Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8).



Which rule represents the dilation?


Select one:



(x, y) → (18x, 18y)



(x, y) → (x+8, y+4)



(x, y) → (12x, 12y)



(x, y) → (2x, 2y)

a) The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) The regression line is: y = 0.64x + 34.18

d) Interpretation and conclusion:  The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

Correlation analysis:

Using the Pearson correlation coefficient to measure the strength and direction of the linear relationship between two variables.

Hypothesis testing:

Setting up null and alternative hypotheses, and using the t-test to determine whether the correlation coefficient is statistically significant.

Linear regression:

Finding the equation of the regression line that best describes the relationship between the two variables.

Interpretation and conclusion:

Using the results of the analysis to draw meaningful conclusions about the relationship between the two variables and the sample population as a whole.

Here we have

A study was conducted to determine the relationship existing between the grade in English and the grade in mathematics. a random sample of 10 students in uc was taken and the following are the results of the sampling

Student           1     2      3     4     5     6     7     8      9    10

English          75   83   80   77   89   78   92   86   93   84

Mathematics 78   87   78   76   92   81    89   89   91   84​  

a) To compute the Pearson correlation coefficient (r), first calculate the mean, standard deviation, and covariance of the two variables:

Mean of English grades (x)

= (75+83+80+77+89+78+92+86+93+84)/10 = 83.7

Mean of Math grades (y)

= (78+87+78+76+92+81+89+89+91+84)/10 = 84.5

The standard deviation of English grades (Sx)

= √((75-83.4)²+(83-83.4)²+...+(84-83.4)²)/9) = 6.52

The standard deviation of Math grades (Sy)

= √((78-84.4)²+(87-84.4)²+...+(84-84.4)²)/9) = 5.47

Covariance of the two variables

= ((75-83.4)(78-84.4)+(83-83.4)(87-84.4)+...+(84-83.4)(84-84.4))/9 = 26.6

Using the formula, r = cov(X,Y)/(SxSy),

we can calculate the correlation coefficient as follows

r = 26.6/(6.52*5.47) = 0.76

Therefore,

The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) To find the equation of the regression line, we need to calculate the slope (b) and the intercept (a) of the line. The formula for the slope is:

b = r(Sy/Sx) = 0.76(5.47/6.52) = 0.64

The formula for the intercept is:

=> a = y - bx = 84.4 - 0.64(83.4) = 34.18

Therefore,

The equation of the regression line is:

y = 0.64x + 34.18

Interpretation and conclusion:

The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

The p-value associated with this correlation coefficient can be used to test the null hypothesis.

The equation of the regression line shows that for every one-point increase in the English grade, the predicted increase in the Mathematics grade is 0.64 points.

Therefore,

a) The Pearson correlation coefficient is 0.76.

b) Null hypothesis: There is no significant correlation between the grades in English and Mathematics (H0: r = 0)

Alternative hypothesis: There is a significant correlation between the grades in English and Mathematics (Ha: r ≠ 0)

c) The regression line is: y = 0.64x + 34.18

d) Interpretation and conclusion:  The Pearson correlation coefficient (r) of 0.76 indicates a strong positive correlation between the grades in English and Mathematics.

Learn more about Correlation analysis at

https://brainly.com/question/29785220

#SPJ4

There is a 95.52% chance that there are no customers in the system, a 9.93% chance that a customer has to wait in line, and a 31.20% chance that the server is busy.

λ = 2.6  guests per hour( Poisson  appearance rate)  μ =  1/ 12 hours per  client( exponential service rate)  c =  1 garçon( design adviser )  Using Little's Law, we can find the average number of  guests in the  staying line   L =  λ * W  

where W is the average time a  client spends in the system(  staying and being served). To find W, we can use the formula  

W =  1/( μ- λ)   Using these formulas, we get  

W =  1/(1/12-2.6) = 0.1154

hours = 6.92  twinkles

L = 2.6 *0.1154 = 0.3000  guests

 So on average, there will be0.3  guests  staying in line and each  client will  stay for6.92  twinkles before being served.

 We can also  cipher the probability that there are no  guests in the system(P_0), the probability that a  client has to  stay(P_w), and the probability that the garçon is busy

(P_b)   =  1- λ/ μ

= 0.9552  

 λ/ μ2 *( 1/( 1- λ/ μ)) = 0.0993  =  λ/ μ = 0.3120

Learn more about queing theroy/ customers at

https://brainly.com/question/24196990

#SPJ4

The coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j

The coordinates of point j' after rotating point jkl 90° clockwise around the origin can be found by applying the following transformation:

j' = (cos(90°) * x - sin(90°) * y, sin(90°) * x + cos(90°) * y)

Since we are rotating 90° clockwise around the origin, we have cos(90°) = 0 and sin(90°) = 1, so the transformation simplifies to:

j' = (0 * x - 1 * y, 1 * x + 0 * y)

j' = (-y, x)

Therefore, the coordinates of point j' after the rotation are (-y, x), where x and y are the original coordinates of point j.

To know more about coordinates, refer here:

https://brainly.com/question/16634867#

#SPJ11

62% of the dancers did not get into the show.

To find the percentage of dancers who did not get into the show.

First, identify the total number of dancers auditioning and the number of dancers who did not get into the show.

In this case, there are 150 dancers in total, and 93 of them did not get in.
Next, divide the number of dancers who did not get into the show by the total number of dancers auditioning.

This will give us the proportion of dancers who did not get in.
  Proportion = (Number of dancers who did not get in) / (Total number of dancers)
  Proportion = 93 / 150
Finally, to find the percentage, multiply the proportion by 100:
  Percentage = Proportion * 100
  Percentage = (93 / 150) * 100.

For similar question on dancers.

https://brainly.com/question/28183590

#SPJ11

The sculpture was worth £332.80 three years ago when it depreciates by 20% each year

To determine how much the sculpture was worth 3 years ago, we need to apply the depreciation rate of 20% per year for the past three years.

First, we need to calculate how much the sculpture would be worth after one year of depreciation:

650 - (0.20)(650) = 520

This means that after the first year, the sculpture would be worth £520.

Next, we can calculate the value of the sculpture after the second year of depreciation:

520 - (0.20)(520) = 416

After two years, the sculpture would be worth £416.

Finally, we can calculate the value of the sculpture after the third year of depreciation:

416 - (0.20)(416) = 332.8

Therefore, the sculpture was worth £332.80 three years ago.

To check this answer, we can also use another method: We can calculate the value of the sculpture using the compound interest formula, where the initial value is £x, the annual depreciation rate is 20%, and the time period is three years:

650 = x[tex](1-0.20)^{2}[/tex]

Simplifying this equation, we get:

x = 650 / [tex]0.80^{2}[/tex] = 332.80

To learn more about depreciates here:

https://brainly.com/question/16919769

#SPJ1

If boat is heading towards a lighthouse, whose beacon-light is 119 feet above the water, the distance from point A to point B is approximately 973 feet.

To find the distance from point A to point B, we can use trigonometry and the fact that the angles of elevation from both points are known.

Let x be the distance from point A to the lighthouse, and y be the distance from point B to the lighthouse. We can set up two equations using tangent function:

tan(5) = 119/x

tan(18) = 119/y

We can solve for x and y by isolating them in each equation:

x = 119/tan(5) ≈ 1343.44 feet

y = 119/tan(18) ≈ 370.79 feet

Therefore, the distance from point A to point B is approximately 1343.44 - 370.79 = 972.65 feet.

We rounded the final answer to the nearest foot, which is 973 feet.

To learn more about distance click on,

https://brainly.com/question/26617773

#SPJ1

Answer:

C. An obtuse triangle has two angles less than 90 degrees and one angle greater than 90 degrees.

The surface area of the pyramid is 390.8 cm².

The surface area of the triangular pyramid is calculated as follows;

S.A = base area   +  ¹/₂ (perimeter + slant height)

The height of the pyramid is calculated by applying Pythagoras theorem;

h = √ (28²  -  14²)

h = 24.2 cm

Area of the base = ¹/₂ x 28 cm x 24.2 cm = 338.8 cm²

The surface area of the pyramid is calculated as follows;

S.A = 338.8 cm²  + ¹/₂ (76 cm + 28 cm)

S.A = 390.8 cm²

Learn more about surface area of pyramid here: https://brainly.com/question/22744289

#SPJ1

Answer:

1,425

Step-by-step explanation:

I got this one correct

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

We have,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l

where:

a and b are the lengths of the two parallel sides (the bases) of the trapezoid

h is the height of the trapezoid (the perpendicular distance between the two bases)

l is the length of the prism (the distance between the two trapezoidal faces)

Now,

a = 9

b = 12

l = 15

Height h can be calculated using the Pythagorean theorem.

15² = (12 - 9)² + h²

h² = 225 + 9

h² = 234

h = √234

h = 15

Now,

The volume of a trapezoidal prism.

V = ((a + b) / 2) × h × l
V = ((9 + 12) / 2) x 15 x 15

V = 2362.5

And,

The surface area (A) of a trapezoidal prism can be calculated using the formula:

A = ph + 2B

where p is the perimeter of the trapezoidal base, h is the height of the prism, and B is the area of one of the bases.

So,

p = 12 + 8 + 12 + 8 = 44

h = 15

B = 12 x 8 = 96

Now,

Total surface area​.
= 44 x 15 + 2 x 96

= 660 + 192

= 852

Thus,

The volume of a trapezoidal prism is 2362.5.

The total surface area​ is 852.

Learn more about Prism here:

https://brainly.com/question/12649592

#SPJ1

Answer: B

Step-by-step explanation:

First, let's convert the 5 pints of fruit punch to cups:

5 pints = 5 x 2 cups/pint = 10 cups

Now we can add up the cups of each ingredient:

6 cups of orange juice + 10 cups of fruit punch + 8 cups of apple juice = 24 cups

Since there are 4 cups in a quart, we can divide by 4 to get the number of quarts:

24 cups ÷ 4 cups/quart = 6 quarts

Therefore, Jackson makes 6 quarts of fruit punch.

The value of x in the given circle is 13.9.

Given that a circle D, having an inscribed angle ∠CFE = 57° and the arc opposite it arc CE = 10x-25, we need to find the measure of x,

Using the inscribed angle theorem,

It states that the angle subtended by an arc at the center of the circle is double the angle subtended by it at any other point on the circumference of the circle.

So,

m ∠CFE = arc CE / 2

57 = 10x-25 / 2

10x-25 = 114

10x = 139

x = 13.9

Hence the value of x in the given circle is 13.9.

Learn more inscribed angle theorem, click;

https://brainly.com/question/5436956

#SPJ1

Answer:

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

A linear equation is an equation of a straight line.

It describes the straight-line graph of a set of ordered pairs (x, y) that are solutions to the equation.

There are different forms of linear equations.

The slope-intercept form of a linear equation is y = mx + b.

The equation y = -2x + 10 is in slope-intercept form. Its graph is a line with slope -2 and y-intercept 10. It shows the set of all solutions to the equation.

As per description above, the correct answer choice is B, all the other options are false.

The value of FE comes out to be 35.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is typically given in degrees or radians, and it describes the amount of rotation needed to move one of the rays or line segments to coincide with the other. Angles are used in many areas of mathematics, physics, engineering, and other sciences to describe and analyze various phenomena.

Parallel lines have the same slope and will never meet, no matter how far they are extended. Parallel lines are important in geometry and other areas of mathematics, as well as in engineering, architecture, and other fields where precise measurements and constructions are required.

[tex]4x-1/x+5 = 60/24\\5x+25= 8x-2\\27= 3x\\x=9[/tex]

Therefore FE= 4×(9)-1

=35

Learn more about lines here:

https://brainly.com/question/2696693

#SPJ1

The values of the combination expressions are ¹²C₁₁ = 12, ¹²C₁₀ = 66, ¹²C₅ = 792, ¹²C₁ = 12, ¹²C₁₂ = 1, ⁵C₄ + ⁵C₃ = 15, ⁵C₃/⁵C₂ = 1 and 4⁷C₂ = 84

Also, the number of ways is 30045015

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

¹²C₁₁

The formula for combination is

ⁿCₓ = n!/[(n - x)! * x!]

So, we have

¹²C₁₁ = 12!/[(12 - 11)! * 11!]

Evaluate

¹²C₁₁ = 12

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

¹²C₁₀ = 12!/[(12 - 10)! * 10!]

¹²C₁₀ = 66

¹²C₅ = 12!/[(12 - 5)! * 5!]

¹²C₅ = 792

¹²C₁ = 12!/[(12 - 1)! * 1!]

¹²C₁ = 12

¹²C₁₂ = 12!/[(12 - 12)! * 12!]

¹²C₁₂ = 1

⁵C₄ + ⁵C₃ = 5!/[(5 - 4)! * 4!] + 5!/[(5 - 3)! * 3!]

⁵C₄ + ⁵C₃ = 15

⁵C₃/⁵C₂ = 5!/[(5 - 3)! * 3!] / 5!/[(5 - 2)! * 2!]

⁵C₃/⁵C₂ = 1

4⁷C₂ = 4 * 7!/[(7 - 2)! * 2!]

4⁷C₂ = 84

For the number of ways to get people hired, we have

n = 30

x = 10

So, we have

³⁰C₁₀ = 30!/[(30 - 10)! * 10!]

³⁰C₁₀ = 30045015

Hence, the number of ways to get them hired is 30045015 ways

Read more about combination at

https://brainly.com/question/11732255

#SPJ1

Relevant parameter is the difference between actual and scheduled arrival time. Also the difference in sample means is -1.70 minutes. We get a p-value of 0.017 and the conclusion is that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

a. Relevant parameter: the difference between actual and scheduled arrival time.

Null hypothesis: The average difference between actual and scheduled arrival time is the same for Delta Air Lines and United Air Lines.

Alternative hypothesis: The average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines.

b. Sample mean for Delta Air Lines: -2.31 minutes

Sample mean for United Air Lines: -4.01 minutes

Difference in sample means: -1.70 minutes

c. To create a randomization distribution, we can pool the data from both airlines and randomly assign them to two groups with the same sample sizes as Delta Air Lines and United Air Lines. We then calculate the difference in sample means for each random assignment. Repeating this process many times gives us a randomization distribution. Using StatKey with 10,000 iterations, we get a p-value of 0.017, which is less than 0.01.

d. At a significance level of 0.01, we reject the null hypothesis and conclude that there is evidence to suggest that the average difference between actual and scheduled arrival time is different for Delta Air Lines and United Air Lines. Specifically, the average difference for United Air Lines is greater than that of Delta Air Lines. This could have implications for travelers who prioritize arriving on time, as they may wish to consider

Delta over United.

To know more about Relevant parameter, visit:

https://brainly.com/question/31311746#

#SPJ11

The outcome with a frequency closest to its expected frequency is C (3).

In a spinner game where the pointer spins on a wheel with six equal-sized sections, the expected frequency of each section is 1/6 or 16.67%. Based on the given spinner, section A has an expected frequency of 1/6, section B has an expected frequency of 4/6, section C has an expected frequency of 4/6, section D has an expected frequency of 1/6, section E has an expected frequency of 2/6, and section F has an expected frequency of 4/6.

To determine the outcome with a frequency closest to its expected frequency, we need to compare the expected frequency to the actual frequency for each section.

Based on the given spinner, section A has an actual frequency of 1/18, section B has an actual frequency of 4/18, section C has an actual frequency of 4/18, section D has an actual frequency of 1/18, section E has an actual frequency of 2/18, and section F has an actual frequency of 4/18.

Calculating the difference between the expected and actual frequency for each section, we find that section C has the smallest difference, making it the outcome with a frequency closest to its expected frequency.

Learn more about Probability

brainly.com/question/30034780

#SPJ11

The required probability 40%

To find the probability that the marble that hits the yard stick between A and D hits it between C and D, we need to find the length of the interval between C and D, and divide it by the length of the interval between A and D.

The length of the interval between C and D is

36 - 26 = 10

The length of the interval between A and D is

36 - 11 = 25

The probability that a marble will strike a yardstick between A and D and C and D is

10/25 × 100 = 40%

Therefore, the probability that a marble will strike a yardstick between A and D and C and D is 40%

Learn more about Probability here

https://brainly.com/question/30902578

#SPJ4

The correct option is the last one, the surface is 3425 m²

Remember that for a sphere of radius R, the volume is:

V = (4/3)pi*R³

S = 4pi*R²

Where pi = 3.14

Here the volume is  6,000π m³, then the radius will be:

R =∛( (3/4)*6,000m³)

R = 16.51 m

Then the surface area is:

[tex]S = 4*3.14*( 16.51 m)^2 = 3,424 m^2[/tex]

The option that is closser to it is the fourth one, so that is the correct option.

Learn more about spheres at:

https://brainly.com/question/10171109

#SPJ1

Answer:

The answer is 9

Step-by-step explanation:

When x = 2,

f(2) = 3×2^2-3

f(2) = 3×4-3

f(2) = 12-3

f(2)= 9

The statements true of the two-dimensional plane sections that could result from one of these slices made by Misha are B, C, D, E, and F.

A. False. The only two-dimensional plane sections that could result from slicing a cube with a plane are squares or rectangles, but not triangles.

B. True. A plane section that is square could result from one of these slices through the cube.

C. True. A plane section that is rectangular but not square could result from one of these slices through the cube.

D. True. A plane section that is triangular could result from one of these slices through the pyramid.

E. True. A plane section that is square could result from one of these slices through the pyramid.

F. True. A plane section that is rectangular but not square could result from one of these slices through the pyramid.

Therefore, the correct statements are B, C, D, E, and F.

Find out more on two-dimensional plane here: https://brainly.com/question/30244871

#SPJ1

The measure of angle m<BEC is 80 degrees

From the information shown, we have that;

m< AD = 120 degrees

m< BC = 80 degrees

To determine the value of m<BEC, we need to know that it is a minor arc in the circle.

Also, a minor arc is described as the shorter arc that connects two endpoints on a circle.

The measure of a minor arc is less than 180° , and  is equal to the measure of the arc's central angle.

We can see than the angle measure of m<BC = m<BEC

Then,

m<BEC = 80 degrees

Learn about minor arc at: https://brainly.com/question/12526346

#SPJ1are

The answer would be D

Since Lucy's number has a digit of 5 which is 10x greater than Ethan's number, 5 x 10 = 50; so 50 would be in the tenth place, and option d is the only one with 5 in the tenth place.

The value of a number moves one decimal place to the left for each position it moves to the right. So, the number that Lucy could have written where the number 5 has a value 10 times larger than Ethan's number is 4974.65.

In order for the value of the digit 5 to be 10 times larger in Lucy's number than it is in Ethan's, the '5' in Lucy's number should reside one place left compared to Ethan's. This means the 5 should be in the tens place, hundreds place, or beyond. So, we should look for a number having digit 5 at those places.

Let's examine the given options:

Therefore, the correct answer is C. 4974.65.

https://brainly.com/question/35447631

#SPJ2

The first derivative of f(x) is f'(x) = -12(-2x + 1)2.  The second derivative is f''(x) =48(-2x + 1), and all higher derivatives have the form f^(n)(x) = (-1)n * 6 * n! * (-2x + 1)^(3-n).

To calculate the derivatives of all orders for f(x) = (-2x + 1)3, we first need to find the first derivative:

f(x) = (-2x + 1)³

f'(x) = 3(-2x + 1)²(-2)
f'(x) = 3(-2x + 1)²(-2)

f'(x) = -12(-2x + 1)2

Next, we find the second derivative:

f''(x) = d/dx(-12(-2x + 1)²)

f''(x) = 2(-2)(-12)(-2x + 1)
f''(x) = -12[2(-2x + 1)(-2)]

f''(x)= 48(-2x + 1)

We can continue this process to find the third and fourth derivatives:

f'''(x) = d/dx(96(-2x + 1))

f'''(x) = -384

f''''(x) = d/dx(-384)

f''''(x) = 0
Notice that the fourth derivative is 0, meaning that all higher derivatives will also be 0.

This is because the original function is a polynomial of degree 3, so its fourth derivative will be the derivative of a constant, which is 0.

Therefore, we can conclude that:

f(4)(x) = 0
f(n)(x) = 0 for all n ≥ 4.

To practice more questions about derivatives:

https://brainly.com/question/23819325

#SPJ11

The sine function for the graph is given as follows:

y = sin(3x).

(a one should be placed on the green blank).

The standard definition of the sine function is given as follows:

y = Asin(Bx).

For which the parameters are given as follows:

The function oscillates between y = -1 and y = 1, for a difference of 2, hence the amplitude is obtained as follows:

2A = 2

A = 1.

The period is of 2π/3 units, hence the coefficient B is given as follows:

B = 3.

Then the equation is:

y = sin(3x).

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The average temperature from month 1 to month 6 is approximately 58.3 degrees Fahrenheit.

The temperature of a town t months after January can be estimated by the function f(t) = –20 cos(64t) + 66. To find the average temperature from month 1 to month 6, we need to evaluate the integral of f(t) from t=1 to t=6 and divide by the number of months:

Average temperature = (1/6 - 1) ∫[1,6] f(t) dt

= (1/6 - 1) ∫[1,6] (-20 cos(64t) + 66) dt

= (1/6 - 1) [-5 sin(64t) + 66t] [1,6]

= (1/6 - 1) [-5 sin(646) + 666 - (-5 sin(641) + 661)]

= (1/6 - 1) [-5 sin(384) + 395]

≈ 58.3 degrees Fahrenheit

Therefore, the average temperature from month 1 to month 6 is approximately 58.3 degrees Fahrenheit.

Learn more about average temperature.

brainly.com/question/29086717

#SPJ11

The area of ΔRST, to the nearest square inch is,

Area = 29,17,735.54 square inches

We have,

In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°.

Apply sine rule formula,

sin S / s = sin T / t

sin 8° / 990 = sin 60° / t

0.14 / 990 = 0.87 / t

0.14t = 990 x 0.87

0.14t = 861.3

t = 6,152 inches

Here, ∠R = 180° - (8 + 60)°

∠R = 180 - 68

∠R = 112°

sin S / s = sin R / r

sin 8° / 990 = sin 112° / r

0.14 / 990 = 0.92 / r

0.14r = 0.92 x 990

0.14r = 910.8

r = 910.8 / 0.14

r = 6505 inches

We use the formula

Heron's formula = √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

Solving for s

s = 990 + 6505 + 6,152 /2

s = 6823.5

Solving for the area of the triangle

= √6823.5 × (6823.5 - 990) × (6823.5 - 6,152) × (6823.5 - 6505)

= √6823.5 x 5833.5 x 671.5 x 318.5

= 29,17,735.54 square inches

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ12

The length of one side of the square is x - 6 units

The formula for calculating the area of a square is expressed as;

A = a²

Such that the a is the length of its side

From the information given, we have that;

Area = x^ 2 − 12 x + 36

solve the quadratic expression, we have that;

x² - 6x - 6x + 36

group in pairs

(x²- 6x) - (6x + 36)

factorize the terms

x(x - 6) - 8(x - 6)

Then, we have;

(x - 6) and (x - 6) units

Learn about squares at: https://brainly.com/question/25092270

#SPJ1

Answer:

the answer is D

Step-by-step explanation:

Answer:

C. x = 2 1/3, y = 1 1/3.

Step-by-step explanation:

To solve this question, we need to plot the two equations on the graph and see where they cross. The graph below shows the two lines in different colors:

The value of (f + g)(−3) given the functions f(x) = x² − 6x − 4 and g(x) = 5x + 3 is 11.

To find (f + g)(-3), we first need to add the functions f(x) and g(x) together, and then evaluate the resulting function at x = -3.

f(x) = x² - 6x - 4
g(x) = 5x + 3

Now, let's add f(x) and g(x):

(f + g)(x) = (x² - 6x - 4) + (5x + 3) = x² - x - 1

Now that we have the combined function, we can evaluate it at x = -3:

(f + g)(-3) = (-3)² - (-3) - 1 = 9 + 3 - 1 = 11

So, (f + g)(-3) = 11.

Learn more about functions here: https://brainly.com/question/30715060

#SPJ11

The height and radius of the cone with maximal volume V and surface area S = 8 are h = (4/(3π^2))^(1/4) and r = (1/(3π^2))^(1/4),

respectively.Explanation: To find the height and radius of the cone with maximal volume and surface area of 8, we need to use the formulas for the surface area and volume of a right-circular cone in terms of r and h. We can then use the method of Lagrange multipliers to find the values of r and h that maximize the volume subject to the constraint that the surface area is equal to 8.Using the formulas for the surface area and volume of a cone, we get:S = πr √(r²+h²)V = 1/3πr²hWe can then set up the Lagrangian function L(r,h,λ) = 1/3πr²h + λ(πr √(r²+h²) - 8), where λ is the Lagrange multiplier.Taking the partial derivatives of L with respect to r, h, and λ and setting them equal to zero, we get:∂L/∂r = 2/3πrh + λ(π√(r²+h²) + r²/√(r²+h²)) = 0∂L/∂h = 1/3πr² + λ(πh/√(r²+h²)) = 0∂L/∂λ = πr √(r²+h²) - 8 = 0Solving these equations, we get:h = (4/(3π^2))^(1/4)r = (1/(3π^2))^(1/4)Therefore, the height and radius of the cone with maximal volume and surface area of 8 are h = (4/(3π^2))^(1/4) and r = (1/(3π^2))^(1/4), respectively.(b) The ratio of height to radius for the cone with minimal surface area S and volume V = 5 is h/r = √2.Explanation: Using the formulas for the surface area and volume of a cone in terms of r and h, we can set up the following optimization problem:Minimize S = πr √(r²+h²)Subject to V = 1/3πr²h = 5Using the method of Lagrange multipliers, we can set up the Lagrangian function L(r,h,λ) = πr √(r²+h²) + λ(1/3πr²h - 5), where λ is the Lagrange multiplier.Taking the partial derivatives of L with respect to r, h, and λ and setting them equal to zero, we get:∂L/∂r = π√(r²+h²) + 2λr/3πh = 0∂L/∂h = πr²h/√(r²+h²) - 5λ/3π = 0∂L/∂λ = 1/3πr²h - 5 = 0Solving these equations, we get:h/r = √2Therefore, the ratio of height to radius for the cone with minimal surface area S and volume V = 5 is h/r = √2.(c) No, a cone with given volume V and maximal surface area does not exist.Explanation: Using the formulas for the surface area and volume of a cone in terms of r and h, we can set up the following optimization problem:Maximize S = πr √(r²+h²)Subject to V = 1/3πr²hUsing the method of Lagrange multipliers, we can set up the Lagrangian function L(r,h,λ) = πr √(r²+h²) + λ(1/3πr²h - V), where λ is the Lagrange multiplier.Taking the partial derivatives of L with respect to r, h, and λ and setting them equal to zero, we get:∂L/∂r = π√(r²+h²) + 2λr/3πh = 0∂L/∂h = πr²h/√(r²+h²) - λ/3πr² = 0∂L/∂λ = 1/3πr²h - V = 0Solving these equations, we get:h = rr³ = 3V/πSubstituting h = r into the surface area formula, we get:S = 2

For more similar questions on topic Mensuration

https://brainly.com/question/22290021

#SPJ11