what is the midpoint of (-3, -5) and (5, 3)

In the context of the least squares procedure, any data point that does not fall on the regression line is the result of unexplained variance. This is represented by option (b).

Unexplained variance refers to the portion of the total variance in the dependent variable that is not accounted for by the regression model. The regression line represents the best-fitting line that minimizes the sum of squared differences between the observed data points and the predicted values. However, due to various factors such as measurement errors, random fluctuations, or unobserved variables, some data points may deviate from the regression line.

These deviations are considered as unexplained variance because they cannot be attributed to the relationship between the independent and dependent variables captured by the regression model. They represent the variability that remains after accounting for the systematic relationship estimated by the regression line.

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Answer:

4

Step-by-step explanation:

\(\sqrt{(5)^{2}-(3)^{2} }=4\)

Given:

The objective is to find the probability of drawing a face card from a deck of card.

The number of cards in a deck is, N = 52.

The number of face cards in a deck is, n(E) = 12.

Then, the required probability can be calculatad as,

Hence, option (A) is the correct answer.

The calculated volume of the solid figure is 64 cubic cm

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

Dimensions = 4 cm by 4 cm by 4 cm

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

Volume = Base area * Height

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

Volume = 4 *4 * 4

Evaluate

Volume = 64

Hence, the volume of the solid figure is 64 cubic cm

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Answer: 25 nickels

Step-by-step explanation:

\(\text{Given that,}\\\\ (x_1,y_1) = (-7,-4) ~~ \text{and slope}~ m = 3\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y +4 = 3(x+7)~~~~~;[\text{Point-slope form.}]\\\\\implies y = 3x +21 -4\\\\\implies y = 3x +17~~~~~~~~~~~;[\text{Slope-intercept form.}]\\\\\text{Hence the answers are A and F.}\)

Answer:

\(\boxed{47.089 \;meters} \\\\\)

Step-by-step explanation:

For any function f(x), the maximum or minimum value can be determined by 1. Finding the first derivative f(x) with respect to x i.e. f'(x)

2. Setting this first derivative to 0, solving for x

3. Substituting for x in the original function to get the maximum/minimum value

\(\textrm{The equation for the function f(t) is }\\f(t) = -4.9t^2 + 20.58t + 25.48\\\\\)

\(\textrm{The first derivative of this function with respect to t is }\\\\f'(t) = - 2\cdot 49t + 20.58\\= -9.8t + 25.48\\\\\)

\(\textrm{Setting this first derivative equal to 0 gives:}\\\\-9.8t + 20.58 = 0\\\\-9.8t = -20.58 \;\;\;\;\;\textrm{(Subtracting 20.58 from both sides)}\\\\9.8t = 20.58 \;\;\;\;\;\; \textrm{ (Multiplying both sides by -1)}\)

\(\textrm{Therefore }\\\\t = \dfrac{20.58}{9.8}\\\\t= 2.1 \textrm{ seconds}\)

\(\textrm{Therefore, at = 2.1 seconds, the ball will reach its maximum height.}\)

To find what this maximum height is, substitute t = 2.1 in the original equation and solve for h(t)

\(h(t)\;at\;t=2.1 \\h(2.1) = 4.9\cdot \:2.1^2+20.58\cdot \:2.1+25.48=47.089 \;meters\\\\\)

\(\textrm{ The maximum height the ball achieves before landing is } \boxed{47.089 \;meters} \\\\\)

\(\textrm {This occurs 2.1 seconds after launch }\)

Answer:

Below.

Step-by-step explanation:

This area = circumference of the base x height

= 2 * pi * 8 * 15

= 754.29 cm^2.

Answer:

The answer is 754.29cm^2

Step-by-step explanation:

radius= 8 cm

height= 15 cm

This is an area question

The formula to calculate the curved surface area will be,:

2 pile r  times h which will be = to: 2 pile r h

2 x 22/7/3.14 x the radius which is 8 x height which is 15.

2 x 22/7 x 8 x 15 =

754.29 cm^2.

Okay.

The probability that a srs of 20 students will spend an average of between 600 and 700 dollars is 0.92081.

We need to find the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars.

To solve this problem, we will use the central limit theorem, which states that the sampling distribution of the sample means will be approximately normally distributed with a mean of μ and a standard deviation of σ/√(n), where n is the sample size.

Thus, the mean of the sampling distribution is μ = 650 and the standard deviation is σ/sqrt(n) = 120/√(20) = 26.83.

We need to find the probability that the sample mean falls between 600 and 700 dollars. Let x be the sample mean. Then:

Z1 = (600 - μ) / (σ / √(n)) = (600 - 650) / (120 / √t(20)) = -1.77

Z2 = (700 - μ) / (σ / √(n)) = (700 - 650) / (120 / √(20)) = 1.77

Using a standard normal distribution table or calculator, we can find the area under the standard normal distribution curve between these two Z-scores as:

P(-1.77 < Z < 1.77) = 0.9208

Therefore, the probability that a simple random sample of 20 students will spend an average of between 600 and 700 dollars is 0.9208, or approximately 0.92081 when rounded to five decimal places.

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Answer:

-0.5

Step-by-step explanation:

Answer:

-0.5

Step-by-step explanation:

I think this is the answer again im very sorry if it isnt

The two possible values for angle H in triangle GHI are approximately 93.1 degrees and 273.1 degrees, rounded to the nearest tenth of a degree

To find the possible values of angle H in triangle GHI, we can use the law of cosines.

Let's label angle H as x. Then, we can use the law of cosines to solve for x:

               cos(x) = (9.3² + 9.6² - 2(9.3)(9.6)cos(109))/ (2 * 9.3 * 9.6)

Simplifying this equation, we get:

                cos(x) = -0.0588

To solve for x, we can take the inverse cosine of both sides:

                       x = cos⁻ ¹ (-0.0588)

Using a calculator, we can find that x is approximately 93.1 degrees.

However, there is another possible value for angle H. Since cosine is negative in the second and third quadrants,

We can add 180 degrees to our previous result to find the second possible value for angle H:

                     x = 93.1 + 180 = 273.1 degrees

So the two possible values for angle H are approximately 93.1 degrees and 273.1 degrees, rounded to the nearest tenth of a degree.

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The solution to the equation log base 16 x + log base 4 x + log base 2 = 7 is x = 256.

To solve the equation:

log base 16 x + log base 4 x + log base 2 = 7

We can use the properties of logarithms to combine the terms on the left-hand side into a single logarithm.

log base 16 x can be rewritten as log base 2 (x) / log base 2 (16) = log base 2 (x) / 4

log base 4 x can be rewritten as log base 2 (x) / log base 2 (4) = log base 2 (x) / 2

Therefore, the original equation becomes:

log base 2 (x) / 4 + log base 2 (x) / 2 + log base 2 (2) = 7

Simplifying, we get:

log base 2 (x) × (1/4 + 1/2) + 1 = 7

log base 2 (x) × 3/4 + 1 = 7

log base 2 (x) × 3/4 = 6

log base 2 (x) = 8

Now, we can use the definition of logarithms to rewrite the equation as an exponential equation:

\(2^{8}\) = x

x = 256

Therefore, the solution to the equation log base 16 x + log base 4 x + log base 2 = 7 is x = 256.

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The linear function for this problem is defined as follows:

y = x + 50.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph touches the y-axis at y = 50, hence the intercept b is given as follows:

b = 50.

When x increases by 10, y also increases by 10, hence the slope m is given as follows:

m = 10/10

m = 1.

Hence the function is given as follows:

y = x + 50.

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Answer:

cross out 4

Step-by-step explanation:

explanation

The multiple linear regression equation corresponding to macrohard's analysis is y = b0 + b1 * x1 + b2 * x2 + e.

It is given that Macrohard conducted a multiple linear regression analysis to predict the loading time (y) in milliseconds for Macrohard workstation files based on the file size (x1) in kilobytes and the processor speed (x2) in megahertz. The analysis was based on a random sample of 400 Macrohard workstation users, with file sizes ranging from 110 to 5,000 kilobytes and processor speeds ranging from 500 to 4,000 megahertz.

The multiple linear regression equation corresponding to Macrohard's analysis can be written as:

y = b0 + b1 * x1 + b2 * x2 + e

Where:
y is the loading time in milliseconds
x1 is the file size in kilobytes
x2 is the processor speed in megahertz
b0, b1, and b2 are the regression coefficients
e is the error term

These coefficients are estimated based on the sample data and represent the expected change in y for each unit increase in x1 and x2, holding all other variables constant. This equation allows Macrohard to estimate the loading time of a workstation file based on its size and the processor speed. To make predictions using this equation, simply plug in the values for x1 (file size) and x2 (processor speed) and solve for y (loading time).

However, it is important to note that the accuracy of these predictions may be limited by the variability of the data and the assumptions underlying the regression model. Additionally, there may be other factors that influence loading time that were not included in the analysis.

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The inverse of the given matrix, if it exists, is (1/(a^2 + b^2)) times the matrix [a b; -b a].

To find the inverse of a 2x2 matrix [a -b; b a], we can use the formula for the inverse of a 2x2 matrix. The formula states that if the determinant of the matrix is non-zero, then the inverse exists, and it can be obtained by taking the reciprocal of the determinant and multiplying it by the adjugate of the matrix.

In this case, the determinant of the given matrix is a^2 + b^2. Since the determinant is non-zero for any non-zero values of a and b, the inverse exists.

The adjugate of the matrix [a -b; b a] is [a b; -b a].

Therefore, the inverse of the given matrix is (1/(a^2 + b^2)) times the matrix [a b; -b a].

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Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

see explanation

Step-by-step explanation:

from the diagram

DF = DE + EF , that is

4x + 2 = x + 7 + 7

4x + 2 = x + 14 ( subtract x from both sides )

3x + 2 = 14 ( subtract 2 from both sides )

3x = 12 ( divide both sides by 3 )

x = 4

Then

DE = x + 7 = 4 + 7 = 11

DF = 4x + 2 = 4(4) + 2 = 16 + 2 = 18

\( \huge \boxed { \sf Answer}\)

\( \cos(21°) = \frac{9}{y} \\ = > 0.9336 = \frac{9}{y} \\ = > \frac{y}{9} = 0.9 336\\ = > y = 9 \times 0.9336 \\ = > y = 8.4024 \\ = > y = 8.4\)

Hope you could understand.

If you have any query, feel free to ask.

The two missing reasons in the two column proof are:

∠3 ≅ ∠5 and ∠1 ≅ ∠4 ⇒ alternate interior angle theorem.

m∠1 = m∠4 and m∠3 = m∠5  ⇒  congruent angles have equal measures.

The two-column proof is defined as the method we use to present a logical argument using a table with two columns.

In Mathematics, congruent angles can be defined as a theorem that states that two (2) angles are congruent if the measure of their angles are equal.

This definitely let's us to know that, two (2) congruent angles would always have equal measures as depicted in triangle ABC with line DE;

m∠1 = m∠4 and m∠3 = m∠5

With the aid of the Alternate Interior Angles Theorem on triangle ABC and line DE, we can say that:

∠3 ≅ ∠5 and ∠1 ≅ ∠4

The complete two column proof is:

The statement to prove that the sum of the interior angles of ΔABC is 180° should be completed as follows;

Statements                                                        Reasons

Points A, B, and C form a triangle.        ⇒        Given

Let DE be a line passing through B and parallel to AC. ⇒ definition of parallel lines

∠3 ≅ ∠5 and ∠1 ≅ ∠4             ⇒    alternate interior angle theorem.

m∠1 = m∠4 and m∠3 = m∠5  ⇒    congruent angles have equal measures.

m∠4 + m∠2 + m∠5 = 180°    ⇒    angle addition and definition of a straight line

m∠1 + m∠2 + m∠3 = 180°      ⇒  substitution

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The required probability that the total number of spots showing is less than 7 is 9.26%

The probability of an event is found by considering all possibilities that follow the given condition. The probability value cannot exceed the interval [0,1].

Three six-sided dice are rolled at the same time.

It is asked to calculate the probability that the total number of spots showing is less than 7.

If the die is rolled, possible outcomes are as given below.

S: {1, 2, 3, 4, 5, 6}

Number of elements in sample space, n(S) = 6.

Probability of any specific outcome from S = 1/6

If the three dice are rolled together, the total number of elements in the sample space will be \((6^3)\)

Then, the probability of getting any of any specific outcome from this sample will be given by: \(\frac{1}{6^3} =\frac{1}{216}\)

Find the total possibilities for which the total of outcomes of all three dice is less than 7. It is possible when we get the following outcomes.

The minimum total that we get is 3 with outcomes (1,1,1) on three dice.

For a total of 3:

Possible outcomes: [1, 1, 1]

The number of possibilities \(A_1=1\)

For total 4:

Possible outcomes: [1,1,2], [1,2,1], [2, 1, 1]

Number of possibilities \(A_2=3\)

For a total of 5:

Possible outcomes:  [1,1,3], [1,3,1], [3, 1, 1],  [1,2,2], [2,2,1], [2, 1, 2]

The number of possibilities \(A_3=6\)

For a total of 6:

Possible outcomes :  [1,1,4], [1,4,1], [4, 1, 1],[1, 2, 3] ,[1,3,2],[2, 3, 1], [3,2,1], [3, 1, 2],[2,1,3], [2, ,2 ,2]

The number of possibilities : \(A_4=10\)

The number of possibilities for which the total number of spots showing is less than 7 is given by,

\(A_1+A_2+A_3+A_4\)

=> 1+ 3+ 6+ 10

=> 20

The probability that the total number of spots showing are less than 7 is calculated below.

P = 20/216

P = 0.0926

P = 9.26%

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The given question is incomplete, complete question is:

Explain how to solve this problem:

You have three six-sided dice. When all three dice are rolled at the same time, calculate the probability of the following outcomes:

a. The total number of spots showing is less than 7

Answer:

9

Step-by-step explanation:

9... if you do 24÷8/3 you will get 9

Answer:

ITS 9!!!!!!!!!!

Step-by-step explanation:

BRAINLIEST PLS

Answer:

Im not sure but i believe it is A. 5

Step-by-step explanation:

Hope this helps please mark brainlist if im right.

Answer:

B) A = 25π

Step-by-step explanation:

The area of a circle is calculated with the formula \(\pi * r^2\)

The radius is half of the diameter, which in this case is 10.

Plugging it in, you get \(5^2\pi\)

\(5^2 = 25\\\)

\(A = 25\pi\)

Proportional relationship for the given table is true and is define as

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

As given in the question,

Value of x and y in the given table are :

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

To check the proportional relationship there should exist constant of proportionality that ratio of corresponding y/x should be constant.

y / x for all the values of x and y:

First values:

y /x = 6.4 / 25.6

      = 0.25

Second values:

y/x = 18.2/ 72.8

    = 0.25

Third values :

y /x = 19.3/ 77.2

      = 0.25

0.25 is equivalent to One fourth ( 1/4).

Constant of proportionality exist = 0.25 or One fourth.

Therefore, in the table first option: yes, it is proportional because all y over x ratio are equivalent to one fourth is correct.

The complete question is:

Determine if the table how a proportional relationship.

x :  25. 6,  72. 8,  77. 2

y : 6. 4, 18. 2, 19. 3

Yes, it is proportional because all y over x ratio are equivalent to one fourth.

Yes, it is proportional because all y over x ratio are equivalent to one third.

No, it is not proportional because 25. 6 over 6. 4 doe not equal 18. 2 over 72. 8.

No, it is not proportional because 18. 2 over 72. 8 doe not equal 77. 2 over 19. 3

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Answer:

1.finite

2.infinite

.3.infinite

5.finite

6.infinite

9.finite

A) the three inequalities that must be satisfied are:

B) Graph shaded and satisfying all conditions is attached.

An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions.

It is most commonly used to compare the sizes of two numbers on a number line.

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Answer:

Her commission for item 1:

5% of 2,000 = 100

Her commission for item 2:

5% of 9,800 = 490

Total commission for each item;

Item 1 : 2,000

Item 2 : 9,800

In Option (c) we have functions f(x) = x⁵ and g(x) = 5x + 2, which satisfy the equation f o g = H(x) = (5x + 2)⁵.

Option (a) : To find functions f and g such that f o g = H, where H(x) = (5x + 2)⁵, we evaluate the composition f(g(x)) and equate it to H(x).

Let us substitute the given functions f(x) = (x-2)/5 and g(x) = \((x)^{1/5}\) into the composition:

f(g(x)) = f(\((x)^{1/5}\)) = (\((x)^{1/5}\) - 2)/5,

To simplify further, we substitute this expression into H(x) and check if they are equal:

(\((x)^{1/5}\) - 2)/5 ≠ (5x + 2)⁵

The given functions f(x) = (x-2)/5 and g(x) = \((x)^{1/5}\) do not satisfy the equation f o g = H.

Option (b) : We substitute the given functions f(x) = \((x)^{1/5}\) and g(x) = (x-2)/5 into the composition:

f(g(x)) = f((x-2)/5) = ((x-2)/5\()^{1/5}\)

Equating this expression to H(x), we have:

((x-2)/5\()^{1/5}\) ≠ (5x + 2)⁵

The given functions f(x) = \((x)^{1/5}\) and g(x) = (x-2)/5 do not satisfy the equation f o g = H.

Option (c) : Substituting f(x) = x⁵ and g(x) = 5x + 2 into composition:

f(g(x)) = f(5x + 2) = (5x + 2)⁵

We see that f(g(x)) matches H(x), so the functions f(x) = x⁵ and g(x) = 5x + 2 satisfy f o g = H.

Option (d) : We substitute f(x) = 5x + 2 and g(x) = x⁵ into composition:

f(g(x)) = f(x⁵) = 5(x⁵) + 2

This expression does not-match H(x), so the functions f(x) = 5x + 2 and g(x) = x⁵ do not satisfy f o g = H.

Therefore, the correct option is (c).

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The given question is incomplete, the complete question is

Find functions f and g so that f o g = H,

H(x) = (5x + 2)⁵,

(a) f(x) = (x-2)/5, g(x) = \((x)^{1/5}\),

(b) f(x) = \((x)^{1/5}\), g(x) = (x-2)/5,

(c) f(x) = x⁵, g(x) = 5x + 2,

(d) f(x) = 5x + 2, g(x) = x⁵.