What is a6/7 as a decimal

Answer:

u = 24, v = 92, and w = 184

Step-by-step explanation:

According to circle theorem, we have;

∠ACD = ∠ABD = 88° by angle inscribed in a circle and also subtending the same chord

∠DOA = 2 × ∠ABD by angle subtended at the center = 2 × Angle subtended at the circumference

∴ ∠DOA = 2 × ∠ABD = 2 × 88° = 176°

w° + ∠DOA = 360  by the sum of angles at a point

∴ w° = 360° - ∠DOA = 360° - 176° = 184°

w° = 184°

w° = 2 × v° by angle subtended at the center = 2 × Angle subtended at the circumference

∴ v° = w°/2 = 184°/2 = 92°

v° = 92°

In triangle ΔCDY and ΔABY, we have;

∠ABD = ∠ABY by reflexive property

∠ACD = ∠ACY by reflexive property

∠ACD = ∠ABD = 88°

∴ ∠ABY = 88°

∠CYD = ∠AYB  by vertically opposite angles are equal

∴ ∠CYD = 68° = ∠AYB

u° + ∠ABY + ∠AYB = 180° by angle sum property

∴ u° = 180° - (∠ABY + ∠AYB)

u° = 180° - (88° + 68°) = 24°

u° = 24°.

1. Component form of a force vector: An engineer analyzes forces on a car's suspension system during turns. Breaking down the force vector into components ensures stability and safety.

2. Overlaying a polar coordinate system: Air traffic controllers use polar coordinates to guide aircraft during landings, accurately representing positions relative to a control tower for efficient airspace management and safety.

Let us discuss in a detailed way:

1. To find the component form of a force vector, let's consider the following real-world situation:

Imagine you are an engineer designing a suspension system for a new car model. One of the crucial design factors is ensuring the system can handle forces acting on the wheels during turns. To analyze these forces, you need to break down the resultant force acting on the wheels into its component form.

By breaking down the force vector into its components, you can determine the specific forces acting in the horizontal and vertical directions. This information is vital for calculating the stresses and strains on various suspension components, such as springs and shock absorbers, and ensuring they can handle the load.

Analyzing the component form of the force vector allows you to understand the individual forces acting on the suspension system. It helps you determine the necessary design parameters and select appropriate materials to ensure the system's stability, performance, and safety.

2. Now, let's consider a real-world situation where overlaying a polar coordinate system is useful:

Imagine you are an air traffic controller responsible for guiding aircraft during landing procedures. To efficiently direct the planes, you need to determine the positions of the aircraft relative to a specific reference point, such as the control tower.

In this situation, overlaying a polar coordinate system allows you to represent the positions of the aircraft accurately. By choosing the control tower as the pole and extending the polar axis outward, you can use polar coordinates to specify the distance and direction of each aircraft from the control tower.

This polar coordinate system enables you to quickly identify the location of each aircraft, calculate the distances between them, and provide precise instructions for landing sequences. By using polar coordinates, you can effectively manage the airspace, ensure the safety of incoming aircraft, and prevent any potential collisions.

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Answer:

1264

Step-by-step explanation:

is the answer...........

Jenna has collected a data set by asking her friends how many times they have been to the aquarium. To describe the distribution of this data set, we can use the following terms: left or right, mean or medium, and IQR or Range of IQR.

1. Left or Right: This refers to the skewness of the distribution. If most of the values are concentrated on the left side and the tail is longer on the right, it is right-skewed. If most values are concentrated on the right side and the tail is longer on the left, it is left-skewed.

2. Mean or Median: These are measures of central tendency. The mean is the average of all the values, while the median is the middle value when the data set is ordered. The median is less sensitive to extreme values (outliers) than the mean.

3. IQR or Range of the IQR: The interquartile range (IQR) is a measure of dispersion that shows the spread of the middle 50% of the data. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The range of the IQR provides information about the variability of the data within the interquartile range.

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Answer:

2x X 6 = 11x - 7/6

12x = 11x - 7/6

12x - 11x = -7/6

x = - 7/6

Step-by-step explanation:

let the unknown be x

twice of the number is 2x multipled by 6

2x(6) equating to eleven times the number 11x minus 7/6

gives an equation as in step 1

multiply 6 by 2x to give a more simple equation

collect like terms so you have an equation as in step 3

simplify to get your final answer

Answer:

\(x=\frac{7}{30}\)

Step-by-step explanation:

Given the following question:

\(x+\frac{2}{3} =\frac{9}{10}\)

In order to find the answer to this question we need to subtract 9/10 from 2/3. To do this we need to find the common denominator, and then subtracting the numerators.

\(\frac{9}{10} -\frac{2}{3}\)
\(\frac{9}{10} \times3=\frac{27}{30}\)
\(\frac{2}{3} \times10=\frac{20}{30}\)
\(27-20=7=\frac{7}{30}\)
\(x=\frac{7}{30}\)

Hope this helps.

The equation of the line through the points (−9,3) and (−6,−3) is y = -2x - 15.

To find the equation of the line through the points (−9,3) and (−6,−3), we use the point-slope formula given as

`y - y1 = m(x - x1)` where `m` is the slope of the line and `(x1, y1)` is the coordinates of a point on the line. The slope of the line can be found using the formula:

m = (y2 - y1) / (x2 - x1)Here, (x1, y1) = (−9,3) and (x2, y2) = (−6,−3)

Substitute the values in the formula, m = (-3 - 3) / (-6 + 9) = -6/3 = -2.Therefore, the slope of the line is -2.Now, we need to use one of the given points, say (−9,3), and the slope, m = -2, in the point-slope formula to find the equation of the line.y - y1 = m(x - x1)Here, (x1, y1) = (−9,3).

Substitute the values in the formula,y - 3 = -2(x - (-9))y - 3 = -2(x + 9)y - 3 = -2x - 18y = -2x - 18 + 3y = -2x - 15

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Answer:

No

Step-by-step explanation:

We can use the rule [ x^y * x^z = x^y+z ]

h^3 * h^4

h^3+4

h^7

Best of Luck!

Answer:

Step-by-step explanation:

Medium is 28

Mean is 29

Range is 11

Midrange is 29.5

The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.

To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.

If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.

However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.

Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.

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After we Critique the statement by Ann, we conclude that her father was poor because of inflation is not necessarily accurate.

While inflation can lead to an increase in the cost of living and a decrease in the purchasing power of money, it is important to consider other factors that affect an individual's financial situation. Inflation can also be offset by increases in wages and other forms of income. Additionally, the rate of inflation varies across different sectors and regions, so its impact on an individual's financial situation can vary. Therefore, it is not accurate to solely attribute Ann's father's financial situation to inflation.

Inflation can be measured using the consumer price index (CPI), which tracks changes in the prices of a basket of goods and services typically consumed by households. The CPI is used to calculate the rate of inflation, which reflects the percentage change in the average price level of the basket of goods and services over time. The rate of inflation is affected by factors such as changes in the money supply, government policies, and global economic conditions.

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Complete Question:

Critique the following:

ann’s father told her that when he graduated from gsu back in 1971 with a degree in economics his first job paid him $9,860 per year. she said, "dad you were so poor".

The n-point DFT of the signal x[n] = ax1[n] + bx2[n] is given by the linear combination of the individual DFTs: X[k] = a * X1[k] + b * X2[k], where X[k] is the n-point DFT of x[n], X1[k] is the n-point DFT of x1[n], X2[k] is the n-point DFT of x2[n], and a and b are constants.

The Discrete Fourier Transform (DFT) is a mathematical transformation that converts a discrete-time signal from the time domain to the frequency domain. When we have two signals x1[n] and x2[n] with their respective n-point DFTs X1[k] and X2[k], we can combine them in a linear manner to obtain the DFT of their sum or scaled versions.

In the case of x[n] = ax1[n] + bx2[n], where a and b are constants, we can apply the DFT to both sides of the equation. By linearity property of the DFT, the DFT of the left-hand side (x[n]) can be expressed as the sum of the DFTs of the individual terms on the right-hand side (ax1[n] and bx2[n]).

Thus, the n-point DFT of x[n], denoted as X[k], is given by the linear combination of the individual DFTs:

X[k] = a * X1[k] + b * X2[k],

This equation states that each frequency bin of the DFT of x[n] is obtained by multiplying the corresponding frequency bin of the DFTs of x1[n] and x2[n] by their respective constants (a and b), and then summing these contributions.

In summary, the DFT of a linear combination of signals can be computed by taking the corresponding linear combination of their individual DFTs.

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Answer:

See below

Step-by-step explanation:

Quadratic equations with one solution are:

\( (x+2)^2 = 0, \:\: (2x-8)^2 = 0\)

Quadratic equations with two solutions are:

\( (2x-11)^2 = 1 \)

Quadratic equations with no solution are:

\( (x+2)^2 = - 4, \:\: x^2 + 6 = - 3\)

Answer: EDMENTUM + PLATO

Step-by-step explanation:

Answer:

Solution:

(1/12)^(-2b) * 12^(-2b+2) = 12

(12^-1)^(-2b) (12)^(-2b+2) = 12

(12^2b)(12)^(-2b+2) = 12

12^(2b-2b+2) = 12

12^2 = 12

144 does not equal 12

No solution.

Step-by-step explanation:

The measure of angle PNL will be equivalent to 69 degrees.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle KLM such that N is a midpoint of KL and P is a midpoint of LM.

Triangles LMP and LKM are similar to each other. Therefore, PN will be parallel to MK. So angle PNL will be equal to angle MKN. Therefore -

2x + 61 = 97 - 7x

9x = 97 - 61

9x = 36

x = 4

So, angle PNL will be equal to -

2 x 4 + 61

69 degrees

Therefore, the measure of angle PNL will be equivalent to 69 degrees.

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Answer: 18

Step-by-step explanation:

      To evaluate this expression, we will substitute known values and simplify.

Given:

3ab

Substiue a = 2 and b = 3:

3(2)(3)

Order of Operations, multiply left to right:

(3)(2)(3) = (6)(3) = 18

                              For a = 2 and b = 3, 3ab = 18.

Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

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The table of values that represents exponential decay is (c)

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

The table of values

An exponential function is represented as

y = abˣ

Where

Rate = b

When the rate is less than 1, then the table represents a decay

i.e when y reduces as x increases

The table that has the above features is the table (c)

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The speed of the plane relative to the ground if no action is taken by the pilot is 79.5 km/h westward.

Given information: The speed of the plane with respect to still air is 160 km/h.

West wind starts to blow at a constant speed of 80.5 km/h.

Let us consider Vp be the speed of the plane relative to the groundVw be the speed of the wind

So, the speed of the plane with respect to the ground is given by

                         Vp = Vp + VwVp = 160 + (-80.5)

Thus, the speed of the plane relative to the ground if no action is taken by the pilot is 79.5 km/h westward.

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The Laplace transform of the given function \((t)-{: 01277 1, 0\)is given by:

\(L{(t)-{: 01277 1, 0} = L{(t - 1)e^(-2t) u(t - 1)} + L{e^(-2t) u(t)}\) where u(t) is the unit step function.

Step-by-step solution is given below: Given function is (t)-{: 01277 1, 0Laplace transform of the given function is \(L{(t)-{: 01277 1, 0}=L{(t-1)e^-2t u(t-1)}+L{e^-2t u(t)}\) Where u(t) is the unit step function.

We have to find the Laplace transform of the given function.\((t)-{: 01277 1, 0 = (t-1)e^-2t u(t-1) + e^-2t u(t)\)Laplace Transform of \((t-1)e^-2t u(t-1) = L{(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)} = e^{-as} * F(s)So, (t-1)e^-2t u(t-1) = 1(t-1)e^-2t u(t-1)\)

Taking Laplace transform on both sides,\(L{(t-1)e^-2t u(t-1)} = L{1(t-1)e^-2t u(t-1)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\)(On substituting a = 2)

Now, Let's solve \(L{e^-2t u(t)}\)

Taking Laplace transform on both sides,\(L{e^-2t u(t)}= e^{-as} * L{f(t-a)}= e^{-as} * F(s)= e^{-as} * L{e^{at}f(t)}= F(s-a) = F(s+2)\) (On substituting a = 2) Laplace transform of the given function L{(t)-{: 01277 1, 0}= L{(t-1)e^-2t u(t-1)} + L{e^-2t u(t)}= F(s+2) + F(s+2)= 2F(s+2)= 2L{e^-2t} = 2 / (s+2)

Hence, the Laplace transform of the given function is 2 / (s+2) which is a transfer function of a system with a first-order differential equation.

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The probability of getting all heads or all tails is 0.18 as per the concept of probability.

To find the probability of getting all heads or all tails in 6 tosses of a loaded coin, we can use the concept of independent events.

Since the coin is loaded, the probability of getting a head on a single toss is 3/4, and the probability of getting a tail is 1/4.

To calculate the probability of getting all heads or all tails in 6 tosses, we need to consider the different combinations of outcomes that satisfy this condition.

The probability of getting all heads in 6 tosses can be calculated as (3/4) x (3/4) x (3/4) x (3/4) x (3/4) x (3/4) = (3/4)⁶.

Similarly, the probability of getting all tails in 6 tosses is (1/4) x (1/4) x (1/4) x (1/4) x (1/4) x (1/4) = (1/4)⁶.

To find the probability of either of these events occurring, we can sum up the probabilities:

P(all heads or all tails) = P(all heads) + P(all tails)

= (3/4)⁶ + (1/4)⁶

= 0.18.

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Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Angle u is 32°.

A line can go on forever. The line continues forever in both directions. There are no endpoints on the lines. The following are the angles of lines: Equal angles are those that are vertically opposed, such as a = d and b = c. As an example, the angles a + b and a + c add up to 180 degrees. Angles that correspond to one other are equal, such as a = e, b = f, c = g, and d = h. A line is a geometric form with only one dimension. There is no thickness to the line; it merely has length. Lines that cross at an angle will do so only once.

Given that angle Y at the q line is 32°. Since line p and line q are parallel. From properties of a line. angle made by the same cross line with two parallel lines will be the same.

Therefore, Angle u will be the same as angle y which is 32°.

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Answer:

23 miles per hour. This is their speed.

Answer:  23 miles per hour

Another way to get a unit rate is the number of minutes it takes to travel 1 mile.  1 mile takes her about 2.61 minutes miles to drive.

Step-by-step explanation:  Divide the number of miles by the time  to get the unit rate in miles per hour.

138 ÷ 6 = 23 miles per hour.

If you divide the minutes by the distance, you get the unit rate in minutes per mile.

6 hours is 360 minutes.  60 minutes per hour is a unit rate.

138 ÷ 360  ≈ .3833 miles per minute

360 ÷ 138 ≈ 2.61 minutes per mile

a) The number of possible committees of 3 people out of 8 candidates, where there is no distinction between committee members, is determined using the combination formula. Applying the formula, we find that there are 56 possible committees. b) Since we are considering only whole numbers, we round down to obtain 476 as the count of integers that meet the criteria.

a) To calculate the number of possible committees of 3 people out of 8 candidates, we can use the concept of combinations. Since there is no distinction between committee members and the order of selection doesn't matter, we need to find the number of combinations. The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of candidates and r is the number of committee members.

Substituting the values, we have C(8, 3) = 8! / (3!(8-3)!). Simplifying this expression, we get C(8, 3) = 8! / (3!5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56.

Therefore, there are 56 possible committees of 3 people out of a pool of 8 candidates.

b) To find the number of integers from 1 through 10,000 that are multiples of both 3 and 7, we need to find the number of common multiples of these two numbers. We can use the concept of the least common multiple (LCM) to determine the smallest number that is divisible by both 3 and 7, which is 21.

To find the count of multiples of 21 within the range of 1 through 10,000, we divide the upper limit (10,000) by the LCM (21) and round down to the nearest whole number. This gives us 10,000 / 21 ≈ 476.19.

Since we can only have whole numbers of multiples, we round down to the nearest whole number. Therefore, there are 476 integers from 1 through 10,000 that are multiples of both 3 and 7.

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The outcome is random if we know the possible values it can have, but not which particular value it takes.

Randomness refers to the property of a process or system where the outcome is uncertain, unpredictable, and not predetermined. In a random process, we know the set of possible outcomes.

But we cannot determine which particular outcome will occur until it actually happens. For example, when flipping a fair coin, the possible outcomes are heads or tails.

But we do not know which one will come up until the coin is flipped. Randomness is a fundamental concept in probability theory and is used to model and analyze a wide range of phenomena.

Including games of chance, genetics, and quantum mechanics.

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Answer:

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

Let Anita be x now.

Her mother is 5 times older and in two years time she will be 5x + 2.

Rita is half the age of Anita and in two years time she will be (x/2) + 2.

The sum of ages after two years will be 58:

Anita is 8 years old.

Answer:

b) angle bisector of angle ABC

Answer:the slope and unit rate are 4/5

Step-by-step explanatrise is 4

Answer:

I hope this helps u

have a nice day