Marathon Race. Carlos, Maura, and Jacob are running a marathon-26 miles. Carlos runs at a rate of 6 miles per hour. Carlos runs at a rate that is 25% slower than Maura's rate. Jacob takes 2 hours and 36 minutes to finish the marathon. Determine and clearly show everyone's speed. Show or explain your
calculations. Clearly show the exact time it takes for each person to finish the race.

Answers

Answer 1

First, let's find Maura's running speed by using the information that Carlos runs at a rate that is 25% slower than Maura's rate. If Carlos runs at a rate of 6 miles per hour, then Maura runs at a rate of 6 * 1.25 = 7.5 miles per hour.

How to calculate time?

Next, let's calculate how long it takes for Carlos to finish the marathon. We know that Carlos runs at a rate of 6 miles per hour and the marathon is 26 miles long. So we can use the formula:

time = distance/rate

time = 26/6

time = 4.33 hours

Now let's find how long it takes for Maura to finish the marathon. We know that Maura runs at a rate of 7.5 miles per hour and the marathon is 26 miles long. So we can use the formula again:

time = 26/7.5

time = 3.47 hours

Finally, let's convert Jacob's time of 2 hours and 36 minutes to hours. We can use the formula:

time = 2 + (36/60)

time = 2 + 0.6

time = 2.6 hours

In conclusion, Carlos takes 4.33 hours, Maura takes 3.47 hours and Jacob takes 2.6 hours to finish the marathon.

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Related Questions

Convert the polar equation to rectangular form [tex]r=5cot(\theta)csc(\theta\))[/tex]

Answers

Answer:

[tex]\displaystyle x=\frac{1}{5}y^2[/tex]

Step-by-step explanation:

[tex]\displaystyle r=5\cot(\theta)\csc(\theta)\\\\r=5\biggr(\frac{\cos(\theta)}{\sin(\theta)}\biggr)\biggr(\frac{1}{\sin(\theta)}\biggr)\\\\r=\frac{5\cos(\theta)}{\sin^2(\theta)}\\\\r^2=\frac{5r\cos(\theta)}{\sin^2\theta}\\\\r^2\sin^2(\theta)=5r\cos(\theta)\\\\(r\sin(\theta))^2=5x\\\\y^2=5x\\\\x=\frac{1}{5}y^2[/tex]

Write an equation

Y=|x| 10 units down

Answers

To translate the point P(x,y) , a units left and b units down, use P'(x−a,y−b) .

Write an equation Y=|x| 10 units down?

y=|x-10|-3

Inside, is opposite. So therefore, to move it right 10 units, you subtract ten. However, outside of the absolute value, it is normal, so to move it down 3 units, you subtract 3.The number –45.3 is 45.3 units away from zero and the number 10 is 10 units away from zero. Therefore, the absolute value of any number is really a positive number (or zero).As we know that absolute value means remove the negative sign from the number and make it positive. So we get the absolute value of -10 as 10. So we get the absolute value of 10 as 10. Hence absolute value of -10 and 10 is 10 and 10 respectively

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Prime numbers are the _______ _______of all numbers

Answers

The numbers which have only two factors either 1 and the number itself are called prime numbers.

What is prime numbers?

Prime number is a natural number greater than 1 that is not a product of two smaller natural numbers while a natural number greater than 1 that is not prime is called a composite number

Therefore a prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29

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Simplify to a single trig function

Answers

On solving the provided question we can say that - the value of the trignometric function will be -cos(t)+2cosec(t)

what is trigonometry?

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

here,

(sint(t) + cos(t))[tex]^{2}[/tex] =(sint +cost)(sint - cost)

=|  -cos(t)+2cosec(t) |

= -cos(t)+2cosec(t)

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Help ASAP PLSSS!! I’d really appreciate it! Thank youuu!

Answers

Angle 1 (R) and angle C are congruent since they have no markings

C = 180 - (80 + 45)
C = 180 - 125
C = 55

I teach geometry :)

i have been trying to figure this out for hours-

answer choices:

SSS

SAS

ASA

AAS

HL

Not Congruent

Answers

Answer:  The answer is SAS

Which of the following tables represents a linear relationship that is also proportional?


x y
0 3
3 6
6 9

x y
0 4
2 6
4 8

x y
0 0
6 3
12 6

x y
0 3
5 5
10 7

Answers

The solution is Option A. , Option C.

The equations which are also proportional is y = 3x and x = 2y

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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Answer: The solution is Option A. , Option C.

Step-by-step explanation:

The equations which are also proportional is y = 3x and x = 2y

What is Proportion?

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the values of x = { 0 , 3 , 6 }

Let the values of y = { 3 , 6 , 9 }

Now , the proportional equation is y = 3x

So , the proportionality constant is k = 3

b)

Let the values of x = { 0 , 6 , 12 }

Let the values of y = { 0 , 3 , 6 }

Now , the proportional equation is x = 2y

So , the proportionality constant is k = 2

Hence , the equations are y = 3x and x = 2y

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What is the domain of f(x)=[1/2]*

Answers

Here we need to find the domain of the given function.

We will see that the domain is the set of all real numbers.

The first thing we need to do is to define the domain of a function.

For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.

Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.

Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.

Particularly, in our function: f(x) = (1/2)^x

We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).

Concluding, because there is no problem with any real value,  we can see that the domain is the set of all real numbers

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1/3m = 12-m

Please explain step by step to get marked as brainliest.

Answers

Step-by-step explanation:

cross multiply

12-m(3m)= 1

12-3m²-1=0

multiply by -1

3m²+1-12=0

3m²= 11

m²= 11/3

m=√11/3.

100 points please answer

Answers

The best answer is to simplifying each of the identity separately to get the same expression on both sides. Option C

What are trigonometric identities?

Trigonometric identities are described mathematically as equalities consisting of trigonometric functions that proves true for all the value of occurring variables for which both sides of equality are defined.

These involve certain functions of one, two or more angles.

They also are different from triangle identities, which involves angles and side lengths of a triangle.

To verify a trigonometric identity, we take the following steps;

Convert the equalities to terms of sine and cosine.Solve the identities at possible timesThen, simplify the left-hand side of the equation, before simplifying the right-hand side.

Hence, the best option is C

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Question
Enter a linear equation that models the situation.
A drugstore sells pens for $1.40 each and notebooks for $2 each. The owner would like to sell $40 of these
items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 40.

Answers

A linear equation that models the situation is 1.4p + 2n = 40.

This equation represents the total daily revenue from the pens (1.4p) and notebooks (2n) and sets it equal to the target revenue of $40. The variables p and n represent the number of pens and notebooks sold, respectively. This equation can be used to determine the number of pens and notebooks that need to be sold in order to reach the target revenue of $40.

Answer:

1.40p+2n=40

Step-by-step explanation:

There are 9 players on a baseball team there are 6 teams in the league how many baseball players are in the league

Answers

Answer:

54

Step-by-step explanation:

Multiply 9 (players per team) and 6 (teams in the league) to find the total players in the league.

9 times 6 = 54

Polynomial in standard form

1.
7-3x^3+6x^2

2.
2y-3-8y^2

Answers

Answer:

[tex]-3x^3+6x^2+7[/tex][tex]-8y^2+2y-3[/tex]

Step-by-step explanation:

The terms are ordered from greatest to least degree.

the image point using the translation (x,y) (x + 4, y -1) for the point (3,3) is?

Answers

The image of the point (3, 3) after a translation 4 units right and one unit down is (7, 2)

What is transformation?

Transformation involves moving an object from its original position to a new position on the coordinate plane. This can be a translation, dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane. Translation is a rigid transformation that preserves the shape and size. Other types of rigid transformation are reflection, and rotation

The translation using the rule (x, y) ⇒ (x + 4, y -1) is a translation 4 units right and 1 unit down.

The image of the point (3, 3) using the rule (x, y) ⇒ (x + 4, y -1) is (7, 2)

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a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?

Answers

Answer:

Step-by-Step:5 cars and 14 bikes

Write the equation of the line shown on graph (-1,-5) and (2,1)

Answers

Answer:

  y = 2x -3

Step-by-step explanation:

You want the equation of the line through the points (-1, -5) and (2, 1).

Slope

The slope of the line is given by ...

  m = (y2 -y1)/(x2 -x1)

  m = (1 -(-5))/(2 -(-1)) = 6/3 = 2

Y-intercept

The y-intercept of the line can be found from ...

  b = y -mx

  y = -5 -2(-1) = -3

Slope-intercept form

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . . . . line with slope m and y-intercept b

Using our found values, the equation is ...

  y = 2x -3 . . . . . . . . line with slope 2 and y-intercept -3

A store buys 14 sweaters for $84 and sells them for $504. How much profit does the store make per sweater?

Answers

Answer:

$30 per sweater is how much profit the store will make

Step-by-step explanation:

The cost of 1 sweater (for the store) is $6.

The store sells the sweater for $36 (504/14).

The store is making $30 per sweater.

Rewrite (2x+v)^2 without parentheses and simplify

Answers

Answer:

[tex]4x^2+4vx + v^2[/tex]

Step-by-step explanation:

[tex](2x+v)^2 \\(2x)^2+2(2x)(v)+(v)^2\\4x^2+4vx + v^2[/tex]

2. What number is a common multiple of
5 and 9?

Answers

Pretty sure the answer is 45

I need to know the first and last one

Answers

The lines FE and GH are parallel to each orther.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Given that

ΔPEI = ΔGHI

here ∠pie = ∠gih

PI =HI

GI=EI

So both triangles are congruent

So the FE║GH.

Hence the lines FE and GH are parallel to each orther.

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simplify expression: 3f+8(2m-7)

Answers

After simplification we got the above expression in the form 3f + 16m -56

What is simplify in mathematics?

The word "simplify" implies to turn something in a simpler form.

In mathematics, simplify an expression means write an expression in such a way that is comparatively less complicated than before. The main purpose of simplify an expression is to make it easy to solve as well as calculation.

How to simplify the above expression?

3f + 8(2m-7)

we rearrange the expression by removing the parenthesis.

we remove the parenthesis by multiplying the factors.

3f + 8 × 2m - 8 × 7

3f + 16m -56

the above expression has no like terms to add or subtract so it is kept in this form.

Hence, 3f + 16m -56 is the simpler form.

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Help please! How do I write an equation in standard form using the information on the graph?

Answers

Answer:

  3x -y = 2

Step-by-step explanation:

You want a standard form equation for the line through the points (0, -2) and (2, 4).

Slope

The slope of the line is the "rise" divided by the "run". The given point on the right is 3 grid squares above the one on the left. It is one grid square to the right. So, the slope is ...

  m = (squares above)/(squares to the right) = 3/1 = 3

If we consider the actual x- and y-values represented by these grid squares, then the slope is ...

  m = (4 -(-2))/(2 -0) = 6/2 = 3

Intercept

The point (0, -2) tells you the y-intercept is -2. That is where the line crosses the y-axis.

Slope-intercept equation

With this information, we can write the slope-intercept form equation for the line:

  y = mx +b . . . . . . . line with slope m and y-intercept b

  y = 3x -2 . . . . . . . . line with slope 3 and y-intercept -2

Standard form

The standard form of an equation for a line is ...

  ax +by = c

where a, b, c are generally mutually-prime integers with a ≥ 0. If a=0, then b > 0.

We can rearrange the slope-intercept equation to put it into this form.

  y = 3x -2

  3x -y -2 = 0 . . . . . subtract y

  3x -y = 2 . . . . . . . add 2. This is the standard-form equation of the line.

TEXT ANSWER
How can you use the unit price to find the cost of 10
pounds of tomatoes? Please help

Answers

To find the cost of 10 pounds of tomatoes, multiply 10 by the unit cost of tomatoes.

What is the unit cost?

The cost a business incurs to create, store, and sell one unit of a specific product is known as the unit cost. All fixed and variable production expenses are included in unit costs. Cost units are a way to measure the quantity of a good or service.

Unitary method: The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

The unitary method is used to find the unit cost of an object.

To find the cost of a unit object, multiply a by unit cost.

Given that, the unit cost of a unit pound of tomatoes.

The cost of 10 pounds of tomatoes is 10 ×  unit price of tomatoes.

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3p-3p+2s-6s+2q-3q+8r-7r

Is it ok to not put the p in this equation as the 3p is minus

Answers

Answer:

- 4s - q + r

Step-by-step explanation:

that's right. You do not put the p since 3p and -3p cancel out to give zero. I'll solve the question for you:-

⇒3p-3p+2s-6s+2q-3q+8r-7r

add or subtract the like terms(terms having same variables), then out of the two like terms, put the sign of the greater number, for e.g. 2q-3q = -1q

⇒0 - 4s - 1q + 1r

⇒- 4s - q + r Answer

hope that helps...

True or False: 10, 8, 6, 4, … is a geometric sequence.

Answers

Answer:

  False

Step-by-step explanation:

You want to know if it is true that 10, 8, 6, 4, ... is a geometric sequence.

Geometric sequence

A geometric sequence has a common ratio between adjacent terms. Here the ratios are ...

  8/10 = 0.8

  6/8 = 0.75

These numbers are different, so there is no common ratio. The sequence is not a geometric sequence. (False)

Mental Math In a toy​ store, the ratio of the number of dolls to the number of teddy bears is . If the store has 240​ dolls, how many teddy bears are in the​ store? Use pencil and paper. Describe the mental math steps you use to solve this problem.

Answers

Answer:

Step-by-step explanation:

Dolls:240 Teddy Bears:120

120:240

Please Describe the fraction If Possible.

Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2

Answers

System of equations y = 5x + 11 and y = 5x has no solution,  y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given system of equations are

a. y = 5x + 11 and y = 5x

Substitute the y value in first equation

5x=5x+11

So the system of equations y = 5x + 11 and y = 5x has no solution.

b. y = 6x + 3 and y = 3x

Substitute the y value in first equation

3x=6x+3

-3x=3

x=-1

y=-3

The system of equations has one solution

c. x + 4y = 8 and y = -1/4x + 2

x+4(-1/4x + 2)=8

x-x+2=8

The  system of equations has one solution has no solution

Hence, system of equations y = 5x + 11 and y = 5x has no solution,  y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.

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Find the measurement of the angle I dictated for each trapezoid.

Answers

The measures of missing angles in trapezoids are listed below:

Case 5: m ∠ J = 75°, Case 7: m ∠ T = 118°

How to determine the measures of missing angles

In this question we must determine the measures of missing angles in trapezoids. There are two hints to determine the values of the missing angles:

Any pair of angles along one of the two parallel lines and between the other two congruent sides have the same measure. Any pair of angles between two parallel lines are supplementary angles. Two angles are supplementary when the sum of their measures equals 180°.

Now we proceed to determine the missing angles in every trapezoid:

Case 5

m ∠ K + m ∠ J = 180°

21 · x + 15 · x = 180°

36 · x = 180°

x = 5

m ∠ J = 15 · x

m ∠ J = 15 · 5

m ∠ J = 75°

Case 7

m ∠ U = m ∠ T

m ∠ T = m ∠ U

m ∠ T = 118°

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Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.
What does g(30)≥20 tell you?

Answers

The inequality g(30) ≥ 20 us that: D. Mona found no more than 20 seashells in the first 30 minutes.

What is an inequality?

In Mathematics, an inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values, numbers, and variables in an algebraic equation, especially based on any of the following inequality symbols:

Greater than or equal to (≥).Greater than (>).Less than (<).Less than or equal to (≤).

How to determine the required function?

Assuming the variable g represents the total number of seashells and the variable x represents the total number of time (minutes), an inequality which would model the situation is given by;

g(x) ≥ x

when x = 30, we have;

g(30) ≥ 20

Therefore, Mona found no more than (less than or equal to) 20 seashells in the first 30 minutes.

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Complete Question:

Mona loves the ocean, so she was thrilled to visit the beach and collect some seashells. The function g(x) gives the number of seashells Mona found after x minutes of searching.

What does g(30) ≥ 20 tell you?

It took at least 20 minutes for Mona to find 30 seashells.

Mona found at least 20 seashells in the first 30 minutes.

It took at least 30 minutes for Mona to find 20 seashells.

Mona found no more than 20 seashells in the first 30 minutes.

Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.
g(t) = t^2 - 27/t

Answers

The coordinates of the inflection points are (3, 0) and it concave upwards

How to determine the coordinates of the inflection points.

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

g(t) = t^2 - 27/t

Express properly

So, we have

g(t) = t² - 27/t

Calculate the second derivative

So, we have

g''(t) = 2 - 54/t³

Set the differentiated equation to 0

2 - 54/t³ = 0

So, we have

2t³ = 54

Divide by 2

t³ = 27

Take the cube roots

t = 3

Substitute t = 3 in g(t) = t² - 27/t

g(3) = 3² - 27/3

g(3) = 0

This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)

How to determine the point of concave upward and concave downward

Recall that

g''(t) = 2 - 54/t³

Next, we check if the second derivative exist at t = 0,

g''(0) = 2 - 54/0³

g(0) = undefined

The undefined value implies that the graph has a vertical inflection point at t = 0

And as such, the graph of the function is concave upward

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What is the solution of 2x 3 7? What are the top 3 largest cities by area? It take Thorton 4 hour to edit a video for hi chool. If he ha already pent 2. 5 hour on thi video, what percent of the video i edited? Please helpWhich poly nominal has the zeros 1,-2i and 3 Which hypersensitivity reaction is antibody-dependent and includes the immediate cytotoxic response seen in maternal-fetal Rh incompatibility or mismatched blood transfusion How does Daisy's voice relate to the American Dream? How many terms are there in the expression 2p3 3p2 4p 7 *? Fill in the blank with the correct form of the verb in parenthei: 1. Mi hijo ____ a la nueve de la noche todo lo da. (dormir)2. Lorena ____ dormir temprano todo lo da. (preferir)3. Eduardo y y Miguel ____ que el examen e muy difcil. (penar)4. Nootro ____ a la diez y cincuenta toda la maana. (almorzar)5. Eteban y yo ____ ir al cine et tarde. (querer)6. Maril e ____ elegantemente para la boda. (vetir) 7. Yo ___ hablar epaol, ingle y franc. (poder)8. Netor ___ hoy de lo Etado Unido. (volver)9. La eorita ___ el libro a la biblioteca. (devolver)10. La clae ___ a la iete y quince de la maana. (empezar)11. T ___ balonceto y ftbol Americano? (jugar)12. Ello ___ el patel de chocolate con frea. (probar)13. El ___ la clae de matemtica a la once y media. (comenzar) A spinning disk has an initial angular speed of 12.5 rad/s. It is pushed by a kid with a constant angular acceleration of 3.41 rad/s2. a) What will be the angular speed in 5.26 s. What will be the angle turned in 5.26 s The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x. (A) Find the average cost per unit if 200 frames are produced. (B) Find the marginal average cost at a production level of 500 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 501 frames are produced. Which statement about the elements in Group 0 is correct?Tick () one box.A. All elements in the group are very reactive. B. All elements in the group form negative ions. C. The boiling points increase down the group.D. The relative atomic masses (Ar) decrease down the group. What is the importance and benefits of organic farming? How does improved technology allow the economy to operate more efficiently? Read the following quote from a group discussing a good charity to donate money from a recent fundraiser: "I think we should give the money to an animal shelter." What iswrong with this idea?A. It lacks support.B. It is off topic. ________ leadership model posits that an effective leader makes desirable rewards available, clarifies how employees can achieve objectives, and provides them support in doing so. The anthropologit i attending the annual conference of the American Aociation of Phyical Anthropologit (AAPA) and he i chatting with another paleoanthropologit named Jane who work at a nearby foil ite in Eatern Africa. Jane ak if he will hare hi foil data with her o he can compare the information uncovered at thi ite, and he worrie that haring the data with Jane will undermine hi authority in the dicipline. How hould he proceed? If a marketing team successfully defines a product's market requirements, what is an additional benefit of that process Beth is making a garden plot which measures 6 open parentheses square root of x plus 2 end root close parentheses units in length and open parentheses 5 square root of x plus 2 end root close parentheses units in width. What is the area of the garden? Which one of the following is not the formula for the quantity theory of money? O M x Y = P x V. O V = P x Y/MO M = 1/v x P x Y. O M x V = P x Y. QuestionWhich of the following conventions describes how Egyptian artists created tomb sculptures?They depicted lifelike proportion and anatomy.They depicted lively poses that entertained the pharaohs ka.They created dramatic facial expression and emotion.They used forms with no projecting parts that could break.