The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant. In eight traffic fatalities, find the probability that the number which involve an intoxicated or alcohol-impaired driver or nonoccupant is
Answer:
[tex]P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}[/tex]
In which x is the number of which we want to find the probability.
Step-by-step explanation:
For each traffic fatality, there are only two possible outcomes. EIther it involved an intoxicated or alcohol-impaired driver or nonoccupant, or it didn't. Traffic fatalities are independent of other traffic fatalities, which means that the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant.
This means that [tex]p = 0.4[/tex]
Eight traffic fatalities
This means that [tex]n = 8[/tex]
Find the probability that the number which involve an intoxicated or alcohol-impaired driver or nonoccupant is
This is P(X = x), in which x is the number of which we want to find the probability. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}[/tex]
Based on the binomial probability principle, the probability involving the number of non-occupant is [tex] P(x = k) = 8Ck \times 0.40^{k} \times 0.60^{8-k} [/tex]
Let :
Number of alcohol - impaired or non-occupant = kNumber of trials, n = 8Probability of success, p = 0.40q = 1 - p = 1 - 0.40 = 0.60Using the binomial probability relation :
[tex] P(x = x) = nCx \times p^{x} \times q^{n-x} [/tex] x = kSubstituting the values into the relation :
[tex] P(x = k) = nCk \times 0.40^{k} \times 0.60^{n-k} [/tex]
Hence, the required probability expression is [tex] P(x = k) = 8Ck \times 0.40^{k} \times 0.60^{8-k} [/tex]
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PLEASE PLEASE PLEASE!
Answer:
70
Step-by-step explanation:
The area of one of the four triangles is [tex]\frac{1}{2}\times 5 \times 7 = 17.5[/tex]. So together the area of all the four traingles is [tex]4\times 17.5 = 70[/tex]
The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.9 cm. a. Find the probability that an individual distance is greater than 207.50 cm. b. Find the probability that the mean for 20 randomly selected distances is greater than 193.50 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30
Answer:
a) P(X > 207.50) = 0.0808
b) P(X-bar > 193.5) = 0.7734
c) It matters only in sampling distribution when we does not know the shape of distribution.
Step-by-step explanation:
Given - The overhead reach distances of adult females are normally distributed with a mean of 195 cm and a standard deviation of 8.9 cm.
To find - a. Find the probability that an individual distance is greater than 207.50 cm.
b. Find the probability that the mean for 20 randomly selected distances is greater than 193.50 cm.
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30 ?
Proof -
Given that,
μ = 195 cm
σ = 8.9 cm
a)
P(X > 207.50) = 1 - P(X < 207.5)
= 1 - P(Z < [tex]\frac{207.5 - 195}{8.9}[/tex] )
= 1 - P(Z < 1.4)
= 1 - 0.9192
= 0.0808
⇒P(X > 207.50) = 0.0808
b)
n = 20
μₓ- = μ = 195
σₓ⁻ = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{8.9}{\sqrt{20} }[/tex] = 1.99
Now,
P(X-bar > 193.5) = 1 - P(X-bar < 193.5)
= 1 - P(Z < [tex]\frac{193.5 - 195}{1.99}[/tex] )
= 1 - P(Z < -0.75)
= 1 - 0.2266
= 0.7734
⇒P(X-bar > 193.5) = 0.7734
c)
Given that If the population is normally distributed , then the sample does not have to be greater than 30.
It matters only in sampling distribution when we does not know the shape of distribution.
Find the area of the polygon.
Answer:
Step-by-step explanation:
A = (7 + 4)(24) ÷ 2 = 132 units²
Solve the exponential equation.
2-x = 16
4
1/4
-4
Answer:
-4
Step-by-step explanation:
what does 5 cards to 7 cards mean?
Answer:
That is a ratio. Like for every 5 blue cards there are 7 red cards, read the context and you'll be able to see the ratio.
Step-by-step explanation:
Hope this helps :)
Please and I’ll give Brain list to you
Answer:
e
Step-by-step explanation:
e
Answer:
6
Step-by-step explanation:
Find the GCF of the numbers. 8, 16
Answer:
8
Step-by-step explanation:
Answer:
What is the Greatest Common Factor of 8 and 16? Greatest common factor (GCF) of 8 and 16 is 8.
hope it help plz heart and vote plz po..help mee pleaseeeeee
Answer:
Option 1
Step-by-step explanation:
PLEASE HELP mathematics
Answer:
21+10.5 which would equal 31.5
Step-by-step explanation:
Answer:
21+10.5 which would equal 31.5
Step-by-step explanation:
A large factory that builds machines has three shifts, one that starts at 4:00 A.M., one that starts at noon, and one that starts at 8:00 P.M. The manager of the factory wanted to know whether there is an association between an employee’s work experience (less than five years with the company, between five and twenty years with the company, over twenty years with the company) and the time of the employee’s shift. The manager selected a random sample of 125 employees and classified employees by their shift time and work experience. What is an appropriate pair of hypotheses for the manager to use?
Answer:
if the worker has more experience, then they will have longer shifts because they will be better at their job and be able to complete more tasks.
Step-by-step explanation:
use and "if then because" structure in a hypothesis, and use common logic based on the info provided :)
Answer:
[tex]H_{0}[/tex] : Work experience is independent of the time of an employee's shift
[tex]H_{A}[/tex] : Work experience is dependent on the time of an employee's shift
Step-by-step explanation:
Since we have one population but multiple variables, so we are using a chi-square test of independence. Thus, our null should be that there is no association, and the alternative that there IS an association.
What is the ratio as a fraction 9 and 6
Answer:
9/15 will become 3/5 and 6/15 will become 2/5.
⚠️PLEASE HELP⚠️
What is the value of the interquartile range of the data below?
25
30
35
40
45 50
Answer:
5
Step-by-step explanation:
The value of the interquartile range of the data below is 5.
What is Interquartile Range?The difference between the third and the first quartile is defined by the interquartile range. There are so three quartiles.
The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.
From the Plot we can write
Minimum = 27
Lower quartile = 32
Median = 36
Upper Quartile = 37
Maximum = 40
So, Interquartile range (IQR)
= Third Quartile (Q3) - First Quartile (Q1)
= 37 - 32
= 5
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The angle -456° terminates in which quadrant?
Answer:
Step-by-step explanation:
n o The angle terminates in Quadrant II In degrees, the reference angle for the given angle is 30°.
is 32/24 equivalent to 12/9
Answer:
32/24 is equivalent to 12/19
yes
Please answer quick just super small explanation pls hurry quick for brainlessly
Answer:
A = 81
Step-by-step explanation:
When there is a number above the other. You will need to multiply it.
There is a 4 so its 4 times.
-3 x -3 = 9
9 x -3 = -27
-27 x -3 = 81
------
When you multiply a negative number by a negative number it will be a positive.
If you multiply a positive number by a negative it will be negative.
6xq=54 what is q? PLEASE HURRY THIS IS DUE TOMORROW!!!!!!!!!
The true answer is 3.75
Answer:
interesting
Step-by-step explanation:
very interesting
Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?
y = 12x - 16
y = 12x + 16
y = 16x - 12
y = 16x + 12
Answer:
the first one
Step-by-step explanation:
y-y1=m(x-x1)
y-20=12(x-3)
[tex]y-20+20=12\left(x-3\right)+20[/tex]
simplify:
[tex]y=12x-16[/tex]
What is the correct answer I’m offering brainalist + 10 points don’t just say A please can you explain to me why you chose what you chose
Answer:
Answer is Complementary.
Step-by-step explanation:
This is because complementary angles add up to 90 degrees. In this example, the angles are exactly 45 degrees. Therefore, because there are two angles 45 * 2 is 90. Answer is B.
Answer:
D. vertical
Step-by-step explanation:
We can rule out A and B because they wont equal 180 or 90 they will be somewhere in between. We can rule out C because those are acute angles. So we are left with D. These angles are vertical because they are opposite angles made by two intersecting lines and they have equal values.
how do you solve the inequality -8x is greater than 72
Answer:
8n < 72
Step-by-step explanation:
Eight times a number (n) is less than 72.
Which table or graph shows the value of y going down as the value of x goes
up?
Answer:
A
Step-by-step explanation:
That's your answer...
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just look at the one that has the letter x going up it is c or d
construct a triangle with is side ab 6.5 cm BC as 4cm and angle b as 120°
Answer
A triangle can be constructed if we are given 2 sides and an angle. For these ... AB=4 cm, Angle A =30˚, AC=5 cm. 2.) BC=3 cm, Angle B=80˚, BA=6 cm ... Angle A=20˚, AC=6.5 cm, Angle C=90˚ ... Angle A=25˚, Angle B=120˚, Angle C=35˚.
Step-by-step explanation:
Only answer if you know!!! Which expression represents 5 less than y? (1 point)
Oy-5
O 5-y
Oy
5
O5y-1
Answer:
5 less than y isn’t up there but if you mean 5 minus y it’s the second one, and y minus 5 is the first
Step-by-step explanation:
Ms. Perry spent $2000 to buy some new computer equipment. Of this money, $120 was used to
buy some new keyboards. What percent of the money was spent on keyboards?
Answer: 6%
Step-by-step explanation: Step 1: We make the assumption that 2000 is 100% since it is our output value.
Step 2: We next represent the value we seek with x.
Step 3: From step 1, it follows that 100%=2000$.
Step 4: In the same vein, x%=120.
Step 5: This gives us a pair of simple equations:
100%=2000(1).
x%=120(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
[tex]\frac{100\%}{x\%}=\frac{2000}{120}[/tex]
Step 7: Taking the inverse (or reciprocal) of both sides yields
[tex]\frac{x\%}{100\%}=\frac{120}{2000}[/tex]
[tex]\Rightarrow x=6\%[/tex]
Therefore, 120 is 6% of 2000$.
PLS PLS PLS HELP ME
Answer:
A) x > -5
Step-by-step explanation:
if you saw one of your best friends getting bullied what would you do would you A help him/she B Just walk away C ask someone else for help D laugh at him cause I would help
Answer:
A. help him/her
funny story, i once got into trouble for defending my friend from being bullied and the person doing the bullying didn't get punished smh
Answer:
a
Step-by-step explanation:
duhh
The quotient of 6 and a
number (n)
Answer:
n divided by 6 (n/6)
Step-by-step explanation:
The mathematical expression for 'the quotient of 6 and a number (n)' is, 6/n or (6 ÷ n).
Used the concept of mathematical expression which can be stated that,
A mathematical expression is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.
Given that,
The algebraic expression is,
''The quotient of 6 and a number (n).''
Now, the mathematical expression for 'the quotient of 6 and a
number (n)' is,
6 ÷ n
= 6 / n
So, the mathmatical notation is 6/n.
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Baba Yaga lost her broom somewhere between her hut and Bald Mountain, and wants to get it back. She calculates that with a tailwind of 2 km/ h, she can fly from her hut to Bald Mountain in 6 hours. Baba Yaga starts her trip, finds her broom 40 km before Bald Mountain, and turns around and flies home. The entire journey takes 9 hours. Find the speed Baba Yaga flies in quiet weather (with no tailwind or headwind).
Answer:
18 km/hStep-by-step explanation:
Let the speed of Baba Yaga is x
The speed with tailwind: x + 2The speed with headwind: x - 2The distance to Bald Mountain:
6(x + 2)The distance she actually travelled is less by 40 km:
6x + 12 - 40 = 6x - 28The time she spent:
(6x - 28)/(x+2) + (6x - 28)/(x -2) = 9Solve for x to find the speed:
((6x + 12) - 40)/(x + 2) + ((6x - 12) - 16)/(x - 2) = 96 - 40/(x + 2) + 6 - 16/(x - 2) = 940/(x + 2) + 16/(x - 2) = 340(x - 2) + 16(x + 2) = 3(x+2)(x - 2)40x - 80 + 16x + 32 = 3x² - 123x² - 56x + 36 = 0Solving the quadratic equation we get:
x = 18 km/h(x = 2/3 discounted as not realistic)Find the measure of 43.
92 88°
43
88
43 = [?]
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Answer:
88°
Step-by-step explanation:
Because, vertically opposite angles are equal