The mean of the data is given by the equation M = 679.3846 and the standard deviation σ = 34.1535
What is Standard Deviation?The standard deviation refers to a measurement of the data dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Standard Deviation is calculated by
Each number's deviation from the mean must be determined, and then squared.
Next, add up all of these values.
Divide the result by the quantity of numbers.
Then calculate its square root.
σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²
Given data ,
Let the data be represented as Set A
Now , the value of set A is
Set A = { 688 , 711 , 625 ,701 , 688 , 667 , 694, 630, 547, 703, 688, 697, 703, 656, 677, 700, 702, 688, 691, 664, 688, 679, 708, 699, 667, 703 }
The mean of the sample data = Sum of all the values / number of values
The mean M = 17664 / 26
The mean M = 679.3846
Now , the standard deviation is calculated by
σ = √ ( 1/N ) ( ∑₁ⁿ ( x₁ - μ )²
Substituting the values in the equation , we get
The standard deviation σ = √ ( 30328.153846154 / 26 )
The standard deviation σ = √ ( 1166.4674556213 )
The standard deviation σ = 34.1535
Hence , the standard deviation is 34.1535
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A ball bounces to a height of 5.2 feet on the first bounce. Each subsequent bounce reaches a height that is 83% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to thousandths place.
1.680 ft
2.048 ft
2.468 ft
4.316 ft
Answer:
Below
Step-by-step explanation:
5.2 * .83 second
(5.2 * .83) * .83 = 5.3 * .83^2 third
.
= 5.2 ( .83)^4 Fifth = 2.468 ft
An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below.
1) From Given output confidence level, is 95% level of significance = 1-0.95
10.05
How to calculate the value2) null hypothesis : M = 150000
=
3) Alternative hypothesis Ha: [M> 150000]
4) since P value = 0.033 is less than d=0.05 Reject null hypothesis.
5) There is sufficient evidence to conclude that the mean life of transmissions is over 1500 comity
6) 95% CI = â ± E
-1519±1.129
=(151.2-1.129, 151.2+1.129)
=(150.071, 152.329)
7) Since M=150 fall out side of the C. We Shoul retect null hypothesis.
8) The null hypothesis value fall outside of the Confidence Interval.
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x = [ √(a+2) + √(a-2) ]/[ √(a+2) - √(a-2) ], then a =? the correct answer is a = x+(1/x). explain
how.
The inverse of the radical equation x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)] is the equation a = x + 1 / x. (Correct choice: A)
How to clear a variable in a radical equation
In this problem we find the case of a radical equation in explicit form, that is, a variable x only in terms of a variable a, and we need to obtain the inverse of the function, that is, an expression in terms of a variable x. This problem can be solved by algebra properties.
First, write the original equation:
x = [√(a + 2) + √(a - 2)] / [√(a + 2) - √(a - 2)]
Second, rationalize the expression:
x = [[√(a + 2) + √(a - 2)] · [√(a + 2) + √(a - 2)]] / [[√(a + 2) - √(a - 2)] · [√(a + 2) + √(a - 2)]]
x = [√(a + 2) + √(a - 2)]² / [(a + 2) - (a - 2)]
x = [a + 2 - 2 ·√(a² - 4) + a - 2] / 4
x = [a - √(a² - 4)] / 2
2 · x = a - √(a² - 4)
Third, eliminate the square root operator by algebra properties:
√(a² - 4) = a - 2 · x
a² - 4 = (a - 2 · x)²
Fourth, find the solution to the expression:
a² - 4 = a² - 4 · x · a + 4 · x²
- 4 = - 4 · x · a + 4 · x²
1 = x · a - x²
1 + x² = x · a
a = (1 + x²) / x
a = 1 / x + x
a = x + 1 / x
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3ab2 +1
3a²b-1
(a = 2 ; b = -2)
EVALUATE THE EXPRESSION
Answer:
3ab2+1 = -23
3a^2b-1 =-25
Step-by-step explanation:
A line with a slope of 7 passes through the points (-7, 5) and (g, -2). What is the value of g?
g=
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{g}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{g}-\underset{x_1}{(-7)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ 7 }\implies \cfrac{-7}{g+7}=7\implies -7=7(g+7) \\\\\\ \cfrac{-7}{7}=g+7\implies -1=g+7\implies \boxed{-8=g}[/tex]
Why we use Permutation to find the number of ways of something can be arranged when order matters. While use Combination when order does not matter.
The permutation formula is used when the order matters as it does not remove the combinations with the same elements and different order from the equation.
For the combination formula, the term x! is removed, as it removes all the combinations with the same elements but different order.
What is the combination formula?The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
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Find the value of sin D rounded to the nearest hundredth, if necessary.
The value of the trigonometric equation sin D = 0.923
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as ΔBCD
Now , the measure of BC = 24
The measure of side CD = 10
So , the measure of hypotenuse BD = √ ( BC )² + ( CD )²
Substituting the values in the equation , we get
The measure of BD = √ ( 576 ) + 100
The measure of BD = √ ( 676 )
The measure of BD = 26
Now , from the trigonometric relations ,
sin θ = opposite / hypotenuse
Substituting the values in the equation , we get
sin D = 24 / 26
On simplifying the equation , we get
sin D = 0.923
Hence , the equation is sin D = 0.923
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could you please help me find out how to add m+x
Answer:
i got u i have your email
Step-by-step explanation:
The table represents an exponential function. What is the multiplicative rate of change of the function? 2 5.
From the table which represents the exponential function , the multiplicative rate of change of function is (a) 1/5 .
The exponential function is expressed mathematically as : y = a(b)ˣ ;
where "a" is = initial value of function , and "b" is = multiplicative rate of change ;
We first substitute , the first two values from the exponential table ;
we get ;
⇒ 2 = a(b)¹
⇒ 2 = ab ,...,,....equation(1) ;
Now substituting the second value ,
we get ;
⇒ 2/5 = a(b)² ,....equation(2) ;
On dividing equation(2) by equation(1) ,
we get;
⇒ 2/(2/5) = ab/ab² ;
⇒ 5 = 1/b ;
⇒ b = 1/5 .
Therefore , the multiplicative rate of change is b = 1/5 .
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The given question is incomplete , the complete question is
The table represents an exponential function.
What is the multiplicative rate of change of the function ?
(a) 1/5
(b) 2/5
(c) 2
(d) 5
What is the surface area of the cylinder with height 8 in and radius 8 in? Round your
answer to the nearest thousandth.
Answer:
The surface area of a cylinder can be calculated using the formula:
Surface area = 2πr^2 + 2πrh
Where r is the radius and h is the height of the cylinder.
Plugging in the values we have:
Surface area = 2π(8^2) + 2π(8)(8) = 2π(64) + 2π(64) = 128π
Rounding to the nearest thousandth, we have:
Surface area = 128π = 403.23 in^2 (rounded to the nearest thousandth)
So the surface area of the cylinder with height 8 in and radius 8 in is 403.23 in^2.
Step-by-step explanation:
composite functions homework
The composite function has its value to be g o h(x) = -20x^2 - 30x
How to determine the composite functionfrom the question, we have the following parameters that can be used in our computation:
h(x) = 4x + 6
g(x) = -5x
Using the above as a guide, we have the following:
g o h(x) = g(x) * h(x)
substitute the known values in the above equation, so, we have the following representation
g o h(x) = (4x + 6) * -5x
Evaluate
g o h(x) = -20x^2 - 30x
Hence, the value is g o h(x) = -20x^2 - 30x
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Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5 ft at midnight, rises to a high of 9.5 ft, falls to a low of 0.5 ft, and then rises to 5 ft by the next midnight.
Give the value of each given that x represents time in hours since the beginning of the 24 hour period that models the situation.
Answer:
Step-by-step explanation:
The tide over a 24-hour period can be modeled by a sinusoidal function of the form:
f(x) = A * sin(Bx) + C
where A is the amplitude, B is the frequency, and C is the vertical shift.
To determine the values of A, B, and C, we need three points. Let's use the following points:
(0, 5): This is the value of the tide at midnight, 5 ft.
(12, 9.5): This is the value of the tide at its high, 9.5 ft.
(6, 0.5): This is the value of the tide at its low, 0.5 ft.
Using the first point (0, 5), we can calculate the vertical shift, C:
C = 5
Using the second point (12, 9.5), we can calculate the amplitude, A:
A = (9.5 - 5) / 2 = 2.25
Using the third point (6, 0.5), we can calculate the frequency, B:
0.5 = 2.25 * sin(B * 6) + 5
4.5 = 2.25 * sin(B * 6)
2 = sin(B * 6)
B * 6 = sin^-1(2)
B * 6 = pi / 2
B = pi / (2 * 6) = pi / 12
So, the final equation is:
f(x) = 2.25 * sin(pi * x / 12) + 5
This represents one period of the sinusoidal function that models the tide over a 24-hour period, with time x measured in hours since midnight.
Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=
The solution is, the required cost of the used game X= 19.
What is equation?An equation which can be expressed as a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
So he bought the $120 game with $82
and 2 equally priced game.
This can be changed to an equation: 120= 82+2X.
The X represents the cost of the used game.
120= 82+2X
-82 -82
——————-
38= 2X
38= 2X
Divide by 2 on both sides
X= 19
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Need Help Asap Today
The area of the wall is 275 ft square
The number of gallon to cover the wall approximately is 3
the price of the paint is $73.5
How to solve for the area of the wall1. The area of the wall is given as l * w
this is the value that is used to solve for the area of a rectangle
the length is given as 10 ft
the width is given as 22 ft
the area would be 10 * 22
= 220 ft square
find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft
base = 22 ft
area = 1/2 b h
= 0.5 * 22 * 5
= 55
total area = 220 + 55 = 275 ft square
2. If 1 gallon of paint covers 105 ft
the amount that would cover 275 ft would be gotten when we cross multiply
1 = 105 ft
x = 275 ft
275 ft = 105 x
x = 275 / 105
x = 2.619
x ~ 3 gallons of paint
3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5
= $73.5
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find two numbers if their sum is 91 and their ratio is 6:7
Answer:
Step-by-step explanation:
The two numbers are 42 and 49.
Let us suppose the numbers are x and y.
From the above question,
=> x + y = 91 ------(1)
Also,
=> x:y = 6:7
If we express y in terms of x,
Then, x/y = 6/7
It can also be written as,
=> y = 7x/6 ------(2)
On substitution of value from (2) into (1),
We get,
=> x + 7x/6 = 91
=> 13x/6 = 91
=> x = 6*7
=> x = 42
Now, Substituting the value of x in (1),
We get,
=> 42 + y = 91
=> y = 91 - 42
=> y = 49
Therefore, The values of the two numbers are 42 and 49.
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Mrs. Imperiale's credit card has an APR of 13.2%. She does not ever pay her balance off in full, so she always pays a finance charge. Her next billing cycle starts today. The billing period is 31 days long. She is planning to purchase $7,400 worth of new kitchen cabinets this billing cycle. She will use her tax refund to pay off her entire bill next month. If she purchases the kitchen cabinets on the last day of the billing cycle instead of the first day, how much would she save in finance charges? Round to the nearest ten dollars.
If Mrs. Imperiale's credit card has an APR of 13.2%. The amount she would save in finance charges Round to the nearest ten dollars is $80.
What is the amount saved?Finance charge if bought on the first day
Finance charge = (31 × 7400 ÷ 31) × (0.132 ÷ 12)
Finance charge = 7400 × 0.011
Finance charge= $81.40
Finance charge if bought on the last day
Finance charge = (1 × 7400 ÷ 31) × (0.132 ÷ 12)
Finance charge = 238.709677 × 0.011
Finance charge= $2.625
Finance charge = $2.63
Savings = $81.40 - $2.63
Savings = $78.77
Savings = $80 ( Approximately)
Therefore the savings is $80.
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In country A, there were 131,000 foreign students from country B. This number is 23% more than the number from country C. How many foreign students were from country C
There were a total of 95,082 students from country C.
What is percentage?A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviatiοns "pct.," "pct," and "pc" are alsο occasionally used. It is frequently denοted using the percent symbol "%," though. The amοunt of percentages has no dimensions. With a denominatοr of 100, percentages are basically fractiοns.
To shοw that a number is a percentage, place a percent symbol (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questiοns on a test (75/100), you receive a 75%. Tο compute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.
x represents the number οf students from cοuntry C.
then 122percent of x = 116,000
122/100 * x = 116000
x = 116000 * 100/122 = 95,082 students
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Complete the inequality to represent the following: 13 times a number x
is less than or equal to 200.
The value for the Inequality 13x ≤ 200 is x ≤ 15.384.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
13 times a number x is less than or equal to 200.
Now, Writing the Inequality Mathematically
13x ≤ 200
x ≤ 200 / 13
x ≤ 15.384
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the company bought $15000 worth of equipment beginnning of year 2018 the equipment is est. to increase in value at a rate of 15.9% per year how many yers, t , after which the value of the company's new equipment will be less than 7500
The number of years, t , after which the value of the company's new equipment will be less than 7500 is 2.64 years
How to determine the valueTo solve this problem, we can use the formula for exponential growth:
V(t) = V₀ * (1 + r)^t
Given that the parameters are;
V(t) is the value of the equipment at a time tV₀ is the initial value of the equipment ($15,000)r is the growth rate (15.9% or 0.159)t is the time in yearsTo determine time t when the value of the equipment will be less than $7500.
Let's set up an inequality;
V(t) < 7500
Substituting the formula for V(t), we get:
V₀ * (1 + r)^t < 7500
Substitute the values
(1 + 0.159)^t < 0.5
t * log(1 + 0.159) < log(0.5)
t > log(0.5) / log(1 + 0.159)
Using a calculator, we get:
t > 2.64
Hence, the value is 2.64 years.
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Can anyone help me solve this? Thank you!
Your friend sings every Saturday night at your favorite bar in San Diego. During his show, people show up at the rate of 1 person every minute.
a) What is the probability that on a random minute, at least 3 people show up?
b) What is the probability that he will have to wait at least 3 minutes for the next person to show up?
c) If he has already waited for 1 minute for the next person to show up, what is the probability that he will have to wait at least 3 more minutes for the next person to show up?
Answer:
Step-by-step explanation:
a) The number of people showing up at the bar during any given minute is a Poisson process with an average rate of 1 person per minute. Let X be the number of people who show up during a random minute. Then X follows a Poisson distribution with parameter λ = 1. The probability of at least 3 people showing up in a random minute is:
P(X >= 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:
P(X = k) = (e^-λ) * (λ^k) / k!
Plugging in λ = 1, we get:
P(X = 0) = e^-1 / 0! = 1/e
P(X = 1) = e^-1 * 1^1 / 1! = 1/e
P(X = 2) = e^-1 * 1^2 / 2! = 1/2e
So, the probability of at least 3 people showing up in a random minute is:
P(X >= 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2)) = 1 - (1/e + 1/e + 1/2e) = 1 - (2/e + 1/2e) = 1 - (5/2e)
b) The probability of having to wait at least 3 minutes for the next person to show up is equal to the probability of having 0, 1, or 2 people show up during the first three minutes. Using the same calculation as above, we find:
P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2) = (1/e) + (1/e) + (1/2e) = (2/e + 1/2e) = (5/2e)
So, the probability of having to wait at least 3 minutes for the next person to show up is 1 - (5/2e) = 1 - P(X <= 2).
c) If he has already waited for 1 minute, the probability of having to wait at least 3 more minutes for the next person to show up is equal to the probability of having 0 or 1 people show up during the next 2 minutes. Using the same calculation as above, we find:
P(X <= 1) = P(X = 0) + P(X = 1) = (1/e) + (1/e) = 2/e
So, the probability of having to wait at least 3 more minutes for the next person to show up is 1 - (2/e) = 1 - P(X <= 1).
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Is 2/9 = 10/45 a true proportion?
Answer:
Yes
Step-by-step explanation:
To find this out. If you divide the denominators by each other, they would need to be the same value as if you divide the numerators by each other
[tex]45 \div 9 = 5[/tex]
^ 45 and 9 were the denominators, we divide and get 5
Now for the numerators
[tex]10 \div 2 = 5[/tex]
^ 10 and 2 we're the numerators, dividing also gave 5
Answer:
yes.
Step-by-step explanation:
let us check. to be a proportion they must be equivalent
however, what do we multiply to get there? let us check..
[tex]\frac{2x}{9x} =\frac{10}{45}[/tex]
cross multiply...
2x * 45 = 9x * 10
90x = 90x
yes, they will be proportional!
you can even do it without the X, i just put x in to make it clearer.
Task
You put two targets in the field. The coordinates for target 1 (6 Points)
The coordinates for target 2 (4 points). See the figure below.
Informe the coach
You asked the players to shoot the ball on the targets 4 times. You added that if
they hit one of the targets, they get the target points.
Test 1:
Messi shot the ball. His ball followed the path of the equation where x is the target
points:
3(3x-4)= 24
6.8 (2.3x + 5.7) = 132.6
Test 2:
Ronaldo shot the ball. His ball followed the path of the equation where y is the
target points.
2/3 (6y - 18) = -16.4. : 2 times
8.2 (x/2 - 5) = - 16.4. : 2 times
Answer:
Step-by-step explanation:
3/2*2/3(6y)=30*3/2
6y=45
6y/y=45/y
y=7.5
Drag the numbers to complete the column two-way relative frequency table. Numbers may be used once, more than once, or not at all.
2829383949100
7th 8th Total
0–300 61%
% 50%
300+
% 62% 50%
Total
%
% 100%
Answer:
YOU L HAHA
Step-by-step explanation:
LOS ER
3. If 17 and 36 are the lengths of two sides of a triangle, what is the range of possible values for the length of the third side?
Answer:
19 < x < 53
Step-by-step explanation:
given 2 sides of a triangle then the third side x is in the range
difference of 2 sides < x < sum of 2 sides , that is
36 - 17 < x < 36 + 17
19 < x < 53
For his birthday, Tyler's parents gave him $7,000.00 which they put into a savings account that earns 15% interest compounded quarterly. When Tyler started college, he withdrew the entire balance of $26,725.00 and used it to pay for tuition. How long was the money in the account?
The number of years the interest was compounded quarterly is given by the equation b = 9.098 years
What is Compound Interest?Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.
The formula for calculating Compound Interest is
A = P ( 1 + r/n )ⁿᵇ
where A = Final Amount
P = Principal
r = rate of interest
n = number of times interest is applied
b = number of time periods elapsed
Given data ,
Let the amount after b years be A = $ 26,725.00
The number of years be = b
The number of times the interest is applies n = 4 ( quarterly )
Let the principal amount be P = $ 7,000
A = P ( 1 + r/n )ⁿᵇ
Substituting the values in the equation , we get
t = ln ( A/P ) / n [ ln ( 1 + r/n ) ]
t = b = n ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.15/4 ) ] )
On simplifying the equation , we get
b = ln ( 26,725.00 / 7,000.00 ) / ( 4 × [ ln ( 1 + 0.0375 ) ] )
b = ln ( 3.81785714 ) / 4 [ ln ( 1.0375 ) ]
On further simplification , we get
b = 9.098 years
Hence , the number of years the interest was applied is 9 years 1 months
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help with this problem, I don't get it, I will give brainliest
The equation cos (π/6 + β) is solved to get
√3 / 2How to solve for the cosineFrom the question it was given that sine β = -0.8
solving for β
sine β = -0.8
β = arc sine ( -0.8 )
β = -0.9273
β ≈ -π/3
substituting the value into cos (π/6 + β)
cos (π/6 + β)
cos (π/6 - π/3)
cos (π/6 - π/3)
= √3 / 2
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Set up two equations and solve.
9. The perimeter of a rectangle is 400 meters. The length is 20 meters longer than the
width. Find the length and width of the rectangle.
The width of rectangle = 90 m
And, The length of rectangle = 110 m
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The perimeter of a rectangle is 400 meters.
And, The length is 20 meters longer than the width.
Now, Let the width of rectangle = x
Then, The length of rectangle = x + 20
We know that;
⇒ Perimeter of rectangle = 2 ( Length + width )
Substitute values ,
⇒ 400 = 2 (x + x + 20)
⇒ 400 = 2 (2x + 20)
⇒ 200 = 2x + 20
⇒ 2x = 200 - 20
⇒ 2x = 180
⇒ x = 90
Thus, The width of rectangle = x = 90 m
And, The length of rectangle = x + 20 = 90 + 20 = 110 m
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How do you do part ii
The value of k is,
The probability distribution as a table:
r 1 2 3
P(X) 0 1/15 2/15
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
To find the value of k, we can use the fact that the sum of the probabilities for all possible values of X must equal 1.
Therefore, we have:
P(X = 1) + P(X = 2) + P(X = 3) = k(4(1)(1²) + 4(2)(2²) + 4(3)(3²))
= 24k
Since we also know that P(X = 1) = 0, we have:
P(X = 1) + P(X = 2) + P(X = 3) = P(X = 2) + P(X = 3) = 0.8
Substituting this into the equation above, we get:
0.8 = 24k
k = 0.8/24 = 1/30
Therefore, the probability distribution can be written as:
r 1 2 3
P(X) 0 1/15 2/15
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Based on the records for the past several seasons a sports fan believes the probability the red team wins is 0.55. The fan also believes the probability the blue team will wins is 0.60. In a season with 160 games, how many fewer games should the fan expect the red team to win?
The fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
If the probability that the red team wins is 0.55, then the probability that they lose is 1-0.55 = 0.45.
Similarly, if the probability that the blue team wins is 0.60, then the probability that they lose is 1-0.60 = 0.40.
If we assume that the outcomes of each game are independent of each other and that there are no ties, then the expected number of games that the red team will win in a season of 160 games is:
Expected number of wins for the red team = (probability of winning) x (number of games)
= 0.55 x 160
= 88
Similarly, the expected number of wins for the blue team is:
Expected number of wins for the blue team = (probability of winning) x (number of games)
= 0.60 x 160
= 96
Therefore, the fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games (96 - 88 = 8).
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Can someone please me with this
Answer:
It would be C.
Step-by-step explanation:
It would be C.
JKP, the smaller triangle, needs to be turned into J'K'P' to show proof the the triangles are similar. So the first thing you would have to do, because J'K'P' is exactly 2 times bigger than JKP, is multiply the x and the y by 2. However, this shifts the triangle, and we need the triangles to overlap to prove they are also the same size. So comparing the x and y values after we increase the sides of JKP, we would see we need to subtract the x value by 3, and the y value by 2.
