Winston-Salem is halfway between Boone and Raleigh. Burlington is halfway between Winston- Salem and Raleigh. If Boone is located at the coordinates (-1,3) and Raleigh is at (-5, 9), what are the coordinates of Burlington?

Step-by-step explanation:

a)[tex] \sf \: Factor 6x2−3x \\ \sf {6x}^{2} −3x \\ \sf \: =3x(2x−1) \\ \sf \: Answer:3x(2x−1) \\ [/tex]

b)Let's factor x²+3x−28

⇒x²+3x−28

⇒x² - 4x + 7x - 28

⇒(x² - 4x) + (7x - 28)

⇒x( x - 4) + 7(x - 4)

⇒(x -4) (x + 7)

Answer:

(x−4)(x+7)

Answer:

=57

Step-by-step explanation:

Multiply and divide left to right

then add and subtract left to right

This is the war between the communist governmrnt of Vietnam North and the South Vietnam.  The United States of America were the main ally of the Vietnam south during the war.

The communist Vietnam North later united with the south with a common name Socialist Reepublic of Vietnam, After a fierce onslaught that took the life of about 58000 americans and over 2 million Vietnamese.

The influence of the Vietnam war in United States today

1. End of the drafts

The drafts is the method of conscription to the military that requires vitually every male between the age of 18 - 25 in United States to register with the selective service. since the end of the Vietnam war in 1975 the draft stopped hence no penalty for not registering to the draft.

2. Granting 18 years old the right to vote

26th Amendment of the United States Constitution gave right to vote to the 18 years old citizens. Today 18 tear old American has right to vote. This was evolvement of the war and still holds till date.

3. It is easier getting into a war than getting out of a war

Americans was pulling out of the Vietnam war when they suffered the huge massacre. This lesson was helpful for president George H W Bush during the 1991 Persian Gulf War were he systematically exited after liberating Kuwait

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Using the Central Limit Theorem, it is found that the condition that applies to this test is:

C. The sample includes at least 30 employees from each department.

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

From this, since we have a skewed variable, it is found that a sample size of at least 30 is needed, hence option C is correct.

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Answer:

Smith should use 900 minute plan and Jones should use 1500 minute plan

Step-by-step explanation:

There are best answers

1. Equations/Inequalities for Each Plan:

Plan A: Cost = $39.99 + 0.25 * (m - 450), m ≤ 450

Plan B: Cost = $59.99 + 0.30 * (m - 900), m ≤ 900

Plan C: Cost = $99.99 + 0.35 * (m - 1500), m ≤ 1500

2. Best Plan for Customers:

Customer Smith (750 min): Plan B ($59.99)

Customer Jones (1350 min): Plan C ($84.99)

3. For both customers, Plan B offers the best value for 750 minutes, while Plan C is optimal for 1350 minutes due to its lower cost per minute overages.

4. Plan A is the least cost-effective for both. The chosen plans reflect the importance of base minutes and overage charges.

1. Equations/Inequalities for Each Plan:

Let's denote the number of minutes used as "m."

Plan A:

Cost: $39.99 for 450 minutes, then $0.25/minute for each additional minute.

Equation: Cost = $39.99 + 0.25 * (m - 450), if m > 450

Inequality: m ≤ 450

Plan B:

Cost: $59.99 for 900 minutes, then $0.30/minute for each additional minute.

Equation: Cost = $59.99 + 0.30 * (m - 900), if m > 900

Inequality: m ≤ 900

Plan C:

Cost: $99.99 for 1500 minutes, then $0.35/minute for each additional minute.

Equation: Cost = $99.99 + 0.35 * (m - 1500), if m > 1500

Inequality: m ≤ 1500

2. Determine the Best Plan for Customers:

Let's evaluate the cost for both customers using the given plans:

Customer Smith:

Usage: 750 minutes

Plan A: Cost = $39.99 + 0.25 * (750 - 450) = $112.49

Plan B: Cost = $59.99

Plan C: Cost = $99.99

Best Plan: Plan B ($59.99)

Customer Jones:

Usage: 1350 minutes

Plan A: Cost = $39.99 + 0.25 * (1350 - 450) = $297.49

Plan B: Cost = $59.99 + 0.30 * (1350 - 900) = $374.99

Plan C: Cost = $99.99 + 0.35 * (1350 - 1500) = $84.99

Best Plan: Plan C ($84.99)

3. Explanation and Recommendation:

Customer Smith's usage of roughly 750 minutes falls within the range of Plan B's base minutes (900) and is more cost-effective with Plan B. However, for Customer Jones, who uses around 1350 minutes, Plan C offers a lower overall cost due to its higher base minutes (1500). Plan A is the least cost-effective option for both customers due to its lower base minutes and higher per-minute charges.

4. Summary for Employees:

Dear Team,

When assisting customers with choosing a cell phone plan, please consider the following options:

Plan A: $39.99 for 450 minutes, then $0.25/minute.

Plan B: $59.99 for 900 minutes, then $0.30/minute.

Plan C: $99.99 for 1500 minutes, then $0.35/minute.

For customers using around 750 minutes per month, recommend Plan B for its competitive pricing. For customers using around 1350 minutes, advise them to opt for Plan C to optimize cost efficiency. Always ensure to guide customers toward the most suitable plan based on their usage patterns.

Thank you for your dedication to excellent customer service.

Sincerely,

[Your Name]

[Your Position]

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Answer:

The correct answer is D:-15,120

[tex]^{n}P_{r}=\dfrac{n!}{(n-r)!}\\\\\implies ^{9}P_5 = \dfrac{9!}{(9-5)!} =\dfrac{9!}{4!} = 15120[/tex]

The answer is D.

Answer:

18 pupils

Step-by-step explanation:

11 like cola

32 like other stuff

11+32=43 - 50-43=7

therefore 11+7=18

18 students like cola the best

Answer:

the answer is; 68% of 7000 which gives 4760 football fans rooting for the home team

Answer:

⠀

Step-by-step explanation:

⠀

We know,

[tex] {\longrightarrow \qquad \boldsymbol{\pmb{Total \: \: surface \: \: area_{(cube)} = 6a {}^{2} }}}[/tex]

⠀

Where,

⠀

Now, Substituting the values in the formula :

⠀

[tex]{\longrightarrow \qquad \rm{{Total \: \: surface \: \: area_{(cube)} = \sf 6 \times( 2.5) {}^{2} }}}[/tex]

⠀

[tex]{\longrightarrow \qquad \rm{{Total \: \: surface \: \: area_{(cube)} = \sf 6 \times6.25 }}}[/tex]

⠀

[tex]{\longrightarrow \qquad \boldsymbol{ \pmb{Total \: \: surface \: \: area_{(cube)} = \it 37.5 }}}[/tex]

⠀

Therefore,

Answer:

37.5 cm²

Step-by-step explanation:

Given:-

To find:-

Solution:-

Total surface area of cube :- 6a²

6(2.5)² sq. cm

37.5 cm²

Answer:

120

Step-by-step explanation: 4x10x2 +2x5x4 =80+40=120 cubic inches

Answer:

Step-by-step explanation:

The value of x determined algebraically given the total area of the rectangle is 1.5 inches

Initial dimensions:

Length = 14 inches

Width = 10 inches

New dimensions:

Length = 14 + x

Width = 10 + x

Area = 320 square inches

Area of a rectangle = Length × Width

320 = (14 + x) × (10 + x)

320 = 14x × 10x

320 = 140x²

x² = 320/140

x² = 2.28571428571428

x = √2.28571428571428

x = 1.511857892036908908858066144936720243

Approximately,

x = 1.5

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Answer:

28

Step-by-step explanation:

a is equal to 7,

so where there is 'a' you replace

with 7

4(7)=7×4=

28

Answer:

Step-by-step explanation:

Since it must be an integer, 5 would make it up to the full length of the longest line. What you get is not quite a triangle. The way to get a triangle is to add one more to the 5 to make 6

Answer: 6 cm

Answer:

(7, -1)

Step-by-step explanation:

Let's remember our key words:

Down/up means to translate the y axis.

Right/left means to translate the x axis.

Now that we know what to do, let's look at our equation.

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

A point located at (5, 3) is translated down 4 units and right 2 units.

Let's work on the x axis first.

It says that you are translating to the right. That means your value is going higher, so you go to the right 2. 5+2=7

So now that we have our x, (7), let's rewrite our equation. (7, 3)

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

Next, let's do y.

The points are translating down. That means our value will lessen.

Since we are going down on our y axis by 4, we will subtract our current y coordinate with 4. 3-4=-1.

Now we know our y, so let's rewrite our equation with our new y. (7, -1).

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

Our final coordinates are (7, -1).

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I hope this helps!

-No one

[tex]v(y) = 0[/tex]

[tex] - 32t + 105 = 0[/tex]

[tex]t = \frac{ - 105}{ - 32} = 3.28[/tex]

[tex]h = - 16(3.28) {}^{2} + 105(3.28) + 17[/tex]

[tex]h = 189.26[/tex]

Answer:

Step-by-step explanation:

Answer:

570 ft²

Step-by-step explanation:

Basically, you find the area of Juan and Matthew's gardens then add them up.  

First let's find the area of Juan's garden.

Area is equal to length times width ([tex]a = lw[/tex])

So you do 16 * 12 which equals 192.

Now let's find the area of Matthew's garden.

So you do 18 * 21 which equals 378.

Then you add up both areas.

192 + 378 = 570

Answer: −5

Step-by-step explanation:

simplify: (−5)

Re-order terms so constants are on the left:

(−5)f(−5)−5

Answer:

Volume

Step-by-step explanation:

Length times width times height, is volume and the formula of finding what is inside something.

Volume :- it's the amount of the mass a body can hold

Answer: The domain of this function is any real number. More mathematically it is put as

-∞ < x <+∞

Answer:

The domain of this function is any real number. More mathematically it is put as

-∞ < x <+∞

Step-by-step explanation:

Answer:

Not entirely sure about this because it was grabbed from someone else

There are 210 ways to win 1st place

There are 209 ways to win 2nd place

There are 208 ways to win 3rd place

Every time an award is won, a spot if taken, therefore one person is eliminated from possibly taking that spot.

Hope that makes sense :)

The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

The number of contestants is 210.

The number of ways of contestants who won the first prize will be given as,

⇒ ²¹⁰C₁

⇒ 210

The number of ways of contestants who won the second prize will be given as,

⇒ ²⁰⁹C₁

⇒ 209

The number of ways of contestants who won the third prize will be given as,

⇒ ²⁰⁸C₁

⇒ 208

Then the total number of ways of contestants can win first, second, and third prizes will be

⇒ 210 x 209 x 208

⇒ 9,129,120

The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.

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The value of x in the direct and indirect varoation is calculated as: x = 2.

If k is the constant of proportionality among two or more variables (x, y, z), a combined equation of direct and indirect variation is, z = kx/y, if z varies directly with x and indirectly with y.

With the information stated, we would have the following:

z = kx/y³

Find k, by plugging in the values of x, y, and z:

12 = k(8/2³)

12 = k(8/8)

12 = k

k = 12

Find x when y = 1 and z = 24:

24 = 12(x)/1³

24 = 12x

24/12 = x

x = 2.

Therefore, the value of x in the direct and indirect varoation is calculated as: x = 2.

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Step-by-step explanation:

Let w = width and h = height. Then we have

w = 3*h - 17

and

4*w + h = 30 (4 shelves and 1 sides).

Plug in the first equation into the second and solve for h:

4*(3*h - 12) + h = 30

12*h - 48 + h = 30

13*h = 78

h = 78/13

h = 6

Plug that in the first equation to find w = 3*6 - 17 = 1

So width = 1 feet.

height = 6 feet

Step-by-step explanation:

Step 1: Take the First Derivative This means only differentiate once.

Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have

[tex]e {}^{ {x}^{2} - 1 } [/tex]

We have the function x^2-1 composed into the function e^x.

So we use chain rule

Which states the derivative of a function composed is the

derivative of the main function times the derivative of the inside function.

So the derivative of the main function is

[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]

Then we replace x with x^2-1

[tex]e {}^{ {x}^{2} - 1} [/tex]

Then we take the derivative of the second function which is 2x so qe multiply them

[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]

Step 2: Set the equation equal to zero.

[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]

Since e doesn't reach zero. We can just set 2x=0.

[tex]2x = 0 = x = 0[/tex]

So the critical point is 0.

Since e^x will never reach zero

Since 0 is the only critical point, this where the max or min will occur at.

Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.

Any pick less than zero will give us a negative number.

Since the function is decreasing then increasing, we have a minimum.

Since 0 is the only critical point, we have a absolute minimum at 0.

To find the y coordinate, plug 0 in the orginal function.

Which gives us

[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]

So the minimum occurs at

(0,1/e).

Answer:

x > 2

Step-by-step explanation:

The graph starts at x = 2

The graph goes up and to the right so x can't be less than 2.

2a means = 2 x a

if a = 4

3 x (2 x 4 + 6) = 3 x (8 + 6) = 3 x 14 = 42

Answer:

it is the last graph

Step-by-step explanation:

[tex]area \: = 78[/tex]

[tex]area = length \: \times \: width[/tex]

[tex]78 = (x)(2x + 1)[/tex]

[tex]x = 6[/tex]

Thus the dimensions are 6 & 13

Answer:

6&13.All you need to do is find the factors of 78 and plug the smaller number into the equation provided in the equation. 2x+1 is our equation. so6*13 is 78 and 2x+1=13... 6for x to get 2*6+1=13

Step-by-step explanation:

The margin of error would tell how many percentage differs from  Harris County's sample

The range of reasonable means for Harris County's sample is 77.7 to 82.3

The given parameters are:

The range (R) is calculated as:

[tex]R = \bar x \pm E[/tex]

Substitute known values

[tex]R = 80 \pm 2.3[/tex]

Expand

[tex]R = (80 - 2.3,80 + 2.3)[/tex]

Evaluate the difference and sum

[tex]R = (77.7,82.3)[/tex]

Hence, the range of reasonable means for Harris County's sample is 77.7 to 82.3

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