Please simplify step by step

6ab2−4ab2a−ab2​

Answer:

∴Given Δ ABC is not a right-angle triangle

a= AB = √45 = 3√5

b = BC = 12

c = AC = √45 = 3√5

Step-by-step explanation:

Given vertices are A(3,3) and B(6,9)

           AB =

Given vertices are  B(6,9) and C( 6,-3)

            =  

   BC = 12

Given vertices are  A(3,3) and C( 6,-3)

AC² = AB²+BC²

45  = 45+144

45  ≠ 189

∴Given Δ ABC is not a right angle triangle

Step-by-step explanation:

The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

\(\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}\)

Step 2: Replace the value of "y" in the equation (2).

\(35 x=-0.05(x-400)^{2}+9492\)

Step 3: Make the equation above simpler.

\(35 x=-0.05 x^{2}-8000+40 x+9492\)

Step 4: Write the preceding equation in generalised quadratic form.

\(0.05 x^{2}-5 x-1492=0\)

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

The Gauss-Markov theorem states that under the assumptions of the classical linear regression model, the ordinary least squares (OLS) estimator is the Best Linear Unbiased Estimator (BLUE) of the regression coefficients.

To prove this, we need to show that the OLS estimator is unbiased, has minimum variance, and is linear.

Unbiasedness: The OLS estimator is unbiased if its expected value is equal to the true parameter values. In the classical linear regression model, the OLS estimator cap on β is given by cap on β = (X^T X)^(-1) X^T Y, where X is the design matrix and Y is the vector of observed responses. Under the assumptions of the classical linear regression model, the OLS estimator is unbiased.

Minimum Variance: The OLS estimator has the minimum variance among all linear unbiased estimators. This means that for any other linear unbiased estimator, the variance of that estimator is greater than or equal to the variance of the OLS estimator. The proof of this property relies on matrix algebra and the properties of the Gauss-Markov theorem.

Linearity: The OLS estimator is a linear function of the observed responses Y. It can be written as cap on β = c^T Y, where c is a vector of constants. This shows that the OLS estimator is a linear combination of the observed responses.

Therefore, under the assumptions of the classical linear regression model, the OLS estimator satisfies the properties of unbiasedness, minimum variance, and linearity, making it the Best Linear Unbiased Estimator (BLUE) of the regression coefficients.

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The equation in point-slope form is y - 5 = (5/3)(x + 5). The general form of the equation is 5x - 3y + 40 = 0.

To find the equation of a line parallel to the given line and passing through the point (-5,5), we can use the point-slope form of a linear equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. First, we need to find the slope of the given line, and then we can substitute the values into the point-slope form to obtain the equation. Additionally, we can convert the equation to the general form, which is Ax + By + C = 0, by rearranging the terms.

The given line has the equation 5x - 3y - 2 = 0. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m represents the slope. Rearranging the equation gives us:

-3y = -5x + 2

y = (5/3)x - 2/3

From the equation, we can see that the slope of the given line is 5/3. Since the line we want to find is parallel to this line, it will have the same slope.

Now, using the point-slope form with the point (-5,5) and the slope 5/3, we can write the equation:

y - 5 = (5/3)(x - (-5))

y - 5 = (5/3)(x + 5)

This is the equation of the line in point-slope form.

To convert it to general form, we can multiply through by 3 to eliminate the fraction:

3y - 15 = 5x + 25

5x - 3y + 40 = 0

This is the equation of the line in general form.

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The method of documentation that describes the setting up of squares of known dimension over the entire pattern is known as grid method.

Grid method is a method of documentation that involves the setting up of squares of known dimensions over the entire pattern to document a site. This method is commonly used in archaeological surveys and historical preservation.

Therefore, grid method is a simple and effective way of recording data, and it is still widely used in the field of archaeology today.

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Answer:

The answer would be 0

Step-by-step explanation:

Because halfway of 4, -2 is 0

Answer:

You would want to put this in point-slope form. your answer would be

y+2=1/2(x-4). You can also put this is standard form which would be, y=1/2x-4.

I hope this helps!

As a result, the slope-intercept form equation for the line through points (5, 21) and (11, 3) is:

y = -3x + 36

Therefore, the equation of the line through (4, 8) and (12, 20) in slope-intercept form is:

y = (3/2)x + 2

The slope of the line must first be determined using the following formula to determine the equation of a line through two points in slope-intercept form:

slope\((m) =\frac {(y2 - y1)}{(x2 - x1)}\)

where the coordinates for two points are (x1, y1) and (x2, y2).

The line's slope-intercept form is thus applicable, and it is as follows:

y = mx + b

where b is the y-intercept and m is the slope that we just discovered.

We possess

slope \((m) = \frac{(3-21)}{ (11-5)}\),

m = -3

So, using one of our points, we can determine b:

y-21=-3(x-21)

As a result, the slope-intercept form equation for the line through points (5, 21) and (11, 3) is:

y = -3x + 36

9) (4, 8) and (12, 20)

The slope is

\(m= \frac{20-8}{12-4}\\m=\frac{12}{8}=\frac{3}{2}\)

equation is (y-8)=1.5(x-4)

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Answer: Zahid obtained 170 marks.

Step-by-step explanation:

Let's start with the basic rules of the question.

We know that for each question answered correctly, 5 marks will be given. And for each incorrect answer, 3 marks will be deducted. Now the problem says that Zahid's marks have been deducted by 18. There are 3 marks deducted for each wrong answer so we'll divide 18 by 3, which gives us 6. Zahid got 6 questions wrong. However, there are 40 questions in the exam, so if we assume that the only ones he answered incorrectly are the 6 questions, then we should subtract 6 from 40. This leaves us with only the correct answers left which is 34. Now again, we know that for each correct answer 5 marks will be given. Assuming that Zahid answered the rest of the questions correctly, we should multiply 34 by 5, which gives us 170.

In numbers your workings might look like this:

18 ÷ 3 = 6

40 - 6 = 34

34 × 5 = 170

I hope this helped you answer your problem. Please let me know if you need any further explanation :)

If r is < 0, then lambda must be:  Less than 0, Less than 1, Greater than 1  and Greater than 0. The correct answers are: A), B), C), and D).

Recall that the exponential growth or decay model is given by the function:

\(y = y0 * e^(rt)\)

where y0 is the initial value of the function, r is the rate of change (growth or decay), t is the time, and e is the mathematical constant approximately equal to 2.71828.

If r < 0, then the function represents exponential decay, and we have:

\(y = y0 * e^(rt)\)

y/y0 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(y/y0) = rt

r = (1/t) * ln(y/y0)

Since ln(y/y0) is the natural logarithm of a ratio, it can take any real value. Therefore, r can take any negative value, and there is no restriction on the value of lambda (which is\(e^r\)).

So, the correct answers are: A), B), C), and D).

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Answer:

The slope of the model is \(m = 2\,\frac{USD}{yr}\).

The value of the slope indicates that the average cost of a hair cut is increased by 2 US dollars each year.

Step-by-step explanation:

We have to notice that given function is a linear function, that is, a first order polynomial, whose standard form is described below:

\(y =m\cdot x + b\)

Where:

\(m\) - Slope, dimensionless.

\(x\) - Independent variable, dimensionless.

\(y\) - Dependent variable, dimensionless.

\(b\) - y-Intercept, dimensionless.

In this case, we use the linear function \(y = 2\cdot x + 28\), where \(x\) is the time after 2000, measured in years, and \(y\) is the average cost of a hair cut. The slope of the model is \(m = 2\,\frac{USD}{yr}\).

The value of the slope indicates that the average cost of a hair cut is increased by 2 US dollars each year.

Answer:

Let s be the speed of the plane. Then s - 100 is the speed of the car.

640/s = 240/(s - 100)

640(s - 100) = 240s

8(s - 100) = 3s

8s - 800 = 3s

5s = 800, so s = 160 mph

The speed of the plane is 160 mph, and the speed of the car is 60 mph.

The correlation between variables x and y is 0.50 . The true option is option (c) .

that's the regression coefficient is positive for given bivariata.

Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The

sample correlation coefficient r quantifies the strength of the relationship.

Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.

Here:

Pearson's correlation coefficient is denoted by "r" and is

r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)

We have given that correlation between x and y is 0.50.

cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2

=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)

Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.

Symbolically it can be expressed as:

bₓᵧ= r σ ₓ /σ ᵧ

where x and y are correlated

σ ₓ --> standard deviation of X

σᵧ ---> standard deviation of y

We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.

Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.

Hence, Regression cofficient is positive.

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The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459

The acceleration vector can be found from the following formula:

\(a(t) = r''(t) = (-3,-10t,-8t3).\)

To find the tangential component of the acceleration vector, we first need the velocity vector v(t).

\(v(t) = r'(t) = (-3,-10t,-8t3) .\)

Next, we need to normalize the velocity vector using the following formula:

\(T(t) = v(t) / ||v(t)||,\)

Where ||v(t)|| is the magnitude of the velocity vector.

\((1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .\)

Then, the tangential component of a(1) is:

\(aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.\)

To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.

\(aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)}  = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}\)

Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:

\(aT(1) = 233/3\) and \(aN(1) = (1/3)\sqrt{10459}\)

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Answer:

w>6

Step-by-step explanation:

1.) you will distribute the -2 into the parentheses.

-2w-8+9<-11

2.) combine like terms

-2w+1<-11

3.) isolate the variable

-2w<-12

4.) continue to isolate the variable

w>6

(the sign will flip because if the negative devision)

Answer:

72.3sqmm

Step-by-step explanation:

To solve this you need to split the arrow into two shapes. One rectangle and one triangle. First you want to solve the area of the rectangle or the triangle and then vice versa. When you get the area for both add them together, and then round to the nearest tenth.

Since the height of the triangle is currently unknown we must take the total length of the arrow and subtract it by the rectangle's portion of the length, and then that will give us the height of the triangle. After that we take the height, multiply it by the base of 8.4, and finally divide it by 2.

Now that we have both areas we simply add both, and the round.

The height is changing by 0.5 units per minute as evident in the given table.

It follows from the task content that the table given indicates that at, 0min, the height was 150.

While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.

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Answer:

1.6 mph

Step-by-step explanation:

I did the math

Answer:

1. 16 miles per gallon

2. 560 miles

Step-by-step explanation:

400miles = 25 gallons

x miles = 1 gallon

x = (400*1)/25

x = 16 miles per gallon

35 gallon = 35*16 = 560 miles

a. The probability P(X < 10) is U(0, 50) is 0.20.

b. The probability P(X > 595) is U(0, 1,000) is 0.405.

c. The probability P(21 < X < 49) is U(19, 68) is 0.4762.

a. For a uniform continuous distribution U(0, 50), the probability of an event X < 10 can be calculated by dividing the length of the interval [0, 10] by the length of the entire interval [0, 50]. Since the lengths of both intervals are equal, the probability is 10/50 = 0.20.

b. Similarly, for a uniform continuous distribution U(0, 1,000), the probability of an event X > 595 can be calculated by dividing the length of the interval [595, 1,000] by the length of the entire interval [0, 1,000]. The length of the interval [595, 1,000] is 1,000 - 595 = 405, and the length of the entire interval is 1,000 - 0 = 1,000. Thus, the probability is 405/1,000 = 0.405.

c. For a uniform continuous distribution U(19, 68), the probability of an event 21 < X < 49 can be calculated by dividing the length of the interval [21, 49] by the length of the entire interval [19, 68]. The length of the interval [21, 49] is 49 - 21 = 28, and the length of the entire interval is 68 - 19 = 49. Therefore, the probability is 28/49 = 0.5714.

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The correct value of point of tangency is R and Z.

The point of tangency refers to the point where a curve and a tangent line meet and have a common point. In geometry, a tangent line touches a curve at only one point and has the same slope as the curve at that point. The point of tangency is significant because it represents the precise intersection of the curve and the tangent line.

At the point of tangency, the tangent line acts as a local approximation of the curve's behavior. It provides an instantaneous measure of the curve's slope and direction at that specific point. This concept is widely used in calculus and differential geometry to analyze the properties and behavior of curves and functions.

The point of tangency plays a crucial role in determining the derivative of a function at a particular point, as it allows for the calculation of the slope of the curve at that point. It is an essential concept in understanding the behavior and characteristics of curves and functions in various mathematical and scientific fields.

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Answer:

Step-by-step explanation: okay so, all you have to do is put for example, 4 quarters and 3 nickels. Nickels are 5 cents and quarters are 25. 25x4 is 100 which is a dollar. 5x3 is 15 which is 15 cents. Simple right? Now for this problem we do the same thing. 13 quarters is 13x25 which is 325, which is 3.25 cents. Now it says 3 nickels, which is 3x15, which is also 15 cents. Then you add that together and get $3.40 dollars. So the answer is C.

The given statement is true

One benefit of statistical sampling compared to non-statistical sampling is that statistical sampling provides mathematically-sound methods to control for sampling risk. Statistical sampling techniques allow for the application of probability theory to estimate and control sampling errors and uncertainties.

By using statistical methods, one can determine the appropriate sample size, select samples randomly or systematically, and apply inferential statistics to make reliable inferences about the population being sampled. Non-statistical sampling, on the other hand, does not provide the same level of rigor in terms of controlling for sampling risk and may not yield reliable and representative results.

Therefore, given statement is true.

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Answer:

irrational

Step-by-step explanation:

Answer:

Irrational.

Step-by-step explanation:

When we simplify √42, we get:

And 6.48074069841 is an irrational number.

Hoped this helped.

\(GeniusUser\)

Explanation:

Plot all of the data points on the same xy grid as shown below.

I used GeoGebra to make the diagram.

The points seem to be randomly scattered about without any apparent pattern (though there might be some symmetry going on). The data does not seem to be periodic.

Periodic data repeats itself at some point in time, for example like a waveform pattern, which unfortunately these data points don't reflect.

Answer:

300.104

Step-by-step explanation:

let me know if i am right or wrong i hope you have a good day :)

Answer:

the value of the expression above in standard form is 1.2x10^-1

Answer:

y=1/2x-5

Step-by-step explanation:

From the picture you can see that (0, -5) is a point on the function and that (2, -4) is another point. Using these you can find the slope of the function with the equation

\((y_{2} -y_{1})/(x_{2}-x_{1} )\)

We can substitute in the points so it looks like

\((-4--5)/(2-0)\)  or  \(1/2\) which is the slope of the function

Now, since the y-intercept is (0, -5) on the graph, the b part in the slope-intercept form of the equation would be -5, leaving us with the equation y=1/2x-5

Answer:

-8x^2+2x+5

Step-by-step explanation:

Distributive Property

Answer: It's a B answer.

Show your work here:

In an ordered pair the first coordinate is x the coordinate, and the second coordinate corresponds to the y coordinate.

Then we must substitute the given value of x in the equation and verify that we get in return the defined value for y.

the options are (-2,4)

in this one x=-2, and y=4, so let's confirm:

y=-3x-4

y=-3(-2)-4

y=-6-4

y=2

this is not a solution since the y values are not the same.

in this one x=-3 and y=5, let's also confirm:

y=-3(-3)-4

y=9-4

y=5

in this one the values for y are equal, this is a solution for the equation.

so give me a brainlest!