The probability of person being a heavy smoker given person died is 0.57 .
Baye's Theorem helps in finding the probability of any event A given that event B has already occurred.
For Example the probability of event A given that event B has already occurred is denoted by
[tex]P(A/B)=\frac{P(B/A)P(A)}{P(B)}[/tex]
In the given question
Let H denoted heavy smokers , L denote Light smokers , N denote Non smokers.
Given the probability of non smokers P(N) = 50%=0.5
the probability of light smokers P(L)=20%=0.2
the probability of heavy smokers P(H)=30%=0.3
let P(D/H) denoted the person died given he was a heavy smoker.
let P(D/L) denoted the person died given he was a light smoker.
let P(D/N) denoted the person died given that he was a non smoker.
According to question
"heavy smokers twice as likely to die as light smokers" means
P(D/H)=2P(D/L)......(1)
and "light smokers twice as likely to die as nonsmokers" means
P(D/L)=2P(D/N)
On simplifying we get
[tex]P(D/N)=\frac{1}{2} P(D/L)\\ \\ P(D/N)=0.5 P(D/L)[/tex].....(2)
According to Baye's Theorem
[tex]P(H/D)=\frac{P(D/H)P(H)}{P(D/N)P(N)+P(D/L)P(L)+P(D/H)P(H)}[/tex]
Substituting values of P(D/H) from ...(1) and values of P(D/N) from ....(2)
we get [tex]P(H/D)=\frac{2*P(D/L)P(H)}{0.5*P(D/L)P(N)+P(D/L)P(L)+2*P(D/L)P(H)}[/tex]
taking P(D/L) common from each term
[tex]P(H/D)=\frac{P(D/L)}{P(D/L)} (\frac{2*P(H)}{0.5*P(N)+P(L)+2*P(H)})[/tex]
[tex]P(H/D)= (\frac{2*P(H)}{0.5*P(N)+P(L)+2*P(H)})[/tex]
Substituting the values of P(N), P(H), P(L) from above we get
[tex]P(H/D)= (\frac{2*(0.3)}{0.5*(0.5)+(0.2)+2*(0.3)})[/tex]
[tex]P(H/D)= (\frac{0.6}{0.25+0.2+0.6})[/tex]
=[tex]\frac{0.6}{1.05}=0.57[/tex]
Therefore , the probability of person being a heavy smoker given person died is 0.57 .
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Which expression is equivalent to quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity? negative forty nine over 8 times d minus one tenth forty nine over eight times d minus one tenth negative three eighths times d minus one and three tenths negative three eighths times d minus one tenth
Answer: The Answer would be -49/8d -1/10
Step-by-step explanation: I got it right on the test
have a good day
The answer for the given expression is -49d/8 - 1/10. Thus, the correct option is option A.
The expression can be solved by simple arithmetic operation.
(-3 1d/4 + 3/5) - (2 7d/8 + 7/10)
In the next step simplify the terms and open brackets.
-13d/4 + 3/5 -23d/8 - 7/10
Taking the like terms together.
-13d/4 - 23d/8 + 3/5 - 7/10
Solving the terms by taking L.C.M.
(-104d-92d/32) + (30-35/50)
-196d/32 - 5/50
Simplifying the terms.
-49d/8 - 1/10.
Thus, the value of the expression is -49d/8 - 1/10.
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What is the answer to the.
-2(x - 5) = 6(2- 1/5x) and show me how you solved it
Answer:
x = -2.5
Step-by-step explanation:
Evaluate: 3a x 5w (Not simplified)
The value of the expression otherwise termed it's simplified form as required that the expression be evaluated in the task content is; 15aw.
What is the value of the expression otherwise termed it's simplified form as required that the expression be evaluated?It follows from the task content that the expression which is as given in the task content be evaluated, and hence, expressed in its simplified form.
Given;
3a × 5w
Since, the constants can be multiplied and their product determined, it follows that we have;
(3 × 5) (a × w)
And ultimately, we have the value of the expression to be; 15aw.
Therefore, The value of the expression otherwise termed it's simplified form as required that the expression be evaluated in the task content is; 15aw.
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find the lines slope and point on the line
picture below
The slope is 4 and point on the line is origin (0,0).
What is line?A line is a straight one-dimensional figure having no thickness and extending infinitely in both directions. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. The two points which lie on the same line are said to be collinear points.
Given:
The equation of the line is
y+4=4(x-2)
We have to find the slope and point on the line.
y+4=4(x-2)
y+4=4x-8
Substract 4 from both sides we get,
y=4x-12
Since the equation now is in y = mx + b form, we can identify the slope m=4 and the y-intercept b=-12 and point on the line origin (0,0).
Therefore, the slope is 4 and point on the line is origin (0,0).
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Mrs. Schott gets a biweekly paycheck of $1,230.90.
What is her annual salary?
Answer:
Step-by-step explanation:
Answer:
biweekly salary =
365/14=
23
then total salary
of her is =$1230.90
*23
=
Step-by-step explanation:
Simplify the expression 11c+3(−5c+4d)
step by step explanation:
-4c+12d
1. Distribute:
11c+3(-5c+4d)
11c-15c+12d
2. Combine like terms:
11c-15c+12d
-4c+12d
What's the lcd of 1/3 and 3/9
Answer:
LCD = 9
Step-by-step explanation:
1/3 = 3/9
3/9 =3/9
I dont understand what i am supposed to do
Applying the alternate exterior angles theorem, the value of x = 10.
How to Apply the Alternate Exterior Angles Theorem?According to the alternate exterior angles theorem, the following alternate interior angles are congruent to each other:
m<JPM = m<NQK
Given the following:
m<JPM = 125°
m<NQK = (13x - 5)°
Substitute
125 = 13x - 5
125 + 5 = 13x
130 = 13x
Divide both sides by 13
130/13 = 13x/13
10 = x
x = 10
Therefore, applying the alternate exterior angles theorem, the value of x = 10.
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Point P is located 2/5 of the distance from W to Z. Point W is located at (-5, -2) and point P is located at (1, 4). What are the coordinates of point Z?
The coordinates of point Z is (-5/7, 16/7)
Calculating the midpoint of a line using a ratioThe formula for calculating a coordinate points using the points (-5, -2) and point P is located at (1, 4) in the ratio 2:5 is expressed as:
Z (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}
Substitute the coordinates and ratios to have;
Z (x, y) = {(2(-5)+5(1))/2+5, (2(-2)+5(4))/2+5}
Z(x, y) = {-10+5/7, -4+20/7}
Z(x, y) = (-5/7, 16/7)
Hence the coordinates of point Z is (-5/7, 16/7)
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8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables (letters). use the sketch area if needed. combine the like terms and submit your answer. *always combine like terms in alphabetical order and write your constant term last!
When combining the like terms of 8+3a+7b-5+2a-7b, the result will be 5a+3
Given,
The expression =8+3a+7b-5+2a-7b
Rearrange the terms alphabetical order and combine the like terms
8+3a+7b-5+2a-7b =3a+2a+7b-7b+8-5
=(3+2)a+(7-7)b+(8-5)
=5a+0b+3
=5a+3
Hence, When combining the like terms of 8+3a+7b-5+2a-7b, the result will be 5a+3
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A survey showed that 8 out of 20 homeowners in a neighborhood had cable television. if there were 320 homeowners in the neighborhood, how many could be expected to have cable television?
The number of homeowners in the neighborhood could be expected to have cable television is 128.
Given that, a survey showed that 8 out of 20 homeowners in a neighborhood had cable television.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Now, 8/20 × 320
= 8 × 16
= 128
Hence, the number of homeowners in the neighborhood could be expected to have cable television is 128.
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What is the quotient?
1.242 ÷ 1.8 =
Answer: 0.69
Step-by-step explanation:
1.242 ÷ 1.8=
1.242/1.8=0.69
When finding multiples of a number, you _________ the original number by 1, then 2, then 3 and so on.
Answer:
Step-by-step explanation:
jlfhwfhwfh
What does x equals to
The value of x is 20°
According to the question we have been given two parallel lines which is cut by a transversal line. There are total 8 angles and given is the measure of
∠4 = 5x + 35° and ∠7 = 45°.
We need to find the value of x.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
Now using these rules we will solve this problem
Because of corresponding angles , ∠3 = ∠7 = 45°
Also ∠3 and ∠8 make a linear pair and sum of linear pair is 180°.
Therefore , ∠3 + ∠8 = 180°
45° + 5x + 35° = 180°
5x = 180° - 80°
x = 20°
Hence the value of x is 20°
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find the solutions to the equation in the interval 0 ≤ theta ≤ ????/2 . enter your answers as a comma-separated list. 2cos(4theta) − 1
The values of θ, i.e. the general solution of the given trigonometric equation that satisfy the given equation are: 5π/12, π/12.
What is the general solution of a trigonometric equation?The general solution of a trigonometric equation is a formula employing the integer n that provides all solutions.
Given:
EQuation: 2 cos( 4θ) - 1 = 0.Interval: 0 ≤ θ ≤ π/2TO find: Values of θ.
Finding:
In the given equation: 2 cos( 4θ) - 1 = 0,
=> cos (4θ) = 1/2
=> cos (4θ) = cos (π/3)
=> 4θ = 2nπ ± π/3
=> θ = nπ/2 ± π/12
For n = 0, θ = ± π/12
For n = 1, θ = π/2 ± π/12
Since θ ∈ [0, π/2], the possible values of θ = π/12, π/2 - π/12 = 5π/12.
Hence, The values of θ that satisfy the given equation are: 5π/12, π/12.
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Please help for my homework
Answer:
260 m2
Step-by-step explanation:
for how many different digits n is the 3 digit number 14n divisible by n, 14n refers to a three digit number with the unit digit of n
0, 1, 2, 4, 5, and 7.
So that would be 6 digits.
In mathematics, the only single symbol used to represent a number is a digit. For instance, there are two digits in the numbers 89: 8 and 9. As a result, in everyday life, digits like 0, 1, 2, 3, 4, 5, 6, 7, 8, and 0 are employed to represent groups of numbers and perform mathematical operations. A positional numeral system uses a single sign, such as "2," or a set of symbols, such as "25," to represent numbers. The word "digit" derives from the fact that the ten fingers of the hands, or digit in Latin, corresponding to the ten symbols of the decimal system, which uses the base-10 numeral system.
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what is square root 25/49
A. 25/49
B. 5/9
C. 5/7
D. 5/8
Answer: C. 5/7
CALCULATOR
a $5.62
b $7.42
At the grocery store, Ruby buys 3 packs of juice for $2.12 each, and 4 bags of popcorn for $3.50 each. What is the total amount that Ruby
spends on the juice and popcorn?
c) $18.98
Line
Guide
$20.36
Answer:
20.36 is the answer
2.12x3=6.36
3.50x4=14
14+6.36=20.36
Answer:
20.36
Step-by-step explanation:
1)3*2.12=6.36
2)4*3.50=14
3)6.36+14=20.36
Please help with problem 29
Answer:
Step-by-step explanation:
So, basically, the slope intercept form is y = mx + b
m is rise over run x is well x and b is where the original y is.
So 2x-3 is up two over one
And 1x-1 is up one over one
And take for example 2/3x + 5
That would be up two over three
If 6 burgers cost $7.74, how many can you buy for $19.35? Pls show work and explain how you did it :)
Answer: 15 burgers
Step-by-step explanation:
7.74/6=$1.29 per burger
$19.35* 1 burger/$1.29=
19.35*1/1.29=
19.35/1.29=15 burgers
the population standard deviation for the height of college baseball players is 3.0 inches. if we want to estimate 95% confidence interval for the population mean height of these players with a 0.68 margin of error, how many randomly selected players must be surveyed?
The number of players randomly selected is 381 and the standard deviation is 1.96.
What is the standard deviation?The standard deviation is a measurement of how much a group of values varies or is dispersed. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection. The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD. A random variable, sample, statistical population, data set, or probability distribution's standard deviation is equal to the square root of its variance.
[tex]Z(\alpha /2)=1.96[/tex]
Sample size = n = [tex][Z(\alpha /2 * \sigma/E) ]^{2}[/tex]
n = [1.96 * 3.0 / 0.95]²
n = 381.85
n ≈ 381
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A car detailing shop charges $30 for materials, plus $50 per hour for labor to paint pinstripes on a car. Which function can be used to find the total cost C(h) to get pinstriping that requires h hours to complete?
The function that can be used to find the total cost C(h) to get pinstriping that requires h hours to complete is; C(h) = 50h + 30
How to create Cost Function?
We are given the following costs in the car detailing shop as follows;
Cost of Materials = $30
Cost per hour for labor = $50
Since the equation of a line in slope intercept form is; y = mx + c, then we can say that the equation here can also be expressed as;
C(h) = 30 + 50h
The function that can be used to find the total cost C(h) to get pinstriping that requires h hours to complete is; C(h) = 30 + 50h
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i need help with this problem it says
one less than triple a number is the same as six times a number reduced by 7
15 points
Answer:
3x - 1 = 6x - 7
x = 2
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1. To solve it, first get the variable on same side.
3x - 1 = 6x - 7
- 3x - 3x
- 1 = 3x - 7
2. Isolate the variable by doing the inverse operation which is in this case addition (adding 7).
- 1 = 3x - 7
+ 7 + 7
6 = 3x
3. Isolate variable by doing the inverse operation which is in this case division (dividing by 3).
6 = 3x
3 3
2 = x
OR
x = 2
Check:
1. Substitute x with 2 and solve.
3(2) - 1 = 6(2) - 7
6 - 1 = 12 - 7
5 = 5
True statement.
The area of a closet is 100 sq feet. write the number in exponent form and word form.
For given number 100
the exponent form = 10²
the word form = One Hundred
For given question,
The area of a closet is 100 square feet.
We need to write the number in exponent form and word form.
First we write given number in exponent form
⇒ 100 = 10 × 10
⇒ 100 = 10²
So, the exponent form given number 100 is 10²
And the word form of given number is : One Hundred
Therefore, for given number 100
the exponent form = 10²
the word form = One Hundred
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HELP 50 PTS AND BRAINLY!!!
Answer:
Last option
Step-by-step explanation:
→ Find the sum for how much he spent
[tex]\frac{2}{3} +\frac{1}{4} =\frac{11}{12}[/tex]
Answer:
C
Step-by-step explanation:
Solve the equation. Show all steps of your work and justify each step with an algebraic property of equality.
5x+1/3 (3x-6)=10
Answer:
x=2Step-by-step explanation:
5x+1/3(3x−6)=10
Simplify both sides of the equation:5x+1/3(3x−6)=10
5x+(1/3)(3x)+(1/3)(−6)=10 (Distribute)
5x+x+−2=10
(5x+x)+(−2)=10 (Combine Like Terms)
6x+−2=10
6x−2=10
Add 2 to both sides:6x−2+2=10+2
6x=12
Divide both sides by 6:6x/6=12/6
x=2
in a large population, 63 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated? give your answer as a decimal (to at least 3 places) or fraction.
The probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical summaries of how likely an event is to occur or how likely a proposition is to be true. The likelihood of an event occurring is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.To find the probability that at least one of them has been vaccinated:
In a huge number, 63% of people are vaccinated, leaving 37% unvaccinated. The point of concern for the probability that at least one of the four randomly selected people has been vaccinated. As a result, we must account for the possibility that one, two, three, or four randomly selected people were vaccinated.We use P(1) for only one person; the same reasoning should apply to other subscripts.
P(1) = (63/100)(37/100)(37/100)(37/100) = 0.03089833P(2) = (63/100)(63/100)(37/100)(37/100) = 0.05094049P(3) = (63/100)(63/100)(63/100)(37/100) = 0.08398297P(4) = (63/100)(63/100)(63/100)(63/100) = 0.13845841Adding all these probabilities given 0.3042802.
As a result, the probability of at least one person being vaccinated out of four people chosen at random is 0.30, or 30%, rounded to the nearest hundredths.
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0.5{3x + 4(3 + 2x)}
please simplify!!
Answer:
0,5(3x+12+8x)
0,5(11x+12)
5,5x+6
Answer:
5.5x + 6
Step-by-step explanation:
0.5{3x + 4(3 + 2x)}
Apply the distributive property, multiply 4 by 3 and 4 by 2x.
0.5(3x + 12 + 8x)
Add 3x and 8x
0.5(11x + 12)
Apply the distribdistributive proproperty again and multiply 0.5 by 11x and 0.5 by 12.
The product would be 5.5x + 6.
what is the probability that a single card drawn from a standard deck of cards is either an 8 or a heart?
The probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.
Probability of an event E denoted by P(E) is defined as (number of favorable outcomes )/( total number of outcomes).
For example : the probability of getting Head in single toss of an unbiased coin. P(H)=1/2.
According to the given question
Total number of cards in a standard deck of cards is 52.
There are 4 suit in a deck each having 13 card each.
number of 8 card in a deck = 4
Number of hearts in a deck = 13-1=12 (-1 because 8 of heart is counted before.)
number of favorable cases of getting either an 8 or a heart is 4+12=16.
The probability of getting either an 8 or a heart is [tex]\frac{16}{52} =\frac{4}{13}[/tex].
Therefore , the probability that a single card drawn from a standard deck of cards is either an 8 or a heart is 4/13.
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