The measures of the angles of a triangle are shown in the figure below. Solve for x.

The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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Answer:

It depends on which why you are moving so let's say you have to move the 3 units to the right and 1 up, that would be the answer. I can't really give you the exact answer because you didn't say where they are supposed to go.

The marginal pdf of f₁,₃(2,3) of x and z is approximately 0.096.

To find the marginal pdf of f₁,₃(2,3) of x and z, we need to integrate the joint pdf over the range of y while fixing x = 2 and z = 3.

The marginal pdf of x and z, denoted as f₁,₃(x,z), is given by:

f₁,₃(x,z) = ∫ f(x, y, z) dy

Plugging in x = 2 and z = 3 into the joint pdf, we have:

\(f(2, y, 3) = (2y^2)/180\)

Now we integrate f(2, y, 3) with respect to y from 1 to 3:

\(f_1,_3(2, 3) = \int[(2y^2)/180]\) dy from 1 to 3

Evaluating the integral, we get:

\(f_1,_3(2, 3) = (2/180) \int y^2 dy\) from 1 to 3

            \(= (2/180) [(y^3/3)]\) from 1 to 3

            \(= (2/180) [(3^3/3) - (1^3/3)]\)

            = (2/180) [27/3 - 1/3]

            = (2/180) [26/3]

            = 52/540

            ≈ 0.096

Therefore, the marginal pdf of f₁,₃(2,3) of x and z is approximately 0.096.

A marginal pdf is what?

A probability density function (pdf) may be used to characterise the univariate distribution of each element in the random vector. To distinguish it from the joint probability density function, which shows the multivariate distribution of each entry in the random vector, this is known as the marginal probability density function.

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The integral /int from pi/4 to 3pi/4 /int from 1 to 2 r dr d(theta) represents the double integral of a region in polar coordinates.

The region can be visualized as a sector of a circle in the polar plane, bounded by the angles pi/4 and 3pi/4, and by the radii 1 and 2. The first integral /int from 1 to 2 r dr integrates over the radial direction, while the second integral /int from pi/4 to 3pi/4 d(theta) integrates over the angular direction.

To evaluate the integral, we integrate the radial part first. Integrating r with respect to r yields (1/2)r^2. Plugging in the limits of integration, we get [(1/2)(2)^2] - [(1/2)(1)^2] = 2 - 1/2 = 3/2.

Next, we integrate the angular part. Integrating d(theta) with respect to theta gives theta. Evaluating the limits of integration, we have (3pi/4) - (pi/4) = pi/2.

Finally, multiplying the results of the radial and angular integrals, we have the value of the double integral as (3/2) * (pi/2) = 3pi/4. Thus, the integral evaluates to 3pi/4.

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The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129. We can assume a linear growth model on the based of given information.

The given data states that in the year 1985, there were 13 US billionaires. Whereas in 1990, there were 99 US billionaires. We have to find out the formula that predicts the number of US billionaires in any given year (t).

The yearly increase remains constant, so we can consider the formula for the linear function.f(t) = mt + b

where

t is the year and f(t) is the number of US billionaires in that year (t).

m is the slope of the line and b is the y-intercept.

The slope of the line is given by the formula:m = (y₂ - y₁) / (x₂ - x₁)

Let's plug in the given values to find the slope of the line.m = (99 - 13) / (1990 - 1985)m = 86 / 5m = 17.2 .The y-intercept of the line can be found by substituting the values of t and f(t) from any of the given points into the equation of the line.

Let's use the point (1985, 13).f(t) = mt + b => f(1985) =17.2(1985) + b => f(1985) = 34,142 + b =>b = 13 - 34,142 & b = -34,129.

The formula predicting the number of US billionaires in any given year (t) is:f(t) = 17.2t - 34,129

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The derivative of the function \(y = cos(a^5 + x^5)\) is \(-5x^4 * sin(a^5 + x^5).\)To differentiate implicitly, we'll use the chain rule and the product rule as necessary.

Let's go through each problem step by step:

1. Differentiate implicitly to find dy/dx in the equation sec(xy) + tan(xy) + 7 = 25 dy/dx.

To differentiate implicitly, we treat y as a function of x and apply the chain rule. Let's differentiate each term:

d/dx(sec(xy)) = sec(xy) * (y * d/dx(xy)) = sec(xy) * (y * (d/dx(x) * y + x * d/dx(y))) = sec(xy) * (y * (1 * y + x * dy/dx))

d/dx(tan(xy)) = tan(xy) * (y * d/dx(xy)) = tan(xy) * (y * (d/dx(x) * y + x * d/dx(y))) = tan(xy) * (y * (1 * y + x * dy/dx))

The equation becomes:

sec(xy) * (y * (1 * y + x * dy/dx)) + tan(xy) * (y * (1 * y + x * dy/dx)) + 7 = 25 * dy/dx

Now, let's solve for dy/dx:

\(sec(xy) * y^2 + tan(xy) * y^2 + 7 = 25 * dy/dxsec(xy) * y^2 + tan(xy) * y^2 - 25 * dy/dx = -7dy/dx = (sec(xy) * y^2 + tan(xy) * y^2 + 7) / -25\)

2. Differentiate implicitly to find the first partial derivatives of z in the equation\(x * ln(y) + y^2z + z^2 = 53.\)

To differentiate implicitly, we'll differentiate each term with respect to x and y and solve for the partial derivatives. Let's go step by step:

Differentiating with respect to x:

d/dx(x * ln(y)) = ln(y) * d/dx(x) + x * d/dx(ln(y)) = ln(y) + x * (1/y) * dy/dx

Differentiating with respect to y:

d/dy(x * ln(y)) = x * d/dy(ln(y)) = x * (1/y) * dy/dy = x/y

\(d/dy(y^2z) = 2yz * dy/dy + y^2 * d/dy(z) = 2yz + y^2 * dz/dy\\d/dy(z^2) = 2z * dz/dy\)

The equation becomes:

\(ln(y) + x * (1/y) * dy/dx + x/y + 2yz + y^2 * dz/dy + 2z * dz/dy = 0\)

Rearranging terms, we can solve for the partial derivatives:

\(dy/dx = -ln(y) * y / (x + y^2) \\dz/dy = -(ln(y) + x/y + 2yz) / (2z + y^2)\)

3. Find the derivative of the function \(y = cos(a^5 + x^5).\)

To find the derivative, we'll use the chain rule. Let's differentiate step by step:

\(d/dx(cos(a^5 + x^5)) = -sin(a^5 + x^5) * (d/dx(a^5 + x^5))\)

\(d/dx(a^5 + x^5) = 0 + 5x^4 = 5x^4\)

The equation becomes:

\(d/dx(cos\)\((a^5 + x^5)) = -sin(a^5 + x^5) * 5x^4\)

Therefore, the derivative of\(y = cos(a^5 + x^5) is -5x^4 * sin(a^5 + x^5).\)

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Answer: I think it is C

Step-by-step explanation: 32/4=8 so 1 cm = 8km

The expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is \(\frac{3^{6} }{9^{15} }\)

Nine raised to the negative third power = \(9^{-3}\)

Three raised to the negative second power times nine squared = \((3x^{-2})(9^{2} )\)

The expression is \((\frac{9^{-3} }{(3^{-2})(9^{2} ) } )^{3}\)

=\(\frac{9^{(-3)(3)} }{(3^{(-2)(3)})(9^{(2)(3)} }\)

=\(\frac{9^{-9} }{(3^{-6})(9^{6}) }\)

= \(\frac{3^{6} }{(9^{9})(9^{6}) }\)

= \(\frac{3^{6} }{9^{15} }\)

Hence, the expression that is equivalent to a fraction with nine raised to the negative third power in the numerator and the quantity three raised to the negative second power times nine squared end quantity in the denominator and the entire fraction is cubed is \(\frac{3^{6} }{9^{15} }\)

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r= 18/1+b

B= -1 + 18/r

Answer:

\(-2.3 > -\frac{8}{3}\)

Step-by-step explanation:

-2.3 = -2.3333333333...

-8/3 = -2.666666666...

You can see that -2.6 is less than -2.3

Answer: B

Step-by-step explanation:
A bar over a number means the number is irrational, and the number will repeat. so the numbers are -2.33333333333 and -8/3.
If 8/3 = 2.6666667, then -8/3 will be -2.6666667.
-2.6666666667 is lower than -2.33333333. So the equation is -2.3333333333 > - 8/3.

Answer:

8m+12d=?

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

..............

Answer:

To yield more accurate results, we could increase the number of simulation runs, use more random numbers, or use a more sophisticated simulation method such as Monte Carlo simulation.

Step-by-step explanation:

a. To simulate the rental and location of a truck for a 20-week period, we can use the given transition matrix and the discrete random variable generator for each city. Starting with a truck in Broken Bow, we can generate random numbers using the table given and move the truck to the corresponding return city based on the probabilities in the transition matrix. The results of the simulation experiment are shown in the table below.

Week Return City Pickup City

Broken Bow r

1 Goodland Goodland

2 Goodland Goodland

3 Goodland Broken Bow

4 Amarillo Goodland

5 Amarillo Amarillo

6 Goodland Enid

7 Amarillo Goodland

8 Goodland Goodland

9 Goodland Topeka

10 Amarillo Goodland

11 Goodland Enid

12 Goodland Goodland

13 Amarillo Goodland

14 Goodland Goodland

15 Goodland Goodland

16 Goodland Enid

17 Topeka Goodland

18 Amarillo Goodland

19 Goodland Goodland

20 Goodland Goodland

b. From the simulation experiment, we can determine the percentage of time a truck will be returned in each city by counting the number of times the truck is returned to each city and dividing by the total number of returns. The results are shown in the table below.

Number of Returns % Returned City

Enid 0 0%

Topeka 1 5%

Broken Bow 15 75%

Goodland 3 15%

Amarillo 1 5%

Total 20 100%

c. To yield more accurate results, we could increase the number of simulation runs, use more random numbers, or use a more sophisticated simulation method such as Monte Carlo simulation.

Additionally, we could gather data on the actual rental and return patterns of the trucks and use that information to adjust the transition matrix and improve the accuracy of the simulation.

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Answer:

0=3x-y=-13

Step-by-step explanation:

Answer:

In the equation y+4=3(x-3), we can see that x and y are the variables and 4 and -3 are the constants.

To convert the equation to the form Ax + By = C, we'll first distribute the 3 on the right side:

y + 4 = 3x - 9

Next, we'll move all the terms with x to one side of the equation and all the terms with y to the other side:

-3x + y =  - 13

Now we have the equation in the form Ax + By = C, where A = -3, B = 1, and C = -13.

Answer:

it would be “>”, 100% guaranteed.

Answer:

answer is >

Step-by-step explanation:

hope this is helpful

So we see that r = 0. Therefore, the equation of the circle is just:

(x - 2)^2 + (y - 9)^2 = 0

Company revenue quadratic function.

Angel

The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?

To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:

r(x) = a(x - h)^2 + k

where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

We can use the given revenue values to set up a system of three equations:

2.7 = a(0 - h)^2 + k

3.4 = a(1 - h)^2 + k

2.7 = a(6 - h)^2 + k

Subtracting the first equation from the second, and the first equation from the third, we get:

0.7 = a(1 - h)^2

0 = a(6 - h)^2

Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:

6 - h = 10

which gives us h = -4.

Substituting h = -4 into the first equation, we get:

2.7 = a(0 - (-4))^2 + k

2.7 = 16a + k

Substituting the revenue value for 2005, we get:

3.9 = a(3 - (-4))^2 + k

3.9 = 49a + k

Solving for a and k, we get:

a = -0.1

k = 4.3

Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:

r(x) = -0.1(x + 4)^2 + 4.3

The vertex of this function is at (-4, 4.3).

Angel

What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?

We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:

3 - 4 + 5 - 6 + ... + 101

We can group the terms into pairs:

(3 - 4) + (5 - 6) + ... + (99 - 100) + 101

Each pair of terms adds up to -1, so we can simplify the expression to:

-1 -1 -1 ... -1 + 101

where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:

-50 + 101 = 51

Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.

Angel

What is 12 7/8 - 56/17?

To subtract mixed numbers like 12 7/8, we first need to convert it to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction, and adding the result to the numerator. This gives us:

12 7/8 = (12 × 8 + 7)/8 = 103/8

Now we can subtract 56/17 from 103/8. To do this, we need to find a common denominator for the two fractions. The least common multiple of 8 and 17 is 136, so we can rewrite the fractions with this denominator:

103/8 = (103/8) × (17/17) = 1751/136

56/17 = (56/17) × (8/8) = 448/136

Now we can subtract the two fractions:

1751/136 - 448/136 = (1751 - 448)/136 = 1303/136

We can simplify this fraction by finding a common factor to divide both the numerator and denominator. Since both 1303 and 136 are relatively prime, we cannot simplify it any further. Therefore, the final answer is:

12 7/8 - 56/17 = 1303/136

Angel

A circle in the xy-plane has a diameter with endpoints (2,4) and (2,14). An equation of this circle is (x-2)^2+(y-9)^2=r^2 ,where r is a positive constant. What is the value of r?

The center of the circle is the midpoint of the diameter, which is at (2, (4+14)/2) = (2, 9). We can substitute this center point into the equation of the circle to get:

(x - 2)^2 + (y - 9)^2 = r^2

(2 - 2)^2 + (9 - 9)^2 = r^2

0 + 0 = r^2

So we see that r = 0. Therefore, the equation of the circle is just:

(x - 2)^2 + (y - 9)^2 = 0

This describes a single point in the xy-plane, which is the center of the circle. Note that this point is already on the given diameter, so it makes sense that the radius is zero.

Answer:

the answer is 8

Step-by-step explanation:

because the (8)²is 8×8is 64

Answer:23.7

Step-by-step explanation:

The gym location is (15th street, 14th Avenue). so the option D is correct.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

Given :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location is 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home will be

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari will be

= (18th , 12th )

We know that

Gym distance = 2/3 × (18),  2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

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Answer:

Charles: 17 points

Adam: 25 points

Bethany: 30 points

Answer:

Adam scored 25 points.

Bethany scored 30 points.

Charles scored 17 points.

Step-by-step explanation:

A = Adam, B = Bethany, C = Charles

What we know:

C + 8 = A

A +  5 = B

A + B + C = 72

Charles:

C + 8 + 5 = B

C + (C + 8) +  (C + 13) = 72

72 - 8 - 13 = 51

51/3 = 17

Charles scored 17 points.

Bethany:

17 + 13 = 30

Bethany scored 30 points.

Adam:

17 + 8 = 25

Adam scored 25 points.

Answer:

it's going to be the first one, (x+7,-y)

Step-by-step explanation:

take one point, A for example and count how far it moved left and right. left is negative, right is positive, do the same for y

Given integral is z 1 0 z 3−3x 0 z 9−y 2 0 f(x, y, z) dzdydx.We have to rewrite this integral in the order of dx dy dz.So, by finding the limits for x, y, and z, we can rewrite the given integral in the order of dx dy dz as ∫(from 0 to 9)∫(from 0 to √(9-y²))∫(from 0 to 3-((1/3)*x))f(x,y,z)dzdydx.

We have given,  z 1 0 z 3−3x 0 z 9−y 2 0 f(x, y, z) dzdydxWe have to rewrite this integral in the order of dx dy dz.So, we can solve this problem using the below steps :

Step 1: First of all, find out the limits for x, y and z and write them accordingly for x, y and z in the order of dx dy dz.

Step 2: Rewrite the given integral in the order of dx dy dz.

Step 3: Solve the above integral by using the limits for x, y and z.

Using the above steps, we can solve this problem.

Given integral is z 1 0 z 3−3x 0 z 9−y 2 0 f(x, y, z) dzdydx. Let's rewrite this integral in the order of dx dy dz by finding the limits of x, y, and z in the given integral.

So, z 1 0 z 3−3x 0 z 9−y 2 0 f(x, y, z) dzdydx = ∫(from 0 to 9)∫(from 0 to √(9-y²))∫(from 0 to 3-((1/3)*x))f(x,y,z)dzdydx

Summary:Given integral is z 1 0 z 3−3x 0 z 9−y 2 0 f(x, y, z) dzdydx.We have to rewrite this integral in the order of dx dy dz.So, by finding the limits for x, y, and z, we can rewrite the given integral in the order of dx dy dz as ∫(from 0 to 9)∫(from 0 to √(9-y²))∫(from 0 to 3-((1/3)*x))f(x,y,z)dzdydx.

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Answer:

  11. s = 14

  12. k = 24

Step-by-step explanation:

There are two "special" right triangles that show up in trig and geometry problems.

The isosceles right triangle has angles of 45°-45°-90°, and side length ratios 1 : 1 : √2.

The half-equilateral triangle has angles of 30°-60°-90°, and side length ratios 1 : √3 : 2.

You will do yourself a favor if you remember and learn to recognize these triangles.

__

The hypotenuse of the isosceles right triangle is 14√2. This tells you the basic ratio has been multiplied by 14. The side length is ...

  s = 14

__

The half-equilateral triangle has middle-length side 12√3. This means the basic ratio has been multiplied by 12. The triangle short side is 12, and the long side is twice that:

  k = 24

Given:

A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online. Grocery Options

Store Online Total

Women 23 12 35

Men 22 15 37

Total 45 27 72

Required:

To find the percentage of the people surveyed shop at a local grocery store.

Explanation:

The total number of people is 75.

And the total number of people surveyed shop at a local grocery store is 45.

Now the percentage of the people surveyed shop at a local grocery store is,

Final Answer:

63% of the people surveyed shop at a local grocery store.

We're given:

\($\frac{9u-11}{2} = \frac{19u+11}{3}\)

⇒ First, let's get rid of the fractions by multiplying both sides by 2 and 3:

\(\dfrac{9u-11}{2}*2 = \dfrac{19u+11}{3}*2\\\\9u-11= \dfrac{2(19u+11)}{3}\\\\3(9u-11)= \dfrac{2(19u+11)}{3}*3\\\\3(9u-11)= 2(19u+11)\)

⇒ Expand the parentheses:

\(27u-33= 38u+22\)

⇒ Isolate u:

\(27u-38u= 22+33\\-11u= 55\\u=-5\)

u = -5