A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease. Calculate the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease. (A) 0.115 (B) 0.173 (C) 0.224 (D) 0.327 (E) 0.514
Answers
Answer:
The correct option is (B) 0.173.
Step-by-step explanation:
The law of total probability states that:
\(P(A)=P(A\cap B)+P(A\cap B^{c})\)
The conditional probability of an event A given that another event B has already occurred is:
\(P(A|B)=\frac{P(A\cap B)}{P(B)}\)
Then the probability of intersection of A and B is:
\(P(A\cap B)=P(A|B)\cdot P(B)\)
Denote the events as follows:
H = a man died from causes related to heart disease.
X = a man had at least one parent who suffered from heart disease
The information provided is:
\(P(H)=\frac{210}{937}\\\\P(X)=\frac{312}{937}\\\\P(H|X)=\frac{102}{312}\)
The probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease is, \(P(H|X^{c})\).
Compute the value of \(P(H|X^{c})\) as follows:
\(P(H)=P(H|X)\cdot P(X)+P(H|X^{c})\cdot P(X^{c})\)
\(\frac{210}{937}=[\frac{102}{312}\cdot \frac{312}{937}]+[P(H|X^{c})\cdot (1-\frac{312}{937})]\\\\\frac{210}{937}-\frac{102}{937}=[P(H|X^{c})\cdot \frac{625}{937}]\\\\\frac{108}{937}=P(H|X^{c})\cdot \frac{625}{937}\\\\P(H|X^{c})=\frac{108}{937}\times \frac{937}{625}\\\\P(H|X^{c})=0.1728\\\\P(H|X^{c})\approx 0.173\)
Thus, the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease is 0.173.
The correct option is (B).
Related Questions
A bottle holds 6 ounces of cough syrup. If May needs to drink 0.4 ounces of cough syrup each day, in how many days will she finish it?
Answers
Answer: If May drinks 0.4 ounces of cough syrup each day she will finish the bottle in 15 days.
Answer:
15 days
Step-by-step explanation:
6/0.4 is basically 60/4
60/4=15
The given point P is located on the unit circle, similar to what is seen in the image below, determine the sine and cos e(P is
not necessarily in Quadrant I).
(0,1)
(-1,0)
(0,-1)
(1,0)
PLS HELP ME ASAP
Answers
The sine and cosine of the angle of point P are sin θ = 143/145 and cos θ = -24/145 respectively. Option b. is the answer
How to determine the sine and cosine of the angle of point P?Given the coordinate of the point as P (-24/145, 143/145)
This implies x = -24/145 and y = 143/145
To determine the sine and cosine of the angle of point P, we can make a sketch using this information (see attached image).
opposite = 143/145, adjacent = -24/145
hypotenuse = √[(-24/145)² + (143/145)²] = √1 = 1
Using trigometric ratios:
sin θ = (143/145) / 1 = 143/145 [sin θ = opposite/ hypotenuse]
cos θ = (-24/145) / 1 = -24/145 [cos θ = adjacent/ hypotenuse]
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Which of the following is true about the graph of \large f\left(x\right)=-4x^2? Select all that apply.
Answers
Answer:
In 2015, the financial statements of Ultimate Medical Center reported $500,000 in total revenues and $145,000 in net income. The balance sheet showed net assets of $350,000. Calculate the operating margin ratio and the return on equity rate for Ultimate Medical Center.
Step-by-steIn 2015, the financial statements of Ultimate Medical Center reported $500,000 in total revenues and $145,000 in net income. The balance sheet showed net assets of $350,000. Calculate the operating margin ratio and the return on equity rate for Ultimate Medical Center.
simplify the expression
4.2v - 5 -6.5v =
Answers
Answer:
-5 - 2.3v
Step-by-step explanation:
You want to combine like terms and since two of the numbers have variables, then you can add them both together
4.2v - 6.5 v = -2.3 v
So... -5 - 2.3v or
-2.3v - 5
either or there both same
Hope this helped!
At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is that chance
Answers
Answer:
10%
Step-by-step explanation:
According to the scenario, given data are as follows:
Students over age 21 = 30
Students under age 21 = 20
Choose student over age 21 = 3
Choose student under age 21 = 2
So, we can calculate chances by using following method,
Chances of student over age 21 = Number of choose student ÷ Total students
= 3 ÷ 30 = 0.10 = 10%
Similarly, Chances of student under age 21 = Number of choose student ÷ Total students
= 2 ÷ 20 = 0.10 = 10%
Hence, in both condition, chances are 10%.
What is the range of f(x) = 3* + 9?
O {yly<9}
O {yly>9}
O {yly> 3}
O {yly<3}
Answers
On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)
What is range?Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.
The regions where the absolute values are zero are known as the vertex points of an absolute value function.
\(|x + 1| = 0\\x + 1 = 0\\x = -1\)
\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)
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You have two pitchers and each can contain 600 ml of liquid. One pitcher is one-third full and contains vinegar. The other pitcher is two-fifths full of vinegar. Oil is added to fill each pitcher completely. The contents of each pitcher are poured into one large container. What fraction of the mixture in the large container is vinegar?
Answers
Answer:
answera c
Step-by-step explanation:
The slope of a line is 2/3. What is the slope of a line that is perpendicular to this line?
Answers
Answer:
-3/2
Step-by-step explanation:
The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite.
Hi! Could someone help me with this?
Answers
Answer:
480 in^3
Step-by-step explanation:
Volume = B*h
Base of the triangle = B*h*1/2
= 10*8*1/2
B = 40
Volume = 40*12 = 480
6. What is the area of a rectangular floor that is 7-3" long
and 4-2” wide?
Answers
The area of the rectangle will be 4350 Inches squared.
What is the area of the rectangle?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.
Given that a rectangular floor is 7-3" long and 4-2” wide. Here 7 ft 3 in = 87 in. 4ft 2 in = 50 in.
The area of the rectangle is calculated by using the formula below:-
Area = Length x Width
Area = 87 x 50
Area = 4350 Inches
Therefore, the area of the rectangle will be 4350 Inches squared.
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Selected financial data for Amberjack Corporation follows.
Answers
We provide recruitment solutions for your Future Talent and Volume Hiring needs. Platform. Services.
Define Decimal place?
A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc. In the figure given above, the decimal point separates the whole number 42 from the fractional part . In words, it is written as Forty Two Point Eight Five.One decimal place to the left of the decimal point is the ones place. One decimal place to the right of the decimal place is the tenths place. Keep your eye on the 9 to see where the decimal places fall.Rounding a decimal number to two decimal places is the same as rounding it to the hundredths place, which is the second place to the right of the decimal point. For example, 2.83620364 can be round to two decimal places as 2.84, and 0.7035 can be round to two decimal places as 0.70.To learn more about decimal place refers to:
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(a) Find a vector function, r(t), that represents the curve of intersection of the two surfaces.The cylinderx^2 + y^2 = 25and the surfacez = xyr(t)=??
Answers
A possible vector function that represents the curve of intersection of the two surfaces is r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))
The cylinder x^2 + y^2 = 25 represents the set of points in 3D space where the distance from the origin to the point (x, y, z) is equal to 5. The surface z = xy represents the set of points in 3D space where the height of the point (x, y, z) is equal to its x-y coordinate.
The curve of intersection of the two surfaces is given by the set of points in 3D space that are simultaneously on the cylinder and on the surface z = xy. This means that for any point on the curve of intersection, the distance from the origin to the point must be equal to 5, and the height of the point must be equal to its x-y coordinate.
We can find a vector function that represents the curve of intersection by parameterising the points on the curve in terms of a scalar parameter t. For example, a possible parameterization of the curve of intersection is:
r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))
where t is a scalar parameter that ranges over all values between 0 and 2π. The values of x, y, and z are given by 5 cos(t), 5 sin(t), and 5 cos(t) sin(t), respectively, and represent a point on the curve of intersection for each value of t.
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If the probability that your DVD player breaks down before the extended warranty expires is 0.034, what is the probability that the player will not break down before the warranty expires
Answers
Answer:
0.966
Step-by-step explanation:
Given that:
Probability of DVD player breaking down before the warranty expires = 0.034
To find:
The probability that the player will not break down before the warranty expires = ?
Solution:
Here, The two events are:
1. The DVD player breaks down before the warranty gets expired.
2. The DVD player breaks down after the warranty gets expired
In other words, the 2nd event can be stated as:
The DVD does not break down before the warranty gets expired.
The two events here, have nothing in common i.e. they are mutually exclusive events.
So, Sum of their probabilities will be equal to 1.
\(\bold{P(E_1)+P(E_2)=1}\\\Rightarrow 0.034+P(E_2)=1\\\Rightarrow P(E_2)=1-0.034\\\Rightarrow P(E_2)=\bold{0.966}\)
5/8 entre 6 personas
Answers
Based on the information we can infer that 5/8 between 6 people is equal to 15/24.
How to divide 5/8 between 6 people?To calculate the part that corresponds to each person, divide the fraction 5/8 by the number of people, which in this case is 6. To simplify the fraction, you can reduce the numerator and denominator by dividing both by their maximum common factor, which is 3.
5 ÷ 3 = 1 and 2 remainder8 ÷ 3 = 2 and 2 remainder
So the fraction can be simplified to 1 2/8, which can also be expressed as 1 1/4 or 5/4 in its most simplified form. This means that each person would receive 5/4 of the original share, and since there are 6 people in total, you can multiply 5/4 by 6 to get the total share that corresponds to all 6 people:
(5/4) x 6 = 30/4 = 15/2 = 15/24
So each person would receive 15/24 of the original amount.
Note: Here is the question in English:
5/8 divided in 6 people
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Enter the ratio as a fraction in lowest terms.
5 ft to 70 in.
Answers
Answer:
1/14
Step-by-step explanation:
The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14
Is the square root of 21 a rational number
Answers
Answer:
No
Step-by-step explanation:
But as we've stated, these prime factorizations are unique, so this can't be right. Therefore 21≠a2 , so a≠√21 , meaning that our earlier assumption of √21 being rational turns out to be wrong, therefore √21 is irrational.
Kavin made the 10 number cardsshown below.444N11997Gavin shuffled the cards and thenflipped them over so his friend Rickcould not see the numbers. If Rickrandomly chose one of the cards, hewas more likely to choose a card witha 4 than a card withA an odd numberB a prime numberC another even numberD an odd number less than 7
Answers
We have a total of 10 cards.
From these 10 cards, three cards are number 4, so the probability of choosing a number 4 is P = 3/10.
Calculating the probability for each option, we have:
A. Odd number
There are 6 odd numbers among the cards, so the probability is P = 6/10
B. Prime number
There are 3 prime numbers among the cards, so the probability is P = 3/10
C. Another even number
There are 4 even numbers among the cards, so the probability is P = 4/10
D. An odd number less than 7.
There are 3 odd numbers less than 7, so the probability is P = 3/10
The bigger probability is for an odd number, therefore the correct option is A.
In an assembly-line production of industrial robots, gearbox assemblies can be installed in one minute each if holes have been properly drilled in the boxes and in ten minutes if the holes must be redrilled. Twenty-four gearboxes are in stock, 6 with improperly drilled holes. Five gearboxes must be selected from the 24 that are available for installation in the next five robots. (Round your answers to four decimal places.) (a) Find the probability that all 5 gearboxes will fit properly. (b) Find the mean, variance, and standard deviation of the time it takes to install these 5 gearboxes.
Answers
Answer:
The right answer is:
(a) 0.1456
(b) 18.125, 69.1202, 8.3139
Step-by-step explanation:
Given:
N = 24
n = 5
r = 7
The improperly drilled gearboxes "X".
then,
⇒ \(P(X) = \frac{\binom{7}{x} \binom {17}{5-x}}{\binom{24}{5}}\)
(a)
P (all gearboxes fit properly) = \(P(x=0)\)
= \(\frac{\binom{7}{0} \binom{17}{5}}{\binom{24}{5}}\)
= \(0.1456\)
(b)
According to the question,
\(X = 91+5\)
Mean will be:
⇒ \(\mu = E(x)\)
\(=E(91+5)\)
\(=9E(1)+5\)
\(=9.\frac{nr}{N}+5\)
\(=9.\frac{5.7}{24} +5\)
\(=18.125\)
Variance will be:
⇒ \(\sigma^2=Var(X)\)
\(=V(9Y+5)\)
\(=81.V(Y)\)
\(=81.n.\frac{r}{N}.\frac{N-r}{N}.\frac{N-n}{N-1}\)
\(=81.5.\frac{7}{24}.\frac{24-7}{24}.\frac{24-5}{24-1}\)
\(=69.1202\)
Standard deviation will be:
⇒ \(\sigma = \sqrt{69.1202}\)
\(=8.3139\)
In circle F with m/EFG = 62°, find the angle measure of minor arc EG.
Answers
The angle measure of the minor arc is 62°
What is a circle?A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
The diameter is the length of the line that passes through the center circle touching two points on the circle's circumference.
The arc of a circle is the part or segment of the circumference of a circle.m∠EFG = minor arc EGminor arc EG = 62°
The measure of the arc is 62°
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what is the first term of an infinitely decreasing G.P whose sum is 16 and the second term is -0.5?
Answers
Answer:
8 + 6√2Step-by-step explanation:
Sum of infinite GP is:
a/(1 - r) = 16 andThe second term is:
ar = -0.5Eliminate r in the system:
a/(1-r) = 16 ⇒ a = 16 - 16r ⇒ 16r = 16 - a ⇒ r = 1 - a/16ar = -0.5 ⇒ r = -0.5/aCompare the two equations and solve for a:
1 - a/16 = -0.5/aMultiply both sides by 16a:
16a - a² = -8a² - 16a = 8 a² - 16a + 64 = 72(a - 8)² = 72a - 8 = ±√72a = 8 ± √72a = 8 + 6√2 a = 8 - 6√2, excluded as it is negative and makes common difference positive and so an increasing functiona = 8 - 6√2 = -0.4852 ⇒ r = -0.5/a = -0.5/-0.4852 = 1.03 > 1
Given sinz = -4/5 for pi < z < (3pi)/2, find the value of cosz.
Answers
The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.
Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.
According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.
The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:
Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25
Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.
So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.
Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.
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A 2 meter television camera at ground level is filming the lift-off of a space shuttle at a point 750 meters from the launch pad. The camera’s angle of elevation to the shuttle is 32° at this specific time . Find the height of the shuttle.
Answers
To find the height of the shuttle, we can use trigonometry and the concept of similar triangles. The height of the shuttle is approximately 468.675 meters.
Let's assume that the height of the shuttle is represented by 'h' meters. From the information given, we know that the distance between the camera and the launch pad is 750 meters, and the angle of elevation from the camera to the shuttle is 32 degrees.
Using trigonometry, we can set up the following equation:
tan(32°) = h / 750
To find the value of h, we can rearrange the equation:
h = tan(32°) * 750
Using a calculator, we can find the value of tan(32°) ≈ 0.6249.
Now we can calculate the height of the shuttle:
h ≈ 0.6249 * 750
h ≈ 468.675 meters
Therefore, the height of the shuttle is approximately 468.675 meters.
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In a party, the first time the door bell rang, 6 guest arrived. On each succeeding ring, two more guests arrived than on the previous ring. After 10 rings, what was the number of guests at the party?
answer choices;
A. 21
B. 31
C. 29
D. 24
E. 28
Answers
How many 50ml can be filled from 5L
Answers
Help me solve please y-9 terms,variables, coefficient s,constants
Answers
The terms in given expression like variables, coefficient, constant are respectively, y, 1, -9
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.
For example, 2x+3
Given that,
An expression,
⇒ y-9
In given expression, y is term which is variable
And coefficient of y is 1
constant term is -9
Therefore, we can write our terms are, y, 1, -9
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A study was conducted of Long Beach School District schools regarding how
many require school uniforms. In 2006, of the 296 schools questioned, 184 said
they required school uniforms. (Gentile & Imberman, 2009) Find the proportion
of schools that require a school uniform.
Answers
The alternative hypothesis is Ha : μa ≠ μb Ha : μa - μb ≠ 0
Since they want to find out if the difference in the mean times spent studying by the students of the two schools is statistically significant, it means that it is a two directional test. Also called a two tailed test. The hypothesis would be as follows:
Null Hypothesis: There is no difference in the mean times spent by the schools' students.
Alternative Hypothesis: There is at least some difference in the mean times spent by the schools' students.
By using the appropriate symbols, it becomes
The null hypothesis is
H0 : μa = μb H0 : μa - μb = 0
The alternative hypothesis is
Ha : μa ≠ μb Ha : μa - μb ≠ 0
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Guys my main account is gone i dont know why. Am I baned?
Answers
Answer:
Try contacting the Help center located at the bottom part of the home page of this site. It is recoverable as long as no violation committed
Answer please ? Find the perimeter of the figure ( must include all sides )
Answers
Answer:
32 ft
Step-by-step explanation:
First we can add up all the sides we already know as perimeter is the sum of all the lengths of a shape. 9+6+3+4 = 22
There are two unknown side lengths in the diagram, the long one at the top, and the short one between the 3ft side and the 4ft side. Luckily these can be easily found using the given sides. Since this shape is rectangular in nature (all 90-degree angles), the top length is the same as the bottom length. We know the total bottom length to be 7ft (3+4) so the top length must be 7ft as well.
Similarly, all the vertical lengths on the right side must be equal to the 9ft length on the left side, therefore the unknown length is 3ft (9-6).
Adding on these two new lengths and our total perimeter is 22+7+3 = 32ft.
Hope this helped!
The function f(x)=-(x-3)^2+9 can be used to represent the area of a rectangle with a perimeter of 12 units, as a function of the length of the rectangle, x. What is the maximum area of the rectangle?
A)3 square units
B)6 square units
C)12 square units
D)9 square units
Answers
Answer:
D) 9 square units
Step-by-step explanation:
The squared term will always be non-negative, so the least it can be is zero (for x=3). The squared term is subtracted from 9, so the most the function value can be is 9.
The maximum area of the rectangle is 9 square units.
Answer:
9 square units
Step-by-step explanation:
Opal saves $7. A week for 16 weeks. Her brother saves $27. A month for 4 months. Who saves more money?
Answers
Answer:
Opal saves more
Step-by-step explanation: