Question 11 of 12 < > 1 Two sides and an angle are given. Determine whether a triangle (or two) exist, and if so, solve the triangle(s) a-√2.b-√7.p-105 How many triangles exist? Round your answers

Waterways should retain the old backhoes equipment.

To determine whether it is more favorable to purchase new backhoes or overhaul the old ones, we will evaluate the net present value (NPV), profitability index (PI), and internal rate of return (IRR) for both options.

Net Present Value (NPV):

For the new backhoes:

The initial cost of investment = Purchase cost when new - Salvage value now

= $199,994 - $15,200 = $184,794

The net cash flow generated each year for the new backhoes remains unspecified, so we cannot calculate its NPV.

For the old backhoes:

Initial investment = Cost of the overhaul = $41,400

Net cash flow generated each year = $15,200

Using the provided PV table, we can calculate the NPV for the old backhoes:

NPV = Net cash flow generated each year * PV factor for 8 years - Initial investment

= $15,200 * 5.76162 - $41,400 ≈ $55,689.69

Since the NPV for the old backhoes is positive, retaining the old equipment is favorable.

Profitability Index (PI):

The profitability index is calculated by dividing the present value of cash inflows by the initial investment.

For the new backhoes:

Since the net cash flow generated each year is unspecified, we cannot calculate the PI.

For the old backhoes:

PI = (Net cash flow generated each year * PV factor for 8 years) / Initial investment

= ($15,200 * 5.76162) / $41,400 ≈ 2.11

The profitability index for the old backhoes is 2.11.

Based on the PI, the old backhoes have a higher profitability index than the new backhoes, indicating that retaining the old equipment is more profitable.

Internal Rate of Return (IRR):

The IRR factor for the new and old backhoes is not provided, so we cannot calculate the exact IRR.

In summary, based on the net present value (NPV) and profitability index (PI), it is more favorable for Waterways to retain the old backhoes equipment.

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a).  2^38 bytes of memory

b). 12 bits

c). The maximum number of entries in the single-level page table would be 2^38.

d). The size would be 2^38 * 4KB, which equals 2^20 pages.

e). The maximum number of entries it can have depends on the remaining bits of the logical address.

f). The amount of bits required to denote an index into the inner page table is obtained by subtracting the offset and outer page index bits from the logical address.

a. To address a physical memory size of 128GB (2^37 bytes), a 64-bit architecture would require 38 bits for the logical address, allowing access to a maximum of 2^38 bytes of memory.

b. Given that the page size is 4KB (2^12 bytes), 12 bits would be needed to specify the displacement into a page. This means that the lower 12 bits of the logical address would be used for page offset or displacement.

c. With a single-level page table, the maximum number of entries would be equal to the number of possible logical addresses. In this case, since the logical address requires 38 bits, the maximum number of entries in the single-level page table would be 2^38.

d. The size of the single-level page table is determined by the number of entries it contains. Since each entry maps to a page of size 4KB, the size of the single-level page table can be calculated by multiplying the number of entries by the size of each entry. In this case, the size would be 2^38 * 4KB, which equals 2^20 pages.

e. For a two-level page table, the size of the outer page table is determined by the number of entries it can contain. Since the outer page table uses 4KB pages, the maximum number of entries it can have depends on the remaining bits of the logical address. The number of bits used for the index into the outer page table is determined by subtracting the bits used for the inner page index and the offset from the total number of bits in the logical address.

f. The number of bits used to specify an index into the inner page table can be determined by subtracting the bits used for the offset and the bits used for the outer page index from the total number of bits in the logical address. The remaining bits are then used to specify the index into the inner page table.

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Answer:

Step-by-step explanation:

Step one:

given data

initial height of plane= 20000ft

rate of descending= 25ft per minute

let x be the number of minutes it took the plane to descend

and let y be the height after x minutes

Step two:

Required

the mathematical expression for the height

the expression for the situation mathematically is

y=20000-25x

A minimum sample size of 121 individuals needs to be surveyed, ensuring a rounded-up value to estimate the proportion of non-graduates within the 25 to 30 age group with a 10% margin of error and 90% confidence.

To determine the sample size required to estimate the proportion of non-graduates within the 25 to 30 age group with a certain level of confidence and margin of error, we can use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n is the required sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence corresponds to a Z-score of approximately 1.645)

p is the estimated proportion of non-graduates (0.21 based on the information provided)

E is the desired margin of error (10% or 0.10)

Substituting the values into the formula:

n = (1.645^2 * 0.21 * (1 - 0.21)) / 0.10^2

n ≈ 120.41

Rounding up to the nearest integer, the required sample size is 121.

Therefore, you would need to survey at least 121 individuals in the 25 to 30 age group to estimate the proportion of non-graduates within 10% margin of error with 90% confidence.

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As a result, g(x) and h(x) have the following composition: f(x) = 2 as to determine the composition of g(x) and h(x) .

With the input (the x-value) drawn on the x plane and the output (the y-value) written on the vertical axis, functions can be represented graphically. Understanding a function's behaviour, for example, if it is going up or down, and locating significant characteristics like peaks and minima, can be done by looking at its graph. Many branches of arithmetic, as well as physics, construction, computer science, sociology, and a wide range of other disciplines, use functions. They are a crucial tool for problem-solving across a broad spectrum and for simulating real-world occurrences.

given

We may utilise the distributive property of multiplication to multiply the two functions:

\(g(x) * h(x) = (x - 2) * 4\)

= 4x - 8

Hence, f(x) = 4x - 8 is the result of the two functions' product.

Composition: To determine the composition of g(x) and h(x), we must replace every instance of x with h(x) in g(x):

\(g(h(x)) = g(4) (4)\)

= 4 - 2

= 2

As a result, g(x) and h(x) have the following composition: f(x) = 2 as to determine the composition of g(x) and h(x) .

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Melanie will end up with 7 pieces of paper for her craft project. This is determined by dividing the total length of the paper (17.5 inches) by the desired length for each piece (2.5 inches).

To determine the number of pieces Melanie will end up with, we need to divide the total length of the paper by the desired length for each piece.

Total length of the paper = 17.5 inches

Desired length for each piece = 2.5 inches

To calculate the number of pieces, we divide the total length by the desired length:

Number of pieces = Total length / Desired length

Number of pieces = 17.5 inches / 2.5 inches

Number of pieces = 7

Melanie will end up with 7 pieces of paper for her craft project. This is determined by dividing the total length of the paper (17.5 inches) by the desired length for each piece (2.5 inches). The resulting quotient gives us the number of pieces, which in this case is 7.

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===================================================

Explanation:

let's find the prime factorization for each value. If the value is prime, then just move onto the next value

2 = 2 ... already prime, nothing needed to do here

3 = 3

4 = 2*2

5 = 5

6 = 2*3

8 = 2*2*2

9 = 3*3

10 = 2*5

The list of prime factors that show up are: {2, 3, 5}

We have '2' show up at most 3 times, the prime '3' show up at most 2 times, and the prime '5' show up at most 1 time.

This means 2^3*3^2*5 = 360 is the LCM of the list {2,3,4,5,6,8,9,10}

Any multiple of 360 will also be a common multiple of the original list of values.

Multiples of 360: {360, 720, 1080, ...}

We see that 1080 is the smallest 4-digit multiple of 360.

Being 95% confident in an inference means that, based on the statistical analysis performed, there is a 95% probability that the true population parameter (in this case, μ) falls within the calculated confidence interval (in this case, (1000, 2100)).

Confidence intervals are used in statistics to estimate the true value of a population parameter (such as the mean, μ) based on a sample of data. In this case, the confidence interval is (1000, 2100).

The confidence level, in this case, 95%, represents the probability that the calculated confidence interval contains the true population parameter. This means that if the same statistical analysis were repeated multiple times, we would expect the true population parameter to fall within the confidence interval in approximately 95% of those repetitions.

The confidence interval is calculated based on the sample data and the chosen confidence level. In this case, the interval (1000, 2100) was calculated based on the sample data and a 95% confidence level.

The interpretation of the confidence interval (1000, 2100) is that there is a 95% probability that the true population parameter, μ, falls within this interval. It does not mean that there is a 95% probability that the interval contains the true value of μ; rather, the confidence level reflects the long-term frequency of intervals that will contain the true value of μ when similar analyses are repeated.

Therefore, based on the given information, we can conclude that being 95% confident in an inference means that there is a 95% probability that the true population parameter, μ, falls within the calculated confidence interval of (1000, 2100).

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1) 2 and 12

2) 12 and -2.  

Explanation:1)Below we illustrate and prove that 2 and 12 multiply to 24 and add up to 14:

2 × 12 = 24

2 + 12 = 14

Are you asking because you are trying to figure out how to factor the following quadratic equation?

x2 + 14x + 24 = 0

If so, the solution to factor the quadratic equation above is:

(x + 2 ) (x + 12)

To summarize, since 2 and 12 multiply to 24 and add up 14, you know that the following is true:

x2 + 14x + 24 = (x + 2 ) (x + 12)

2)x + y = 10 and xy = -24

Since xy = -24, y = -24/x.

So, x - 24/x = 10

x2 - 24 = 10x

x2 - 10x - 24 = 0

(x - 12)(x + 2) = 0

So, x = 12 or -2

The numbers are 12 and -2.  

Answers  in bold:

=====================================

Explanation:

This is something you do using trial and error. Here are the ways to multiply to 24 using positive factors

We cross "1*24" off the list since 1+24 = 25 when we want the factors to add up to 14. But 2+12 = 14 works perfect.

Problem 2 is handled the same way, but this time 4+6 = 10 is what we're after.

Answer:

The Correct answer is 381

Step-by-step explanation:

5334÷14

=381

Answer:

a

Step-by-step explanation:

Part A: A system of equations to model this situation includes:

Equation 1: x + y = 461

Equation 2: 3x + 4y = 1624.

Part B: The solutions of the equations show that 220 students bought tickets at $3 each, while 241 adults bought the tickets at $4 each to give the total sales revenue as $1,624.

A system of equations means simultaneous equations.

Simultaneous equations are two or more equations solved at the same time.

Simultaneous equations can be solved by graphing, substitution, and elimination methods.

In this situation, we decided to solve the equations by substitution after equating x = 461 - y from the first equation.

The total number of tickets sold for the school play = 461

The cost of student tickets per unit = $3

The cost of adult tickets per unit = $4

The total revenue raised = $1,624

Let the number of students = x

Let the number of adults = y

x + y = 461  ... Equation 1

3x + 4y = 1624  ... Equation 2

From Equation 1:

x = 461 - y  ... Equation 3

Substitute x in Equation 2

3(461 - y) + 4y = 1624

1,383 - 3y + 4y = 1624

y = 241

From Equation 1:

x = 461 - y

= 461 - 241

= 220

Check:

3x + 4y = 1624

3(220) + 4(241) = 1624

660 + 964 = 1624

1624 = 1624

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Answer:

  x,y = -4, -15

Step-by-step explanation:

SOLUTION

Given the graph of the transformed function g(x) in the image on the question tab.

Considering the rules of transformation below;

Final answer:

Answer:

\(equation \: for \: pythagorean \: theorem \: is \: \\ {3.8}^{2} + {6.8}^{2} = {x}^{2} \)

Answer:

Step-by-step explanation:

see attached

Answer:

(1,000 * (100 + 12))/100 = 1,120 - 1,000 = 120 turtles/ per year

Step-by-step explanation:

The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1.12)¹²ⁿ

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

That's population of turtles in a lake is estimated at 1,000.

And,  The population projected to increase 12% per year.

Hence, The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1 + 12/100)¹²ⁿ

⇒ y = 1000 (1 + 0.12)¹²ⁿ

⇒ y = 1000 (1.12)¹²ⁿ

Thus, The exponential function which can be use to identify the monthly growth is,

⇒ y = 1000 (1.12)¹²ⁿ

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Answer:

a. (3,-2) that is the answer

, I already study this lesson

Answer:

Step-by-step explanation:

Geoff is feeling peckish, so he decides to pop into the shop and grab some snacks. He picks up a packet of crisps for 25p, a can of soup for 68p and a watermelon for £1.47. He wonders why the watermelon is so cheap, but he doesn't question it. He goes to the cashier and hands over a £5 note. The customer behind Geoff wonders "how much change does he get back?"

To figure this out, we need to add up the price of the snacks and take it away from the money Geoff gave. We can use a dot to show the pence as parts of a pound. For example, 25p = 0.25 pounds.

The price of the snacks is:

0.25 + 0.68 + 1.47 = 2.40 pounds

The money Geoff gave is:

5.00 pounds

The change is:

5.00 - 2.40 = 2.60 pounds

So, Geoff gets £2.60 in change and a bargain watermelon.

Answer:

Answer:

2.60

Step-by-step explanation:

25+68+147=240

500-240=260

turn into pounds 2.60

Step-by-step explanation:

The answer number line is G.

Given that the inequality 3.3w - 9 > -22.2, we need to find the value of w,

So,

3.3w - 9 > -22.2

Add 9 to both sides,

3.3w > -13.2

w > -4

Since the value of w is greater than -4 and the sign is > so the number line is G.

Hence the answer number line is G.

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the empirical probability based on 1000 flips provides a better estimate of the theoretical probability p(h) for the unfair coin.

The empirical probability is based on observed data from actual trials or experiments. It involves calculating the ratio of the number of favorable outcomes (e.g., getting a "heads") to the total number of trials (flips). The larger the number of trials, the more reliable and accurate the estimate becomes.

When estimating the theoretical probability of an unfair coin, it is important to have a sufficiently large sample size to minimize the impact of random variations. With a larger number of flips, such as 1000, the estimate is based on more data points and is less susceptible to random fluctuations. This helps to reduce the influence of outliers and provides a more stable and reliable estimate of the true probability.In contrast, with only 30 flips, the estimate may be more affected by chance variations and may not fully capture the underlying probability of the coin. Therefore, the empirical probability based on 1000 flips provides a better estimate of the theoretical probability p(h) for the unfair coin.

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Answer:

Experimental probability

Step-by-step explanation:

Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial.

The relative frequencies for the car riders are given as follows:

A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

The total number of car riders is given as follows:

78.

The number in each grade is given as follows:

Hence the relative frequencies are given as follows:

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The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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The actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

The margin of error in the report stating that a 10-year-old American child spends an average of 20.02 to 25.36 minutes playing outdoors per day can be calculated by subtracting the lower value from the higher value and dividing by 2. In this case, the margin of error is :

To find the margin of error, we need to calculate the halfway point between these two values.
(25.36 - 20.02) / 2 = 2.67

Therefore, the margin of error is approximately 2.67 minutes. This means that the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

Thus, the actual average time spent playing outdoors by 10-year-old American children could be 2.67 minutes higher or lower than the reported range of 20.02 to 25.36 minutes.

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Answer:

the red car is traveling at 102.44 ft/s along the road

Step-by-step explanation:

From the given information:

Let consider p be how far the car is up the road and  q be how far the police is off the road.

Also, suppose that r is the distance between the police and the car.

Then, we can have a right triangle in which  we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)

NOW,

p² + q² = r²

r² = 40² + 180²

r² = 1600 + 32400

r² = 34000

r = \(\sqrt{34000}\)

r = 184.39

If we consider q'  to be how fast the car is traveling down the road.

And, p' be how fast the police is traveling toward the road.

r' be how fast the distance between the police and the car is changing.

then , the derivative of our equation, p² + q² = r² with respect to time can now be:

2p(p') +2q(q') = 2r(r')

p(p') +q(q') = r(r')

By replacing our values; we have:

40(0) +180(y') = \(\sqrt{34000} \times 100\)    (given that the police is not moving p' =0)

180(y') = \(\sqrt{34000} \times 100\)

\((y') = \dfrac{\sqrt{34000} \times 100}{180}\)

\((y') = \dfrac{184.39 \times 100}{180}\)

\(\mathbf{(y') = 102.44 \ ft/s}\)

the red car is traveling at 102.44 ft/s along the road

The equation that demonstrates the distributive property is c) 38(5) = 5(38). The distributive property is a fundamental algebraic concept that states that the product of a number and a sum is equal to the sum of the products of that number and each term in the sum.

In mathematical terms, for any numbers a, b, and c, the distributive property can be written as a(b + c) = ab + ac.
Given the four options, the equation that demonstrates the distributive property is c) 38(5) = 5(38). According to the distributive property, we can rewrite this equation as 38 * 5 = 5 * 38, which demonstrates that the order of multiplication does not affect the result. The other equations do not show the distributive property, as they represent different mathematical concepts:
a) 15 + 40 = 55 is an example of addition.
b) 15 x 40 = 40 x 15 demonstrates the commutative property of multiplication.
d) 15 - 40 - 5(13 - 8) is an expression involving subtraction and multiplication, but does not demonstrate the distributive property.

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Assume a businessman has 7 suits and 8 ties. He is planning to take 4 suits and 3 ties with him on his next business trip. Possibilities of selection he have 1960.

A businessman has 7 suits

A businessman has 8 ties.

He is planning to take 4 suits and 3 ties with him on his next business trip.

We have to determining possibilities of selection he have.

Number of possible selections = \(^{7}C_{4}\times ^{8}C_{3}\)

Simplify

Number of possible selections = \(\frac{7!}{4!(7-4)!}\times\frac{8!}{3!(8-3)!}\)

Number of possible selections = \(\frac{7!}{4!3!}\times\frac{8!}{3!5!}\)

Number of possible selections = \(\frac{7\times6\times5\times4!}{4!\times3\times2\times1}\times\frac{8\times7\times6\times5!}{3\times2\times1\times5!}\)

After simplification we get

Number of possible selections = 7 × 5 × 8 × 7

Number of possible selections = 1,960

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Answer: 3 and -5

Step-by-step explanation:

45, 33, 22, 12,

differences =

45-33 = 12

33-22=11

22-12=10

pattern = decreases by one so

12- 9 = 3

3- 8 = -5

Answer:

208 in

Step-by-step explanation:

\((8x8)+(\frac{1}{2} x8x9)x4in^{2} \\\\=64+36x4 in\\ \\=208 in^2\)

have a great day!!

Answer:

\(208 in^2\)

Step-by-step explanation:

Total surface area

(8×8)+(1/2×8×9)×4in²

= 64+36×4in²

=64+144in²

= 208 in²

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