Express 0.55555... as a fraction in
simplest form.

The position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

The position is the object can depend on where you are, and the description might also change if it is based on where other objects are.

The velocity is the time rate of change of position of a body in a specified direction. the rate of speed with which something happens.

Acceleration is the act or process of moving faster or happening more quickly: the act or process of accelerating rapid acceleration is the acceleration of economic growth.

a(t) = 3t

d^2/dx^2=(3t)

x(t) = [tex]\int\limits {3t} \, dt[/tex]

    = 3 *t^2 / 2

Hence the position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

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Answer:

1.2

Step-by-step explanation:

Answer:[tex]2/3+5/9= \frac{2x3}{3x3} + 5/9 =6/9 +5/9+\frac{6+5}{9} = 11/9[/tex]

Step-by-step explanation: answer : 11/9

Hope this helps u ; )

Answer:

Step-by-step explanation:

3

2

​

−

2

3

​

y+

3

1

​

y+4=0

Combine −

2

3

​

y and  

3

1

​

y to get −

6

7

​

y.

3

2

​

−

6

7

​

y+4=0

Convert 4 to fraction  

3

12

​

.

3

2

​

−

6

7

​

y+

3

12

​

=0

Since  

3

2

​

 and  

3

12

​

 have the same denominator, add them by adding their numerators.

3

2+12

​

−

6

7

​

y=0

Add 2 and 12 to get 14.

3

14

​

−

6

7

​

y=0

Subtract  

3

14

​

 from both sides. Anything subtracted from zero gives its negation.

−

6

7

​

y=−

3

14

​

Multiply both sides by −

7

6

​

, the reciprocal of −

6

7

​

.

y=−

3

14

​

(−

7

6

​

)

Multiply −

3

14

​

 times −

7

6

​

 by multiplying numerator times numerator and denominator times denominator.

y=

3×7

−14(−6)

​

Do the multiplications in the fraction  

3×7

−14(−6)

​

.

y=

21

84

​

Divide 84 by 21 to get 4.

y=4

We can use the pythagorean theorem to answer this question.

We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.

So, we can build the equation:

[tex]7^2+7^2 = l^2[/tex]

[tex]98 = l^2[/tex]

[tex]\sqrt{98} = l[/tex]

According to the question, ABCD is a rectangle with different coordinate values and they are as follows: A(-2,7); B(4,4); C(2,0); D(-4,3), The perimeter will be 14cm.

Using the standard definition of the perimeter that is perimeter is the sum of all the sides.

Therefore,

Perimeter = Sum of all the sides

Perimeter = -2+7+4+4+2+0-4+3 = 14 cm

And using the standard formula of the area that is the multiplication of length and width.

Now,

Area = (4)(4) = 16 cm

Hence, the calculated area = 16 cm^2 and calculated perimeter = 14 cm.

What is the area and perimeter of a rectangle?

The perimeter of a rectangle can be calculated by adding all the four lengths from all the sides. Similarly, to know the area of the rectangle by multiplying length and width.

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The value of x using the given equation is -5.

Define the solution of an equation.

A solution of an equation is defined as the set of all possible values of unknown variables that will make the equality hold.

Solving for the value of x

Given the equation, 4(x - 5) + x = 8x - 10 - x

4x - 20 + x = 8x - 10 - x

5x - 20 = 7x - 10

Rearranging the equation, we get,

7x - 10 - 5x + 20 = 0

2x + 10 = 0

x = -10 / 2

x = -5

Hence, the value of x on solving given equation is -5.

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Answer:

4/12

Step-by-step explanation:

If the ratio 4:8 is a part-to-part ratio, it means that there are 4 of something and 8 of something else with a total of 12. To convert a part-to-part ratio such as 4:8 as a fraction, you make the left side of the colon the numerator and the total the denominator: 4:8 → 4/12

By determining the conjecture is not valid by the law of detachment.

A statement in mathematics that has not been formally proven is referred to as a conjecture. Observing a pattern that holds true in numerous instances leads to conjectures. But just because a pattern appears frequently, it does not imply that it will appear frequently in all instances. The mathematical observation cannot be fully accepted unless conjectures are proven. A conjecture becomes a theorem if it has been thoroughly proven.

Hypothesis: Tommy makes cookies tonight.

Conclusion: Tommy must have an oven.

Even though the stated statement, "Tommy has an oven," matches the conclusion, the hypothesis is not always true. Tommy might own an oven, but he could bake something other than cookies in it.

Hence, the hypothesis is unfounded.

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The 5th term of the given geometric sequence is 768.

A geometric sequence is a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a ratio.

a(n) = a(n-1) . r

Where:

a(n) = nth term

r = ratio

The given geometric sequence is:

   3,12,48,192, . . .

Find the ratio

r = a(n)/a(n-1)

  = a(2)/a(1) = 12/3 = 4

Use the formula for the nth term.

a(n) = a(1) . r^(n-1)

In the given sequence a(1) = 3.

Substitute a(1) = 3, r = 4, and n = 5:

a(5) = 3 . 4⁵⁻¹

      = 3 . 4⁴ = 768

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Circle J has a radius of 10 units and BC = 5.4 units then the measure of AB is 14.6 units.

A radius of a circle or sphere is any of the line segments from its center to its perimeter in classical geometry, and in more modern usage, it is also their length. The name is derived from the Latin radius, which means both rays and spoke of a chariot wheel.

The radius of a circle is the distance between the circle's center and any point on its circumference. It is usually represented by the letters 'R' or 'r'. This number is significant in almost all circle-related formulas. A circle's area and circumference are also measured in terms of radius.

Since AC is the diameter of circle J and the radius is 10,  AC = 2(10) or 20 units.

AB + BC = AC

Where the value of BC = 5.4, we get

substitute the value of BC in the above equation, then we get

AB + 5.4 = 20

subtract 5.4 from both sides

AB + 5.4 - 5.4 = 20 - 5.4

simplifying the above equation,

AB = 14.6

Therefore, the measure of AB is 14.6 units.

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Answer: 100 is four times as large as 25.

Step-by-step explanation:

[tex]100 \div25=4[/tex]

Hence, 100 is four times as large as 25.

Answer:

The answer is 100 is four times as large as 25

Step-by-step explanation:

Division compares numbers by telling you how many times larger the first number is then the second number. In this problem, 100/25=4.

Put another way, 25 x 4 = 100. Therefore,100 is four times as large as 25

The total number of fiction books are 2385.

What is constant of proportionality?

The constant of proportionality is the ratio of two proportional values at a constant value is known as the constant of proportionality. When either their ratio or product results in a constant, two variables' values are said to be proportionally related. The ratio between the two stated quantities determines the value of the proportionality constant.

Given that,

Let the total number of fiction books be f and nonfiction books be n.

The constant of proportionality between the number of fiction book(f) and the number of non-fiction books(n) in a library is 15/22 .

f/n= 15/22

Also, the total number of nonfiction books is 3498.

Therefore,

f/3498 = 15/22,

f= 15/22 x 3498,

f= 15 x 159,

f= 2385.

Hence, the total number of fiction books in the library are 2385.

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Answer:

D.

[tex]x > - 3[/tex]

Step-by-step explanation:

[tex] - 2x - 7 > 5x + 14 \\ - 2x - 5x < 14 + 7 \\ - 7x < 21 \\ x < \frac{21}{ - 7} \\ x > - 3[/tex]

The variable expression for the word phrase, "the product of a number z and 7", is C. 7z.

A variable expression is defined as a mathematical phrase that contains variables and numbers combined together with any mathematical operations. The most common variable used to denote something is the variable x.

Given the word phrase "the product of a number z and 7"

let z be the variable denoted for a number

and a product of a number z and 7 can be written as:

7z

Therefore, the variable expression for the word phrase "the product of a number z and 7" is 7z.

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The linear function is:

f(x) = $10*x

Where the domain is:  [10, 25]

And the range is: [$100, $250]

Here we know that x represents the number of hours that he works per week, and we also know that he wins $10 per hour, then if he works x hours, the amount that he wins is x times $10, so the equation is just:

f(x) = $10*x

Now we also want to get the domain and range for this function. We know that he needs to work at least 10 hours and at maximum of 25 hours, so we have the restrictions:

10 ≤ x ≤25

So the domain is D: [10, 25]

To find the range we evaluate in the values of the domain, the minimum of the range is f(10) = $10*10 = $100

The maximum of the range is f(25) = $10*25 = $250

Then the range is R: [$100, $250]

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There are 91% of players weighing less than or equal to 246 pounds that the players' weights are given in the box plot.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that the box plot

Here, the total number of players = 40

And the minimum weight of players  = 152 pounds

Third quartile (Q₃) = 246

In the box plot, approximately 10 of the 11 coverage intervals occur between 152 and 254.

So the approximate percentage of students that weigh 246 kg or less would be

⇒ (10 / 11)×100

⇒ 90.90

Therefore,  there are 91% of players weigh less than or equal to 246 pounds.

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Answer:

A. F/5 = 4

Step-by-step explanation:

F is the total of fish so F is divided by the total of dolphins, which is 5

so F/5 = 4

Answer:

F/5=4

Step-by-step explanation:

F is the total amount of fish. Since there are 5 dolphins to feed, you should divide F by 5.

The integer that makes the expression, (____ + -3 = -4), true is -1.

According to the question,

We have the following expression:

__ + (-3) = -4

Now, let's take the integer to be filled in the blank as x.

Now, putting x in the given expression:

x + (-3) = -4

x = -4+3 (3 was negative on the left hand side. So, it is positive on the right hand side.)

x = -1

(More to know: when two numbers are given with two different signs then the smaller number is subtracted from the larger number but the sign remains of the number which is larger.)

Hence, the integer that makes the given addition sentence true is -1.

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Step-by-step explanation:

16. [tex]PQ = \frac{IK}{2} ⟹ \frac{24}{2} [/tex]

[tex]PQ = 12[/tex]

I can't really solve no. 17

The statement that the orthocenter of a right triangle is located at the vertex of the right angle is always true.

The orthocenter of a triangle is the point where the perpendicular drawn from the vertices to the opposite sides of the triangle intersect each other.

You can see in the image, there is a right-angled triangle ABC right angled at B. When we draw perpendiculars from each of  vertices of the triangle, they intersect at the vertex of the right angle. Hence, we can say that the orthocenter of a triangle is always located at the vertex of the right angle.

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Step-by-step explanation:

Combine like terms on the right side,

42= 3x+6.

Subtract 6 from each side

36=3x

Divide each side by 3

x=12, which is our lowest integer.

The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.

Hope this helps.

A)  x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.

B) The maximum revenue is 6060 dollars.

C) Two prices between which a profit is made are $19 and $21.

Given:

profit function P(x)= -15x² + 600x + 60

The value of a is -15, which is negative, so the graph is opening downwards.

The graph of the function is a parabola and it opens downward therefore it has a maximum point. The formula used to find the vertex of the parabola  f(x) is given by

x-coordinate of the vertex = -b/2a

y-coordinate of the vertex =  f(-b/2a)

We have the x-coordinate of the parabola as:

⇒  -600 / 2(-15)

⇒ -600/-30 = 20

A)  x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.

B) y-coordinate of the vertex is given by

    f(20) = -15(20)² + 600(20) + 60

             = 6060

The maximum revenue is 6060 dollars.

C)   f(21) = -15(21)² + 600(21) + 60

             = 6045

       f(19) = -15(19)² + 600(19) + 60

             = 6045

   at $21, the profit is $6045

   at $19, the profit is $6045

Two prices between which a profit is made are $19 and $21.

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The value of x is 4.89 ≈ 5 units

Given,

The figure includes two right angled triangles.

Consider the first right angled triangle:

Hypotenuse = 7 units

Base = 3 units

Altitude = a

By using Pythagorean theorem, we can find a.

That is,

Hypotenuse² = Altitude² + Base²

7² = a² + 3²

49 = a² + 9

a² = 49 - 9

a² = 40

Altitude = [tex]\sqrt{40}[/tex]  units

Now consider second right angled triangle:

Hypotenuse = [tex]\sqrt{40}[/tex] units

Altitude = 4 units

Base = x units

Apply Pythagorean theorem:

Hypotenuse² = Altitude² + Base²

([tex]\sqrt{40}[/tex])² = 4² + x²

40 = 16 + x²

x² = 40 - 16

x² = 24

x = [tex]\sqrt{24}[/tex]

Base, x = 4.89 ≈ 5 units.

Therefore, the value of x is 4.89 which is approximately equals to 5 units.

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The given infinite geometric series 2/3+4/9+8/27+ ...... is convergent and the sum is 2

The given geometric series is:

  2/3 + 4/9 + 8/27 + ......

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 2/3

a(2) = 4/9

a(3) = 8/27

Hence, the common ratio is

   r = a(2) / a(1) = (4/9) / (2/3) = 2/3

An infinite geometric series is convergent if 0 < | r | < 1.

Since r = 2/3, then the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 2/3  and r = 2/3 into the formula:

S = (2/3) / (1 - 2/3)

   = (2/3) / (1/3)

   =  2

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Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.​

To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.

Solving gives:

= 3¹/₃ ÷ 1²/₃

= 10/ 3 ÷ 5/3

= 10/3 x 3/5

= 30/ 15

= 2 times more

In conclusion, Samir walked two times more.

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Answer:

Step-by-step explanation:

Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.​

How many times more did Samir walk?

To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.

Solving gives:

= 3¹/₃ ÷ 1²/₃

= 10/ 3 ÷ 5/3

= 10/3 x 3/5

= 30/ 15

= 2 times more

In conclusion, Samir walked two times more.

Probability of spinner pointer not landing on green is equal to 2/3 if the spinner lands on a line it is spun again.

As given in the question,

Total colors in the spinner is equal to 6

Each color is 2 times

Total number of colored region =6

Number of green region = 2

Probability of pointer landing on green color  P(G)= 2 /6

Probability of pointer not landing on green P(G') = 1- P(G)

                                                                            = 1- (2/6)

                                                                             = 2/3

Therefore, probability of spinner pointer not landing on green is equal to 2/3, if the spinner lands on a line it is spun again.

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2. For the given cylinders, we have that:

A. The volume is of 72π cm³ and the curved surface area is of 48π cm².

B. The volume is of 112π cm³ and the curved surface area is of 56π cm².

5. There are 330 liters of water in the container.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

The curved surface area of a cylinder of radius r and height h is given as follows:

S = 2πrh.

For problem 2 item a, we have that the parameters are given as follows:

r = 3, h = 8.

Hence:

The volume is of 72π cm³ and the curved surface area is of 48π cm².

For problem 2 item b, we have that the parameters are given as follows:

r = 8/2 = 4, h = 7.

Hence:

The volume is of 112π cm³ and the curved surface area is of 56π cm².

For item 5, the parameters are given as follows:

r = 0.65/2 = 0.325m, h = 1m.

Hence the volume is:

V = πr²h = π(0.325)² = 0.33 m³.

Each m³ has 1000 liters, hence:

0.33 x 1000 = 330 liters.

There are 330 liters of water in the container.

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