How many revolutions does a go kart with a wheel circumference of 62.8318 inches make in a 1609 m race? Please answer as quickly as possible!

Check the picture below.

so then, the distance from the center to that point is really the radius.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(9-3)^2+(3-2)^2}\implies r=\sqrt{36+1}\implies r=\sqrt{37} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{2}{ k})\qquad \qquad radius=\stackrel{\sqrt{37}}{ r} \\\\\\ (x-3)^2+(y-2)^2=(\sqrt{37})^2\implies (x-3)^2+(y-2)^2=37[/tex]

Answer:

The product is equal to [tex]3\sqrt{15}[/tex]

Step-by-step explanation:

Ok,

First, you have

[tex](3\sqrt{-3})(\sqrt{-5})[/tex]

We must follow the rule for multiplying radicals, in this case:

[tex](3\sqrt[2]{-3})(\sqrt[2]{-5})=(3\sqrt[2]{(-3)(-5)})[/tex]

Note that the types of root, n, have to match, in this case is 2 for each root

Then, we know that two negative numbers multiplied give a positive number, in this case

[tex](3\sqrt[2]{-3} )(\sqrt[2]{-5})=(3\sqrt[2]{(-3)(-5)})=(3\sqrt[2]{(15)})[/tex]

So, the correct answer is [tex](3\sqrt{-3})(\sqrt{-5} )=3\sqrt{15}[/tex]

Answer:

Step-by-step explanation:

Vertically stretched. The action of vertically stretched is accomplished by altering a in

y = a* abs(x)

What that means is that you make a > 1. In this case, a = 2

So far, what you have is

y = 2*abs(x)

Six units down. The action of 6 units down is accomplished by a number added or subtracted to/from absolute(x). down is minus, up is plus.

y = 2*abs(x) - b. Since we are moving down, b<0

y = 2*abs(x) - 6

Four Units Right. This is the tough one because it is anti intuitive. You would think you should be adding something somewhere to get a right hand movement.

Not true.

To move right you subtract something in the brackets.

y = 2*abs(x - 4) - 6

Graph

Just to make things complete, I have graphed this for you. Desmos is wonderful for this kind of problem.

red: y = abs(x)

blue: y = 2*abs(x - 4) - 6

Answer:

Step-by. step explanation:

Answer:

f(x) = (x + 1)² + 2 in vertex form ⇒ 3rd answer

Step-by-step explanation:

* Lets revise how to find the vertex form the standard form

- Standard form ⇒ x² + bx + c, where a , b , c are constant

- Vertex form ⇒(x - h)² + k, where h , k are constant and  (h , k) is the

  vertex point (minimum or maximum)  of the function

- At first we must find h and k

- By equating the two forms we can find the value of h and k

* Lets solve the problem

∵ f(x) = x² + 2x + 3 ⇒ standard form

∵ f(x) = (x - h)² + k ⇒ vertex form

- Put them equal each other

∴ x² + 2x + 3 = (x - h)² + k ⇒ open the bracket power 2

∴ x² + 2x + 3 = x² - 2hx + h² + k

- Now compare the like terms in both sides

∵ 2x = -2hx ⇒ cancel x from both sides

∴ 2 = -2h ⇒ divide both sides by -2

∴ -1 = h

∴ The value of h is -1

∵ 3 = h² + k

- Substitute the value of h

∴ 3 = (-1)² + k

∴ 3 = 1 + k ⇒ subtract 1 from both sides

∴ 2 = k

∴ The value of k = 2

- Lets substitute the value of h and k in the vertex form

∴ f(x) = (x - -1)² + 2

∴ f(x) = (x + 1)² + 2

* f(x) = (x + 1)² + 2 in vertex form

First number = 23+x

Second number = 2(23+x)-18 = 46 +2x -18 = 2x +28

Now multiply each term by each term :

23 +x * 2x +28

23 * 2x + 23 * 28 + x *2x + x*28=

46x + 644 + 2x^2 + 28x =

Final answer = 2x^2 +74x +644

The answer is D.

Answer:

The product of two numbers is  [tex]P(x)=2x^2+74x+644[/tex]

Step-by-step explanation:

We are given that The first number is the sum of 23 and x,

First number = 23+x

The second number is 18 less than two times the first number.

Second Number = [tex]2(23+x)-18[/tex]

The product of two numbers :  [tex](23+x)(2(23+x)-18)[/tex]

                                                    [tex](23+x)(46+2x-18)[/tex]

                                                    [tex](23+x)(28+2x)[/tex]

                                                    [tex]2x^2+74x+644[/tex]

Let P(x) denotes the product

So, The product of two numbers is  [tex]P(x)=2x^2+74x+644[/tex]

Hence Option D is true .

The product of two numbers is  [tex]P(x)=2x^2+74x+644[/tex]

Answer:

they both have the equilateral lines on each side

Step-by-step explanation:

Answer:

$48

Step-by-step explanation:

we know that

$80 represent 100%

so

using proportion

Find how much is 60%

80/100=x/60

x=80*60/100

x=$48

Answer:

  2³² -1

Step-by-step explanation:

The sequence has a₁ = 1 and r = 2. Filling in the numbers for n=32, we have ...

S₃₂ = 1·(1 -2³²)/(1 -2)

S₃₂ = 2³² -1

Answer:

D. (–3, –6) and (5, 10)

Step-by-step explanation:

The system has equations:

[tex]y=2x[/tex]...(1)

and

[tex]y=x^2-15[/tex]...(2)

Equate both equations;

[tex]x^2-15=2x[/tex]

Rewrite in standard form:

[tex]x^2-2x-15=0[/tex]

We factor to obtain:

[tex](x+3)(x-5)=0[/tex]

By the zero product principle;

[tex](x+3)=0,(x-5)=0[/tex]

[tex]\implies x=-3,x=5[/tex]

When x=-3, y=2(-3)=-6

This yields the ordered pair (-3,-6).

When x=5, y=2(5)=10

This yields the ordered pair (5,10).

The correct choice is D.

Answer:

B. Multiply 5 times 3. Multiply 5 times 4. Add the two products

Step-by-step explanation:

Right from the start the question is only asking for squash plants so the other two rows don't need to be counted.

7-2 = 5

In each row there's 3 yellow squash = 5*3 = 15

And 4 green squash = 5*4 = 20

which means there's 35 squash total in the garden.

Answer:

jump discontinuity at x = 0; point discontinuities at x = –2 and x = 8

Step-by-step explanation:

From the graph we can see that there is a whole in the graph at x=-2.

This is referred to as a point discontinuity.

Similarly, there is point discontinuity at x=8.

We can see that both one sided limits at these points are equal but the function is not defined at these points.

At x=0, there is a jump discontinuity. Both one-sided limits exist but are not equal.

The accurate discontinuities for the graph that we have here is jump discontinuity at x = 0; point discontinuities at x = –2 and x = 8.

This is the point in the graph where the values that are supposed to be in the equation would have to jump instead of being continuous. This is the point where there are broken lines.

The points in the graph that we have here can be gotten in the second option of the question.

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Answer:

There are a total of 4 + r + 6 marbles in the bag

The probability of a blue is  [tex]\frac{4}{10+r}[/tex]  

The probability of a red is  [tex]\frac{r}{10+r}[/tex]  

The probability of choosing a blue, replacing it and then a red is

[tex]\frac{4}{10+r}[/tex] × [tex]\frac{r}{10+r}[/tex]  =  [tex]\frac{4r}{100+20r+ r^{2} /[tex]

Step-by-step explanation:

Answer:

18 Quarts

Step-by-step explanation:

there are 4 quarts per gallon

I multiplied 4 x 5 = 20 then subtracted the 2 quarts left which comes out to 18 quarts used.

Answer:

b. [tex]\frac{p-1700}{10}[/tex]

Step-by-step explanation:

We have that the server's salary can be expressed as

[tex]p = $1700+$10t[/tex]

Counting the $ 1700 dollars as the fixed amount of your salary and contemplating the variable salary that would be $ 10 * t being t the number of overtime worked  

from this expression we can clear the number of overtime worked by clearing t, so I finally have

[tex]p=$1700+$10t\\ $10t = p - $1700 \\ t= \frac{p-1700}{10}[/tex]

Done

Answer:

The measure of angle 6 is m∠6=50°

Step-by-step explanation:

we know that

m∠3+m∠6=180° ----> supplementary angles (interior consecutive angles)

so

we have

m∠3=130°

substitute

130°+m∠6=180°

m∠6=180°-130°=50°

Answer:

(-.5, 0)

Step-by-step explanation:

y ---- 2÷2=1, y-1= 1-1=0

x ---- 3÷2 =1.5, x-1.5= 1-1.5= -.5

Answer:

( -0.5, 0 )

Step-by-step explanation:

Add the 0 before 5, it matters if its right or wrong. The Answer is ( -0.5 , 0 ). ADD THE 0 !!!!!

Im pretty sure this is the answer F (x) = e^2x + 1

Answer:

10976π/3 cm³

Step-by-step explanation:

Volume of a sphere is:

V = 4/3 π r³

where r is the radius (half the diameter).

The diameter is 28 cm, so the radius is 14 cm.

V = 4/3 π (14 cm)³

V = 10976π/3 cm³

Final answer:

The volume of a basketball with a diameter of 28 cm is 4,304π cm³ when expressed in terms of π.

Explanation:

To find the volume of a basketball in terms of π (pi), we start by noting that the formula for the volume of a sphere is V = ⅔πr³, where r is the radius of the sphere. Given that the diameter of the basketball is 28 cm, we will first find the radius by dividing the diameter by 2, which gives us a radius of 14 cm. We then plug this into the formula:

V = ⅔π(14 cm)³

After simplifying, we get:

V = ⅔π(2744 cm³)

And finally, the volume V in terms of π is:

V = 4,304π cm³

Answer:

Step-by-step explanation:

A parameter describes a population, and a statistic describes a sample.

The first one is a statistic.  A sample was surveyed.

The second one is a parameter.  It describes the entire soccer team.

The third one is a statistic.  A sample was surveyed.

The fourth one is a parameter.  It describes the entire golf team.

Answer:

Read the explanation

Step-by-step explanation:

- The Fibonacci Sequence is the series of numbers:

 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

- The next number is found by adding up the two numbers before it

# Example:

- The 2 is found by adding the two numbers before it (1+1)

- The 3 is found by adding the two numbers before it (1+2),

- The 5 is (2+3) and so on

- The rule of it is x(n) = x(n-1) + x(n-2) where

# x(n) is term number ⇒ n

# x(n-1) is the previous term ⇒ (n-1)

# x(n-2) is the term before that ⇒ (n-2)

- Example: the 8th term is  the 7th term plus the 6th term:

 x(8) = x(7) + x(6)

# Note: When we take any two consecutive Fibonacci Numbers,

 their ratio is very close to the Golden Ratio φ

- The Golden Ratio φ is approximately 1.618034...

- We can calculate any Fibonacci Number using the Golden Ratio:

  x(n) = [φ^n - (1 - φ)^n]/√5

- The answer is a whole number, exactly equal to the addition of the

  previous two terms.

# There is an interesting patterns in Fibonacci sequence:

  every nth number is a multiple of x(n)

- Example:

* x3 = 2 ⇒ every 3rd number is a multiple of 2 (2, 8, 34, 144, 610, ...)

* x4 = 3 ⇒ Every 4th number is a multiple of 3 (3, 21, 144, ...)

* x5 = 5 ⇒ Every 5th number is a multiple of 5 (5, 55, 610, ...)

- The man who invented it.

 His real name was Leonardo Pisano Bogollo, and he lived between

 1170 and 1250 in Italy.

- Fibonacci was his nickname

- Fibonacci sequence is it used for:

# Reflects patterns of growth spirals (a spiral curve , shape , pattern ,

  object) found in nature

# It is the closest approximation in integers to the logarithmic spiral

  series, which follows the same rule as the Fibonacci sequence

The Fibonacci sequence is a series of numbers important in mathematics and nature, introduced to European mathematics by Leonardo of Pisa, also known as Fibonacci. It describes various natural phenomena, appears in plants' growth patterns, contributes to arts and sciences, and has practical uses in algorithms and market analysis.

The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, and so forth. This mathematical concept was brought to European mathematics by Leonardo of Pisa, known as Fibonacci. He described this sequence in his book 'Liber Abaci' in 1202, although the sequence had been previously described in Indian mathematics.

The Fibonacci sequence is not just a number theory curiosity but has many applications and appears in the natural world. Notably, it is used to describe various phenomena in quantum computing, stock market analysis, and in nature, such as the branching of trees, the arrangement of leaves on a stem, or the fruitlets of a pineapple. In the context of spirals and botany, the mechanism of the spirals of plants follows the Fibonacci sequence, as explored in resources like 'Doodling in Math: Spirals, Fibonacci, and Being a Plant' by Vihart and 'How to Count the Spirals' by MoMath: National Museum of Mathematics.

The Fibonacci sequence also finds itself being applied to areas such as computer algorithms, especially in recursive algorithms where an operation needs to be repeated on a smaller scale. It also helps build a bridge between mathematics and the arts, showing how mathematics can inspire beautiful patterns and structures in man-made and natural art forms. The prevalence of the Fibonacci sequence and the golden ratio in aesthetic compositions demonstrates the union between form and number that fascinates both mathematicians and artists alike.

Answer:

Step-by-step explanation:

sum of angle of triangle is 180 degree

5x+8x+50degree =180 degree

13x= 180-50

13x= 130

x= 130/13

x=10

5x= 5*10=50degree

8x= 8*10 =80degree

The value of other two angles of triangle are 50 and 80 degrees.

Let us consider that other two angles of triangle are 5x and 8x.

Given that, one angle of triangle is 50 degree.

By property of triangle, sum of all three angles is equal to 180 degrees.

                [tex]5x+8x+50=180\\\\13x=130\\\\x=130/13=10[/tex]

Other two angles of triangle are,

             [tex]5x=5*10=50\\\\8x=8*10=80[/tex]

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Answer:

1/36 or 0.0277... or approximately a 3% chance of rolling a sum greater than 11 (i.e., a sum of 12)

Step-by-step explanation:

Create a 6 x 6 grid on a piece of graph paper. Number the 6 columns 1-6 at the top (for the value of the first die) and number the rows 1-6 on the side (for the value of the second die). You must imagine that you are rolling one die then the other (rather than how people "normally" roll both simultaneously). In the 36 empty boxes in your grid below the column numbers and to the right of the row numbers, put the sums of rolling the die at the top of the column + its corresponding die from the row (for example, use your fingers to match column number 4, say, with row 4 to get a sum of 8). When you've filled out the grid, you will see that a sum of 2 and sum of 12 have the same probability (there's only one way to get a sum of 2 or sum of 12, either 1 + 1 or 6 + 6). But there are many more ways, for example, to get a sum of 7

Answer:

D

Step-by-step explanation:

Obtain the equation of the circle in standard form

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (- 13, - 12), thus

(x + 13)² + (y + 12)² = r²

The radius is the distance from the centre (- 13, - 12) to the point on the circumference (- 17, - 12)

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 17, - 12) and (x₂, y₂ ) = (- 13, -12)

r = [tex]\sqrt{(-13+17)^2+(-12+12)^2}[/tex] = [tex]\sqrt{16}[/tex] = 4

Hence

(x + 13)² + (y + 12)² = 16 ← in standard form

Substitute the coordinates of each point into the left side of the equation and check

A (- 17, - 13) : (- 4)² + (- 1)² = 16 + 1 = 17 ≠ 16

B (- 9, - 17) : 4² + (- 5)² = 16 + 25 = 41 ≠ 16

C (- 12, 13) : 1² + 25² ≠ 16

D (- 9, - 12) : 4² + 0² = 16

Since (- 9, - 12) satisfies the equation, it is on the circle → D

Point D (-9, -12) is on the circumference of the circle centered at (-13,-12) with a radius of 4 units.

To determine which point is on the circumference of a circle with the center at (-13,-12) and a known point on the circumference (-17, -12), we must first find the radius of the circle. The radius can be found by calculating the distance between the center and the known circumference point, which here is the horizontal distance between (-13,-12) and (-17, -12), equal to 4 units. Now, we have to check which of the given points is 4 units away from the center (-13,-12). After checking all options, the correct answer is D. (-9, -12).

To confirm, calculate the distance between the center and point D:

Distance = √((-9 - (-13))^2 + (-12 - (-12))^2)\

Distance = √((4)^2 + (0)^2)\

Distance = √(16)\

Distance = 4

Therefore, point D lies on the circumference of the circle as it is the same distance (radius) from the center as the known point (-17, -12).

Answer:

The weight of the enlarged paperweight is [tex]1.2\ lb[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes (or its weights) is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x ----> the enlarged paperweight weight

y ----> the original paperweight weight

[tex]z^{3}=\frac{x}{y}[/tex]

we have

[tex]z=2[/tex]

[tex]y=0.15\ lb[/tex]

substitute and solve for x

[tex]2^{3}=\frac{x}{0.15}[/tex]

[tex]x=2^{3}(0.15)=1.2\ lb[/tex]

Answer:

The expression for 8y - 2(y+4) is 6y - 8

Step-by-step explanation:

An expression is a mathematical phrase which can contain symbols like a,b,c,x,y,z or numbers like 1,2,3,4,5, etc, or both. Expression is one sided where as equation in mathematics is a two sided expression. There is no left or right side in an Expression, there is always one side.

The given phrase is simplified as follows:

8y - 2(y+4)

8y -2y - 8

6y - 8

Your answer is A) Acute

Answer:

Your answer should be 4 pounds 6 ounces.

Step-by-step explanation:

If you subtract how much the potato sack was before she made the potato salad from how much it was after, this gives you how much the potato she used weighed.

2/3

There are 4 green marbles and 6 red marbles, making 10 green or red marbles.  The probability of drawing a red or a green marble is then 10/15 total marbles, which can be simplified to 2/3 by dividing the numerator and denominator each by 5.

Answer:

Q13. y = sin(2x – π/2); y = - 2cos2x  

Q14. y = 2sin2x -1; y = -2cos(2x – π/2) -1

Step-by-step explanation:

Question 13

(A) Sine function

y = a sin[b(x - h)] + k

y = a sin(bx - bh) + k; bh = phase shift

(1) Amp = 1; a = 1

(2) The graph is symmetrical about the x-axis. k = 0.

(3) Per = π. b = 2

(4) Phase shift = π/2.  

2h =π/2

h = π/4

The equation is

y = sin[2(x – π/4)} or

y = sin(2x – π/2)

B. Cosine function

y = a cos[b(x - h)] + k

y = a cos(bx - bh) + k; bh = phase shift

(1) Amp = 1; a = 1

(2) The graph is symmetrical about the x-axis. k = 0.

(3) Per = π. b = 2

(4) Reflected across x-axis, y ⟶ -y

The equation is y = - 2cos2x  

Question 14

(A) Sine function

(1) Amp = 2; a = 2

(2) Shifted down 1; k = -1

(3) Per = π; b = 2

(4) Phase shift = 0; h = 0

The equation is y = 2sin2x -1

(B) Cosine function

a = 2, b = -1; b = 2

Phase shift = π/2; h = π/4

The equation is

y = -2cos[2(x – π/4)] – 1 or

y = -2cos(2x – π/2) - 1

[tex]\vec r(t)=14t^4\,\vec\imath+t^6\,\vec\jmath[/tex]

[tex]\mathrm d\vec r=(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt[/tex]

[tex]\vec f(x,y)=xy\,\vec\imath+6y^2\,\vec\jmath\implies\vec f(x(t),y(t))=14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath[/tex]

Then the line integral is

[tex]\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^1(14t^{10}\,\vec\imath+6t^{12}\,\vec\jmath)\cdot(56t^3\,\vec\imath+6t^5\,\vec\jmath)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(36t^{17}+784t^{13})\,\mathrm dt=\boxed{58}[/tex]

The line integral c f dot dr for the given parameters can be calculated by substituting values of functions r(t) and f(x, y) into the line integral, then integrating over t from 0 to 1.

To solve this problem, we start by writing the vector valued function r(t) and the vector field f(x, y) in component form. Given that r(t) = 14t4i + t6j and f(x, y) = xyi + 6y2j, the line integral c f dot dr becomes a definite interval where we integrate over t from 0 to 1.

In this case, we're essentially finding the work done by the vector field f as a particle moves along the path described by r(t). To calculate this, we need to find dr/dt which in our case evaluates to 56t3i + 6t5j.

Subsequent substitution of x = 14t4 and y = t6 into f will provide a new vector ft for f dot dr. Now we can find f dot dr by multiplying corresponding components of ft and dr/dt, add them up, and then integrate over t from 0 to 1.

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