Question 3: (14 Marks = 10+4) (1) Suppose that the response variables Y₁, ₂, Y₁ are independent and Y₁-Bin(n.) for cach Y. Consider the following generalized linear model: In (1Z) = Bo + P₁

Answer:

wrong

Step-by-step explanation:

Answer: 2535

Step-by-step explanation:

use order of operations (parenthesis, exponents, multiplication/division, addition/subtraction)

first ill handle the two innermost parenthesis

(4 + 3(2 - 8))

(4 + 3(-6))

(4 - 18)

-14

now lets move on to the next parenthesis

( 3 - 5^2(-14))

(3 - 25( - 14)

( 3 + 350)

353

now onto the last part of the problem

8^2 + 7 (353)

64 + 2471

2535 :))

\(\\ \bull\tt\dashrightarrow f(x)=6^x\)

\(\\ \bull\tt\dashrightarrow f(-2)=6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}\)

\(\\ \bull\tt\dashrightarrow f(-1)=6^{-1}=\dfrac{1}{6}\)

\(\\ \bull\tt\dashrightarrow f(0)=6^0=1\)

\(\\ \bull\tt\dashrightarrow f(1)=6^1=6\)

\(\\ \bull\tt\dashrightarrow f(2)=6^2=36\)

Answer: Yes

Step-by-step explanation:

15/60 divided both by 15:

15/15=1 and 60/15=4

Answer:

yes

Step-by-step explanation:

15/60 divided by 15/15 = 1/4, or you could day that 15/60 simplified = 1/4, making the answer yes

the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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Hey there! :)

Answer:

(2, 3) and (-2, 11).

Step-by-step explanation:

To solve this system of equations, we can set both equations equal to each other:

x² -2x + 3 = -2x + 7

Combine like terms:

x² -4 = 0

Factor using difference of squares:

(x - 2)(x + 2) = 0

Therefore, x = 2 and -2. Plug both of these into an equation to solve for the 'y' value:

f(x) = -2(2) + 7

f(x) = -4 + 7

f(x) = 3

------------------

f(x) = -2(-2) + 7

f(x) = 4 + 7

f(x) = 11

Therefore, the two ordered pairs are (2, 3) and (-2, 11).

Step-by-step explanation:

Solving

3x + -6y = 42

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6y' to each side of the equation.

3x + -6y + 6y = 42 + 6y

Combine like terms: -6y + 6y = 0

3x + 0 = 42 + 6y

3x = 42 + 6y

Divide each side by '3'.

x = 14 + 2y

Simplifying

x = 14 + 2y

The slope of the equation 3x +6y = 42 is - 1 / 2.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore, the equation a line can be represented in slope intercept form as follows;

y = mx + b

where

Therefore,

3x + 6y = 42

6y = -3x + 42

divide both sides by 6

y = -3x / 6 + 42 / 6

y = - 1 / 2 x + 7

Therefore, the slope is - 1 / 2.

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Answer:

1. 0.37037037037

2. 0.88888888888

3. 1

4. 2.28571428571

Answer:

1) 10/27

2) 8/9

3) 2/2 or 1

4) 16/7 or 2 2/7

Step-by-step explanation:

Whenever fractions are to be be divided, it should first be rewritten with a multiplication sign with the second fraction's reciprocal.

The area of a circle with a radius r is given by the following formula:

In this case we know that the diameter is 8cm which means that its radius is 4cm. Using 3.14 for pie we get:

Then the answer is 50.24 cm².

As per the given confidence interval, the value of P is lees than significant.

Confidence interval:

In statistics, a range around a measurement that conveys how precise the measurement is referred as confidence interval.

Given,

A precision instrument is guaranteed to read accurately to within 2 units. a sample of four instrument readings on the same object yielded the measurements 353, 351, 351, and 355. find a 90% confidence interval for the population variance.

Here we need to find the assumptions of the given situation,

From the given question we have identified the following,

Reading of instruments = 353, 351, 351, and 355.

Confidence interval = 90% = 0.09

Number of units = 2.

Based on these details, the standard deviation of this temple is 0.7.

So, the Z score is the same as the sample mean minus the population mean divided by the standard error, which is 2.857.

Therefore, P value was less than significant.

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the limit of the given expression as x approaches 8 is \((e^8 + 144)^{(1/8)}\).

To find the limit of the given expression, we can simplify it and then apply l'Hôpital's Rule if necessary.

The given expression is:

lim \((e^x + 18x)^{(1/x)}\) as x approaches 8

First, let's simplify the expression:

lim \((e^x + 18x)^{(1/x)}\) = (\(lim (e^x + 18x))^{lim(1/x) }\)as x approaches 8

Now, let's evaluate each part of the expression separately.

1. Evaluating lim \((e^x + 18x)\) as x approaches 8:

Plugging in x = 8 directly into the expression, we get:

\((e^8 + 18(8)) = (e^8 + 144)\)

2. Evaluating lim (1/x) as x approaches 8:

As x approaches 8, 1/x approaches 1/8.

Now, we can rewrite the original expression as:

lim \((e^x + 18x)^{(1/x) }\)= (lim\((e^x + 144))^{(1/8)}\)

Since the exponent 1/8 is a constant, we can simply evaluate the limit of the base, which is (\(e^8\) + 144):

lim (\(e^x\) +\(18x)^{1/x}\)) = (\(e^8\) +\(144)^{(1/8)}\))

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In the given scenario, we need to determine whether each cache miss is a true sharing miss, a false sharing miss, or a hit. The variables xl, x2, and x3 are in the same cache block, which is shared in the private caches of both pi and p2.

1. First access:

- Assuming the cache block is initially empty, accessing xl would result in a cache miss since the block is not present in the cache. This miss is a true sharing miss because the block needs to be fetched from the shared state.

2. Second access:

- Since the cache block containing xl, x2, and x3 is now in the cache, accessing x2 would result in a cache hit because it is already present in the cache.

3. Third access:

- Accessing x3 after x2 would also result in a cache hit because x3 is in the same cache block as x2 and is already present in the cache.

In summary, the first access (xl) would result in a true sharing miss as the cache block needs to be fetched from the shared state. The second (x2) and third (x3) accesses would both result in cache hits since the cache block is already in the cache.

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Answer:

\( - \frac{ \sqrt{3} }{2} \)

Goodluck

m<EBA = m<DBC because the triangle has the same angle measures

To prove that m<EBA = m<DBC, we need to know the following;

From the information given, we have that;

m<1 = m<3

Then, we can say that m<EBA = m<DBC because the triangle has the same angle measures

Triangle EDB is an isosceles triangle such that two of its sides and angles are equal

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Answer:

N

Step-by-step explanation:

Have a great day! Hope this helps :)

Answer:

Angle ADC = 7x - 6°

Step-by-step explanation:

4x - 12 + 3x + 6 = 7x - 6

Answer:

Step-by-step explanation:

Diagonal BD of a given rhombus is angle bisector of ∠ADC, so:

Substitute the values and solve for x:

Find the value of ∠ADC:

Answer:

$312.5

Step-by-step explanation:

#250÷8=$31.25

#$31.25*10=$312.5

Answer: The answer is 0.

X = 0 when evaluated.

Step-by-step explanation:

Answer:

4.0 hope this helps!!6

If the null hypothesis is true and there is no treatment effect, the expected value on average for the F-ratio would be 1.00. The correct answer is option (b) 1.00

In hypothesis testing using the F-test, the F-ratio is calculated by dividing the variance between groups (treatment effect) by the variance within groups (random variation). When the null hypothesis is true and there is no treatment effect, the numerator (variance between groups) and the denominator (variance within groups) would be similar, resulting in an F-ratio close to 1.

Therefore, the correct answer is b. 1.00, as the expected value for the F-ratio would be around 1 when the null hypothesis is true and there is no treatment effect.

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Answer:

(a)5 and 8

(b)5 and 5

(c) 7 and 5

(d)6 and 2

(e)6 and -2

Step-by-step explanation:

(a)a negative integer

We consider the integers 5 and 8

Difference = 5-8 =-3

3 is a negative integer.

(b)Zero

We consider the integers 5 and 5

Difference = 5-5 =0

(c) an integer smaller than both the integer.

We consider the integers 7 and 5

Difference = 7-5 =2

2 is smaller than both integers.

(d) an integer smaller than only one of the integers.

We consider the integers 6 and 2

Difference =6-2=4

4 is smaller than only 6.

(e)an integer greater than both the integers

We consider the integers 6 and -2

Difference =6-(-2)=6+2=8

8 is greater than both 6 and -2.

The XYZ corporation will receive $1500000 for all the shares sold.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

Given: Cost of 1 share = $15

To find: Money received on selling 100000 shares.

Finding:

By unitary method,

Money received on selling 1 share = $15

Money received on selling 100000 shares = 15(100000) = $1500000

Hence, The XYZ corporation will receive $1500000 for all the shares sold.

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245.31 (dollars) is the cost (in dollars) of materials for the least expensive such container.

Calculus maxima and minima are found  using the concept of derivatives. Knowing that the derivative concept gives information about the slope/slope of a function, we find the point where the slope is zero. These points are called inflection points/stationary points. These are the points associated with the maximum or minimum (local) values ​​of the function.

Knowledge of maxima and minima is essential for our everyday problems. In addition, this article also explains how to find the absolute maximum and minimum values.

Solvable maximum and minimum arithmetic problems  are discussed in this article.

Suppose the width is x (m), length of the base is 2x (m), the base area is 2x^2 (m^2).

Since the volume is 10 (m^3), the height has to be 10/2x^2 (m) = 5/x^2.

The cost of making such container is

cost of base: 2x^2*15 = 30x^2

cost of sides: (2*2x*5/x^2 + 2*x*5/x^2)*9 = 270/x

The overall cost is hence the sum of the base and the sides: f(x) = 30x^2 + 270/x

The get the minimum,

df(x)/dx = 30*(2x - 9/x^2) = 0

so x = (9/2)^(1/3) = 1.651 (m)

f(x) = 245.31 (dollars)

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Step-by-step explanation:

Hey there!

\(\tt{\dfrac{\dfrac{1}{x^2} + \dfrac{2}{y}}{\dfrac{5}{x} - \dfrac{6}{y^2}}}\)

So, what we can do here is first take the Least Common Multiple here, on both Numerator and Denominator.

\(\tt{\dfrac{\dfrac{y + 2y^2 (1)}{x^2 y (2)}}{\dfrac{5y^2 - 6x (3) }{xy^2 (4)}}}\)

[The number in brackets is for the next step :-

When we will further simplify it, we will multiply 1st with 4th and 2nd with 3rd.

\(\tt{\dfrac{y + 2y^2 \times xy^2 }{x^2 y \times 5y^2 - 6x }}\)

\(\tt{\dfrac{y + 2y^2 \times y }{x \times 5y^2 - 6x }}\) is the framed answer.

Answer:

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

Step-by-step explanation:

Lets do the numerator and denominator seperately:

Numerator:

1/x^2 + 2/y

Find common denominator and add these 2 fractions:

This is x^2y (I just multiplied the 2 denominators together’

Now, do what you have done to x^2 to make it x^2y, ie. multiplied by y, to the 1. This = y

And do what you have done to y to make it x^2y, ie. multiplied by x^2, to the 2. This = \(2^{2}\)

Now, arrange all numbers we have found into the correct order in the fraction. This is:

\(\frac{y+2x^{2}}{x^{2} y}\)

Denominator:

5/x - 6/y^2

Find the common denominator  and subtract these two fractions:

This is xy^2

Now, do what you have done to x to make it xy^2, ie. multiply by y^2, to the 5. This = 5y^2

And do what you have done to the y^2 to make it xy^2, ie. multiply by x, to the 6, this is = 6x

Now, arrange all the numbers we have found into the correct order in the fraction

\(\frac{5y^{2}-6x}{xy^2}\)

Now that we have the numerator and the denominator, we can solve the equation.

The original question asks us to divide the 2 fractions, so:

\(\frac{y+2x^{2}}{x^{2} y}\)  divided by \(\frac{5y^{2}-6x}{xy^2}\)

For the division of fractions, you just have to multiply the inverse of the 2nd fraction by the first, so

\(\frac{y+2x^{2}}{x^{2} y}\) x \(\frac{xy^2}{5y^2-6x}\)

Use cross multiplication to simplify the above expression to:

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

Hope this helps, sorry its long ...

The radius of convergence is 1/3. To find the radius of convergence for the power series using the ratio test, we need to analyze the general term of the series. The given series is:

Σ(an * x^n)

where an is the coefficient of the term with x raised to the power n. The coefficients in the given series are:

a1 = 3
a2 = 36
a3 = 243
a4 = 1296
a5 = 6075
...

Notice that each coefficient is a multiple of 3^n. Thus, we can write the general term as:

an = 3^n

Now, we apply the ratio test. The ratio test states that the series converges if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is less than 1:

lim (n → ∞) |(a(n+1) * x^(n+1)) / (an * x^n)|

= lim (n → ∞) |(3^(n+1) * x^(n+1)) / (3^n * x^n)|

To simplify, divide 3^(n+1) by 3^n:

= lim (n → ∞) |(3 * x)|

The series converges when |3 * x| < 1. To find the radius of convergence, solve for |x|:

|x| < 1/3

The radius of convergence is 1/3.

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Answer:

scientific notation

Step-by-step explanation:

This number is shown in scientific notation.

Answer:

0.00000146

Step-by-step explanation:

I took the test

He traveled 7.2 hours towards his grandfather house and took him 4.8 hours to return.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. The substitution method can be used to algebraically solve a linear problem. The one y-value in the replacement procedure is replaced with the other. We'll give an example to illustrate this. Since y = y, we may replace y in the second equation with y from the first equation.

Given,

We set

x as the travel time John took to reach his uncle's house,

y as the travel time John took to return from his uncle's house.

So,

x + y = 12  ...(1)

Equating velocities,

24x = 36y

x = 3/2 y

Substituting in equation (1), using substitution method

3/2 y + y = 12

\(\frac{3y +2y}{2}\)

5y = 12 (2)

y = 4.8

Substituting in equation (1)

x = 12 - 4.8

x = 7.2

He traveled 7.2 hours towards his grandfather house and took him 4.8 hours to return.

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Answer:

A = 20

B = 12.5

C = 10.2

Step-by-step explanation:

A = (10 + 20 + 30)/3 = 20

B = (5 + 10 + 15 + 20) = 12.5

C = (1 + 5 + 10 + 15 + 20) = 10.2