Change the rational number 18 to a decimal. Show work (worth 3 points).

Answer:

C) 1/2

Step-by-step explanation:

We know that 3/8 cup of brown sugar and 1/3 cup of white sugar are mixed together to make the sugar mixture.

From this sugar mixture, 1/4 cup is set aside for the crumb topping.

To find out how much sugar mixture is used to make the cake, we need to subtract the amount set aside for the crumb topping from the total sugar mixture.

We can start by converting the mixed unit of measurement (brown sugar in cups and white sugar in cups) to a single unit of measurement (cups)

3/8 cup of brown sugar + 1/3 cup of white sugar = (3/8)+(1/3) = 5/12 cup + 4/12 cup = 9/12 cup.

1/4 cup is set aside for the crumb topping.

So, the remaining sugar mixture used to make the cake is 9/12 cup - 1/4 cup = (9/12) - (1/4) = (9-3)/12 = 6/12 cup = 0.5 cup

The use of "i" to represent the imaginary unit, which is defined as the square root of -1, is attributed to Leonhard Euler, a Swiss mathematician, and physicist who lived in the 18th century.

The concept of using the imaginary unit "i" to represent the square root of -1 was first introduced by mathematicians in the 16th century, such as Rafael Bombelli and Gerolamo Cardano. However, it was not fully accepted and understood until the 18th century, when mathematicians like Leonhard Euler and Jean-Robert Argand developed the idea of representing complex numbers as points in a 2D plane using the real and imaginary axes. This idea revolutionized the field of mathematics, allowing for the development of complex analysis and leading to important applications in physics, engineering, and other sciences. Today, the use of the imaginary unit is fundamental in many areas of mathematics and its applications.

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No, the LDA classifier and the Bayes classifier would not necessarily give similar boundaries when trained on a large amount of training data from an arbitrary distribution.

The LDA (Linear Discriminant Analysis) classifier assumes that the input features are normally distributed and that the class covariances are equal. It finds linear boundaries that maximize the separation between classes based on these assumptions. On the other hand, the Bayes classifier makes decisions based on the class conditional probabilities and prior probabilities of the classes. It can handle arbitrary distributions and does not make assumptions about the class covariances. Therefore, even with a large amount of training data, if the distribution of the data does not conform to the assumptions of LDA (e.g., non-normal distributions or unequal class covariances), the LDA classifier may not give similar boundaries to the Bayes classifier.

The LDA and Bayes classifiers may not give similar boundaries when trained on data from an arbitrary distribution, as the LDA classifier relies on specific assumptions about the data distribution that may not hold true in practice.

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Given that the Masses Mi are located at the points Pγ, we have to find the Moments Mx and My and the Center of Mass of the system. The Moments Mx and My and the Center of Mass of the system are 49 units, 40 units, and (40/9, 49/9) respectively.

Moment about the x-axis can be given as M_x = ∑y_i m_i .

Moment about the y-axis can be given as M_y = ∑x_i m_iCenter of Mass can be given as X = ∑x_i m_i/ MTotal & Y = ∑y_i m_i/ MTotal

Here, the position vectors of the masses Mi are P1 = 2i + 3jP2 = 4i + 5jP3 = 6i + 7j and masses are m1 = 2, m2 = 3, m3 = 4.  The center of mass is the point where the system can be balanced.

Let's start by calculating M_x and M_y.We can calculate M_x and

M_y using the below formula,M_x = m1 * y1 + m2 * y2 + m3 * y3M_x = 2 * 3 + 3 * 5 + 4 * 7M_x = 6 + 15 + 28M_x = 49M_y

= m1 * x1 + m2 * x2 + m3 * x3M_y = 2 * 2 + 3 * 4 + 4 * 6M_y = 4 + 12 + 24M_y

= 40 Hence, the Moment Mx is 49 units and Moment My is 40 units.

Now, let's calculate the Center of Mass using the below formula

,X = m1 * x1 + m2 * x2 + m3 * x3 / MTotalY

= m1 * y1 + m2 * y2 + m3 * y3 / MTotalM

Total = m1 + m2 + m3X = (2 * 2 + 3 * 4 + 4 * 6) / (2 + 3 + 4)X

= (4 + 12 + 24) / 9X = 40/9 Y = (2 * 3 + 3 * 5 + 4 * 7) / (2 + 3 + 4)Y

= (6 + 15 + 28) / 9Y

= 49/9

Hence, the Center of Mass is (40/9, 49/9).

Therefore, the Moments Mx and My and the Center of Mass of the system are 49 units, 40 units, and (40/9, 49/9) respectively.

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The true statement of the right triangle are as follows;

sin ∅ = 4 / √97

tan β = 9 / 4

cos β = 4 / √97

4² + 9² = √97

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The side and angles of the right angle triangle can be found using trigonometric ratios as follows:

sin ∅ = opposite / hypotenuse

cos ∅ = adjacent / hypotenuse

tan ∅ = opposite / adjacent

Therefore, using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

4² + 9² = (√97)²

4² + 9² = √97

Using trigonometry,

sin ∅ = 4 / √97

tan β = 9 / 4

cos β = 4 / √97

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Answer:

I have been proved in attachment

Answer:

QR = 15

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(QR+5) *5 = 10^2

(QR+5) *5 = 100

Divide each side by 5.

(QR+5) *5/5 = 100/5

(QR+5)  = 20

Subtract 5 from each side.

QR = 20-5

QR = 15

Image is attached below.

If the sum of the digits its divisible by 9,

then the original number is divisible by 9.

Since 18 (the sum of the digits) is divisible by 9,

the number 540,171 is also divisible by 9.

Answer:

Yes, The number is divisible by 9

Step-by-step explanation:

If you divide the number by 9 you will get 60019. Also if we add the numbers we will get 18 which is also divisible by 9.

Hope this helps.

The existing power plant in West Fremont can produce 96,000,000 kWh of electrical energy in a year.

The existing power plant in West Fremont has a capacity of 12 megawatts (MW) and can operate at full capacity for 8,000 hours/yr.

This means that the plant can produce 12 MW x 8,000 hours = 96,000 megawatt hours (MWh) of electrical energy in a year.

This energy can be further converted to 96,000 MWh/1,000 kWh/MWh = 96,000,000 kilowatt hours (kWh) of electrical energy in a year.

Therefore, the existing power plant in West Fremont can produce 96,000,000 kWh of electrical energy in a year.

The town currently pays $0.10 per kWh of energy, which means it would cost $9,600,000 to purchase this energy from the electric utility.

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On solving the provided questyion, As a result, the answer to the given function issue is k = 0.01238 and 24,390 years.

One variable in a function is defined in terms of another. The phrase "Y is a function of x" (symbolized as y = y(x)) indicates that y varies according to the value that the x expression assumes. Despite the fact that it is usually asserted that "x causes y," this is not always the case.

Given :  t = 2005 -2000 = 5 years

a=6.124

Population  =a

\(6.515 = 6.124\\= > =6.515/ 6.124\\= > ln( 6.515/ 6.124 ) = 5k\\= > k = 0.01238\)

\(7.5 = 6.124\\= > = 7.5/ 6.124\\= > t = 150/280\\= > t =24,390 years.\\\)

Therefore , the solution to the given problem of function comes out to be

\(k = 0.01238 and 24,390 years.\)

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The solution of the equation is c= 2/5 and d= 3/2.

We have Equation.

5c + 4d = 8

-5c + 2d = 1

Solving above equation we get

5c + 4d = 8

-5c + 2d = 1

___________

         6d = 9

          d = 3/2

and, 5c + 4(3/2)= 8

5c = 8 - 6

5c = 2

c= 2/5

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Answer:

-2.46

Step-by-step explanation:

151/24=6.29

6.29-8.75=-2.46

Answer:

-2.45833333333

Step-by-step explanation:

151 divided by 24= 6.29166666667

6.29166666667-8.75=-2.45833333333

2dp=2.46

Answer:

(A = 2,3)(B = -2,-5)(C = 4,4)(D = -6,8)(E = 8,-6)(F = -8,-6)(G = 3, 2.5)

The value of x is 22.

Given is a parallelogram ABCD, in which angle B and C are 4x+12 and 3x+14, we are asked to find the value of x,

We can make use of the fact that a parallelogram's adjacent angle sum equals 180 degrees.

According to the given information, the adjacent angles B and C are 4x + 12 and 3x + 14, respectively.

The equation:

(4x + 12) + (3x + 14) = 180

Combine like terms:

7x + 26 = 180

Subtract 26 from both sides:

7x = 154

Divide both sides by 7:

x = 22

Therefore, the value of x is 22.

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Answer:

11.88 $ (approximately)

Step-by-step explanation:

10.99 is approximately 11

So

100$ …8$

1$ .… 8/100 $

11$… 8/100×11 $

22/25 $

0.88 $

So she total has to pay

11 + 0.88 $

11.88 $ (approximately)

The missing value in the equation 3(y - 2) = 18 using the properties of equality is 6.

Given that 3(y - 2) = 18. To solve for y, use the properties of equality and fill the missing value as follows: 3(y - 2) = 18. The first step is to simplify the left side of the equation by multiplying 3 to the brackets.

3 * y - 3 * 2 = 183y - 6 = 18

Add 6 to both sides of the equation to isolate the term 3y on one side.

3y - 6 + 6 = 18 + 63y = 24

Finally, divide both sides of the equation by 3 to obtain the value of y.

3y/3 = 24/3y = 8

Therefore, the solution for y is 8.

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The critical value of 2.576. If |z| > 2.576, reject the null hypothesis; otherwise, fail to reject the null hypothesis.

To test the manufacturer's claim at a 1% significance level, we need to perform a hypothesis test. Let's define the null and alternative hypotheses:

Null hypothesis (H₀): The medicine is 90% effective in relieving backache.

H₀: p = 0.9

Alternative hypothesis (H₁): The medicine is not 90% effective in relieving backache.

H₁: p ≠ 0.9

Where p represents the true proportion of people who experience relief from backache after taking the medicine.

To conduct the hypothesis test, we will use the sample proportion and perform a z-test.

Calculate the sample proportion:

p = x/n

where x is the number of people who experienced relief (160) and n is the sample size (200).

p= 160/200 = 0.8

Calculate the standard error:

SE = √(p(1 - p)/n)

SE = √((0.8 * (1 - 0.8))/200)

Calculate the test statistic (z-score):

z = (p - p₀) / SE

where p₀ is the hypothesized proportion (0.9 in this case).

z = (0.8 - 0.9) / SE

Determine the critical value for a two-tailed test at a 1% significance level.

Since we have a two-tailed test at a 1% significance level, the critical value will be z* = ±2.576 (obtained from a standard normal distribution table or calculator).

Compare the absolute value of the test statistic to the critical value to make a decision:

If the absolute value of the test statistic is greater than the critical value (|z| > z*), we reject the null hypothesis.

If the absolute value of the test statistic is less than or equal to the critical value (|z| ≤ z*), we fail to reject the null hypothesis.

Substituting the values into the equation, we can determine the test statistic and compare it to the critical value.

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The product of the numbers or expressions is determined as  (3k³ - 24k² + 45k ) / (5k⁴ - 25k³).

The product of the numbers or expressions given is calculated by applying the following method as follows;

The given expression;

(k² −8k + 15) / 5k³   ·   3k / (k - 5)

The product of the numbers or expressions is calculated as follows;

the product of the numerators = (k² −8k + 15)·(3k)

= 3k³ - 24k² + 45k

the product of the denominators = (5k³) · (k - 5)

= 5k⁴ - 25k³

Finally, write the solution properly in fraction form as follows;

(k² −8k + 15) / 5k³   ·   3k / (k - 5) = (3k³ - 24k² + 45k ) / (5k⁴ - 25k³)

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Answer:

x = 8

Step-by-step explanation:

Since < A and < B are vertical angles, then it means that they have the same measure.

Given that m < A = (3x - 21)°, and m < B = (2x - 13)°:

We can set up the following equation to solve for the value of x:

m < A  = m < B

(3x - 21)° = (2x - 13)°

3x - 21 = 2x - 13

Subtract 2x from both sides:

3x - 2x - 21 = 2x - 2x - 13

x - 21 = -13

Add 21 to both sides to isolate and solve for the value of x:

x - 21 + 21 = -13 + 21

x = 8

We must verify if we have the correct value for x by plugging in 8 into the equality statement:

(3x - 21)° = (2x - 13)°

[3(8) - 21]° = [2(8) - 13]°

(24 - 21)° = (16 - 13)°

3° = 3° (True statement. This means that we have the correct value for x).

Therefore, the value of x = 8.

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The most common age among the teacher dataset can be found using the mode. Items that are FOB destination have ownership transferred from the seller to the buyer when the items are received.

To find the most common age among the teacher dataset, we would use the mode. The mode represents the value that appears most frequently in the dataset, and in this case, it would give us the age that is most common among the teachers.

If a company focuses primarily on providing superior customer service to differentiate itself from competitors, it is exhibiting a service positioning strategy. By prioritizing customer service and offering exceptional support and assistance to customers, the company aims to create a competitive advantage based on the quality of service it provides.

Items that are FOB destination are those where ownership transfers from the seller to the buyer when the items are received by the buyer. This means that the seller retains ownership and responsibility for the items until they reach the buyer.

When considering how a product will last under specific conditions, the quality dimension being evaluated is durability. Durability refers to the product's ability to withstand wear, usage, or environmental factors over time and maintain its functionality and performance.

When a business runs out of stock, it incurs shortage costs. These costs arise from the unavailability of products to meet customer demand, leading to lost sales opportunities, potential customer dissatisfaction, and the need to expedite orders or source products from alternative suppliers. Shortage costs can include lost revenue, customer loyalty, and the potential for reputational damage.

In conclusion, the mode is used to find the most common age among the teacher dataset. A company focusing on superior customer service exhibits a service positioning strategy. Items that are FOB destination have ownership transferred when received by the buyer. Evaluating how a product will last under specific conditions relates to its durability. Running out of stock incurs shortage costs for a business.

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Individual : a male in the United States

Variable : income

Population : All males in the United States

Sample : 2500 males of which the information is collected

Parameter : Median income of males in the U.S

Statistic : Median income of the 2500 males sampled

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Answer: C = D x pie = 62.8

A= pie x 20/2 = 31.4

pie = 3.14

D= 20

Step-by-step explanation:

The adjusted trial balance for revenue in the accounting worksheet is 20,000.

Trial balance in the accounting worksheet is a financial report where the credit entries and debit entries are listed which is used to audit the accounting system of business or organization internally. It is used to confirm that the sum of all credits and debits must be equal.

Here we have the credit of 15,000 for revenues.

Then the trial balance is adjusted with a credit of 5000.

If we have two debits or credits, we will add them.

So the adjusted trial balance = 15,000 + 5,000 = 20,000

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Answer:

27

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

Answer:

w=-6

Step-by-step explanation:

2(w-9)=5w+6+w

multiply 2 to the (w-9), also add the 5w to the other w

2w-18=6w+6

subtract 2w to 6w

-18=4w+6

subtract 6 to -18

-24=4w

divide 4 to -24

THE ANSWER IS -6

Answer:

N = I ( 1 + 50% )^t

Step-by-step explanation:

Given that The population of Columbus in 2015 was 840,000 people. In 2018 (three years later), The population grew to 972,405 people.

Write an exponential equations that models this situation.

From the question, the following parameters are given :

Initial number of population = 840,000

The new number of population = 972,405

The number of years = 3

Let the initial population = I

The new population = N

And the number of years = t

Since the population is increasing, the exponential equation can be written as

N = I ( 1 + R% )^t

Where R% is the percentage increase.

Solve for R

972405 = 840,000 ( 1 + R% )^3

972405/840000 = ( 1 + R% )^3

1.157625 = ( 1 + R% )^3

( 1 + R% ) = 1.05

Make R% the subject of formula

R% = 1.05 - 1

R% = 0.5

R = 0.5 × 100

R = 50%

Therefore, the exponential equations that models this situation can be expressed as:

N = I ( 1 + 50% )^t

Answer:

4. 3

Step-by-step explanation:

If you multiply 2 by 3 it'll equal to 6. Same with 7 x 3= 21.

You could also subtract 7 from 2 equalling 5 and 21 - 6 equal to 15. Then you would but y over x giving you 15/5. 15 divided by 5 is 3. So both ways you get 3.

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It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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We can plot in the coordinate plane if an ordered pair is known to us.

The space or plane in where location of points is represented by a pair of numerical terms with respect to some reference lines or reference direction is called coordinate plane.

let we have some pair of numerical terms such as A (4, 9) and B (6, 10)

that is needed to plot in the coordinate plane.

At first, we will plot the point A (4, 9)

we will start from the origin and move horizontally along the direction of X axis up to 4 unit. In the next, start again and move up vertically in the direction of y axis up to 9 unit. And we will draw a point at the final location.

By the same way, we can plot the point B.

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Answer:

$613.30

Step-by-step explanation:

8.75% = 0.0875

8.75% of $ 563.95 is  $ 0.0875*563.95

$ 0.0875*563.95 is tax in dollars

the total cost = $ 563.95 + $ 0.0875*563.95  = $ 613.295 = $613.30