Right angled triangle calculation. the opposite is 150mm and the only known angle is the right angle how can i calculate the other two sides and angle??

Answers

Answer 1

Answer: You can't. One side and one angle is never enough to define a unique triangle.

If the side opposite the right angle is 150mm, the other 2 sides could be . . .

-- 75 and 129.9
-- 100 and 111.8
-- 110 and 101.98
-- 120 and 90
-- 130 and 74.83
-- both 106.07

or any one of an infinite number of other possibilities.

You need to know one more side, or one more angle.

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The time , in hours , it takes to repair an electrical breakdown in a certain factory is represent by a random variable x where repair time follow a normal distribution with mean 5 hour and standard deviation 1 hour , if 5 electrical breakdown ore randomly chosen , Find the probability that ( a all repaired time below 6 hours ( b ) exactly 3 of them repaired below 6 hours

Answers

Answer:

a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Step-by-step explanation:

To solve this question, we need to understand the normal and the binomial probability distributions.

Binomial probability distribution

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

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

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

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

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion repaired below 6 hours:

Mean 5 hours and standard deviation 1 hour, which means that $\mu = 5, \sigma = 1$

This proportion is the p-value of Z when X = 6. So

$Z = (X - \mu)/(\sigma)$

$Z = (6 - 5)/(1)$

$Z = 1$

$Z = 1$ has a p-value of 0.8413.

0.8413 repaired below 6 hours.

For the binomial distribution, this means that $p = 0.8413$

5 are chosen:

This means that $n = 5$

a) Probability that all are repaired in less than 6 hours

This is P(X = 5). So

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 5) = C_(5,5).(0.8413)^(5).(0.1587)^(0) = 0.4215$

0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) Probability that exactly 3 of them repaired below 6 hours

This is P(X = 3). So

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 3) = C_(5,3).(0.8413)^(3).(0.1587)^(2) = 0.15$

0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

What is the focal length of the parabola whose graph is shown? focus: (-3, 2.6) and directrix: (-0.6)

Answers

The distance from the focus to the directrix is twice the focal length. Using the distance formula, 2.6+(-0.6) = 3.2. Half of this value is the focal length. 3.2/2 = 1.6. Therefore, the focal length of the parabola with a focus of (-3,2.6) and directrix of -0.6 is 1.6.

Final answer:

The focal length of a parabola is the distance from its focus to the directrix. In this case, the focal length is calculated to be 2.4 units.

Explanation:

In Mathematics, particularly in the study of conic sections, the focal length of a parabola is the distance from the focus to the directrix of the parabola. Given the focus as (-3, 2.6) and the directrix as (-0.6), we can calculate the focal length by using the formula for the distance between a point and a line in a plane, which is |x-x1|. |x-x1| is the absolute value of the difference between the x-coordinate of the focus and the equation of the directrix. Here, x1 is -3 (from the focus) and x is -0.6 (from the directrix). So, the focal length of the parabola is |-0.6 - (-3)| = |-0.6 + 3| = 2.4 units.

Learn more about Focal Length here:

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Determine the most efficient way to use the Binomial Theorem to show the following. (11)^4= 14641A)Write 11=5+6 and expand.
B) Write 11= 10+1 and expand.
C) Write 11= 3+3+2 and expand.
D)Write 11= 4+4+3 and expand.

Answers

The formula for binomial theorem is

$(a+b)^n=( \left \ {{n} \atop {0}} \right.)a^(n)+( \left \ {{n} \atop {1}} \right.)a^(n-1)b+( \left \ {{n} \atop {0}} \right.)a^(n-2)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n$

Now this shall be very easy if the value of a = 1

The formula shall become

$(1+b)^n=( \left \ {{n} \atop {0}} \right.)1^(n)+( \left \ {{n} \atop {1}} \right.)1^(n-1)b+( \left \ {{n} \atop {0}} \right.)1^(n-2)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n$

Which shall be

$(1+b)^n=( \left \ {{n} \atop {0}} \right.)+( \left \ {{n} \atop {1}} \right.)b+( \left \ {{n} \atop {0}} \right.)b^2+...+( \left \ {{n} \atop {n}} \right.)b^n$

So to find 11^4

We must break it as 1 + 10.

Option B) is the right answer.

Write (1+10) and expand. As you will have nCr *(10)^(n-r)
Where r index n count ( less terms)

A rocket is launched from the ground. The function h(t)= -4.9t^2 +180t models the height of a rocket launcher from the ground t seconds after it is launched. If all other factors remain the same, which of the following function models the height of a rocket above the ground after t seconds if it is launched from a platform 100 feet in the air?

(1) h(t) = -4.9t^2 +280t

(2) h(t) = -4.9t^2 +180t -100

(3) h(t) = -4.9t^2 +180t +100

(4) h(t) = -4.9t^2 +180 (t+100)

Answers

The answer would be (1).

(please help me) (I've been trying to figure this out for hours) (I screenshot the question and choices D: <3 )

Answers

It would be the third answer choice. m<1= 60, m<2= 30, and m<3= 60

The hexagon is split equally, making all the triangles there equilateral, and their angles equal all 60 degrees. That automatically makes angle one and three 60 degrees. For angle two, there is a line, splitting the triangle in half. There are two ways to consider this:

1. Think about the 30°, 60°, 90° special triangles.

or

2. divide 60° by 2, and having 30° in return.

Solve for h.

-18 + h = 28
h =

Answers

+18 on each side

h=46

Answer: h = 46

Step-by-step explanation:

hope this helps what your looking for

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