1) Determine whether the number described is a statistic or a parameter. a) A survey of 187 law firms in a country found that the average hourly billing rate for partners was $658. b) The average salary of all employees in the City of Joliet is $78,302. 3) Determine whether the data described are nominal or ordinal. a) Brand name of a pair of running shoes. b) Highest degree conferred (high school, bachelor's, and so on).

Answer:

7, 7.1, √51, 7.2

Step-by-step explanation:

√51 is 7.14

Comparing with the approximations obtained in parts (a) and (b), we see that the approximation using Euler's method with step size 0.1 is closer to the exact solution

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

The given differential equation is:

dy/dx = x + y

with initial condition y(0) = 1.

(a) Using Euler's method with step size 0.2, we have:

x₁ = 0 + 0.2 = 0.2

y₁ = 1 + 0.2(0 + 1) = 1.2

x₂ = 0.2 + 0.2 = 0.4

y₂ = 1.2 + 0.2(0.2 + 1.2) = 1.44

Therefore, the approximation of y(0.4) using Euler's method with step size 0.2 is 1.44.

(b) Using Euler's method with step size 0.1, we have:

x₁ = 0 + 0.1 = 0.1

y₁ = 1 + 0.1(0 + 1) = 1.1

x₂ = 0.1 + 0.1 = 0.2

y₂ = 1.1 + 0.1(0.1 + 1.1) = 1.22

x₃ = 0.2 + 0.1 = 0.3

y₃ = 1.22 + 0.1(0.2 + 1.22) = 1.364

x₄ = 0.3 + 0.1 = 0.4

y₄ = 1.364 + 0.1(0.3 + 1.364) = 1.537

Therefore, the approximation of y(0.4) using Euler's method with step size 0.1 is 1.537.

(c) The given differential equation can be solved exactly by the separation of variables:

dy/(x+y) = dx

ln|x+y| = x + C

\(|x+y| = e^(x+C) = Ce^x\)

\(x+y = \pm Ce^x\)

Using the initial condition y(0) = 1, we have:

0 + 1 = ±C

C = -1

So the solution to the differential equation is:

x + y = -eˣ

Substituting x = 0.4, we get:

\(y(0.4) = -e^{0.4}\)

≈ -1.491

Hence, Comparing with the approximations obtained in parts (a) and (b), we see that the approximation using Euler's method with step size 0.1 is closer to the exact solution.

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The check for independence in a one- sample is

The population size is further than 10 times the sample size.

The Correct option is D.

What is Z- test?

A Z- test is a statistical thesis test used to determine whether a sample mean significantly differs from a given population mean when the population standard divagation is known.

For a one- sample z- test for a population proportion, the sample is named without relief from a finite population.

In order for the test to be valid, it's necessary to insure that the sample is small relative to the population size.

still, it can be considered large enough to satisfy the independence supposition, If the population size is further than 10 times the sample size. This supposition is necessary for the validity of statistical conclusion in this environment.

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You're looking for "parabola" like shapes in which the lowest point has a y coordinate of y = 0. In this case, it would be the "parabola" portion on the right that has its lowest point at (3,0). The only interval that fits is \(2 \le x \le 4\) which in interval notation is written as [2,4]. So this fits with choice D.

y1(t) = t is a solution to the given second-order differential equation, while y2(t) = sin(t) is not. the general solution of the given second-order differential equation is:y(t) = C1t + C2sin(t) (where C1 and C2 are constants

a) To determine if y1(t) = t and y2(t) = sin(t) are both solutions to the given second-order differential equation:

(1 - t⋅cot(t))y'' - ty' + y = 0

Let's calculate the derivatives of y1(t) and y2(t) and substitute them into the differential equation:

For y1(t) = t:

y1'(t) = 1

y1''(t) = 0

Substituting into the differential equation:

(1 - t⋅cot(t))(0) - t(1) + t = 0

-t + t = 0

The equation holds true for y1(t) = t. Therefore, y1(t) is a solution to the differential equation.

For y2(t) = sin(t):

y2'(t) = cos(t)

y2''(t) = -sin(t)

Substituting into the differential equation:

(1 - t⋅cot(t))(-sin(t)) - t(cos(t)) + sin(t) = 0

This equation can be simplified using trigonometric identities and algebraic manipulations, but it does not reduce to 0. Therefore, y2(t) = sin(t) is not a solution to the differential equation.

In conclusion, y1(t) = t is a solution to the given second-order differential equation, while y2(t) = sin(t) is not.

b) To determine if y1(t) = t and y2(t) = sin(t) are linearly independent, we need to check if there exist constants C1 and C2, not both zero, such that C1y1(t) + C2y2(t) = 0 for all values of t.

Assume there exist C1 and C2:

C1t + C2sin(t) = 0

To prove linear independence, we need to show that C1 = C2 = 0 is the only solution.

For t = 0:

C1(0) + C2(0) = 0

0 = 0

For t = π:

C1(π) + C2(0) = 0

C1π = 0

Since C1 can be any constant, the only solution is C1 = 0.

Therefore, C1y1(t) + C2y2(t) = 0 reduces to C2sin(t) = 0.

To satisfy this equation for all t, we must have C2 = 0 as well.

Since the only solution is C1 = C2 = 0, y1(t) = t and y2(t) = sin(t) are linearly independent.

Hence, the general solution of the given second-order differential equation is:

y(t) = C1t + C2sin(t) (where C1 and C2 are constants).

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Answer:

14 square units

Step-by-step explanation:

Answer:

0.5 X 6 X 2 = 6 square units

Answer:

D) 2/4

Step-by-step explanation:

2/4 is equivalent to 4/8 which is less than 5/8

1. The area of the circle with radius r = 4 is 200.96 square cm. 2. The area of the circle is approximately 113.04 square cm.

A circle's radius is equal to twice its diameter. In other words, if d is the diameter and r is the radius, then d = 2r. On the other hand, a circle's radius is equal to half of its diameter. Finding the circumference or area of a circle are only two examples of computations involving circles for which this connection is crucial.

The area of the circle is given by the formula:

A = πr²

Substituting the value r = 8 we have:

Area = 3.14(8)² = 200.96 square cm

2. For circle with d = 12 cm we have the radius as:

r = 12/2 = 6

A = 3.14(6)² = 113.04 square cm

Hence, the area of the circle with radius r = 4 is 200.96 square cm. 2. The area of the circle is approximately 113.04 square cm.

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The primary market transaction is (a) Johnson & Johnson issues 2,000,000 shares of new stock and sells them to the public through an investment banker.

The primary market is where companies issue new securities to raise capital. In option (a), Johnson & Johnson is issuing new stock and selling it to the public through an investment banker. This is a typical example of a primary market transaction because the company is raising new capital by issuing new shares to investors who are purchasing them for the first time.

Option (b) is a secondary market transaction because it involves the buying and selling of existing shares between two financial institutions, rather than new shares issued by the company. Option (c) is also a secondary market transaction because the shares are being sold on the NYSE, which is a secondary market. Option (d) is not a market transaction at all because it involves the direct exchange of shares between two parties, without any involvement of a broker or a market.

Finally, option (e) involves investing in a mutual fund, which in turn invests in Johnson & Johnson shares on the NYSE. This is also a secondary market transaction because the mutual fund is buying existing shares on the stock exchange.

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Answer:

  3 79/100

Step-by-step explanation:

  \(3\dfrac{1}{5}+2\dfrac{1}{5}\div\dfrac{5}{11}-3\dfrac{2}{5}\times\left(-1\dfrac{1}{4}\right)\qquad\text{given}\\\\=\dfrac{16}{5}+\left(\dfrac{11}{5}\cdot\dfrac{11}{5}\right)-\left(\dfrac{17}{5}\cdot\dfrac{5}{4}\right)\\\\=\dfrac{16}{5}+\dfrac{121}{25}-\dfrac{17}{4}=\dfrac{320+484-425}{100}=\dfrac{379}{100}\\\\=\boxed{3\dfrac{79}{100}}\)

Answer:

is A:

Step-by-step explanation:

Dino has 7 times as many coins as he has bills.

Suppose A and B are dependent events. If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

The probability of an event is described as a number that indicates how likely the event is to occur which is usually  expressed as a number in the range from 0 and 1, or preferably using percentage notation ranging  from 0% to 100%.

The relationship between two dependent events is expressed in the following equation below according to the rules of probability,

P(A|B) = P(A∩B) / P(B)

we then substitute ,

0.25 = P(A∩B) / 0.8

P(A∩B)  = 0.2

In conclusion, If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

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Since each trait is inherited independently, we can multiply the probabilities together. The probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

The probability of obtaining A/a; B/b; C/c; D/d offspring can be calculated by multiplying the probabilities of each individual trait. Since each trait is inherited independently, we can multiply the probabilities together.

The probability of obtaining A/a offspring is 1/2 (A is dominant and a is recessive).

The probability of obtaining B/b offspring is 1/2 (B is dominant and b is recessive).

The probability of obtaining C/c offspring is 1/2 (C is dominant and c is recessive).

The probability of obtaining D/d offspring is 1/2 (D is dominant and d is recessive).

Therefore, the probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

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Answer:

Apple cost $0.85

Banana cost $1.2

Step-by-step explanation:

Given data

let the number of apples be x

and the number of bananas be y

Patricia bought 5 apples and 7 bananas for $12.65

5x+7y= 12.65----------1

Jose bought 10 apples and 8 bananas for $18.10

10x+8y= 18.10-----------2

solve 1 and 2 above

5x+7y= 12.65 X 2

10x+8y= 18.10 X 1

 10x+14y= 25.3

- 10x+8y= 18.10

         6y= 7.2

y= 7.2/6

y= 1.2

put y= 1.2 in 1

5x+7(1.2)= 12.65

5x+ 8.4= 12.65

5x= 12.65- 8.4

5x= 4.25

x= 4.25/5

x= 0.85

Hence each apple cost $0.85

Banana cost $1.2

Answer: (4x-1)(3x+2)

Step-by-step explanation:

do u know how to factor?

Answer: (4y - 1)(3y + 2)

Step-by-step explanation:

\(12y^{2} +5y-2\\=(4y - 1)(3y + 2)\)

You can also do it the long way using the quadratic formula:\(\frac{-b+-\sqrt{b^{2} -4ac} }{2a}\), where a = 12, b = 5, and c = -2.

Answer: 4

The ratio in which the chocolates are divided into types can be seen as splitting the chocolates into 1+2+2 = 5 equal parts. Since there are 20 chocolates, each part corresponds to 20/5 = 4 chocolates. Thus, there are 1*4=4 chocolates with nuts, 2*4=8 plain chocolates, and 2*4=8 chocolates with caramel. Now, the three boys are dividing the chocolates into 3+1+1 = 5 equal parts. Thus, each part again corresponds to 4 chocolates. So, Andy will receive 3*4=12 chocolates, Bert will receive 1*4=4 chocolates, and Charles will receive 1*4=4 chocolates. Because neither Andy nor Charles can eat nuts, and there are four chocolates with nuts, and Bert receives four chocolates, Bert must take all of the chocolates with nuts. Charles receives four chocolates total, and, since he prefers caramel, he will take four of the eight caramels. This leaves eight plain chocolates and four caramels to make up Andy's twelve chocolates. Thus, Andy receives 4 pieces of chocolate with caramel.

Simplified form of the expression 8 ( 3 + 4 ) using the Distributive Property of Multiplication over Addition is 56

To apply the Distributive Property of Multiplication over Addition, you need to multiply the number outside the parentheses by each term inside the parentheses and then add the products together.

In this case, the number outside the parentheses is 8, and the terms inside the parentheses are 3 and 4. So, you can apply the distributive property as follows:

8 ( 3 + 4 ) = 8 × 3 + 8 × 4

Multiply the numbers

= 24 + 32

Add the numbers

= 56

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Answer:

Step-by-step explanation:

1st box. -3x

2nd and 3rd box. -21 on each side

4th box. 0

and you have the rest I hope I could help you.

Answer:

20

Step-by-step explanation:

-3x+20=-5x+20+2x

reduced:

-3x+20=-3x+20

subtract 20 from each side

Then

-3x=-3x

Answer:

it's 60!

Step-by-step explanation:

10

×6

-------

60

Answer:

1, 2, 4

Step-by-step explanation:

Okay so all of these CAN be true, but the question asks which ones MUST be:

As long as you add or multiply both sides by the same amount,  that keeps them even. Subtraction and addition can change it though because we don’t know if it’s positive or negative.

I Hope this Helps!

Answer: (A)(B)(D)    

Step-by-step explanation:

hope this helps here is proof

You can get 11 different numbers by multiplying two or more distinct members of the set (1, 2, 3, 5, and 11) together.

To find the number of numbers you can get by multiplying two or more distinct members of the set {1, 2, 3, 5, 11} together, we can use the concept of combinations. There are 5 elements in the set, and we want to choose 2 or more elements to multiply.

To choose 2 elements, there are 5C2 = 10 combinations.
To choose 3 elements, there are 5C3 = 10 combinations.
To choose 4 elements, there are 5C4 = 5 combinations.
To choose all 5 elements, there is 1 combination.

However, we need to subtract the cases where we multiply by 1, as 1 does not change the result.

For choosing 2 elements including 1, there are 4C1 = 4 combinations.
For choosing 3 elements including 1, there are 4C2 = 6 combinations.
For choosing 4 elements including 1, there are 4C3 = 4 combinations.
For choosing all 5 elements including 1, there is 1 combination.

Subtracting the cases with 1, we get:
(10 - 4) + (10 - 6) + (5 - 4) + (1 - 1) = 6 + 4 + 1 + 0 = 11 numbers.

So, you can get 11 different numbers by multiplying two or more distinct members of the set {1, 2, 3, 5, 11} together.

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Answer:

2 2/5 (For the word problem)

For the graph (In order)

4/5

1 1/4

12/30 (Or 2/5)

2 6/12 (or 2 1/2)

Step-by-step explanation:

1:

12 pounds make 5 pies, turn it into a fraction.

12/5

Now turn it into a mixed number. How many fives can go into 12?

Two fives equal ten, subtract it from twelve. Bring the amount of fives to the left.

2 2/5

2: Oh, that's really easy.

Four divided by five is 4/5

Five divided by four is 5/4 which as a mixed number is 1 1/4

3: 12 divided by thirty is 12/30, you can simplify it by dividing both sides of the denominator by three, then two. But if it's not required then just don't 12/30

4: 30 divided by 12 is 30/12, how many twelves can go into 30? Two.

30 - 24 = 6

2 6/12

By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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Answer:

110

Step-by-step explanation:

10% of 100 is 10

100+10=110

If multiple Option 1 and 2. If Only 1 option 1

A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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It would take about 8.59 months for the football player to double his current following, assuming that his follower count continues to increase at a rate of 9% per month.

To find out how long it would take for the football player to double his current online following of 105,326, we need to find the distance from his starting point to the doubling point. In other words, we need to find out how many followers he needs to gain in order to have 2 times his current following.

To do this, we can use the formula for exponential growth:

A = P(1 + r)ⁿ

where A is the final amount, P is the initial amount, r is the rate of growth (in decimal form), and t is the time (in months).

In this case, we want to find t, the time it would take for the football player to double his current following. So we can rewrite the formula as:

2P = P(1 + 0.09)ⁿ

Simplifying this equation, we can divide both sides by P:

2 = (1 + 0.09)ⁿ

Taking the natural logarithm of both sides, we get:

ln(2) = t ln(1 + 0.09)

Solving for t, we divide both sides by ln(1 + 0.09):

t = ln(2) / ln(1 + 0.09)

Using a calculator, we get t ≈ 8.59 months.

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