A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=72t-16t^2. What is the maximum height that the ball will reach?
Do not round your answer

Answers

Answer 1

Answer:

The maximum height that the ball will reach is 81 ft

Step-by-step explanation:

Note that the tray of the ball is given by the equation of a parabola of negative main coefficient. Then, the maximum value for a parabola is at its vertex.

For an equation of the form

[tex]at ^ 2 + bt + c[/tex]

So

the t coordinate of the vertice is:

[tex]t =-\frac{b}{2a}[/tex]

In this case the equation is:

[tex]h(t)=72t-16t^2[/tex]

So

[tex]a=-16\\b=72\\c=0[/tex]

Therefore

[tex]t =-\frac{72}{2(-16)}[/tex]

[tex]t=2.25\ s[/tex]

Finally the maximum height that the ball will reach is

[tex]h(2.25)=72(2.25)-16(2.25)^2[/tex]

[tex]h=81\ ft[/tex]

Answer 2
Final answer:

The ball thrown vertically upwards will reach the maximum height of 81 feet after 2.25 seconds.

Explanation:

To find the maximum height the ball will reach, first, we need to recognize that the equation 'h(t)=72t-16t^2' is a quadratic function in the form of 'f(t)=at^2+bt+c'. The maximum point of a quadratic function, also known as the vertex, happens at 't=-b/2a'. In this case, 'a' is -16 and 'b' is 72.

So the maximum height is achieved at 't=-72/(2*-16)' or 't=72/32 = 2.25' seconds.

To find out the maximum height, we just need to substitute this value of t into the equation for h(t):

h(2.25)=72*2.25-16*2.25^2

The above calculation gives a maximum height of 81 feet.

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Related Questions

Solve for the indicated variable. Express numbers as integers or simplify fractions.

Answers

-288/5 or - 57.6 I used a calculator so I cannot solve step by step

I need help with Precal asap !!!! I’ll mark u as brainliest, please if you don’t know the correct answer don’t write down.

Answers

Answer:

Equation 1:  r = 4 +( 3 * cos theta  )

Equation 2: r = sqrt ( 5² * sin(2 theta) )

Step-by-step explanation:

GRAPH 1:  

The first graph is a dimpled limacon.

General equation for dimpled limacon:

r = a + b cos theta                     ∴ if dimple is along the x- axis

r = a + b sin theta                      ∴ if dimple is along the y-axis

y-intercept : { a, -a }  = { 4, -4 }   ∴ the points at which limacon intersects y-axis

Negative side of x-axis = ( a – b ) ⇒ 1

Positive side of x-axis = ( a + b ) ⇒ 7

Subtract the value of a from sum of a and b to find b:

b = 7 – 4 ⇒ 3

Equation1:  r = 4 +( 3 * cos theta  )

GRAPH 2:  

The second graph is a lemniscates.  

General equation for lemniscates is:

r² = a² cos(2theta)                        ∴ if petals of graph are on coordinate axis

r² = a² sin(2 theta)                ∴ if petals of graph are not on coordinate axis

now, according to the graph:

a = 5 ⇒ a² = 25

angle of graph:  cos2θ, simply divide 360° by 2:

[tex]\frac{360}{2}[/tex] ⇒ 180°

The petals cannot be on coordinate axis, we start from 45° and then the next petal will be on:

45° + 180° = 225°

Since the graph is not on the coordinate axis, so

r² = 5² sin(2 theta)   ⇒    r = sqrt ( 5² * sin(2 theta) )      

Equation 2: r = sqrt ( * sin(2 theta) )      

Given: m EH =85°, m∠EYV=35°. Find: m EV .

Answers

Answer:

  155°

Step-by-step explanation:

∠EYV is half the difference of arcs EV and EH

  (1/2)(EV -EH) = ∠EYV

  (1/2)(EV -85°) = 35° . . . . fill in the given values

  EV -85° = 70° . . . . . . . . .multiply by 2

  EV = 155° . . . . . . . . . . . . add 85°

______ of symmetry- ALine that divides an object into two congruent halves.

Answers

Answer:

"A line"

Step-by-step explanation:

A line of symmetry is a line that divides an object into two congruent halves.

_____

However, not every line that does so is a line of symmetry. The vertical line in the attached diagram divides both figures into congruent halves. It is only a line of symmetry for the green figure.

Answer:

Axis of symmetry

Step-by-step explanation:

That's the "axis of symmetry."  It's most often associated with parabolas.

PLEASE HELP ME WILL RATE AND MARK BRAINLIEST PLEASE I NEED TO PASS IMAGE ATTACHED

Answers

Answer:

  x = 21

Step-by-step explanation:

From the rules of secants (and tangents), you know that ...

   x^2 = 7·(7 +56)

   x = √(7·63) = √441 = 21

_____

When secant lines intersect, the product of distances from the point of intersection to the two points on the circle is a constant. The tangent line is a degenerate case where the two points of intersection are the same point (hence the product of distances is x^2). For the other secant, the near distance is 7, and the far distance is 7+56  = 63.

Interestingly, this property holds whether the secants intersect inside the circle or outside (as here). That makes it easier to remember, since there's really only one rule, not three.

Choose the correct graph for the equation y=2x+3

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

PLEASE ANSWER THIS... WILL VOTE FOR U


Answers

The answer is g(x) = (1/4 x)^2

It has a horizontal stretch of 4. Since it is horizontal it goes inside the parentheses and becomes the reciprocal of 4  which is  1/4

Hope this helped!

~Just a girl in love with Shawn Mendes

The perimeter of a rectangle is 72 centimeters. The base is 2 times the height. What are the dimensions of the rectangle? a. h = 9 cm, b = 18 cm c. h = 12 cm, b = 24 cm b. h = 19 cm, b = 38 cm d. h = 10 cm, b = 20 cm

Answers

The answer is c. This is the ONLY possible answer.

Help please............​

Answers

Answer:

  (9x -2)(9x +2)

Step-by-step explanation:

Each of the terms in the difference is a perfect square, so the "perfect square trick" applies. The factors are the sum and difference of the square roots of the given terms.

√(81x²) = 9x√4 = 2

  81x² - 4 = (9x +2)(9x -2)

14. Simplify 3! (1 point) 2 5 3 6

Answers

Answer: the answer is 6

Step-by-step explanation: 3 times 2 is 6 then 6 times 1 is still 6

Answer: [tex]3!=6[/tex]

Step-by-step explanation:

The factorial function has the following symbol: "!" (As you can observe, it is an exclamation mark).

 The factorial functions are applied to the numbers greater than zero. Then, the factorial of a positive integer "n" is representend as:

[tex]n![/tex]

Since you need to simplify 3!, you has to multiply all the positive  integer numbers that are between the number 3 and and the number 1.

Therefore, for 3! you get the following result:

[tex]3!=3*2*1\\3!=6[/tex]

A car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012. Create an exponential expression to model the number of cars serviced after t years. Then, match each part of the exponential expression to what it represents in the context of the situation. The quarterly rate of growth is 0.03 or 3%. The growth rate is 1.03. The growth factor is represented by 1.03. The compound periods multiplied by the number of years is 4t. 920(1.03) is the number of cars multiplied by 1.03. The initial number of cars serviced is 920. Coefficient arrowRight Exponent arrowRight Rate arrowRight Base arrowRight

Answers

Answer:

N=920 (1+0.03)^4t

where N=number of cars serviced after t years

Step-by-step explanation:

Apply the compound interest equation

N=P( 1+r/n)^nt

where N ending number of cars serviced , P is the number of cars serviced in 2012, r is the interest rate, n is the number of compoundings per year, and t is the total number of years.

Matching parts of the exponential function

Initial number of cars serviced=920

The quarterly rate of growth = if interest is compounded quarterly, n=4

r=12% ÷ 4 = 0.03 or 3%

The growth rate is given by (1 +r/n) = 1+0.03 = 1.03

number of compoundings for t years= nt= 4t

The compound period multiplied by the number of years = 920(1.03)^4t

HELP. See attached for question and choices.

Answers

Answer: Second Option

{m| [tex]m\leq-0.48[/tex]}

Step-by-step explanation:

We have the following equation

[tex]10(10m+6)\leq12[/tex]

To solve this equation apply the distributive property

[tex]10(10m+6)\leq12[/tex]

[tex]10*10m+6*10\leq12[/tex]

[tex]100m+60\leq12[/tex]

Subtract 60 on both sides of the inequality

[tex]100m+60-60\leq12-60[/tex]

[tex]100m\leq12-60[/tex]

[tex]100m\leq-48[/tex]

Divide between 100 both sides of the inequality

[tex]m\leq-\frac{48}{100}[/tex]

[tex]m\leq-0.48[/tex]

The solution is

{m| [tex]m\leq-0.48[/tex]}

A computer company produced this graph to show how many computers it expects to sell based on
how much the company spends on Internet advertising. The company expects to sell 40 million
computers, spending $5 million on Internet advertising. Which set of units and scales are appropriate
for the two axes?

Answers

Answer: Hence, Fourth option is correct.

Step-by-step explanation:

Since we have given that

Number of computers expected to sell = 40  millions

Cost price of internet advertising = $5 million

According to the graph, we can see that

40 millions is the y-coordinate and $5 million is the x-coordinate.

so, Horizontal axis - y- axis is the "Number of computers".

Vertical axis - x- axis is the "Advertising cost ":

Hence, Fourth option is correct.

Horizontal axis will have number of computers in millions and vertical axis will have advertising dollars in millions.

Given information:

The graph of computer production and advertising amount spent is given in the question.

Total number of computer sell = 40 millions

Cost of internet advertising = $5 million

Now , by looking the graph one can conclude that, Y coordinate of the graph is 40 million and the X coordinate of the graph is $5 million.

Hence, from the above conclusion one can write as:

Horizontal axis (X-axis) is the number of computers and the Vertical axis is (Y-axis) the advertising cost of computers.

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Factor and Simplify the expression sin^2x+sin^2xcot^2x

Answers

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)+sin^2(x)cot^2(x)\implies sin^2(x)+\underline{sin^2(x)}\cdot \cfrac{cos^2(x)}{\underline{sin^2(x)}} \\\\\\ sin^2(x)+cos^2(x)\implies 1[/tex]

PLEASE HELP!!!!! TIMED!!! Will give brainliest!! 70 POINTS!!!!!
Matteo wants to write a statement that can be represented by the inequality P<9 Which describes the correct method to write a statement to match this inequality?

Use the inequality symbol to determine the relationship between the variable and the constant. Decide what the variable will represent. Decide what the constant will represent. Write a statement using the same relationship. An example is “Alva spent more than $9.”

Decide what the variable will represent. Decide what the constant will represent. Write a statement using the same relationship. An example is “Alva spent less than $9.” Use the inequality symbol to determine the relationship between the variable and the constant.

Decide what the variable will represent. Decide what the constant will represent. Use the inequality symbol to determine the relationship between the variable and the constant. Write a statement using the same relationship. An example is “Alva spent less than $9.”

Decide what the variable will represent. Decide what the constant will represent. Use the inequality symbol to determine the relationship between the variable and the constant. Write a statement using the same relationship. An example is “Alva spent more than $9.”

Answers

Answer:C

Step-by-step explanation:

The constant and the variable relationship is p<9.That means it is "Alva spent less than 9%"

Answer:

it is c

Step-by-step explanation:

i'm gonna need help with this one

Answers

Answer:

  KM = 20

Step-by-step explanation:

Point V is the midpoint of KM, so ...

  KV = VM

  2.5z = 5z -10

  10 + 2.5z = 5z . . . . . add 10

  10 = 2.5z . . . . . . . . . subtract 2.5z

This is sufficient to answer the question:

  KV = VM = 2.5z = 10

  KM = KV + VM = 10 + 10

  KM = 20

_____

In this case, it is not necessary to find the value of z. If you wanted to, you could divide by the coefficient of z in the last equation:

  10/2.5 = z = 4

Members at a yoga school pay $10 per class plus a one time $100 membership fee.non members pay $15 per class.how many classes would a member have to take to save money compared to taking classes as a non-member?

Show work Plz!!

Answers

Answer:

21 classes

Step-by-step explanation:

Let’s set up equations for both memebers and non-members!

Let c = classes

To find how many classes it would take to make the two things even, we set them equal.

10c+100 = 15c

Solving for c,

5c = 100

So c = 20.

Since you need 20 classes to break even, to save money as a member, you need 21 classes.

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = x i + y j + 9 k S is the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8

Answers

[tex]S[/tex] is a closed surface with interior [tex]R[/tex], so you can use the divergence theorem.

[tex]\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+9\,\vec k\implies\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(x)}{\partial x}+\dfrac{\partial(y)}{\partial y}+\dfrac{\partial(9)}{\partial z}=2[/tex]

By the divergence theorem, the flux of [tex]\vec F[/tex] across [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over [tex]R[/tex]:

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

Convert to cylindrical coordinates, setting

[tex]x=u\cos v[/tex]

[tex]y=y[/tex]

[tex]z=u\sin v[/tex]

The integral is then

[tex]\displaystyle2\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}\int_{y=0}^{y=8-u\cos v}u\,\mathrm dy\,\mathrm du\,\mathrm dv=\boxed{16\pi}[/tex]

Final answer:

The flux of a vector field across a surface is calculated using a surface integral, which involves integrating the dot product of the vector field and the differential area element over the surface. For closed surfaces, the outward orientation is used. Electric flux, the flux of the electric field across a surface, is mentioned as an example.

Explanation:

The flux of a vector field across a surface can be calculated using a surface integral. For the given vector field F(x, y, z) = x i + y j + 9 k and the surface S defined as the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8, the flux is evaluated by integrating F·dS over the surface S.

The orientation of the surface is important in this process. For a closed surface, the positive (outward) orientation is used. The normal vector at any point on the surface points from the inside to the outside, and this outward normal is used to compute the flux through a closed surface.

Conceptually, this is like breaking the surface up into infinitesimally small patches dA and summing up the contributions of the vector field F (in this case, x i + y j + 9 k) through each patch - this is referred to as electric flux in the context of electric fields. This calculation embodies the concept of electric flux, which is defined as the scalar product of the electric field and the area vector.

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*help please* What is the amplitude of the function graphed?

Answers

So amplitude is the length from the highest (or lowest) point from the mid-line of the function

In this case the mid-line is y = 1

The highest point, which has a y of 3 is 2 units away from the mid-line. This means that the amplitude is 2!

Hope this helped!

The amplitude of the function graphed will be 2.

What is amplitude ?

The amplitude of a function is the amount by which the graph of the function travels above and below its midline, i.e. it is the height from the mean value of the function to its maximum or minimum.

We have,

A graph,

The highest value = 3,

Lowest value = -1

So,

From the definition mentioned above,

Amplitude [tex]=\frac{3+|-1|}{2}[/tex]

We get,

Amplitude = 2

Hence, we can say that the amplitude of the function graphed will be 2.

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Write an equation for the line below.

Answers

Answer:

  x = 3

Step-by-step explanation:

A vertical line has the form x = constant. The graph shows the constant you want is 3.

Thaddeus and lan start at the same location and drive in opposite directions, but leave at different times. When they are 365 miles apart, their combined travel is 16 hours. If Thaddeus drives at a rate of 20 miles per hour and lan drives at a rate of 25 miles per hour, how long had each been driving?

Thaddeus has been driving____? hours and lan has been driving_____? hours.


I NEED HELP RIGHT NOW PLEASE

Answers

Answer:

Thaddeus: 7 hIan: 9 h

Step-by-step explanation:

If Thaddeus drives the whole 16 hours, the distance between them is ...

  distance = speed · time

  distance = 20 mi/h · 16 h

  distance = 320 miles.

It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...

  (45 mi)/(5 mi/h) = 9 h

The rest of the 16 hours is the time that Thaddeus drove: 7 hours.

___

Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...

  distance = speed · time

  365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)

  45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms

  (45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x

_____

Comment on the solution

You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.

Final answer:

To solve the problem, we need to set up two equations based on the information given in the problem. Solving the equations simultaneously gives Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.

Explanation:

First, we'll define the variables. Let's say the time Thaddeus has been driving is T hours, and the time Ian has been driving is I hours. The total distance they covered is the sum of the distances each one traveled, which is 365 miles. Thaddeus travels at a rate of 20 mph, while Ian travels at 25 mph. This is represented by the equation 20T + 25I = 365.

Next, we know that the total time they have been driving is 16 hours, which gives us another equation, T + I = 16. Now we have a system of linear equations that we can solve simultaneously to find the values of T and I. The solution gives T = 7 hours and I = 9 hours. Hence, Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.

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In a concert band, the probability that a member is in the brass section is 0.50. The probability that a member plays trombone, given that he or she is in the brass section, is 0.24. What is the probability that a randomly selected band member is in the brass section and plays trombone?

Answers

Answer:

B. 0.12

Step-by-step explanation:

To obtain this probability, you need to multiply the two probabilities.. since it's comprised of two events: one that he's in the brass section, one that he plays trombone.  The probably of him playing trombone only happens if he's in the brass section.

So, you have the possibility he's in the brass section: 0.50

The possibility he's playing trombone, if he's in the brass section: 0.24

P = 0.5 * 0.24 = 0.12

Answer:

B: 0.12

Step-by-step explanation:

ap3x

Find the slope of the line that passes through the points (2.1) and (-1.-1).​

Answers

Answer: The slope is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The slope can be calculated with the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then, knowing that the line passes through the points (2,1) and (-1,-1), we can substitute the coordinates into the formula.

In this case:

[tex]y_2=-1\\y_1=1\\x_2=-1\\x_1=2[/tex]

Therefore, the slope of the line that passes through the points (2,1) and (-1,-1) is:

[tex]m=\frac{-1-1}{-1-2}\\\\m=\frac{-2}{-3}\\\\m=\frac{2}{3}[/tex]

A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions? 2 cm and 6 cm 3 cm and 4 cm 1.5 cm and 8 cm 1 cm and 12 cm

Answers

Answer:

  2 cm and 6 cm

Step-by-step explanation:

The product of the dimensions must be 12 cm². (All answer choices meet that requirement.)

Opposite sides of a rectangle are the same length, so the sum of the two dimensions must be half the perimeter, 8 cm. The sums of the answer choices are ...

8 cm7 cm9.5 cm13 cm

Only the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.

6

×

2

Explanation:

For the rectangle

Length

=

Breadth

=

b

Area is  

12

 

cm

2

b

=

12

Perimeter is  

16

 

cm

2

(

+

b

)

=

16

+

b

=

8

Substitute  

b

=

12

from first equation

+

12

=

8

2

+

12

=

8

2

8

+

12

=

0

Use quadratic formula (

x

=

b

±

b

2

4

a

c

2

a

) to find  

=

(

8

)

±

(

8

)

2

(

4

×

1

×

12

)

2

×

1

=

8

±

16

2

=

8

±

4

2

1

=

8

+

4

2

=

6

2

=

8

4

2

=

2

If  

1

is taken as length then  

2

is the breadth of the rectangle.

What are the solution(s) to the quadratic equation 50 – x2 = 0?

x = ±2
x = ±6
x = ±5
no real solution

Answers

Answer:

x = ±[tex]5\sqrt{2}[/tex]

Step-by-step explanation:

We have been given the quadratic equation;

[tex]50-x^{2}=0[/tex]

The first step is to subtract 50 from both sides of the equation;

[tex]50-x^{2}-50=0-50[/tex]

[tex]-x^{2}=-50[/tex]

Multiplying both sides by -1 yields;

[tex]x^{2}=50[/tex]

The final step is to obtain square roots on both sides;

[tex]\sqrt{x^{2} }=\sqrt{50}\\x=+/-\sqrt{50}[/tex]

Therefore, x = ±[tex]5\sqrt{2}[/tex]

Given: AB ≅ BC BD − median of ΔABC, m∠ABD = 40° Find: m∠ABC, m∠BDC

Answers

Answer:

m∠ABC= 80°, m∠BDC= 90°

Step-by-step explanation:

If m∠ABD = 40°, then add 40°+40° to get m∠ABC because AB ≅ BC, meaning their angles would be congruent.

For m∠BDC, just look at the picture and deduce that it's a 90 degree angle.

Answer:

m∠ABC=80° and m∠BDC=90°

Step-by-step explanation:

Given the ΔABC in which AB ≅ BC, m∠ABD = 40° and BD is median of ΔABC.

we have to find the measure of angle ∠ABC and ∠BDC.

As the median of isosceles triangle split the angle at the vertex into two equal parts i.e ∠ABC is twice the angle ∠ABD

[tex]\angle ABC=2\angle ABD[/tex]

[tex]\angle ABC=2\times 40=80^{\circ}[/tex]

Also the median of isosceles triangle is perpendicular to the opposite side i.e to the base. Here, BD is perpendicular to AC

⇒  ∠BDC=90°

Therefore, the measure of angle ABC and BDC is 80° and 90° respectively.

Use Green's Theorem to evaluate the line integral along the given positively oriented curve. C cos(y) dx + x2 sin(y) dy C is the rectangle with vertices (0, 0), (5, 0), (5, 4), (0, 4)

Answers

By Green's theorem,

[tex]\displaystyle\int_C\cos y\,\mathrm dx+x^2\sin y\,\mathrm dy=\iint_D\left(\frac{\partial(x^2\sin y)}{\partial x}-\frac{\partial(\cos y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

where [tex]D[/tex] is the region with boundary [tex]C[/tex], so we have

[tex]\displaystyle\iint_D(2x+1)\sin y\,\mathrm dx\,\mathrm dy=\int_0^5\int_0^4(2x+1)\sin y\,\mathrm dy\,\mathrm dx=\boxed{60\sin^22}[/tex]

Find the value of x in each case. Give reasons to justify your solutions!

Answers

Answer:

  x = 11°

Step-by-step explanation:

The parallel lines suggest we look to the relationships involving angles and transversals. The angle marked 33° and ∠CAB are alternate interior angles, hence congruent:

  ∠CAB = 33°

5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:

  5x = 2x + 33°

  3x = 33° . . . . . . . . . subtract 2x

  x = 11° . . . . . . . . . . . divide by 3

a weight lifter uses both 2 kg blocks as well as 5 kg blocks to set up his bar. he has a total of 30 blocks if the total weight of the bar is observed to be 120 kg then calculate the number of 5 kg blocks and 2 kg blocks​

Answers

Answer:

The number of the 2 kg blocks is 10

The number of the 5 kg blocks is 20

Step-by-step explanation:

Let the number of the 2 kg blocks be x and the number of the 5 kg blocks be y.

The total number of blocks in terms of x and y is;

x + y

We are informed that he has a total of 30 blocks, implying that;

x + y = 30

The total weight of the bar in terms of x and y will be;

2x + 5y

We are also informed that the total weight of the bar is observed to be 120, implying that;

2x + 5y = 120

We therefore have two equations in two unknowns.;

x + y = 30

2x + 5y = 120

We can solve these equations simultaneously via elimination method;

multiply the first equation by 2;

2x + 2y = 60

2x + 5y = 120

Subtracting the first equation from the second one yields;

5y - 2y = 120 - 60

3y = 60

y = 20

But x + y = 30, implying that;

x = 30 - 20

x = 10

What is Mean Absolute Deviation (MAD)? How do I do it? (Please have an example to show.)

Answers

Explanation:

It is the average (mean) of the absolute values of the differences between a set of numbers and their mean.

Example: consider the set {1, 2, 4}. The mean is computed in the usual way: the sum divided by the number of contributors —

mean = (1 + 2 + 4)/3 = 7/3 = 2 1/3

Then the deviations are ...

1 -2 1/3 = -1 1/3 . . . . the absolute value of this is 1 1/3

2 -2 1/3 = -1/3 . . . . . the absolute value of this is 1/3

4 -2 1/3 = 1 2/3 . . . . the absolute value of this is 1 2/3

The mean of these absolute values is their sum divided by the number of them:

(1 1/3 +1/3 +1 2/3)/3 = (3 1/3)/3 = 1 1/9

The MAD of {1, 2, 4} is 1 1/9.

_____

Your graphing calculator or spreadsheet program may have a function that will calculate this for you.

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