:

(x, y) → (x + 2, y - 1)

(3, 2) → (3 + 2, 2 - 1)

(3, 2) → (5, 1)

The distance between two opposite corners of the given floor is 17 feet.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

Given that the floor of a storage unit is 15 feet long and 8 feet wide.

Let x would be the distance between two opposite corners of the floor

As per the figure, We have a right triangle with legs 15 and 8 and with hypotenuse x.

According to Pythagoras's theorem,

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

Thus, the distance is 17 feet between two opposite corners.

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Cindy is correct. The height of the parallelogram is equal to the height of the trapezoid. Let h represent the height. The area of the parallelogram is 5h. The area of the trapezoid is 10h divided by 2 or 5h.

In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:

Area of a parallelogram, A = b × h

Where:

Area of a parallelogram, A = b × h

Area of a parallelogram, A = 5 × h

Area of a parallelogram, A = 5h square inches.

Area of trapezoid, A = ½ × (a + b) × h

Area of trapezoid, A = ½ × (3 + 7) × h

Area of trapezoid, A = 10h/2 or 5h inches.

Therefore, only Cindy is correct.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

29

Step-by-step explanation:

multiply by 2

Yes, there are experts here in data forecasting methods who can help you with the topics you've mentioned including time series (holts, holts winter), naive method, regression, acf, pacf, arima, stl method and multivariate time series.

Below are brief explanations of each of these terms:

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If algebraic expressions are a³ᵇ = x and aᵇ = y, then, by algebra properties, x / y² is equal to aᵇ.

Herein we find the following two algebraic expressions with two positive integers a and b:

a³ᵇ = x

aᵇ = y

From these equation we need to find the result associated to algebraic expression x / y² in terms of the integers given. This can be done by means of algebra properties. First, square the second expression:

(aᵇ)² = y²

Second, divide the first expression by the given formula found in previous step:

x / y² = a³ᵇ / (aᵇ)²

Third, simplify the resulting expression to a single power:

x / y² = a³ᵇ / a²ᵇ

x / y² = a³ᵇ - ²ᵇ

x / y² = aᵇ

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Answer: tbh

Step-by-step explanation:

Answer: Answer is D, a 55° angle

Step-by-step explanation:

The volume of a cube is 15.625 cubic cm.

What is the volume of a cube?

A cube is a three-dimensional shape having 6 square faces, all the faces are of equal length, breadth, and height.

The volume of the cube is given by side * side * side.

The volume of a cube is given by:

V = a³,

where a is the side length of the cube.

Each side of a cube is 2.5 cm long.

Then, the volume of the cube will be:-

V = (2.5)³,

=  15.625

Hence, the volume of a cube is 15.625 cubic cm.

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The correct equation is,

⇒ 8(x + 6) = 144

Now, We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

Thus, The correct equation is,

8(x + 6) = 144

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Answer:

x = -3 and x = 17

Step-by-step explanation:

x² - 51 = 14x

x² - 14x - 51 = 0

(x + 3)(x - 17) = 0

x = -3 and x = 17

Answer:

x=-3 and x=17. Success to the homework.

Step-by-step explanation:

here is the answer with the solution.

Answer: 4x^2 - 10x - 6

Step-by-step explanation:

You can use FOIL to do this. First terms, Outer terms, Inner terms, Last terms.

(x - 3)(4x + 2)

First terms: x * 4x = 4x^2

Outer terms: x * 2 = 2x

Inner terms: -3 * 4x = -12x

Last terms: -3 * 2 = -6

Now add these together:

4x^2 + 2x - 12x - 6 = 4x^2 - 10x - 6

Answer:

4x^2 - 10x - 6

Step-by-step explanation:

If you truly want to multiply these binomials, remove the " + " sign and replace it with " * " for multiplication:

(x - 3) (4x + 2)  =  4x^2 + 2x - 6 - 12x

Combining like terms, we get 4x^2 - 10x - 6

Answer:

x > 2/3

Step-by-step explanation:

2x -x - 2 > 0  

add 2x and x (It becomes 3x)

3x -2 >0

subtract 0 from both sides

3x> 2

divide 3 on both sides

And the answer is

X> 2/3

The sampling method that is most likely to be appropriate for calculating confidence intervals is simple random sampling.

This method ensures that every member of the population has an equal chance of being selected for the sample. This reduces the risk of bias and ensures that the sample is representative of the population. Stratified sampling is also a useful method for calculating confidence intervals, especially when the population has subgroups that need to be represented in the sample. However, other sampling methods like convenience sampling or quota sampling are not appropriate for calculating confidence intervals as they can introduce bias into the sample and do not guarantee a representative sample. Therefore, it is important to use an appropriate sampling method when calculating confidence intervals to ensure that the results accurately reflect the population.

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