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Answer 1


h = 79 m

Step-by-step explanation:

The length of the string, H = 125 m

The kite forms 39° angle.

We need to find the height of the kite. Let it is h. We can find it using trigonometry i.e.



P is perpendicular and H is Hypotenuse


\sin\theta=(h)/(H)\n\nh=H* \sin\theta\n\nh=125* \sin(39)\n\nh=78.66\ m


h = 79 m

So, the kite is flying at a height of 79 m.

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A limited edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value,y, after x years? (Round money values to the nearest penny.)


y= 3.11x+ 17.59

I got this equation by doing 23.81-20.70 to find m, which is 3.11.
Then to find b, or y-intercept, I subtracted 3.11 from 20.70 to get the origin all price and got 17.59

Odessa starts counting the frogs in the small pond that the forest service just set up by her house. She marks the data in this graph. If y equals the number of frogs and x equals the number of months that have passed, the frog population can be described by the mathematical formula y = x.



B. 2

Step-by-step explanation:

Just took the quiz.


Answer is 2

Step-by-step explanation:

If it shows a graph with Frog Population on top

Find all missing angles in the diagrams below, please help​



x= 80°, y= 100°

Step-by-step explanation:

Please see the attached picture for the full solution.


x = 80,

y = 80

Step-by-step explanation:

This is difficult to explain, so here are the theorems used

two lines parallel, with a transversal; alternate interior angles,

verticle angles theorem,

parts - whole postulate,

verticle angles theorem,

parts- whole postulate,

sum angles in a triangle,

supplementary angle, definition straight angle,

parts- whole postulate,

there are many other ways to reach the answer, I just whent this way.

Whats the equavalent to log8 64+log8 8



The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 10 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 3 flights arrive late.



There is a 32.22% probability that at least 3 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives on time, or it arrives late. This means that we can solve this problem using binomial probability concepts.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)

In which C_(n,x) is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_(n,x) = (n!)/(x!(n-x)!)

And \pi is the probability of X happening.

In this problem, we have that:

There are 10 flights, so n = 10.

A success in this case is a flight being late.  80% of its flights arriving on time, so 100%-80% = 20% arrive late. This means that \pi = 0.2.

(a) Find the probability that at least 3 flights arrive late.

Either less than 3 flights arrive late, or at least 3 arrive late. The sum of these probabilities is decimal 1. This means that:

P(X < 3) + P(X \geq 3) = 1

P(X \geq 3) = 1 - P(X < 3)

In which

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = C_(n,x).\pi^(x).(1-\pi)^(n-x)

P(X = 0) = C_(10,0).(0.2)^(0).(0.8)^(10) = 0.1074

P(X = 1) = C_(10,1).(0.2)^(1).(0.8)^(9) = 0.2684

P(X = 2) = C_(10,2).(0.2)^(2).(0.8)^(8) = 0.3020


P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778


P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222

There is a 32.22% probability that at least 3 flights arrive late.

Final answer:

The problem is solved by calculating the probability of the complementary event (0,1,2 flights arriving late) using the binomial distribution, then subtracting this from 1 to find the probability of at least 3 flights arriving late.


This problem is typically solved by using a binomial probability formula, which is used when there are exactly two mutually exclusive outcomes of a trial, often referred to as 'success' and 'failure'.
Here, our 'success' is a flight arriving late. The probability of success, denoted as p, is thus 20% or 0.2 (since 80% arrive on time, then 100%-80% = 20% arrive late). The number of trials, denoted as n, is 10 (the number of randomly selected flights).
We want to find the probability that at least 3 flights arrive late, in other words, 3,4,...,10 flights arrive late. The problem can be solved easier by considering the complementary event: 0,1,2 flights arrive late. Then subtract the sum of these probabilities from 1.

The binomial probability of exactly k successes in n trials is given by:

P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))
Where C(n, k) is the binomial coefficient, meaning choosing k successes from n trials.
We calculate like so:
P(X=0) = C(10, 0) * (0.2)^0 * (0.8)^10
P(X=1) = C(10, 1) * (0.2)^1 * (0.8)^9
P(X=2) = C(10, 2) * (0.2)^2 * (0.8)^8
Sum these up and subtract from 1 to get the probability that at least 3 flights arrive late. This gives the solution to the question.

Learn more about binomial probability here:


Which expression represents the perimeter of thetrapezoid?
2x - 1
2x + 3
6x +4
11x + 4
O 4x + 2
15x + 6
13x + 8


Final answer:

The correct option is c.

The total length, or perimeter, of the trapezoid is calculated by adding the lengths of its sides. Once we add and simplify the like terms, we find that the expression representing the perimeter of the trapezoid is 15x + 6.


The perimeter of a shape is calculated by adding up the lengths of all its sides. In the case of a trapezoid with sides of length: 5x, 2x - 1, 2x + 3, 6x + 4, the total length, or the perimeter, would be the sum of these four sides.

To calculate the perimeter, we simply add the lengths of the sides: 5x + (2x - 1) + (2x + 3) + (6x + 4).

When we simplify this, we first combine like terms, which are the x's and the constants. Combining the x terms 5x, 2x, 2x, and 6x gives us 15x. Next, we combine the constants -1, 3, and 4 which gives us + 6. Therefore, the expression representing the perimeter of the trapezoid is 15x + 6, that is answer option c.

Learn more about Perimeter of Trapezoid here:


The complete question is:

Which expression represents the perimeter of the trapezoid whose length of sides are:

5x, 2x - 1, 2x + 3, 6x +4

a. 11x + 4

b. 4x + 2

c. 15x + 6

d. 13x + 8

Answer: 15x + 6
5x + 2x+3 = 7x+3
6x+4 + 7x+3 = 13x + 7
13x+7 + 2x-1 = 15x+ 6