Answer:
Step-by-step explanation:
Hello!
Regarding the reasons that traffic accidents occur:
28% are caused by distracted drivers using cell phones or texting
11% of the drivers' user their phones at any time
The probability of a driver having an accident is 5.26%
a)
DC = event that a randomly selected driver is using a cell phone.
P(DC)= 0.11
b)
TA = event that a randomly selected driver has a traffic accident.
P(TA)= 0.0526
c) and f)
If both events are related, i.e. dependent, then you would expect that the occurrence of one of these events will affect the probability of the other one. If they are not related, i.e. independent events, then their probabilities will not be affected by the occurrence of one or another:
If both events are independent P(TA|DC)= P(TA)
If they are dependent, then:
P(TA|DC)≠ P(TA)
P(TA|DC)= 0.28
P(TA)= 0.0526
As you can see the probability of the driver having an accident given that he was using the cell phone is different from the probability of the driver having an accident. This means that both events are related.
d) and e)
You have to calculate the probability that "the driver was distracted with the phone given that he had an accident", symbolically P(DC|TA)
P(DC|TA) = [tex]\frac{P(DCnTA)}{P(TA)}[/tex]
[tex]P(TA|DC)= \frac{P(TAnDC}{P(DC)}[/tex] ⇒ P(DC∩TA)= P(TA|DC)*P(DC)= 0.28 * 0.11= 0.0308
P(DC|TA) = [tex]\frac{0.0308}{0.0526}= 0.585= 0.59[/tex]
I hope this helps!
ASAP PLEASE HELP!!!!!! Find the y-intercept of the rational function. A rational function is graphed in the first quadrant, and in the second, third and fourth quadrants are other pieces of the graph. The graph crosses the x axis at negative 10 and crosses the y axis at negative 2.
Answer:
(0,-2)
Step-by-step explanation:
The y-intercept is simply when the function touches or crosses the y-axis.
We're told that the graph crosses the y-axis at -2. In other words, the y-intercept is at -2.
The ordered pair would be (0,-2)
Identify the parameter n in the following binomial distribution scenario. A basketball player has a 0.479 probability of
making a free throw and a 0.521 probability of missing. If the player shoots 17 free throws, we want to know the probability
that he makes more than 9 of them. (Consider made free throws as successes in the binomial distribution.)
Answer:
n = 17
Step-by-step explanation:
Assuming
- probability of success (making free throw) does not vary
We have
n = 17 (trials)
p = 0.479
x > 9
The answer is "[tex]\bold{p(x>9)=0.2550319}[/tex]"
[tex]\to X:[/tex] Number of creating free throws in a set [tex]\bold{17\ \ x \sim bin(17,0.479)}[/tex]
Know we calculating the P(makes more than 9 of them)
[tex]=\bold{9(X>9)=1-P(Z<=9)}[/tex]
Using the R-code:
[tex]\to \bold{1-p\ binom(9,17,0.479)}\\\\\to \bold{[1]0.2550319}\\\\\bold{\therefore}\\\\ \to \bold{p(x>9)=0.2550319}[/tex]
Learn more:
binomial distribution: brainly.com/question/9065292
Which correlation coefficient could represent the relationship in the scatterpot. Beach visitors
Answer:
A. 0.89.
Step-by-step explanation:
The value of correlation coefficient ranges from -1 to 1. Any value outside this range cannot possibly be correlation coefficient of a scatter plot representing relationship between two variables.
The scatter plot given shows a positive correlation between average daily temperatures and number of visitors, as the trend shows the two variables are moving in the same direction. As daily temperature increases, visitors also increases.
From the options given, the only plausible correlation that can represent this positive relationship is A. 0.89.
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 6x + 9 = 11
Answer:
x = 3 ± sqrt(11)
Step-by-step explanation:
x^2 - 6x + 9 = 11
Recognizing that this is a perfect square trinomial
(x-3) ^2 =11
Taking the square root of each side
sqrt((x-3) ^2) = ± sqrt(11)
x-3 =± sqrt(11)
Add 3 to each side
x = 3 ± sqrt(11)
Answer:
[tex]\large\boxed{\sf \ \ x = 3+\sqrt{11} \ \ or \ \ x = 3-\sqrt{11} \ \ }[/tex]
Step-by-step explanation:
Hello,
[tex]x^2-6x+9=11\\<=> x^2-2*3*x+3^2=11\\<=>(x-3)^2=11\\<=> x-3=\sqrt{11} \ or \ x-3=-\sqrt{11}\\<=> x = 3+\sqrt{11} \ or \ x = 3-\sqrt{11}[/tex]
Do not hesitate if you have any question
Hope this helps
A company has five employees on its health insurance plan. Each year, each employee independently has an 80% probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000.
Calculate the probability that the company's total hospital costs in a year are less than 50,000.
Answer:
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
Step-by-step explanation:
From the given information:
the probability that the company's total hospital costs in a year are less than 50,000 will be the sum of the probability of the employees admitted.
If anyone is admitted to the hospital, they have [tex]\dfrac{1}{3}[/tex] probability of making at least one more visit, and a [tex]\dfrac{2}{3}[/tex] probability that this is their last visit.
If zero employee was admitted ;
Then:
Probability = (0.80)⁵
Probability = 0.3277
If one employee is admitted once;
Probability = [tex](0.80)^4 \times (0.20)^1 \times (^5_1) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{2}{3})[/tex]
Probability = 0.2731
If one employee is admitted twice
Probability = [tex](0.80)^3 \times (0.20)^2 \times (^5_2) \times (\dfrac{2}{3})^2[/tex]
Probability = [tex](0.80)^3 \times (0.20)^2 \times (\dfrac{5!}{(5-2)!}) \times (\dfrac{2}{3})^2[/tex]
Probability = 0.1820
If two employees are admitted once
Probability = [tex](0.80)^4\times (0.20)^1 \times (^5_1) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = [tex](0.80)^4 \times (0.20)^1 \times (\dfrac{5!}{(5-1)!}) \times (\dfrac{1}{3}) \times (\dfrac{2}{3})[/tex]
Probability = 0.0910
∴
the probability that the company's total hospital costs in a year are less than 50,000 = 0.3277 + 0.2731 + 0.1820
the probability that the company's total hospital costs in a year are less than 50,000 = 0.7828
HELP number 12 pls i do nor have long more
Answer:
Dian has $250 originally.
Step-by-step explanation:
Let the total money Dian has originally = $S
Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,
Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]
Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]
= [tex]\frac{\text{5S-2S}}{5}[/tex]
= [tex]\frac{3S}{5}[/tex]
Since Dian has $150 left then the equation will be,
[tex]\frac{3S}{5}=150[/tex]
S = [tex]\frac{150\times 5}{3}[/tex]
S = $250
Therefore, Dian has $250 originally.
The length of a rectangle is 4yd longer than its width. If the perimeter of the rectangle is 36yd, find its area
Answer:
[tex] \boxed{\sf Area \ of \ the \ rectangle = 91 \ yd^{2}} [/tex]
Given:
Length of the rectangle = 4 yd longer than its width
Perimeter of the rectangle = 36 yd
To Find:
Area of the rectangle
Step-by-step explanation:
Let the width of the rectangle be 'w' yd
So,
Length of the rectangle = (w + 4) yd
[tex] \therefore \\ \sf \implies Perimeter \: of \: the \: rectangle = 2(Length + Width) \\ \\ \sf \implies 36 = 2((4 + w) + w) \\ \\ \sf \implies 36 = 2(4 + w + w) \\ \\ \sf \implies 36 = 2(4 + 2w) \\ \\ \sf 36 =2(2w+4) \: is \: equivalent \: to \: 2(2w + 4) = 36: \\ \sf \implies 2(2w + 4) = 36 \\ \\ \sf Divide \: both \: sides \: of \: 2 (2w + 4) = 36 \: by \: 2: \\ \sf \implies 2w + 4 = 18 \\ \\ \sf Subtract \: 4 \: from \: both \: sides: \\ \sf \implies 2w = 14 \\ \\ \sf Divide \: both \: sides \: of \: 2w = 14 \: by \: 2: \\ \sf \implies w = 7[/tex]
So,
Width of the rectangle = 7 yd
Length of the rectangle = (7 + 4) yd
= 13 yd
[tex] \therefore \\ \sf Area \ of \ the \ rectangle = Length \times Width \\ \\ \sf = 7 \times 13 \\ \\ \sf = 91 \: {yd}^{2} [/tex]
Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers who floss twice a day is less than 40%. To test this claim, a group of 400 teenagers are randomly selected and its determined that 149 floss twice a day. The following is the setup for this hypothesis test: H0:p=0.40 H0:p<0.40 The p-value for this hypothesis test is 0.131. At the 5% significance level, should the dentist reject or fail to reject the null hypothesis?
Answer:
The dentist should fail to reject the Null hypothesis
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The sample mean is [tex]\= x = 149[/tex]
The level of significance is 5% = 0.05
The Null hypothesis is [tex]H_o : p = 0.40[/tex]
The Alternative hypothesis is [tex]H_a : p < 0.40[/tex]
The p-value is [tex]p-value = 0.131[/tex]
Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis
What is the value of the expression iºxi1 x 2 x 3 xi4?
a) 1
b) -1
c) i
d) -i
Answer:
Option b.
Step-by-step explanation:
Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].
Let as consider the given expression is
[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]
We know that,
[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]
Using these values, we get
[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]
[tex]=i^2[/tex]
[tex]=-1[/tex]
The value of given expression is -1.
Therefore, the correct option is b.
can someone help me with this question?l
Answer:
1. 32x³ - 25x² + 35x2. 6x - 11y + 14z - 7Step-by-step explanation:
1).(4x³ - 5x² + 3x ) - 4(5x² - 7x³ - 8x)
Remove the brackets and simplify.
We have
4x³ - 5x² + 3x - 20x² + 28x³ + 32x
Group like terms and simplify
That's
4x³ + 28x³ - 5x² - 20x² + 3x + 32x
We have the final answer as
32x³ - 25x² + 35x2).- 3 - ( 4x + 3y - 2z ) - 4 + 2( 5x - 4y + 6z)
Remove the brackets and simplify
That's
- 3 - 4x - 3y + 2z - 4 + 10x - 8y + 12z
Group like terms and simplify
- 4x + 10x - 3y - 8y + 2z + 12z - 3 - 4
We have the final answer as
6x - 11y + 14z - 7Hope this helps you
What is the sum of the series? ∑j=152j Enter your answer in the box.
Answer:
Hope this is correct
HAVE A GOOD DAY!
given g(x)=3/x^2+2x find g^-1(x)
Answer:
A
Step-by-step explanation:
[tex]g(x) = \frac{3}{{x}^{2} + 2x} \\ {x}^{2} + 2x - \frac{3}{g(x)} = 0 \\ x = \frac{1}{2} \Big( - 2 + \sqrt{12 + \frac{12}{g(x)} }\Big) \\ x = - 1 + \sqrt{1 \pm \frac{3}{g(x)} } [/tex]
Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.
Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)
Answer:
Length is 17m and Breadth is also 17mStep-by-step explanation:
The perimeter of a rectangle is expressed as 2(L+B) where;
L is the length and B is the breadth of the triangle.
P = 2(L+B)
68 = 2(L+B)
L+B = 68/2
L+B = 34
L = 34 - B ... 1
Area of the rectangle A = LB... 2
Substituting equation 1 into 2 will give;
A = (34-B)B
A = 34B-B²
To maximize the area of the triangle, dA/dB must be equal to zero i.e
dA/dB = 0
dA/dB = 34 - 2B = 0
34-2B = 0
2B = 34
Dividing both sides of the equation by 2 we will have;
B = 34/2
B = 17
Substituting B = 17 into equation 1 to get the length L
L = 34-17
L = 17m
This shows that the rectangle with maximum area is a square since L = B = 17m
The dimension of the rectangle is Length = 17m and Breadth = 17m
The dimensions are 17m and 17m.
The perimeter of a rectangle is given as:
= 2(length + width)
Since in their case, the lengths have same values, this will be:
Perimeter = 2(l + l)
Perimeter = 4l
4l = 68
L = 68/4
L = 17m
Therefore, the dimensions are 17m and 17m.
Read related link on:
https://brainly.com/question/15366172
15 points + brainliest if you can figure this out!
Answer:
(H1, T1)
Step-by-step explanation:
Since we know that the only number option is 1, we can cancel out the first 3 options. and obviously, there are only heads, and tails. So, using only the # 1 and heads and tails, we can conclude that the answer is (H1, T1).
Answer:
D. (H1, T1)
Step-by-step explanation:
Since all outcomes require card #1 is chosen, so any answer with 2 or 3 can be rejected, therefore the answer is
D. (H1, T1)
Find the surface area of the attached figure and round your answer to the nearest tenth, if necessary.
Answer:
[tex] S.A = 246.6 in^2 [/tex]
Step-by-step explanation:
The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.
Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]
Where,
B.A = Base Area of the pyramid = 9*9 = 81 in²
P = perimeter of the base = 4(9) = 36 in
L = slant height of pyramid = 9.2 in
Plug in the values into the given formula to find the surface area
[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]
[tex] = 81 + 18*9.2 [/tex]
[tex] = 81 + 165.6 [/tex]
[tex] S.A = 246.6 in^2 [/tex]
A section of concrete pipe 3.0 m long has an inside diameter of 1.2 m and an outside diameter of 1.8 m. What is the volume of concrete in this section of pipe?
Answer:
4.24m³
Step-by-step explanation:
The inside diameter of 1.2 m of the pipe
Radius of the inside pipe = Diameter/2 = 1.2/2 = 0.6m
The outside diameter of 1.8 m
Radius of the outer of the pipe = 1.8/2 = 0.9m
Height of the pipe = 3.0m
A Pipe looks like the shape of the cylinder. Hence,
Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe
Volume of the outer section of the Pipe = πr²h
h = 3.0m
r = 0.9
= π × 0.9² × 3.0
= 7.63m³
Volume of the inner section of the Pipe = πr²h
h = 3.0m
r = 0.6
= π × 0.6² × 3.0
= 3.39m³
Volume of concrete in the pipe = Volume of the outer section of the Pipe - Volume of the inner section of the pipe
= 7.63m³ - 3.39m³
= 4.24m³
Therefore, volume of concrete in the pipe is 4.24m³
HELPNEEDED.Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate.
What is the probability that the pianist will be a boy and the alternate will be a girl?
30%
40%
50%
60%
The coordinates of the vertices of a rectangle are given by R(- 3, - 4), E(- 3, 4), C (4, 4), and T (4, - 4). A. Use the Pythagorean Theorem to find the exact length of ET. B. How can you use the Distance Formula to find the length of ET? Show that the Distance Formula gives the same answer.
Answer:
see explanation
Step-by-step explanation:
Pythagorean Theorem
7² + 8² = x²
49 + 64 = x²
113 = x²
x = √113 or 10.63
Distance Formula
√(-4 - 4)² + (4 - -3)²
= √8² + 7²
= √113 or 10.63
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answer:
lmkjhvjgcfnhjkhbmgnc gfghh
Step-by-step explanation:
the mean monthly income of trainees at a local mill is 1100 with a standard deviation of 150. find rthe probability that a trainee earns less than 900 a month g
Answer:
The probability is [tex]P(X < 900 ) = 0.0918[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 1100[/tex]
The standard deviation is [tex]\sigma = 150[/tex]
The random number value is x =900
The probability that a trainee earn less than 900 a month is mathematically represented as
[tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]
Generally the z-value for the normal distribution is mathematically represented as
[tex]z = \frac{x -\mu }{\sigma }[/tex]
So From above we have
[tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]
[tex]P(X < 900 ) = P( Z <-1.33)[/tex]
Now from the z-table
[tex]P(X < 900 ) = 0.0918[/tex]
TRIANGLE ABC IS DILATED BY A SCALE FACTOR OF 0.5 WITH THE ORIGIN AS THE CENTER OF DILATION, RESULTING IN THE IMAGE TRIANGLE A'B'C. IF A=(2,2). IF A (2,2), B= (4,3) AND C=(6,3), WHAT IS THE LENGTH OF LINE B'C'?
Answer: The length of the line B'C" is 1 unit.
Step-by-step explanation:
Given: Triangle ABC is dilated by a scale factor of 0.5 with the origin as the center of dilation , resulting in the image Triangle A'B'C'.
If A (2,2), B= (4,3) and C=(6,3).
Distance between (a,b) and (c,d): [tex]D=\sqrt{(d-b)^2+(c-b)^2}[/tex]
Then, BC [tex]=\sqrt{(3-3)^2+(6-4)^2}[/tex]
[tex]\\\\=\sqrt{0+2^2}\\\\=\sqrt{4}\\\\=2\text{ units}[/tex]
Length of image = scale factor x length in original figure
B'C' = 0.5 × BC
= 0.5 × 2
= 1 unit
Hence, the length of the line B'C" is 1 unit.
How to do this? what is the answer??
Answer:
I think that is the C
Step-by-step explanation:
Answer:
Option B is the correct answer.
Step-by-step explanation:
here, arc RT =162°
as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.
so, its value must be 81°only.
hope it helps..
13. How long will a man take to cover
a distance of 7 kilometres by
walking 4 kilometres per hour?
(a) 1 hr. 35mins.
b) 1hr. 45mins
(c) Less than 1hr
(d) Exactly 1 hr.
(e) More than 2hrs
7km/ 4km per hour = 1 3/4 hours
3/4 hour = 45 minutes
Total time = 1 hour and 45 minutes.
Write 21/7 as a whole number
Answer: 3
Step-by-step explanation:
7x=21 21/7=3
4. (a) Two years ago a woman was 7 times as old as her daughter, but in 3 years time
she would be only 4
times as old as the girl. How old are they now?
Answer:
woman is 37, girl is 7
Step-by-step explanation:
7(x-2) = y-2
4(x+3) = y+3
7x - 14 = y - 2
7x - 12 = y
4x + 9 = y
3x - 21 = 0
x = 7
y = 37
Which of the following situations may be modeled by the equation y = 2x +20
A. Carlos has written 18 pages of his article. He plans to write an
additional 2 pages per day.
B. Don has already sold 22 vehicles. He plans to sell 2 vehicles per
week.
C. Martin has saved $2. He plans to save $20 per month.
D. Eleanor has collected 20 action figures. She plans to collect 2
additional figures per month
Answer:
D.
m = 2 = figures/month
b = 20 = # of action figures
Assume production time per unit is normally distributed with a mean 40 minutes and standard deviation 8 minutes. Using the empirical rule, what percent of the units are produced in MORE than 32 minutes?
Answer:
84%
Step-by-step explanation:
We find the z-score here
z= x-mean/SD = 32-40/8 = -1
So the probability we want to find is;
P(z>-1)
This can be obtained using the standard score table
P(z>-1) = 0.84 = 84%
A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90. its price-earnings ratio equals:
Answer: Price-earnings ratio= 22.0
Step-by-step explanation:
Given: A company had a market price of $38.50 per share, earnings per share of $1.75, and dividends per share of $0.90
To find: price-earnings ratio
Required formula: [tex]\text{price-earnings ratio }=\dfrac{\text{ Market Price per Share}}{\text{Earnings Per Share}}[/tex]
Then, Price-earnings ratio = [tex]\dfrac{\$38.50}{\$1.75}[/tex]
⇒Price-earnings ratio = [tex]\dfrac{22}{1}[/tex]
Hence, the price-earnings ratio= 22.0
Find the area of the figure. Round to the nearest tenth if necessary. 386.3m^2 194.3m^2 193.1m^2 201.9m^2
Add the top and bottom numbers together, divide that by 2 then multiply by the height.
15.3 + 19.5 = 34.8
34.8/2 = 17.4
17.4 x 11.1 = 193.14
Answer is 193.1 m^2
there are three oranges in 200g of bag . if the weight of them with bag is 1.4kg. find the weight of an orange.i want full methods
the bag is 200g
total weight with oranges is 1400g
deduct the bags weight from total weight
1400 - 200
1200g
this is the weight of the three oranges
so each orange would be
1200 ÷ 3
400g