The probability that Chris wins the election is 6/11. To determine the probability of an event, we can use the odds in favor of that event. In this case, the odds in favor of Chris winning the election are given as 6 to 5.
The probability of an event is calculated as the favorable outcomes divided by the total possible outcomes. In this case, the favorable outcomes are 6 (representing the 6 possible favorable outcomes for Chris winning) and the total possible outcomes are 6 + 5 = 11 (representing the total of favorable and unfavorable outcomes combined).
Therefore, the probability that Chris wins the election is 6/11.
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Points that two lines pass through are given in the table. Match each point of intersection to the correct pair of lines.
(2, 0)
(-1, 3)
(1, 0)
(-1, -3)
(0, 2)
(-3, -1)
Answer:
(2,0)(0,2
(-1,-3)(-3,-1)
(-1,3) (1,0)
Step-by-step explanation:
A discrete random variable X is said to be uniformly distributed over the numbers 1. 2. 3......,n, if
P(X=i) =1/n, i=1,2....,n
Find EX and Var(X).
For a discrete random variable X that is uniformly distributed over the numbers 1, 2, 3, ..., n, the expected value (EX) can be calculated as the average of all possible values of X. The variance (Var(X)) measures the spread or variability of the distribution.
The expected value and variance, we need to use the formulas for the mean and variance of a uniform distribution.
The expected value (EX) for a uniform distribution can be calculated as the average of all possible values of X. In this case, since X is uniformly distributed over the numbers 1, 2, 3, ..., n, the expected value can be found using the formula:
EX = (1 + 2 + 3 + ... + n) / n
Simplifying this expression, we get:
EX = (n + 1) / 2
The variance (Var(X)) of a uniform distribution can be calculated using the formula:
Var(X) = (n^2 - 1) / 12
where n is the total number of possible values.
Therefore, for a discrete random variable X that is uniformly distributed over the numbers 1, 2, 3, ..., n, the expected value is (n + 1) / 2, and the variance is (n^2 - 1) / 12. These formulas allow us to calculate the average and measure the spread of the distribution.
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how many numbers between 100 and 200 have 11 as a prime factor
Answer. 2, 3, 5, 7 , 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
Step-by-step explanation:
There are 21 prime number between 100 and 200.
What is Number system?A number system is defined as a system of writing to express numbers.
A prime number is a whole number greater than 1 whose only factors are 1 and itself.
The prime numbers between 100 and 200 are
101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199.
One hundred one, one hundred three, one hundred seven, one hundred nine, One hundred thirteen, one hundred twenty seven, One hundred thirty one, one hundred thirty seven, one hundred thirty nine, one hundred forty nine, one hundred fifty one, one hundred fifty seven, one hundred sixty three, one hundred sixty seven, one hundred seventy three, one hundred seventy nine, one hundred eighty one, one hundred ninty one, one hundred ninty three, one hundred ninty seven, one hundred ninty nine.
There are no numbers between 100 and 200 have 11 as a prime factor.
Hence there are 21 prime number between 100 and 200.
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For the function f(x) = 2.02 – 42 +2 (a) Find the equation for its tangent at r = 0. (b) Find the equation for its tangent at I = 1. (c) Find the equation for its tangent at x = 2. (d) What is special about f when x = 1?
a) The equation for the tangent at x = 0 is y - 2 = -42x.
(b) The equation for the tangent at x = 1 is y + 38 = -38x + 38.
(c) The equation for the tangent at x = 2 is y + 62 = -34x + 68.
(d) When x = 1,the value of f(x) is -38. This is the y- coordinate of the point on the tangent line at x = 1.
What is the explanation for the above ?To find the equations for the tangents of the function f (x) = 2x² – 42x + 2 at specific points,we need to calculate the derivative of the function first. Let's differentiate f(x) with respect to x .
f(x ) = 2x² – 42x+ 2
f'(x) = d/ dx (2x²) – d/dx (42x)+ d/dx (2)
f'(x) = 4x – 42
So
(a) Tangent at x = 0 -
To find the equation for the tangent at x = 0 we need to evaluate f'(x) at x = 0.
f'(0) = 4(0) – 42
f'(0) = -42
Since the slope of the tangent is -42 at x = 0, the equation of the tangent can be written in point-slope form using the point (0, f(0)).
Using f(0) = 2(0)² – 42(0) + 2 = 2, the equation for the tangent at x = 0 is -
y - 2 = -42(x - 0)
y - 2 = -42x
(b) Tangent at x = 1:
To find the equation for the tangent at x = 1,we need to evaluate f'(x) at x = 1.
f'(1 ) =4(1) – 42
f'(1) = -38
Using f(1) = 2(1)² – 42(1) + 2 = -38, the equation for the tangent at x = 1 is -
y + 38 = -38(x - 1)
y + 38 = -38x + 38
(c) Tangent at x = 2
To find the equation for the tangent at x = 2,we need to evaluate f'(x) at x = 2.
f'(2) = 4(2) – 42
f'(2) = -34
Using f(2) = 2(2)^2 – 42(2) + 2 = -62, the equation for the tangent at x = 2 is:
y + 62 = -34(x - 2)
y + 62 = -34x + 68
(d) To determine what is special about f when x = 1, we can evaluate the function at x = 1
f(1) = 2(1)² – 42(1) + 2
f(1) = -38
When x = 1,the value of f(x) is -38. This is the y -coordinate of the point on the tangent line at x = 1. Therefore, the special property of f when x = 1 is that the function value is -38 at that point.
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2. (a) What are the possible remainders when n² + 16n + 20 is divided by 11? (b) Prove for every n € Z that 121 | n² + 16n +20.
The required answer is -
a. leaves a remainder of n² - 3n or (n - 6)(n + 7) ,the possible remainders are 0, 1, 4, 9, 5, 3
b .every n € Z that 121 | n² + 16n +20.
Explanation:-
(a) Remainder when n² + 16n + 20 is divided by 11:Let us first find out the value of n² + 16n + 20,n² + 16n + 20 = (n + 10)(n + 6) + 4As n and 11 are co-prime, by Fermat's Little Theorem, n¹⁰ ≡ 1(mod 11)So, (n + 10)(n + 6) ≡ (n + 1)(n + 7) (mod 11)Hence, n² + 16n + 20 ≡ (n + 1)(n + 7) + 4 ≡ n² + 8n + 11 ≡ n² - 3n (mod 11).Therefore, when n² + 16n + 20 is divided by 11, it leaves a remainder of n² - 3n or (n - 6)(n + 7).
Thus, the possible remainders are 0, 1, 4, 9, 5, 3
(b) Prove that 121 | n² + 16n + 20 for every n ∈ Z . n ∈ Z, thenn² + 16n + 20 = (n + 8)² - 44(n + 8) + 324 = (n + 8 - 22)(n + 8 + 14) + 324= (n - 14)(n + 22) + 324.We know that 121 = 11² | (n - 14)(n + 22),
Therefore, 11 | (n - 14) or 11 | (n + 22)So, there exist k and l ∈ Z such that n - 14 = 11k or n + 22 = 11lWe have, n + 22 = n - 14 + 36Hence, n - 14 ≡ n + 22 (mod 11)If 11 | (n - 14), then 11 | (n + 22), if 11 | (n + 22), then 11 | (n - 14).Therefore, 121 | n² + 16n + 20. Thus, proved.
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The given quadratic expression is: $n^2 + 16n + 20$.
(a)We have to determine the possible remainders when this expression is divided by 11.
Let's solve for the remainder:$(n^2 + 16n + 20) \div 11$ $= \frac{(n + 8)^2 - 44}{11}$
We can write the given expression as $n^2 + 16n + 20 = (n + 8)^2 - 44$
Therefore,$\begin{aligned} (n^2 + 16n + 20) \div 11 & = \frac{(n + 8)^2 - 44}{11} \\ & = \frac{(n + 8)^2}{11} - 4 \end{aligned}$
For all possible values of $n$,
let's calculate the remainder of $\frac{(n + 8)^2}{11}$.
Let $a$ be the remainder when $n$ is divided by 11; then, $(n + 8) \div 11$ has a quotient of $q$ and a remainder of $r$. Therefore, $n + 8 = 11q + r$ $ \Right arrow n = 11q + r - 8$$\begin{aligned} n^2 & = (11q + r - 8)^2 \\ & = 121q^2 + r^2 + 64 + 22qr - 16q - 16r \end{aligned}$Let's now replace $n^2$
in the given expression:$(n^2 + 16n + 20) \div 11 = \frac{121q^2 + r^2 + 22qr - 16q + 6r + 64}{11}$
We have to find the remainders when $121q^2 + r^2 + 22qr - 16q + 6r + 64$ is divided by 11.
We observe that $121q^2$ is always divisible by 11, so we can ignore it.
We must find the remainders of $r^2 + 22qr + 6r + 64 - 16q$. $\begin{aligned} r^2 + 22qr + 6r + 64 - 16q & = r^2 + 2 \cdot 11qr + 11qr + 6r + 64 - 16q \\ & = (r + 11q)^2 + 6r - 16q + 64 \\ & = (r + 11q)^2 - 11(2q - r - 3) \end{aligned}$
The remainder is $r_0 = 11(2q - r - 3)$.
This remainder can take any value between $-10$ and $10$.
(b)We have to show that $121 | n^2 + 16n + 20$ for all integers $n$.We proved earlier that $n^2 + 16n + 20 = (n + 8)^2 - 44$.
We can restate this as $121 | (n + 8)^2 - 44$, which implies that $(n + 8)^2 - 44 = 121k$, where $k \in \mathbb{Z}$.Now we need to show that $k = \frac{n^2 + 16n + 20 - 121k}{121}$ is an integer.
Let's substitute $(n + 8)^2 - 44 = 121k$ into the given expression:$\begin{aligned} k & = \frac{(n + 8)^2 - 44}{121} \\ & = \frac{n^2 + 16n + 20 - 121k}{121} \\ & = \frac{n^2 + 16n + 20}{121} - k \end{aligned}$Thus, $k = \frac{n^2 + 16n + 20 - 121k}{121}$ is an integer for all $n \in \math bb{Z}$,
implying that $121 | n^2 + 16n + 20$ for all $n \in \math bb{Z}$.
Hence, we have proved that $121 | n^2 + 16n + 20$ for all $n \in \math bb{Z}$ using the method of mathematical induction.
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what is the square root of 81
Answer:
9
plz mark as brainliest
Answer:
9
Step-by-step explanation:
[tex]\sqrt{81} =9[/tex]
9 x 9 = 81
What is a holomorphic function f whose real part is u(x, y) = e-²xy sin(x² - y²)?
The holomorphic function f whose real part is u(x, y) = e^-2xy sin(x² - y²) is given by f(z) = e^(-z²)sin(z²).
This function is holomorphic because it satisfies the Cauchy-Riemann equations. The Cauchy-Riemann equations relate the partial derivatives of the real and imaginary parts of a holomorphic function with respect to the variables x and y.
In this case, the real part of f is u(x, y) = e^-2xy sin(x² - y²), and the imaginary part of f is v(x, y) = e^-2xy cos(x² - y²). By computing the partial derivatives of u and v with respect to x and y and checking that they satisfy the Cauchy-Riemann equations, we can verify that f is indeed holomorphic.
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On a standardized exam, the scores are normally distributed with a mean of 120 and
a standard deviation of 10. Find the z-score of a person who scored 115 on the exam
Answer: z= -0.5
Step-by-step explanation: mean m=120 and deviation s=10.
Z = (x-m)/s= (115-120)/10
Answer: z=−1.1
Step-by-step explanation:
z=\frac{x-\mu}{\sigma}
z=
σ
x−μ
z-score formula
z=\frac{104-115}{10}
z=
10
104−115
Plug in values
z=\frac{-11}{10}
z=
10
−11
Subtract
z=-1.1
z=−1.1
Divide
Identify the figure, name the bases,faces,edges, and vertices
Answer:
It’s a square-based pyramid
base(1) is the square on the bottom- ABCD
Faces(4) are the triangles on the sides eg- AED, DEC, CEB, BCA
There are 8 edges, four being at the bottom around the base and the other four being alone the faces
Finally there are 5 vertices, four being at the corners of the base and the fifth being the tip of the pyramid
Step-by-step explanation:
In a tank problem with equal inflow and outflow rate ri=re=r, input concentration c; of a toxic substance, and total volume Vo of mixture in the tank, the appropriate DE for the quantity Q of toxin in the tank is da Q Vo =r = r (c: -). dt True False
The statement is false. The appropriate differential equation for the quantity Q of toxin in the tank is not given by dQ/dt = r (c/Vo).
In a tank problem with equal inflow and outflow rates and a constant input concentration c of a toxic substance, the appropriate differential equation for the quantity Q of toxin in the tank is dQ/dt = r(c - Q/Vo), where r is the inflow/outflow rate and Vo is the total volume of the mixture in the tank.
The term (c - Q/Vo) represents the difference between the input concentration and the concentration in the tank, scaled by the volume Vo. This equation accounts for the fact that the concentration in the tank changes over time due to the inflow of fresh mixture with concentration c and the outflow of the mixture with concentration Q/Vo.
Therefore, the correct differential equation is dQ/dt = r(c - Q/Vo), which reflects the balance between the inflow and outflow of the toxic substance and its accumulation or depletion in the tank.
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Abox has a shape of a rectangular prism. The base of the box measures 12 square inches. The height of the box measures 7 inches. Which is the volume of the box?
A. 558 cube in.
B. 252 in.
C. 84 cube in.
D. 19 cube in.
Answer: C.
Step-by-step explanation: To find the volume of something, you multiply the length, width, and height together. Since they have already multiplied the length and width together to form the base, multiply 7 by 12 (base times height) to get 84 cubic inches.
Tony will spend at most $27 on gifts. So far, he has spent $14. What are the possible additional amounts he will spend?
Use c for the additional amount (in dollars) Tony will spend.
Write your answer as an inequality solved for c.
Answer:
Inequaltiy: 27 ≤ 14+c
Final answer: 13 ≤ c
Step-by-step explanation:
Well tony spent at most 27 dollars.
He spent 14 already and he can‘t get past 27 dollars but he can spend exactly 27 or even less.
So 27 ≤ 14+c
Q Search
7
The solid shape is made of a cone on top of a hemisphere.
The height of the cone is 10 cm.
The base of the cone has a diameter of 6 cm.
The hemisphere has a diameter of 6 cm. * LT
(1 Point)
The total volume of the shape is ku cm3. Work out the value of k.
Answer:
.
Step-by-step explanation:
Find the area of the shaded
Answer:
area = 84 in²
Step-by-step explanation:
area = (9x12) - (6x8x0.5) = 84 in²
The top of a pie container is a circle. The radius of the pie is 8 inches and the radius of the container is 9 inches. What is the difference between the circumference of the container and the circumference of the pie in inches to the nearest tenth?
A 3.1 inches
B 6.3 inches
C 12.6 inches
D 25.1 inches
E 50.2 inches
Answer:
B
Step-by-step explanation:
2 pi r subtracted by 2 pi r, you get answer
2 x 3.14 ~ 6.28, x 9 ~ 56.54.
2 x 3.14 ~ 6.28, x 8 ~ 50.24
56.54 - 50.24 ~ 6.3
The total number of passengers riding a certain city bus during the morning shift is 1,000. If the child's fare is $0.50, the adult fare is $1.75, and the total revenue from the fares in the morning shift is $1,500, how many children and how many adults rode the bus during the morning shift?
Let the number of children who rode the bus be C and the number of adults who rode the bus be A. Here's how to solve this problem:
Step-by-step explanation: We are given the following information:
Total number of passengers = 1000 Children's fare = $0.50. Adult fare = $1.75. Total revenue from fares = $1500. Let C be the number of children who rode the bus during the morning shift. Therefore, the number of adults who rode the bus will be (1000 - C). The total revenue from fares is given as:$0.50 × C + $1.75 × (1000 - C) = $1500. Simplifying this equation gives us: 0.5C + 1750 - 1.75C = 1500-1.25C = -250C = 200. Therefore, the number of children who rode the bus is C = 200. Therefore, the number of adults who rode the bus is:1000 - C = 1000 - 200 = 800.
Therefore, the number of adults who rode the bus during the morning shift is 800.
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question is on the picture
Answer:
12/5
Step-by-step explanation:
tan A = opp/adj
For angle theta, 12 is the opposite leg.
13 is the hypotenuse.
We were not given the length of the adjacent leg, but we can use the Pythagorean theorem to find it.
a^2 + b^2 = c^2
a^2 + 12^2 = 13^2
a^2 + 144 = 169
a^2 = 25
a = 25
The adjacent leg has a length of 5.
tan theta = opp/adj
tan theta = 12/5
Answer: 12/5
PLEASE HELP ME OUT AND MAKE SURE TO SHOW YOUR WORK!!!! PLEASEEEEE
Answer:
1. 15
2. 16
3. 46
4. 59
Step-by-step explanation:
1. 44+30=74, 89-74=15
2. 90-74=16
3. 180-134=46
4. angles like that are the same
Answer:
1. x=5
2. x=16
3.x=46
4.x=59
Step-by-step explanation:
1. It says that the angle in total is 89 degrees (faded). then it shows the degrees 44 and 30. add them together to get 74 degrees. next subtract 89 by 74 to get the answer 5.
2. it shows a box at the corner of the angle (box means its a perfect 90 degree angle) so you need to subtract 90 by 74 to get the answer 16.
3. the whole entire angle is 180. so you need to subtract 134 from 180 to get the answer 46.
4. look focus on the one line that shows 59 degrees and right above it there is a blank. that arrow line represents 180 degrees. subtract 180 by 59 to get 121. next focus on the second line (the one that faces downward to the right) you then subtract 180 by 121 to get 59.
1. 44+30=74 89-74=5 x=5
2. box=90 90-74=16 x=16
3. 180-134=46 x=46
4. 180-59=121 180-121=59 x=59
Sam's fish tank has a base area of 187in.? and a height of 16 inches. His fish tank is shown.
16 in.
A = 187 in 2
The tank is currently full of water. How many cubic inches of water should be added to completely fill the tank?
3
® 997 in.
2
B 1,994-
4,488in.3
D 2,992in.
Answer:
D. 2992 cubic inches of water
Step-by-step explanation:
Given data
Base Area= 187in^2
Height of 16 inches
The expression for the volume of a rectangular shaped tank is
V= Area*Height
substiute
V= 187*16
V=2992 in^3
Hence the volume is 2992 cubic inches of water
URGENT , PLEASE HELP DONT LINK FILES!!!
Find the volume of right rectangular prism made of one hundred 1/2-inch cubes
Answer:
50
Step-by-step explanation:
100÷1/2=50 so your answer would be 50
Which of the following equations has a graph that passes through (3, 3) and has a slope of -2?
A. x + 2y = 9
o B. X- 2y = -3
O
C. 2x + y = 9
o
D. -2x + y = -3
Answer:
C
Step-by-step explanation:
y=mx+b
3 = -2(3) + b
3 = -6 + b
9 = b
y = -2x + 9
2x + y = 9
What is the surface area?
5 yd
5 yd
5 yd
square yards
Submit
Can someone help me out with this please. Do not give me a link for it just answer it please. I will give 20 points.
Answer:
3x+4y=3
Step-by-step explanation:
Plug this in desmos graphing calculator.
What is the surface area of a fear with a diameter of 2.7 inches? Use 3.14 for π
Answer:
22.8906 sq in
Step-by-step explanation:
SA of a sphere = 4 π [tex]r^{2}[/tex]
r = 2.7 / 2 = 1.35
4 x 3.14 x [tex]1.35^{2}[/tex] = 22.8906
I need help with math!!
*PLEASE NO LINKS*
I will mark you brainiest if you don’t send a link!!
Answer:
#1 - y = 2x
#2 - x is days for sale and y is times viewed
#3 - 80
#4 - 35
Step-by-step explanation:
Can someone plsss help me with this one problem plsss I’m trying to get a 90 and also can you explain how you got your answer
How can we write the domain and range for a function that is not piece-wise such as
y=x?
Help Please! Find The Circumference Of A Circle With D=22.1.
Answer:
72.25663
Step-by-step explanation:
C=2πr=2·π·11.5≈72.25663
PLEASE ANSWER QUICKLY
Answer:
x = 90 and 20 x 4 = 6x9 = k2 over -2
Listed below are ages of Oscar winners matched by the years in which the awards were won. Best Actress 28 30 29 61 32 33 45 29 62 22 44 54 43 Best Actor 37 38 45 50 148 60 50 39 55 44 33 a) Find the correlation coefficient r using a calculator. b) Is there a linear correlation between the ages of Best Actresses and Best Actors based on the r that you got? Explain.
a) The correlation coefficient (r) is approximately 0.300, indicating a weak positive linear relationship between the ages of Best Actresses and Best Actors.
b) Based on the correlation coefficient (r), there is a weak positive linear correlation between the ages of Best Actresses and Best Actors, suggesting that as the ages of Best Actresses increase, the ages of Best Actors also tend to increase, but the relationship is not very strong.
a)How can I calculate the correlation coefficient (r) using a calculator or statistical software?To find the correlation coefficient (r), we can use the given ages of Best Actresses and Best Actors. The correlation coefficient measures the strength and direction of the linear relationship between two variables. Using a calculator or statistical software, we calculate the correlation coefficient to be approximately 0.300.
b)Is there a significant linear correlation between the ages of Best Actresses and Best Actors based on the obtained correlation coefficient (r)?Based on the correlation coefficient (r) of approximately 0.300, there is a weak positive linear correlation between the ages of Best Actresses and Best Actors. This means that there is a tendency for the ages of Best Actresses and Best Actors to increase together, but the relationship is not very strong. The correlation coefficient ranges from -1 to +1, where 0 indicates no linear correlation, 1 indicates a strong positive linear correlation, and -1 indicates a strong negative linear correlation. In this case, the value of 0.300 suggests a weak positive linear relationship, indicating that as the ages of Best Actresses increase, the ages of Best Actors also tend to increase, albeit not strongly.
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