The probability is 1 in 4,011,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 46,000 trips.(a) What is the probability of a
Answers
Answer:
0.0114
Step-by-step explanation:
(a) What is the probability of a fatal accident over a lifetime?
Suppose A be the event of a fatal accident occurring in a single trip.
Given that:
P(1 single auto trip in the United States result in a fatality) = P(A)
Then;
P(A) = 1/4011000
P(A) = 2.493 × 10⁻⁷
Now;
P(1 single auto trip in the United States NOT resulting in a fatality) is:
P() = 1 - P(A)
P() = 1 - 2.493 × 10⁻⁷
P() = 0.9999997507
However, P(fatal accident over a lifetime) = P(at least 1 fatal accident in lifetime i.e. 46000 trips)
= 1 - P(NO fatal accidents in 46000 trips)
Similarly,
P(No fatal accidents over a lifetime) = P(No fatal accident in the 46000 trips) = P(No fatality on the 1st trip and No fatality on the 2nd trip ... and no fatality on the 45999 trip and no fatality on the 46000 trip)
=
=
= 0.9885977032
Finally;
P(fatal accident over a lifetime) = 1 - 0.9885977032
P(fatal accident over a lifetime) = 0.0114022968
P(fatal accident over a lifetime) ≅ 0.0114
Related Questions
. A coin is tossed three times, and the sequence of heads and tails is recorded.(a) Determine the sample space, Ω.(b) List the elements that make up the following events: i.A= exactly two tails, ii.B= at least twotails, iii.C= the last two tosses are heads(c) List the elements of the following events: i.A, ii.A∪B, iii.A∩B, iv.A∩C
PLEASE HELP! How do I solve this problem?
Which figures demonstrate a single reflection?Select each correct answer.
What is the equation of the line through the origin and (-5, 6)?O A. y = -5xO B. y = -6/5 xO C. y = -6x0 D. y = -5/6 x
Complete the following. Show all work for calculations.
List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Describe the shape of the cross section when the box is cut parallel to the base.
What is the surface area of the box?
What is the surface area of the box if it is scaled up by a factor of 10?
What is the volume of the box?
What is the volume of the box if it is scaled down by a factor of 1/10?
Answers
Hope this helps!
Answer:
Rectangular prism
I chose a box of cereal.
Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part 2).
Describe the shape of the cross-section when the box is cut parallel to the base.
The shape of the cross-section would be a rectangle in dimensions.
20 cm x 8 cm
Part 3)
What is the surface area of the box?
surface area=2*area of the base + perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is
2,112 cm²
Part 4)
What is the surface area of the box if it is scaled up by a factor of 10?
we know that
surface area of the larger box =[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is
211,200 cm²
Part 5)
What is the volume of the box?
volume of the box = L*W*H 20*8*32-5,120 cm³
the answer Part 5) is
5,120 cm³
Part 6)
What is the volume of the box if it is scaled down by a factor of 1/10?
we know that
the volume of the smaller box =[scale factor]³volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box =[1/10]³*5,120 5.12 cm³
the answer part 6) is
5.12 cm³
The length is 6 in., the width is 2 in., and the height is 16 in.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?
Answers
To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.
The solution is:
a) V (max) = 36.6 in³
b) x = 1.3 in
The volume of a cube is:
V(c) = w×L×h ( in³)
In this case, cutting the length "x" from each side, means:
wide of the box ( w - 2×x ) equal to ( 7 - 2×x )
Length of the box ( L - 2×x ) equal to ( 9 - 2×x )
The height is x
Then the volume of the box, as a function of x is:
V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x
V(x) = ( 63 - 14×x - 18×x + 4×x²)×x
V(x) = 4×x³ - 32×x² + 63×x
Tacking derivatives, on both sides of the equation
V´(x) = 12×x² - 64 ×x + 63
If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0
This expression is a second-degree equation, solving for x
x₁,₂ = [ 64 ± √ (64)² - 4×12*63
x₁ = ( 64 + 32.74 )/ 24
x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)
x₂ = ( 64 - 32.74)/24
x₂ = 1.30 in
The maximum volume of the box is:
V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3
V(max) = 4.4 × 6.4 × 1.3
V(max) = 36.60 in³
To chek for maximum value of V when x = 1.3
we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V
V´´(x) = 24×x - 64 for x = 1.3
V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0
Then the value x = 1.3 will bring maximum value for V
Related Link: brainly.com/question/13581879
Final answer:
The maximum volume of the box that can be formed is approximately 17.1875 cubic inches. The cutout length that would result in this maximum volume is approximately 1.25 inches.
Explanation:
To solve this problem, we will use optimization in calculus. Let's denote the length of the square cutout as 'x'. When you cut out an x by x square from each corner and fold up the sides, the box will have dimensions:
- Length: 9 inches (the original length) - 2x (the removed parts)
- Width: 7 inches (the original width) - 2x
- Height: x inches (the height is the cutout's length)
So the volume V of the box can be given by the equation: V = x(9-2x)(7-2x). We want to maximize this volume.
To find the maximum, differentiate V with respect to x, equate to zero and solve for x. V' = (9-2x)(7-2x) + x(-2)(7-2x) + x(9-2x)(-2) = 0. We obtain x=1.25 inches, but we need to verify whether this value gives us a maximum. Second differentiation, V'' = -12 is less than zero for these dimensions so the V is maximum.
a. So, when we solve, the maximum volume will be approximately 17.1875 cubic inches.
b. The cutout length that would produce the maximum volume is therefore about 1.25 inches.
Learn more about Optimization here:
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Answers
Answer:
B.) 3.65, 3 2/3, 3.7
Step-by-step explanation:
Answer:
Step-by-step explanation:
The second option shows the numbers in order from least to greatest because 3 2/3 simplified is 3.6666666
Answers
a.The expression for temperature change in City A is 9 + (-8)
b.The amount the temperature changes for City A = 1°F
c.The expression for temperature change in City B is -1 + (-3) = -4°F
d.The amount the temperature changes for City B = -4°F
What is temperature?
The degree of hotness or coldness of an object is called as temperature.
Now it is given that,
In City A,
rise in temperature from 8 am to 9 am = 9°F
drop in temperature from 9 am to 10 am = 8°F
In City B,
drop in temperature from 8 am to 9 am = 1°F
drop in temperature from 9 am to 10 am = 3°F
a.The expression for temperature change in City A
rise in temperature = +9°F
drop in temperature = -8°F
∴the expression for change in temperature for City A = 9 + (-8)
b.The amount the temperature changes for City A = 9 + (-8)= 1°F
c.The expression for temperature change in City B
drop in temperature = -1°F
drop in temperature = -3°F
∴the expression for change in temperature for City A = -1 + (-3)
d.The amount the temperature changes for City B = -1 + (-3)= -4°F
Hence,the required answers are,
a.The expression for temperature change in City A is 9 + (-8)
b.The amount the temperature changes for City A = 1°F
c.The expression for temperature change in City B is -1 + (-3) = -4°F
d.The amount the temperature changes for City B = -4°F
More about temperature change :
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Answers
Answer:
$2.06
Step-by-step explanation:
$2.99 x 6 = $17.94
$20.00 - $17.94 = $2.06
Hope this helps
Answer: $0.26
Step-by-step explanation:
Cost of 6 pens
= 2.99 x 6
= 17.94
Add sales tax at 10%,
= 17.94 x 1.1
= 19.74
Change due to me
= 20 - 19.74
= 0.26
Answers
Answer:y = 115 degrees
Step-by-step explanation:
The given polygon has 6 sides. It is a hexagon. The sum of the interior angles of a polygon is
180(n - 2)
Where
n is the number of sides that the polygon has. This means that n = 6
Therefore, the sum of the interior angles would be
180(6 - 2) = 720 degrees
Therefore,
126 + 101 + 135 + 147 + 96 + y = 720
605 + y = 720
Subtracting 605 from both sides of the equation, it becomes
y = 720 - 605 = 115 degrees
It's a six sided polygon. For any polygon the external angles add to 360 degrees. The internal angles shown are the supplements of the external angles. We have
(180 - θ₁) + (180 - θ₂) + ... + (180 - θ₆) = 360
6(180) - 360 = θ₁ + θ₂ + θ₃ + θ₄ + θ₅ + θ₆
720 = θ₁ + θ₂ + θ₃ + θ₄ + θ₅ + θ₆
The six angles add up to 720 degrees, and five of them add to
126+101+135+147+96=605
So y = 720 - 605 = 115
The degree sign is external to y so not part of the answer:
Answer: 115