1 point If the distance from A(1, 6) to B(x, -2) is 10, then what is a possible value for x? (A) 11 (B) -5 (C) -7 (D) 8 (E) 6​

Answer:

5⁷

Step-by-step explanation:

5³×5⁴

when bases are same powers are added

so..

5(³+⁴)

5⁷

Answer:

5^7

Step-by-step explanation:

Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)

You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!

The expression 60⋅1.2^t models the number of nano-related patents granted in the US as a function of years since 1991.


Start with the number 60.

This represents the initial number of nano-related patents granted in the US in the year 1991.

Multiply 60 by 1.2.

This accounts for a growth factor of 1.2, indicating that the number of patents granted is increasing by 20% each year.

Raise 1.2 to the power of t. The variable t represents the number of years since 1991. This allows the expression to model the increase in patents over time.

The resulting expression, 60⋅1.2^t, gives an estimate of the number of nano-related patents granted in the US for any given year since 1991.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Answer:

y=2/3x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-(-6)=2/3(x-(-6))

y+6=2/3(x+6)

y=2/3x+12/3-6

y=2/3x+4-6

y=2/3x-2

Answer:

5 nights

Step-by-step explanation:

39 divided by 3 = 13

so we divided 65 by 13 hence your answer 5 nights

The Six Sigma process is a quality management approach that aims to reduce the number of defects in a process by identifying and eliminating the causes of variation. True.

It is a data-driven approach that seeks to improve the quality of products or services by reducing variability and increasing process efficiency.

One of the defining characteristics of the Six Sigma process is that it requires the specification limits to be set at least six standard deviations away from the mean of the process.

This means that the process is designed to produce products or services that are within the specifications with a high degree of certainty, as the chances of the output falling outside of the specification limits are very low.

The Six Sigma approach involves several steps, including defining the problem, measuring the process, analyzing the data, improving the process, and controlling the process.

It is a rigorous approach that requires the involvement of all levels of the organization and relies on statistical tools and techniques to identify and eliminate the causes of variation in the process.

The Six Sigma process has been widely adopted by many organizations in various industries, including manufacturing, healthcare, finance, and services, to improve their processes, reduce defects, and increase customer satisfaction.

It has proven to be an effective approach for improving the quality of products and services, reducing costs, and increasing profitability.

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Answer:

1) 151.29 | 2) 413 km | 3) 75 cm

Step-by-step explanation:

1) 12.3 x 12.3 = 151.29 in

2) 17.5 x 23.6 = 413 km

3) 15 x 5 = 75 cm

Answer:

Step-by-step explanation:

2(x+3)/3 + 3(x-6)/2=1-x

2x+6/3 + 3x-18/2=1-x

2(2x+6)/3 + 3(3x-18)=6-6x

4x+12+9x-54=6-6x

13x-49=6-6x

13x+6x=6+42

19x/19=48/19

x=49/19

a. The replacement free cash flows is $255,000

b.  The Payback Period time required to recover the initial investment is 2.7778 years.

d. By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

a. To calculate the replacement free cash flows, we need to consider the cash flows associated with the new fleet of trucks. Here's the calculation:

Initial cash outflow: Purchase cost of new trucks + Shipping cost

= $350,000 + $50,000

= $400,000

Annual cash flows:

Operating cost savings:

Diesel fuel savings: $250,000 - $150,000 = $100,000

Maintenance cost savings: $35,000 - $10,000 = $25,000

Net operating working capital reduction: $20,000

Total operating cost savings per year: $100,000 + $25,000 + $20,000 = $145,000

Revenue increase:

Revenue growth rate: 10%

Year 1 revenue increase: $800,000 * 10% = $80,000

Year 2 revenue increase: $800,000 * 10% = $80,000

Year 3 revenue increase: $800,000 * 10% = $80,000

Year 4 revenue increase: $800,000 * 10% = $80,000

Year 5 revenue increase: $800,000 * 10% = $80,000

Salvage value: Market value of the new trucks at the end of 5 years = $30,000

Free cash flows:

Year 0: Initial cash outflow = -$400,000

Year 1: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 2: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 3: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 4: Cash flow = Operating cost savings + Revenue increase = $145,000 + $80,000 = $225,000

Year 5: Cash flow = Operating cost savings + Revenue increase + Salvage value = $145,000 + $80,000 + $30,000 = $255,000

b. The Payback Period is the time required to recover the initial investment. To calculate it, we sum the cash flows until they equal or exceed the initial investment. Here's the calculation:

Payback Period = Number of years to recover initial investment

= 2 years (Year 1 cash flow + Year 2 cash flow)

+ (Remaining investment / Year 3 cash flow)

= 2 years + ($400,000 - $225,000) / $225,000

= 2 years + 0.7778 years

= 2.7778 years

c. To calculate the Net Present Value (NPV) and Profitability Index (PI), we need to discount the cash flows using the given discount rate of 15%. Here's the calculation:

Discount rate: 15%

Present value factor for each year:

Year 0: 1 / (1 + Discount rate)^0 = 1

Year 1: 1 / (1 + Discount rate)^1 = 0.8696

Year 2: 1 / (1 + Discount rate)^2 = 0.7561

Year 3: 1 / (1 + Discount rate)^3 = 0.6575

Year 4: 1 / (1 + Discount rate)^4 = 0.5718

Year 5: 1 / (1 + Discount rate)^5 = 0.4972

NPV calculation:

NPV = (Year 0 cash flow) + (Year 1 cash flow * Present value factor) + (Year 2 cash flow * Present value factor) + ...

= -$400,000 + ($225,000 * 0.8696) + ($225,000 * 0.7561) + ($225,000 * 0.6575) + ($225,000 * 0.5718) + ($255,000 * 0.4972)

Profitability Index calculation:

PI = NPV / Initial investment

= NPV / $400,000

d. To calculate the Internal Rate of Return (IRR), we find the discount rate that makes the NPV equal to zero. Here's the calculation:

IRR = Discount rate that makes NPV equal to zero

By calculating the NPV at various discount rates, we can determine the rate at which NPV is closest to zero.

e. Based on the information provided, we can determine if the fleet should be replaced by considering the Payback Period, NPV, Profitability Index, and IRR.

If the Payback Period is within the company's acceptable timeframe and the NPV is positive, or the Profitability Index is greater than 1, and the IRR exceeds the company's required rate of return, then replacing the fleet would be financially favorable. If any of these criteria are not met, it would indicate that the replacement may not be the best option.

Please note that the calculation of IRR requires further information, and the final decision should consider additional factors such as qualitative aspects, operational requirements, and strategic considerations.

Without the specific values for cash flows in each year, it is not possible to provide a definitive answer to whether the fleet should be replaced based on the given information.

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Answer:

-4599

Step-by-step explanation:

x-(x(x-y)^3) , x=9, y=1

=9-(9(9-1)^3)

=9-(9(8)^3)

=9-(9*512)

=9-4608

= -4599

Answer:

reflection

Step-by-step explanation:

this is a reflection off y=-x

Answer:

Sorry

Step-by-step explanation:

Sorry I don't know the answer because I haven't learned this yet. Hope you get your answer!

Answer:

0.2666666667

Step-by-step explanation:

Answer:

1630

Step-by-step explanation:

In words you are looking for 6% of what number is 97.80, turn that into an Algebra equation .06x = 97.80 so x = 97.80/.06 so x = 1630

y is sufficient for β

The probability density function (pdf) of an exponential distribution with mean β is given by:

f(y | β) = (1/β)exp(-y/β), for y ≥ 0

To show that f(y | β) is in the exponential family, we need to write it in the form:

f(y | β) = h(y)exp{θT(y) - A(θ)}

where h(y), θ, and A(θ) are functions that depend only on y, θ, and do not depend on β.

First, we can rewrite the pdf as:

f(y | β) = (1/β)exp(-y/β)

= (1/β)exp{(-1/β)y}

= (1/β)exp{(-1/β)yx}

where x = 1.

Next, we can identify the functions h(y), θ, and A(θ):

h(y) = 1

θ = -1/β

A(θ) = -log(-θ)

= -log(1/β)

= log(β)

Substituting these values, we get:

f(y | β) = exp{(-1/β)y}exp{-log(β)}

= exp{(-1/β)y - log(β)}

Therefore, f(y | β) is in the exponential family.

To show that y is sufficient for β, we can use the factorization theorem.

The joint pdf of the sample y1, y2, ..., yn is:

f(y1, y2, ..., yn | β) = (1/β)^n exp{- (y1 + y2 + ... + yn)/β}

= (1/β)^n exp{-n(ybar)/β}

where ybar is the sample mean.

Using the factorization theorem, we can write:

f(y1, y2, ..., yn | β) = h(y)g(T(y), β)

where T(y) = ∑ yi and h(y) does not depend on β.

Therefore, y is sufficient for β.

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The 95% confidence interval for the population mean is between 16.696 hours and 20.504 hours.

To find the 95% confidence interval for the population mean, you'll need to use the following formula:

Confidence Interval = Mean ± (Critical Value × Standard Deviation / √Sample Size)

In this case, the mean is 18.6, the population standard deviation is 6.8, and the sample size is 49 eighth graders. For a 95% confidence interval, the critical value is 1.96 (which is the Z-score for a 95% confidence interval).

Now, plug the values into the formula:

Confidence Interval = 18.6 ± (1.96 × 6.8 / √49)

Calculating the values:

Confidence Interval = 18.6 ± (1.96 × 6.8 / 7)

Confidence Interval = 18.6 ± (1.96 × 0.9714)

Confidence Interval = 18.6 ± 1.904

Now, find the lower and upper limits of the confidence interval:

Lower Limit = 18.6 - 1.904 = 16.696
Upper Limit = 18.6 + 1.904 = 20.504

So, the 95% confidence interval for the population mean is between 16.696 hours and 20.504 hours.

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Answer:

Step-by-step explanation:

so "b" here, represents the off-set,  or in electrical engineering we call it the DC value.  it just means how far off of zero is the line when x = 0 .

So the question is   what is "Y"  when x= 0.   and this is what "b" represents.  

There is a bunch of math that we could do to find  slope and the equation of the line.

But, we can do this by inspection.  I mean, just looking at the numbers.

Note that when x = -1,  Y = 10 ,  then also,  when x = 1 , Y= 4,  sooo zero is excatly between -1 and 1  or,  take the difference of 10-4  , the Y values, and find the middle.    10-4 = 6  and then take half of that to find the middle, or half of 6 is  3.   so we know that at zero,  Y = 4+3  or   10-3  ,  note that these are the same ,  7.  so know we know,  when x=0, Y=7.   So "b" = 7  

got it?  it's a lot of thinking, and understanding.  But  you can see that the math it self is not tough.   :)   any questions?

Answer:

b = 7

Step-by-step explanation:

find slope:

10-16/-1-(-3)

-6/2

= -3

input any coordinate and slope in y=mx+b to get b:

16=-3(-3)+b

16= 9+b

b= 16-9

b = 7

Answer:

x=8

Step-by-step explanation:

Complementary angles are equal to 90 degrees.

angle ABC + angle DBC = 90

6x+13+4x-3=90

Combine like terms

6x+4x+13-3=90

10x+10=90

get x alone by subtracting 10 on both sides

10x=80

divide 10 on both sides

x=8

We cannot simplify this further because 3 and 5 have no factors in common, other than 1. So we just leave it as is.

The random real number between 1.0 and 10.0 can be generated using the formula: 1.0 + (RAND() * 9.0).

To generate a random real number within a specified range, we can use the RAND() function. The RAND() function generates a random decimal number between 0 and 1.0. By multiplying this random number by the range of values we desire and adding the minimum value, we can obtain a random real number within the desired range.

In this case, we want a random number between 1.0 and 10.0. To achieve this, we multiply the random number generated by RAND() by the range, which is 9.0 (10.0 - 1.0). This scales the random number to the desired range. Then, by adding 1.0 (the minimum value) to the scaled random number, we obtain the final random real number within the range of 1.0 and 10.0.

To summarize, the formula for generating a random real number between 1.0 and 10.0 is: 1.0 + (RAND() * 9.0).

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Answer:

4

Step-by-step explanation:

√64 = 8

√4 = 2

8/2 = 4

Answer:4

Step-by-step explanation:

\(\sqrt{64\) = 8

\(\sqrt{4\)  = 2

8÷2=4

\(\tan(x )=\cfrac{\stackrel{opposite}{50}}{\underset{adjacent}{36}} \implies \tan(x)=\cfrac{25}{18}\implies x =\tan^{-1}\left( \cfrac{25}{18} \right)\implies x \approx 54.2^o\)

Make sure your calculator is in Degree mode.

Answer:

40

Step-by-step explanation:

how i did it probably isn't normal but first i did 1/3 of 100 and that's 33.33

then i did 1/3 of 20 and that's 6.66 then you just add them together

33.33+6.66 and that's 39.99

then just round up

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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Answer: y = (1/8)x + 3.625

Step-by-step explanation:

slope: y = mx + b

change from 3 to 4 is 1, this is our rise

change from -5 to 3 is 8, this is our run

1/8 = m

this is a really bad explanation but I know that

1/8 is equal to 0.125.

since there are 5 spaces from (-5,3) to the y axis, and that the slope is 1/8, i can multiply 1/8 x 5 to get 5/8.

5/8 =.625

since the x intercept is in between 3 and 4, it is 3.625.

3.625 = b

Answer:

1) AD = 9 in

2) DE = 9.25 in

3) ∠EDC = 36°

4) ∠AEB = 108°

5) 11.5 in

Step-by-step explanation:

1) AD = BC = 9in

2) AC = BD (diagonals are equal)

⇒ BD = 14.25

⇒ BE + DE = 14.25

⇒ 5 + DE = 14.25

DE = 9.25

3) Since AB ║CD,

∠ABE = ∠EDC = 36°

4) ∠ABE = ∠BAE = 36°

Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)

⇒ 36 + 36 + ∠AEB = 180

∠AEB = 108

5) midsegment = (AB + CD)/2

= (8 + 15)/2

11.5

Answer: 35N

Step-by-step explanation:

Cross multiply and divide to find the missing value

Answer: 35N :)))))))))))))))))))))))))))))

The polygon with vertices A(11, 3), (3, -11), C(-13, -9) and D(-5, 9) is a rhombus

The vertices of a polygon are the points where the sides of the polygon meet. A polygon is a closed shape that is made up of a finite number of straight line segments. The number of sides in a polygon is called its order or its degree.

The vertices of a polygon can be used to identify the shape of the polygon, for example a triangle with vertices (2,3), (4,5) and (6,7) are different from triangle with vertices (3,4), (5,6) and (7,8)

In addition, the vertices can be used to find the lengths of the sides of the polygon and to calculate its area and perimeter. Vertices can also be used to indicate the relative position of a polygon to other shapes or figures.

It's worth noting that the term "vertex" is also used to refer to the top of a pyramid or cone and the peak of a mountain. In these cases, it refers to the highest point of the object.

In this problem, the vertices A(11, 3), (3, -11), C(-13, -9) and D(-5, 9) when plotted on a graphing calculator shows that the two opposite sides are not equal to one another.

The shape with the vertices is a rhombus.

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The linear function of the scenario is y = 33x

From the question, we have the following parameters that can be used in our computation:

Time = 5.5 hours

Cost = $180

This means that

x = 5.5 and y = 180

The constant of proportionality is calculated as

k = Cost/Time

Substitute the known values in the above equation, so, we have the following representation

k = 180/5.5

Evaluate

k = 33

The equation is calculated as

y = kx

So, we have

y = 33x

Hence, the equation is y = 33x

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