If the odds in favor of Chris winning the election are 6 to 5, then what is the probability that Chris wins? The probability that Chris will win the election is (Type an integer or a simplified fraction.)

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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Answer:

50

Step-by-step explanation:

100÷1/2=50 so your answer would be 50

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

Answer:

C

Step-by-step explanation:

y=mx+b

3 = -2(3) + b

3 = -6 + b

9 = b

y = -2x + 9

2x + y = 9

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.

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.

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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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

Answer:

.

Step-by-step explanation:

Answer:

#1 - y = 2x

#2 - x is days for sale and y is times viewed

#3 - 80

#4 - 35

Step-by-step explanation:

Answer:

area = 84 in²

Step-by-step explanation:

area = (9x12) - (6x8x0.5) = 84 in²

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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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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Answer:

72.25663

Step-by-step explanation:

C=2πr=2·π·11.5≈72.25663

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

Answer:

3x+4y=3

Step-by-step explanation:

Plug this in desmos graphing calculator.

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:

Answer:

x = 90 and 20 x 4 = 6x9 = k2 over -2

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.

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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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

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.

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

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.

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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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

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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Answer:

(2,0)(0,2

(-1,-3)(-3,-1)

(-1,3) (1,0)

Step-by-step explanation:

Answer:

9

plz mark as brainliest

Answer:

9

Step-by-step explanation:

[tex]\sqrt{81} =9[/tex]

9 x 9 = 81

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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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