Great Mountain Park: All day pass: 20.25 Mountain coaster: 4.50 Tilt a Loop: 4.75 Water coaster: 4.00 Fast drop: 3.50 Swing a Ling: 2.75 Merry go Around: 2.50. Prices at the Great Mountain Park are shown in the table Above. You and three friends are going to the park on the weekend. Three of you decide to get the all day pass. The other is just going to ride the Mountain coaster twice, the water coaster once and the fast drop once. IF you pay for everyone, what change will you get back from a 100 bill

The relationships between the sides and angles of the right triangles in

the question are given by trigonometric ratios.

1. The given triangle is ΔABC

The side opposite angle B is the side not bearing the letter B which is the side AC

2. The tangent of the angle, F, is given by the following formula;

[tex]\displaystyle tan(F) = \mathbf{\frac{Opposite \ side \ to \ angle \ F}{Adjacent \ side \ to \ angle \ F}}[/tex]

Therefore;

3. The sine of the angle Z is given by the following formula;

[tex]\displaystyle sin (Z) = \mathbf{ \frac{Opposite \ side \ to \ angle \ Z}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]

Therefore;

[tex]\displaystyle sin(Z) = \mathbf{\frac{XY}{40}}[/tex]

XY = √(40² - 32²) = 24

Which gives;

4. The trigonometric ratio for cos(D) is given as follows;

[tex]\displaystyle cos(D) = \mathbf{ \frac{Adjacent \ side \ to \ angle \ \angle D}{Hypotenuse \ side \ of \ right \ triangle}}[/tex]

Therefore;

[tex]\displaystyle cos(D) = \frac{21}{75} = \frac{7}{25}[/tex]

5. The tangent of the angle 63° is expressed as follows;

[tex]\displaystyle tan(63^{\circ}) = \mathbf{\frac{8 \, m}{Distance \ AB \ (ground \ distance \ from \ wall)}}[/tex]

Therefore;

[tex]\displaystyle Distance \ AB = \frac{8 \, m}{tan(63^{\circ})} \approx \mathbf{4.076 \, m}[/tex]

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Final answer:

To create a fireworks display portfolio, you can use physical methods such as printing photos or employ digital tools like a word processor, presentation software, or Web 2.0 tools. Ensure you use your own photos, review them to demonstrate key concepts learned, and include them in your final project.

Explanation:

To create a fireworks display portfolio, you have several options. One method involves printing your photos and physically attaching them to paper or poster board, then writing reflections beside them. For a more modern touch, you might opt to create your portfolio digitally using a word processor. In this format, it's important to only use your own photos rather than those with Creative Commons licenses or other sourced images.

Alternatively, you can employ presentation software or various Web 2.0 tools like Glogster (EDU) or VoiceThread for a dynamic and interactive portfolio. When creating your fireworks display portfolio, it is crucial to consider the visual and descriptive elements that highlight what you've learned. Make sure to review your flash photos, choose the sets that best demonstrate the three distance settings or the three settings in the assignment prompt, and be ready to discuss their relevance to the concepts learned in class, such as conservation of momentum and center of mass regarding fireworks.

Lastly, ensure that you download your photos to a computer to include them in the end-of-course final project portfolio. This portfolio will serve as a cohesive collection of your work and understanding of the subject matter.

Option: C is the correct answer.

                          C.  216

We are asked to evaluate the sum of the following summation:

[tex]\sum_{n=1}^{12} (2n+5)[/tex]

Now, this summation could also be written as:

[tex]\sum_{n=1}^{12} (2n+5)=\sum_{n=1}^{12} 2n+\sum_{n=1}^{12} 5[/tex]

i.e.

[tex]\sum_{n=1}^{12} (2n+5)=2\sum_{n=1}^{12} n+\sum_{n=1}^{12} 5[/tex]

Now, we know that:

[tex]\sum_{n=1}^{12} n=1+2+3+4+....+12\\\\i.e.\\\\\sum_{n=1}^{12} n=\dfrac{12(12+1)}{2}[/tex]

Since,

[tex]\sum_{i=1}^{n} i=\dfrac{n(n+1)}{2}[/tex]

i.e.

[tex]\sum_{n=1}^{12} n=78[/tex]

and

[tex]\sum_{n=1}^{12} 5=5+5+....+5\ (\text{twelve\ times})\\\\i.e.\\\\\sum_{n=1}^{12} 12=12\times 5\\\\i.e.\\\\\sum_{n=1}^{12} n=60[/tex]

Hence, we have:

[tex]\sum_{n=1}^{12} (2n+5)=2\times 78+60[/tex]

i.e.

[tex]\sum_{n=1}^{12} (2n+5)=156+60[/tex]

i.e.

[tex]\sum_{n=1}^{12} (2n+5)=216[/tex]

Answer:

Its A o.22

Step-by-step explanation:

Answer:

10 square feet

Step-by-step explanation:

The explanation is in the picture below.

Your welcome :)

The answer is r(x) = (4x)^7

Answer:

It's 14 inches on Ed

Step-by-step explanation:

Final answer:

The volume of the sphere is given as 1372π/3 cubic inches. Using the volume formula for a sphere, V = (4/3)πr³, we calculate the radius and then double it to find the diameter, which is 14 inches.

Explanation:

The student asks for the diameter of the great circle of a sphere, given its volume is 1372π/3 cubic inches. To find this, we'll make use of the formula for the volume of a sphere, V = (4/3)πr³, where V represents the volume and r is the radius of the sphere.

Let's start by equating the given volume to the volume formula:

1372π/3 = (4/3)πr³

Cancelling out π and the fraction (4/3) on both sides, we get:

1372/4 = r³

This simplifies to:

343 = r³

Taking the cube root of both sides gives us the radius:

r = ∛343

r = 7 inches

The diameter of the sphere is twice the radius, so:

diameter = 2r = 2 × 7 = 14 inches

Therefore, the diameter of the great circle of the sphere is 14 inches.

Solution to y = 3x - 1: B. (2, 5)

Matching equation for "The sum of -4x and 2 is 9": A. -4x + 2 = 9

Solve x - 6 = -18: A. x = -12

Solve 4x + 3 = 47: A. x = 11

Let's solve each of the given equations one by one:

Solution to y = 3x - 1:

The equation y = 3x - 1 represents a linear relationship between x and y with a slope of 3 and a y-intercept of -1. To find the solution, we can substitute the given options for x and see which one satisfies the equation:

A. (4, 1): 1 = 3(4) - 1 => 1 = 12 - 1 => 1 = 11 (Not a solution)

B. (2, 5): 5 = 3(2) - 1 => 5 = 6 - 1 => 5 = 5 (This is a solution)

C. (4, 3): 3 = 3(4) - 1 => 3 = 12 - 1 => 3 = 11 (Not a solution)

D. (0, -3): -3 = 3(0) - 1 => -3 = 0 - 1 => -3 = -1 (Not a solution)

So, the solution is B. (2, 5).

Matching equation for "The sum of -4x and 2 is 9":

The statement can be translated into the equation: -4x + 2 = 9. So, the correct equation is A. -4x + 2 = 9.

Solving x - 6 = -18:

To solve for x, add 6 to both sides of the equation:

x - 6 + 6 = -18 + 6

x = -12

So, the solution is A. x = -12.

Solving 4x + 3 = 47:

To solve for x, subtract 3 from both sides of the equation:

4x + 3 - 3 = 47 - 3

4x = 44

Now, divide both sides by 4 to isolate x:

(4x)/4 = 44/4

x = 11

So, the solution is A. x = 11.

In summary, the solutions to the given equations are:

B. (2, 5)

A. -4x + 2 = 9

A. x = -12

A. x = 11

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Answer:

A) CD

B)  AB

C) Plane ABCD is parallel to EFGH.

Plane BDFH is parallel to ACGE.

Plane ABFE is parallel to CDHG.

Step-by-step explanation:

We are given the following in the question:

A cuboid  ABCDEFGH is given.

A) line segment that is parallel to AB

A line segment that is parallel to AB is CD.

B) line segment that is skew to AB

Skew lines are the line that never lie in the same plane and never intersect each other.

Thus line segment FH is skew to line segment AB.

C) pair of parallel planes.

Plane ABCD is parallel to EFGH.

Plane BDFH is parallel to ACGE.

Plane ABFE is parallel to CDHG.

The compound inequality which represents the recommendation of economists for a GDP growth rate to be between 7.1 and 7.9 percent (inclusive) is given by '7.1 ≤ g ≤ 7.9'. This mathematical expression indicates that the acceptable rates are all the values including and between 7.1 & 7.9.

In the context of mathematics, specifically the subject of inequalities, the student's question is asking to represent the given GDP rates as a compound inequality. A compound inequality is a statement with two inequalities joined by the word 'and' or 'or'.

Here, economists recommend the GDP growth rate to be between 7.1 and 7.9 percent (inclusive). So, the GDP growth rate (let's denote it as 'g') is more than or equal to 7.1 percent and, at the same time, less than or equal to 7.9 percent. So, the compound inequality which represents this situation is 7.1 ≤ g ≤ 7.9. So the correct option from the provided ones is the first one: '7.1 ≤ g ≤ 7.9'.

This inequality tells us that the growth rates 'g' are all the values including and between 7.1 & 7.9. This is crucial information for economists when monitoring the health and progress of a nation's economy. The percentage rate of GDP growth is a measure of economic success and can impact many aspects like standard of living, employment rates, and business growth.

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Answer:

- 3/4

Step-by-step explanation:

this answer is correct

Nitrogen gas makes up approximately 78% of the atmosphere, not 50%, 1%, 99%, or 0.03%.

The correct answer is: d. 78%

Nitrogen gas (N2) makes up a significant portion of the Earth's atmosphere.

To determine the correct percentage, we need to consider the composition of the atmosphere:

The Earth's atmosphere is primarily composed of several gases, with the most abundant being nitrogen (N2) and oxygen (O2).

Other gases such as argon, carbon dioxide, neon, helium, and trace amounts of other gases are also present.

The correct answer is: d. 78%

Nitrogen gas (N2) constitutes approximately 78% of the Earth's atmosphere, making it the most abundant gas.

Oxygen (O2) is the second most abundant gas, accounting for about 21% of the atmosphere.

The remaining 1% consists of trace gases like argon, carbon dioxide, and others.

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Answer: the church was dependent on the princes power

Step-by-step explanation:

Answer:

The answer is How many sticks of gum can you chew at one time? (I got it right on my test)

Step-by-step explanation:

Option A is the correct answer.

We need to find from the given options which is the statistical question.

A statistical question is one that can be answered by collecting data and where there will be variability in that data. This is different from a question that anticipates a deterministic answer.

Now from the given options, we can say that,

The best and most correct answer among the choices provided by your question is the first choice which states that "How many sticks of gum can you chew at one time? "

Therefore, option A is the correct answer.

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A normally distributed result means that when the data is plotted on a graph, we can actually see a bell shaped curve. That highest frequency or peak is centered on the average value. Because it is shaped like this, we can say that:

most scores are around the average with some scores being lower or higher

There are 432 total barns when multiplying 48 chicken farms by 9 barns per farm. For question number 27, without knowing the number of mice per barn, we cannot determine the exact number of cats needed to control the grain destruction.

To determine the number of total barns if there are 48 chicken farms near an Ohio town and each farm has 9 barns, we simply need to multiply the number of farms by the number of barns per farm. This can be represented by the equation: 48 farms times 9 barns/farm = 432 barns. Therefore, there are 432 total barns.Now, addressing the second question (Number 27): To calculate the number of cats required to control the destruction of stored grain by mice, we need to find out how many mice are in each barn, and then see how many cats are needed to kill that number of mice. A mouse eats 521 ikats of grain each year, and if we are to prevent the destruction of grain in each of the 24 barns, we need to find out how many mice a single cat can kill in a year, and then divide the number of mice by this figure.If one cat kills 96 mice a year, and assuming each barn has the same number of mice, then for one barn: Total mice killed in one barn/year = Number of cats times 96 mice/cat/year. Therefore, to find the number of cats needed: Number of cats = Total mice in one barn/year extdiv 96 mice/cat/year. Without the number of mice, we cannot complete the calculation. More information on the number of mice per barn is required to give a definitive answer.

The final velocity of the sprinter is 7.23 meters per second.

Acceleration of any object is defined as the variation in the speed of the object with the variation of time. Acceleration is a vector term and to define it we require both the magnitude and the direction. The unit of acceleration can be m / sec², miles / sec², etc.

Given that a sprinter starts from rest, and accelerates at 1.87 m/s² over a distance of 14.0 m.

The final velocity will be calculated by the equation of the motion formula as below,

V² = u² + 2as

V² = 2 x 1.87 x 14

V² = 52.36

V = √52.36

V = 7.23 meter per second

Hence, the final velocity is 7.23 meters per second.

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Final answer:

The expression x⁴ + 8x² + 16 is a perfect square trinomial and it can be factored completely as (x² + 4)².

Explanation:

To factor completely the expression x⁴ + 8x² + 16, we should first recognize that this is a perfect square trinomial. A perfect square trinomial takes the form a² + 2ab + b², and can be factored into (a + b)².

Comparing our given expression to the perfect square trinomial, we see that x⁴ is the square of x² and 16 is the square of 4. Moreover, 8x² is twice the product of x² and 4, suggesting that the expression is indeed, a perfect square. Thus, we can factor it as:

(x² + 4)²

In conclusion, the expression x⁴ + 8x² + 16 can be factored completely as (x² + 4)².

Final answer:

To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial.

Explanation:

To factor the expression [tex]x^4 + 8x^2 + 16[/tex] t is a perfect square trinomial of the form [tex]a^2 + 2ab + b^2[/tex]. The square root of the first term is [tex]x^2[/tex] the square root of the last term is 4, and twice the product of these square roots is [tex]8x^2[/tex], which matches the middle term of the given expression. Therefore, we can rewrite the expression as [tex](x^2 + 4)^2[/tex]. This is the completely factored form of the expression.[tex]a^2 + 2ab + b^2[/tex]