Answers
Rational functions are fractions where numerator and denominator are polynomials.
Related Questions
To divide a whole number or decimal by 10, move the decimal point
place(s) to the left.
Answers
Answer:
you simply have to move one left. It thats decimal you can simply remove one zero
Answer:
You just have to move to the left once
Step-by-step explanation:
Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume the number of litres sold follows the normal distribution with a standard deviation of 18 L. From his records, he selects a random sample of 18 sales and finds the mean number of litres sold is 56.
a. What is the point estimate of the population mean? (Round the final answer to the nearest whole number.)
The point estimate of the population mean is
litres.
b. Develop a 80% confidence interval for the population mean. (Round the final answers to 3 decimal places.)
The 80% confidence interval for the population mean is between
and
.
c. Interpret the meaning of part (b).
If 100 such intervals were determined, the population
mean
would be included in about
intervals.
Answers
Answer:
a
The point estimate of the population mean is [tex]\= x = 56[/tex]
b
The 80% confidence level is [tex]50.57 < \mu < 61.43[/tex]
c
There is 80% confidence that the true population mean lies within the confidence interval.
Step-by-step explanation:
From the question we are told that
The sample size is n = 18
The standard deviation is [tex]\sigma = 18 \ L[/tex]
The sample mean is [tex]\= x = 56[/tex]
Generally the point estimate of the population mean is equivalent to the sample mean whose value is [tex]\= x = 56[/tex]
Given that the confidence interval is 80% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 80[/tex]
[tex]\alpha = 20 \%[/tex]
[tex]\alpha = 0.20[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The value is [tex]Z_{\frac{ \alpha }{2} } = 1.28[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.28 * \frac{18 }{\sqrt{18} }[/tex]
=> [tex]E = 5.43[/tex]
Generally the 80% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]56 - 5.43 < \mu < 56 + 5.43[/tex]
=> [tex]50.57 < \mu < 61.43[/tex]
The interpretation is that there is 80% confidence that the true population mean lies within the limit
For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
Answers
the graph has 12 segments so angle enclosed by each segment is [tex] {2\pi\over 12}=\frac{\pi}6[/tex]
anti-clockwise is taken as positive, so if you want positive q, you need to rotate 8 segments [tex] q=8\frac,{\pi}6=\frac{4\pi}3 [/tex] , and and 8 circles or units so r=8
and for a negative angle, you need to rotate clockwise
Which is 4 segments from the horizontal line. so [tex]q=-\frac{2\pi}3[/tex] and r will be same, 8 units.
[not sure about -r so I won't include it in answer]
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Find the largest number apart from 840 that is a multiple of 24 and a factor of 840.
Answers
Answer:
168
Step-by-step explanation:
first, split both 840 and 24 into there primes.
840=2×2×2×3×5×7
24=2×2×2×3
therefore any multiples of 24 must have those factor.
so, factors of 840 that are multiples of 24 are
2×2×2×3=24
2×2×2×3×5=120
2×2×2×3×7=168
2×2×2×3×5×7=840
there the answer is 168
Y * 3 = 81 please i need it for today
Answers
Answer:
Y = 27
Step-by-step explanation:
Y * 3 = 81
Divide each side by 3
Y * 3/3 = 81/3
Y = 27
Compare the line passing through the points (–2, –9) and (4, 6) to the line given by the equation y = 25x – 4.
A. They have the same slope.
B. They have the same x-intercept.
C. The two lines are perpendicular.
D. They have the same y-intercept.
Answers
Answer:
D. They have the same y-intercep
Step-by-step explanation:
Before the comparison will be efficient, let's determine the equation of the two points and the x intercept .
(–2, –9) and (4, 6)
Gradient= (6--9)/(4--2)
Gradient= (6+9)/(4+2)
Gradient= 15/6
Gradient= 5/2
Choosing (–2, –9)
The equation of the line
(Y+9)= 5/2(x+2)
2(y+9)= 5(x+2)
2y +18 = 5x +10
2y =5x -8
Y= 5/2x -4
Choosing (4, 6)
The equation of line
(Y-6)= 5/2(x-4)
2(y-6) = 5(x-4)
2y -12 = 5x -20
2y = 5x-8
Y= 5/2x -4
From the above solution it's clear that the only thing the both equation have in common to the given equation is -4 which is the y intercept
A committee of 3 is to be chosen from 4 girls and 7 boys.Find the expected number of girls in a committe, if numbers are chosen at random
Answers
Answer: There is only 1 girl.
Step-by-step explanation:
As you can see the probability of choosing a girl is 4/11 out of the whole people which is 7 boys and 4 girls. And the same way the probability of choosing a boy is 7/11 which is almost doubled the amount of girls. So to think about it, there will be more boys than girls if there is a random selection because the boys chances of getting picked is high.
Solve the right triangle.
a = 3.3 cm, b = 1.7 cm, C = 90°
Round values to one decimal place.
Answers
Answer:
A = 62.7°B = 27.3°c = 3.7Step-by-step explanation:
tan(A) = a/b = 3.3/1.7
A = arctan(33/17) ≈ 62.7°
B = 90° -A = 27.3°
c = √(a²+b²) = √(3.3² +1.7²) = √13.78
c ≈ 3.7
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
Answers
THIS IS THE COMPLETE QUESTION BELOW;
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?
A. 0.10
B.0.50
C. 0.66
D. 0.06
Answer:
OPTION D is correct
d)0.06
the probability that a randomly selected team from Littletown goes to the city and state playoffs is [tex]0.06[/tex]
Step-by-step explanation:
The probability that a baseball team goes to city playoffs is 0.30.
P(baseball team goes to city playoffs)=0.30
The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.20.
P(team goes to state playoffs given that the team goes to the city playoffs)=0.20
From our knowledge of set, we know that
P(A | B)= P(A ∩ C)/P(C)
where A= city playoffs
B= state playoffs
P(State play off | city play off)=0.20
P(State play off ∩ city play off)/P(city play off,)=0.20
P(State play off ∩ city play off)/0.30 =0.20
P(State play off ∩ city play off)= 0.30 × 0.20
= 0.06
Hence,the probability that a randomly selected team from Littletown goes to the city and state playoffs is 0.06
HELP ASAP PLS :Find all the missing elements:
Answers
Answer:
a ≈ 1.59
b ≈ 6.69
Step-by-step explanation:
Law of Sines: [tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
Step 1: Find c using Law of Sines
[tex]\frac{6}{sin58} =\frac{c}{sin13}[/tex]
[tex]c = sin13(\frac{6}{sin58})[/tex]
c = 1.59154
Step 2: Find a using Law of Sines
[tex]\frac{6}{sin58} =\frac{a}{sin109}[/tex]
[tex]a = sin109(\frac{6}{sin58} )[/tex]
a = 6.68961
Emily made a pot cream of pumpkin soup for thanksgiving dinner she put 5 cups of cream in the soup she poured the soup into 24 small bowl show much cream measured in oz is used for each small bowl of soup?
Answers
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.
A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?
a. (160, 240)
b. (140, 260)
c. (120, 280)
d. (200, 320)
Answers
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:
The interval for 95% will be given as,
Pr(X) = μ ± 2σ
Pr(X) = 200 ± 2(40)
Pr(X) = 200 ± 80
Pr(X) = (200 - 80, 200 + 80)
Pr(X) = (120, 280)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
More about the normal distribution link is given below.
https://brainly.com/question/12421652
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Lynn estimates roof jon 1500,bo estimates 2400. What's the ratio to lynn to bo
Answers
Answer:
5:8
Step-by-step explanation:
If I understand your question correctly, we have 1500/2400=15/24=5/8, so we have Lynn:Bo is 5:8, however, in the future please be more clear.
What is "estimates roof jon"? And, instead of saying "ratio to lynn to bo" say "What is the ratio of the estimates?" or whatever you're asking. If this answer is wrong, you only have yourself to blame.
What percent of the area underneath
this normal curve is shaded?
Answers
Answer:
The area shaded is 95%
Step-by-step explanation:
The total area under the curve is 100 percent
1 standard deviation away from the mean is 68 percent
2 standard deviations away is 95 percent
The area shaded is 95%
The percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.
What is the 68-95-99.7 rule?The 68-95-99.7 rule is also referred to as the empirical rule or the three-sigma rule and it can be defined as a shorthand which is used in statistics to determine the percentage of a population parameter that lie within an interval estimate in a normal distribution curve.
Basically, the 68-95-99.7 rule states that 68%, 95%, and 99.7% of the population parameter lie within one (1), two (2), and three (3) standard deviations of the mean respectively.
This ultimately implies that, the percentage of the shaded area underneath this normal curve is 95% because it lie within two (2) standard deviations of the mean.
Read more on 68-95-99.7 rule here: https://brainly.com/question/24768583
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Which is the graph of g(x) = (0.5)x + 3 – 4?
Answers
Answer:
Graph (A)
Step-by-step explanation:
Given question is incomplete; find the question in the attachment.
Given function is g(x) = [tex](0.5)^{x+3}-4[/tex]
Parent function of the given function is,
f(x) = [tex](0.5)^{x}[/tex]
When the function 'f' is shifted by 3 units left over the x-axis, translated function will be,
h(x) = f(x+3) = [tex](0.5)^{x+3}[/tex]
When h(x) is shifted 4 units down, translated function will be,
g(x) = h(x) - 4
g(x) = [tex](0.5)^{x+3}-4[/tex]
g(x) has a y-intercept as (-4).
From the given graphs, Graph A shows the y-intercept as (-4).
Therefore, Graph A will be the answer.
Answer:
The Answer A is correct
Step-by-step explanation:
I took the edg2020 test
will rate you brainliest
Answers
Answer:
[tex] \frac{11x}{3y} [/tex]
Step-by-step explanation:
[tex] \frac{7x}{3y} + \frac{12x}{9y} [/tex]
Make both a single fraction by adding together.
[tex] \frac{3(7x) + 1(12x)}{9y} [/tex]
[tex] \frac{21x + 12x}{9y} [/tex]
[tex] \frac{33x}{9y} [/tex]
Simplify
[tex] \frac{3(11)x}{3(3y)} [/tex]
[tex] \frac{11x}{3y} [/tex]
What is the intersection of the given lines? AB←→and EB←→ point B BE←→ point A point E
Answers
Answer:
point B
Step-by-step explanation:
The names of the lines, AB and BE, tell you that point B is on both lines.
Point B will be the point of intersection.
Answer:
point b
Step-by-step explanation:
i took the test and got it right
Which of the following statements about shapes of histograms is true?
a. A histogram is said to be symmetric if, when we draw a vertical line down the center of the histogram, the two sides are identical in shape and size.
b. A negatively skewed histogram is one with a long tail extending to the left.
c. A positively skewed histogram is one with a long tail extending to the right.
d. All of these choices are true
Answers
Answer:
d. all of these choices are true
Step-by-step explanation:
Histograms have 3 outstanding shapes:
1. they are syymetric:
this is to say that from the middle of the histogram if you cut it into two or half, each side is an exact close representation of the other side.
2. they are positively skewed to the right:
That is it has a long tail that goes off towards the right.
3. they are negativly skewed to the left:
They have a long tail that goes off to the left.
therefore from the question option d is the best answer since a, b, c describes the shape of a histogram.
Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 3 .10 11 .30 19 .20 27 .40
Answers
Answer:
69.76
Step-by-step explanation:
The mean is the average of the numbers. It can be gotten by adding all the numbers, then divide by how many numbers available.
Variance (σ2) measure the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean .
mean value can be computed using below expression
= ∑x(i)P(x(i))
= 3(0.10)+11(0.30)+19(0.20)+27(0.40)
= 18.2
Therefore, the mean value is 18.2
The variance can be calculated using below expression
variance
= ∑(x(i)-mean)^2 P(x(i))
= (3-18.2)^2 (.10) + (11-18.2)^2 (.30) + (19-18.2)^2 (.20)+(27-18.2)^2(0.40)
= 69.76
Therefore, the variance Vale is 69.76
How do "Combinations" work? What's the formula to solve this equation?
Answers
[tex]_nC_k=\dfrac{n!}{k!(n-k)!}\\\\\\_{34}C_{34}=\dfrac{34!}{34!0!}=1[/tex]
In general, [tex]_nC_n=1[/tex]
Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. (a) Find the probability of the event that exactly one of the colors that appears face up is red.
Answers
Answer:
12/27
Step-by-step explanation:
Step 1
We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.
Where
R = Red
B = Blue
Y = Yellow
RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR
We have 27 Total outcomes for this 6 faced die
Step 2
The event that exactly one of the colors that appears face up is red.
RBY, RYB, YBR, YRB, RBB, RYY, BBR,
BRB, BRY, YRY, BYR, YYR
Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12
The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes
= 12/27
Find the area of the region enclosed by the curves x=3y^2, x=0, and y=2
Answers
Answer:
8
Step-by-step explanation:
Hello,
[tex]x=3y^2<=>y=\sqrt{\dfrac{x}{3}} \ \ for \ x\geq 0[/tex]
And for y = 2, x = 3 * 2 * 2 = 12 so first, let's compute
[tex]\displaystyle \int\limits^{12}_0 {\sqrt{\dfrac{x}{3}}} \, dx =\dfrac{1}{\sqrt{3}} \int\limits^{12}_0 {\sqrt{x}} \, dx\\\\=\dfrac{1}{\sqrt{3}} \left[ \dfrac{2}{3}x^{3/2}\right]_0^{12}\\\\=\dfrac{1}{\sqrt{3}} *\dfrac{2}{3}*12*\sqrt{12}\\\\=\dfrac{2*12*2*\sqrt{3}}{3*\sqrt{3}}\\\\=2*4*2=16[/tex]
The area which is asked is 12*2 - 16 = 24 - 16 = 8
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Using integrals, it is found that the area of the region enclosed by the curves in the interval is of 27 units squared.
In this problem:
The curve is [tex]x = 3y^2[/tex], hence the integral is relative to y.The lower limit is when x = 0, hence [tex]0 = 3y^2 \rightarrow y = 0[/tex].The upper limit is when y = 2.Then, the integral for the area is:
[tex]A = \int_{0}^{2} 3y^2 dy[/tex]
[tex]A = y^3|_{y = 0}^{y = 3}[/tex]
[tex]A = 3^3 - 0^3[/tex]
[tex]A = 27[/tex]
The area of the region enclosed by the curves in the interval is of 27 units squared.
You can learn more about the use of integrals to calculate an area at https://brainly.com/question/15127807
In the figure above, ABCD is a parallelogram
with AB = BE = EC. If the area of right triangle
BEC is 8, what is the perimeter of polygon
ABECD?
Answers
The perimeter is 21.66
The figure is something like the one that is in the image below:
We want to find the total perimeter of the polygon ABECD
This will be:
AB + BE + EC + CD + DA
Remember that for a triangle rectangle of catheti A and B, the area is given by:
A*B/2
We know that the sides of the triangle rectangle are:
BE, EC, BC.
Because BE = EC, these can not be the hypotenuse of the triangle, then the catheti are BE and EC
Knowing that the area of the triangle rectangle is 8, we can write:
EC*BE/2 = 8
and EC = BE = x
x^2/2 = 8
x^2 = 8*2 = 16
x = √16 = 4
Then the two catheti of the triangle rectangle are 4 units long.
EC = 4
BE = 4
and we know that:
AB = BE = EC
then:
AB = 4
and because this is a rectangle, we also have:
DC = AB = 4
now we want to find the last side of the figure, AD,
Which we already know is equal to the hypotenuse of the triangle.
Remember the Pythagorean's theorem, which says that the sum of the squares of the catheti is equal to the square of the hypotenuse.
Both catethus are equal to 4, then we have:
H^2 = 4^2 + 4^2 = 32
H = √32 = 5.66
then:
DA = 5.66
Now we have:
AB = BE = EC = DC = 4
DA = 5.66
Then the perimeter is:
AB + BE + EC + CD + DA
4 + 4 + 4 + 4+ 5.66 = 21.66
If you want to read more about this topic, you can read:
https://brainly.com/question/24307347
help pls:Find all the missing elements
Answers
Step-by-step explanation:
Using Sine Rule
[tex] \frac{ \sin(a) }{ |a| } = \frac{ \sin(b) }{ |b| } = \frac{ \sin(c) }{ |c| } [/tex]
[tex] \frac{ \sin(42) }{5} = \frac{ \sin(38) }{a} [/tex]
[tex]a = \frac{5( \sin(38))}{ \sin(42) } [/tex]
[tex]a = 4.6[/tex]
[tex] \frac{ \sin(42) }{5} = \frac{ \sin(100) }{b} [/tex]
[tex]b= \frac{5( \sin(100))}{ \sin(42) } [/tex]
[tex]b = 7.4[/tex]
Diana paints 150 fence posts and chuck paints 130 fence posts. Diana paints 10 more fence posts than chuck. How many fence posts does chuck paint per hour?
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
Step-by-step explanation:
From the question we are told that
The relationship is [tex]\frac{150 }{d} = \frac{130}{c}[/tex]
The number of fence post painted by chuck is [tex]l = 130[/tex]
The number of fence post painted by Diana is [tex]k = 150[/tex]
can paint 10 fences more than chuck so let say the of fence painted in an hour by chuck is [tex]g[/tex]
Then the number of fence post painted by Diana in one hour is
[tex]f = g+ 10[/tex]
So
[tex]\frac{150 }{ g + 10 } = \frac{130}{g}[/tex]
[tex]130 g + 1300 = 150g[/tex]
[tex]g = 65 \ m[/tex]
Amy is a software saleswoman. Let Y represent her total pay (in dollars). Let X represent the number of copies of "English is Fun" she sells. Suppose that X and Y are related by the equation 110X +2300 = Y.
Answer the questions below. Note that a change can be an increase or decrease.
What is the change in Amy's total pay for each copy of "English is Fun"?
What is Amy's total pay if she doesn't sell any copies of "English is Fun"?
Answers
Answer:
1) For every copy she sells, her pay increases by $110
2) Her total pay is 2300
Step-by-step explanation:
1) X is the number of copies she sells. In the equation 110X+ 2300 = Y, X will determine how many times 110 is multiplied. So, for every increase by one in X, Y will also go up by 110
eg.
110(50) + 2300 = 7800 -- if she sells 50 copies
110(51) + 2300 = 7910 -- if she sells 51 copies,
2) If she doesn't sell any copies, the equation becomes 110 * 0 + 2300. Anything multiplied by 0 equals 0, so the equation equals 0 + 2300 = 2300 = Y
Therefore, if she doesn't sell any copies, she will get a pay of $2300
Find all real solutions of the equation: x 2 + 3x − 10 = 0
Answers
Answer: x=8/3 or x= 2.6666....
Step-by-step explanation:
[tex]2+3x-10=0[/tex]
[tex]2-10=-8[/tex]
[tex]3x-8=0[/tex]
add 8 on both sides
[tex]3x-8+8=0+8[/tex]
[tex]3x=8[/tex]
divide 3 on both sides
[tex]x=\frac{8}{3}[/tex]
Answer:
8/3
Step-by-step explanation:
2 +3x + 10 = 0
2-10 +3x = 0
-8 + 3x = 0
3x = 8
x = 8/3
If A = {2,4,6,8,10) and B = [4,8,10), then which of the following statements is false?
A n B = B
B C B
A C B
Answers
A C B because all elements of A are not found in B
At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 3/25. Find the odds in favor of receiving a gift. I got 3/28. A child has a box of candies which might have a toy inside. The odds against the box having a toy are 7/2. What is the probability of the box having a toy? I got 7/9. Are my answers correct?
Answers
Answer:
a) Your answer for part a (I got 3/28) is wrong.
Odds are always expressed as ratios after calculating. Therefore, the odds in favour of receiving a gift = 3:22
b) Your answer in part b(I got 7/9) is correct.
The probability of the box having a toy is 7/9.
Step-by-step explanation:
The question above has to do with odds and probability.
It is important to note that odds are expressed in the form of ratios while probabilities are expressed as fractions.
a) At a certain charity fundraiser, some guests will be randomly selected to receive a gift. The probability of receiving a gift is 3/25. Find the odds in favor of receiving a gift.(I got 3/28)
The formula for calculating odds from probability is Odds = Probability / (1 - Probability).
Probability = 3/25
Odds =(3/25)/(1 - 3/25)
= (3/25)/22/25
= 3/25 ÷ 22/25
= 3/25 × 25/22
= 3/22
Note that odds are always expressed as ratios.
Therefore, the odds in favour of receiving a gift = 3:22
Your answer for part a (I got 3/28) is wrong.
The correct answer is 3:22
b) A child has a box of candies which might have a toy inside. The odds against the box having a toy are 7/2. What is the probability of the box having a toy? I got 7/9.
The formula for calculating probability from odds is P = Odds / (Odds + 1).
Odds = 7/2 or 7:2
We convert the odds to fraction when calculating
Probability = Odds / (Odds + 1).
Probability = (7/2)/ (7/2 + 1)
Probability = (7/2)/9/2
Probability = 7/2 ÷ 9/2
= 7/2 × 2/9
= 7/9
Probability is always expressed as a fraction.
Therefore, the probability of the box having a toy is 7/9.
Your answer in part b(I got 7/9) is correct.
A survey of the adults in a town shows that 8% have liver problems. Of these, it is also
found that 25% are heavy drinkers, 35% are social drinkers and 40% are non-drinkers. Of
those that did not suffer from liver problems, 5% are heavy drinkers, 65% are social
drinkers and 30% do not drink at all. An adult is chosen at random, what is the probability
that this person
i. Has a liver problems? (3 Marks)
ii. Is a heavy drinker (2 Marks)
iii. If a person is found to be a heavy drinker, what is the probability that this person
has liver problem? (2 Marks)
iv. If a person is found to have liver problems, what is the probability that this person
is a heavy drinker? (2 Marks)
v. If a person is found to be a non –drinker, what is the probability that this person has
liver problems. (2 Marks)
(b) The director of admiss
Answers
Answer:
The data is:
From the adults in town:
8% have liver problems, of those:
25% heavy drinkers
35% social drinkers
40% non-drinkers.
92% do not have liver problems (100% - 8% = 92%)
5% heavy drinkers
65% social drinkers.
30% non-drinkers
a) An adult is chosen at random, then:
Has a liver problems
We know that 8% of the adults have liver problems, so the probability is 8%, or 8%/100% = 0.08.
Is a heavy drinker
Out of the 8%, 25% are heavy drinkers, and out of the other 92%, 5% are heavy drinkers, so the total percentage of heavy drinkers is:
(i will use decimal math, because you always should work with decimals instead of percentages)
P = 0.08*0.25 + 0.92*0.05 = 0.066
or 6.6% in percentage form
If a person is found to be a heavy drinker, what is the probability that this person
the proability that some one is a heavy drinker was already found, it is p = 0.066.
Now, of those 0.066 we have:
p1 = 0.08*0.25 = 0.02 have liver problems.
So the probability that, given that some one is a heavy drinker, that her/him also have liver problems is:
P = 0.02/0.066 = 0.3 or 30%.
If a person is found to have liver problems, what is the probability that this person is a heavy drinker?
]We already know that out of the 8% with liver problems, a 25% are heavy drinkers, so here the answer is 25% or 0.25.
If a person is found to be a non –drinker, what is the probability that this person has liver problems.
From the 8% with liver problems, we have 40% of non-drinkers,
So the total proportion of non-drinkers with liver problems is:
p1 = 0.8*0.40 = 0.032
From the 92% with no liver problems, we have that 30% of them are non-drinkers, so here we have:
p2 = 0.92*0.30 = 0.276
The total proportion of non drinkers is:
p1 + p2 = 0.032 + 0.276 = 0.308.
Then if we know that some one is non drinker, the proability that the person has liver problems is equal to the quotient between the proportion of non-drinkers with liver problems ( 0.032) and the total proportion of non-drinkers.
p = 0.032/0.308 = 0.104
or 10.4% in percentage form.
