Answer:
0
Step-by-step explanation:
The lines of symmetry of a parallelogram must either be a diagonal of the parallelogram or must be bisectors of opposite sides. There is no way to draw such lines through a general parallelogram and have it produce mirror images on either side of the line. Thus, it has no lines of symmetry.
Jack works in a supermarket. He earns $186 a week. How much does he earn in a 52 week year?
Answer:
9672 per year
Step-by-step explanation:
Take the amount he earns per week times the number of weeks he works
186* 52
9672 per year
Answer:
$9672
Step-by-step explanation:
Jack earns $186 in 1 week.
In 52 weeks,
186 × 52 = 9672
He earns $9672.
Which polynomial function could be represented by the graph below? On a coordinate plane, a cubic function crosses the x-axis at (negative 3, 0), (0, 0), (2, 0). f(x) = x3 + x2 – 6x f(x) = x3 – x2 – 6x f(x) = –2x3 – 2x2 + 12x f(x) = –2x3 + 2x2 + 12x
Answer:
third one
Step-by-step explanation:
when
x=0, y=0
x=1, y=8
x=2 y=0
and so on.
Answer:
C. f(x)= -2x^3 -2x^2 +12x
Step-by-step explanation:
edge 2020
Find the x-intercepts for the quadratic function y= -1/2(x+3)^2 +4
Answer:
x= -3 +√2 ≈ -0.1716, and x = - 3 -2√2 ≈ -5.8284
Step-by-step explanation:
y= -1/2(x+3)² +4
For x -intercept, y = 0.
0 = - 1/2(x+3)² + 4 /*(-2)
0 = (x+3)² - 8
(x+3)² = 8
√(x+3)² = +/-√8
x+3 = +/-√8
x = - 3+/- 2√2
x= -3 +√2 ≈ -0.1716, and x = - 3-2√2 ≈ -5.8284
In a bag there are 2 red, 3 yellow, 4 green, and 6 blue marbles.
What is the probability of P (yellow or green)?
Answer:
7/15
Step-by-step explanation:
There are 15 marbles total. -->
3 of them are yellow => 4 of them are green
3 + 4 = 7
7/15
Hope This Helps!
Answer: 7/15=46%
Step-by-step explanation:
There is in total of 15 marbles
but 3 of them are yellow and 4 are green.
4+3=7
7/15=0.466...
7/15≈0.46
0.46=46%
How do you plot 2 2/3 on a number line?
Answer:
find 2 then from 2 and 3 find about 2/3 of the way from 2-3 and plot it there
Step-by-step explanation:
We can plot 2 2/3 on a number line by using the given method.
To plot 2 2/3 on a number line, we have to :
Determine the interval on the number line. For example, if the number line spans from -5 to 5, you need to identify where 2 2/3 falls within that range.
Divide the whole number part of the mixed number, which is 2, into equal intervals on the number line.
In this case, if the number line spans from -5 to 5, divide it into 10 equal intervals.
Place a point on the number line at the appropriate interval corresponding to the whole number part of the mixed number. In this case, place a point at the interval labeled 2.
Move to the right from the point corresponding to the whole number part. Now, focus on the fractional part, which is 2/3.
Divide the space between two intervals into three equal parts since the fractional part is 2/3. Each part represents 1/3 of the interval.
Count two of the three equal parts from the point corresponding to the whole number part (2). Place a point at this location.
The point you placed in step 6 represents 2 2/3 on the number line.
You can label it as 2 2/3 or use a decimal approximation if necessary.
By following these steps, you can plot 2 2/3 on a number line accurately.
To learn more on number line click:
brainly.com/question/29162579
#SPJ2
Why do you think writing is an effective way to convince others
Answer:
Considering the audience helps a writer identify the types of details and language needed in the writing. Considering the audience helps the writer identify what is important to him or her. Considering the audience allows the writer to write about what he or she wants. Knowing the audience for a particular essay is important because it determines the content that will appear in the writing. If you are arguing for a change to occur, identifying the level at which you want this change to occur and/or the people you want to persuade to help create this change (audience) is important step by step
A large restaurant is being sued for age discrimination because 15% of newly hired candidates are between the ages of 30 years and 50 years when 50% of all applicants were in that age bracket. You plan to use hypothesis testing to determine whether there is significant evidence that the company's hiring practices are discriminatory. Part A: State the null and alternative hypotheses for the significance test. (2 points) Part B: In the context of the problem, what would a Type I error be
Answer:
See explanation below.
Step-by-step explanation:
Let's take P as the proportion of new candidates between 30 years and 50 years
A) The null and alternative hypotheses:
H0 : p = 0.5
H1: p < 0.5
b) Type I error, is an error whereby the null hypothesis, H0 is rejected although it is true. Here, the type I error will be to conclude that there was age discrimination in the hiring process, whereas it was fair and random.
ie, H0: p = 0.5, then H0 is rejected.
What is the value of g(9)?
A homogeneous second-order linear differential equation, two functions y1 and y2 , and a pair of initial conditions are given below. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form
y = c1y1 + c2y2 that satisfies the given initial conditions.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
y(x)=?
Answer:
Step-by-step explanation:
Check part
[tex]y= C_1y_1 + C_2y_2 = C_1cos(7x)+C_2sin(7x)[/tex]
[tex]y'= -7 C_1sin(7x)+7C_2cos(7x)[/tex]
[tex]y"= -49 C_1cos(7x) - 49 C_2sin(7x)[/tex]
Now, replace to the original one.
[tex]y"+49 y = -49C_1cos(7x)-49 C_2 sin(7x) + 49 C_1cos(7x) +49 C_2sin(7x) = 0\\[/tex]
Done!!
Particular solution
[tex]y(0) = C_1cos(0) + C_2 sin(0) = C_1= 10[/tex]
I believe that y'(0) = 4, not y(0) anymore. Since y(0) CANNOT have two different solution.
[tex]y(0)'= -7 C_1sin(0) + 7 C_2 cos (0) = 7 C_2= -4[/tex]
[tex]C_2 = -4/7[/tex]
The last step is to put C1, C2 into your solution. You finish it.
please help
Problem:
Find P (green and odd)
Answers:
2/10
1/10
1/2
3/10
Answer:
2/10
Step-by-step explanation:
The are 10 tiles
There are 2 that are green and odd ( 3 and 5)
P ( green and odd) = green and odd/total
=2/10
=1/5
(m-3)/(7)=(m)/(m+8) Solve the proportion.
Answer: m=6, m=-4
Step-by-step explanation:
To solve this proportion, we have to cross multiply.
[tex]\frac{m-3}{7} =\frac{m}{m+8}[/tex]
[tex](m-3)(m+8)=7m[/tex]
Now that we have cross multiplied, we actually need to FOIL the left side to expand the equation.
[tex]m^2+8m-3m-24=7m[/tex]
Combine like terms.
[tex]m^2+5m-24=7m[/tex]
We can move all terms to one side and then solve for m.
[tex]m^2-2m-24=0[/tex]
We can actually factor this to:
[tex](m-6)(m+4)=0[/tex]
We set each factor equal to 0 to find m.
m-6=0
m=6
m+4=0
m=-4
In a recent household telephone survey of 2,550 adults in a certain country, 27% reported that they own at least one gun. The researchers want to estimate the true percentage of adults in that country that own at least one gun. Complete parts a through f below a. Identify the population of interest to the researchers. Choose the correct answer below.
a. The set of adults that responded to the survey
b. The set of guns in the country
c. The set of adults in the country that own a gun (CMD.
d. The set of all gun ownership status (yes/no) values for all adults in the country.
Answer
option D
Step-by-step explanation:
The population of interest to the research is the set of all gun ownership status (yes/no) values for all adults in the country. Or all total adults in a country including those that own a gym or not. This is the population of interest. The sample is the 2550 individuals adults surveyed in the household telephone survey.
What is the product of 2x + y and 5x - y + 3?
22+
py +
be +
y24
Y
Answer:
10x² + 3xy + 6x + 3y - y²
Step-by-step explanation:
Step 1: Distribute
10x² - 2xy + 6x + 5xy - y² + 3y
Step 2: Combine like terms
10x² + 3xy + 6x + 3y - y²
And we have our final answer!
How much money will I need to have at retirement so I can withdraw $60,000 year for 20 years from an account earning 8% compounded annually? a) How much do you need in your account at the beginning b)How much total money will you pull out of the account? c) How much of that money is interest?
Answer:
a) $ 589,088.84
b) $ 1,200,000
c) $ 610,911.16
Step-by-step explanation:
We have that the time is 20 years and a rate of 8%, that is to say 0.08
We solve each point:
a) How much do you need in your account at the beginning, we can calculate it using the present value:
PV = 60000 * (1 - (1 + 0.08) ^ - 20) /0.08
PV = 589088.84
In other words, you need in your account at the beginning $ 589,088.84
b) How much total money will you pull out of the account?
Total money would be:
20 * 60000 = 1200000
In other words, the total money will be $ 1,200,000
c) How much of that money is interest?
It is the subtraction of the total money and the one that you need in your account at the beginning, that is:
1200000 - 589088.84 = 610911.16
In other words, $ 610,911.16 would be in interest
help me please! which bisects the chord?
Answer:
B. 3
Step-by-step explanation:
Since you are given that chord AB's length is 8 and is bisected by segment XC, that means segment BC's length is 4 and ∠XCB is a right angle. From there, we use Pythagorean Theorem to solve for length XC:
4² + b² = 5² (Or remember 3-4-5 makes a Pythagorean triple)
c = √(5²-4²)
c = 3
(d) A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 100ml of coffee. The machine actually dispenses a mean amount of 105ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispenses into each cup is normally distributed, find the standard deviation of the amount of coffee dispensed per cup in ml.
Answer:
The standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
Step-by-step explanation:
Let the random variable X denote the amount of coffee dispensed by the machine.
It is provided that the random variable, X is normally distributed with mean, μ = 105 ml/cup and standard deviation, σ.
It is also provided that a sign on the machine indicates that each cup contains 100 ml of coffee.
And 10% of the cups contain less than the amount stated on the sign.
To compute the probabilities of a normally distributed random variable, first convert the raw score to a z-score,
[tex]z=\frac{X-\mu}{\sigma}[/tex]
This implies that:
P (X < 100) = 0.10
⇒ P (Z < z) = 0.10
The value of z for the above probability is, z = -1.28.
*Use a z-table
Compute the value of standard deviation as follows:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]-1.28=\frac{100-105}{\sigma}[/tex]
[tex]\sigma=\frac{-5}{-1.28}[/tex]
[tex]=3.90625\\\\\approx 3.91[/tex]
Thus, the standard deviation of the amount of coffee dispensed per cup in ml is 3.91.
American adults are watching significantly less television than they did in previous decades. In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day. 1. Find the probability that an average American adult watches more than 309 minutes of television per day. Answer in three decimal places. 2. Find the probability that an average American adult watches more than 2,250 minutes of television per week. Answer in three decimal places.
Answer:
1. 0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.
2. 0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the normal distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval, which is the same as the variance.
Normal distribution:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex]
In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day.
This means that [tex]\lambda = 320n[/tex], in which n is the number of days.
1. Find the probability that an average American adult watches more than 309 minutes of television per day.
One day, so [tex]\mu = 320, \sigma = \sqrt{320} = 17.89[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 309. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{309 - 320}{17.89}[/tex]
[tex]Z = 0.61[/tex]
[tex]Z = 0.61[/tex] has a pvalue of 0.729
1 - 0.729 = 0.271
0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.
2. Find the probability that an average American adult watches more than 2,250 minutes of television per week.
[tex]\mu = 320*7 = 2240, \sigma = \sqrt{2240} = 47.33[/tex]
This is 1 subtracted by the pvalue of Z when X = 2250. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2250 - 2240}{47.33}[/tex]
[tex]Z = 0.21[/tex]
[tex]Z = 0.21[/tex] has a pvalue of 0.583
1 - 0.583 = 0.417
0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.
The formula for the area of a parallelogram is A = bh,
where b is the base and h is the height.
(x-4) cm
(2x2 + 2x-6) cm
(Not drawn to scale)
Answer:
B) 2x³ – 6x² – 14x + 24 square centimetersStep-by-step explanation:
The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.
"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"
Area of a parallelogram = Base * Height.
Given the height of the parallelogram = (x-4)cm
Base = (2x² + 2x-6) cm
Area of the parallelogram = (x-4)cm * (2x² + 2x-6) cm
Area of the parallelogram = (x-4)(2x²+2x-6)
Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24
= 2x³+2x²-8x²-6x-8x+24
= (2x³-6x²-14x+24)cm²
The numerator of a rational number is greater than its denominator by 3. If the new number becomes 13/4 when the numerator is tripled and the denominator is decreased by23, find the original number.
Answer:
Step-by-step explanation:
Let x represent the numerator and y represent the denominator.
The numerator of a rational number is greater than its denominator by 3. It means that
x = y + 3
If the new number becomes 13/4 when the numerator is tripled and the denominator is decreased by 23, it means that
3x/(y - 23) = 13/4
Cross multiplying, it becomes
3x × 4 = 13(y - 23)
12x = 13y - 299- - - - - - - - - - -1
Substituting x = y + 3 into equation 1, it becomes
12(y + 3) = 13y - 299
12y + 36 = 13y - 299
13y - 12y = 36 + 299
y = 335
x = y + 3 = 335 + 3
x = 338
The original number is 338/335
I earn $20.00 in 4 hours. At this rate, how much will i earn in 28 hours (show your work)
Answer:
140$
Step-by-step explanation:
4 hours = 20
28 hours divided by 4 is 7
7 x 20 = 140
Find the sum of the first 100 terms of the arithmetic sequence with the first term 2 and the common difference 5. plz only answer if you actually have read the question and know the answer.
Answer:
25,200
Step-by-step explanation:
To find the sum of an arithmetic series, one can use the formula for an arithmetic series: n×[tex]\frac{(term 1)+(final term)}{2}[/tex]=the sum of the series.
To find the final term we need to use the rule: the first term is 2, so you will have to add on two at the end, and then each term is 5 larger than the last, so if you want to quickly calculate the 100th term you can multiply (which is basically just fast addition). The formula for the 100th term is 5(100)+2=502.
Now you have all of the necessary parts for the sum of the series formula: n=100, first term=2, final term=502.
100×[tex]\frac{2+502}{2}[/tex]=100×[tex]\frac{504}{2}[/tex]=100×252=25,200.
Answer:
24950
Step-by-step explanation:
100th term is 497 and we then use the gause method which is (1+497)*497/2
A sample of 26 offshore oil workers took part in a simulated escape exercise, and their escape time (unit: second) were observed. The sample mean and sample standard deviation are 370.69 and 24.36, respectively. Suppose the investigators had believed a priori that true average escape time would be at most 6 minutes. Does the data contradict this prior belief
Answer:
[tex]t=\frac{370.69-360}{\frac{24.36}{\sqrt{26}}}=2.238[/tex]
The degrees of freedom are given by:
[tex] df = n-1= 26-1=25[/tex]
And the p value would be:
[tex]p_v =P(t_{25}>2.238)=0.0172[/tex]
If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change
Step-by-step explanation:
Information given
[tex]\bar X=370.69[/tex] represent the sample mean
[tex]s=24.36[/tex] represent the sample standard deviation
[tex]n=26[/tex] sample size
[tex]\mu_o =6*60 =360 s[/tex] represent the value to verify
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to check if the true mean is at most 360 seconds, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 360[/tex]
Alternative hypothesis:[tex]\mu > 360[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
We can replace in formula (1) the info given like this:
[tex]t=\frac{370.69-360}{\frac{24.36}{\sqrt{26}}}=2.238[/tex]
The degrees of freedom are given by:
[tex] df = n-1= 26-1=25[/tex]
And the p value would be:
[tex]p_v =P(t_{25}>2.238)=0.0172[/tex]
If we use a 5% of significance level we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 360 second or 6 minutes. We need to be careful since if we use a significance level of 1% the result change
Researchers are conducting a study in an attempt to establish a linear relationship between the number of online music video views and the number of guitar sales. A computer output for regression is shown and is based on a sample of seven observations.
Predictor Coeff St. Dev t Ratio p-Value
Constant 7.85671094 1.316226455 5.969118 0.001889
Music Video Views 0.094781123 0.027926367 3.393965 0.019378
What represents the 99% confidence interval for the slope of the regression line?
Answer:
[tex] 0.094781123 - 4.032* 0.027926367 =-0.0178180[/tex]
[tex] 0.094781123 + 4.032* 0.027926367 =-0.2073802[/tex]
Step-by-step explanation:
For this case we have the following output:
Predictor Coeff St. Dev t Ratio p-Value
Constant 7.85671094 1.316226455 5.969118 0.001889
Music Video Views 0.094781123 0.027926367 3.393965 0.019378
For this case the slope of the regression we have:
[tex] \hat b = 0.094781123[/tex]
We assume that the standard error is:
[tex] SE_b = 0.027926367[/tex]
The confidence interval would be given by:
[tex] \hat b \pm t_{n-2} SE_b[/tex]
The degrees of freedom are given by:
[tex] df= 7-2=5[/tex]
And the critical value using a significance level of [tex]\alpha=0.01[/tex] is:
[tex] t_{\alpha/2} = 4.032[/tex]
And replacing we got;
[tex] 0.094781123 - 4.032* 0.027926367 =-0.0178180[/tex]
[tex] 0.094781123 + 4.032* 0.027926367 =-0.2073802[/tex]
Pls answer either of these questions with step by step explanation
Answer:
C and B
Step-by-step explanation:
31. Thrice means 3 times as much. Let's call Rahul and Shivam's present ages r and s respectively. We can write:
r = 3s
r + 8 = 1 + (s + 8) * 2
Simplifying the second equation gives us r + 8 = 2s + 17. When we substitute r = 3s into the second equation we get 3s + 8 = 2s + 17 which gives us s = 9. This means r = 9 * 3 = 27 so Rahul's age 8 years before the present is 27 - 8 = 19.
32. Let's call Ravi and Kishan's ages r and k. We can write:
r + k = 69
r - 8 = 2(k - 8) - 4
Rewriting the first equation gives us r = -k + 69 and when we substitute this into the second equation we get -k + 69 - 8 = 2k - 16 - 4. Solving for k we get k = 27 which means r = 42. 42 - 27 = 15.
The table shows the battery lives, in hours, of ten Brand A batteries and ten Brand B batteries.
Battery Life (hours)
Brand A
Brand B
22.5 17.0 21.0 23.0 22.0 18.5 22.5 20.0 19.0
20.0 19.5 20.5 16.5 14.0 17.0 11.0 19.5 21.0
23.0
12.0
Which would be the best measure of variability to use to compare the data?
Only Brand A data is symmetric, so standard deviation is the best measure to compare variability.
Only Brand B data is symmetric, so the median is the best measure to compare variability.
Both distributions are symmetric, so the mean is the best measure to compare variability.
Both distributions are skewed left, so the interquartile range is the best measure to compare variability
Answer:
D. Both distributions are skewed left, so the interquartile range is the best measure to compare variability.
Step-by-step explanation:
Plotting the data roughly shows that the data is skewed to the left. In other words, data is skewed negatively and that the long tail will be on the negative side of the peak.
In such a scenario, interquartile range is normally the best measure to compare variations of data.
Therefore, the last option is the best for the data provided.
please mark me brainliest :)
Find the center (h,k) and radius r of the circle. Graph the equation. x^2 + y^2 - 2x - 10y + 1 = 0
Answer:
Center: (1, 5)
Radius: r = 5
Step-by-step explanation:
Step 1: Rewrite equation
x² - 2x + y² - 10y = -1
Step 2: Complete the Square (x2)
x² - 2x + 1 + y² -10y + 25 = -1 + 1 + 25
(x - 1)² + (y - 5)² = 25
Step 3: Find answers
Center = (h, k)
(1, 5) as Center
Radius = r
r² = 25
r = 5
Answer: Center = (1, 5)
Radius = 5
Step-by-step explanation:
The standard form for a circle is: (x - h)² + (y - k)² = r² where
Center = (h, k)Radius = rFirst, group the x's and group the y's in order to complete the square.
x² - 2x + y² - 10y = -1
↓ ↓
(-2/2)²=1 (-10/2)²=25
Add those values to BOTH sides:
x² - 2x + 1 + y² - 10y + 25 = -1 + 1 + 25
Rewrite the left side as perfect squares and simplify the right side.
(x - 1)² + (y - 5)² = 25
We end up with (h, k) = (1, 5) this is the center
and r² = 25 --> r = 5 this is the radius
To graph the circle, place an x at the center (1, 5). Plot a point 5 units (the radius) to the right of the center, another point 5 units up from the center, a third point 5 units left from the center, and a fourth point 5 units down from the center. "Connect the dots" to create a circle.
What is the value of x?
A-17
B-20
C-28
D-38
Answer:
B
Step-by-step explanation:
Let's use the Pythagorean Theorem.
x² + 21² = 29²
x² + 441 = 841
x² = 400
x = 20
A game popular in Nevada gambling casinos is Keno, which is played as follows: Twenty numbers are selected at random by the casino from the set of numbers 1 through 80. A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house. The payoff is a function of the number of elements in the player’s selection and the number of matches. For instance, if the player selects only 1 number, then he or she wins if this number is among the set of 20, and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is , it is clear that the "fair" payoff should be $3 won for every $1 bet). When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20.A) What would be the fair payoff in this case? Let P, k denote the probability that exactly k of the n numbers chosen by the player are among the 20 selected by the house. B) Compute Pn, k.C) The most typical wager at Keno consists of selecting 10 numbers. For such a bet, the casino pays off as shown in the following table. Compute the expected payoff.
The missing part in the question;
and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is [tex]\dfrac{1}{4}[/tex]........
Also:
For such a bet, the casino pays off as shown in the following table.
The table can be shown as:
Keno Payoffs in 10 Number bets
Number of matches Dollars won for each $1 bet
0 - 4 -1
5 1
6 17
7 179
8 1299
9 2599
10 24999
Answer:
Step-by-step explanation:
Given that:
Twenty numbers are selected at random by the casino from the set of numbers 1 through 80
A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house
Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.
Let assume the random variable X has a hypergeometric distribution with parameters N= 80 and m =20.
Then, the probability mass function of a hypergeometric distribution can be defined as:
[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]
Now; the probability that i out of n numbers chosen by the player among 20 can be expressed as:
[tex]P(X=k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]
Also; given that ; When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20
So; n= 2; k= 2
Then :
Probability P ( Both number in the set 20) [tex]=\dfrac{(^{20}_2)(^{60}_{2-2})}{(^{80}_2)}[/tex]
Probability P ( Both number in the set 20) [tex]= \dfrac{20*19}{80*79}[/tex]
Probability P ( Both number in the set 20) [tex]=\dfrac{19}{316}[/tex]
Probability P ( Both number in the set 20) [tex]=\dfrac{1}{16.63}[/tex]
Thus; the payoff odd for [tex]=\dfrac{1}{16.63}[/tex] is 16.63:1 ,as such fair payoff in this case is $16.63
Again;
Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.
Let assume the random variable X has a hypergeometric distribution with parameters N= 80 and m =20.
The probability mass function of the hypergeometric distribution can be defined as :
[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]
Now; the probability that i out of n numbers chosen by the player among 20 can be expressed as:
[tex]P(n,k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]
From the table able ; the expected payoff can be computed as shown in the attached diagram below. Thanks.
"Flip a coin; if it is heads, pick item A; if it is tails, flip the coin again; this time, if it is heads, choose B; if it is tails, choose C. Explain why this is a probability sample but not a simple random sample"
Answer:
It is a probability sample because it utilizes some form of random selection. It is not a simple random sample because there is not an equal possibility of A, B, or C.
Step-by-step explanation:
Identify an equation in point-slope form for the perpendicular to y= -1/2x+11 that passes through (4, -8). A. y - 4 = 2(x + 8) B. y - 8 = 1/2(x+4 C. y + 8 = 2(x - 4) D. y + 8 = 1/2(x - 4)
Answer:
C.
Step-by-step explanation:
Perpendicular ⇒ So the slope will be the negative reciprocal to this slope
Slope = m = 2
Point = (x,y) = (4,-8)
So, x = 4, y = -8
Putting in the slope-intercept form
[tex]y = mx+b[/tex]
-8 = (2)(4) + b
b = -8-8
b = -16
Now we'll put it in the slope-intercept form
y = 2x-16
=> y = 2x-8-8
=> y+8 = 2(x-4)