How would you find the two triangles are similar?

To determine the number of tons of metal per year needed for Machine A to be favored over Machine B, we compare their costs. Machine A costs $323,000 with an annual operating cost of $2.40/ton, while Machine B costs $178,000 with an annual operating cost of $8.00/ton. The machines have useful lives of 10 years and 6 years, respectively, and the minimum attractive rate of return (MARR) is 18% per year.

By calculating the equivalent annual costs (EAC) for each machine using the given formula and comparing them, we can determine the point at which Machine A becomes more favorable. However, specific values for the discounting factors and the tons per year needed are missing, making it impossible to provide an exact answer.

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Answer:

x^2 - 2x - 4 = 0.

Step-by-step explanation:

Written in factor form we have:

(x - ( 1 + √5)( x - (1 - √5)) = 0

(x - 1 -√5)( x - 1 +√5)) = 0        Expanding:

x^2 - x +√5x  - x + 1 - √5 - √5x + √5 - 5 = 0

x^2 - 2x - 4 = 0.

Answer: D!!!!!!!

Step-by-step explanation:

Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

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The probability that the mean blood pressure will be less than 125 is 0.9938

The mean of the pressure readings = 123

The standard deviation = 9.6

Total population = 144

The value is less than 125

The equation of the z-score is

z-score = (Observed value - Mean ) / (Standard deviation /\(\sqrt{N}\))

Substitute the values in the equation

z-score = (125 - 123) / (9.6/\(\sqrt{144}\))

= 2 / (9.6/12)

= 2 / 0.8

= 2.5

Using the statistical table

The probability of that their mean blood pressure less than 125

P(z < 2.5) = 0.9938

Therefore, the probability is 0.9938

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Answer: 3x+y=8

Step-by-step explanation:

In standard form: 3x+y=8

Answer:

Difference

Step-by-step explanation:

The Difference of boys and girls in the school coyld change the ratios

Answer:

yes why

Step-by-step explanation:

okay

Answer:

53 sets

Step-by-step explanation:

730 - 204 = 526

526 / 10 = 52 r 6

therefore he'd have to buy 53 sets to have enough knives.

There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The restaurant needs at least 730 knives.

There are currently 204 knives.

And, each set on sale contains 10 knives.

Now,

By the given condition, we formulate;

⇒ 730 ≤ 204 + 10x

Solve for x as;

⇒ 730 ≤ 204 + 10x

⇒ 730 - 204 ≤ 204 + 10x - 204

⇒ 529 ≤  10x

Divide by 10 as;

⇒ 52.9 ≤ x

After rounding, we get;

⇒ 53 ≤ x

Thus, There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.

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Answer:

4 feet

Step-by-step explanation:

If the standard step height is 8", this means that every step in a staircase will have a height of 8". If there are a total of 6 steps in the staircase we can simply multiply the number of steps by the height of each individual step to get the total height of the top landing. Like so...

6 * 8 = 48"

Finally, we can see that the top landing for the stairs is 48". We can turn this into feet by dividing by 12 since there are 12" in a foot

48 / 12 = 4 feet

Therefore, the top landing will have 4 feet ( or 48 inches)

Answer:

cos15 is equivalent to sin(75)

Step-by-step explanation:

solving for cos15 degrees gives you ((√(3)+1)*√(2))/4 which is the same as the sin(75)

Al-Fatihah is an Islamic prayer recited during the five daily prayers. Comparing radio and television in reading Al-Fatihah from its beginning requires an analysis of how each medium conveys the prayer to its audience. Radio precedes television in reading Al-Fatihah from its beginning.

This is because radio broadcasting began in the early 1900s while television broadcasting began in the late 1940s.

This delay can range from a few seconds to a few minutes depending on several factors such as the geographical location of the audience, the strength of the signal, and the quality of the receiver. Therefore, the time difference between radio and television in reading Al-Fatihah can vary depending on the factors mentioned above.

Mathematically, the time difference between radio and television can be calculated using the formula: d = s / tWhere d is the distance between the transmitter and the receiver, s is the speed of the signal, and t is the time it takes for the signal to reach the receiver.

In this case, d is the distance between the broadcasting station and the audience, s is the speed of the signal which is constant (i.e., the speed of light), and t is the time it takes for the signal to reach the audience. Since the speed of light is approximately 299,792,458 m/s, the time it takes for the signal to reach the audience can be calculated using the following formula:t = d / s

Therefore, the time difference between radio and television in reading Al-Fatihah can be calculated by subtracting the time it takes for the radio signal to reach its audience from the time it takes for the television signal to reach its audience. This difference can range from a few milliseconds to a few minutes depending on the factors mentioned above.

In network concepts, the time difference between radio and television in reading Al-Fatihah can be affected by the bandwidth of the network. The bandwidth is the amount of data that can be transmitted over a network in a given time. If the bandwidth is low, it can cause a delay in the transmission of the signal which can affect the time difference between radio and television.

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The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.

The given function is:

d(t) = 40|t-1.25|

Here, t represents the time elapsed in hours and d represents the distance from the river in miles.

To find Mia's distance from the river, we need to plug in values of t into the function.

For example, if t=2, then:

d(2) = 40|2-1.25|

d(2) = 40|0.75|

d(2) = 30

So Mia's distance from the river after 2 hours of driving is 30 miles.

Similarly, we can find Mia's distance from the river at other points in time.

To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.

Graph of the function d(t) = 40|t-1.25|

The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.

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The division expression 1 2/5 divided 1 3/10 is 1 1/13

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

1 2/5 divided 1 3/10

This can be expressed as

1 2/5 divided 1 3/10 = 1 2/5 ÷ 1 3/10

Convert the fractions to improper fractions

So, we have

1 2/5 divided 1 3/10 = 7/5 ÷ 13/10

Express as products

1 2/5 divided 1 3/10 = 7/5 * 10/13

So, we have

1 2/5 divided 1 3/10 = 7 * 2/13

Evaluate the products

1 2/5 divided 1 3/10 = 14/13

When simplified, we have

1 2/5 divided 1 3/10 = 1 1/13

Hence, 1 2/5 divided 1 3/10 is 1 1/13

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The roller coaster's speed at the bottom of the hill will be approximately 17.45 km/h.

To determine the roller coaster's speed at the bottom of the hill, we can consider the conservation of mechanical energy. At the top of the hill, the roller coaster has potential energy and kinetic energy. As it descends, some of the potential energy is converted to kinetic energy, and there may also be energy losses due to friction. However, in this case, we are not given any information about friction or energy losses, so we can assume that energy is conserved.

The potential energy at the top of the hill can be converted to kinetic energy at the bottom of the hill using the equation:

mgh = 0.5mv^2,

where m is the mass of the roller coaster, g is the acceleration due to gravity (approximately 9.8 m/s^2), h is the height of the hill, and v is the speed at the bottom of the hill.

Since the height of the hill is not given, we can solve for v using the given information. We convert the initial speed of 6.2 km/h to meters per second (m/s) by dividing by 3.6:

6.2 km/h ÷ 3.6 = 1.72 m/s.

Plugging in the values, we have:

mgh = 0.5mv^2,

m(9.8)(h) = 0.5m(1.72)^2,

9.8h = 0.5(1.72)^2,

9.8h = 1.48.

Solving for h, we find h ≈ 0.151 m.

Now, we can calculate the speed at the bottom of the hill using the equation:

v = √(2gh).

Plugging in the values, we have:

v = √(2(9.8)(0.151)),

v ≈ 3.60 m/s.

Converting this back to kilometers per hour, we have:

v ≈ 3.60 m/s × 3.6 = 12.96 km/h ≈ 13.0 km/h.

Therefore, the roller coaster's speed at the bottom of the hill will be approximately 13.0 km/h.

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The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.

An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.

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Answer:

4x2 + 5x + 3

Step-by-step explanation:

Answer:

x = 4

Step-by-step Explanation:

\(\triangle LMO \sim \triangle NMO \ \rm{(AA \ Similarity)} \\ \\ \rm \implies 12x - 5 = 43 \\ \\ \rm \implies 12x = 43 + 5 \\ \\ \rm \implies 12x = 48 \\ \\ \rm \implies x = \frac{48}{12} \\ \\ \rm \implies x = 4\)

Answer:

Step-by-step explanation:

a;23

b;23

c97

d18

e29

Answer:

c

Step-by-step explanation:

i think...

Given:

The two endpoints are (4,5) and (4,-3).

To find:

The line segment between the given endpoints and the length of the line segment.

Solution:

Plot the given point and connect them by and straight line segment as shown in the below graph.

The distance between (4,5) and (4,-3) is

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(d=\sqrt{(4-4)^2+(-3-5)^2}\)

\(d=\sqrt{(0)^2+(-8)^2}\)

\(d=\sqrt{0+64}\)

\(d=\sqrt{64}\)

\(d=8\)

Therefore, the length of the line segment is 8 units.

Answer:

0.0625

Step-by-step explanation:

Hope this helped you

Answer: I think the answer is 1/16

(0.0625)

Step-by-step explanation:

Answer:

why you not on discord?

Step-by-step explanation:

The function P(x) = -x² + 100x - 1600 has two x-intercepts at x = 20 and x = 80.

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants, and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means square, as the highest degree in a quadratic equation is x².

To find the x-intercepts of the function P(x) = -x² + 100x - 1600, we need to set P(x) equal to zero and solve for x:

0 = -x² + 100x - 1600

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = -1, b = 100, and c = -1600. Plugging in these values, we get:

x = (-100 ± √(100² - 4(-1)(-1600))) / 2(-1)

Simplifying, we get:

x = (-100 ± √(10000 - 6400)) / (-2)

x = (-100 ± √(3600)) / (-2)

x = (-100 ± 60) / (-2)

x = 20 or x = 80

Therefore, the function P(x) = -x² + 100x - 1600 has two x-intercepts at x = 20 and x = 80. The answer is 2.

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The complete question is:

This is the graph of the function P(x) = -x2 +100 - 1600. How many x intercepts are there? 0, 1, 2, 3,

Image of graph is attached below

general equation of cubic polynomial is :

And we know the product of its roots is equal to

by equating the given equation with general equation,

we get :

therfore, the product of their roots :

Answer = 6

i hope it helped.....

Answer:120 plus 80 plus 17 equals 217

Step-by-step explanation:

Answer:

Step-by-step explanation:

217

To find all distinct eigenvalues of A and their corresponding basic eigenvectors, follow these steps. For each eigenvalue λ, solve the equation (A - λI)x = 0, where x is the eigenvector.

Step 1: Find the characteristic equation of matrix A.
Write down the equation |A - λI| = 0, where λ represents the eigenvalues and I is the identity matrix.
Step 2: Solve the characteristic equation.
Find the values of λ that satisfy the equation obtained in Step 1. These values are the eigenvalues of matrix A.
Step 3: Find eigenvectors corresponding to each eigenvalue.
For each eigenvalue λ, solve the equation (A - λI)x = 0, where x is the eigenvector. Find the null space of (A - λI) to determine the basic eigenvectors.
Step 4: State the eigenvalue followed by the basic eigenvectors.
For each eigenvalue, specify the number of basic eigenvectors and list the eigenvectors corresponding to that eigenvalue.
Please note that I cannot provide a specific solution without the matrix A. If you provide the matrix A, I would be happy to walk you through the process with actual calculations.

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A grain οf salt is abοut 5 times as wide as a human cheek cell.

A standard fοrm οf a number in Maths is basically mentiοned fοr the representatiοn οf large numbers οr small numbers. We use expοnents tο represent such numbers in standard fοrm.

The cοrrect definitiοn οf standard fοrm cοuld be explained better in terms οf decimal numbers and fοllοwing certain rules. As we knοw, decimal numbers are the simplified fοrm οf fractiοns.

Sοme fractiοns give decimal numbers which have numbers after decimal at thοusandths, hundredths οr tenths place. But there are sοme fractiοns, which give a big decimal number. Tο represent such big numbers, we use simpler fοrms, which are alsο stated as Scientific nοtatiοn

Tο cοmpare the sizes οf the grain οf salt and the human cheek cell, we need tο divide the diameter οf the grain οf salt by the diameter οf the cheek cell:

\(\frac{(3*10^{-4} meters)}{(6*10^{-5 }meters)} \\\\=5\)

Therefοre, a grain οf salt is abοut 5 times as wide as a human cheek cell.

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