Which of the following equations contains the point (8, 5) and is perpendicular to the line y = 2x − 3?

Recall that

Var[aX + bY] = a ² Var[X] + 2ab Cov[X, Y] + b ² Var[Y]

Then

Var[3X - 7Y] = 9 Var[X] - 42 Cov[X, Y] + 49 Var[Y]

Now, standard deviation = square root of variance, so

Var[3X - 7Y] = 9×6² - 42×2 + 49×8² =  3376

The general result is easy to prove: by definition,

Var[X] = E[(X - E[X])²] = E[X ²] - E[X]²

Cov[X, Y] = E[(X - E[X]) (Y - E[Y])] = E[XY] - E[X] E[Y]

Then

Var[aX + bY] = E[((aX + bY) - E[aX + bY])²]

… = E[(aX + bY)²] - E[aX + bY]²

… = E[a ² X ² + 2abXY + b ² Y ²] - (a E[X] + b E[Y])²

… = E[a ² X ² + 2abXY + b ² Y ²] - (a ² E[X]² + 2 ab E[X] E[Y] + b ² E[Y]²)

… = a ² E[X ²] + 2ab E[XY] + b ² E[Y ²] - a ² E[X]² - 2 ab E[X] E[Y] - b ² E[Y]²

… = a ² (E[X ²] - E[X]²) + 2ab (E[XY] - E[X] E[Y]) + b ² (E[Y ²] - E[Y]²)

… = a ² Var[X] + 2ab Cov[X, Y] + b ² Var[Y]

Answer:

answer:8a + 3b - 2a - b

=8a-2a+3b-b

=6a+2b or 2(3a+b) is your answer

Answer

45

Explanation

What is my perfect crime? I break into Tiffany's at midnight. Do I go for the vault? No, I go for the chandelier. It's priceless. As I'm taking it down, a woman catches me. She tells me to stop. It's her father's business. She's Tiffany. I say no. We make love all night. In the morning, the cops come and I escape in one of their uniforms. I tell her to meet me in Mexico, but I go to Canada. I don't trust her. Besides, I like the cold. Thirty years later, I get a postcard. I have a son and he's the chief of police. This is where the story gets interesting. I tell Tiffany to meet me in Paris by the Trocadero. She's been waiting for me all these years. She's never taken another lover. I don't care. I don't show up. I go to Berlin. That's where I stashed the chandelier.

The inverse statement is false.

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Answer:

FAIL TO REJECT

NOT ENOUGH

Step-by-step explanation:

Given a Pvalue of 0.32

Decision region :

When Pvalue < α ; Reject the Null and conclude that there is significant or enough evidence to accept the alternative hypothesis.

Otherwise, fail to reject reject the null and conclude that, there is not enough evidence to accept the alternative hypothesis

Therefore, for the scenario above, where Pvalue = 0.32

Possible α values are ; 0.1, 0.05, 0.01

For all α - values listed, the Pvalue is greater than α

Pvalue > α ; Hence, FAIL TO REJECT the Null.

Conclusion :

There is NOT ENOUGH evidence to support the alternative that the proportion of students who have ear infection at one school and the other is different.

The perimeter of the triangle OQR is 68 cm

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

Circles with the centers O, Q and R

When these centers are connected, the connection forms a triangle

The triangle OQR

Also from the question, we have the following values of radii

Radii = 8 cm, 11 cm and 15 cm

The perimeter of the triangle OQR is calculated as

Perimeter = Twice the sum of the radii

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

Perimeter = 2 *(8 + 11 + 15)

Evaluate the sum

Perimeter = 2 * 34

Evaluate the products

Perimeter = 68

Hence, the perimeter is 68 cm

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Let x be the number of gallons consumed by the first car.

Then, the number of gallons consumed by the second car is 65-x (since the total gas consumption is 65 gallons).

Using the formula distance = fuel efficiency x gas consumption, we can set up two equations:

First car: distance = 30x

Second car: distance = 20(65-x)

Since the total distance is 1700 miles, we can set up another equation:

Total distance: 30x + 20(65-x) = 1700

Simplifying this equation, we get:

30x + 1300 - 20x = 1700

10x = 400

x = 40

Therefore, the first car consumed 40 gallons and the second car consumed 65-40 = 25 gallons.

Let's assume that the first car traveled x miles and the second car traveled y miles during that week. We can set up two equations based on the given information:

x + y = 1700 (the combined total of miles traveled by both cars)

x/30 + y/20 = 65 (the total gas consumption)

To solve for x and y, we can use the first equation to express one variable in terms of the other. For example, we can solve for y as follows:

y = 1700 - x

Substituting this into the second equation, we get:

x/30 + (1700 - x)/20 = 65

Multiplying both sides by the common denominator 60, we can simplify the equation:

2x + 3(1700 - x) = 3900

2x + 5100 - 3x = 3900

-x = -1200

x = 1200

So the first car traveled 1200 miles during the week. We can use this value to find the second car's mileage:

y = 1700 - x = 1700 - 1200 = 500

Therefore, the second car traveled 500 miles during the week. To find the gallons of gas consumed by each car, we can use the fuel efficiency rates:

Gallons used by first car = 1200 miles / 30 mpg = 40 gallons

Gallons used by second car = 500 miles / 20 mpg = 25 gallons

So the first car consumed 40 gallons of gas and the second car consumed 25 gallons of gas during that week.

The surface area of the vase is 168.4 square inches.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

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Answer

7/9 chance to pick a brown sock first and 1/4 chance to get a black sock after

Step-by-step explanation:

there are 9 total socks and 7 are brown so you will have a 7/9 chance to get a brown sock

then if you do get a brown the total number of socks will be 8 in the bag so then you have a 2/8 chance which can be simplified to 1/4

Answer:

\(134^{\circ}\)

Step-by-step explanation:

Using the exterior angle theorem,

\(m\angle z=m\angle A+m\angle B=134^{\circ}\)

Using the exterior angle theorem, angle z is measured as 134°.which is the correct answer that would be an option (D).

The exterior angle theorem is a triangle theorem that asserts that the measure of the external angle created by an extended side of a triangle is equal to the sum of the measures of the triangle's remote interior angles.

The given data will be the following as:

Exterior angle to angle C of triangle ABC = z

The remote interior angle of triangle ABC are angled A = 58° and angle B = 44°.

Therefore:

The measure of angle z = measure of angle A + measure of angle B [according to the exterior angle theorem]

Substitute the values and we get

Measure of ∠z = 77 + 57

Measure of ∠z = 134°

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Answer: 45

Step-by-step explanation: the fub

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

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

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Complete Question

The complete question is shown on the first uploaded image

Answer:

The score of the student is  x = 779.42

Step-by-step explanation:

Generally we can mathematically represent the z-score as

         \(z = \frac{x - Mean}{ stDev}\)

Here x is the score of the student

substituting 1045.7 for the Mean, 221.9 for the stDev and -1.2 for z we have  

          \(-1.2 = \frac{x - 1045.7 }{ 221.9}\)

=>       \(-266.28 = x -1045.7\)

=>     x  =  -266.28 + 1045.7

=>     x = 779.42

The student scored 779.42 for him to have a z score of - 1.2;

z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

\(z=\frac{x-\mu}{\sigma/ } \\\\where\ x\ is\ raw\ score,\mu\ is\ mean, \sigma\ is\ standard\ deviation\)

Given that μ = 1045.7, σ = 221.9 Hence for z = -1.2:

\(-1.2=\frac{x-1045.7}{221.9} \\\\x=779.42\)

The student scored 779.42 for him to have a z score of - 1.2;

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The angle formed between the hour line at 10 and the minute line at 1 is 90 degrees.

When two straight lines or rays intersect at a shared terminal, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

There are different parts of angle, such as:

A vertex is an angle's corner or the place where two lines/sides meet. In the diagram, O represents the vertex.

Arms: The angle's two sides united at a common termination. OA and OB are angle arms.

Initial Side: A straight line from which an angle is drawn, also known as the reference line. The reference line is OB.

The terminal side is the side from which the angle is measured. OA is the terminal side in the figure below.

Angle between every 5 minute period =

So, Time period between 10 and 1 = 15 minutes

Angle formed between 10 and 1 = 30 × 3 = 90°

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Answer:

the answer is 100

Step-by-step explanation:

(-2-8)^2

(-2-8)(-2-8)

-2(-2-8)-8(-2-8)

4+16+16+64

20+80

100

Answer:

Equations 1 & 3 are correct.

Explanation:

Equation 2's actual answer is -8, and Equation 4's actual answer is positive 7.

Answer:

1 and 3 are correct

Step-by-step explanation:

Answer:

205 x 2=410+20=430

Step-by-step explanation:

Answe 6-6

Step-by-step explanation: i hade 6 point and i lost 6 points hint 6-6

Answer:

-6 :(

Step-by-step explanation:

Answer:

x=5

y=2

Step-by-step explanation:

5x + 3y= 31

-6x - 3y = -36  (multiple  by -3)

-x=-5

x=5

2(5)+y=12   or         25 + 3y= 31

10+y=12                  3y=6

y=2                          y=2

Answer:

x = 5, y = 2

Step-by-step explanation:

I'll use substitution on this one, which makes me choose one of the equation and solve for x. (5x + 3y = 31 was chosen)

5x + 3y = 31

Subtracct 3y from both sides

5x = -3y + 31

Divide both sides by 5

x = 1/5 (-3y + 31)

Multiply 1/5 by -3y + 31

x = -3/5y + 31/5

Substitute -3/5y + 31/5 for x in the other equation (2x + y = 12)

2 (-3/5y + 31/5) + y = 12

Multiply -3/5y + 31/5 by 2.

-6/5y + 62/5 + y = 12

Add -6/5y to y

-1/5y + 62/5 = 12

Subtract 62/5 from both sides

-1/5y = -2/5

Multiply both sides by -5

y = 2

Now head back to the previous equation, except substitute y for 2.

x = -3/5 * 2 + 31/5

Multiply -3/5 by 2.

x = (-6 + 31)/5

Add -6 and 31

x = 25/5

Divide 25 by 5.

x = 5

Formulate 5 and 2 for x and y in the equation.

5(5) + 3(2) = 31

2(5) + 2 = 12

25 + 6 = 31; true

10 + 2 = 12; true

x is 5 and y is 2.

The relative percentages of the column-wise frequencies are different, indicating that there is indeed an association between the variables.

A user-defined collection of related groups and items is referred to as a data association. It may include one or more groupings, as well as some, all, or neither of the items found inside those groups. It is helpful to initially identify various groups and components that you believe to be connected in some way before establishing Rules of Visibility.

Because of the differences in the relative percentages of the column-wise frequencies, there is a link between the variables. The animal mascot in the first column has 74% victories and 26% defeats. These percentages fluctuate greatly from one another. The other type of mascot, which similarly has a significant disparity between them, has 49% victories and 51% losses. The association between the variables is stronger the larger the difference.

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The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

Tο cοmplete the assignment, use the tried-and-true straightfοrward methοdοlοgy, the real variables, and any pertinent details frοm the preliminary and specialized questiοns. In respοnse, custοmers might be given anοther οppοrtunity tο range sample the prοducts. In the absence οf such changes, majοr advances in οur knοwledge οf prοgrammes will be lοst.

Here,

We must divide the tοtal cοst by the quantity οf cupcakes in οrder tο determine the unit cοst οf each οptiοn:

Twelve cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  Unit cοst: $29 fοr 12 cupcakes.

=>  $2.42 is the unit cοst per cupcake.

Tο make 24 cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=> 24 cupcakes equals $56 fοr the unit.

=>  $2.33 is the unit cοst per cupcake.

50 cupcakes =

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  $129 fοr a unit οf 50 cupcakes.

=>  Unit cοst: $2.58 fοr each cupcake

As a result, 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

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According to the given information, the final equation is g(x) = (x - 1)/4 - 3, the slope of the line is 1/4 & the vertical intercept is -3.

What is the function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

a) To find the equation for g(x), we need to apply the given transformations to f(x) = x:

Vertical compression by 1/4: this means that the y-values of f(x) will be multiplied by 1/4. So, the new function is g(x) = (1/4) * f(x) = (1/4) * x = x/4.

Shift right by 1: this means that the x-values of g(x) will be shifted 1 unit to the left. So, the new function is g(x) = (x - 1)/4.

Shift down by 3: this means that the y-values of g(x) will be shifted 3 units down. So, the final equation for g(x) is g(x) = (x - 1)/4 - 3.

b) The slope of this line is the coefficient of x, which is 1/4.

c) The vertical intercept of this line is the y-intercept, which is -3. To find this, we can set x = 0 in the equation for g(x):

g(0) = (0 - 1)/4 - 3 = -3

So, the vertical intercept is -3.

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a) The summation (Ex) of the given data set, we add up all the values

Ex = 77

b) n = 5

c) x = 15.4

a) To compute the summation (Ex) of the given data set, we add up all the values:

19 + 10 + 15 + 17 + 16 = 77

b) The sample size (n) is the total number of data points in the set. In this case, there are 5 data points, so:

n = 5

c) To calculate the sample mean (x), we divide the summation (Ex) by the sample size (n):

x = Ex / n

x = 77 / 5

x = 15.4

Therefore, the answers are:

a) Ex = 77

b) n = 5

c) x = 15.4

The summation is 77, the sample size is 5, and the sample mean is 15.4.

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Answer:

x = 47

Step-by-step explanation:

x + 121 = 4x - 20

-3x + 121 = - 20

-3x = -141

x = 47

So, the answer is x = 47

Answer:

The value is  \(0.152 \le \frac{\sigma_1^2}{\sigma_2^2} \le 1.835\)

Step-by-step explanation:

From the question we are told that

  The number of observation for X  is \(n_1 = 8\)

  The sample mean for X  is  \(\= x _1 = 15.7 5\)

  The sample variance for X is \(s^2_1 = 46.21\)

   The number of observation for Y  is \(n_1 = 10\)

  The sample mean for Y  is  \(\= x _1 = 23.3\)

  The sample variance for Y is \(s^2_1 = 92.8\)

Generally the degree of freedom for X is      

     \(df_1 = n_1 - 1\)

=>  \(df_1 = 8 - 1\)

=>  \(df_1 = 7\)

Generally the degree of freedom for X is      

     \(df_2 = n_2 - 1\)

=>  \(df_2 = 10 - 1\)

=>  \(df_2 = 9\)

From the question we are told the confidence level is  90% , hence the level of significance is    

      \(\alpha = (100 - 90 ) \%\)

=>   \(\alpha = 0.10\)

=>  \(\frac{\alpha}{2} = \frac{0.10}{2}\)

=>  \(\frac{\alpha}{2} = 0.05 }\)

Generally the 90% confidence interval for the ratio of variances is mathematically represented as

     \(\frac{s_1^2}{s_2^2 } * \frac{1}{F_{ 1 - \frac{\alpha }{2} , df_1 , df_2 }} \le \frac{\sigma_1^2}{\sigma_2^2} \le \frac{s_1^2}{s_2^2 } * \frac{1}{F_{ \frac{\alpha }{2} , df_1 , df_2 }}\)

=>  \(\frac{46.21}{92.68 } * \frac{1}{F_{ 1 - 0.05 , 7 , 9 }} \le \frac{\sigma_1^2}{\sigma_2^2} \le \frac{46.21}{92.68 } * \frac{1}{F_{ 0.05 , 7 , 9 }}\)

=>  \(\frac{46.21}{92.68 } * 0.304 \le \frac{\sigma_1^2}{\sigma_2^2} \le \frac{46.21}{92.68 } * 3.677\)

=>  \(0.152 \le \frac{\sigma_1^2}{\sigma_2^2} \le 1.835\)

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.

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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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