The expected profit of the man from the horse race is $22,400.
Given data:
To find the man's expected profit, calculate the probability of each outcome and multiply it by the corresponding profit.
To determine the probability of each outcome based on the given information:
Probability of winning both races = 0.30 * 0.40
Probability of winning both races = 0.12
Probability of winning one race = 0.30 * 0.60 + 0.70 * 0.40
Probability of winning one race = 0.46
Probability of losing both races = 0.70 * 0.60
Probability of losing both races = 0.42
Next, calculate the expected profit for each outcome:
Profit from winning both races = $90,000 - $20,000
Profit from winning both races = $70,000
Profit from winning one race = $55,000 - $20,000
Profit from winning one race = $35,000
Profit from losing both races = $15,000 - $20,000
Profit from losing both races = -$5,000 (a loss of $5,000)
Now, determine the man's expected profit by multiplying the probability of each outcome by the corresponding profit and summing them up:
Expected profit = (0.12 * $70,000) + (0.46 * $35,000) + (0.42 * -$5,000)
Expected profit = $8,400 + $16,100 - $2,100
Expected profit = $22,400
Hence, the man's expected profit is $22,400
To learn more about probability, refer:
https://brainly.com/question/17089724
#SPJ12
PLS HELP ASAP!! For brainliest answer!!!!
Based on the similar triangles shown below, Theodore claims that ∆TUV is transformed to ∆WXY with a scale factor of 32. Is Theodore correct? Yes, the triangles are similar with a scale factor of 32. No, the triangles are similar with a scale factor of 21. No, the triangles are similar with a scale factor of 23. No, the triangles are similar with a scale factor of 43.
Answer:
Yes, the triangles are simirar with a scale factor of 3/2.
Step-by-step explanation:
We find the scale factor by dividing corresponding sides:
12/8=3/2
18/12=3/2
24/16=3/2
Find the
(i) Radius of the smaller sector.
(ii) Perimeter of the shape.
(iii) The angle
Answer:
Radius of the smaller sector = 12 cmPerimeter of the shape = 68 cmAngel = 47.72° (Approx)Step-by-step explanation:
Computation:
Length of arc = Θ/360[2πr]
20 = Θ/360(2)(22/7)(24)
Θ = 47.72°
Angel = 47.72° (Approx)
Length of arc = Θ/360[2πR]
10 = [47.72 / 360][2][22/7][R]
R = 12 cm
Radius of the smaller sector = 12 cm
Perimeter of the shape = 20 + 24 + 24
Perimeter of the shape = 68 cm
What does 3ˣ + 4·3ˣ⁺¹ =
a. 13·3ˣ⁺¹
b. 5·3ˣ⁺¹
c. 5·3²ˣ⁺¹
d. 13·3ˣ
Answer:
D. 13*3^x
Step-by-step explanation:
[tex]3^x +4*3^x^+^1= \\3^x+4*3(3^x)=\\3^x(1+[4*3])=\\3^x(1+12)=\\3^x(13)=\\13*3^x[/tex]
The solution of 3ˣ + 4·3ˣ⁺¹ is 13·3ˣ which is the correct answer would be an option (D)
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
It is a relation of the form y = aˣ in mathematics, where x is the independent variable
⇒ 3ˣ + 4·3ˣ⁺¹
⇒ 3ˣ + 4·3ˣ3¹
⇒ 3ˣ( 1 + 4·3)
⇒ 3ˣ( 1 + 12)
⇒ 3ˣ(13)
⇒ 13·3ˣ
Hence, the solution of 3ˣ + 4·3ˣ⁺¹ is 13·3ˣ which is correct answer would be option (D)
Learn more about exponential function here:
https://brainly.com/question/11487261
#SPJ2
Rodell wants to find the favorite gaming app among the students at his school. He decides to poll the thirty students
on his football team and the fifteen students on his basketball team to gather the data. What is wrong with Rodell's
method for collecting his data?
Rodell only polled fellow athletes, this sample does not represent nonathletes at the school.
* Rodell needs a larger sample size than two sports teams to represent a whole school.
Rodell polled everyone on his teams; he should have only polled every other student for it to be a true sample.
Rodell’s polling method only included fall and winter sports, he should have also included a spring sport like
baseball
(it’s not B on edge, don’t answer if you don’t know thanks)
Rodell needs a larger sample size than two sports teams to represent a whole school.
Important Information : Study is conducted about favourite gaming app among students at school, 30 & 15 students of football & basketball team are polled.
Finding : Issue in Rodell's method of collecting data
The issue in this sampling : Rodell needs a larger sample size than two sports teams to represent a whole school.
Sample selected from universe should be very carefully chosen, to be a good representative of universe.
Here, Rodell has chosen only two sports' team members as sample for the study of favourite gaming app. Such kind of sample having more uneven concentration of any type of population members doesn't denote sample being a good representative of population.
To learn more Sampling, refer https://brainly.com/question/24842573?referrer=searchResults
Dan paid $498.09 (including sales tax) for a laptop computer. The sales tax in his state is 7%. What was the price of the laptop before the sales tax was added?
Answer:
$465.50
Step-by-step explanation:
Let the price be x, then:
x + 0.07x = 498.091.07x = 498.09x = 498.09/1.07x = 465.50four times the difference of a number and 7 is 12
answer
20
Step-by-step explanation:
I think you mean for times the difference of seven and 12 or (12-7)×4 if not sorry
Answer: 10
Step-by-step explanation:
4(x - 7) = 12
x - 7 = 3
x = 10
solve this asap plsss Giving 20 points ty <3
Answer:
24
Step-by-step explanation:
first 2×2=4
then 16÷4
4×6
24
Describe the sampling distribution of p(hat). Assume the size of the population is 30,000.n=800, p=0.6a) Determine the mean of the sampling distributionb) Dtermine the standard deviation of the sampling distribution
Answer:
Standard deviation of the binomial distribution
= [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]
Step-by-step explanation:
Explanation:-
Given size 'n' = 800
The population proportion 'p'=0.6
Let 'X' be the random variable of the binomial distribution
a) mean of the binomial distribution = n p = 800 ×0.6
μ = 480
b) variance of the binomial distribution
= n p q
= 800 X 0.6 ×0.4
σ² = 192
Standard deviation of the binomial distribution
σ = [tex]\sqrt{n p q} = \sqrt{192} = 13.856[/tex]
Please help me please thank you
Answer:
x = 15
Step-by-step explanation:
angles 2 and 4 are supplementary so they add up to 180
2x + 10 + 4x + 80 = 180
6x + 90 = 180
6x = 90
x = 15
Answer:
x=15
Step-by-step explanation:
Angles 2 and 4 are same-side interior angles. This means that if they are supplementary angles, then the lines A and B are parallel.
Supplementary angles, when added together, will equal a total of 180°. Set up an equation in which the angles are added and are equal to 180:
[tex](2x+10)+(4x+80)=180[/tex]
Solve for x. Remove the parentheses and combine like terms:
[tex]2x+10+4x+80=180\\\\2x+4x+10+80=180\\\\6x+90=180[/tex]
Work to isolate the variable, x. Subtract 90 from both sides:
[tex]6x+90-90=180-90\\\\6x=90[/tex]
Isolate x. Divide both sides by 6:
[tex]\frac{6x}{6}=\frac{90}{6} \\\\x=15[/tex]
The value of x is 15.
:Done
If you want to check your work, insert the value of x into the angles, and add them. If the answer is 180, then the value of x is true:
[tex]2x+10\\\\2(15)+10\\\\30+10\\\\40[/tex]
∠2=40
[tex]4x+80\\\\4(15)+80\\\\60+80\\\\140[/tex]
∠4=140
∠2+∠4=180
40+140=180
The value of x is true.
The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) are given below. Find a 99% confidence interval on the difference in mean life. Which brand would you prefer based on this calculation?
Answer:
-727.5034 and 2464.2534
Step-by-step explanation:
Find explanation in the attachment
Your manufacturing plant produces air bags, and it is known that 20% of them are defective. Five air bags are tested. (a) Find the probability that two of them are defective. (Round your answer to four decimal places.)
Answer:
1.0000
Step-by-step explanation:
It is know that 20% of air bags produced by the manufacturing plant are defective.
20% of x
Therefore, the probability that two are defective will be
20/100 × 5
0.2×5=1.0000
Find the limit of the function algebraically. alt='limit as x approaches zero of quantity negative seven plus x divided by x squared.'
Answer:
lim x->0 (-8+x)/x^2
just plug in x = 0
(-8+0)/0
now this fraction is a negative number divided by 0.
So, it equals -infinity.
The limit value is infact -infinity,
so the given option, "Does Not Exit" is the best choice.
Find out the mystery sequence hidden in the diminoes,dominoes, decide which number should replace the question mark.
Answer:
80?
Step-by-step explanation:
i counted the numbers on the first domino and that would be the first number, counted on the second one that would be the second number but since c had a two digit number they added the first number of the two digit number to the first domino number and that is what i did with d
hope it's correct:)
Answer:
80
Step-by-step explanation:
Basically, the first domino represents the tens place of the number and the second domino represents the units place. For a, we see that there are 3 dots on the first domino and 4 dots on the second domino so the number is 30 + 4 = 34. The same goes for b. For c, there are 6 tens and 11 ones so the number is 60 + 11 = 71. For d, there are 7 tens and 10 ones so the number is 70 + 10 = 80.
The coordinates on a map for City A are (57, 11) and those for City B are (121, 79). Note that coordinates represent miles. Find the distance between the cities to the nearest mile.
Answer:
93 miles
Step-by-step explanation:
Use the distance formula:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
Plug in the values:
d = [tex]\sqrt{(121 - 57)^2 + (79 - 11)^2}[/tex]
d = [tex]\sqrt{4096 + 4624}[/tex]
d = [tex]\sqrt{8720}[/tex]
d = 93.4
= 93 miles
Answer:
93 miles.
Step-by-step explanation:
To find this answer, we can use the distance formula: D= SQ root of (X2 - X1)^2 + (Y2-Y1)^2
Then, we have to plug in the corrdinates accordingly:
D = SQ root of (121 - 57)^2 + (79 - 11)^2
D = SQ root of (64^2) + (68^2)
D = SQ root of 4096 + 4624
D = SQ root of 8720
D = 93.3809402394
D rounded to the nearest mle is 93 miles
Hope this helps :)
The park shown is in the shape of a square. Is the perimeter rational or irrational? Area = 24,200 yd 2
Answer:
irrational
Step-by-step explanation:
A = s^2
s^2 = 24,200
[tex] s = \sqrt{24200} [/tex]
[tex] s = \sqrt{242 \times 100} [/tex]
[tex] s = \sqrt{100 \times 121 \times 2} [/tex]
[tex] s = 10 \times 11\sqrt{2} [/tex]
[tex] s = 110\sqrt{2} [/tex]
P = 4s
[tex] P = 4 \times 100 \sqrt{2} [/tex]
[tex] P = 440 \sqrt{2} [/tex]
The perimeter is irrational.
The students of a certain college were asked to choose which of six movie genres was their favorite. The pie chart below shows the distribution of the students’ answers. If there are 18,500 students at the college, how many chose Drama , Other, or Comedy ?
Answer:
12950
Step-by-step explanation:
comedy : 20% => 20 × 18500 ÷ 100 = 3700
drama : 23% => 23 × 18500 ÷ 100 = 4255
other : 27% => 27 × 18500 ÷ 100 = 4995
all together: (20 + 23 + 27) × 18500 ÷ 100 = 3700+4255+4995 = 12950
The solution is 12950.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
from the given graph, we get,
comedy : 20%
=> 20 × 18500 ÷ 100
= 3700
drama : 23%
=> 23 × 18500 ÷ 100
= 4255
other : 27%
=> 27 × 18500 ÷ 100
= 4995
so, we get,
all together: (20 + 23 + 27) × 18500 ÷ 100
= 3700+4255+4995
= 12950.
To learn more on percentage click:
brainly.com/question/13450942
#SPJ5
The volume of a cube is 1,000 cubic meters. What is the length (in meters) of one edge of the cube
Answer:
10
Step-by-step explanation:
Cube root of 1000
That's 10
Answer:
Calculator to find all the properties of a cube given any one property. ... Definition: The number of cubic units that will exactly fill a cube. Try this ... The volume of a cube is found by multiplying the length of any edge by itself twice.
In a sample, 76 people or 38% of the people in the sample said that the mayor should be prosecuted for misconduct. How many people were in the sample
Answer: 200
Step-by-step explanation:
given data:
In a sample 76 people or 38% voted the mayor to be prosecuted.
solution:
how many people were in that sample
if 38% = 76 people
therefore;
let
p = total number of people
76/p = 38/100
cross multiply both sides
38p = 7600
divide both sides by 38
38p /38 = 7600 /38
p = 200
the number of people in the sample original was 200.
Round 765 mm to the nearest 100mm
Answer:
It is over then 749mm. so 800mm.
If it is less or same as 749mm, It is 700mm.
Answer:
[tex]\huge \boxed{\mathrm{800 \ mm}}[/tex]
Step-by-step explanation:
765 mm to nearest 100 mm would be to round up 765 to nearest hundred.
765 rounded up to nearest hundred’s place would be 800.
The place after 7 is 6, which is higher or equal to 5, so we add 1 to the hundred’s place followed by zeros.
Assume that adults have IQ scores that are normally distributed with a mean 105 of and a standard deviation 20 . Find the probability that a randomly selected adult has an IQ between 88 and 122 .
Answer:
0.6048
Step-by-step explanation:
Given the following :
Assume a normal distribution :
Mean (m) = 105
Standard deviation (sd) = 20
Find the probability that a randomly selected adult has an IQ between 88 and 122 .
Z = (x - m) / sd
For IQ score of 88:
Z = (88 - 105) / 20
Z = (-17) / 20
Z = - 0.85
For IQ score of 122:
Z = (122 - 105) / 20
Z = (17) / 20
Z = 0.85
P(-0.85<Z<0.85) = P(Z < 0.85) - P(Z < - 0.85)
P(-0.85<Z<0.85) = (0.8023 - 0.1977)
P(-0.85<Z<0.85) = 0.6048
Simplify please and show steps:
Sec (x) tan (x) csc (x) cot (x) sin (x) cos (x)
Answer:
The answer is 1Step-by-step explanation:
First of all transform the expression using trigonometric identities
That's
[tex] \sec(x) = \frac{1}{ \cos(x) } [/tex]
[tex] \csc(x ) = \frac{1}{ \sin(x) } [/tex]
[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]
So we have
[tex] \frac{1}{ \cos(x) } \times \tan(x) \times \frac{1}{ \sin(x) } \times \frac{1}{ \tan(x) } \times \sin(x) \times \cos(x) [/tex]
Reduce the expression with tan x
We have
[tex] \frac{1}{ \cos(x) } \times \cos(x) \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]
Reduce the expression with cos x
That's
[tex]1 \times \frac{1}{ \sin(x) } \times \sin(x) [/tex]
Reduce the expression with sin x
We have
[tex]1 \times 1[/tex]
We have the final answer as
1Hope this helps you
The boiling point of jet fuel is 329°F. Rounded to the nearest degree, what is the temperature in degrees Celsius? Use the formula C = 59(F – 32), where C represents degrees Celsius and F represents degrees Fahrenheit. A. 165°C B. 183°C C. 201°C D. 535°C
Answer:
17523° Celsius
Step-by-step explanation:
using the formula c=59(F-32), you have to plug the 329 into F like so-
C=59(329-32)
and then you're free to calculate! first you distribute the 59 like so...
C= (59 times 329)(59 times -32) getting C=19411-1888 which u then solve again to get 17523° Celsius
Olivia has a big bag of 324 skittles.She divides the bag into thirds for herself and 2 friends.How many Skittles will each person get?
Answer:
108 skittles
Step-by-step explanation:
If she divides a bag of 324 skittles between 3 people, then we want to find a third of 324 - aka [tex]324\div3[/tex].
324 divided by 3 is 108, so each person will get 108 skittles.
Hope this helped!
Write the decimal number in numerical form: Six hundred eighty-two ten-
thousandths
Answer: 0.0682
Definition
Numerical: It's involving only numbers.
This means we will convert this number from word into numbers.
Answer:
Step-by-step explanation:
682.010
Complete the table of values for the following function.
Answer/Step-by-step explanation:
To complete the table, given the function, [tex] f(x) = \frac{1}{3}x^2 [/tex], plug in each value of x to find f(x).
Thus:
x = -6
[tex] f(-6) = \frac{1}{3}(-6)^2 = \frac{1}{3}(36) [/tex]
[tex] f(-6) = 12 [/tex]
[tex] f(-3) = \frac{1}{3}(-3)^2 = \frac{1}{3}(9) [/tex]
[tex] f(-3) = 3 [/tex]
[tex] f(0) = \frac{1}{3}(0)^2 = \frac{1}{3}(0) [/tex]
[tex] f(0) = 0 [/tex]
[tex] f(3) = \frac{1}{3}(3)^2 = \frac{1}{3}(9) [/tex]
[tex] f(3) = 3 [/tex]
[tex] f(6) = \frac{1}{3}(6)^2 = \frac{1}{3}(36) [/tex]
[tex] f(6) = 12 [/tex]
if a number is doubled, and 16 is added to it, the resault is 40. what is the number
Answer:
The number is 12
Step-by-step explanation:
Let x = number
2x+16 = 40
Subtract 16 from each side
2x+16-16 =40-16
2x = 24
Divide by 2
2x/2 =24/2
x = 12
Shirley wants to find the distance her unicycle moves on the sidewalk when the tire makes one complete revolution. If the diameter of her unicycle tire is 14 inches, find the distance the unicycle moves in one complete revolution. Use as an approximation for pi.
Answer:
44 in
Step-by-step explanation:
The circumference of the tire will be the same as the distance the unicycle moves in one complete revolution.
Find the circumference with the formula C = [tex]\pi[/tex]d, where d is the diameter
Plug in the values:
C = [tex]\pi[/tex](14)
C = approx. 44 in
You measure 46 watermelons' weights, and find they have a mean weight of 60 ounces. Assume the population standard deviation is 8.5 ounces. Based on this, construct a 99% confidence interval for the true population mean watermelon weight. Give your answers as decimals, to two places.
Answer:
A 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .
Step-by-step explanation:
We are given that you measure 46 watermelons' weights, and find they have a mean weight of 60 ounces.
Assume the population standard deviation is 8.5 ounces.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean weight = 60 ounces
[tex]\sigma[/tex] = population standard deviation = 8.5 ounces
n = sample of watermelons = 46
[tex]\mu[/tex] = population mean watermelon weight
Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.
So, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{} n} }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99
P( [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ) = 0.99
99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] , [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{} n} }[/tex] ]
= [ [tex]60-2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] , [tex]60+2.58 \times {\frac{8.5}{\sqrt{46} } }[/tex] ]
= [56.77 ounces, 63.23 ounces]
Therefore, a 99% confidence for the true population mean watermelon weight is [56.77 ounces, 63.23 ounces] .
Find the angle measure x in the figure
Answer:
x = 25
Step-by-step explanation:
Make use of the fact that the sum of angle measures in a triangle is 180°.
(2x+15)° +(3x+5)° +(x+10)° = 180°
6x +30 = 180 . . . collect terms, divide by °
x +5 = 30 . . . . . . divide by 6
x = 25 . . . . . . . . . subtract 5
_____
Check
This value of x makes the angle measures be ...
A = (x+10)° = 35°
B = (3x+5)° = 80°
C = (2x+15)° = 65°
These angles total 180°.