use the circle below to find the angle measures and arc measure

Answer:

240 hours

Step-by-step explanation:

1 week = 20 hours

12 weeks = 20 × 12

= 240 hours

Answer:

9 ft

Step-by-step explanation:

Hope this helps!

Have a great day!

Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

The kilograms of apple she sell at the farmer's market is A = 2.175 kg

Given data ,

To find the weight of apples sold by the farmer, we can subtract the weight of pears from the total weight

Given that 3/4 of the weight is pears, we can calculate the weight of pears by multiplying the total weight by 3/4:

Weight of pears = (3/4) x 8.7 kilograms = 6.525 kilograms

Since the total weight is 8.7 kilograms, we can subtract the weight of pears to find the weight of apples

On simplifying the equation , we get

Weight of apples = Total weight - Weight of pears

A = 8.7 kilograms - 6.525 kilograms = 2.175 kilograms

Hence , the farmer sold approximately 2.175 kilograms of apples at the farmer's market

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The phasor method involves converting the sinusoidal functions into phasors, which are complex numbers representing the amplitude and phase of the sinusoidal function. The phasor for a sinusoidal function y = A sin(ωt + φ) is A e^(iφ), where A is the amplitude and φ is the phase angle.

(a) To find the amplitude of y, we need to add the phasors of y1, y2, and y3. The phasor for y1 is 11 e^(i0) = 11, the phasor for y2 is 21 e^(i30°), and the phasor for y3 is 7.0 e^(-i50°). Therefore, the phasor for y is:

Y = 11 + 21 e^(i30°) + 7.0 e^(-i50°)

To find the amplitude of Y, we can take the magnitude of this phasor:

|Y| = sqrt[(11)^2 + (21)^2 + (7.0)^2] = 24.2

Therefore, the amplitude of y is 24.2.

(b) To find the phase constant of y, we need to find the angle that the phasor Y makes with the positive real axis. We can write the phasor Y in rectangular form:

Y = (11 + 21 cos 30° - 7.0 cos 50°) + (21 sin 30° - 7.0 sin 50°) i

The angle that the phasor Y makes with the positive real axis is:

tan^(-1)[(21 sin 30° - 7.0 sin 50°) / (11 + 21 cos 30° - 7.0 cos 50°)]

Using a calculator, we find that this angle is approximately -6.5°. Therefore, the phase constant of y is -6.5°, or we can say that the phase angle of the phasor Y is -6.5°.

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a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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The sampling distribution of the mean for a sample size of 11 from a normally distributed population can be used to determine probabilities and intervals.

a. The sampling distribution of the mean for a sample size of 11 will be approximately normal. This is because, according to the Central Limit Theorem, when the sample size is sufficiently large (typically considered as n ≥ 30) and the population is approximately normally distributed, the sampling distribution of the mean will also be approximately normal. Therefore, option A is correct.

b. To find the probability that the sample mean is less than 2.60 inches, we need to calculate the area under the sampling distribution curve to the left of 2.60. This can be done using the z-score formula and the known mean and standard deviation of the population. By calculating the z-score for 2.60 and referring to the standard normal distribution table or using statistical software, we can find the corresponding probability.

c. Similarly, to find the probability that the sample mean is between 2.62 and 2.65 inches, we need to calculate the area under the sampling distribution curve between these two values. This involves calculating the z-scores for both 2.62 and 2.65 and finding the area between these two z-scores using the standard normal distribution table or statistical software.

d. The probability of 51% indicates that there is a symmetric interval around the population mean that contains 51% of the sample means. To find the lower and upper bounds of this interval, we need to determine the z-scores that correspond to the cumulative probabilities of 0.245 and 0.755 (which sum up to 51%). These z-scores can be found using the standard normal distribution table or statistical software. By converting these z-scores back to the corresponding values in inches using the population mean and standard deviation, we can determine the lower and upper bounds of the interval.

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Answer:

usage patterns are a variable used in market segmentation.

Step-by-step explanation:

Usage patterns are a variable used in behavioral segmentation.

Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.

Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.

By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.

Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.

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Answer:

(1,-2) for the last time

Step-by-step explanation:

Substitute the values and cancel the common factor in the equation

Step-by-step explanation:

you need to use the midpoint formula which is

(x1 + x2 / 2 ; y1 + y2/2)

Answer:

13.5 square units

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

The area of the triangle is 13.5 square units

Step-by-step explanation:

The easiest way to find the area of of a triangle is to find the area of rectangle surrounding it, and divide by two.

In this case, we can use the bottom line and the distance from that to the top point as the side lengths of our "rectangle"

The bottom line has a length of 9, and the distance from that line to the top point is 3.  We can say then that the area of the triangle is half of three times nine:

3 × 9 ÷ 2 = 3 × 4.5 = 13.5

So the total area of the triangle is 13.5 square units

Distance (D): 150 miles

Time (t): 3 hours

Answer: 50 miles / hour

The value for p is 30.

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We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

Which nation experienced the hottest summer?

We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.

Country A: (21.4°C) (18+20+22+23+24)/5

(24+26+28+29+27)/5 = 26.8°C for Country B.

The summer was therefore hotter in Country B, with an average temperature of 26.8°C.

b) Over the summer, which nation saw more erratic weather?

We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.

24°C - 18°C equals 6°C in Country A.

29°C - 24°C equals 5°C in country B.

As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

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Answer:

four billion two hundred fifty-eight million one hundred forty-five thousand three hundred ninety-seven

Step-by-step explanation:

Answer:

Word form-

four billion, two hundred fifty-eight million, one hundred forty-five thousand, three hundred ninety-seven.

Step-by-step explanation:

Answer:

Parece que quieres factorizar la expresión 3x^4 -+12. Sin embargo, el signo -+ no es válido en álgebra. ¿Quieres decir 3x^4 - 12 o 3x^4 + 12?

Step-by-step explanation:

Factorization of 3x⁴+ 12 , is 3(x²₋ 2x ₊ 2) (x²₊2x₊2)

we known that the given equation needs to be factorized.

therefore, let us use the basic principle of factorization here, then using the splitting the middle term theorem find out the factorization

Given;

3x⁴₊12

Here, let us take 3 common from the base equation

Therefore,

3( x⁴ ₊ 4)

Furthermore let us split the middle sub equation into simple terms,

Therefore,

3(x⁴ ₋ 2x + 2) (x²₊ 2x₊2)

Hence, Factorization of 3x⁴+ 12 , is 3(x²₋ 2x ₊ 2) (x²₊2x₊2).

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Answer:

It's the first one

Step-by-step explanation:

The transformation that relates f(x) to g(x) is a horizontal shift of the graph of f(x) by 2 units to the right, followed by a vertical shift of the resulting graph downwards by 7 units. This is evident from the given expressions of f(x) and g(x).

Specifically, the vertex of the graph of f(x) is located at (0,0), while the vertex of the graph of g(x) is located at (2,-7). Therefore, g(x) can be obtained from f(x) by first replacing x with x-2 to shift the vertex to (2,0), and then subtracting 7 to move the vertex to (2,-7). This transformation preserves the shape of the graph of f(x) but changes its position. More generally, any function of the form g(x) = f(x-a) - b represents a horizontal shift of f(x) by a units to the right, followed by a vertical shift of the resulting graph downwards by b units.

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Answer:

Step-by-step explanation:

The amount to be paid = The new price

where;

New price = (100-x)/100 * Original price

Original price = 40.00

x = discount

100-35/100 * 40.00

65/100 *40

26 shilling

Two triangles that have equal base lengths and equal heights, have equal areas

The ratio of the areas of ΔAEB and ΔDEC is one

The reason the ratio is one is that the area of ΔAEB is equal to the area of ΔDEC

The reasons for giving the above values are are follows;

The given parameters are;

Triangle ABC and DBC overlap

The base length of triangle ABC = The base length of triangle DBC

The height of triangle ABC = The height of triangle DBC = 8

Required:

To find the ratio of the areas of the triangle AEB and DEC

Solution:

The area of a triangle = (1/2) × Base length × Height

Given that the base, and height of triangles ΔABC and ΔDBC are equal, we have;

Area of triangle ΔABC = Area of triangle ΔDBC

The area of ΔABC = Area of ΔAEB + Area of ΔECB

Area of triangle ΔDBC =  Area of ΔDEC + Area of ΔECB

Therefore;

Area of ΔAEB + Area of ΔECB = Area of ΔDEC + Area of ΔECB by substitution property of equality

Subtracting area of ΔECB from both sides gives;

Area of ΔAEB = Area of ΔDEC by subtraction property of equality

Therefore;

\(\dfrac{\Delta AEB}{\Delta DEC} = 1\)

ΔAEB:ΔDEC = 1:1

The ratios of the areas of the triangle AEB and DEC is 1

The reason why the ratio of the area of the two triangles is 1 is that ΔAED and ΔDEC are each obtained from ΔABC and ΔDBC which are equal to each other by subtracting ΔBEC from each, and therefore, by subtraction property of equality, the two triangles are equal

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Each statement about integer is:

Statement A: If positive is subtracted from a negative integer, the difference is negative integer.

This statement is sometimes true.

If a positive integer is subtracted from a negative integer, the difference can be a negative integer or a positive integer. For example, if -5 is subtracted from -3, the difference is -8, which is a negative integer. However, if -3 is subtracted from -5, the difference is 2, which is a positive integer. The difference sign depends on which value is the bigger one.

Statement B: If a positive integer is subtracted from a positive integer, the difference is a positive integer.

This statement is sometimes true.

If a positive integer is subtracted from a positive integer, the difference can be a positive integer or a negative integer. For example, if 3 is subtracted from 5, the difference is 2, which is a positive integer. However, if 5 is subtracted from 3, the difference is -2, which is a negative integer.

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Answer:

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Step-by-step explanation:

2)

a) elimination method

b) substitution method

c) substitution method

For the first part we can elimate the y variable by subtracting the equations. We can then find the value of x.

For the second part we can substitute y as 2x+5 in the second equation and solve for x.

For the third part we can substitute y as 4x+3 in the first equation and solve for x.

3)

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To solve this problem, we can set up a proportion based on the given information. Let's assume that the number of machines is directly proportional to the number of devices produced .

The time taken is inversely proportional to the number of devices produced. From the given information: 24 machines can make 5 devices in 30 minutes. let's assign variables:  Let m1 be the number of machines.

Let d1 be the number of devices. Let t1 be the time taken. We have the following ratios: m1:d1 = 24:5 (number of machines to number of devices)

t1:d1 = 30:5 (time taken to number of devices).  Now we need to find the time it would take for 4 machines to make 15 devices. Let m2 be the number of machines (4 in this case). Let d2 be the number of devices (15 in this case). Let t2 be the time taken (to be determined). We can set up the following proportion:  m1:d1 = m2:d2.  Substituting the values we have: 24:5 = 4:15.  To find t2, we can set up the following proportion:

t1:d1 = t2:d2.  Substituting the values we have: 30:5 = t2:15.   Now we can solve for t2: 24/5 = 4/d2 (Cross-multiply).  24d2 = 4 * 5.  24d2 = 20.  d2 = 20/24. d2 = 5/6. So, 4 machines will make 15 devices in 5/6 of the time it took 24 machines to make 5 devices. To find the time, we can set up a proportion: 30/5 = t2/(5/6) (Cross-multiply). 30 * (5/6) = t2. 25 = t2. Therefore, 4 machines will take 25 minutes to make 15 devices. To convert this to hours, divide the time by 60: 25 minutes = 25/60 hours

25/60 = 5/12(Answer) .

Therefore , if 24 machines can make 5 devices in 30 minutes,  4 machines will take 5/12 of an hour to make 15 devices.

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An ogive is used to plot cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class when displaying quantitative data. Option B.

An ogive is a graph that represents a cumulative distribution function (CDF) of a frequency distribution. It shows the cumulative relative frequency or cumulative frequency of each class plotted against the upper limit of the corresponding class. In other words, an ogive can be used to represent data through graphs by plotting the upper limit of each class interval on the x-axis and the cumulative frequency or cumulative relative frequency on the y-axis.

An ogive is used to display the distribution of quantitative data, such as weight, height, or time. It is also useful when analyzing data that is not easily represented by a histogram or a frequency polygon, and when we want to determine the percentile or median of a given set of data. Based on the information given above, option B: "Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class" is the correct answer.

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The sale price of the piglet after the 60% discount is $72.05.

To find the size of the discount, we must first consider 60% of the original price:

0.6 x $180.15 = $108.09

Therefore, the discount amount is $108.09.

To round it to the nearest cent, we look at the third decimal place, which is 9. If it's 5 or higher, we round up, so the answer is $108.09 rounded to $108.10.

So Latasha can buy a piglet between 180.15 and 108.10 for $72.05.

It's always a good idea to double-check our answer to make sure that the discount is indeed 60% of the original price and that the sale price is correct. We can calculate the selling price as follows:

Original price - amount of discount = sale price

$180.15 - $108.10 = $72.05

So after the 60% discount, the selling price of the piglet is $72.05.

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Answer:

{2.86, 2.57}

Step-by-step explanation:

To solve a system of equations, you would want to use the eliminaton or the substitution method. These methods are sujective, so use the one you like the most. I will show you both methods to get a better understanding.

Elimination:

To do the elimination method, you will need to find common terms (x or y) and have an opposite each (-5 or 5). Look at the first equation. Now look at the second equation. Which equation do you think would need to be changed in order to receive a -5 and 5? The second equation. Multiply the second equation by -5. This would give you -5x-10y=-40. Now you are ready to add the two equations together. Notice how the x's cancel out. this leaves you with -14y=-36. To get the y by itself, you will need to divide each side by -14. You will soon get y=2.57. YOU ARE NOT FINISHED. You will need to get the x value. Take one of the equations and add substitute the y into it. Looking at both equations, the second one will be easier to substitue. By adding y into the mix, you will get x+5.14=8. Subtract 5.14 by both sides and you will get x=2.86. You solution should by {2.86, 2.57}.

Substitution:

to do the substitution method, you will look for a variable that is isolated from a coefficient. As seen in the second equation, x is isolated. Use the second equation to isolate x on one side of the equal sign. You would end up with x=8-2y. Substitute the x into the first equation. This would look somethign like this: 5(8-2y)-4y=4. Multiply what is needed. You should end up wiht 40-10y-4y=4. Combine the like terms of the y: 40-14y=4. Subtract 40 from both sides. You should end up with -14y=-36. DOESN'T THIS LOOK FAMILIAR!!! To get the y by itself, you will need to divide each side by -14. You will soon get y=2.57. You will need to get the x value. Take one of the equations and add substitute the y into it. Looking at both equations, the second one will be easier to substitue. By adding y into the mix, you will get x+5.14=8. Subtract 5.14 by both sides and you will get x=2.86. You solution should by {2.86, 2.57}.

To apply the Gram-Schmidt process to find an orthonormal basis for the subspace W of R3, spanned by the given vectors, we can follow these steps:

Let v1 be the first vector in the basis for W.

Step 1: Normalize v1 to get the first vector in the orthonormal basis.

v1* = v1 / ||v1||, where ||v1|| is the magnitude or length of v1.

Step 2: Project the second vector v2 onto the subspace orthogonal to v1.

Let u2 = v2 - proj(v2, v1), where proj(v2, v1) is the projection of v2 onto v1.

Step 3: Normalize u2 to get the second vector in the orthonormal basis.

v2* = u2 / ||u2||, where ||u2|| is the magnitude or length of u2.

Step 4: Project the third vector v3 onto the subspace orthogonal to both v1 and v2.

Let u3 = v3 - proj(v3, v1) - proj(v3, v2), where proj(v3, v1) and proj(v3, v2) are the projections of v3 onto v1 and v2, respectively.

Step 5: Normalize u3 to get the third vector in the orthonormal basis.

v3* = u3 / ||u3||, where ||u3|| is the magnitude or length of u3.

The set {v1*, v2*, v3*} is an orthonormal basis for the subspace W.

Note that the choice of v1 affects the resulting orthonormal basis, but any choice of v1 that spans W will result in an orthonormal basis for W.

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Answer:

59040

Step-by-step explanation:

Answer:

Step-by-step explanation:

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