Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum. Select all that apply: a. f(x)=In( 1-x) over [0.2] b. g(x)=ln(1+1) over 10, 2] c. h(x)= √(x-1) over [ 1.4] d. k(x)= 1/√(x-1) over [1,4] e. None of the above.

Answers

Answer 1

The correct answer is: b, c, and d.  This extreme value theorem guarantees the existence of an absolute maximum and minimum

The extreme value theorem guarantees the existence of an absolute maximum and minimum for a function if the function is continuous on a closed interval.

Let's examine each function and interval to determine if the extreme value theorem applies:

a. f(x) = ln(1-x) over [0, 2]:

The function f(x) is not defined for x > 1, so it is not continuous on the interval [0, 2]. Therefore, the extreme value theorem does not guarantee the existence of an absolute maximum and minimum for this function.

b. g(x) = ln(1+1) over [10, 2]:

The function g(x) is constant, g(x) = ln(2), over the interval [10, 2]. Since it is a constant function, there is only one value, and therefore, the extreme value theorem does guarantee the existence of an absolute maximum and minimum, which are both ln(2).

c. h(x) = √(x-1) over [1, 4]:

The function h(x) is continuous on the closed interval [1, 4]. Therefore, the extreme value theorem guarantees the existence of an absolute maximum and minimum for this function.

d. k(x) = 1/√(x-1) over [1, 4]:

The function k(x) is continuous on the closed interval [1, 4]. Therefore, the extreme value theorem guarantees the existence of an absolute maximum and minimum for this function.

Based on the analysis above, the functions for which the extreme value theorem guarantees the existence of an absolute maximum and minimum are:

b. g(x) = ln(2) over [10, 2]

c. h(x) = √(x-1) over [1, 4]

d. k(x) = 1/√(x-1) over [1, 4]

Therefore, the correct answer is: b, c, and d.

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Related Questions

The temperature is -3F at 7:00 a.m during the next 4 hours,the temperature increases to 21F.what is the temperature at 11:00 a.m?

Answers

Answer:

I believe it is 24°F

Step-by-step explanation:

I'm just cool like that

Erisa collected quarters. After a year he had quite a few of them. In fact, when he counted them in groups of two, three, four, and so on, up to groups of 16, there was always one left over. What is the smallest number of quarters Erisa could have collected

Answers

Erisa collected quarters. After a year he had quite a few of them. The smallest number of quarters that Erisa could have collected is 17.

What is the smallest number?

Generally, Erisa collected quarters. After a year he had quite a few of them.

The smallest number of quarters that Erisa could have collected is 17.

This is because 17 is a prime number, and when it is divided into groups of 2, 3, 4, and so on, up to 16, there will always be one left over.

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What is value of x? enter your answer in the box. X = a triangle with vertices labeled as a, b, and c. Side b c is the base. A line segment is drawn from vertex a to base b c that bisects angle b a c into two parts marked with single arcs. Side a b is labeled as 8. Side a c is labeled as 12. Side b c is divided into two equal parts labeled as x plus 4 and 2 x plus 1.

Answers

The value of x calculated by using the Pythagorean theorem is equal to 6.

This can be found by using the Pythagorean theorem to solve for the length of side bc, which is the base of the triangle. By using the two given side lengths of 8 and 12, we can find that the length of the hypotenuse (bc) is equal to the square root of 8^2 + 12^2, which is equal to 16.

Since the base is divided into two equal parts, we can divide 16 by 2 and get 8. We then subtract the given length of 2x + 1 from 8 and get 7, which means x is equal to 6.

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p) find the sum of the infinite geometric series:
a1 = -20 a5 = -1650 r = 3

Answers

The sum of the infinite geometric series is 10

How to solve for the infinite geometric series

From the values that we have, the first term a1 = - 20, the common ratio r = 3

From the above we can get the first 5 terms of the geometric series. We do this by multiplying each number derived by 3

this would be :

-20, -60, -180, -540 , -1650 ...

The formula for the sum of the infinite geometric series is given as

S = a1 / 1 - r

from the question we have

a1 = -20

r = 3

we would put the values into the formula

S = -20 / 1 - 3

S = -20 / -2

s = 10

Hence the sum is given as 10

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A tunnel is constructed with a semielliptical arch. The width of the tunnel is 70 feet, and the maximum height at the center of the tunnel is 20 feet. What is the height of the tunnel 10 feet from the edge? round your answer to the hundredths place.

Answers

Considering the equation of an ellipse, it is found that the height of the tunnel 10 feet from the edge is of 14 feet.

The following is the equation for a horizontal ellipse of center with coordinates (h,k):

(x - h)²/a² + (y - k)²/b² = 1.

In relation to this issue, we have that:

The origin is where the center is.

Since the major axis is 70, 2a = 70 and a = 35.

The maximum height is 20, therefore b is equal to 20.

As a result, the ellipse's equation is as follows:

x²/35² + y²/20² = 1.

It is determined that x = 25 when the tunnel is 10 feet from the edge since 35 – 10 = 25; therefore, the height y is calculated as follows:

25²/35² + y²/20² = 1

0.51 + y²/20² = 1

y²/20² = 0.49

y² = 20² x 0.49

y =√(20² x 0.49)

y = 14 feet.

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I don’t understand this very well, help me with an explanation please?

Answers

Answer:

what is this on

Step-by-step explanation:

What is the first step to solving quadratic equations in factored form?

Answers

Transform the equation using standard form in which one side is zero is the first step to solving quadratic equations in factored form.

What is quadratic equations in factored form?Form factored (of a quadratic expression) A quadratic expression is said to be in factored form if it can be represented as the sum of a constant and two linear factors. If and only if its discriminant is a perfect square, a quadratic equation with integer coefficients can be factored over integers. To begin factorising an expression, "take away" any shared factors that the terms have. As x appears in both terms, if you were asked to factor x2 + x, you would write x(x + 1). It is common to refer to a polynomial as "irreducible" if it cannot be factored. It might not be factorable if the coefficients lack common components or are not reasonable.Use standard form to transform the equation so that one side is zero.Factor the non-zero side, step 2.3. Reset each component to zero (Remember: a product of factors is zero if and only if one or more of the factors is zero).Solve each of the ensuing equations.

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Simplify (s^-5)^3 write your answers using only positive exponents

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(s^-5)^3 can be simplified by using the property that (a^b)^c = a^(bc). So, (s^-5)^3 = s^(-5*3) = s^-15., the simplified version is s^-15 using only positive exponents.

What are the 3 exponent properties?

Answers

The 3 main exponent properties are:

The product of powers property: (a^m) * (a^n) = a^(m+n)The quotient of powers property: (a^m) / (a^n) = a^(m-n)The power of a power property: (a^m)^n = a^(m*n)

The product of powers property states that when you multiply two numbers with the same base, you can add the exponents to find the result. For example, (2^3) * (2^4) = 2^(3+4) = 2^7

The quotient of powers property states that when you divide two numbers with the same base, you can subtract the exponents to find the result. For example, (2^5) / (2^3) = 2^(5-3) = 2^2

The power of a power property states that when you raise a power to another power, you can multiply the exponents to find the result. For example, (2^3)^2 = 2^(3*2) = 2^6

These three properties help simplify algebraic expressions that include exponents and make it easier to solve equations and perform other mathematical operations.

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The table shows the length and width of proportional rectangles. Length (in inches) 4 6 12 16 width (in inches) 10 15 30 40 using the table, find the width of a rectangle that has a length of 24.

Answers

The width of a rectangle that has a length of 24 inches would be 60 inches.

According to the data, we can assume that all the rectangles in the table have the same ratio of measurement.

To find unknown width of the rectangle, we can use this equation:

A/B = C/D

Where:

A represents the length of the first rectangle  

B represents the width of the first rectangle

C represents the length of the second rectangle

D represents the width of the second rectangle

In this case, we are going to use 12 as the length of the first rectangle, and 30 as its width.

12/30 = 24/D

12D = (30 x 24)

12D = 720

D = 60

Thus, the width of the rectangle that has a length of 24 inches is 60 inches.

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Please Help ASP...... One and Two please

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The triangle that has two angles measuring 17 degrees and 107 degrees is a B. Obtuse triangle.

A triangle with sides of length 5, 6, and 7 would be a C. Scalene triangle.

What are some types of triangles ?

There are several types of triangles and one of them is an obtuse triangle. Such a triangle would have an angle that is larger than 90 degrees, much like the triangle mentioned that has an angle with 107 degrees.

There are also Scalene triangles where all their dimensions do not have the same measurement. This is why the triangle shown has sides of 5, 6, and 7.

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On the third grid, create a graph of the set of points (2+5t, 3-4t) for -2 ≤ t ≤ 7 pm the xy-plane

Answers

The graph of the set of the points has the constraints  -8≤2+5t≤37 &    -25≤3-4t≤11

What is an inequality?

An inequality is an inequation separated by <,>≥,≤

Given here: The set of points (2+5t,3-4t) in the xy-plane

when -2≤t≤7 set of points (2+5t,3-4t)

then 2+5×-2≤2+5t≤2+5×7

        -8≤2+5t≤37

     Again, 3-4×-2≤3-4t≤3-4×7

             -25≤3-4t≤11

We can construct a graph using the above accordingly

Hence, The graph of the set of the points has the constraints  -8≤2+5t≤37 &    -25≤3-4t≤11

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Please help me with my work

Answers

In algebra, fractions can be added, subtracted, multiplied, and divided just like in basic arithmetic.

In algebra, what does a fraction mean?

The components of a whole or group of objects are represented by fractions. A fraction consists of two parts. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the whole or collection. The denominator is the figure that appears below the line.

What are the Algebra Fundamentals?

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the fundamentals of algebra. Additionally, the algebraic expressions contain the fundamental arithmetic operations of addition, subtraction, multiplication, and division.

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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $11. The auditorium can hold a maximum of 130 people. The drama club must make a minimum of $1100 from ticket sales to cover the show's costs. Also, they can sell at least 90 adult tickets. If x x represents the number of student tickets sold and y y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.

Answers

The graph for the inequality is attached below.

What is Inequality?

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Each student ticket sells for $6.50 and each adult ticket sells for $11.

let the number of student ticket sold be x and number of adult ticket sold be y.

so, the inequality is

x + y < 130

and, 6.5x + 11y >1100.

Solving the inequality we get

x= 73.33 and y = 56.667

Now, if they sell at least 90 adult tickets then they sell at most 40 children ticket.

Hence, the solution is (73.33, 56.667).

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If A =3L(2h+pie R)find r in terms of A,L,pie and R

Answers

The value of the equation is r = ( 1/2 ) ( A / 3L - πR )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 3L ( 2r + πR )   be equation (1)

Now , on simplifying the equation , we get

( 2r + πR ) = A / 3L

Subtracting πR on both sides of the equation , we get

2r = A / 3L  - πR

Divide by 2 on both sides of the equation , we get

r = ( 1/2 ) ( A / 3L - πR )

Therefore , the value of r is ( 1/2 ) ( A / 3L - πR )

Hence , the equation is r = ( 1/2 ) ( A / 3L - πR )

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Question 6 of 22
Question 6
An air-conditioning and heating company has a fixed monthly cost of $3000. Furthermore, each service call costs the company $20.
Write an equation in slope-intercept form to represent the total cost for 1 month, y, if x service calls are made during the month.
y=

Answers

Answer:

For each service call cost of 20$ will be added to fixed cost of 3000$.

Step-by-step explanation:

The total cost for 1 month is the sum of the fixed monthly cost and the cost of all the service calls, so we can write the equation as:

y = 3000 + 20x

This equation is already in slope-intercept form, where "y" is the dependent variable, "x" is the independent variable, 3000 is the y-intercept (the point where the line crosses the y-axis, when x=0), and 20 is the slope of the line.

This equation can be interpreted as

For each service call cost of 20$ will be added to fixed cost of 3000$.

f(x) = 3(0.5)* transformation?

Answers

Answer: Vertical stretch by a factor of 3.



Tony has 8 yd fabric how many inches does he have ​

Answers

Answer:

Each yardn is 36 inches. Multiply the number of yards. times inches and that will be the total number of inches for 8 yards.

Step-by-step explanation:

I yd = 36 inches

you have 8 yards

36 x 8 = 288 inches

Answer:

answer is 288 inches

Step-by-step explanation:

8 yards is equal to 288 inches

Find the additive inverse of the linear expression. −2x+5 __

Answers

The answer is 2x-5

What are like and unlike terms in an expression?

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here:  linear expression. −2x+5

Thus the additive inverse is -2x+5+2x-5=0

Hence, the additive inverse is 2x-5

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If a and b are positive integers such that [tex]a^{3b}[/tex] = x and [tex]a^{b}[/tex] = y, then [tex]\frac{x}{y^{2} }[/tex] = ?

Answers

If algebraic expressions are a³ᵇ = x and aᵇ = y, then, by algebra properties, x / y² is equal to aᵇ.

How to find the result of an algebraic expression based on two given expression by algebra properties

Herein we find the following two algebraic expressions with two positive integers a and b:

a³ᵇ = x

aᵇ = y

From these equation we need to find the result associated to algebraic expression x / y² in terms of the integers given. This can be done by means of algebra properties. First, square the second expression:

(aᵇ)² = y²

Second, divide the first expression by the given formula found in previous step:

x / y² = a³ᵇ / (aᵇ)²

Third, simplify the resulting expression to a single power:

x / y² = a³ᵇ / a²ᵇ

x / y² = a³ᵇ - ²ᵇ

x / y² = aᵇ

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. The points (–5, 26) and (3, 26) are located on the same parabola. What is the equation for the axis of symmetry for this parabola?

Answers

The equation for given two points of parabola will be (x+1)^2=y-10.

What is parabola?

A parabola is a U-shaped plane curve where any point is at an equal distance from a fixed point (known as the focus) and from a fixed straight line which is known as the directrix.

In general, if the directrix is parallel to the y-axis in the standard equation of a parabola is given as:

y^2 = 4ax

If the parabola is sideways i.e., the directrix is parallel to x-axis, the standard equation of a parabola becomes,

x^2 = 4ay

Apart from these two, the equation of a parabola can also be y2 = -4ax and x2 = -4ay if the parabola is in the negative quadrants.

Now,

the parabola having points  (–5, 26) and (3, 26) is given in graph

and the equation will be (x+1)^2=y-10

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This is due soon please help out????

Answers

a) The equation of line is y = 270x + 10640.

b) The annual cost value in 2013 for age 17 is $15,320.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Points (8, 12800) and (14, 14420)

So, the slope is

= (14420 - 12800)/(14-8)

= 1620/6

= 270

and, the slope intercept form

(y - 12800) = 270 (x - 8)

y- 12800 = 270 x  - 2160

y = 270x + 10640

b) Now, x= 17

y= 270(17) +10640

y = 15, 320

Thus, In 2013 at age of 17 the amount is $15320.

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Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.


Please select the best answer from the choices provided.

T
F

Answers

True, Recreational water illnesses can only be contracted in fresh water sources, not swimming pools.

What is Recreational water illnesses?

Recreational water infections (RWIs) are contracted by ingesting, inhaling mists or aerosols from, or coming into touch with contaminated recreational water and are brought on by microorganisms.

                        In addition to swimming pools, hot tubs, water slides, water play zones, interactive fountains, lakes, rivers, and seas are all examples of recreational water.

What exactly is a recreational water?

Incorporated into this are swimming, diving, water skiing, and surfing. Recreation involving secondary touch, where you come into direct contact with the water but are unlikely to ingest it Paddling, wading, boating, and fishing all fall under this category.

                     without any physical interaction with the water, passive recreation.

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Hello! Please help I need this done tonight! I have no clue on how to do this! I have included a picture of the problem.

Answers

Answer:  x = 1,  y = -1

Step-by-step explanation:

The elimination method is a technique for solving systems of linear equations.

1) 4x-6y=10

2) 9x+2y=7

in the second equation

it multiply with 3

then

3×(9x+2y=7)

= 27+6y= 21

We notice that the first equation has a 6y term and the second equation has a -6y term. These terms will cancel if we add the equations together—that is, we'll eliminate the x terms:

then add 1 + 2 equations

    4x-6y =  10 _____1)

   27+6y= 21   _____2)

then we will get

    31x+0  =  31

     31x= 31

     where x = 31/31= 1

          then x = 1

      if value of  x substitute in the equation ____1)

                           4x+6y =  10

                           4×1+6y =  10

                            6y = -6

                            y = -6/6

                             y = -1

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If grapes are $1.99/pound and you buy 2.25 pounds of grapes, how much change will you receive if you hand the cashier a $5 bill

Answers

Using simple mathematical operations, we know that we will get a change of $0.5.

What are mathematical operations?

An operation is a function in math that transforms zero or more input values into a strictly delineated output value.

The operation's arity is influenced by the number of operands.

For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-" Multiplication (Identifying the result; "×" Finding the quotient in division ("÷)

So, we know that:

Grapes cost $1.99.

We purchased 2.25 pounds of grapes.

The change we will receive if we gave a $5 bill will be:

5 - (1.99*2.25)

5 - 4.4775

0.5225

Rounding off: $0.5

Therefore, using simple mathematical operations, we know that we will get a change of $0.5.


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Classifying Triangles Card ​

Answers

The triangle problem's solution is given by the relationship amongst x,y and z, which is z²= x²+y² .

Explain the triangle.

Due to its three vertices and three sections, a triangles is a polygon. It has a simple geometric form. Triangle ABC refers to a triangular with the points A, B, and C. When three factors are not collinear, a singular plane and triangle are found. Triangles are regarded as polygons since they have three corners and a right side. The points where a triangle's three sides intersect are known as the triangle's corners. By summing three triangle angles, one gets 180 degrees.

Here,

Given: In this situation, triangle XYZ is a right triangle.

Thus,

We discover:

Z, X, and Y components

They are linked in the following ways:

It being a right triangle,

So,

According to the Pythagoras Theorem,

=>z²= x²+y²

The triangle problem's solution can be found by using the relationship among z, x, and y, which is given by z2=x2+y2.

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the festival organizers expect 10,000 people to attend the four day festival at the end they have exceeded their attendance by 2000 people determine the average number of people that attended the festival per day

Answers

Answer:

500 people came each day

Step-by-step explanation:

2000 divide by 4= 500

21 500 ml + 31 650 ml​

Answers

Answer:

53,150 ML

Simply add both of the numbers and you have your answer.

someone help please thank you

Answers

Answer:

distance = (62t) + 22

Step-by-step explanation:

Distance = speed * time

distance = (62*t) + 22

Hope this helps!

URGENT!!!
In the figure [FD]=[FE] and [DM]=[NE] prove that the triangle FMN is two sided

Answers

Therefore , the solution of the given problem of congruences comes out to be [FD]=[FE] and [DM]=[NE]

What is congruency?

SSS stands for “side, side, side” and means that we have two triangles with all three sides equal.

SAS stands for “side, angle, side” and means that we have two triangles where we know two sides and the included angle are equal.

SAS theorem of congruence: The SAS (side-angle-side) theorem of congruence states that if two sides and their included angle in one triangle are exactly equal to the corresponding two sides and their included angle in another triangle, then the two triangles are congruent.

Here,

SSS – side, side, and side. ...

SAS – side, angle, and side. ...

ASA – angle, side, and angle. ...

AAS – angle, angle, and side. ...

HL – hypotenuse and leg.

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A force of 57. 1 newtons is applied for 0. 977 meters; what work was done on the object?. Show your workx+2y=-4-4x-3y=16 Select the correct answer from each drop-down menu.Flow chart, The Rock Cycle. Top, rectangular block Igneous points to blocks A (left), B (right). Block B points to middle block Magma to Igneous block. Words read, increasing pressure and temperature, weathering, deposition, lithification.In this model of the rock cycle, A represents rock and arrow B represents the process of Help me solve this pls because i need to solve this fast help me Someone has offered to buy you a financial instrument that has the following cash flows:- You will not receive any cash for the first five years. The first time you will receive a cash flow will be at the end of year 6. You will receive $100 at the end of year 6, $200 at the end of year 8, and $300 at the end of year 10.- You will receive another payment of $100 at the end of year 11, and the payment will grow at a rate of 6% forever.- You will need to pay a service fee. The service fee is as follows: you will pay $100 each year from year 1 to year 5 (i.e. you will make 5 payments in total. The first payment will occur at the end of year 1, and the last payment will occur at the end of year 5)Suppose that the discount rate is 10%. How much this financial instrument is worth to you? What is the surface area of this shape? overallhow americans opinion about foreign polciy were divided if f(x)=x^3+13x^2+44x+32 and f(-1)=0, then find all of the zeros of f(x) algebraically Select the correct answer.Which statement best expresses how the author connects art and craftsmanship in this text? A. The author insists that craftsmanship, and not beauty, is most significant in life. B. The author describes why it is important that artists make mistakes when learning craftsmanship. C. The author suggests that functional craftsmanship requires beautiful artwork. D. The author demonstrates how craftsmanship can be useful without being beautiful. Write a theme statement for "The World on the Turtle's Back." Ronald pushes a box up an inclined plane with 35% efficiency. If 224 joules of energy went into moving the box, how much energy did ronald put into the inclined plane?. BRAINLIEST + 50 POINTS!!!I need a little assistance... ( ;) pls!*please try to answer all!! tyy* Which of the following is an example of a behavior?A.A man imagines that he is a bat.B.A student remembers an answer to a questionC.A woman drives to work.D.An old man forgets his birthday. there are two types of cellular phones: handheld phones (h) that you carry and mobile phones (m) that are mounted in vehicles. phone calls can be classified by the traveling speed of the user as fast (f) or slow (w). monitor a cellular phone call and observe the type of telephone and the speed of the user. the probability model for this experiment has the following information: p(f) who was the original host of the late show, the first late-night talk show on fox? Tom works in chilled food department in a supermarket all fresh juices should be kept at a certain temperature as shown on thermometer Which of the following is not a way to determine whether a relation is a function? Can someone help me, please? Use the drop-down menus to complete the statements to match the information shown by the graph. Scheduling in service-providing firms focuses on when to assign employees and equipment to accomplish the work most efficiently without the benefit of:A. EmployeesB. Physical InventoryC. CustomersD. Gobal Network.