if 5+2\(\sqrt[2]{3}\)/7+\(\sqrt[4]{3}\)=a+b\(\sqrt{3}\) then what will a and b be equal to

Answer:

I think it is the last option I am not really sure but I think it is the last option

Step-by-step explanation:

Its the last one , cause it got the ÷ sign .

And we know that equivalent sets contain same elements or symbols even if the number are different .

Answer:

\(\displaystyle 5\)

Step-by-step explanation:

\(\displaystyle \boxed{y = -5cos\:(\frac{39}{64}\pi{x} + \frac{\pi}{2}) + 1} \\ \\ y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{32}{39}} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{39}{64}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\frac{11}{39}} \hookrightarrow \frac{2}{\frac{39}{64}\pi}\pi \\ Amplitude \hookrightarrow 5\)

OR

\(\displaystyle \boxed{y = -5sin\:(\frac{39}{64}\pi{x} + \pi) + 1} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 1 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1\frac{25}{39}} \hookrightarrow \frac{-\pi}{\frac{39}{64}\pi} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{3\frac{11}{39}} \hookrightarrow \frac{2}{\frac{39}{64}\pi}\pi \\ Amplitude \hookrightarrow 5\)

As you can see, the right-centred photograph displays the trigonometric graph of \(\displaystyle y = -5cos\:\frac{39}{64}\pi{x} + 1,\)in which you need to replase "sine" with "cosine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the sine graph [photograph farthest to the left], accourding to the horisontal shift formula above. Also keep in mind that −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so be very careful with your calculations. So, between both photographs, we can tell that the cosine graph [centre right photograph] is shifted \(\displaystyle \frac{32}{39}\:unit\)to the right, which means that in order to match the sine graph [photograph farthest to the left], we need to shift the graph BACKWARD \(\displaystyle \frac{32}{39}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you get \(\displaystyle \boxed{-\frac{32}{39}} = \frac{-\frac{\pi}{2}}{\frac{39}{64}\pi}.\)So, the cosine graph of the sine graph, accourding to the horisontal shift, is \(\displaystyle y = -5cos\:(\frac{39}{64}\pi{x} + \frac{\pi}{2}) + 1.\)Intermediate, we have two sine graphs [centre left photograph and the photograph farthest to the left]. The left-centred photograph displays the trigonometric graph of \(\displaystyle y = -5sin\:\frac{39}{64}\pi{x} + 1.\)So, just like before, we need to figure out the appropriate C-term that will horisontally shift the graph back into position ["position", meaning shifting this sine graph back in plase (matching the sine graph in the photograph on the left)]. So, between the two photographs, we can tell that the left-centred sine graph is shifted \(\displaystyle 1\frac{25}{39}\:unit\)to the right, which means that in order to match the leftward sine graph, we need to shift the graph BACKWARD \(\displaystyle 1\frac{25}{39}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-1\frac{25}{39}} = \frac{-\pi}{\frac{39}{64}\pi}.\)So, when shifted back into original position, the sine graph is \(\displaystyle y = -5sin\:(\frac{39}{64}\pi{x} + \pi) + 1.\)Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \(\displaystyle [-6\frac{22}{39}, 1],\)from there to \(\displaystyle [-3\frac{11}{39}, 1],\)they are obviously \(\displaystyle 3\frac{11}{39}\:units\)apart, telling you that the period of the graph is \(\displaystyle 3\frac{11}{39}.\)Now, the amplitude is obvious to figure out because it is the A-term, and in case you want to be certain, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 1,\)in which each crest is extended five units beyond the midline, hence, your amplitude. Now... the sine graph in the photograph farthest to the right is the OPPOCITE of the sine graph in the photograph farthest to the left, and the reason for this is because of the negative inserted in front of the amplitude value. Whenever you insert a negative in front of the amplitude value of any trigonometric equation, the whole graph reflects over the midline. Keep this in mind moving forward. So, overall, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

I am delighted to assist you at any time.

The outlier of 2 decreases the mean page count.

What is mean and median?

The mean is that the variety you get by dividing the total of a collection of values by the quantity of values within the set.

In distinction, the median is that the middle variety in an exceedingly set of values once those values square measure organized from smallest to largest.

Main Body:

From the picture we can  know that outlier of 2 does not effect the median page count.

But outlier of 2 decreases the mean page count.

it can be found out by taking mean

(1+2+3+2+1+2+2+1)/8= 1.75

and if we remove outlier of 2 ,then

(1+3+2+1+2+2+1)/7 = 1.86

Hence ,the outlier of 2 decreases the mean page count.

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Answer:

the answer is d

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

Square root (39*39 + 52*52)

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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9514 1404 393

Answer:

  28

Step-by-step explanation:

Let x represent the even number between them. Then the desired sum is 2x.

The given relation is ...

  7(x -1) = 1 +6(x +1)

  x = 14 . . . . . . . add 7-6x

 2x = 28 = sum of those numbers

__

The two numbers are 13 and 15.

The equation of each line in slope intercept form y = 2x + 3,x = 4

The equation of a line in slope-intercept form (y = mx + b), the slope (m) and the y-intercept (b). The slope-intercept form is a convenient way to express a linear equation.

Equation of a line with slope m and y-intercept b:

y = mx + b

Equation of a vertical line:

For a vertical line with x = c, where c is a constant, the slope is undefined (since the line is vertical) and the equation becomes:

x = c

An example for each case:

Example with given slope and y-intercept:

Slope (m) = 2

y-intercept (b) = 3

Equation: y = 2x + 3

Example with a vertical line:

For a vertical line passing through x = 4:

Equation: x = 4

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Answer:

y=mx+b

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first one is equal to.  203/203 is equal to 1.  1 times any number is itself.

The second on is less than.  9/37 is a proper fraction and when a number is multiplied by a proper fraction, it gets smaller.

The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.

The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.

The conversion factor from inches to meters is 0.0254 meters per inch.

Width in meters = 14.60 inches * 0.0254 meters/inch

Height in meters = 10.95 inches * 0.0254 meters/inch

Area = Width in meters * Height in meters

We calculate the area:

Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters

Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters

Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters

Now, we determine the number of significant figures.

The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.

Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.

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Answer:

part A: the warmer the city temp was the more lemonade that was sold so a hotter day will sell more lemonade

part B: i used points 40,8 and 90,20 and got m= 25/6 then i did y=mx+b

90=25/6(1)+b

90/1=25/6+b

25/6   25/6

and then B= 21.6

Step-by-step explanation: im not sure if i did it right so i would check i havent done this since like the 6th grade like 4 years or so ago lol

The approximate mean of the assembly volume is 3144.52 cubic units, and the approximate variance is 190.91 cubic units squared.

The volume of the assembly can be calculated as the sum of the volume of the cube and the volume of the cylinder. The volume of the cube is given by length times width times height, while the volume of the cylinder is given by pi times the radius squared times the height.

The mean of the assembly volume can be calculated by taking the expected value of the sum of the individual components, while the variance of the assembly volume can be calculated by summing the variances of the individual components.

Using the given mean and variance values for each variable and the formulas for the volumes of the cube and cylinder, we can calculate an approximate mean and variance for the assembly volume.

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To compare which school has a greater fraction of students in band or orchestra, we need to find the equivalent fractions for each school.

The fraction of students in band or orchestra at Coleman School is 3/7.To find an equivalent fraction for Tompkins School, we need to find a denominator that is the same as 7.To do that, we can multiply the denominator of 11 by 7, which gives us 77.

Next, we need to figure out what we multiplied the denominator by, which was 7, so we need to multiply the numerator by the same number. 5 x 7 = 35. So the equivalent fraction for Tompkins School is 35/77.Now that we have equivalent fractions for each school, we can compare them.

3/7 is equivalent to 33.3/77.35/77 is equivalent to 45.5/100.Since 45.5 is greater than 33.3, we can conclude that a greater fraction of students at Tompkins School are in band or orchestra than at Coleman School.

Therefore, the answer to this question is "At Tompkins School, a greater fraction of students are in band or orchestra than at Coleman School."

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9514 1404 393

Answer:

  C  none of the above

Step-by-step explanation:

We can simply drop the parentheses and collect terms.

  2r +(t +r) = 2r + t + r = (2r +r) +t

  = 3r +t

Given:

a.) A plot of land for sale has a width of x ft. and a length that is 8 ft. less than its width.

b.) A farmer will only purchase the land if it measures 240 ft.

From the given description of the measurement of the land, we generate the following equations:

Width = w

Length = w - 8

Area of the Land = 240 ft.^2

Area = Width x Length

240 = (w)(w - 8)

240 = w^2 - 8w

w^2 - 8w - 240 = 0

Question 1: Create an equation in terms of w that models this situation.​

Answer: 240 = w^2 - 8w

Factoring out 240 = w^2 - 8w, we get:

240 = w^2 - 8w

w^2 - 8w - 240 = 0

w^2 - 8w - 240 = 0 → (w - 20)(w + 12) = 0

First possible measure of the width,

w - 20 = 0

w = 20 ft.

Second possible measure of the width,

w + 12 = 0

w = -12 ft.

A dimension must never be a negative value, therefore, the width must be equal to 20 ft.

Let's determine the length,

Length = w - 8

= 20 - 8

Length = 12 ft.

Summary:

The equation that models the situation: 240 = w^2 - 8w or w^2 - 8w = 240

The measure of the length = 12 ft.

The measure of the width = 20 ft.

Step-by-step explanation:

basically what + 4 will get you 27 I think

Answer:

x=11

Step-by-step explanation:

The standard form of the Polynomial is \(x^4\) ( x³ -13x² + 145x /4 - 5/4) = 0.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

given:

The zeroes are 5/2 (multiplicity 2), 3 (multiplicity 1) and 0 (multiplicity 4.)

So, the standard form is

(x- 5/2)² (x-3) \(x^4\) = 0

(x² + 25/4 - 10x) (x-3) \(x^4\) = 0

(x³ + 25x /4 - 10x² - 3x² -5/4 + 30x) \(x^4\) = 0

\(x^4\) ( x³ -13x² + 145x /4 - 5/4) = 0

Thus, the Standard form

\(x^4\) ( x³ -13x² + 145x /4 - 5/4) = 0

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True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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The arc length of the circle will be 0.35 units.

Using the formula Length of an Arc = r x θ, where is in radians, one can determine the arc length of a circle given its radius and central angle. Arc length is equal to Arc = θ × (π/180) × r, where r is the radius in degrees.

Given that a circle has a radius of 3. An Arc in this circle has a central angle of 20 degrees.

The length of the arc of the circle will be calculated as:-

Arc = θ × (π/180) × r

Arc = 20 x  (π/180) × 3

Arc = 0.35 units

Therefore, the arc length of the circle will be 0.35 units.

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The x-intercepts for the expression which is used by Jen and her friends to represent the height of the arch, in inches, at any value of x along the arch are 8,0) and (-3,0).

The factor of a quadratic is the terms in linear form, which are when multiplied together, give the original quadratic equation as a result.

Jen and her friends need to consider the robot’s height and its width at its base. The robot must be short enough and narrow enough to navigate through several arches along the obstacle course.

The expression to represent the height of the arch, in inches, at any value of x along the arch:

\(-x^2 + 5x + 24.\)

Factorize this expression by equating it to zero and changing its sign,

\(\begin{aligned}-x^2 + 5x + 24=0\\x^2 - 5x - 24=0\\x^2 - 8x +3x- 24=0\\x(x - 8)+3(x - 8)=0\\(x-8)(x+3)=0\\x=8,-3\end\)

Thus, the x intercept of the equation is (8,0) and (-3,0)

Hence, the x-intercepts for the expression which is used by Jen and her friends to represent the height of the arch, in inches, at any value of x along the arch are 8,0) and (-3,0).

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Answer: x = 8,0 and x = -3,0

Step-by-step explanation:

The answer is:

\(\large\textbf{They aren't equivalent.}}\)

In-depth explanation:

To determine the answer to this problem, we will use one of the exponent properties:

\(\sf{x^{-m}=\dfrac{1}{x^m}}\)

And

\(\sf{\dfrac{1}{x^{-m}}=x^m}\)

Now we apply this to the problem.

What is 4⁻³ equal to? Well according to the property, it's equal to:

\(\sf{4^{-3}=\dfrac{1}{4^3}}\)

And this question asks us if 4⁻³ is the same as 1/4⁻3.

Well according to the calculations performed above, they're not equivalent.

\(\qquad\qquad\huge\underline{{\sf Answer}}♨\)

Let's solve ~

Perimeter of square is :

\(\qquad \sf  \dashrightarrow \:4 \times side \: length\)

so, we can take side length as a, and solve for a ~

\(\qquad \sf  \dashrightarrow \:4a = 60\)

\(\qquad \sf  \dashrightarrow \:a = 60 \div 4\)

\(\qquad \sf  \dashrightarrow \:a = 15\)

Now, since we know the side length. let's find Area of square :

\(\qquad \sf  \dashrightarrow \: {15}^{2} \)

\(\qquad \sf  \dashrightarrow \:area = 225 \: m {}^{2} \)

To find a plane containing the point (-8, 2, 7) and the line of intersection of the planes 3x + 2y + 4z = -1 and -4x + 4y - 6z = 56, we can use the cross product of the normal vectors of the given planes.

Given two planes, we first find their normal vectors. The normal vector of a plane with equation Ax + By + Cz = D is (A, B, C). For the first plane, 3x + 2y + 4z = -1, the normal vector is (3, 2, 4), and for the second plane, -4x + 4y - 6z = 56, the normal vector is (-4, 4, -6).

Next, we take the cross product of the normal vectors to obtain a vector perpendicular to both planes. The cross product of two vectors, (a, b, c) and (d, e, f), is given by the formula. Performing the cross product of (3, 2, 4) and (-4, 4, -6), we get (-8, -10, -4).

Now, we have a direction vector for the line of intersection of the given planes. We can use this direction vector along with the given point (-8, 2, 7) to define a new plane. The equation of a plane can be written as ax + by + cz = d, where (a, b, c) is the normal vector and (x, y, z) is a point on the plane. Substituting (-8, 2, 7) and (-8, -10, -4) into the equation, we get -8x - 10y - 4z = -96.

Therefore, the plane containing the point (-8, 2, 7) and the line of intersection of the planes 3x + 2y + 4z = -1 and -4x + 4y - 6z = 56 is -8x - 10y - 4z = -96.

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The critical value for a 98% confidence interval with a sample size of n=30 and known standard deviation  is 2.756.

When constructing a confidence interval, the critical value represents the number of standard errors above and below the sample mean that encompasses the specified confidence level. A larger confidence level requires a larger critical value, and a larger sample size will generally result in a smaller critical value, assuming that the population standard deviation is known. In this case, with a sample size of 30 and a 98% confidence level, the critical value is calculated to be 2.756, rounded to 3 decimal places.

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Answer:

b

Step-by-step explanation:

Answer:

i am pretty sure the answer is d

Step-by-step explanation:

let me know if this is wrong

Answer:

\(\textsf{1)} \quad y=x+\dfrac{17}{4}\)

\(\textsf{2)} \quad y=2x+4\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.

At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(y=4+2x-x^2\)

Differentiate the given function:

\(\implies \dfrac{\text{d}y}{\text{d}x}=2-2x\)

If the tangent to the parabola forms an angle of 45° with the negative direction of the x-axis, then the gradient of the tangent is 1.

Set the differentiated function to 1 to find the x-value of the point where the gradient of the tangent is 1:

\(\implies \dfrac{\text{d}y}{\text{d}x}=1\)

\(\implies 2-2x=1\)

\(\implies -2x=-1\)

\(\implies x=\dfrac{1}{2}\)

Substitute x = 1/2 into the given function to find the y-value of the point:

\(\implies y=4+2\left(\dfrac{1}{2}\right)-\left(\dfrac{1}{2}\right)^2=\dfrac{19}{4}\)

Therefore, the point at which the tangent of the parabola forms an angle of 45° with the negative direction of the x-axis is:

Substitute the found point and slope into the point-slope formula to create an equation of the tangent:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-\dfrac{19}{4}=1\left(x-\dfrac{1}{2}\right)\)

\(\implies y=x+\dfrac{17}{4}\)

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

Given function:

\(y=4+2x-x^2\)

Differentiate the given function:

\(\implies \dfrac{\text{d}y}{\text{d}x}=2-2x\)

If the tangent to the parabola is parallel to the line y = 2x - 4 then the gradient of the tangent is 2 (since parallel lines have the same gradient).

Set the differentiated function to 2 to find the x-value of the point where the gradient of the tangent is 2:

\(\implies \dfrac{\text{d}y}{\text{d}x}=2\)

\(\implies 2-2x=2\)

\(\implies -2x=0\)

\(\implies x=0\)

Substitute x = 0 into the given function to find the y-value of the point:

\(\implies y=4+2\left(0\right)-\left(0\right)^2=4\)

Therefore, the point at which the tangent of the parabola is parallel to the line y = 2x - 4 is:

Substitute the found point and slope into the point-slope formula to create an equation of the tangent:

\(\implies y-y_1=m(x-x_1)\)

\(\implies y-4=2\left(x-0\right)\)

\(\implies y=2x+4\)

Work Shown:

y = 15.6 - 3.8x

y = 15.6 - 3.8*3

y = 4.2

Marina's gross earnings for the week of 5/12 were $517.

Gross earnings refers to total amount of income earned over a period of time by an individual or household or a company.

Data given:

Marina's base salary = $487 per week

Commission $15,000 up to $25,000 = 0.5%

Commission rate on sales in excess of $25,000 = 1.4%

Sales for the week of 5/12 = $21,000

Commission on sales above $15,000 up to $25,000:

= 0.5% * ($21,000 - $15,000)

= 0.005 * $6,000

= $30

Commission on sales in excess of $25,000:

= 1.4% * ($21,000 - $25,000)

= 0.014 * $0 as no sales

= $0

Total earnings for the week of 5/12:

= Base salary + Commission

= $487 + $30 + $0

= $517.

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