To the nearest whole number it would be 35
Step-by-step explanation:
4x2 - 14x + 6
x3 - 7x2 + 12x
What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common
factors.
Answer:
Answer is given below.
Step-by-step explanation:
let us solve the numerator first
=4x²-14x+6
=2(2x²)+2(-7x)+2(3)
= GCF of the terms of the numerator is 2.
denominator
x³-7x²+12x
x(x²)+x(-7x)+x(12)
GCF of the terms of the denominator is x.
factorise the numerator
4x²-14x+6
4x²-2x-12x + 6 (by splitting the middle term; the numbers should produce the product 4*6 and when the no.s are added they should give -14)
(4x²-2x) + (-12x+6)
2x(2x-1) -6(2x-1)
(2x-6)(2x-1)
factors are
(2x-6), (2x-1)
denominator
this can also be done by splitting the middle term
x³-7x²+12x
x³-3x²-4x²+12x
(x³-3x²) + (-4x²+12x)
x²(x-3) -4x(x-3)
(x²-4x)(x-3)
factors are
(x²-4x), (x-3)
Solve 3(xx)+x-5 using the first principle
Answer:
[tex]3x^2+x-5[/tex]
Step-by-step explanation:
[tex]3\left(xx\right)+x-5[/tex]
Remove parenthesis
[tex]3xx+x-5[/tex]
Multiply [tex]x \times x=x^2[/tex]
[tex]3x^2+x-5[/tex]
Answer:
3x²+x-5
Step-by-step explanation:
= 3(xx)+x-5
According to the rule, when bases are same powers are to be added.
= 3(x¹x¹)+x-5
= 3(x¹⁺¹)+x-5
= 3x²+x-5
Autism is a serious and lifelong disability that is characterized by a severely decreased ability to engage in communication and social interaction. In 1998 citizens in a New Jersey town were concerned about the number of children diagnosed with autism, and a study was undertaken to establish the prevalence in the community. Data from the study are reported below:
Numbers of Children Diagnosed with Autistic Disorder
Age Category (y) Diagnosed with Autistic Disorder Number of Children in Population
3-5 19 3479
6-10 17 5417
Required:
a. Calculate the prevalence rate of autism for these children for the two age categories.
b. Convert the prevalence rate to a rate per 1,000
Answer:
a. Calculate the prevalence rate of autism for these children for the two age categories.
3-5: prevalence rate = 0.55%6-10: prevalence rate = 0.31%b. Convert the prevalence rate to a rate per 1,000
3-5: prevalence rate = 5.5 per thousand6-10: prevalence rate = 3.1 pér thousandStep-by-step explanation:
Generally prevalence is calculated using the following formula:
(number of people with autism / number of people measured) x 100%
age category
3-5: prevalence rate = (19/3,479) x 100% = 0.55%
6-10: prevalence rate = (17/5,417) x 100% = 0.31%
if you want to convert to a rate per 1,000, allyou need to do is multiply by 1,000 instead of 100
3-5: prevalence rate = (19/3,479) x 1,000 = 5.5
6-10: prevalence rate = (17/5,417) x 1,000 = 3.1
Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally
symmetric if the grid can be rotated 90, 180, or 270 degrees to achieve the same pattern.
Two colorings are called rotationally distinct if neither can be rotated to match the
other. How many rotationally distinct ways are there for Sam to color the grid such
that the colorings are not rotationally symmetric?
Answer:
65,280
Step-by-step explanation:
Consider the 4×4 grid ...
[tex]\left[\begin{array}{cc}a&b\\d&c\end{array}\right][/tex]
where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.
The same will be true of 270° rotational symmetry, for the same reason.
__
For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)
__
The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...
65,536 -256 = 65,280 . . . . colorings not rotationally symmetric
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
2 is the answer
Step-by-step explanation:
area=1/2*base*height
as height = 2*base and area =4 it comes
1/2*2*base*base=4
so base *base=4
so base = 2
A box contains 16 transistors, 4 of which are defective. if 4 are selected at random, find the probability that
a. all are defective.
b. none are defective.
Answer:
(a)0.0005
(b)0.2720
Step-by-step explanation:
Total Number of Transistors = 16
To find the probability that 4 selected at random are defective (or non-defective), we find the probability of the 1st, 2nd, 3rd, and 4th defective (or non-defective) items in that order, Note that the selection is without replacement.
(a)Probability that all are defective
Number of Defective Transistors =4
P(all are defective) [tex]=\dfrac{4}{16} \times \dfrac{3}{15} \times \dfrac{2}{14} \times \dfrac{1}{13}[/tex]
=0.0005
(b)Probability that none are defective
Number of Non-Defective Transistors =16-4=12
P(none are defective) [tex]=\dfrac{12}{16} \times \dfrac{11}{15} \times \dfrac{10}{14} \times \dfrac{9}{13}[/tex]
=0.2720
winnie and kevin like to create their own triathlon courses to challenge each other. last weekend, winnie created a course that included a swim of 3/4 of a mile, a bike ride of 57/4 miles and a run of 13/4 miles. how long was the course winnie created?
Discover the area of a circle with a diameter of 17 feet ?
Answer: A≈226.98 ft²
Step-by-step explanation:
The formula for area of a circle is A=πr². The formula doesn't include diameter , but we can certainly find the radius from the diameter.
d=2r
17=2r
r=17/2=8.5 ft
Now that we have the radius, we can plug it in to area formula.
A=πr²
A=π(8.5ft)²
A=π72.25ft²
A≈226.98 ft²
Area of a circle: A = πr²
Get the radius by dividing the diameter by 2.
17 / 2 = 8.5
Now, solve with the given values.
A = π(8.5)²
A = 72.25π
A = 226.865
Therefore, the area is 226.865ft³
Best of Luck!
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
The function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem. (6, 10); The vertex represents the maximum profit. (6, 10); The vertex represents the minimum profit. (8, 4); The vertex represents the minimum profit. (8, 4); The vertex represents the maximum profit.
Answer:
A.
f is a quadratic function, which means it's graph is a parabola.
Notice that the coefficient of is negative, so the parabola opens downwards.
the x-coordinate of a parabola is always determined by the formula:
where a is coefficient of the term, and b is the coefficient of the x term.
Thus, x-coordinate of the vertex of the graph of f is :
the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.
The vertex is (8, 4).
This means that the maximum daily profit is when exactly 8 candles are sold.
B.
The x-intercepts are the values of x such that f(x)=0,
so to find these values we solve:
complete the square:
so x-8=2 or x-8=-2
the roots are x=10 and x=6, are the roots.
This means that when the shop sells exactly 6 or 10 candles, it makes no profit.
Answer: d (8, 4); The vertex represents the maximum profit.
Explanation: i got it right on the test
Please answer this correctly
Answer:
10.71
Step-by-step explanation:
The arc length is
2*3*3.14/4 = 4.71
Add to the two side lengths to get the perimeter
4.71+3+3 = 10.71
[tex]answer = 10.71 \: millimeters \\ solution \\ radius = 3 \: millimeters \\ perimeter \: of \:quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 3}{4} + 2 \times 3\\ = \frac{18.84}{4} + 6 \\ = \frac{18.84 + 6 \times 4}{4} \\ = \frac{18.84 + 24}{4} \\ = \frac{42.84}{4} \\ = 10.71 \: millimeters \\ hope \: it \: helps[/tex]
please please solve for x
Answer:
Step-by-step explanation:
This equation is an example of:
A. Dividing two binomials
B. FOIL
C. Vertical multiplication
D. Complex conjugates
Answer:
B. FOIL
Step-by-step explanation:
FOIL stands for Firsts, Outsides, Insides, and Lasts
This is a mnemonic to help you to remember how to multiply two binomials
From the image, we can see that the on the right side of the equals,
[tex](x)(-5x^2)[/tex] is the product of the firsts of the binomials
[tex](x)(x)[/tex] is the product of the outsides of the binomials
[tex](-2)(-5x^2)[/tex] is the product of the insides of the binomials
[tex](-2)(x)[/tex] is the product of the lasts of the binomials.
Answer:
B. FOIL
Step-by-step explanation:
"FOIL" is an acronym for First, Outer, Inner, Last. It refers to the relative positions of the terms in the multiplication of binomials.
The given equation shows the result of such a multiplication. It is an example of the application of FOIL.
A national organization that conducts research on the cost and quality of health care in the U.S. reported that, in 2012, U.S. families spent an average of $9,590 on health care expenses. Suppose you decide to test whether the average in 2015 is greater than the average in 2012. After conducting the appropriate statistical test, you find a P-value of 0.022. If the level of significance is 0.05, which of the following is the best interpretation of the P-value?
a. The P-value of 0.022 indicates that there is a 2.2% chance that the 2015 average is greater than the average amount spent in 2012.
b. The P-value of 0.022 provides weak evidence that the average in 2015 average is greater than the average amount spent in 2012.
c. The P-value of 0.022 provides strong evidence that the 2015 average is greater than the average amount spent in 2012.
d. The P-value of 0.022 indicates that there is a very low probability that the 2015 average is different than average amount spent in 2012.
Answer:
c. The P-value of 0.022 provides strong evidence that the 2015 average is greater than the average amount spent in 2012.
Step-by-step explanation:
The P-value indicates the probability of having this sample results given that the null hypothesis is true. If the P-value is low enough (smaller than the significance level), we have evidence to reject the null hypothesis, as there is little chance the null hypothesis is true and this sample result is due to chance.
How would I solve this problem. A researcher wishes to estimate the mean height of women aged between 60 and 65 in the U.S. She desires a margin of error of 0.3 inches. Past studies suggest that a population standard deviation of 3.3 inches is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
Answer:
465
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
Assuming 95% confidence, CV = z = 1.96.
Standard error is:
SE = σ / √n
SE = 3.3 / √n
Given margin of error of 0.3:
0.3 = 1.96 × 3.3 / √n
n = 465
A bucket that has a mass of 30 kg when filled with sand needs to be lifted to the top of a 30 meter tall building. You have a rope that has a mass of 0.3 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 15 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building.
Answer:
765 J
Step-by-step explanation:
We are given;
Mass of bucket = 30 kg
Mass of rope = 0.3 kg/m
height of building= 30 meter
Now,
work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand
Or W = W1 + W2
Work done in lifting the rope is given as,
W1 = Force x displacement
W1 = (30,0)∫(0.2x .dx)
Integrating, we have;
W1 = [0.2x²/2] at boundary of 30 and 0
W1 = 0.1(30²)
W1 = 90 J
work done in lifting the sand is given as;
W2 = (30,0)∫(F .dx)
F = mx + c
Where, c = 30 - 15 = 15
m = (30 - 15)/(30 - 0)
m = 15/30 = 0.5
So,
F = 0.5x + 15
Thus,
W2 = (30,0)∫(0.5x + 15 .dx)
Integrating, we have;
W2 = (0.5x²/2) + 15x at boundary of 30 and 0
So,
W2 = (0.5 × 30²)/2) + 15(30)
W2 = 225 + 450
W2 = 675 J
Therefore,
work done lifting the bucket (sand and rope) to the top of the building,
W = 90 + 675
W = 765 J
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
Question 2 of 10
2 Points
What is the sum of the rational expressions below?
2x+3/3x+x/x+1
Answer:
5x^2+5x+3/3x^2+3x
Step-by-step explanation:
A student is getting ready to take an important oral examination and is concerned about the possibility of having an "on" day or an "off" day. He figures that if he has an on day, then each of his examiners will pass him, independently of one another, with probability 0.8, whereas if he has an off day, this probability will be reduced to 0.4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student believes that he is twice as likely to have an off day as he is to have an on day, should he request an examination with 3 examiners or with 5 examiners?
Answer:
The students should request an examination with 5 examiners.
Step-by-step explanation:
Let X denote the event that the student has an “on” day, and let Y denote the
denote the event that he passes the examination. Then,
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
The events ([tex]Y|X[/tex]) follows a Binomial distribution with probability of success 0.80 and the events ([tex]Y|X^{c}[/tex]) follows a Binomial distribution with probability of success 0.40.
It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,
[tex]P(X)=2\cdot P(X^{c})[/tex]
Then,
[tex]P(X)+P(X^{c})=1[/tex]
⇒
[tex]2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}[/tex]
Then,
[tex]P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}[/tex]
Compute the probability that the students passes if request an examination with 3 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}[/tex]
[tex]=0.715[/tex]
The probability that the students passes if request an examination with 3 examiners is 0.715.
Compute the probability that the students passes if request an examination with 5 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}[/tex]
[tex]=0.734[/tex]
The probability that the students passes if request an examination with 5 examiners is 0.734.
As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.
Determine the least number of patties that will share equally among groups og 6, 9, 12
Answer:
72.
Step-by-step explanation:
Given a group of 6, 9 and 12.
We are to determine the least number of patties that will be shared equally among the groups.
This we do by determine the Least common multiple of the three numbers.
[tex]6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72[/tex]
Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.
En una encuesta sobre preferencias entre los deportes Tenis (T), Surf (S) y Golf (G) se sabe que:
90 personas fueron encuestadas
15 personas prefieren Golf
10 no prefieren ninguno de estos deportes
ninguno de los que prefiere los deportes Tenis ó Surf prefieren Golf
30 prefieren sólo Surf
20 prefieren sólo Tenis
a) ¿Cuántas personas prefieren dos de estos deportes?
b) ¿Cuántos prefieren sólo uno de estos deportes?
Answer:
a) 15
b) 65
Step-by-step explanation:
Adjunto se encuentra el diagrama asociado a esta situación. Comenzamos por ubicar aquellas afirmaciones que relacionan todos los deportes. Sabemos que 10 personas no prefieren ningún deporte. Luego, ubicamos 10 fuera de los conjuntos mostrados. Sabemos que 30 personas prefieren sólo surf y 20 personas prefieren sólo Tenis. Es decir, hay 30 personas en el conjunto S que no intersectan a los otros dos. En este momento, hemos ubicado a 60 personas. Nos hacen falta 30 personas. La afirmación "15 personas prefieren Golf" significa que la suma de los números dentro del conjunto G es 15. La afirmación "ninguno de los que prefieren los deportes Tenis o Surf prefieren el golf. Es decir, que la intersección de G con T y con S son vacías. Es decir que las 15 personas que prefieren golf, lo prefieren únicamente. Esto nos deja con 15 personas por ubicar. El único lugar donde podemos ubicar a dichas 15 personas es en en la intersección de T y S.
a). ¿cuántas personas prefieren dos de estos deportes? Por el diagrama, son aquellas personas que prefieren Tenis o Surf. Es decir, 15.
b) ¿Cuánto prefieren sólo uno de estos deportes? Es la suma de aquellos que prefieren sólo un deporte. Es decir, sólo G, sólo T o sólo S. Es decir 15+20+30 = 65.
Consider the scatterplot above. Write a sentence explaining the meaning of the value of the slope for this linear model. The is an average of per year .
Answer:
Slope: The percent that voted falls by 0.1271 units per year.
Step-by-step explanation:
The slope of a regression line represent the average rate of change in the dependent variable (y) based upon the changes in the independent variable (x).
In this case the regression equation provided is:
y = -0.1271 x + 307.53
The slope of the line is -0.1271.
The dependent variable is the percent that voted and the independent variable is the year.
The slope of -0.1271 indicates that every year, on average, the percent that voted decreases by 0.1271 units.
Or the percent that voted falls by 0.1271 units per year.
f(n) = 5n for n = 2
Answer:
10
Step-by-step explanation:
F(2) = 5 * 2 = 10
Answer:
f(2) =10
Step-by-step explanation:
f(n) = 5n
Let n=2
f(2) = 5*2
f(2) =10
What is the measure of <6?
Answer: Choice B. 54degrees
Step-by-step explanation:
Angles 1 4 5 8 are equal and angles 2 3 6 7 are also equal. These two sets of angles of supplementary(you‘d get 180 by adding them).
so
13x+9=180-(5x+9)
by simplifying the equation youll get
18x+18=180
x=9
so angle 7(and therefore angle 6) equals
5*9+9=54
gary mixes a solution using two types of concentration of sale: .70 gallons of 5% and .30 gallons of 22% salt. what is the concentration of the mixed solutions
Answer:
10.1%
Step-by-step explanation:
The first thing we should do is calculate the total volume of the solution when mixing them would be:
0.7 + 0.3 = 1
Now, we have that the resulting concentration (x) would be equal to the sum of the multiplications between the volumes and the concentrations to be mixed, as follows:
x * 1 = 0.7 * 0.05 + 0.3 * 0.22
x = 0.035 + 0.066
x = 0.101
That is, the concentration of the resulting mixture would be 10.1% (0.101 * 100)
Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, x3 = 188, x5 = 6.6, and x6 = 10. Use these data to predict x4 (advertising costs) and find an 80% confidence interval for your prediction. (Use 2 decimal places.)
Answer:
The advertising cost, X₄ = 5.626 million
The 80% confidence limits for X₄ is (5.041 , 6.100)
The 80% prediction limits for X₄ is (4.048 , 7.094)
Step-by-step explanation:
Using MINITAB
The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆
Predictor Coef SE Coef T P
Constant 4.142 1.626 2.55 0.019
X₁ 0.043089 0.009466 4.55 0.000
X₂ -0.7998 0.2515 -3.18 0.005
X₃ 0.000590 0.004221 0.14 0.890
X₅ -0.6606 0.1542 -4.28 0.000
X₆ 0.0574 0.1254 0.46 0.652
S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 5 345.966 69.193 59.42 0.000
Residual Error 21 24.454 1.164
Total 26 370.420
Source DF Seq SS
X₁ 1 309.464
X₂ 1 8.699
X₃ 1 5.994
X₅ 1 21.566
X₆ 1 0.244
Unusual Observation
Obs X₁ X₄ Fit SE Fit Residual St Resid
17 398 5.500 7.714 0.641 -2.214 -2.55 R
27 400 7.000 7.366 1.025 -0.336 -1.00 X
Where R is observation with a large standardized residual.
Where X is observation whose X values give it large influence.
Predicted values for new Observations
New
Obs Fit SE Fit 80% Cl 80% Pl
1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)
Values of Predictors for New Observations
New
Obs X₁ X₂ X₃ X₅ X₆
1 163 2.40 188 6.60 10.0
∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)
Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the standard deviation of the speeds in Excel file Q-14.xlsx.
Answer and Step-by-step explanation: Standard Deviation is the measure of how diferent a number is from the mean of the data set. It is the spread of a data set. To calculate it manually:
1) Find the mean of the data set. Mean, represented by μ, is the sum of all the values divided by the total number of elements forming the set;
2) Subtract each number with the Mean and square the result;
3) Add the differences and divide it by the total number of elements of the set;
4) Take the square root of the result and that is the Standard Deviation.
The calculations can be done by a calculator like Excel:
1) In each cell of a same column, write the data you want to know the deviation.
2) On the last cell, write: =stdev.p(A1:A10) or =stdev.s(A1:A10).
3) Press Enter. The deviation will appeared on the same cell.
The function STDEV.P is used when the data represents the entire population, whereas STDEV.S is used when the data is for a sample of the population. Inside the parenthesis, put the cells where your data is. For example, if you put your data in the column A, from cell 1 to cell 10, you write like it's written above.
You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.
A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.
Answer:
Step-by-step explanation:
Given that :
The probability of winning is 0.8
i.e P(winning) = 0.8
Then P(losing) = 0.2
a) Y ~ Geometric distribution
[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]
b) Y ~ Negative Binomial Distribution
[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]
c) Y ~ Binomial Distribution;
n = 100 ; P = 0.8
[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]
Order the numbers from greatest to least.
4. 234,358; 23,208; 23,098
Answer:
23,098; 23,208 ; 234,358
Step-by-step explanation:
Hope this helps