Find the measures of the angles of following triangle.
The ratio of the measures of the three angles is 3: 6: 1 .

Answer:

\(x^{2}\)+3x-18=0

Step-by-step explanation:

3x-18= -\(x^{2}\)

+\(x^{2}\)       +\(x^{2}\)

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

\(x^{2}\)+3x-18=0

Answer: 15

Step-by-step explanation:

This is a right angle and right angles always add up to 90 degrees.

You would take away 30 from 90 which equals 60.

Then because it is 4x you would do the inverse and divide 60 by 4 to get x on its own.

60/4=15

The equation of the line passing through the point (-1,2) with slope m is y = mx + m-2. This is a general equation of the line and we can find different equations by putting different values of m.

We know that when a point and slope of the equation are given, an equation can be written as

\(\frac{y-y_{1} }{x - x_{1} } =m\)

which is known as the slope-point form

where m is the slope of the equation

y1 is the  y coordinate of the given point

x1 is the x coordinate of the given point

In the given question, y1 = 2 and x1 = -1

Substituting the value of coordinates in the slope point equation, we get

\(\frac{y-2}{x-(-1)} = m\)

\(\frac{y-2}{x+1}=m\)

y-2 = mx + m

y = mx + m-2

Hence, the equation of the line passing through the point (-1,2) with slope m is y = mx + m-2.

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What is the equation of the line passing the point (-1, 2) with a slope m?

The maximum value of standard deviation that does not lead to out-of-tolerance bars exceeding 1% is approximately 0.002 inches.

Let's first calculate the upper limit of the acceptable tolerance for the aluminum bar:

Upper limit = 0.9 + 0.005 = 0.905

We want to find the maximum value of standard deviation (σ) such that the probability of the width of the bar exceeding this upper limit does not exceed 1%.

To solve this problem, we need to standardize the distribution using the standard normal distribution, which has a mean of 0 and a standard deviation of 1.

Z-score = (upper limit - mean) / σ

Since we want to find the maximum value of σ, we can rearrange the formula to solve for σ:

σ = (upper limit - mean) / Z-score

To find the corresponding Z-score for a probability of 1%, we can use a standard normal distribution table or calculator. The Z-score that corresponds to a probability of 1% is approximately -2.33.

Substituting the values given in the problem, we get:

σ = (0.905 - 0.9) / (-2.33)

σ ≈ 0.002

Therefore, the maximum value of standard deviation that does not lead to out-of-tolerance bars exceeding 1% is approximately 0.002 inches.

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Answer:

= 1

Step-by-step explanation:

0.4131 + 0.5868 = 0.999 --> 1

Answer:

The building is worth $129,375 now.

Step-by-step explanation:

To find the value of the building now, you can use the following formula:

Current value = Original value + (Original value * Increase percentage)

Plugging in the values given in the problem, you get:

Current value = $125,000 + ($125,000 * 3.5%)

= $125,000 + $4,375

= $129,375

The Maclaurin series of \(xe^{8x}=\frac{\sum^\infty_0(8^n * x^n)}{n!}\)

What is the Maclaurin series?

The Maclaurin series is a special case of the Taylor series expansion, where the expansion is centered around x = 0. It represents a function as an infinite sum of terms involving powers of x. The Maclaurin series of a function f(x) is given by:

\(f(x) = f(0) + f'(0)x +\frac{ (f''(0)x^2}{2!} + ]\frac{(f'''(0)x^3)}{3! }+ ...\)

To find the Maclaurin series of the function f(x) = \(xe^{8x}\), we can start with the general formula for the Maclaurin series expansion:

\(f(x) = \frac{\sum^\infty_0(f^n(0) * x^n) }{ n!}\)

where\(f^n(0)\) represents the nth derivative of f(x) evaluated at x = 0.

Let's determine the appropriate series for the function \(f(x) = xe^{8x}\) from the given options:

a) \(\frac{\sum^\infty_0(8^n * x^{n+1})}{n!}\)

b) \(\frac{\sum^\infty_0(x^n )} {8^n*n!}\)

c)\(\sum^\infty_0(8^n * x^n)/n!\)

d)\(\frac{\sum^\infty_0(x^n )} {n!}\)

Comparing the given options with the general formula, we can see that option (c) matches the required form:

f(x) = \(=\frac{\sum^\infty_0(8^n * x^n)}{n!}\)

Therefore, the Maclaurin series of \(f(x) = xe^{8x}\) can be written as:

f(x) = \(=\frac{\sum^\infty_0(8^n * x^n)}{n!}\)

Option (c) is the correct series to represent the Maclaurin series of \(xe^{8x}.\)

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Answer:

The unit price is $5.19.

Step-by-step explanation:

The unit price of the pairs of socks is the price for a package of 3 pairs divided by 3 pairs:

$15.57

---------- = $5.19

 3 pr

The unit price is $5.19.

Answer:  This is linear and it's written slope.  it has a positive slope. I saw the line go up and it's straight.

1) In this question, we can notice that theta is in Quadrant IV. In this quadrant, the cosine of theta yields a positive value.

2) So, let's make use of a Pythagorean Identity to find the value of the cosine of theta, given the sine of that same angle:

3) Thus the cosine of theta is 4/5 for in Quadrant IV cosine is positive.

Answer:

it is -3/15

Step-by-step explanation:/ im not good at explning it

Answer:

\(-\frac{4}{15}\)

Step-by-step explanation:

\(-\frac{3}{5} +\frac{1}{3}\\\\ \text{LCM 5,3: 15}\\\\\frac{-3}{5}=\frac{-9}{15}\\\\\frac{1}{3}=\frac{5}{15}\\\\\\\frac{-9}{15}+\frac{3}{15}=\frac{-9+5}{15}=\boxed{-\frac{4}{15}}\)

Hope this helps.

Answer: a+b=b+a is a clear example of commutative property.

Step-by-step explanation: The commutative property applies to addition and multiplication. The property states that terms can “commute,” or move locations, and the result will not be affected. This is expressed as a+b=b+a for addition, and a×b=b×a for multiplication. The commutative property does not apply to subtraction or division.

Answer:

147/99

Step-by-step explanation:

(1.48 x 100) - 1 99

The parallax problem is a phenomenon that arises when measuring the distance to a celestial object by observing its apparent shift in position relative to background objects due to the motion of the observer.

The parallax effect is based on the principle of triangulation. By observing an object from two different positions, such as opposite sides of Earth's orbit around the Sun, astronomers can measure the change in its apparent position. The greater the shift observed, the closer the object is to Earth.

However, the parallax problem introduces challenges in accurate measurement. Firstly, the shift in position is extremely small, especially for objects that are very far away. The angular shift can be as small as a fraction of an arcsecond, requiring precise instruments and careful measurements.

Secondly, atmospheric conditions, instrumental limitations, and other factors can introduce errors in the measurements. These errors need to be accounted for and minimized to obtain accurate distance calculations.

To overcome these challenges, astronomers employ advanced techniques and technologies. High-precision telescopes, adaptive optics, and sophisticated data analysis methods are used to improve measurement accuracy. Statistical analysis and error propagation techniques help estimate uncertainties associated with parallax measurements.

Despite the difficulties, the parallax method has been instrumental in determining the distances to many stars and has contributed to our understanding of the scale and structure of the universe. It provides a fundamental tool in astronomy and has paved the way for further investigations into the cosmos.

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If the probability of obtaining a score less than x = 70 is p = 0.0013, the score that corresponds to a probability of 0.0013 is x = 38.2.

We are referring to a normal distribution with a mean (µ) of 100 and a standard deviation (σ) of 20. You want to find the probability of obtaining a score less than x = 70, and you provided that the probability (p) is 0.0013. In a normal distribution with µ = 100 and σ = 20, the probability of obtaining a score less than x = 70 is p = 0.0013. Based on the information given, we know that the probability of obtaining a score less than x = 70 is p = 0.0013. This means that the z-score for x = 70 is -3.09 (found using a standard normal distribution table or calculator).

To find the z-score, we use the formula:

z = (x - µ) / σ

Plugging in the values we know:

-3.09 = (70 - 100) / 20

Solving for x:

-3.09 = (x - 100) / 20

-3.09 * 20 = x - 100

-61.8 + 100 = x

x = 38.2

Therefore, the score that corresponds to a probability of 0.0013 is x = 38.2.

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If the bond angle between two adjacent hybrid orbitals is 120° the hybridization is Sp2 hybridization .

Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.

sp2 hybridization

There are other ways to combine the orbitals than sp3 hybridization when an excited state carbon atom is produced. As opposed to the three p orbitals in the sp3 hybridization, the s orbital only interacts with two p orbitals in the sp2 hybridization. As a result, three orbitals are combined to create three hybrid orbitals, also known as sp2 hybrid orbitals.

The sp2 hybridization occurs when the s orbital is mixed with only two p orbitals as opposed to the three p orbitals in the sp3 hybridization

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The pairwise comparisons that need to be made for this anova result will be b.3

In order to determine the number of pairwise comparisons needed for a one-way between-subjects ANOVA with three groups, we can use the formula:

N = (k * (k-1)) / 2

Where N represents the number of pairwise comparisons and k represents the number of groups. In this case, k = 3.

Plugging in the values:

N = (3 * (3-1)) / 2

N = (3 * 2) / 2

N = 6 / 2

N = 3

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Answer:

Length: 10 m

Width: 6 m

Step-by-step explanation:

The layout of the floor is l x w, which is 100 cm by 60 cm. Now, the confusing part: 1 meter (m) = 10 centimeters (cm)

To set this problem up, you'd first have to go through the logic. For every 10 centimeters of the floor layout, it is equal to 1 meter of the actualy floor plan. So you would have to scale 100 cm and 60 cm by \(\frac{1}{10}\) (or divide by 10).

We will ignore the units, for now

Length: 100 * \(\frac{1}{10}\) = 10    or    (100/10 = 10)

Width: 60 * \(\frac{1}{10}\) = 6       or    (60/10 = 6)

Now that we've finalized the numerical value, lets move on to the units. Since the question wants us to respond in meters, the length of 10 and the width 6 6 would be in meters.

So the answer would be:

Length: 10 m

Width: 6 m

Hope this helped!

Answer:

THE ANSWER IS 18/42 IF YOU LOOKED THIS UP FOR HEGARTY MATHS THEN THIS IS RIGHT!!!!!

Step-by-step explanation:

Answer:

(Hegarty Maths Answer)

The correct answer is:

15 of 32

Step-by-step explanation:

There is a bag filled with 3 blue and 5 red marbles.

A marble is taken at random from the bag, the colour is noted and then it is replaced.

Another marble is taken at random.

What is the probability of getting exactly 1 blue?

The correct answer is:

15 of 32

Step-by-step explanation:

Area of square

\( {s}^{2} \)

\(6.7 \times 6.7 = 44.89 {mm}^{2} \)

Answer:

8/4 or just 2

Step-by-step explanation:

3/4 + 1/2 + 3/4 = 4/8

but 4/8 simplified get you 2

Let's assume the amount invested at the higher interest rate (16%) is x dollars.

The amount invested at the lower interest rate (6%) would then be ($80,000 - x) dollars, as the total investment is $80,000.

The interest earned from the investment at 16% is calculated as (x * 16%) = 0.16x dollars.

The interest earned from the investment at 6% is calculated as (($80,000 - x) * 6%) = 0.06(80,000 - x) dollars.

According to the given information, the retiree receives a total interest of $8,900 per year. So we can set up the equation:

0.16x + 0.06(80,000 - x) = 8,900

Now, let's solve the equation to find the value of x:

0.16x + 0.06(80,000 - x) = 8,900

0.16x + 4,800 - 0.06x = 8,900

0.1x + 4,800 = 8,900

0.1x = 8,900 - 4,800

0.1x = 4,100

x = 4,100 / 0.1

x = 41,000

Therefore, $41,000 is being invested at the higher interest rate (16%).

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The race is 40 miles long, since there are two repair and two water stations evenly spaced between the start and finish lines, and the third water station is located 8 miles after the first repair station.

The race is 40 miles long because the start and finish lines are 20 miles apart, and there are evenly spaced water and repair stations between them. The figure indicates that the first repair station is located at the start line, and the second repair station is 20 miles after the start line. The first water station is located 8 miles after the first repair station, and the second water station is located 16 miles after the second repair station. Therefore, the third water station is located 8 miles after the first repair station. Since there are two repair and two water stations evenly spaced between the start and finish lines, the race is 40 miles long.

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Answer:

24 USA pints

Step-by-step explanation:

24 in US to turn gallons to pints multiply the volume value by 8

Answer:

35 c 36 d

Step-by-step explanation:

The reward of 600 points will be earned by spending the amount of $300.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, Omar earns 800 reward points for spending 300 dollars.

The amount of money spent to earn 600 reward points will be calculated as,

800 reward points = $300 spending

1 reward point = $300 / 800 spending

600 reward point = ($300 x 600) / 800

600 reward points = $225

Therefore, the reward of 600 points will be earned by spending the amount of $300.

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a) Dijkstra's algorithm is a greedy algorithm used to find the shortest path from a source node to all other nodes in a graph.

It works by maintaining a set of unvisited nodes and their tentative distances from the source node. Initially, all nodes except the source node have infinite distances.

The algorithm proceeds iteratively:

Select the node with the smallest tentative distance from the set of unvisited nodes and mark it as visited.

For each unvisited neighbor of the current node, calculate the tentative distance by adding the distance from the current node to the neighbor. If this tentative distance is smaller than the current distance of the neighbor, update the neighbor's distance.

Repeat steps 1 and 2 until all nodes have been visited or the smallest distance among the unvisited nodes is infinity.

The algorithm guarantees that once a node is visited and marked with the final shortest distance, its distance will not change. It explores the graph in a breadth-first manner, always choosing the node with the shortest distance next.

b) Let's apply Dijkstra's algorithm to graph G1:

       2

   S ------ A

  / \      / \

 3   4    1   5

/     \  /     \

B       D       E

\     / \     /

 2   1   3   2

  \ /     \ /

   C ------ F

       4

The source node is S.

The numbers on the edges represent the distances.

Step-by-step execution of Dijkstra's algorithm on G1:

Initialize the distances:

Set the distance of the source node S to 0 and all other nodes to infinity.

Mark all nodes as unvisited.

Set the current node to S.

While there are unvisited nodes:

Select the unvisited node with the smallest distance as the current node.

In the first iteration, the current node is S.

Mark S as visited.

For each neighboring node of the current node, calculate the tentative distance from S to the neighboring node.

For node A:

d(S, A) = 2.

The tentative distance to A is 0 + 2 = 2, which is smaller than infinity. Update the distance of A to 2.

For node B:

d(S, B) = 3.

The tentative distance to B is 0 + 3 = 3, which is smaller than infinity. Update the distance of B to 3.

For node C:

d(S, C) = 4.

The tentative distance to C is 0 + 4 = 4, which is smaller than infinity. Update the distance of C to 4.

Continue this process for the remaining nodes.

In the next iteration, the node with the smallest distance is A.

Mark A as visited.

For each neighboring node of A, calculate the tentative distance from S to the neighboring node.

For node D:

d(A, D) = 1.

The tentative distance to D is 2 + 1 = 3, which is smaller than the current distance of D. Update the distance of D to 3.

For node E:

d(A, E) = 5.

The tentative distance to E is 2 + 5 = 7, which is larger than the current distance of E. No update is made.

Continue this process for the remaining nodes.

In the next iteration, the node with the smallest distance is D.

Mark D as visited.

For each neighboring node of D, calculate the tentative distance from S to the neighboring node.

For node C:

d(D, C) = 2.

The tentative distance to C is 3 + 2 = 5, which is larger than the current distance of C. No update is made.

For node F:

d(D, F) = 1.

The tentative distance to F is 3 + 1 = 4, which is smaller than the current distance of F. Update the distance of F to 4.

Continue this process for the remaining nodes.

In the next iteration, the node with the smallest distance is F.

Mark F as visited.

For each neighboring node of F, calculate the tentative distance from S to the neighboring node.

For node E:

d(F, E) = 3.

The tentative distance to E is 4 + 3 = 7, which is larger than the current distance of E. No update is made.

Continue this process for the remaining nodes.

In the final iteration, the node with the smallest distance is E.

Mark E as visited.

There are no neighboring nodes of E to consider.

The algorithm terminates because all nodes have been visited.

At the end of the algorithm, the distances to all nodes from the source node S are as follows:

d(S) = 0

d(A) = 2

d(B) = 3

d(C) = 4

d(D) = 3

d(E) = 7

d(F) = 4

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