A thief steals an ATM card and must randomly guess the correct three-digit pin code from a 10-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

Answers

Answer 1

Since repetition is allowed, there are 10(10)(10) choices available; 10 for the first digit, 10 for the second digit, and 10 for the third digit, coming out to a possible 1000 combinations. The probability of getting the 1 correct on the first try would be 1/1000.

Answer 2

The probability of a correct guess on the first try will be [tex]0.001[/tex] .

What is Probability ?

Probability is the ratio of number of favorable outcome to the

i.e. Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]

We have,

An ATM Card having three-digit code.

Repetition of digits is allowed.

So,

As Repetition is allowed, and we have [tex]10-[/tex]key keypad, and have to guess [tex]3[/tex] digit code,

Then

Total number of outcomes [tex]=10*10*10=1000[/tex]

And

Number of favorable outcome [tex]=1[/tex]

So,

Probability [tex]P(E)=\frac{number\ of\ favorable\ outcome}{Total\ number\ of\ outcomes.}[/tex]

[tex]P(E)=\frac{1}{1000}[/tex]

[tex]P(E)=0.001[/tex]

So, the Probability of correct guess is [tex]0.001[/tex] .

Hence, we can say that the probability of a correct guess on the first try is [tex]0.001[/tex] .

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Related Questions

Find the area of the figure.

Answers

Area of the big rectangle =
40yd x 36yd = 1440yd2

Area of the small rectangle =
20yd x 10yd = 200yd2

area of the figure = big rectangle - small rectangle

1440-200
=1240yd2

a game is played where 26 tiles are in a bag. each tile has a different letter of the alphabet on it. if you draw 5 letters what is the probability of the letters being m-u-s-i-c in order if there is no replacement?

Answers

Final answer:

The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement is approximately 0.000207.

Explanation:

The probability of drawing the letters M-U-S-I-C in order from a bag of 26 tiles without replacement can be calculated as follows:

First, we need to determine the total number of ways to draw 5 tiles from 26, which is represented by the combination formula: C(26,5) = 26! / (5! * (26-5)!).Next, we need to determine the number of ways to draw the letters M-U-S-I-C in order. Since there is only 1 M, 1 U, 1 S, 1 I, and 1 C in the bag, the number of ways to draw these 5 letters in order is 1.Finally, we divide the number of ways to draw the letters M-U-S-I-C in order by the total number of ways to draw 5 tiles from 26 to get the probability: P = 1 / C(26,5).

Using a calculator or computer program, the probability can be calculated to approximately 0.000207.

Final answer:

The probability of drawing the letters 'M-U-S-I-C' in order from a bag of 26 alphabetic tiles without replacement is calculated by multiplying the individual probabilities of drawing each letter consecutively, starting with 1/26 and decreasing with each draw.

Explanation:

The question involves calculating the probability of drawing a specific sequence of letters from a bag containing all the letters of the alphabet without replacement. Here's how to calculate it step by step:

The probability of drawing the letter 'M' first is 1/26 since there are 26 letters and only one 'M'.

After drawing 'M', the probability of drawing 'U' is 1/25 because there are now 25 letters remaining.

Following this pattern, the probability of then drawing 'S' is 1/24, 'I' is 1/23, and 'C' is 1/22.

To find the combined probability of drawing 'M-U-S-I-C' in that order, multiply these probabilities together: (1/26) * (1/25) * (1/24) * (1/23) * (1/22).

The final calculation gives us the probability of the sequence occurring without any tiles being replaced.

I WANT DIAGRAM
A vertical tower subtends a right angle on the top of 10m high flagstaff.if distance between them is 20m,find the height of the tower

Answers

Let us consider a triangle where AB to be the flagstaff of 10 m and BC to be of 20 m as the distance between the tower and the flag.
Considering ABC and ADE as triangle
AB = 10 = CE
BC = 20 = AE
Calculating the values of ABC
tan x = AB/BC
tan x = 10/20
10/tan x = 20..............(1)
Calculating the values of ADE
tan(90-x) = DE/AE
cot x = DE/20
DE/cot x = 20 .............(2)
Solving equations 1 & 2
10/tan x = DE/cot x
DE = 40
Hence the total height of the tower is DE+CE = 40+10= 50 m.

What is the simplest form of this binomial expression?

a4 − b4

Answers

Answer:

[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]

Step-by-step explanation:

The given expression is

[tex]a^{4}-b^{4}[/tex]

This expression is the difference of two perfect squares, and their square roots are

[tex]\sqrt{a^{4}} =a^{2}\\ \sqrt{b^{4}} =b^{2}[/tex]

Now, the difference of two perfect squares can be factored as

[tex]x^{2} -y^{2}=(x+y)(x-y)[/tex]

So, if we apply this rule, the result would be

[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]

Therefore, the simplest form of the binomial expression is

[tex]a^{4}-b^{4}=(a^{2}+b^{2})(a^{2}-b^{2})[/tex]

Answer and work in images

Find the perimeter of the shaded figure

Answers

The perimeter of the shaded figure is 38 units.

Perimeter of the given figure is 38 units.

Perimeter is the measure of the boundary of any figure. It measures the total length around the outside of a shape. Generally it is calculated as the sum of all sides of the figure.

Name the figure as ACDEFGHB, image attached below:

Perimeter of the given figure,P = Sum of all its sides.

P= AC+CD+DE+EF+FG+GH+HB+AB...........................1

AC=7 units

CD=2 units

DE=2 units

EF=6 units

FG=2 units

GH=2 units

HB=7 units

AB=10 units

On substituting values in 1

P=7+2+2+6+2+2+7+10

P=38 units.

Thus, perimeter is 38 units.

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If you see these clouds in the sky, which type of weather might you expect?

(Points : 3)
fog
no precipitation
heavy rain or snow
thunderstorms

Answers

The answer to your question is thunderstorms.
The picture is filled with a lot of dark clouds, in which there will be a probability for thunderstorms to occur. We all know that when there is lightning, thunder will occur after it. With the photo given, there will be the probability of thunderstorm with heavy rain.

PLEASE HELP ME! 50 POINTS IF YOU GET IT RIGHT!!

Darren flipped a quarter 40 times. The quarter landed on heads 65% of the time. How many times did the quarter land on tails ?

A 14

B 26

C 35

D 65

Answers

The correct answer is A, because if it was b, that would not be possible. Because the total is 40, the answer cannot be more than 20.

The sequence an= 27(1/3)^n-1 is graphed below. find the average rate of change between n=2 and n=4

A. - 1/4
B. 1/4
C. -4
D. 4

Answers

the average rate of change, is pretty much just the "slope" of the graph, therefore since we know that when n = 2, y = 9, notice the point (2,9), and when n = 4, y = 1, notice the point (4,1), thus

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 2 &,& 9~) % (c,d) &&(~ 4 &,& 1~) \end{array} \\\\\\ % slope = m \stackrel{\textit{average rate of change}}{slope} = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-9}{4-2}\implies \cfrac{-8}{2}\implies -4[/tex]

Eudora ran from her home to her secret laboratory at an average speed of 12\text{ km/h}12 km/h12, space, k, m, slash, h. she then took one of her jetpacks and flew to her school at an average speed of 76\text{ km/h}76 km/h76, space, k, m, slash, h. eudora traveled a total distance of 120120120 kilometers, and the entire trip took 222 hours. how long did eudora spend running, and how long did she spend flying using her jetpack? eudora ran for hours and flew for hours using her jetpack.

Answers

Let x be the amount of time she runs. 12x would then represent the distance she runs (d=rt; distance = speed (rate) * time). 2-x, or the total time minus the time she spends running, would be the amount of time she uses her jetpack. 76(2-x) would then represent the distance she flies on her jetpack. We know the total distance is 120 km; so
12x + 76(2-x) = 120
Use the Distributive Property:
12x + 76*2 - 76*x = 120
12x + 152 - 76x = 120
Combine like terms:
-64x + 152 = 120
Cancel the 152 by subtracting:
-64x + 152 - 152 = 120 - 152
-64x = -32
Cancel the -64 by dividing:
-64x/-64 = -32/-64
x = 0.5
She runs for 0.5 hours. She would use her jetpack for 2-0.5=1.5 hours.

Eudora ran 0.5 hours and flew 1.5 hours using her jetpack.

Given that, Eudora ran from her home to her secret laboratory at an average speed of 12 km/h.

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x = the time she ran (in hours) and y = the time she flew (in hours).

Remember that distance traveled is simply the rate times the time. So she traveled 12x kilometers by running and 76y kilometers by flying.

The total time is simply the running time plus the flying time: x + y = 2.

The total distance is simply the running distance plus the flying distance: 12x + 76y = 120

If you solve the time equation for x, you get: y = 2 - x.

This allows you to substitute 2 - x into the distance equation for y.

12x + 76(2 - x) = 120

12x + 152 - 76x = 120

152 - 64x = 120

-64x = -32

x = 0.5

Using the result, we can find y.

y = 2 - 0.5 = 1.5

Therefore, Eudora ran 0.5 hours and flew 1.5 hours using her jetpack.

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Miss Watson runs a distance of 200 meters in 25 seconds. Workout the average speed of Mrs Watson in meters per second.

Answers

Hey there!

Divide 200 by 25.

200/25= 8

She is running an average of 8 m/s. (that's how we represent meters per second)

I hope this helps!
~kaikers

The correct answer to your question is... 8mps. (meters per second)

Explanation:
To workout the average speed of Mrs Watson in meters per second, you would solve the problem 200 ÷ 25.

200 ÷ 25 = 8

So... we now figured out that the average speed Mrs Watson runs, is 8 meters per second.

I hope this helps!
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Peter has 6 sweaters, 4 pairs of jeans, and 3 pairs of shoes. how many different outfits can peter make using one sweater, one pair of jeans, and one pair of shoes?

Answers

the answer is 72 because 6x4x3=72

James needs to clock a minimum of 9 hours per day at work. The data set records his daily work hours, which vary between 9 hours and 12 hours, for a certain number of days.

{9, 9.5, 10, 10.5, 10.5, 11, 11, 11.5, 11.5, 11.5, 12, 12}.

The median number of hours James worked is 10 11 12 13 . The skew of the distribution is negative positive zero zero with symmetry .

Answers

The median is the 11 as median is the middle value

and it will be a negative skew

SHIFT 2: 18 25 56 42 29 38 54 47 35 30. SHIFT 2: 23 19 50 49 67 34 30 59 40 33. SHIFT 3: 19 22 24 40 45 29 33 29 39 59. SHIFT 4: 21 23 25 40 35 19 70 40 22 23. The summary statistics for all of the workers at a steel factory are shown. Four sample groups were taken from each of the four shifts. For which sample group is the mean closest to the population mean?

Answers

To answer this question you will need to calculate the mean for each of the Shifts and then compare those means to the mean of all the data given. I have attached a picture of the means for each shift and the population mean (all the data).

Shift 1 is the closest to the population mean. It is 37.4, and the population mean is 35.9.

Is this right???? Can someone please help?

Answers

This is a logistic growth model, so, we can set the function's differential equation equal to 0 and solve for p, then for y. So, let's take the derivative of this function and set it to 0:
[tex] \frac{dp}{dt} = 0.005p(300-p) = 1.5p-0.005p^2 [/tex]
[tex] \frac{d^2p}{dt^2} = 1.5 - 0.01p =0 [/tex]
[tex]-0.01p = -1.5[/tex]
[tex]p = \frac{-1.5}{-0.01} = 150 [/tex]

Now, for a logistic model, the general solution is in the form of:
[tex]p = \frac{L}{1+Ce^{-ky}} [/tex]
for
[tex] \frac{dp}{dt} = kp(L-p) [/tex]

You haven't been given the 'C' constant, so I don't have a clue as to where to go after this. Sorry, we are yet to go over logistic growth in BC class. I could take you this far by just researching. If you have further questions, I'd be happy to answer them.

At school athletic events you can buy 3 drinks and 2 hot dogs for $4.80 or you can buy 1 drink and 1 hot dog for $2.00. How much does 1 hot dog cost?

Answers

Let the cost of each drink is $x and the cost of each hot dog is $y.
According to the given data, 3 drinks and 2 hot dogs cost $4.80. In equation form, we can write it as:

[tex]3x+2y=4.80[/tex]

1 drink and 1 hot dog costs $2.00. In equation form, we can write it as:

[tex]x+y=2[/tex]
[tex]x=2-y[/tex]

Using this value of x in first equation, we get:

[tex]3(2-y)+2y=4.80 \\ 6-3y+2y=4.80 \\ 6-y=4.80 \\ y=6-4.80 \\ y= 1.20[/tex]

Thus the cost of one hot dog is $1.20

this is a question in which simultaneous equations are used to find out the answer.
There are 2 unknown values which we name as x and y
x - price of a drink
y - price of a hotdog

although we don't know the values of the above 2 terms x and y, we know the relationships of these 2 terms as the the sums of these 2 have been given
therefore we can build 2 equations using the information we have been given

3 drinks = 3*x and 2 hotdogs = 2*y
we build the first equation using this information

1 - 3x + 2y = $ 4.80

1 drink and 1 hotdog costs $2.00
we can build the second equation using this information

2 - x + y = $ 2.00

first we have to find out the value of one unknown term, for this we need to eliminate the second unknown so that we are left with one unknown term in the equation
if we want to eliminate y, 2nd equation should be multiplied by 2
2. 2(x + y = 2)
the answer after multiplying all the terms by 2, lets call that the 3rd equation

3. 2x + 2y = 4
when we subtract 1st from the 2nd equation,
3x + 2y = 4.8 ( - ) 2x + 2y = 4
lets subtract like terms from like terms
3x - 2x = x
2y - 2y = 0
4.8 - 4 = 0.8
after subtracting the final equation looks like this;
x = 0.8
since we know x now, substitute x in the equation 2
x + y = 2
0.8 + y = 2
to find out y
y = 2 - 0.8
y = 1.2
Therefore price of a drink is $0.80
and price of hotdog is $1.20

How to write a fraction with a numerator of 12 and a denominator of 13

Answers

The numerator is the number on top
And the denominator is the number on the bottom

If the numerator is 12 and the denominator is 13, then the fraction would be:

12 / 13

A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches. The width of the bag is w, the length is 2w+4, and the height of the bag is 18-w (which is greater than the width). What are the dimensions of the bag?

Answers

1. You must use the formula for calculate the volume of a rectangular prism, which is:

V=(h)(l)(w)

V: It is the volumen of the rectangular prism (V=1152 inches³).
h: It is the height of the rectangular prism (h=18-w).
l:It is the lenght of the rectangular prism (l=2w+4).

2. When you substitute these calues into the formula, you obtain:

V=(h)(l)(w)
1152=(18-w)(2w+4)(w)
(18-w)(2w+4)(w)-1152=0

3. Then, you should mutiply them:

36w²-2w³+72w-4w²-1152=0
32w²-2w³+72w-1152=0

4. When you factor, you obtain:

2(w-16)(w-6)(w+6)

w1=16
w2=6
w3=-6

5. The problem says that the height is greater than the width, therefore, the widht is:

w=6 inches

6. The length is:

l=2w+4
l=2(6)+4
l=16 inches

7. And the height is:

h=18-w
h=18-6
h=12 inches

What are the dimensions of the bag?

The dimensions of the bag are:

l=16 inches
h=12 inches
w=6 inches

Final answer:

In this high school math question, you will solve for the dimensions of a gift bag shaped like a rectangular prism using the given volume and expressions for width, length, and height.

Explanation:

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume of the gift bag is 1152 cubic inches, so we have 1152 = w(2w+4)(18-w).

Solving this equation leads to w = 8, which means the width is 8 inches, length is 20 inches, and height is 10 inches.

Therefore, the dimensions of the gift bag are 8 inches width, 20 inches length, and 10 inches height.

In the problem · N = 1, N must be _____. the additive inverse of the multiplicative inverse of the additive identity the multiplicative identity NEXT

Answers

The value N as shown in the question must be the multiplicative identity.

Multiplicative identity

The term multiplicative identity refers to that with which a number is multiplied and the result remains that number. Multiplying a number by its multiplicative identity returns the same value.

Therefore, the the problem, we can see that the value N as shown in the question must be the multiplicative identity.

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Answer: the multiplicative inverse of 3/4

Step-by-step explanation: its right :)

Quick!!!Geoffrey buys 48 shares of Ignyta, Inc. (RXDX) at $6.15 each, and his broker charges him a commission of $81. How much did Geoffrey pay for his stock?A.$376.20
B.$295.20
C.$450.30
D.$219.60

Answers

B, Add 48 with 6.15 and add the sum with 81

There are 18 girls and 12 boys in class. What is the probability that a new kid in senior class will be a boy?

Answers

there are 18 + 12 total students.

18 are girls and 12 are boys, since the total is 30 students, that's the amount of probable outcomes, and since there are 12 boys, that's the amount of favorable outcomes, thus

12/30 or 0.4, 0.4 * 100 is 40%.

helpppppppppppppppppppppppppppppp

Answers

The answer is A. \sqrt(-108)=sqrt(-1*108)=sqrt(-1)*sqrt(108)=i*\sqrt(36*3)=i*\sqrt(36)*\sqrt(3)=6i*\sqrt(3). \sqrt(-3)=\sqrt(-1*3)=\sqrt(-1)*\sqrt(3)=i*\sqrt(3). \sqrt(-108)-\sqrt(-3)=6i*\sqrt(3)-i*\sqrt(3)=5i*\sqrt(3).

root (-108) -raiz (-3)
First we rewrite the expressions:
root (-36 * 3) -raiz (-3)
6 * root (-3) -raiz (-3)
5 * root (-3)
5 * root (3) * root (-1)
By definition:
i = root (-1)
Substituting:
5 * root (3) * i
Answer:
5 * root (3) * i
option 1

The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is a quadratic equation the represents the area of the screen? What are the dimensions of the screen?

Answers

1. The problem says that the television has a rectangular shape. So, the formula for caculate the area of a rectangle is:

A=LxW

"A" is the area of the rectangle (A=3456 inches²).
"L" is the the length of the rectangle.
"W" is the width of the rectangle.

2. The width of the screen is 24 inches longer than the length. This can be expressed as below:

W=24+L

3. Then, you must substitute W=24+L into the formula A=LxW:

A=LxW
3456=L(24+L)
3456=24L+L²

4. The quadratic equation is:

L²+24L-3456=0

5. When you solve the quadratic equation, you obtain:

L=48 inches

6. Finally, you must substitute the value of the length, into W=24+L:

W=24+L
W=24+48
W=72 inches

7. Therefore, the dimensions of the screen are:

L=48 inches
W=72 inches

Final Answer:

Quadratic equation: [tex]$ x^2 + 24x - 3456 = 0 $[/tex]

Dimensions: Length = 48 inches, Width = 72 inches

Explanation:

To find the quadratic equation representing the area of the screen, we first need to express the area as a product of its length (L) and width (W). Given that the width is 24 inches longer than the length, we can represent the width as [tex]$ L + 24 $[/tex]. Thus, the equation becomes [tex]$ L \times (L + 24) = 3456 $[/tex], which simplifies to the quadratic equation [tex]$ x^2 + 24x - 3456 = 0 $[/tex], where x represents the length of the screen. Solving this equation yields the length x as 48 inches. Substituting this value back into [tex]$ L + 24 $[/tex] gives the width as 72 inches. Therefore, the dimensions of the screen are 48 inches by 72 inches.

Im really confused can someone help me

Answers

I believe you would create and equation to find x and y.

Based on the graphic, which three-dimensional figure has the greatest volume?

Answers

Using the assumptions that the prisms have a square base and that the side of the square is the same length as the diameter:
The first prism would have a volume of s²h.
The second prism, under Cavalieri's principle, would have the same area as the first (if they have the same cross-sectional area and same height, they have the same volume).
The cylinder at the end would have a volume of π(r²)h = π(1/2s)²h = π(1/4s²)h = 1/4πs²h. 1/4 of π is less than 1, so that means the cylinder would have the smallest volume.

Answer:

all three have the same volume

Step-by-step explanation:

Cavalieri's principle states that if the areas of the cross sections of two solids are equal, and the height of the two solids are equal, then the volumes of the two solids are equal.

Solve these simultaneous equations:

5x+2y=24 and 4x+3y=10

Answers

From the second equation: y=(10-4x)/3
Substitute y to the first equation:
5x+2[(10-4x)/3] = 24

5x+[(20/3)-(8x/3)]=24

5x-(8x/3)=24-(20/3)

(15x-8x)/3=17.333

7x=17.333(3)

x=7.428

Using the second equation to find value of y:

y=(10-4x)/3; Substitute the value of x=7.428

y=[10-4(7.428)]/3

y= -6.571 (negative 6.571)

To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we use the elimination method, leading to a solution of x = 7.43 and y = -6.575.

To solve the simultaneous equations 5x+2y=24 and 4x+3y=10, we can use the method of elimination or substitution. Here, we will solve it using the elimination method.

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y equal in magnitude. This gives us 15x + 6y = 72 and 8x + 6y = 20.

Subtract the second new equation from the first to eliminate y. This gives 7x = 52.

Divide by 7 to solve for x, which gives x = 52 / 7 or x = 7.43 (approximately).

Substitute x = 7.43 back into one of the original equations to solve for y. Using the first equation, 5(7.43) + 2y = 24, we get 2y = 24 - 37.15, which simplifies to 2y = -13.15, and finally y = -6.575.

Therefore, the solution to the simultaneous equations is x = 7.43 and y = -6.575.

During a construction project, heavy rain filled construction cones with water. The diameter of a cone is 12 in. and the height is 27 in.

What is the volume of the water that filled one cone?

Enter your answer as a decimal in the box. Use 3.14 for pi.

Answers

volume of cone=[tex]\frac{1}{3}h \pi r^2[/tex]

diameter/2=r
12/2=6=r
h=27

volume=[tex]\frac{1}{3}(27)(3.14)(6^2)[/tex]
volume=[tex]1017.36 in^3[/tex]

x + y = 21 3y + x = 19 Which value of x is part of a solution to this system of equations?

Answers

we have that
x + y = 21
3y + x = 19

using a graph tool
see the attached figure

the solution is the point (22,-1)

the answer is
the value of x is 22

Final answer:

The value of x that is part of a solution to this system of equations is 22.

Explanation:

To find the value of x in the system of equations:

x + y = 213y + x = 19

We can use the method of elimination or substitution. Let's use substitution for this example:

Solve the first equation for y: y = 21 - x.Substitute the expression for y into the second equation: 3(21 - x) + x = 19.Simplify and solve for x: 63 - 3x + x = 19.Combine like terms: 63 - 2x = 19.Subtract 63 from both sides: -2x = -44.Divide by -2: x = 22.

Thus, the value of x that is part of a solution to this system of equations is 22.

Suppose the probability that a randomly selected man, aged 55-59, will die of cancer during the course of the year is startfraction 300 over 100 comma 000 endfraction 300 100,000. how would you find the probability that at least 1 man out of 1,000 of this age will die of cancer during the course of the year?

Answers

Final answer:

To assess the likelihood of at least one cancer death among 1,000 men, calculate the probability none die and subtract from one. The actuarially fair premiums for men with and without family cancer history are different, but when combined for the whole group, there's a risk of adverse selection affecting the company.

Explanation:

To find the probability that at least one man out of 1,000 aged 55-59 will die of cancer in a year, given that the probability for any one man is 300/100,000, we first find the probability that no man dies of cancer and then subtract this from 1 (the certainty). The probability that a randomly chosen man will not die from cancer in the year is 1 - 300/100,000 = 99,700/100,000.

The probability that all 1,000 men do not die of cancer is (99,700/100,000)^1,000. Subtracting this from 1 gives us the probability that at least one man out of 1,000 will die of cancer in the year:

1 - (99,700/100,000)^1,000

For the life insurance question, to calculate the actuarially fair premium for each group, we use the probability of death and expected payout. For the group with family history (20% of 1,000 men), the probability is 1/50, and for the group without (80% of 1,000 men), it's 1/200. Thus, the premiums would be:

Group with history: (1/50) * $100,000 = $2,000Group without history: (1/200) * $100,000 = $500

An actuarially fair premium for the group as a whole requires weighted averaging:

Premium whole group = (20% * $2,000) + (80% * $500) = $400 + $400 = $800

If the company charges this combined premium, it faces adverse selection; higher-risk individuals are more likely to purchase insurance, driving costs up.

What is the area of the composite figure whose vertices have the following coordinates?

(−4, 3) , (2, 3) , (4, −1) , (0, −3) , (−2, −1)

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Answer:

30 square units

Step-by-step explanation:

There are several ways to determine the area of the figure from its coordinates. A straightforward method is to plot the coordinates on a graph and decompose the resulting figure into simple shapes whose area formulas are known

Area from simpler shapes

A plot reveals the figure to be a parallelogram with a base length 6 and a height of 4, together with a triangle of base 6 and height 2.

The area of the parallelogram is given by the formula ...

A = bh

The area of the triangle is given by the formula ...

A = 1/2bh

In each case, 'b' represents the base of the figure, and 'h' represents its height.

Parallelogram area

A = bh = (6)(4) = 24

Triangle area

A = 1/2bh = 1/2(6)(2) = 6

Total area

The composite area will be the sum of the parallelogram and triangle areas:

A = 24 +6 = 30 . . . . square units

The area of the composite figure is 30 square units.

Area from coordinates

The area can also be figured directly from the coordinates. The formula for that can be written ...

[tex]\displaystyle A=\dfrac{1}{2}\left|\sum_{k=1}^n (x_k(y_{k+1}-y_{k-1}))\right|\qquad\text{where $y_0=y_n$ and $y_{n+1}=y_1$}[/tex]

Using this formula, we find the area to be ...

A = 1/2|(-4(3-(-1)) +2(-1-3) +4(-3-3) +0(-1-(-1)) -2(3-(-3))|

= 1/2|-16 -8 -24 +0 -12| = 1/2|-60| = 30

The area of the figure is 30 square units.

How will buying auto insurance help you?

Answers

if you get in a wreck they help pay for the damage

When buying a (auto insurance), this can help you so as if you were about to get in a wreck, this insurance can help you pay to what ever happened, but it also depends on the case, either the other person will pay it though his own insurance, so yes, this would really help you.

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