After some not so high practice dives by the circus owner, the circus performers decide to do a practice run of the show with the diver himself. but they decide to set it up so they will not have to worry about a moving cart. instead, the cart containing the tub of water is placed directly under the ferris wheel’s 11o’clock position. as usual, the platform passes the 3o’clock position at t=0


how many seconds will it take for the platform to reach the 11 o’clock position?


what is the diver’s height off the ground when he is at the 11 o’clock position?


radius = 50 ft

center of wheel is 65 feet off ground

turns counterclockwise at a constant speed, with a period of 40 seconds.

platform is at 3 o’clock position when it starts moving

Answer:

n = 8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

-6 = n/2 - 10

Step 2: Solve for n

Step 3: Check

Plug in n into the original equation to verify it's a solution.

Here we see that -6 does indeed equal -6.

∴ n = 8 is the solution to the equation.

The rate of change of the volume of a spherical ball is equal to the derivative of its volume with respect to time.  The rate of change of the volume of the ball when the radius is 5 cm is given by:dV/dt = 4π(5)²(-3) = -300π cubic cm/s

Given, the radius of a spherical ball is decreasing at a constant rate of 3 cm per second. Find, in cubic centimeters per second, the rate of change of the volume of the ball when the radius is 5 cm.To solve the problem, we need to find the rate of change of the volume of the spherical ball when the radius is 5 cm.The formula for the volume of a sphere is given by V = (4/3)πr³. So, the volume of the spherical ball is proportional to the cube of the radius of the ball.

This means that the rate of change of the volume of the ball is also proportional to the square of the radius. So, if the radius of the ball decreases at a constant rate, then the rate of change of the volume of the ball also decreases at a constant rate.To find the rate of change of the volume of the ball when the radius is 5 cm, we need to differentiate the volume with respect to time. Using the formula for the volume of a sphere, we getV = (4/3)πr³Differentiating both sides of the equation with respect to time, we get:dV/dt = 4πr² (dr/dt)where r is the radius of the sphere and dr/dt is the rate of change of the radius with respect to time. Since the radius of the ball is decreasing at a constant rate of 3 cm/s, we have dr/dt = -3 cm/s. Therefore,dV/dt = 4πr² (-3) = -12πr² cubic cm/sWhen the radius is 5 cm, we have r = 5 cm. Thus,dV/dt = -12π(5)² = -300π cubic cm/sTherefore, the rate of change of the volume of the ball when the radius is 5 cm is -300π cubic cm/s.

Therefore, option (B) -3001 is the correct answer.

To know more about volume of a spherical ball visit:

brainly.com/question/29053535

#SPJ11

Answer:

The answer is below

Step-by-step explanation:

A polynominal function that describes an enclosure is v(x)=1500x-x2 where x is the length of the fence in feet what is the maximum area of the enclosure

Solution:

The maximum area of the enclosure is gotten when the differential with respect to x of the enclosure function is equal to zero. That is:

V'(x) = 0

V(x) = x(1500 - x) = length * breadth.

This means the enclosure has a length of x and a width of 1500 - x

Given that:

v(x)=1500x-x². Hence:

V'(x) = 1500 -2x

V'(x) = 0

1500 -2x = 0

2x = 1500

x = 1500 / 2

x = 750 feet

The maximum area = 1500(750) - 750² = 562500

The maximum area = 562500 feet²

Answer:

562500 feet²

Step-by-step explanation:

Answer:

Final answer is: 2(3x^2 - 6x + 8)

Step-by-step explanation:

Answer:s

see attachment

Step-by-step explanation:

The set of side measurement that will form a triangle is 8, 9 and 15.

A triangle is a polygon with 3 sides. The sum of angles in a triangle is 180 degrees.

Therefore, the triangle inequality theorem can be used to know the length of sides that can form a triangle.

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

If the length are a, b and c. Therefore,

a + b > c

a + c > b

b + c > a

Therefore, applying this principle the measurement that will form a triangle is  8, 9 and 15.

learn more on triangle here: https://brainly.com/question/29362574

#SPJ1

Answer:

5x + y = 25

Dillon can buy 25 flowers.

Dillon can buy 5 trees

Step-by-step explanation:

Equations

The standard form of a linear equation is:

ax + by = c

Where a, b, and c are constants, and x, y are the variables.

Given the conditions of the problem, we'll build the equation that represents the situation.

Let's call:

x=number of trees

y=number of flowers

Since the landscaping company sells trees for $25 each and flowers for $5 each, buying x trees and y flowers cost:

25x+5y dollars

Knowing Dillon has $125 to spend, then:

25x + 5y = 125

Dividing by 5:

5x + y = 25

This is the equation that models the situation.

If Dillon decides to buy only one type of plant, then the other must be set to zero.

If he buys only flowers, then x=0. Solving for y:

5(0) + y = 25

y = 25

Dillon can buy 25 flowers.

If he buys only trees, then y=0. Solving for x:

5x + 0 = 25

x = 5

Dillon can buy 5 trees

Answer:

c

Step-by-step explanation:

that's the answer dudnjdkdkd

Identify the equation: Write down the given equation in the form |x - a| = b, where 'a' represents the number being subtracted or added and 'b' represents the absolute value.

Graphing absolute value equations on a number line is a process that involves several steps. First, you need to identify the equation and rewrite it in the form |x - a| = b, where 'a' represents the number being subtracted or added and 'b' represents the absolute value.

This form helps determine the critical points of the graph. Next, you set the expression inside the absolute value bars equal to zero and solve for 'x' to find the critical points. These points indicate where the graph may change direction. Once the critical points are determined, you plot them on the number line, using an open circle for critical points and a closed circle for any additional points obtained by adding or subtracting the absolute value.

After plotting the points, you can draw the graph by connecting them with a solid line for the portion of the graph that is positive and a dashed line for the portion that is negative. This representation helps visualize the behavior of the absolute value equation on the number line.

To know more about Number line visit.

https://brainly.com/question/32029748

#SPJ11

Answer:

x = 65 degrees

Step-by-step explanation:

Sum of all three sides in a triangle is 180

48 + 67 + n = 180

180 - (48 + 67) = 65

The missing angle and angle X are vertical angles, so they are the same angle.

angle X = 65 degrees

Answer:

15x+30y−220

Step-by-step explanation:

hope this helps

Answer:

Positive thread.

(It's making a positive slope.)

SOLUTION

Write out the equation

The first step in solving this equation is to multiply both sides by 2 this is called

MULTIPLICATION PROPERTY OF EQUALITY

Step1; MUltiply both sides by 2

The next step in solving this equation is to add 7 to both sides of

the equation this is called ADDITION PROPERTY OF EQUALITY

step2: Add 7 to both sides of the equation

Hence the solution to the equation is y=-15

The steps are

Step1; MULTIPLICATION PROPERTY OF EQUALITY

Step2: SIMPLIFYING

Step3: ADDITION PROPERTY OF EQUALITY

Step4: SIMPLIFYING

Therefore, the probabilities P(X = 1) and P(X = 2) are given by: P(X = 1) = c/4 P(X = 2) \(= (2 - 16c^2)/(64c + 8)\).

To determine the probabilities P(X = 1) and P(X = 2) based on the given cumulative distribution function (CDF) F(x), we need to calculate the difference in probabilities at those specific points.

P(X = 1):

P(X = 1) is the probability that the random variable X takes the value 1. We can calculate this probability by subtracting the CDF values at x = 0 and x = 1:

P(X = 1) = F(1) - F(0)

Substituting the given CDF function:

\(P(X = 1) = (c(1)^2)/(3(1)^2 + 1) - (c(0)^2)/(3(0)^2 + 0)\)

= c/4

P(X = 2):

P(X = 2) is the probability that the random variable X takes the value 2. We can calculate this probability by subtracting the CDF values at x = 1 and x = 2:

P(X = 2) = F(2) - F(1)

Substituting the given CDF function:

\(P(X = 2) = (c(2)^2)/(3(2)^2 + 2) - (c(1)^2)/(3(1)^2 + 1)\)

= (4c)/(16c + 2) - c/4

= (4c - c(16c + 2))/(16c + 2)(4)

\(= (4c - 16c^2 - 2c)/(64c + 8)\)

\(= (2 - 16c^2)/(64c + 8)\)

To know more about probabilities,

https://brainly.com/question/31969034

#SPJ11

Answer:

30 ft²

Step-by-step explanation:

The formula to find the area of a rectangle is:

Length x Width

Answer:

Factor using difference of cubes and set each factor equal to

0

.

x

=

2

,

−

1

+

i

√

3

,

−

1

−

i

√

3

Step-by-step explanation:Factor using difference of cubes and set each factor equal to

0

.

x

=

2

,

−

1

+

i

√

3

,

−

1

−

i

√

3

Hey there!

“x³ – 8 = 0”

• ADD BOTH of your SIDES BY 8

x³ – 8 + 8 = 0 + 8

• CANCEL out: –8 + 8 because that gives you 0

• KEEP: 0 + 8 because it helps us solve for your x-value

0 + 8 = 8

x³ = 8

• SECOND: TAKE your CUBE ROOT

x = 8^1/3

SOLVE ABOVE AND YOU HAVE YOUR x-value!

x = 2 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

So, the values of the trigonometric functions of t are sin(t) = 1/7, cos(t) = -√(1 - (1/7)^2) and tan(t) = -(1/7)/(-√(1 - (1/7)^2)).

Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.

csc(t) = 1/sin(t), so sin(t) = 1/7

Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the third quadrant.

Therefore, the values of the trigonometric functions of t are:

sin(t) = 1/7

cos(t) = -√(1 - sin^2(t)) = -√(1 - (1/7)^2)

tan(t) = sin(t)/cos(t) = -(1/7)/(-√(1 - (1/7)^2))

Note that the values of the other trigonometric functions, such as cot(t), sec(t), and csc(t), can be found using the definitions of these functions and the values of sin(t) and cos(t) that we have found.

To learn more about Trigonometric Functions

Visit; brainly.com/question/14746686

#SPJ4

So, the values of the trigonometric functions of t are  \(Sin(t)=\frac{1}{7}\), \(Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }\)  and  \(tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }\).

Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.

\(Cosec(t)=7\)

We known

⇒ \(Sin(t)=\frac{1}{Cosec(t)} =\frac{1}{7}\)

Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the second quadrant.

Therefore, the values of the trigonometric functions of t are:

⇒ \(Sin(t)=\frac{1}{7}\)

⇒ \(Cos(t)=-\sqrt{[1-(Sin^2t)]}\)

⇒ \(Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }\)

⇒ \(tan(t)=\frac{Sin(t)}{Cos(t)}\)

⇒ \(tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }\)

∴ Note that The definitions of the other trigonometric functions, along with the values of Sin(t) and Cos(t), can be used to determine the values of cot(t), Sec(t), and Cosec(t).

To learn more about trigonometric functions

brainly.com/question/14746686

#SPJ4

The value of y is -1 so that line PQ is perpendicular to line RS.

A slope of a line is the change in y-coordinate with respect to the change in x-coordinate. The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

If PQ is perpendicular to RS, therefore, the slope of RS would be the negative reciprocal of PQ.

Slope of PQ:

Slope of RS:

Slope of RS is the reciprocal of the slope of PQ, since they are perpendicular.

⅘ is the reciprocal of -⁵/4. Therefore, the slope of RS = ⅘.

Use the slope formula to find the value of y in R(-4, 3), S(-9, y).

\(\text{slope(m)}=\dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

Plug in the value

\(\dfrac{4}{5} =\dfrac{\text{y}-3}{-9-(-4)}\)

\(\dfrac{4}{5} =\dfrac{\text{y}-3}{-5}\)

Cross multiply

\((4)(-5)=(\text{y}-3)(5)\)

\(-20=5\text{y}-15\)

Add 15 to both sides

\(-20+15=5\text{y}-15+15\)

\(-5=5\text{y}\)

Divide both sides by 5

\(\dfrac{-5}{5} =\dfrac{5\text{y}}{5}\)

\(-1=\text{y}\)

\(\bold{y=-1}\)

Hence, The value of y is -1 so that line PQ is perpendicular to line RS.

Learn more about the slope of a line at:

https://brainly.com/question/30733383

The complete question is in the attachment below.

We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

Foe similar question on sample mean.

https://brainly.com/question/29368683

#SPJ11

Answer:4

Step-by-step explanation:i did the quiz

Answer:

h = √72 in

Step-by-step explanation:

When looking at the triangle formed inside the cone we know we already have a value to replace c for in the Pythagorean Theorem

a² + b² = c²

a² + b² = 9²

Now in order to find a value for b, we just have to get the value for the base of the cone, 6 in, and divide it by two, since the base of the cone is twice of the size of the base of the triangle:

a² + 3² = 9²

Now, we just solve for a:

a² + 3² = 9²

a² + 9 = 81

a² = 72

a = √72

So the height of the cone is √72 in.

You can also substitute √72 for a in the equation to check your work:

a² + 3² = 9²

(√72)² + 3² = 9²

72 + 9 = 81

81 = 81   True!!

hope this helps! :)

Answer:

0.782 in decimal form or 7 square root of

Step-by-step explanation:

5 over 20

Helping a patient diagnosed with post-traumatic disorder reframe catastrophizing thought patterns is an evidence-based practice of cognitive restructuring.

Helping a patient diagnosed with post-traumatic disorder reframe catastrophizing thought patterns is an evidence-based practice of cognitive restructuring. Catastrophizing is a cognitive distortion characterized by the tendency to focus on the worst-case scenarios. Patients with post-traumatic disorder often struggle with this cognitive distortion, leading to increased anxiety and avoidance behavior.
Cognitive restructuring involves identifying and challenging negative thought patterns and replacing them with more adaptive and realistic ones. The process involves identifying automatic negative thoughts, examining the evidence supporting or contradicting them, and generating alternative thoughts that are more balanced and accurate.
Cognitive restructuring is a well-established cognitive-behavioral technique used in the treatment of various mental health disorders, including post-traumatic disorder. This technique aims to help patients develop more flexible and adaptive thinking patterns that can improve their mood, behavior, and overall quality of life.
In conclusion, cognitive restructuring is an evidence-based practice used in helping patients diagnosed with post-traumatic disorder reframe catastrophizing thought patterns. It is an effective technique for challenging negative thoughts and replacing them with more adaptive ones, leading to improved mental health outcomes.

To know more about post-traumatic disorder visit: https://brainly.com/question/13097232

#SPJ11

The coefficients obtained by the student may be less efficient and have larger standard errors compared to the professor's regression.

If the student enters each observation twice, resulting in a sample size of 100 instead of the original 50, the assumption of independent observations is violated in Ordinary Least Squares (OLS) regression. The OLS assumption assumes that the observations are independent, meaning that the value of one observation does not depend on the value of another observation.

In this case, the student's dataset contains repeated observations, which introduces dependence between observations. This violation of the independence assumption can lead to biased and inconsistent parameter estimates in the regression analysis.

Regarding the slope coefficients, if the student runs a regression using the duplicated data, the estimated coefficients may be different from the professor's regression. The duplication of observations inflates the sample size, potentially affecting the precision and accuracy of the estimates.

However, the direction and overall relationship between the variables may still be captured by the student's regression, although the estimates may not be as reliable.

learn more about coefficients here

https://brainly.com/question/1594145

#SPJ11

Answer: Hello:

Slope - intercept form is y = mx + b.

Since -1/2 is your slope and 5 is your y - intercept, all you need to do is substitute those values into the equation:

y = -1/2 + 5

Hope this helps!

Answer:

90 degrees

Step-by-step explanation:

90 degrees hhgffdfkgdf

Answer:

90 degrees clockwise rotation

Step-by-step explanation:

Because

To find the factors of the expression 12x^2 - 4x - 1, we can use the factor theorem. The factor theorem states that if a polynomial expression evaluates to zero when a certain value is substituted for the variable, then that value is a factor of the polynomial.

To determine if a certain value is a factor of the expression, we can use synthetic division. Synthetic division involves dividing the polynomial expression by the possible factor to check if the remainder is zero. If the remainder is zero, then the value is a factor.

Let's start by checking if x = 1 is a factor of the expression:

    1 | 12 - 4 - 1
      |     12   8
      |____________
       12   8   7

Since the remainder is not zero, x = 1 is not a factor of the expression.

Next, let's check if x = -1 is a factor of the expression:

   -1 | 12 - 4 - 1
      |    -12  16
      |____________
       12 -16  15

Again, the remainder is not zero, so x = -1 is not a factor of the expression.

Now, let's check if x = 2 is a factor of the expression:

    2 | 12 - 4 - 1
      |     24 40
      |____________
       12  20 39

Once again, the remainder is not zero, so x = 2 is not a factor of the expression.

Finally, let's check if x = -2 is a factor of the expression:

   -2 | 12 - 4 - 1
      |    -24 56
      |____________
       12 -28 55

As we can see, the remainder is not zero, so x = -2 is not a factor of the expression.

After checking all the possible factors, we can conclude that none of the values tested (1, -1, 2, -2) are factors of the expression 12x^2 - 4x - 1.

to know more about factors here:

brainly.com/question/30517179

#SPJ11

Toby has cycled a total of 36 kilometres  

The unit rate is 3

The unit rate can be calculated as follows

24 kilometres makes 8 trips

x= 1

Cross multiply both sides

8x= 24

x= 24/8

x= 3

The unit rate is 3 kilometres for 1 trip

The kilometres cycled for 12 trips is, this means we have to calculate the kilometres for the remaining 4 trips (12-8= 4)

3= 1

y= 4

cross multiply both sides

y= 12

Total kilometres= 12 + 24

= 36

Hence Toby cycled a total of 36 kilometres

Read more on kilometres here

https://brainly.com/question/19426332

#SPJ1