Jewelers emphasize that the price of a diamond is
determined by cut, carat weight, color and clarity.
Draw a line that passes through the points
(0.35,1629) and (0.12,334.50).
Use your line to predict the price of a 0.17-carat
diamond.
C
Price
Check
X
Question 2
Price (U.S. $)
1500
1000
500-
T
√

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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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

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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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

Therefore , the solution of the given problem of function comes out to be Option 2 is correct.

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm. Functions are typically denoted by the letter f. (x). The input contains an x.

Here,

=> f(x) = 3x³ + 2

=> g(x) = 3√ x-2 / 3

For ,

=> f(g(x)) =   3x³ + 2

=>  f(g(x)) = 3(3√ x-2 / 3)³ + 2

=>   f(g(x)) = (9/√x - 2/3)³ + 2

Thus ,

Option 2 is correct.

Therefore , the solution of the given problem of function comes out to be Option 2 is correct.

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Option D is the correct answer. The probability that a test correctly rejects a false null hypothesis is called the significance level.

The significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant.

The probability of making a type II error (failing to reject the null hypothesis when it is actually false) is called β (beta). The quantity (1 - β) is called power, the significance level is the probability of rejecting the null hypothesis when it is true.

For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. Lower significance levels indicate that you require stronger evidence before you will reject the null hypothesis.

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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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The required solution of the simultaneous equation is given as x = 10 and y = -1.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

here,
Given equations,
x – y = 11  - - - - - (1)
2x + y = 19 - - - -- -(2)

Put x form equation 1 in equation 2
2 [11 + y] + y = 19
y = -1

Now,
x = 11 + y
x = 10

Thus, the required solution of the simultaneous equation is given as x = 10 and y = -1.

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Answer:

yup! its true. They are supplementary angles.

Step-by-step explanation:

Answer: 1440

Step-by-step explanation:

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

In testing for the equality of k population means that the number of treatments is K. option(b) is the correct answer.

The average treatment deviation is significantly correlated with the average error deviation when the k population means are truly unique from one another. N is the total number of observations included in the analysis, and k is the number of independent groups, in this case, k=4. Hence, option B is the relevant choice.

The two-sample t-test, also known as the independent samples t-test, is a method for determining whether or not the unknown population means of two groups are equal. When your data values are independent, randomly picked from two normal populations, and the variances of the two independent groups are equal, you can utilise the test.

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Answer:The most efficient step to finding the solution to the given inequality is, to subtract 4 from both sides. Option D is correct.

Given that,

To determine which step is the most efficient way to find the solution of x + 4 > -8.

Step-by-step explanation:

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.

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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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:

Step-by-step explanation:

180 - 110 = 70°

180 - 70 - 70 =

40°

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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Answer:

1. Growth

2. Decay

3. Decay

Step-by-step explanation:

Growth means as x increases, y increases too. On the other hand, decay means as x increases, y decreases. There's the theory for exponential function regarding this growth and decay.

Growth

If the base is not a decimal or a fraction then it's growth.

Decay

If the base is a decimal or a fraction then it's decay.

From the problem, first function has base of 5. Hence, it's growth. On the other hand, second and third function both have decimal and fraction as the base. Hence, it's decay.

When considering growth or decay graph, we can ignore the coefficient since it doesn't determine the growth and decay. The only thing that determines if a function increases or decreases is the base under the exponent.

First you turn the equation into y=mx+b form.

2y-3x=10

2y=3x+10

2y/2=(3x+10)/2

y=3/2x+5

Next you take the opposite of the slope.

Slope = 3/2

Opposite = 2/3

Then you insert your values into y-y1=m(x-x1)

y+1=2/3(x+8)

y+1=2/3x+16/3

The answer is

y=2/3x+13/3

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 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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Answer:

8

Step-by-step explanation:

First look at the left, under the weight 2 there are 2 little boxes one of them is 1. so the other one must be one.  that'll make this small group 2+1+1 =4, which means the other side to balance it, it is also 4.

now we've got 2*4 = 8 under 13. so left side total = 13+8 = 21

now look at the right side, it also must be 21. we already know there is a 5, then under neath the 5, to balance the remaining weight 21-5 = 16, each side must be equal. so each side = 8.  

watermelon itself is one side, so it's 8.

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

Step-by-step explanation:

.

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: 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.

Answer:

Step-by-step explanation:

yooooooooooooooooooo

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

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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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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