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A line passes through the point (-2,3) and has a slope of 1/5.

show work to write the equation of the line in point-slope form.

Etta needs to add the source of the information to better arrange these notes.

A note is a place where information about a specific item is recorded for later reference. The main goals of taking notes are to promote active learning and create study materials for tests. You should be able to organise material into an understandable format that will aid in your learning process by developing note-taking skills.

As a result, it is clear from the question that Etta is making notes for the purpose of creating a webpage about healthy eating. Once her notes have been organised with the relevant facts and information, Etta will need to cite her sources.

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The measure of ∠JMK =52° and ∠KML = 38°.

Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove:  is a right angle.

Proof:

Statements  Reasons

1. m∠JMK = 52°                  Given

2. m∠KML = 38°                  Given

3. m∠JMK + m∠KML = m∠JML

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. 52° + 38° =m∠JML            Substitution property of equality

5. 90° = m∠JML                    Simplification

6. ∠JML is a right angle.      Definition of right angle

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Based on the number of waffles that each server can deliver at a time, the number of servers needed for 300 waffles in an hour is 6 servers

The number of trips the servers will have to make is 33 trips

If each server can deliver nine waffles at a time and they take 10 minutes per trip, the number of waffles they can deliver in an hour is:

= Number of waffles per trip x Number of minutes in an hour / Number of minutes per trip

= 9 x 60 / 10

= 54 waffles

If there are 300 waffles to be delivered, the number of servers needed is:
= 300 / 54

= 5.56

= 6 servers

The number of trips that the servers will make altogether is:

= Number of servers x trips per hour for each server

= 5.5555 x 60 / 10

= 33 trips

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Answer:21

14 divided by 2 would be 7 which is 50% of 14, so now you just add 14+7 and you should get 21.

Answer:

Step-by-step explanation:

you start off with 14 a way I do it for 50% is that I half the number so half of 14 is 7

14 + 7 = 21

The answer is 21

Answer:

(∛125)^5

=  3125.

Step-by-step explanation:

125 ^ (5/3)

= (cube root of 125) to the 5th power

= (∛125)^5

= 5^5

=

Answer:

Step-by-step explanation:

1) The smaller sticks will range in length from almost 0 unit up to a maximum of 0.5 unit, with each length equally possible.

Therefore, the average length will be about (0 + 0.5)/2 = 0.25 unit

2)If you assume that each break in the stick is uniformly distributed along the length of the stick and is independent of the location of the other break, then the odds are 25% that you will be able to form a triangle with the 3 pieces.

We'll call the length of the stick 1, so each break can occur at a position in the interval [0,1]. Let x and y represent the two breaks. Then we can look at the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is our probability.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square, so the probability that you can form a triangle is 25%

Since the sales representative calls on four hospitals in westchester county, the numbers of ways can he organize his calls is option A: 24  possible ways.

Throughout every stage of the sales process, a sales representative deals directly with customers. They must determine a customer's needs, make a compelling case for pertinent items or services, and guarantee a positive overall experience.

Note that:

For the first call he makes, he has 4 choices.

For the first call he makes, he has  3 choices.

For the first call he makes, he has choices.

For the first call he makes, he has choice.

Solution:

4 x 3 x 2 x 1 = 24 possible combinations.

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See options below

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?

24

7

120  

37

Hello!

Answer:

\(f^-1 (x)= 4x^2+3\)

Hope this helps!

Answer:

$87

Step-by-step explanation:

See below for the solution to each expression

Expression 1

The expression is given as:

(x-y)(y-z)(x+z)/(2x^2+4yz+6)

Expand the numerator

(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)

Further, expand the numerator

(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Evaluate the like terms

(x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Expression 2

The expression is given as:

4(x+y)(x-y)(y-x)

Apply the difference of two squares

4(x^2 - y^2)(y - x)

Expand the expressions in the brackets

4(x^2y - x^3 - y^3 + xy^2)

Open the bracket

4x^2y - 4x^3 - 4y^3 + 4xy^2

Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2

Expression 3

The expression is given as:

(√25+√9/2) + √21675

Take the square roots of 25, 9 and 21675

(5 +3/2) + 5√867

Evaluate the sum

13/2 + 5√867

Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867

Expression 4

The expression is given as:

(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z

Factor out 3 and 2 from the numerator

3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z

This gives

18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

The expression cannot be further simplified.

Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

Expression 5

The expression is given as:

(x^2+6x+5)/(x+2)(x+6)

Factorize the numerator

(x + 1)(x + 5)/(x + 2)(x + 6)

Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)

Expression 6

6) (xy/m) + (xm/y) - (m/x) = 63

Factor out x

x(y/m + m/y) - m/x = 63

Evaluate the sum

x(y^2 + m^2)/y - m/x = 63

Multiply through by xy

x^2(y^2 + m^2) - my = 63xy

Add my to both sides

x^2(y^2 + m^2)  = 63xy + my

The above implies that the variable x cannot be isolated from the equation

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Answer:

Organize into a table for good gatherings.

The percentage of his income he saved is 44.4%.

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a proportion or share of a whole, such as a percentage of a total amount, a percentage of a target or goal, a percentage of a population, etc.

In mathematical terms, a percentage can be represented as a decimal or a fraction, and is expressed as a symbol, such as "%".

If Ravindra's monthly income is rupee 90000 and saves rupee 40000 per month, then the percentage can be calculated as:

percentage = (40,000/90,000) x 100% = 44.4%

Hence, she saves 44.4% of his income per month.

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we have proven that the equation a + b > 0 and\(a^2 < b^2\) , then a < b.

1. Solution:

We have the equation:

\($$3x-1\left| -2-3 \right|=2x-1$$\)

Since \($-2-3=-5$,\)

we have \($$3x-1\left| -5 \right|=2x-1$$$$\Leftrightarrow \left\{ \begin{matrix} 3x+4=2x-1 & (1) \\ 3x+6=2x-1 & (2) \end{matrix} \right.$$$(1) $\Leftrightarrow x=-5$.$(2) \Leftrightarrow x=-7$.\)

The set of the values of $x$ that satisfy the given equation is $\left\{ -7,-5 \right\}$.$$\\$$2.

Proof: Suppose that \($a + b > 0$\) and \($a^2 < b^2$.\)

We want to prove that\($a < b$.\)

From the given condition, we have the following inequalities:

\($$a + b > 0 \Leftrightarrow a > -b \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (1)$$$$a^2 < b^2 \Leftrightarrow \left( {a - b} \right)\left( {a + b} \right) < 0 \Leftrightarrow a - b < 0\Leftrightarrow a < b\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)$$\)

To prove that a < b, it suffices to show that a > -b.

From $(1)$, we know that a + b > 0, which implies that a > -b as required.

Hence, we have proven that if a + b > 0 and\(a^2 < b^2\) , then a < b.

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The rate of change of the volume when radius of sphere is 11 inch is 2904π inch³/minutes

According to the question,

The radius r of a sphere is increasing at a rate of 6 inches per minutes

Volume of sphere is 4/3 πr³

We have to find Rate of change of volume when r = 11 inch

Differentiating volume of sphere w.r.t time

V = 4/3 πr³

=> dV/dt = 4 πr² . dr/dt ---------(1)

As it is given that ,

dr/dt = 6

Substituting the value in equation (1)

=>  dV/dt = 4 πr² . 6

=> dV /dt = 24 πr²

r = 11

=> dV /dt = 24 π(11)²

=> 2904 π inch³/minutes is rate of change of volume

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Answer: C

Step-by-step explanation:

4/8 ×3/1

a. There are 10 choices for each digit and 26 choices for each letter, so the number of different license plates possible without repetition is 10 * 10 * 10 * 10 * 26 * 26 * 26 * 26 = 456,976,000.

b. With repetition allowed, there are still 10 choices for each digit and 26 choices for each letter. Since repetition is permitted, each digit and letter can be chosen independently, so the total number of different license plates possible is 10^4 * 26^4 = 45,697,600.

In part (a), where repetition is not allowed, we consider each position on the license plate separately. For the four digits, there are 10 choices (0-9) for each position. Similarly, for the four letters, there are 26 choices (A-Z) for each position. Therefore, we multiply the number of choices for each position to find the total number of different license plates possible without repetition.

In part (b), where repetition is permitted, the choices for each position are still the same. However, since repetition is allowed, each position can independently have any of the 10 digits or any of the 26 letters. We raise the number of choices for each position to the power of the number of positions to find the total number of different license plates possible.

It's important to note that the above calculations assume that the order of the digits and letters on the license plate matters. If the order does not matter, such as when considering combinations instead of permutations, the number of possible license plates would be different.

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Answer:

x=4

Step-by-step explanation:

Answer:

\(\frac{\sqrt{2} }{8}\)

Step-by-step explanation:

Using the exact values of the given trig functions, then

sin45° × sin30° × cos60°

= \(\frac{\sqrt{2} }{2}\) × \(\frac{1}{2}\) × \(\frac{1}{2}\) = \(\frac{\sqrt{2} }{8}\)

Answer: (1) C. 65 + 28H < 250

(2) 6

Step-by-step explanation:

Here is the correct question:

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Since the initial fee charged by the plumber is $65 and an hourly rate of $28, and Anand would like to spend no more than $250. This means that the addition of the initial fee plus the hourly fee based on number of hours worked will have to be less than $250. This can be mathematically expressed as:

= 65 + 28H < 250

That means option C is the correct answer.

Option B and D are incorrect because the greater sign was used but Anand doesn't want to spend more than $250 but the options denoted that he spent more than $250 which isn't correct.

2)'The largest whole number of hours that Anand can afford goes thus:

65 + 28H < 250

28H < 250 - 65

28H < 185

H < 185/28

H < 6.6

Therefore, the largest whole number of hours that Anand can afford is 6.

Answer: The Answer is 65+28H < 250 and the largest amount of hours is 6

Step-by-step explanation:

Answer:

I thought you were quoting danganronpa for a second ...

I hope you feel better!!

Step-by-step explanation:

Answer: $3.75

Step-by-step explanation:

Answer:

The cost of 6 cans of soup is 3.75

Step-by-step explanation:

12 = 7.50

1 can = x

12x = 7.50

We need to find the cost of 1 can. So we divide 7.50 by 12.

x = 0.625

Then multiply by 6.

0.625 x 6 = 3.75

As a result the cost of 6 cans of sup is $3.75

Answer:

Bias from using a convenience sample (C)

Step-by-step explanation:

This sampling method is an example of taking a convenience sample because the mobile phone service provider is only taking samples from the people that responded. The availability of certain people causes a bias in the data drawn from this sampling method.

Answer:

4

Step-by-step explanation:

y = kx

Use point (3, 12).

12 = k * 3

k = 12/3 = 4

y = 4x

Answer: 4

Divide y by x:

12/3 = 4

36 / 9 = 4

The constant of variation is 4

The mean was calculated for each sample, and the distribution of sample means was visualized using histograms for three different values of n: 1, 5, and 30.

For the uniform distribution, as the sample size (n) increased from 1 to 30, the distribution of sample means shifted towards a more symmetrical and bell-shaped curve. This is consistent with the Central Limit Theorem, which suggests that larger sample sizes lead to a more normal distribution of sample means. Additionally, the mean and standard deviation of the sample means approached the population mean and standard deviation, respectively, as n increased. This further confirms the Central Limit Theorem, as it states that the mean of the sample means is equal to the population mean, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size.

In the second part of the analysis, the same steps were repeated using data generated from a Gaussian (Normal) distribution with a mean of 5 and a standard deviation of 1. Similar to the uniform distribution, as the sample size increased, the distribution of sample means approached a normal distribution. The mean and standard deviation of the sample means were also consistent with the properties described by the Central Limit Theorem.

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Answer: 8

Step-by-step explanation:

\(15 + 3(\frac{6}{2} )-4^2\)

Using order of operations, solve parenthesis first

\(15 + 3(3 )-4^2\\15 + 9-4^2\)

Next, solve exponents. Note that only the '4' is getting raised to the '2' power, not '-2'

\(15 + 9-(4^2)\\15 + 9-16\)

Simplify

\(15+9-16\\=8\)

Answer:

C

Step-by-step explanation:

Line of symmetry

Having the right product means that the software being developed meets the needs and requirements of its intended users.

This involves identifying the target audience, understanding their needs, and designing the software in a way that meets those needs. In addition to functionality, having the right product also means ensuring the software is user-friendly, reliable, and efficient. Achieving the right product requires effective communication between developers and stakeholders, as well as ongoing testing and feedback to ensure that the software meets its intended purpose.

Ultimately, having the right product leads to greater user satisfaction, increased productivity, and improved overall performance of the software.

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Answer:

1st answer is correct yourwelcome

Answer: D. This triangle does not exist because the sum of 4 and 12 is less than 17

Step-by-step explanation:

Edge