A lottery game contains 28 balls numbered 1
through 28. What is the probability of choosing
a ball numbered 29?

Answers

Answer 1

The probability of choosing a ball numbered 29 is among the 28 balls numbered 1 through 28 is 0

Probability: Calculating the probability of choosing a ball

From the question, we are to calculate the probability of choosing a ball numbered 29

From the formula for probability

P(A) = Number of favorable outcomes to A / Total number of possible outcomes

From the given information,

"A lottery game contains 28 balls numbered 1 through 28"

This means there are only 28 balls and they are numbered from 1, 2, 3, up until 28.

Now,

We are to determine the probability of choosing a ball numbered 29. Since there is no ball numbered 29,

Number of favorable outcomes = 0

Total number of possible outcomes = 28

Thus,

Probability of choosing a ball numbered 29 = 0/28

Probability of choosing a ball numbered 29 = 0

Hence,

Probability of choosing a ball numbered 29 is 0

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Related Questions

Solve the quadratic equation 2x2 – x = 15 using the quadratic formula.

Answers

Answer:

x = 3, -5/2

Step-by-step explanation:

First, you move the 15 onto the left of the equation by subtracting it from both sides.

Second, you plug your info into the quadratic equation.  (1 +- sqrt(1+4*15*2))/4

A laptop computer is purchased for $4700. Each year, it’s value is 80% of its value the year before. After how many years will the laptop computer be worth $1000 or less?

Answers

Answer:

Step 1:

Let x = number of years

Let y = Value of the laptop after x years

Step 2:

Write an equation that expresses the value of the laptop after x years y = 0.8((4700)x)

Step 3:

Set the equation equal to 1000 and solve for x

1000 = 0.8((4700)x)

1 = 0.8(4700)x

1/0.8 = 4700x

1.25 = 4700x

x = (1.25/4700)

Answer: The laptop will be worth $1000 or less after 0.0026608 years.

Answer:

1 year

Step-by-step explanation:

4700 x .8= 3760

4700 - 3760 = 940$

In 1 year the laptop will be $940

You buy a $256,000 home with a down payment of 24%. Find the amount of the down payment and the mortgage amount.

Answers

The down payment is 24% of the home price, which is:

0.24 * $256,000 = $61,440

Therefore, the amount of the down payment is $61,440.

The mortgage amount is the difference between the home price and the down payment, which is:

$256,000 - $61,440 = $194,560

Therefore, the mortgage amount is $194,560.

The amount of the down payment and the mortgage amount are $61440 and $194560

Finding the amount of the down payment and the mortgage amount.

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

Buy a $256,000 home with a down payment of 24%

This means that

down payment = 24% * 256,000

So, we have

down payment = 61440

Next, we have

mortgage amount = (1 - 24%) * 256,000

So, we have

mortgage amount = 194560

Hence, the mortgage amount is 194560

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Help pleasee

here is the picture is about Row Ops

Answers

The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

Reducing row matrices

From the question, we are to perform the given row operation on the given matrix

The given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

Now,

From the given information,

The operation we are to carry out is:

Add -4(row 1) to row 3

This means we are to multiply the first row by -4. Then, we will add the results to the corresponding elements on the third row (row)

Multiplying by -4

-4 × [ 1     2    1   | -5

     -4   -8   -4  | 20

Now, we will add the result from the multiplication to the corresponding elements in row 3

Adding the results to corresponding elements in row 3

   4    -1     6  |  -8

+  -4   -8   -4  | 20

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

   0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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​Lisa an experienced shipping​ clerk, can fill a certain order in 9 hours. Felipe a new​ clerk, needs 11 hours to do the same job. Working​ together, how long will it take them to fill the​ order?
The solution is ___Hours

Answers

It will take Lisa and Felipe approximately 4.95 hours to fill the order by working together.

To solve this problem, we can use the formula:

1/T = 1/T₁ + 1/T₂

where T is the time taken to complete the job when both Lisa and Felipe work together, T₁ is the time taken by Lisa to complete the job, and T₂ is the time taken by Felipe to complete the job.

Substituting the given values into the formula, we get:

1/T = 1/9 + 1/11

Simplifying the right-hand side of the equation, we get:

1/T = (11 + 9)/(9 x 11)

1/T = 20/99

Multiplying both sides by 99, we get:

T = 99/20

Therefore, working together, Lisa and Felipe can complete the job in 4.95 hours, or approximately 4 hours and 57 minutes.

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1. Find the zeros of the quadratic function by graphing. Round to the nearest tenth if necessary.
f(x) = -2x² + 3x + 1
A 0.8,2.1) is a zero of the quadratic function because it is the peak of the parabola.
B (0,1) is a zero of the quadratic because it is where the parabola crosses the y-axis.
C (-0,3,0) and (1.8,0) are zeros of the quadratic function because it is where the parabola crosses the x-axis.
D (0.8,2.1) and (0,1) are zeros of the quadratic function because it is where the parabola crosses the x-axis.

Answers

The correct answer is C: (-0.3,0) and (1.8,0) are zeros of the quadratic function because they are the points where the parabola intersects the x-axis.

The right response is C: (- 0.3,0) and (1.8,0) are zeros of as far as possible since they are the places where the parabola meets the x-turn.

plot the y-get at (0,1),

x = - b/2a

To find the x-heading of the vertex, which is x = 3/4. Substitute this worth into the capacity to find the y-course of the vertex, which is

f(3/4) = 1/8.

Plot the vertex at (3/4, 1/8).

Then, utilize this data to plot the remainder of the parabola. The zeros are the places where the parabola crosses the x-focus, which are close (- 0.3,0) and (1.8,0) obviously following changing in accordance with the closest 10th.

To track down the zeros of the quadratic capacity by illustrating, one ought to at first plot the y-get at (0,1) and a brief time frame later utilize the vertex condition to track down the headings of the vertex. Following plotting the vertex, the remainder of the parabola can be drawn. The zeros of the capacity are the x-gets, which can be found by finding the places where the parabola combines the x-turn. For this current situation, the zeros are close (- 0.3, 0) and (1.8, 0) resulting to adjusting to the closest 10th.

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A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answers

The height of the person on the ferris wheel can be modeled by the equation:

h = 20sin(π/4*t) + 21

where h is the height in meters above the ground, t is the time in minutes, and 21 meters is added to account for the height of the platform.

A student is solving the equation shown.
√x+1+2√x-1=0
For the first step in solving the equation, the student subtracts the second term from both sides of the equation.
For the second step, the student squares both sides of the equation.
What is the result of the second step?

Answers

Answer:

C) x + 1 = 4(x - 1)

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

Given equation to solve:

[tex]\sqrt{x+1} +2\sqrt{x-1} =0[/tex]

The result of the first step:

[tex]\sqrt{x+1} =-2\sqrt{x-1}[/tex]

The second step:

[tex](\sqrt{x+1})^2 =(-2\sqrt{x-1} )^2[/tex]

And its result is:

x + 1 = 4(x - 1)

The matching choice is C.

Given: rectangle MNPQ ~ rectangle RSTU

- find the perimeter of rectangle RSTU
- find the area of rectangle RSTU

Answers

The perimeter of rectangle RSTU is 21 cm.

The area of the rectangle RSTU is 27 cm².

How to find the perimeter and area of a rectangle?

A rectangle is a quadrilateral that has opposite side equal to each other and opposite side parallel to each other.

Therefore, let's find the perimeter of the rectangle RSTU and the area of RSTU.

Hence,

Let's find the width of the rectangle MNPQ

14 = 2(4 + w)

14 = 8 + 2w

14 - 8 = 2w

2w = 6

w = 6 / 2

w = 3 cm

Therefore, using similar ratio,

4 / 6 = 3 / RU

cross multiply

4RU = 18

RU = 18 / 4

RU = 4.5 cm

Therefore,

Perimeter of the rectangle RSTU = 2(6 + 4.5)

Perimeter of the rectangle RSTU = 2(10.5)

Perimeter of the rectangle RSTU =21 cm

Area of the rectangle RSTU = 4.5 × 6

Area of the rectangle RSTU = 27 cm²

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n/4.4 =7 Pls Help nowwwwwwwwwwwwwwwwwwwww

Answers

Answer:

n=7

Step-by-step explanation:

[tex] \frac{n}{4} \times 4 = 7 \\ \frac{4n}{4} = 7 \\ 4 \times \frac{4n}{4} = 7 \times 4 \\ 4n = 28 \\ \frac{4n}{4} = \frac{28}{4} \\ n = 7 [/tex]

how much money does she make all together in one week​

Answers

needs more explanation

Fully factorise x ² + 18x​

Answers

Answer: To factorize x² + 18x, we can first find the greatest common factor (GCF) of the two terms, which is x:

x(x + 18)

This is the fully factorized form of x² + 18x.

A side of the triangle below has been extended to form an exterior angle of 125°. Find the value of

Answers

From the given triangle, x has a value of 35°.

As a result, one of the triangle's sides has been stretched to create an exterior angle of 125° outside angle.

Which angles are adjacent?

Angles that are always located near one another, sharing a similar vertex and common side but not overlapping, are said to be adjacent angles.

According to the above figure, the tringle's exterior angle is 125°, and y is an adjacent angle to that.

Now, 125°+ y =180°

y = 180°-125°

y = 55°

As a result, the supplied triangle's value for y is 55°.

The sum of the triangle law,

55°+ 90° + x  = 180°

x = 35°

Therefore the value of x = 35°

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i need answer for this with explanation​

Answers

Answer:

53yd

Step-by-step explanation:

SA1 = 2(4×2)

= 2×8

= 16

SA2 = 2(4×3)

= 2×12

= 24

SA3 = 2(3×2)

= 2×6

= 12

TOTAL SA

16+24+13

= 53

1 Place an X in the table to show the solution that makes each equation true. 6+x=15 244 X 9x = 18 x=9​

Answers

Step-by-step explanation:

| Equation | Solution |

| 6+x=15 | x = 9 |

| 9x = 18 | x = 2 |

The table would look like:

| Equation | Solution |

| 6+x=15 | X |

| 9x = 18 | X |

Ina Crespo rowed 16 miles down the Habashabee River in 2 ​hours, but the return trip took her 4 hours. Find the rate Ina rows in still water and the rate of the current. Let x represent the rate Ina can row in still water and let y represent the rate of the current. I need help asap

Answers

Answer:ina can row 6mph in still water and 2 mph in current

Step-by-step explanation:


This is so hard. Can you help me with this?

Answers

Answer: 70, 6

Step-by-step explanation:

(a)  For <F  that is the same as <D.  The image has little hash marks to indicates the sides across from those angles are the same; therefore, the angles are the same

All of the angles are = 180   if you subtract <E, you are left with 140 to be split between <F and <D

<F= 70

(b) all of the sides are the same because all the angles are the same

so AB=6

The trajectory of a golf ball hit from a tee on the ground at an angle of 40 degrees with an initial speed of 50 meters per second can be modeled by the parabola f(x) = 0.84x − 0.0033x^2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the golf ball travels before hitting the ground.

Answers

Therefore, the horizontal distance the golf ball travels before hitting the ground is approximately 254.55 meters.

What is equation?

In mathematics, an equation is a statement that shows the equality between two expressions, typically separated by an equal sign (=). An equation can contain one or more variables, which are symbols that represent unknown or varying values. The value of the variable(s) can be found by solving the equation.

Here,

The equation of the parabolic trajectory of the golf ball is given by:

f(x) = 0.84x - 0.0033x²

where x is the horizontal distance travelled by the ball and f(x) is the corresponding height at that distance. To find the highest point of the trajectory, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

x = -b / 2a

where a and b are the coefficients of the quadratic term and the linear term in the equation of the parabola, respectively. In this case, we have:

a = -0.0033 and b = 0.84

Substituting these values into the formula, we get:

x = -0.84 / 2(-0.0033)

= 127.27

So the horizontal distance at the highest point of the trajectory is approximately 127.27 meters. To find the height of the highest point, we substitute this value of x into the equation of the parabola:

f(127.27) = 0.84(127.27) - 0.0033(127.27)²

f(127.27) ≈ 21.67

So the highest point of the trajectory is approximately 21.67 meters above the ground.

To find the horizontal distance the golf ball travels before hitting the ground, we need to find the two values of x where the height of the ball is zero (i.e., where the ball hits the ground). We can set f(x) = 0 and solve for x:

0 = 0.84x - 0.0033x²

0.0033x² = 0.84x

x = 0 or x = 254.55

So the golf ball hits the ground twice, once at x = 0 (i.e., where it was hit from the tee) and once at x ≈ 254.55 meters.

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What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?

Answers

The equation of the line passing through the point (-3,-4) and parallel to the x-axis is y = -4.

What is the equation of the line passing through the point (-3,-4) and parallel to the x-axis?

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept

Given that; the line passing through the point (-3,-4) and parallel to the x-axis.

A line that is parallel to the x-axis has a slope of 0, because the y-coordinate of any point on the line does not change as the x-coordinate varies.

Hence;

The equation of the line passing through the point (-3,-4) and parallel to the x-axis can be written in the form y = b, where b is a constant.

To determine the value of b, we substitute the coordinates of the given point (-3,-4) into the equation y = b:

-4 = b

Note that: y = b, where b is a constant.

y = -4

Therefore, the equation of the line y = -4.

Option C) y = -4 is the correct answer.

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Who can help mee??

Answers

The answer is $119
You need to multiply the 2 numbers that they give you and divide by 100 (for example: 4700 X 8 and divide by 100)

well, let's find out how much she made on each week

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8\% of 4700}}{\left( \cfrac{8}{100} \right)4700}\implies 376\qquad \textit{ first week} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{9\% of 5500}}{\left( \cfrac{9}{100} \right)5500}\implies 495\qquad \textit{ second week}\hspace{8em}\underset{ \textit{more on the 2nd week} }{\stackrel{ 495~~ - ~~376 }{\text{\LARGE 119}}}[/tex]

Help pleaseeeee I would appreciate it

Answers

(1) The result of the row operation R₂ ↔ R₃ is [ -5   1    0    8]

                                                                            [  8  8    -7   5 ]

                                                                            [ 2   2     6   -5]

(2) The result of the row operation  3R₁ ↔ R₁ is  [24  - 27   -21   - 18]

                                                                                [8       9      -4      -5]

                                                                                 [2       2       -7     -8]

What is the result of the row operation?

The result of the row operation in the matrix is calculated as follows;

R₂ ↔ R₃, implies changing row 2 and row, and the result would be;

[ -5   1    0    8]

[  8  8    -7   5 ]

[ 2   2     6   -5]

The result of obtained from 3R₁;

3R₁ = [24  - 27   -21   - 18]

3R₁ ↔ R₁ is determined as; (the row interchange)

[24  - 27   -21   - 18]

[8       9      -4      -5]

[2       2       -7     -8]

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You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

Answers

In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually

What is investment compounded annually?

When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.

For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960

Then new total amount after one year will be $12,000 + $960 = $12 960 ,

This process will continue for each year of the investment and the  formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n

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complete quesation:

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

a.

3.99% compounded monthly

b.

4% compounded quarterly

c.

4.175% compounded annually

d.

4.2% simple interest

Find the lengths of each triangle…
2x ft
6x ft
200ft

Answers

Answer:

[tex]2x=20\sqrt{10}\; \textsf{ft} \approx 63.25\; \sf ft[/tex]

[tex]6x=60\sqrt{10}\; \textsf{ft} \approx 189.74\; \sf ft[/tex]

Step-by-step explanation:

Assuming the given triangle is a right triangle, we can use Pythagoras Theorem to calculate the value of x and then find the measurers of the side lengths.

Pythagoras Theorem

[tex]\large{\boxed{a^2+b^2=c^2}[/tex]

where:

a and b are the legs of the right triangle.c is the hypotenuse (longest side) of the right triangle.

From inspection of the given diagram:

a = 2xb = 6xc = 200

Substitute these values into the formula and solve for x.

[tex]\begin{aligned} (2x)^2+(6x)^2&=200^2\\2^2\cdot x^2+6^2\cdot x^2&=40000\\4x^2+36x^2&=40000\\40x^2&=40000\\x^2&=1000\\x&=\sqrt{1000}\\x&=\sqrt{100 \cdot 10}\\x&=\sqrt{100}{\sqrt{10}\\x&=10\sqrt{10}\end{aligned}[/tex]

Substitute the found value of x into the expression for each side length.

[tex]2x=2 \cdot 10\sqrt{10}=20\sqrt{10}[/tex]

[tex]6x=6\cdot 10\sqrt{10}=60\sqrt{10}[/tex]

Therefore, the exact side lengths of the given right triangle are:

[tex]20\sqrt{10}\; \textsf{ft}, \;\;60\sqrt{10}\; \textsf{ft}, \;\; 200\; \textsf{ft}[/tex]

The side lengths to the nearest hundredth are:

63.25 ft189.74 ft200 ft

Which of the following points represents a striking deviation in the box plot above?
A.
P
B.
R
C.
S
D.
Q

Answers

Answer:

  A.  P

Step-by-step explanation:

You want to identify the point that represents a striking deviation in the given box plot.

IQR

The interquartile range for this box plot is the difference between the upper and lower quartiles:

  29 -26 = 3

Outlier

The "fence" that is 1.5 times the IQR below the lower quartile is ...

  26 -3·1.5 = 21.5

Point P lies beyond this fence, so is considered an outlier in the data set.

Point P represents a striking deviation, choice A.

<95141404393>

Please I want the answer!

Answers

The subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

Writing the subtraction expressions to calculate the lengths

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

O = (3, 2)

A = (-7, 5)

B = (-7, 2)

The distance between (or length of) the coordinates is calculated as

Length = √[(x2 - x1)² + (y2 - y1)²]

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

OB = √[(3 -- 7)² + (2 - 2)²]

OB = √[(3 -- 7)² + 0²]

OB = √[(3 -- 7)²]

OB = 3 -- 7

AB = √[(-7 -- 7)² + (5 - 2)²]

AB = √[0² + (5 - 2)²]

AB = √[(5 - 2)²]

AB = 5 - 2

Hence, the subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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Please help!!!
The number of miles m (in billions) traveled by vehicles in City A can be modeled by
2.86 + 112 where t is the number of years since 1994. Use a graphing calculator to
approximate the year in which the number of vehicle miles of travel in City A was 140 billion.
m ==
Based on the linear model, the number of vehicle miles of travel in City A was 140 billion in the
year

Answers

The year in which  the number of vehicle miles of travel in City A was 140 billion is 9.79 years. Thus, the linear model suggests that the number of vehicle miles traveled in city A was 140 billion in the 10th year approximately.

What is a linear model?

The word linear model is used differently in statistics depending on the context. The most common usage is in relation to regression models, and the phrase is frequently used interchangeably with linear regression models.

To derive the number of year,

140 = 2.86t + 112

Subtracting 112 from both sides gives:

28 = 2.86t

Dividing both sides by 2.86 gives:

t ≈ 9.79 years

See attached graph.

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Help please


The half-life of Radium-226 is 1590 years. If a sample contains 500 mg, how many mg will remain after 1000 years? -----------

Answers

after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.

what is approximately ?

Approximately means "about" or "roughly" and is used to indicate an estimated or approximate value or quantity, rather than an exact or precise one. For example, if someone says "the population of the city is approximately 1 million people," it means that the population is around 1 million,

In the given question,

The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original sample will have decayed. After another 1590 years (or a total of 2 half-lives), half of the remaining sample will have decayed, leaving 25% of the original sample.

To find how much of the original sample remains after 1000 years, we need to first determine how many half-lives have passed.

Number of half-lives = elapsed time ÷ half-life = 1000 years ÷ 1590 years/half-life = 0.63

So, approximately 0.63 half-lives have passed. Therefore, the fraction of the original sample remaining is:

fraction remaining = (1/2)⁰°⁶³ ≈ 0.518

To find the remaining mass, we can multiply the fraction remaining by the initial mass:

remaining mass = fraction remaining x initial mass

remaining mass = 0.518 x 500 mg ≈ 259 mg

Therefore, after 1000 years, approximately 259 mg of the original 500 mg sample of Radium-226 will remain.

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The solution set of the following equations 2x-y=8 , 3x+2y=5 is ..............
*​

Answers

Answer:

x = 3,

y = -2

Step-by-step explanation:

Let's write the given equations into a system:

{2x - y = 8,

{3x + 2y = 5;

Let's make y the subject from the 1st equation:

-y = 8 - 2x / × (-1)

y = 2x - 8

Replace y in the 2nd equation with its value from the 1st one:

3x + 2(2x - 8) = 5

Expand the brackets:

3x + 4x - 16 = 5

Collect like-terms:

7x = 5 + 16

7x = 21 / : 7

x = 3

y = 2 × 3 - 8 = -2

Answer is ( 3, -2 ) solution to the given set of equations

Step by step

We can use elimination method for this set of standard equations

2x-y=8 EQ.1
3x+2y=5 EQ.2

We can multiple each term in EQ.1 by 2 to eliminate y

2(2x - y = 8)
4x -2y = 16

we can add the equations and eliminate y

4x -2y = 16 EQ.1
3x+2y=5 EQ.2
——————
7x = 21

Divide both sides by 7 to solve x

7/7x = 21/7

x = 3

Now substitute value of x = 3 into EQ.2

3x+2y=5 EQ.2
3(3) + 2y = 5
9 + 2y = 5
Subtract 9 from both sides to isolate y
9-9+ 2y = 5 -9
Simplify
2y = -4
Divide both sides by 2 to solve y

2/2y = -4/2

y= -2

Your solution set is ( 3, -2 )

Check your work, sub x and y values into EQ.2

3x+2y=5 EQ.2

3(3) + 2(-2) = 5
9 - 4 = 5
5 = 5

This equals so your solution is correct!

Un elevador de taller mecánico tiene pistones de entrada y salida de 5 cm y de 60 cm de radio respectivamente. Con este dispositivo se mantiene levantado un auto de 2000 kg. ¿Cuál es la fuerza aplicada al pistón de entrada?

Answers

The force applied to the input piston is  136.25 N.

How to find the force applied to the intake piston?

This problem can be solved using the principle of hydraulic systems, which states that pressure in a confined fluid is transmitted equally in all directions.

Thus, we can equate  the pressure on the input piston to the pressure on the output piston, and solve for the force on the input piston. That is:

P₁ = P₂

F₁/A₁ = F₂/A₂    (Pressure = Force/Area)

F₂ = 2000 * 9.81 = 19620 N   (F = mg)

A₁ = π * r₁² = π * 5² = 25π cm²

A₂  = π * r₂ ² = π * 60² = 3600π cm²

F₁ = F₂/A₂ * A₁

F₁ = (19620/3600π) * 25π

F₁ = 136.25 N

Therefore, the force applied to the input piston is  136.25 N.

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Question in English

A machine shop lift has input and output pistons of 5 cm and 60 cm radius respectively. With this device, a 2000 kg car is kept lifted. What is the force applied to the intake piston?

help please i need help with this answer

Answers

The initial value (a) of the exponential function f(x) = 4ˣ is 1.

How to solve an exponential equation?

The standard form of an exponential equation is:

y = abˣ

where a is the initial value and b is the multiplication factor.

If b > 1, it is a growth function and if b < 1, it is a decay function.

Given the exponential function:

f(x) = 4ˣ

The initial value (a) = 1 and the multiplication factor (b) = 4.

The graph of the exponential function f(x) = 4ˣ is attached below.

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