Thirty-five points on the line!!!

A bag contains five plain muffins and six blueberry muffins. Without looking, Sherman selects a muffin, hands it to his sister and then selects a second muffin for himself. What is the probability that Sherman gets a plain muffin, and his sister gets a blueberry muffin?

A. 30/121

B. 3/11

C. 5/11

D. 5/6

Answer: False

Step-by-step explanation:

The measure of the created angle is equal to the difference of the measure of the arcs.

The angle formed by the intersection of a secant and a tangent is equal to half the measure of the intercepted arc, not the sum of the measures of the intercepted arcs.

The statement is False. The angle formed by the intersection of a secant and a tangent is half the measure of the intercepted arc, not equal to the sum of the measures of the intercepted arcs.

For example, let's consider a circle with a secant and a tangent line intersecting at a point. The intercepted arc is represented by the section of the circumference between the two points of intersection. The angle formed by the intersection of the secant and the tangent is equal to half the measure of this intercepted arc.

So, in conclusion, the angle formed by the intersection of a secant and a tangent is equal to half the measure of the intercepted arc.

Answer:

C

Step-by-step explanation:

Answer:  The correct option is

(A) 7.

Step-by-step explanation:  Given that for a school fundraiser, Jeff sold large boxes of candy for three dollars each and small boxes of candy for two dollars each.

Also, Jeff sold 37 boxes in all for total of $96.

We are to find the number of large boxes more than that of small boxes.

Let x and y represents the number of large boxes and small boxes respectively.

Then, according to the given information, we have

[tex]x+y=37~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x+2y=96~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Multiplying equation (i) by 2 and subtracting from equation (ii), we get

[tex](3x+2y)-(2x+2y)=96-37\times2\\\\\Rightarrow x=96-74\\\\\Rightarrow x=22.[/tex]

From equation (i), we get

[tex]22+y=37\\\\\Rightarrow y=37-22\\\\\Rightarrow y=15.[/tex]

We have,

[tex]x-y=22-15=7.[/tex]

Thus, there are 7 more large boxes than small boxes.

Option (A) is CORRECT.

For this case we have that by definition, the perimeter of the quadrilateral shown is given by the sum of its sides:

Let "p" be the perimeter of the quadrilateral, then:

[tex]p = 7 + y + 7 + x\\p = 7 + 7 + x + y\\p = 14 + x + y[/tex]

So, the perimeter of the figure is: [tex]14 + x + y[/tex]

Answer:

[tex]p = 14 + x + y[/tex]

Answer:

  perimeter = x + y + 14

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  perimeter = x + 7 + y + 7

The constants can be combined to give ...

  perimeter = x + y + 14

___

An "equation" will have an equal sign somewhere. Since you want to find the perimeter, it makes sense for the equation to show you how to find the perimeter. (I have used "perimeter" to represent the perimeter. It is often represented using the letter P. Of course, you can choose any variable or other representation you like.)

For this case we have that according to the order of PEMDAS algebraic operations, it is established that:

P: Any calculation is made inside the parentheses, making the most internal ones first.

E: Any exponential expressions are simplified.

MD: All the multiplications and divisions are made, from left to right, as they appear.

AS: All sums and subtractions are made, from left to right, as they appear.

So:

[tex]2 ^ 3[/tex] + 5 * 10 ÷ 2-[tex]3 ^ 3[/tex] + (11-8) =

[tex]2 ^ 3[/tex]+ 5 * 10 ÷ 2-[tex]3 ^ 3[/tex] + 3 =

8 + 5 * 10 ÷ 2-27 + 3 =

8 + 50 ÷ 2-27 + 3 =

8 + 25-27 + 3 =

33-27 + 3

6 + 3 =

9

Answer:

9

3³ X 3⁶ > 3⁸ is the correct expression.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Here, Let first equation is true,

then, LHS = 2⁴ X 2³

                  = 2⁴⁺³

                 = 2⁷

                ≠ RHS

Option A is false.

Again assume option B is true.

Now check, LHS = 3³ X 3⁶

                           = 3³⁺⁶

                          = 3⁹

                          >3⁸

                 LHS > RHS

Thus, 3³ X 3⁶ > 3⁸ is the correct expression.

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Step-by-step explanation:

First we need to find which function is the outside radius and which is the inside radius (by which I mean which is farther and which is closer to the axis of rotation).  We can do this by graphing, but we can also do this by evaluating each function at the end limits.

At x = 0:

y = 5 sin 0 = 0

y = 5 cos 0 = 5

At x = π/4:

y = 5 sin π/4 = 5√2 / 2

y = 5 cos π/4 = 5√2 / 2

So y = 5 cos x is the outside radius because it is farther away from y = -1, and y = 5 sin x is the inside radius because it is closer to y = -1.

Here's a graph:

desmos.com/calculator/5oaiobcpww

The volume of the rotation is:

V = π ∫ₐᵇ [(R−y)² − (r−y)²] dx

where a is the lower limit, b is the upper limit, R is the outside radius, r is the inside radius, and y is the axis of rotation.

Plugging in:

V = π ∫₀ᵖ [(5 cos x − -1)² − (5 sin x − -1)²] dx

V = π ∫₀ᵖ [(5 cos x + 1)² − (5 sin x + 1)²] dx

V = π ∫₀ᵖ [(25 cos² x + 10 cos x + 1) − (25 sin² x + 10 sin x + 1)] dx

V = π ∫₀ᵖ [25 cos² x + 10 cos x + 1 − 25 sin² x − 10 sin x − 1] dx

V = π ∫₀ᵖ [25 (cos² x − sin² x) + 10 cos x − 10 sin x] dx

V = π ∫₀ᵖ [25 cos (2x) + 10 cos x − 10 sin x] dx

V = π [25/2 sin (2x) + 10 sin x + 10 cos x] from 0 to π/4

V = π [25/2 sin (π/2) + 10 sin (π/4) + 10 cos (π/4)] − π [25/2 sin 0 + 10 sin 0 + 10 cos 0]

V = π [25/2 + 5√2 + 5√2] − 10π

V = π (5/2 + 10√2)

V ≈ 52.283

In this exercise it is necessary to calculate the volume of the rotating solid, in this way we have:

[tex]V= 52.3[/tex]

First we need to find which function is the outside radius and which is the inside radius (by which I mean which is farther and which is closer to the axis of rotation).  We can do this by graphing, but we can also do this by evaluating each function at the end limits.

[tex]x=0\\y=5sin(x)\\y=5sin(0)=0\\y=5cos(0)= 5\\\\x=\pi/4\\y=5sin(\pi/4)= 5(\sqrt{2/2})\\y=5cos( \pi/4)= 5/\sqrt{2}[/tex]

So [tex]y = 5 cos x[/tex] is the outside radius because it is farther away from y = -1, and [tex]y = 5 sin x[/tex] is the inside radius because it is closer to y = -1. Here's a graph (first image). The volume of the rotation is:

[tex]V=\pi\int\limits^a_b {[(R-y)^2-(r-y)^2]} \, dx[/tex]

Where a is the lower limit, b is the upper limit, R is the outside radius, r is the inside radius, and y is the axis of rotation. Plugging in:

[tex]V=\pi\int\limits^a_b {[(R-y)^2-(r-y)^2]} \, dx\\= \pi\int\limits^p_0 {[(5 cos(x) + 1)^2-(5 sin(x) + 1)^2]} \, dx\\=\pi\int\limits^p_0 {[(25 cos^2 (x) + 10 cos (x) + 1)-(25 sin^2 (x) + 10 sin (x) + 1)]} \, dx\\=\pi\int\limits^p_0 {[(5 cos^2 (x) + 10 cos (x) + 1 -25 sin^2 (x)- 10 sin (x)- 1]} \, dx\\=\pi\int\limits^p_0 {[(25 (cos^2( x)- sin^2( x)) + 10 cos( x)- 10 sin( x)]} \, dx\\=\pi\int\limits^p_0 {[(25 cos (2x) + 10 cos (x)- 10 sin (x)]} \, dx\\[/tex]

[tex]=\pi[(25/2 sin (2x) + 10 sin x + 10 cos (x)]\\\\=\pi[(25/2 sin (\pi/2) + 10 sin (\pi/4) + 10 cos (\pi/4)] - \pi [25/2 sin( 0) + 10 sin( 0) + 10 cos(0)]\\\\=\pi[25/2+5\sqrt{2}+5/\sqrt{2}]-10\pi\\\\\V= 52.3[/tex]

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Answer:

x= 1.8

Step-by-step explanation:

We have been given the equation;

-(6)^(x-1)+5=(2/3)^(2-x)

We are required to determine the value of via graphing. To do this we can split up the right and the left hand sides of the equation to form the following two separate equations;

y = -(6)^(x-1)+5

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

We then proceed to graph the two equations on the same graph. The solution will be the point where the equations will intersect. Find the attachment below for the graph;

The value of x is 1.785. To the nearest tenth we have x = 1.8

Answer:

  24 cm

Step-by-step explanation:

The product of height and width will remain the same, so the new width (w) will be given by ...

  w·(new height) = (old width)·(old height)

  w·(1.25·40 cm) = (30 cm)(40 cm)

  w = (30 cm)/1.25 = 24 cm . . . . . . . divide by 1.25·40 cm and simplify

_____

This derives from the fact that volume and length are unchanged. The formula for the volume in terms of length, width, and height is ...

  V = LWH

Then the product of W and H is the constant ...

  V/L = WH . . . . . divide by L

For our purpose, we only need to know that V and L are unchanged, so the product WH is unchanged. We don't need to know their values.

Of course, increasing the height by 25% is equivalent to multiplying it by 1.25:

  H + 25/100·H = H·(1 + 0.25) = 1.25H

Answer:

D

Step-by-step explanation:

[tex]\left[\begin{array}{cc}Flow Rate&Eroded Soil\\0.31&0.82\\0.85&1.95\\1.26&2.18\\2.47&3.01\\3.75&6.07\end{array}\right][/tex]

As we can see, as flow rate increases, eroded soil also increases.  So the association is positive.

The association between flow rate and amount of eroded soil is positive.

The association between flow rate and amount of eroded soil is:

D. positive

The data shows that as the water flow rate increases, the amount of eroded soil also increases. This positive relationship indicates that higher water flow leads to more soil erosion.

Answer:

[tex]P=25\%[/tex]

Step-by-step explanation:

We have a sample of 100 clients.

To find the probability that a randomly selected customer chooses a cold drink, we must first count how many people in the sample chose cold drinks.

The table shows that cold drinks were

8 small, 12 medium and 5 large.

Then the number of cold drinks was:

[tex]8 + 12 + 5 = 25[/tex]

Now the probability of someone selecting a cold drink is:

[tex]P = \frac{25}{100}[/tex]

[tex]P = 0.25 = 25\%[/tex]

Answer:p=25%

For the acellus people

Step-by-step explanation:

The sum of angles in ΔABD is ...

  2a + b + d = 180

The sum of angles in ΔAHG is ...

  a + h + 90 = 180

Solving this second equation for a, we have ...

  a = 180 -90 -h = 90 -h

Substituting this into the first equation, we have ...

  2(90 -h) +b +d = 180

  180 -2h +b +d = 180 . . . . . eliminate parentheses

  b + d = 2h . . . . . . . . . . . . . add 2h-180

  h = (1/2)(b+d) . . . . . . . . . . divide by 2

Answer:

Step-by-step explanation:

The leftmost piece of the function is constant at -3.

The middle piece is a line with a slope of 2 that intersects the y-axis at -3, so has equation y = 2x-3. (The slope-intercept form of the equation of a line is y = slope·x + y-intercept. The slope is found by counting the number of vertical grid squares that correspond to each horizontal grid square.)

The rightmost piece is constant at +5.

___

We don't know what your choices are, so we can't tell you which to select.

The piecewise function is a horizontal line restricted between x = 0 and x = 20. To evaluate the function, substitute the given values into the function.

The given piecewise function is:

f(x) =

To evaluate the function for given values of the domain, you can substitute the given values of x into the function and calculate the corresponding y-values. For example, to find f(5), substitute x = 5 into the function and evaluate.

It is important to note that the question does not provide the equation or specific values of the function, so the evaluation of the function cannot be performed without additional information.

Answer:

Part 1) The height of the triangle when θ = 30° is equal to [tex]8.66\ ft[/tex]

Part 2) The height of the triangle when θ = 40° is equal to [tex]12.59\ ft[/tex]

Part 3) The area of triangle with θ = 30° is less than the area of triangle with θ = 40°

Step-by-step explanation:

Part 1) What is the height of the triangle when θ = 30 ° ?

we have

[tex]y=15tan(\theta)[/tex]

substitute the value of theta in the equation and find the height

[tex]y=15tan(30\°)=8.66\ ft[/tex]

Part 2) What is the height of the triangle when θ = 40 ° ?

we have

[tex]y=15tan(\theta)[/tex]

substitute the value of theta in the equation and find the height

[tex]y=15tan(40\°)=12.59\ ft[/tex]

Part 2) Vance is considering using either θ = 30 ° or θ = 40 ° for his garden

Compare the areas of the two possible gardens

step 1

Find the area when θ = 30 °

The height is [tex]8.66\ ft[/tex]

Remember that the area of a triangle  is equal to the base multiplied by the height and divided by two

so

[tex]A=(1/2)(30)(8.66)=129.9\ ft^{2}[/tex]

step 2

Find the area when θ = 40°

The height is [tex]12.59\ ft[/tex]

Remember that the area of a triangle  is equal to the base multiplied by the height and divided by two

so

[tex]A=(1/2)(30)(12.59)=188.85\ ft^{2}[/tex]

Compare the areas of the two possible gardens

The area of triangle with θ = 30° is less than the area of triangle with θ = 40°

For each Y value to have more than one x value would be a linear function.

It would make a straight line.

The correct answer is B: many-to-one function. This is the type of function where one y value is associated with multiple x values, differing from linear, nonlinear, and one-to-one functions.

A function in which each y value has more than one corresponding x value is known as a many-to-one function. This type of function allows for multiple x values to be paired with a single y value. This should not be confused with nonlinear functions or one-to-one functions. Moreover, while linear function is often associated with straight lines, in algebra, a linear function may actually include more than one term, each having a single multiplicative parameter. For example, y = ax + bx² is linear in this algebraic sense because terms x and x² each have one parameter (a and b). However, a function like y = [tex]x^b[/tex], where b is an exponent rather than a multiplicative parameter, is an example of a nonlinear function as it cannot be accurately described using linear regression.

Answer:

x = 3

Step-by-step explanation:

3/2.25 = 4/x                 Cross multiply

3x = 2.25 * 4                Combine the right

3x = 9                           Divide by 3

3x/3 = 9/3

x = 3

Answer:

Option A is correct.

Step-by-step explanation:

64 < x < 68

This inequality represent that the height x should be greater than 64 and less than 68.i.e.

x>64 and x<68

So, Option A is correct.

Answer:

x>64 and x<68

Step-by-step explanation:

Answer:

Step-by-step explanation:

The volume of a rectangular box is width times length times height:

V = wlh

After the cardboard is folded, the width is 12 - 2x, the length is 16 - 2x, and the height is x.

So the volume is:

V = (12 - 2x) (16 - 2x) x

If we graph this, we get a wave: desmos.com/calculator/rsjosgzuxz

The wave is the highest at around x = 2.3 in.

If we set x = 2.3:

w = 12 - 2x = 7.4

l = 16 - 2x = 11.4

h = x = 2.3

x= 8 is the correct answer

Answer:

x = 8

Step-by-step explanation:

Given equation is,

[tex]log_5(10x-1)=log_5(9x+7)[/tex]

We know that,

[tex]log_a(b)=log_a(c)\implies b = c[/tex]

[tex]\implies 10x -1 = 9x + 7[/tex]

Subtracting 9x on both sides,

[tex]x - 1 = 7[/tex]

Adding 1 on both sides,

[tex]x = 8[/tex]

Hence, the solution would be x = 8

iits probalty like based analyse

Answer:

A.Probability-based inference

Step-by-step explanation:

Inferential statistics uses a random sample of data from a population to draw inferences about the population. One can make generalizations about a population.

The answer as per scenario is A.Probability-based inference.

The manager made an inference based on probability.

Answer:

y= 2x+8

Step-by-step explanation:

The standard form of an equation of line in slope-intercept form is:

y= mx+b

Where m is the slope of the line and b is the y-intercept of the line.

To obtain the equation from the given information we need to put the values of m and b into the standard form of equation.

We are given

m = 2

and

b = 8

So putting the values of m and b

y = (2)x +8

y= 2x+8 ..

THE ANSWER IS :y=2x +8

just know its right.

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

Answer:

  C. The statement is true because the 95th percentile for men is greater than the 5th percentile for women.

Step-by-step explanation:

We suspect relevant data is missing, including exactly what clearance the the statement is referring to. It would be nice to know where the various men's and women's percentiles lie.

We give the above answer on the basis of the assumption that the largest of men are always larger than the smallest of women.

To find the multiplicative inverse of x modulo n, we need to find an integer s such that (x * s) mod n = 1. We can calculate the multiplicative inverses for the given values: (a) x = 52, n = 77: s = 65. (b) x = 77, n = 52: s = 33. (c) x = 53, n = 71: s = 51. (d) x = 71, n = 53: s = 9.

To find the multiplicative inverse modulo n of x, we need to find an integer s such that (x * s) mod n = 1. Let's calculate the multiplicative inverses for the given values:

a) For x = 52 and n = 77:

x * s ≡ 1 (mod n)

52 * s ≡ 1 (mod 77)

s ≡ 65 (mod 77)

So, the multiplicative inverse of 52 modulo 77 is 65.

b) For x = 77 and n = 52:

77 * s ≡ 1 (mod 52)

s ≡ 33 (mod 52)

The multiplicative inverse of 77 modulo 52 is 33.

c) For x = 53 and n = 71:

53 * s ≡ 1 (mod 71)

s ≡ 51 (mod 71)

The multiplicative inverse of 53 modulo 71 is 51.

d) For x = 71 and n = 53:

71 * s ≡ 1 (mod 53)

s ≡ 9 (mod 53)

The multiplicative inverse of 71 modulo 53 is 9.

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Dang that’s tuff I feel bad

Answer:

  (n+54)/9 = 21

Step-by-step explanation:

A number: n

Is increased by 54: n+54

The sum is divided by 9: (n +54)/9

and the result is 21:

  (n +54)/9 = 21

Answer:

[tex]127,000\ members[/tex]

Step-by-step explanation:

In this problem we have an exponential function of the form

[tex]f(x)=a(b)^{x}[/tex]

where

a is the initial value

b is the base

The base is equal to

b=1+r

r is the average rate

In this problem we have

a=23,000 members

r=5%=5/100=0.05

b=1+0.05=1.05

substitute

[tex]f(x)=23,000(1.05)^{x}[/tex]

x ----> is the number of years since 1985

How many members will there be in 2020?

x=2020-1985=35 years

substitute in the function

[tex]f(x)=23,000(1.05)^{35}=126,868\ members[/tex]

Round to the nearest thousand

[tex]126,868=127,000\ members[/tex]

The club is expected to have about 126868 members in 2020.

[tex]\[N(t) = N_0 \times (1 + r)^t\][/tex]

In this problem:

[tex]- \( N_0 = 23,000 \)- \( r = 0.05 \) (5% growth rate)- \( t = 2020 - 1985 = 35 \)[/tex]

Substituting these values into the formula, we get:

[tex]\[N(35) = 23,000 \times (1 + 0.05)^{35}\][/tex]

[tex]\[N(35) = 23,000 \times (1.05)^{35}\][/tex]

[tex]\[(1.05)^{35} \approx 5.516\][/tex]

Now, multiply by the initial number of members:

[tex]\[N(35) = 23,000 \times 5.516 \approx 126,868\][/tex]

ANSWER

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EXPLANATION

We want to find the slope of a line that is perpendicular to the line y = 1

The line y=1 is parallel to the x-axis.

In other words, the line y=1 is a horizontal line.

The line perpendicular to y=1 is a vertical line.

The slope of a vertical line is undefined

Answer:

its an undefined slope

Step-by-step explanation:

the line y=−1 has slope 0 so any line perpendicular to it will have an undefined slope

Surface area of [tex]\(r_2(u,v)\)[/tex]  is [tex]\(25\)[/tex] times the area of parameter domain[tex]\(D\),[/tex] yielding [tex]\(1600\)[/tex] if [tex]\(D\)[/tex] is [tex]\(8 \times 8\).[/tex]

Let's break it down step by step:

step:-1. **Define the parametric surfaces**: We have two parametric surfaces: [tex]\( r_1(u,v) = f(u,v)i + g(u,v)j + h(u,v)k \)[/tex] and [tex]\( r_2(u,v) = 5r_1(u,v) \).[/tex]

step:-2. **Calculate the partial derivatives**: Compute the partial derivatives of [tex]\( r_1 \)[/tex]  with respect to [tex]\( u \)[/tex]  and [tex]\( v \)[/tex] denoted by [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \).[/tex]

step:-3. **Multiply by 5**: Since[tex]\( r_2(u,v) = 5r_1(u,v) \),[/tex]  the partial derivatives of [tex]\( r_2 \)[/tex] with respect to [tex]\( u \)[/tex] and [tex]\( v \)[/tex] will be 5 times the corresponding partial derivatives of [tex]\( r_1 \)[/tex], denoted by [tex]\( r_{2u} \)[/tex] and [tex]\( r_{2v} \).[/tex]

step:-4. **Calculate the cross product**: Compute the cross product of [tex]\( r_{2u} \)[/tex] and[tex]\( r_{2v} \),[/tex] denoted by [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex]. This will be 25 times the magnitude of the cross product of [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \),[/tex] as the cross product is linear with respect to the vectors involved.

step:-5. **Surface area integral**: Use the formula for the surface area integral: [tex]\( A = \iint_D \| r_u \times r_v \| \, dA \),[/tex] where [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] replaces [tex]\( \| r_{u} \times r_{v} \| \).[/tex]

step:-6. **Calculate the integral**: Integrate[tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] over the parameter domain [tex]\( D \)[/tex]. Since [tex]\( \| r_{2u} \times r_{2v} \| \)[/tex] is constant and equal to 25 times the magnitude of the cross product of [tex]\( r_{1u} \)[/tex] and [tex]\( r_{1v} \)[/tex], the integral becomes [tex]\( 25 \times \text{Area of } D \).[/tex]

step:-7. **Determine the area of the parameter domain**: If the parameter domain [tex]\( D \)[/tex] is a rectangle with sides of length 8 in both directions, its area is [tex]\( 8 \times 8 = 64 \).[/tex]

step:-8. **Final calculation**: Multiply the area of [tex]\( D \)[/tex] by 25 to get the surface area of[tex]\( r_2(u,v) \)[/tex], which is[tex]\( 25 \times 64 = 1600 \).[/tex]

So, the surface area of the parametric surface given by [tex]\( r_2(u,v) = 5r_1(u,v) \)[/tex] is 1600.

The surface area of the parametric surface [tex]\( \mathf{r}_2(u, v) \)[/tex] is 25.

To find the surface area of the parametric surface given by [tex]\( \mathf{r}_2(u, v) = 5 \mathf{r}_1(u, v) \)[/tex] where [tex]\( -4 \leq u \leq 4 \)[/tex] and [tex]\( -4 \leq v \leq 4 \)[/tex], given that the surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] over the same parameter range is 1, follow these steps:

Surface Area of [tex]\( \mathf{r}_1(u, v) \)[/tex]

  The surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] is given to be 1.

Relationship Between [tex]\( \mathf{r}_1 \) and \( \mathf{r}_2 \)[/tex]

 [tex]\[ \mathf{r}_2(u, v) = 5 \mathf{r}_1(u, v) \][/tex]

Effect of Scaling on Surface Area

  When a surface is scaled by a factor k, the surface area is scaled by a factor of k². This is because surface area is a two-dimensional measure, and scaling each dimension by k multiplies the area by k².

Calculation for [tex]\( \mathf{r}_2(u, v) \)[/tex]

  In this problem, the scaling factor k is 5. Therefore, the surface area of [tex]\( \mathf{r}_2(u, v) \)[/tex] will be [tex]\( 5^2 \)[/tex] times the surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex].

[tex]\[\text{Surface area of } \mathf{r}_2(u, v) = 5^2 \times \text{Surface area of } \mathf{r}_1(u, v)\][/tex]

Substitute the Given Surface Area

  The surface area of [tex]\( \mathf{r}_1(u, v) \)[/tex] is 1.

[tex]\[\text{Surface area of } \mathf{r}_2(u, v) = 5^2 \times 1 = 25\][/tex]

Answer:

hi

Step-by-step explanation:

Answer with Step-by-step explanation:

On spinning the spinner twice,we have 16 different outcomes:.

We write the outcomes with their product:

                      Product

2    2                   4

2    3                   6

2    4                  8

2    9                  18

3    2                   6

3    3                   9

3    4                   12

3    9                   27

4    2                   8

4    3                    12

4    4                   16

4    9                   36

9    2                    18

9    3                    27

9    4                    36

9    9                    81

outcomes have a product less than 20 and contain at least one even number are in bold letters.

Hence, outcomes have a product less than 20 and contain at least one even number are:

10

There are 8 outcomes of spinning the spinner twice that result in a product less than 20 and contain at least one even number.

To determine how many outcomes of spinning a spinner twice result in a product less than 20 and contain at least one even number, we start by listing all possible outcomes.

The spinner is divided into four equal sections: 2, 3, 4, and 9. When spun twice, there are 16 outcomes in total:

We now filter these outcomes to find those with a product less than 20 and at least one even number:

The total number of outcomes that meet the criteria is 8.