An engineer is building a model of SheiKra. She want the model to be about 32 inches high. Choose the appropriate scale for the model. Then use it to find the loop height of the model

Answers

Answer 1

SheiKra is a roller coaster ride at Busch Gardens Tampa Bay, Florida. It is one of the tallest and fastest roller coasters in the world, reaching a height of 200 feet and speeds of 70 mph. An engineer is building a model of SheiKra. She wants the model to be about 32 inches high. Let’s determine the appropriate scale for the model.Appropriate scale for the modelThe actual height of SheiKra is 200 feet = 2,400 inches.The desired height of the model is 32 inches.So, the scale factor is:2,400 : 32 = 75 : 1Hence, the appropriate scale for the model is 1 inch to 75 inches.Loop height of the modelTo determine the loop height of the model, we need to know the actual loop height of the SheiKra roller coaster ride. According to the Busch Gardens website, the height of the loop is approximately 138 feet or 1,656 inches.Using the scale factor, we can find the loop height of the model:1 inch : 75 inches = 1,656 inches : x incheswhere x is the loop height of the model.Cross multiplying, we get:1 * x = 75 * 1,656x = 124,200 inchesDividing by 75 on both sides, we get:loop height of the model = 1,656 inches / 75loop height of the model = 22.08 inchesTherefore, the loop height of the model is approximately 22.08 inches.

Answer 2

An engineer is building a model of SheiKra which is 200 feet high and wants the model to be about 32 inches high. To find the appropriate scale for the model, we can use the following formula:

Scale = (model height/actual height) x 12We know that the actual height of SheiKra is 200 feet, and the engineer wants the model to be 32 inches high. Therefore, the scale for the model is:

Scale = (32/200) x 12 = 1.92We can round this to the nearest whole number, which gives us a scale of 2.The loop height of the model can be found by multiplying the actual loop height by the scale.

The actual loop height of SheiKra is approximately 138 feet. Therefore, the loop height of the model is:Loop height = 138 x 2 = 276 inches or 23 feet.

This means that the engineer needs to make the loop of the model approximately 23 feet high to maintain the scale of the model.

To know more about SheiKra visit:

https://brainly.com/question/29068002

#SPJ11

Related Questions

Two airplanes leave the airport at the same time. Thirty minutes later, they are 250 miles apart. If one plane traveled 230 miles and the other plane traveled 315 miles during that time, find the angle θ between their flight paths. Show all work clearly and neatly. Round to the nearest tenth.

Answers

To answer this question, we can use the Cosine Law. We have that the general formula for it is as follows:

$c^2=a^2+b^2-2ab\cos C$

We need to remember that angle C is the angle in front of the side c. Then we have - from the graph:

• c = 250mi

• a = 230mi

• b = 315mi

And we will find the angle Θ as follows - without using units:

$250^2=230^2+315^2-2(230)(315)\cos \theta$

Then, if we solve the equation for cosΘ, we will have:

$62500=52900+99225-144900\cos \theta$$62500=152125-144900\cos \theta$

Then, we have:

$62500-152125=-144900\cos \theta$$-\frac{89625}{-144900}=\cos \theta\Rightarrow\cos \theta=0.618530020704$

If we need to find the angle, Θ, we need to apply the inverse function of cosine, arccosine, to both sides of the equation to find it. Then, we have:

$\arccos (\cos \theta)=\arccos (0.618530020704)$

Then

$\theta=51.7911319179^{\circ}$

If we round the value to the nearest tenth, then we have that:

$\theta=51.8^{\circ}$

In summary, therefore, the angle Θ between their flights paths is Θ = 51.8º - rounded to the nearest tenth.

New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get a 6 this time, you get your 10 back.a) Create a probability model for this game.b) Find the expected value and standard deviation of your prospective winnings.c) You play this game five times. Find the expected value and standard deviation of your average winnings.d) 100 people play this game. What's the probability the person running the game makes a profit?

Answers

The probability mode for the given value is created. The expected value and standard deviation of prospective winnings are -$0.28 and $18.33. The expected value and standard deviation if the game is played five times are -$1.40 and $40.99. The probability that the person running the game makes a profit is 0.561.

Probability is a way to determine how likely something is to happen. It is computed by dividing the frequency of the event by the total number of outcomes. The formula then becomes P(X) = frequency of the event÷total number of outcomes.

The product of the probabilities determines the likelihood that two or more occurrences will coincide. This is given by, P(A and B) = P(A)P(B).

a) To create a probability model follow the steps. Let X is an occurrence of an event. The table is attached here.

b) The expected value is calculated using the formula, E(X) = μ = ∑ x P(x).

$\begin{aligned}E(X)=\mu&=x_1p_1+x_2p_2+x_3p_3\\&=40\left(\frac{1}{6}\right)+0\left(\frac{5}{36}\right)+(-10)\left(\frac{25}{36}\right)\\&=-\$ 0.28\end{aligned}$

Also,

$\begin{aligned}E(X^2)&={x_1}^{2}p_{1}+{x_2}^{2}p_{2}+{x_3}^{2}p_{3}\\&=(40)^2\frac{1}{6}+(0)\frac{5}{36}+(-10)^2\frac{25}{36}\\&=(1600)\frac{1}{6}+(0)\frac{5}{36}+(100)\frac{25}{36}\\&=266.67+69.44\\&=336.11\end{aligned}$

And the standard deviation is calculated using the formula, σ=√Var[X].

$\begin{aligned}\sigma=\sqrt{\text{Var}(X)}&=\sqrt{E(X^2)-E(X)^2}\\&=\sqrt{336.11-0.08}\\&=\sqrt{336.03}\\&=\$18.33\end{aligned}$

c) The expected value and standard deviation for playing the game 5 times are calculated as follows.

The expected value is,

$\begin{aligned}5\times E(X)&=5(-\$0.28)\\&=-\$1.40\\\end{aligned}$

The standard deviation is,

$\begin{aligned}\sigma&=\sqrt{5\times\tex{Var}(X)\\&=\sqrt{5\times336.03\\&=\sqrt{1680.15}\\&=\$40.99\end{aligned}$

d) The dice rolling is random and the winning chance is independent. The probability the person running the game makes a profit (P(x<0)) is given by,

The population mean, μ(Y) = -$0.28

The standard deviation for a population of 100 is,

$\begin{aligned}\sigma&=\sqrt{\frac{\text{Var}(X)}{n}}\\&=\frac{18.33}{\sqrt{100}}\\&=1.83\end{aligned}$

The z-score for mean winning is,

$\begin{aligned}z&=\frac{x-\mu}{\sigma}\\&=\frac{0-(-0.28)}{1.83}\\&=0.153\end{aligned}$

For a person to make a profit, the mean winning of the player should be less than the z-score. Then,

The P-value from the z-table, P(z<0.153)=0.5608

The answer is 0.561.

The complete question is -

You pay $10 and roll a die. If you get a 6, you win$50. If not, you get to roll again. If you get a 6 this time, you get your $10 back. a) Create a probability model for this game. b) Find the expected value and standard deviation of your prospective winnings. c) You play this game five times. Find the expected value and standard deviation of your average winnings. d) 100 people play this game. What’s the probability the person running the game makes a profit?

To know more about z-score:

https://brainly.com/question/15016913

#SPJ4

New game You pay 10 and roll a 6 die. If you get a you win 50 If not, you get to roll again. If you get

Find the solution of the system of equations. -4x - y = -28
x+y=4

Answers

The solutions of the system of equations are 8 and -4.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

-4x - y = -28 _____(1)

x + y = 4 _____(2)

x = 4 - y _____(3)

Substituting (3) in (1) we get,

-4(4 - y) - y = -28

-16 + 4y - y = -28

-16 + 3y = -28

3y = -28 + 16

3y = -12

y = -4

Substituting y = -4 in (3) we get,

x = 4 - (-4)

x = 4 + 4

x = 8

Thus,

The value of x is 8.

The value of y is -4.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Given the given cost function
C(2) = 4350 + 270x + 0.2x^2 and the demand function p(x) = 810.
Find the production level that will maximize profit.

Answers

The production level that will maximize profit is 1350.

How to determine the production level that will maximize profit

To find the production level that will maximize profit, we need to first calculate the revenue function using the demand function.

The revenue function is given by:

R(x) = p(x) * x

Substituting the given demand function p(x) = 810, we get:

R(x) = 810x

The profit function is given by subtracting the cost function from the revenue function: P(x) = R(x) - C(x)

Substituting the given cost function C(x) = 4350 + 270x + 0.2x^2, and the revenue function R(x) = 810x, we get:

P(x) = 810x - (4350 + 270x + 0.2x^2)

Simplifying this expression, we get:

P(x) = -0.2x^2 + 540x - 4350

To maximize profit, we need to find the production level that corresponds to the maximum value of the profit function.

This can be done by finding the x-value at which the derivative of the profit function is equal to zero:

P'(x) = -0.4x + 540

Setting this expression equal to zero, we get:

-0.4x + 540 = 0

Solving for x, we get:

x = 1350

Learn more about profit maximization at

https://brainly.com/question/29787526

#SPJ11

if p = 2^k + 1 is prime, show that every quadratic nonresidue of p is a primitive root of p.

Answers

Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

Learn more about Euler's criterion here:

brainly.com/question/12977984

#SPJ11

A mathematician develops a program to solve systems of linear equations. When they use distributed computing techniques to run the program on two computers in parallel, they find a speedup of 2. In this case, what does a speedup of 2 indicate

Answers

A speedup of 2 suggests that the program is efficiently utilizing the additional computational resources provided by the second computer, resulting in a significant reduction in computation time.

A speedup of 2 indicates that the program running on two computers in parallel is approximately twice as fast as running it on a single computer. In other words, the distributed computing techniques and parallel processing allow the mathematician to solve the systems of linear equations in half the time compared to running the program on a single computer.

Speedup is a measure of the improvement achieved by using parallel computing techniques. It quantifies the ratio of the time required to execute a task sequentially (on a single computer) to the time required to execute the same task in parallel (using multiple computers). A speedup of 2 suggests that the program is efficiently utilizing the additional computational resources provided by the second computer, resulting in a significant reduction in computation time.

Learn more about linear equations here:

https://brainly.com/question/27664510

#SPJ11

Find the sum of the convergent series. n = 0
∑ (1/4)^n

Answers

The sum of the given convergent series is 4/3.

How to determined the sum of convergent series?

The given series is a geometric series with the first term (a) equal to 1 and the common ratio (r) equal to 1/4.

The formula for the sum of a geometric series is:

S = a(1 - rⁿ)/(1 - r)

where S is the sum of the series, a is the first term,

r is the common-ratio, and n is the number of terms in the series.

Substituting the given values in the formula, we get:

S = 1(1 - (1/4)ⁿ)/(1 - 1/4)S = 4/3(1 - (1/4)ⁿ)

Since the series is convergent, the limit of the series as n approaches infinity is a finite number.

As n approaches infinity, (1/4)ⁿ approaches zero, so we have:

S = 4/3(1 - 0)S = 4/3

Therefore, the sum of the given convergent series is 4/3.

Learn more about convergent series

brainly.com/question/15415793

#SPJ11

Your roommate Venmo's you $604 for rent and utilities. You need to instant transfer said amount. Knowing that the instant transfer fee
is 1.75%, how much will actually be transfered to your account?
O $587.56
O $593.43
O $599.97
O $604

Answers

The correct answer is B: $593.43

20 is what percent of 80? Choose the equation to solve the problem

a. 20 = 80% ∙ x; 25%

b. 80 = 20% ∙ x; 400%

c. 20 = x ∙ 80; 25%

d. x = 20% ∙ 80; 0.25%

Answers

Answer:

Step-by-step explanation:

CAN SOMEONE HELP ME!!!!!!!!!!!!!!!

Answers

Answer: 150 min

Step-by-step explanation:

2 hours = 120 min, 120 + 30 min = 150 min

Answer:

150 min

Work:

2 hours = 120 min, 120 + 30 min = 150 min

1. five friends go to the movie theater together. (a) if there are 5 seats open in a row, how many ways can the friends choose seats? (b) if there are 7 seats open in a row, how many ways can the friends choose seats? (note that two seats will remain empty.) (c) repeat part (b), but where two of the friends are required to sit next to each other. (d) repeat part (b), but where two of the friends are required to not sit next to each other.

Answers

he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040

If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.

(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.

(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.

(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.

Know more about arrangement here:

https://brainly.com/question/28406752

#SPJ11

2 (MC) Explain how the Quotient of Powers was used to simplify this expression. (2 points) 25 = 22 By finding the quotient of the bases to be 1 4 and cancelling common factors F O By finding the quotient of the bases to be 1 4 and simplifying the expression O By simplifying 8 to 23 to make both powers base two, and subtracting the exponents O By simplifying 8 to 23 to make both powers base two, and adding the exponents 3.(MC)

Answers

Answer:

Explain how the Quotient of Powers was used to simplify this expression. (2 points) 25 = 22 By finding the quotient of the bases to be 1 4 and cancelling common factors F O

Step-by-step explanation:

By finding the quotient of the bases to be 1 4 and simplifying the expression O By simplifying 8 to 23 to make both powers base two, and subtracting the exponents O By simplifying 8 to 23 to make both powers base two, and adding the exponents 3.(MC)

PLEASE ANSWER QUICKLY ASAP
READ THE QUESTIONS CAREFULLY

Answers

Answer:

I hope it helps.

The solutions in photo ^_^

variables that indicate the distance a target is from the level achieved are called

Answers

Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.

Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.

Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.

These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.

To know more about metrics visit.

https://brainly.com/question/32738513

#SPJ11

please help this is my last equation on my assignment and its due at 5... -1.2x = 12

Answers

the answer is x = -10

The perimeter of a rectangle is 112 cm and its 10. A group
The tota
breadth is x cm.
(i) Find, in terms of x, an expression for the
length of the rectangle.
(ii) Given that the area of the rectangle is 597 cm²,
formulate an equation in x and show that it
reduces to x²-56x +597 = 0.
(iii) Solve the equation x²-56x + 597 = 0, giving
both answers correct to 2 decimal places.
(iv) Hence, find the length of the diagonal of
the rectangle.

Answers

Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.

What is perimeter?

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.

Here,

(i) Let the length of the rectangle be y cm.

Then, the perimeter of the rectangle is given by:

2(x + y) = 112

x + y = 56

y = 56 - x

(ii) The area of the rectangle is given by:

Area = length x breadth

597 = yx

Substituting y = 56 - x, we get:

597 = x(56 - x)

597 = 56x - x²

x² - 56x + 597 = 0

(iii) Using the quadratic formula,

x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))

x = (56 ± √(3136 - 2388)) / 2

x = (56 ± √(748)) / 2

x = (56 ± 2√(187)) / 2

x = 28 ± √(187)

Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).

(iv) The length of the rectangle is y = 56 - x.

Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:

d² = y² + x²

d² = (56 - x)² + x²

d² = 3136 - 112x + 2x²

d = √(3136 - 112x + 2x²)

Substituting the value of x from part (iii) into the above equation, we get:

d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)

d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))

d = √(37400 ± 168√(187))

d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)

To know more about perimeter,

https://brainly.com/question/6465134

#SPJ1

A survey was given to a random sample of 400 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 168 respondents said they were in favor of the plan. Determine a 95% confidence interval for the proportion of people who favor the tax plan, rounding values to the nearest thousandth.

Answers

The sample proportion of individuals who favor the tax plan is 168/400 = 0.42.

The standard error of the sample proportion is sqrt[(0.42)(0.58)/400] = 0.032.

Using a 95% confidence level, the critical value is 1.96.

The margin of error is 1.96 * 0.032 = 0.063.

The 95% confidence interval is 0.42 ± 0.063, which is (0.357, 0.483).

Therefore, we can be 95% confident that the true proportion of people who favor the tax plan is between 0.357 and 0.483.

Which types of triangles can always be used as a counterexample to the statement "all angles in a triangle are acute"? Select all that apply
equilateral
obtuse
acute
isosceles
scalene
right

Answers

Which types of triangles can always be used as a counterexample to the statement "all angles in a triangle are acute" they include

obtuseisoscelesscaleneright

What is acute angle?

Acute angles are those that are smaller than 90 degrees. 90 degrees is the angle at a right angle.

Obtuse angles are those that are more than 90 degrees.

A right triangle can be isosceles or scalene, meaning that each of its three sides is of a different length (having exactly two sides of equal length).

Equilateral triangle always have angel 60 degrees which as an acute angel

Learn more about acute angles at:

https://brainly.com/question/6979153
#SPJ1

I need help on the picture I sent

Answers

The length of the hypotenuse is as:

a. 25 inches

b. 10.30 m

c. 26 feet

d. 12.65 cm

e. 50 mm

f. 2.24 mile

What is the Formula for a Right-Angled Triangle?

The Pythagoras formula is used to calculate the area of a right-angled triangle. It asserts that the hypotenuse's square is equal to the sum of its other two sides' squares. (Hypotenuse)² = (Base)² + (perpendicular)² is the Pythagorean formula.