simplify
2/9 to the power of 2

The average rate of change of the equation is 7

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information, f(x) = 2x²-5x-2 and x₁ = 2, x₂ = 4

average rate of change =  ([2(4)²-5(4)-2] - ([2(2)²-5(2)-2]) / (4- 2)

average rate of change = (10-(-4)) / 2

average rate of change = 14/2

average rate of change = 7

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Answer:
in attached image :)

The given iterated integral is [tex]\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx[/tex]. The value of this integral is evaluated as 2/3.

The iterated integral is obtained by repeatedly integrating multivariate functions with a single variable each time. The given iterated integral is [tex]\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx[/tex]. This integral is evaluated in the following order [tex]\int dy[/tex], [tex]\int dz[/tex], and [tex]\int dx[/tex].

First, integrate the above expression with respect to y. Then, substitute the limit values, and we get,

[tex]\begin{aligned}\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx&=\int\limits^{\pi}_b\int\limits^1_0z\sin(x)\left[\int\limits^{\sqrt{1-z^2}}_0 \;dy\right]\;dz \;dx\\&=\int\limits^{\pi}_b\int\limits^1_0z\sin(x)[y]^{\sqrt{1-z^2}}_{0}\;dz \;dx\\&=\int\limits^{\pi}_b\int\limits^1_0z\sin(x)\left(\sqrt{1-z^2}\right)\;dz \;dx\end{aligned}[/tex]

Now, integrating with respect to z, we get,

[tex]\begin{aligned}\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx&=\int\limits^{\pi}_b\int\limits^1_0\sin(x)\;z\left(\sqrt{1-z^2}\right)\;dz \;dx\\&=-\frac{1}{2}\int\limits^{\pi}_b\sin x\left[\int\limits^1_0-2z\left(\sqrt{1-z^2}\right)\;dz\right]\;dx\end{aligned}[/tex]

Substitute, 1-z²=u and -2zdz=du in the above expression, and we get,

[tex]\begin{aligned}\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx&=-\frac{1}{2}\int\limits^{\pi}_b\sin x\left[\int\limits^0_1\left(\sqrt{u^2}\right)\;du\right]\;dx\\&=-\frac{1}{2}\int\limits^{\pi}_b\sin x\left[\frac {u^{3/2}}{3/2}\right]^0_1\;dx\\&=\frac{1}{3}\int\limits^{\pi}_b\sin x\left[u^{3/2}\right]^1_0\;dx\\&=\frac{1}{3}\int\limits^{\pi}_b\sin x\;dx\end{aligned}[/tex]

Finally, integrating with respect to x and we get,

[tex]\begin{aligned}\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx&=\frac{1}{3}\int\limits^{\pi}_b\sin x\;dx\\&=\frac{1}{3}[-(-1)-(-(1))]\\&=\frac{1}{3}[2]\\&=\frac{2}{3}\end{aligned}[/tex]

The required answer for the given integral is 2/3.

The complete question is -

Evaluate the iterated integral [tex]\int\limits^{\pi}_b\int\limits^1_0\int\limits^{\sqrt{1-z^2}}_0 z\sin(x)\;dy\;dz \;dx[/tex].

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the answer to this lovely amazing question would and should be 0.28

Step-by-step explanation:

.

This statement is false. Two subspaces of R^n can have the same dimension but still be different.

Here are a few bullet points that elaborate on this:

Therefore, the statement "If s1 and s2 are subspaces of R^n of the same dimension, then s1 = s2" is not true in general.

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Answer: the answer is -11

Answer:

  (d)  3 + x = 14

Step-by-step explanation:

You want to know an equation that can help you find the number who arrived late, if the total of an initial 3 and the number who arrived late is 14.

You want to express that an unknown number, added to three, makes a total of 14:

  3 + x = 14

Answer:

0 on the left side

Step-by-step explanation:

Since RQ is congruent to PS and RS is congruent to QP, QT = SU, therefore QT and SU are congruent which means PT and RU are also congruent

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

One the property of a parallelogram is that the opposite lines are parallel and congruent.

Therefore RQ = PS ( they are both congruent)

PS = RS ( they are both congruent )

Therefore the measure of line PT = line SU = QT.

This means that the value of PT = R U , we can therefore say that PT and RU are congruent.

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Answer: 13

Step-by-step explanation: The number goes up by three each time, so it would be 13.

Answer:

The nᵗʰ term of the sequence is 3n - 2.

Step-by-step explanation:

[tex]\longrightarrow{\sf{a_n = a + (n - 1)d}}[/tex]

where :

Here we can see that the difference between two terms is 3.

Thus, finding the nth term of the sequence by substituting all the given values in the formula :

[tex]\longrightarrow{\sf{a_n = a + (n - 1)d}}[/tex]

[tex]\longrightarrow{\sf{a_n = 1 + (n - 1)3}}[/tex]

[tex]\longrightarrow{\sf{a_n = 1 + (n \times 3 - 1 \times 3)}}[/tex]

[tex]\longrightarrow{\sf{a_n = 1 +(3n - 3)}}[/tex]

[tex]\longrightarrow{\sf{a_n = 1 +3n - 3}}[/tex]

[tex]\longrightarrow{\sf{\underline{\underline{a_n = 3n - 2}}}}[/tex]

Hence, the nth term of the sequence is 3n - 2.

Therefore , the solution of the given problem of surface area comes out to be 18 yd³  is needed to fill the garden with 4 inches of soil.

A measurement of how much space something occupies overall is its surface area. The surface area of a three-dimensional shape includes its whole surroundings. An object's surface area is its entire area. A cuboid's surface area is determined by summing the faces of all of its six oblong sides. The box's measurements could be determined using the formula below: 2lh, 2lw, & 2hw are the same as surface (SA). The whole area is represented by the three-dimensional shape's surface area.

Here,

Given  :

18 × 9 × = 54 ft² = 18 yd³

Thus,

The 4 inches of soil is made at the cubic yards soil .

So , it is correct

Therefore , the solution of the given problem of surface  area comes out to be 18 yd³  is needed to fill the garden with 4 inches of soil.

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Answer:

Step-by-step explanation:

y×8=8y

8y+4=4×7

8y+4=28

8y=24

y=

Answer:

The number is:

3

Step-by-step explanation:

8a + 4 = 4*7

8a + 4 = 28

8a = 28 - 4

8a = 24

a = 24/8

a = 3

Check:

8*3 + 4 = 4*7

24 + 4 = 28

Answer:

Step-by-step explanation:

no, it cannot be a triangle

all triangles add up to 180º

115.1+47.5+93= 255.6

255.6 doesn't equal 180, so no its not a triangle

The solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.

An inequality that combines two other inequalities by using either "and" or "or" is referred to as a compound inequality. In certain cases, "and" won't be stated explicitly, but it is still understood. For instance, 1 x 3 simply means "x > 1 and x 3". However, a compound inequality using "or" is always explained in detail using "or." Compound inequalities may be divided into two categories: conjunction and disjunction.

The given compound inequality is:

1 ≤ | x + 3 | ≤ 4

As the equation contains a mod sign, we can write the inequality as follows:

1 ≤ x + 3 ≤ 4, and

1 ≤ - x - 3 ≤ 4

Simplify the first equation:

1 ≤ x + 3 ≤ 4

Subtract 3 from both the sides of the equation:

1 - 3 ≤ x + 3 - 3 ≤ 4 -3

-2 ≤ x ≤ 1

Simplify the second equation:

1 ≤ - x - 3 ≤ 4

Add 3 on both sides of the equation:

1 + 3 ≤ - x - 3 + 3≤ 4 + 3

4 ≤ -x ≤ 7

Convert the negative term to positive:

-4 ≥ x ≥ -7

Hence, the solution of the compound inequality is -2 ≤ x ≤ 1 and -4 ≥ x ≥ -7.

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Answer:

To find the fraction of the total audience that were students or teachers, you need to add the fractions of students and teachers and simplify the result.

5/12 + 1/8 = (53) / (123) + (16) / (86) = 15/36 + 6/48 = 15/36 + 3/24 = 18/36 + 3/24 = (18+3) / (36+24) = 21/60

So 21/60 of the total audience were students or teachers.

Answer: When dividing two fractions you simply multiply the first one by the reciprocal of the second:

1

4

3

5

=

1

4

⋅

5

3

=

5

12

Let's review the information given to us to answer the question correctly this way:

     Juniors  Seniors   Totals

Yes       28         97          125

No       56         19           75

Totals   84        116          200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125

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It is true that in calculating which means differ, each pair of means needs a unique range.

To determine if two means are different, a statistical test such as a t-test or an ANOVA is typically used. These tests compare the means of two or more groups and require a unique range for each group. This range is typically represented by the variance or standard deviation of the group's data.

For example, if we have two groups of data, group A and group B, and we want to determine if the mean of group A is different from the mean of group B, we would need the range of data for group A and the range of data for group B. The range of data includes the variance or standard deviation which is used to calculate the t-value or the F-value which is used to determine if the means are significantly different. Without this information, we cannot accurately compare the means and determine if they are different.

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Answer:

To graph this linear relationship, we can plot two points on a coordinate plane: (3,12) and (5,20). These points represent the number of hours Jen babysits (x-coordinate) and the amount of money she earns (y-coordinate).

We can connect these two points with a line to form a linear equation that represents the relationship between the number of hours babysat and the money earned.

The slope of this line can be found using the formula: (change in y) / (change in x) = (20-12) / (5-3) = 8/2 = 4

Therefore, Jen earns $4 per hour by babysitting.

It is important to note that this is a linear relationship, and the earnings are proportional to the number of hours babysat. This means that for any number of hours babysat, the earnings can be found by multiplying that number by $4.

Step-by-step explanation:

Answer: For every hour she babysits, she earns $4. ✅

Step-by-step explanation:

To graph the linear relationship, we can start by plotting two points: (3,12) and (5,20).

This represents that for 3 hours of babysitting, Jen earns $12, and for 5 hours of babysitting, she earns $20.

We can then use these points to find the slope of the line, which is the rate at which her earnings change as the number of hours increases.

The slope can be found by using the formula: (change in y) / (change in x) = (20 - 12) / (5 - 3) = 8/2 = 4

This means that for every hour she babysits, she earns $4.

So, the equation of the line is : y = 4x + b

Where b is the y-intercept, which can be found by substituting one of the points into the equation.

For example, by substituting (3,12) in the equation:

12 = 4(3) + b

b = 0

So, she earns per hour $4. ✅

The exact value of cos 105 degrees is (√3-1) / 2√2 .

What is Trigonometric Function ?

Trigonometric functions also are referred to as circular features can be really described as the capabilities of an angle of a triangle. It method that the relationship among the angles and facets of a triangle are given by using these trig capabilities. The fundamental trigonometric features are sine, cosine, tangent, cotangent, secant and cosecant.

So,

we know that ,

cos(A+B) = cosA cosB - sinA sinB

So,

cos(105) can be written as

cos(60+45 ) = cos60 cos 45  - sin60 sin45

= 1/2  *  1/√ 2  - √ 3 / 2 * 1/√2

=1/√2  *  (√3 - 1) / 2

=(√3-1) / 2√2 .

so the value of cos105 is (√3-1) / 2√2 .

Therefore , The exact value of cos 105 degrees is (√3-1) / 2√2 .

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After rewriting the given equation, we have the resultant equations as (B) -2.3p - 10.1 = 6.49p - 4 and (C) -230p - 1010 = 650p - 400 - p.

Two expressions joined by an equal sign form a mathematical statement known as an equation.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

So, we have the equation:
2.3p - 10.1 = 6.5p - 4 - 0.01p

Now, we can rewrite them as follows:

-2.3p - 10.1 = 6.49p - 4

-230p - 1010 = 650p - 400 - p

Therefore, after rewriting the given equation, we have the resultant equations as (B) -2.3p - 10.1 = 6.49p - 4 and (C) -230p - 1010 = 650p - 400 - p.

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Correct question:

Use properties to rewrite the given equation. ch equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.

a. 2.3p - 10.1 = 6.4p - 4

b. 2.3p - 10.1 = 6.49p - 4

c. 230p - 1010 = 650p - 400 - p

d. 23p - 101 = 65p - 40 - p

e. 2.3p - 14.1 = 6.4p - 4

Up until he received an 8% cost of living boost from Mr. Peterson, his pay was $59.166.

Occasionally, the acronyms "pct.," "pct," and "pc" are also used. But it is commonly indicated by the percent sign, "%." The % amount has no dimensions. Percentages are essentially fractions when the denominator is 100. Use the percent sign (%) to indicate that a number is a percentage by placing it next to it. For instance, you score a 75% if you properly answer 75 out of 100 questions on a test (75/100). Divide the money by the total and multiply the result by 100 to calculate percentages. The formula for calculating the percentage is (value/total) x 100%.

given

Mr. Peterson received an 8% cost-of-living rise, increasing his weekly compensation to $739.58.

salary now =  $739.58 * 8/100

= $ 59.166

Up until he received an 8% cost of living boost from Mr. Peterson, his pay was $59.166.

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Model B has a lower RMSE value on the hold-out set and therefore it is more likely to generalize well to new data.

The RMSE (root mean squared error) is a measure of the difference between the predicted values and the true values. A lower RMSE value indicates a better fit of the model to the data. In this case, it is not specified which model has a lower RMSE value on the training set or the hold-out set, but both models are considered to fit the data well.

To solve this question, we need to compare the RMSE values of both models on both the training and hold-out sets.

On the training set, Model A has a lower RMSE value of 0.8 compared to Model B's RMSE value of 0.9. This suggests that Model A is a better fit for the training data. However, it is important to note that a model that performs well on the training set may not necessarily perform well on new data.

On the hold-out set, Model B has a lower RMSE value of 1.1 compared to Model A's RMSE value of 1.2. This suggests that Model B is a better fit for the hold-out data.

The hold-out set is a good approximation of new data and therefore the performance of the model on the hold-out set is a good indicator of the model's performance on new data. Since Model B has a better performance on the hold-out set, it is more likely to generalize well to new data.

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The complete question is:

Two different models were fit to the same time series using the first 100 time periods as the training set and the last 12 periods as a hold-out set. The RMSE values for each of the models on the training set are Model A: 0.8 and Model B: 0.9. The RMSE values for each of the models on the hold-out set are Model A: 1.2 and Model B: 1.1. Which model is more likely to generalize well to new data and why?

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The quadratic equation is y = -25.42x² + 106.66x + 2.06 which fits the given points.

What is Quadratic regression?

Quadratic regression is a method of finding the equation of a parabola that best fits a set of data points. The equation for a parabola is y = ax² + bx + c, where a, b, and c are constants.

A quadratic equation that fits the given points can be found using quadratic regression.

To find the equation that fits the given points (0, 6.1), (1, 71.2), (2, 125.9), and (3, 89.4), we can use the method of least squares.

The method of least squares is a method of finding the equation that minimizes the sum of the squares of the differences between the actual y-values and the predicted y-values.

Using this method, we can find that the equation of the parabola that best fits the given points is y = -25.42x² + 106.66x + 2.06

This equation is in the form of y = ax² + bx + c, where a = -25.42, b = 106.66, and c = 2.06.

This equation can be used to predict the y-value for any x-value within the domain of the given points.

Hence, the quadratic equation is y = -25.42x² + 106.66x + 2.06 which fits the given points.

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Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.

A line's slope determines how steep it is. A gradient-based equation is referred to as having a gradient overflow. By dividing average horizontal difference (run) between 2 places by both the vertically change (rise) between those same two points, the slope is determined. The equation of a horizontal path is expressed as y = mx + b and is known as the hill form of an equation. The y-intercept of the line is located where the grade is m, b = b, and (0, b). In the case of the equations y = 3x - 7, the slope y y-intercept are (0, 7). The y-intercept is situated where the slope of the line is m and b is

Here,

Given :

that m=2, the point (x1,y1)=(— 3, —1)

Equation for the necessary straight line:

=>(y — y1)=m(x — x1)

=>y+1=2(x+3)

X=0 on the y-axis indicates that nothing is being measured.

=>y=2+3

The y-intercept value is 5.

Therefore , the solution of the given problem of slope comes out to be the y-intercept value is 5.

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Solving provided question, we can say that base form of quadratic equation = [tex]ax^2 + bx + c = 0[/tex] ; f(x) = [tex]-3x^2 + x -3 = 0[/tex]

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, zero is = -3

base form of quadratic equation = [tex]ax^2 + bx + c = 0[/tex]

f(x) = [tex]-3x^2 + x -3 = 0[/tex]

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Answer:

Step-by-step explanation:

180 - 110 = 70°

180 - 70 - 70 =

40°

For B>0, the graph of y = sin Bx will have a period of (2π/B) units. The period of a sine function is the length of one complete cycle of the function.

The period of a trigonometric function is the length of one complete cycle of the function.

For the sine function, this is the distance between two consecutive points at which the sine value is equal to zero, or the distance between two consecutive maxima or minima. In this case, the graph of y = sin Bx is multiplied by a factor of B, which will stretch or compress the graph along the x-axis by a factor of B.

Therefore, the period of the graph will be (2π/B) units.

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On solving the provided question related to rectangle we can say that the Perimeter, P = 2(10+20); P = 60 cm

The formula for the perimeter of a rectangle is, P = length + breadth + length + breadth The perimeter of a shape is always calculated by adding up the length of each of the sides. To find the perimeter of a rectangle, we add the lengths of all four sides. Since opposite sides of a rectangle are always equal, we need to find the dimensions of length and width to find the perimeter of a rectangle. We can write the perimeter of the rectangle as twice the sum of its length and width.

In order to find the perimeter, or distance around the rectangle, we need to add up all four side lengths.

This can be done efficiently by simply adding the length and the width, and then multiplying this sum by two since there are two of each side length. Perimeter=(length+width)×2 is the formula for perimeter

here,

we have length, L = 10

and breadth, B = 20

Perimeter, P = 2(10+20)

P = 60 cm

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The result of the addition of the polynomials is -15x^3 + 4x - 11.

We have to note that the polynomials have to do with those kind of functions in which the power of x in the equation may range form 1 to infinity. We have in the question that the expression can be written as;

(−6x^3 + 3 −4x) − (14 − 8x + 9x^3)

Then we have;

−6x^3 + 3 −4x - 14 + 8x - 9x^3

We can now collect the like terms as follows;

−6x^3 - 9x^3 −4x  + 8x + 3 - 14

-15x^3 + 4x - 11

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