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Nesterboy [21]
3 years ago
5

NEED HELP! The ski lift at Thunder Mountain called Devils Canyon is quite dangerous. Usually 2% of the skiers who attempt the ru

n will injure themselves due to falls.
8. What is the probability that exactly 3 of the next 100 skiers who attempt this run will injure themselves?

Answer Choices:
0.126
0.175
0.182
0.215
Mathematics
1 answer:
grigory [225]3 years ago
7 0
We will be using the binomial probability formula to solve the problem

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ⁻ˣ

Where:
n = the number of trials = 100
x = the number of samples we are trying on = 3
p = the probability of success = 2% = 0.02

We can either calculate ⁿCₓ by using the scientific calculator using the ^nC_r button or by doing it manually use \frac{n!}{(n-x)!x!}

P(3) = ¹⁰⁰C₃ (0.02)³ (1 - 0.02)¹⁰⁰⁻³
P(3) = ¹⁰⁰C₃ (0.02)³ (0.98)⁹⁸
P(3) = 0.182 (rounded to three decimal places)

Correct answer: option 3
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garik1379 [7]

Answer:

The transformations needed to obtain the new function are horizontal scaling, vertical scaling and vertical translation. The resultant function is z'(x) = \frac{1}{2}  + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right).

The domain of the function is all real numbers and its range is between -4 and 5.

The graph is enclosed below as attachment.

Step-by-step explanation:

Let be z (x) = \cos x the base formula, where x is measured in sexagesimal degrees. This expression must be transformed by using the following data:

T = 180^{\circ} (Period)

z_{min} = -4 (Minimum)

z_{max} = 5 (Maximum)

The cosine function is a periodic bounded function that lies between -1 and 1, that is, twice the unit amplitude, and periodicity of 2\pi radians. In addition, the following considerations must be taken into account for transformations:

1) x must be replaced by \frac{2\pi\cdot x}{180^{\circ}}. (Horizontal scaling)

2) The cosine function must be multiplied by a new amplitude (Vertical scaling), which is:

\Delta z = \frac{z_{max}-z_{min}}{2}

\Delta z = \frac{5+4}{2}

\Delta z = \frac{9}{2}

3) Midpoint value must be changed from zero to the midpoint between new minimum and maximum. (Vertical translation)

z_{m} = \frac{z_{min}+z_{max}}{2}

z_{m} = \frac{1}{2}

The new function is:

z'(x) = z_{m} + \Delta z\cdot \cos \left(\frac{2\pi\cdot x}{T} \right)

Given that z_{m} = \frac{1}{2}, \Delta z = \frac{9}{2} and T = 180^{\circ}, the outcome is:

z'(x) = \frac{1}{2}  + \frac{9}{2} \cdot \cos \left(\frac{\pi\cdot x}{90^{\circ}} \right)

The domain of the function is all real numbers and its range is between -4 and 5. The graph is enclosed below as attachment.

8 0
3 years ago
Write the slope-intercept form of the equation through (4, 2) perpendicular to LaTeX: y=4x-4
marin [14]

Answer:

y=4x-4

slope of the line=-4/-1

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since perpendicular,

    m1.m2=-1

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    m2=-1/4

The equation of line passing through the point (4,2)is

  y-y1=m2(x-x1)

  y-2=-1/4(x-4)

Step-by-step explanation:

i don't say that you have to mark my ans as brainliest but my friend if  it has helped you a bit also don't forget to thank me.....

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BARSIC [14]
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3 years ago
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Answer:

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3 years ago
Loretta grew 54 watermelons in her garden last year. This year, that number increased by 5/9. Which expression shows the number
Mars2501 [29]

Answer:

54+\frac{5}{9}\times 54

Step-by-step explanation:

We are given that

Loretta grew  watermelons in her garden last year=54

We have to find the expression which shows the number of watermelons Loretta grew this year.

To find the expression which shows the  number of watermelons Loretta grew this year by adding watermelons grew in her garden last year and number of watermelons increased .

According to question

5/9 of 54=\frac{5}{9}\times 54

Therefore, the expression which shows the  number of watermelons Loretta grew this year

=54+\frac{5}{9}\times 54

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