Question 1: (6 Marks) If X₁, X2, ..., Xn be a random sample from Bernoulli (p). 1. Prove that the pmf of X is a member of the exponential family. 2. Use Part (1) to find a minimal sufficient statist

Answer:

C

Step-by-step explanation:

For a relation to be a function, the ordered pairs do not repeat any of the x values.  This is Answer C.

Answer:

x = -2 + 2√2 i and -2 - 2√2 i

Step-by-step explanation:

Given the function, y=-x^2+4x-12

x intercept occurs at y =  0

Substitute y = 0

0=-x^2+4x-12

x^2 - 4x + 12 = 0

Factorize

x = -4±√4²-4(12)/2

x = -4±√16-48/2

x = -4±√-32/2

x = -4 ± √32 i/2

x = -4+4√2 i/2 and x =-4-4√2 i/2

x = -2 + 2√2 i and -2 - 2√2 i

Answer:

\(\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}\)

Step-by-step explanation:

\(\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}\)

Factor x²-9 and x²-5x+6.

\(\frac{2}{\left(x+3\right)\left(x-3\right)}-\frac{3x}{\left(x-2\right)\left(x-3\right)}\)

Least common multiple of (x+3), (x-3), (x-2), and (x-3) is (x+3), (x-3), and (x-2).

Adjust the fractions based on LCM.

\(\frac{2\left(x-2\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}-\frac{3x\left(x+3\right)}{\left(x-2\right)\left(x-3\right)\left(x+3\right)}\)

Subtract the fractions since denominators are equal.

\(\frac{2\left(x-2\right)-3x\left(x+3\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}\)

Expand.

\(\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}\)

The fraction can be in factored form.

\(\frac{-\left(x+1\right)\left(3x+4\right)}{\left(x-2\right)\left(x+3\right)\left(x-3\right)}\)

Answer:

\(-\frac{(x+1)(3x+4)}{(x+3)(x-2)(x-3)}\)

Step-by-step explanation:

STEP 1: Simplify each term.

\(\frac{2}{(x+3)(x-3)}-\frac{3x}{(x-3)(x-2)}\)

\(\frac{2}{(x+3)(x-3)}*\frac{x-2}{x-2} -\frac{3x}{(x-3)(x-2)}\)

\(\frac{2}{(x+3)(x-3)}*\frac{x-2}{x-2} -\frac{3x}{(x-3)(x-2)}*\frac{x+3}{x+3}\)

STEP 2: Write each expression with a common denominator of (x+3)(x−3)(x−2), by multiplying each by an appropriate factor of 1.

\(\frac{2(x-2)-3x(x+3)}{(x+3)(x-2)(x-3)}\)

STEP 3: Simplify the numerator.

\(\frac{(-x-1)(3x+4)}{(x+3)(x-2)(x-3)}\)

STEP 4: Simplify with factoring out.

\(-\frac{(x+1)(3x+4)}{(x+3)(x-2)(x-3)}\)

hi there! here's my answer for you...

i do not think there is an answer since the equation you have given is not a conic section. therefore, there is no vertex form, axis of symmetry, or vertex.

hope this helped. have a good one!

Step-by-step explanation:

solve for y

x-4y =24

-4y = 24-x

 y = x/4 - 6    slope = 1/4, the coefficient of the x term

a perpendicular line has the negative inverse,  change the sign and flip the fraction upside down to get -4/1 or -4

y=-4x + b.  plug in the point x=-2, y=7 to calculate b the y intercept

7=-4(-2) + b

b = 7-8 =-1

y=-4x -1 is the perpendicular line through (-2,7)

general equation in slope intercept form is y=mx +b.  m=-4,  b=-1

The estimation of the function f() allows us to utilize the available data to make informed decisions, gain insights, and understand the behavior of the system or phenomenon we are studying.

1. Prediction: One common reason for estimating a function f() is to make predictions or forecast future values based on available data.

By understanding the relationship between input variables and the corresponding output values, we can estimate the function f() and use it to predict the output for new or unseen input values.

This is particularly useful in various fields such as finance, weather forecasting, sales forecasting, and stock market analysis, where accurate predictions can be valuable for decision-making.

2. Inference: Another reason for estimating a function f() is to gain insights and understand the underlying relationship between the input variables and the output.

By estimating the function, we can examine the effect of different inputs on the output and draw conclusions about the factors influencing the phenomenon we are studying.

This is commonly used in scientific research, social sciences, and data analysis to understand the causal or associative relationships between variables and to uncover patterns or trends in the data.

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Answer:

500442

Step-by-step explanation:

Answer:

500,000

Step-by-step explanation:

Answer:

−x−1+1=−11+1

−x=−10

-x/-1 = -10/-1

x=10

Step-by-step explanation:

Let's solve your equation step-by-step.

Step 1: Add 1 to both sides.

Step 2: Divide both sides by -1.

It costs $0.50 to mail a postcard to Canada, cost of mailing a one ounce letter to Canada is $0.60 and Ahmad wrote to 21 friends and spent $12.00 for postage. This means that he wrote 15 letters and 6 postcards.

Given Information:

Cost of mailing a postcard = $0.50

Cost of mailing a letter = $0.60

Total number of friends Ahmad wrote to = 21

Total cost of postage = $12.00

Let the number of postcards written by Ahmad be x and that of letters be y.

Then, x + y = 21 ............... (1)

0.50x + 0.60y = 12 ................ (2)

Multiplying equation (1) by 0.50, we get,

0.50x + 0.50y = 10.5 ................. (3)

Subtracting equation (3) from (2), we get,

0.1y = 1.5

⇒ y = 15

From equation (1), x = 21 - y

x = 21 - 15

x = 6

Thus, Ahmad wrote 6 postcards at a mailing cost of $0.50 each and 15 letters at a mailing cost of $0.60 each.

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Answer:

scal factor = 1.5

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, that is

scale factor = \(\frac{C'D'}{CD}\) = \(\frac{6}{4}\) = \(\frac{3}{2}\) = 1.5

The  answers to the given formulas are as follows:

1. V = 2 Amps × 6 Ohms

2. I = 12V ÷ 6R

3. R = 12V ÷ 4I

1. Using Ohm's law, the formula V = I × R calculates the voltage (V) when the current (I) and resistance (R) are known. In this case, the given formula V = 2 Amps × 6 Ohms simplifies to V = 12 Volts.

2. The formula I = V ÷ R determines the current (I) when the voltage (V) and resistance (R) are known. In the provided formula I = 12V ÷ 6R, we can rewrite it as I = (12 Volts) ÷ (6 Ohms), resulting in I = 2 Amps.

3. Lastly, the formula R = V ÷ I calculates the resistance (R) when the voltage (V) and current (I) are known. The given formula R = 12V ÷ 4I can be expressed as R = (12 Volts) ÷ (4 Amps), leading to R = 3 Ohms.

By applying Ohm's law, these formulas allow for the calculation of voltage, current, or resistance in a circuit when the other two values are given.

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Answer:

(-5,2)

Step-by-step explanation:

PLZ MARK ME BRAINLIEST

To find the solution to the system of equations, just find where the lines intersect. Since they intersect at (-5,2), the solution is (-5,2)

By evaluating the expression in w=−6, x=−2, and z=−7, we will get the value 35/37.

Here we have the following expression:

(w²*x - 2)/(10*z)

And we want to evaluate this with the following values:

w = -6

x = -2

z = -7

Replacing these in the expression we will get:

( (-6)²*(-2) - 2)/(10*-7)

(36*-2 - 2)/(-70)

-74/-70 = 70/74 = 35/37

That is the value of the expression.

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Answer:

2in

Step-by-step explanation:

Since we are not given the type of polygon, let the polygon be an hexagon. An hexagon is a 6 sides shape. The perimeter of the shape will be the sum of all the sides of the polygon

Perimeter of the polygon = 6L

Length is the length of the side

Given

Perimeter of the polygon = 12in

Substitute and get L

P = 6L

12 = 6L

L = 12/6

L = 2in

Hence the length of side x of the polygon is 2in

If you consider the vertical line test (a graph represent a function is a vertical line crosses the curve of the function only once), you can consider that a vertical line at x=5 crosses the curve at two points.

Then, you can conclude that the given relation is not a function.

The domain are the set of x values with points on the curve. In this case:

domain = [2 , oo)

The range are the set of y values with points on the curve. In this case:

range = (-oo , oo)

Answer:

h(-8)=-8

Step-by-step explanation:

Since we are finding h(-8), we plug -8 into the equation:

h(-8)=((-8)²+3(-8))/(4(-8)+27)

h(-8)=(64-24)/(-32+27)

h(-8)=40/-5

h(-8)=-8

Therefore, h(-8)=-8, which means your answer is correct!

Answer:

C. 66°

Step-by-step explanation:

Given:

m∠FAB = 48°,

m∠ECB = 18°,

Required:

m∠ABC

SOLUTION:

∠CHB ≅ ∠FAB (alternate interior angles theorem)

m∠CHB = ∠FAB

m∠CHB = 48° (substitution)

m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)

48° + 18° + m∠CBH = 180° (substitution)

66° + m∠CBH = 180°

Subtract 66° from each side

m∠CBH = 180° - 66°

m∠CBH = 114°

Thus,

m∠CBH + m∠ABC = 180° (Linear pair)

114° + m∠ABC = 180° (substitution)

Subtract 114° from both sides

m∠ABC = 180° - 114°

m∠ABC = 66°

The angle m∠ABC will be equal to 66° the correct answer is option C.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.

Given:

m∠FAB = 48°,

m∠ECB = 18°,

Required:

m∠ABC

The angle ABC will be calculated as follows:-

∠CHB ≅ ∠FAB (alternate interior angles theorem)

m∠CHB = ∠FAB

m∠CHB = 48° (substitution)

m∠CHB + m∠ECB + m∠CBH = 180° (sum of angles in a ∆)

48° + 18° + m∠CBH = 180° (substitution)

66° + m∠CBH = 180°

Subtract 66° from each side

m∠CBH = 180° - 66°

m∠CBH = 114°

Thus,

m∠CBH + m∠ABC = 180° (Linear pair)

114° + m∠ABC = 180° (substitution)

Subtract 114° from both sides

m∠ABC = 180° - 114°

m∠ABC = 66°

Therefore the angle m∠ABC will be equal to 66° the correct answer is option C.

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Answer:

K=5

This should be right.

Answer:

r(0) = -7

r(2) = -5

r(5) = -12

Step-by-step explanation:

Prime numbers are numbers with no factors other than 1 and themselves.

Use the prime factorization method to find the prime number. Factors should be 1 and the number itself.

What is a prime number?

Natural numbers known as prime numbers can only be divided by one (1) and by the number itself. In other terms, prime numbers are positive integers greater than one that only have the number itself and the number's first digit as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are only a few examples.

A number is prime if it only has the factors 1 and itself. Therefore, we may quickly discover a prime number by prime factorising the provided number.

For example take - 11

The prime factorisation of 11 is 1 × 11 since 11 has only two factors 1 and itself, hence it is a prime number.

Some prime numbers in between 1 to 50 are -

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

Therefore, a prime number has a factor which is 1 and the number itself.

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Answer:

√408

Step-by-step explanation:

First of all, let's name the top triangle n and the bottom one m, you can name them as you'd like.

okay, so, based on the Pythagorean theorem, a^2 + b^2 = c^2

now, we know that the area that is 12 units long, is equivalent to the hypotenuse of m, (it's very important that the bottom right angle is 90 degrees) and therefore, (5^2 = 25)    5^2 + ___ = 12^2  now let's solve that:

25 + _____ = 144 now just fill in the blank. With a simple subtraction, we get 119 (144 - 25 = 119), now remember, this is c^2 of m

and, 12+5=17 so, a of the n triangle is 17.

so let's put everything together: 17^2 + 119 = x^2

now, we're gonna calculate it: 17^2 = 289 and we're gonna add that to 119, so we get 408: 289 + 119 = x^2

But, this is x^2, and we want to find the value of x, so we have to find the square root of 408. Since we get a number with a lot of decimals in front of it, we're just gonna leave it as is, therefore the answer is √408

Hope it helped!

Answer:

Answer (b)

**3.90**

The two integers are 5 and 6.

To solve this problem, we need to set up an algebraic equation based on the information given.

Let's call the first integer x and the second integer y. According to the problem, an integer (x) is 14 less than 4 times another (y).

This can be written as: x = 4y - 14

We are also told that the product of the two integers is 30. This can be written as:

xy = 30

Now we can substitute the first equation into the second equation to solve for one of the variables.

Let's solve for y:

(4y - 14)y = 30

4y^2 - 14y = 30

4y^2 - 14y - 30 = 0

Using the quadratic formula, we can solve for y:

y = (-(-14) ± √((-14)^2 - 4(4)(-30)))/(2(4))

y = (14 ± √(196 + 480))/8

y = (14 ± √676)/8

y = (14 ± 26)/8

y = 5 or y = -1.5

Now we can plug these values of y back into the first equation to find the corresponding values of x:

x = 4(5) - 14 = 6

x = 4(-1.5) - 14 = -20

So the two integers are either 5 and 6, or -1.5 and -20. However, since the problem asks for integers, we can eliminate the second solution.

Therefore, the two integers are 5 and 6.

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Answer:

22%     0.3      19/50

Step-by-step explanation:

Because 22%

0.3=30%

19 out of 50 percentage would be a 38%

So first is 22% then since 0.3=30% it's next andthen 19 out of 50 since that= 38% And then there you go.

Have a great day :)

Answer:

Velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Step-by-step explanation:

The velocity when flying against the wind = 2920 / 4 = 730 miles per hour.

The velocity when flying with the wind = 7140 / 6 = 1190

Let the rate of jet in still Air = x

Let the rate of jet in wind = y

Therefore, velocity against wind = x-y and wind = x + y

x - y = 730

x + y = 1190

Add both equation, 2x = 1920

x = 960

Now find the value of “y” = 1190 – 960 = 230

Thus, velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Answer:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Step-by-step explanation:

Let the speed of jet in still air = \(u\) miles/hr

Let the speed of air = \(v\) miles/hr

So, against the wind, the resultant speed = \((u-v)\) miles/hr

And, with the wind, the resultant speed = \((u+v)\) miles/hr

Distance traveled against the wind = 2920 miles

Time taken against the wind = 4 hrs

Formula for distance is:

\(\bold{Distance =Speed \times Time}\)

\(2920 = (u-v)\times 4\\\Rightarrow u-v=\dfrac{2920}{4}\\\Rightarrow u-v=730\ miles/hr...... (1)\)

Distance traveled with the wind = 7140 miles

Time taken against the wind = 6 hrs

\(\bold{Distance =Speed \times Time}\)

\(7140 = (u+v)\times 6\\\Rightarrow u+v=\dfrac{7140}{6}\\\Rightarrow u+v= 1190 \ miles/hr...... (2)\)

Adding (1) and (2):

\(2u = 1920\\\Rightarrow \bold{u = 960 miles/hr}\)

Putting \(u\) in (1):

\(960 -v = 730 \\\Rightarrow \bold{v=230\ miles/hr}\)

Therefore, the answer is:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Answer:

0.5

Step-by-step explanation:

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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The ticket price that would maximize revenue is $12.

To determine the ticket price that maximizes revenue, we need to analyze the relationship between ticket price and attendance. The problem states that attendance is linearly related to the ticket price. When the ticket price was $12, the average attendance was 22,000, and when the price dropped to $11, the average attendance rose to 25,000.

Since revenue is calculated by multiplying the ticket price by the attendance, we can determine the revenue at each ticket price. At $12, the revenue would be $12 * 22,000 = $264,000, and at $11, the revenue would be $11 * 25,000 = $275,000.

From these calculations, we can see that the revenue is higher at $11 compared to $12. However, the problem asks for the ticket price that maximizes revenue, which means we need to find the price that yields the highest revenue.

Since attendance is linearly related to the ticket price, we can assume that the relationship continues in a linear fashion. To find the revenue-maximizing price, we need to determine the point at which the revenue starts to decline.

In this case, since the revenue at $12 is lower than the revenue at $11, and there is a linear relationship, it suggests that the revenue will continue to decrease if the ticket price is further reduced. Therefore, the ticket price that maximizes revenue is $12.

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Answer:

For a 200 mile journey, 55.5 liters of fuel

is needed

Step-by-step explanation:

Here, we want to estimate the fuel needed for a 200 mile journey

we can use this by having an average

By adding all and dividing by 6

Mathematically, that will be;

(24 + 59 + 44 + 50 + 59 + 97)/6

= 55.5

The reason for this is because if we added all the lengths and divide by 6, what we get is 200

Thus, if we added the liters of fuel used per each and divide by 6, we can have an estimate for a 200-mile journey