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Only when b = 0 or k = 1.

If f(x) = mx + b, then

f (kx) = m (kx) + b = mkx + b

while

k f(x) = k (mx + b) = kmx + kb

The two expression are identical only if

kb = b   ===>   kb - b = 0   ===>   b (k - 1) = 0   ===>   b = 0 or k = 1

Answer:

No.

Step-by-step explanation:

For polygon PQRST to be considered a scaled copy of polygon ABCDE, it means every segments of polygon ABCDE were increased proportionally by a scale factor.

The segments in polygon PQRST were not gotten using the same scale factor, hence, it is not a scaled copy of the original polygon, ABCDE.

Segment CD = 2 units, it corresponds to segment RS = 4 units. Scale factor = RS/CD = 4/2 = 2

Segment BC = 1 unit, it corresponds to segment QR = 1 unit. Scale factor = QR/BC = 1/1 = 1 units.

Varying scale factor shows polygon PQRST is not a scaled copy of polygon ABCDE.

Answer:

attached the drawing

Step-by-step explanation:

hope it works

The information that is needed to write the equation of a line in point-slope form is the location of one ordered pair that lies on the line and the line's slope. The correct option is the first option

From the question, we are to determine the information that is needed to write the equation of a line in point-slope form.

The point-slope form of a line is given as

y - y₁ = m(x - x₁)

Where, (x₁, y₁) is a point on the line

and m is the slope of the line

Thus, in order to write the equation of a line in the point-slope form, the information that are needed are:

1. An ordered pair on the line

2. The slope of the line

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Answer:

m = 8

Step-by-step explanation:

\(\frac{m}{12}\) = \(\frac{10}{5+10}\)

15m = 120

m = 8

Use csc (90) = 10/m.

So, m = 10/csc(90).

m = 8.93997

Answer: m = 8

To dilute 40 quarts of 5% acid solution to a 2% solution, you need to add x quarts of water. To find x, we can use the following formula: Initial amount of acid × initial concentration = final amount of acid × final concentration We know the initial amount of acid is 5% of 40 quarts, which is 2 quarts.

So the formula becomes: 2 quarts × 5% = (40 + x) / 50 quarts × 2%Now we can solve for x:2 × 40 × 5% = (40 + x) / 50 × 2%400% / 2% = 40 + xx = 400 - 40x = 360 quarts Therefore, you need to add 360 quarts of water to 40 quarts of 5% acid solution to dilute it to a 2% solution.

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Answer:

7+3(-4)(2)= -17

Step-by-step explanation:

7+3(-4)(2)

(-4)*2=-8

∴ 7+3(-8)= 7-24

= -17

The number of days that the amount of air in the balloon decrease by 6/8 of a cubic foot is 6 days.

From the information, the amount of air in the balloon decreases at an average rate of 1/8 of cubic foot per day.

The numbers of days that it will take to reduce by 6/8 of a cubic foot will be:

= Fraction given / Reduction per day

= 6/8 ÷ 1/8

= 6/8 × 8/1

= 6

It will take 6 days.

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The area enclosed by one loop of the curve r = sin(6θ) is π/24.

To find the area enclosed by one loop of the curve r = sin(6θ), we can use the formula for the area enclosed by a polar curve:

A = (1/2)∫[a,b] (r(θ))² dθ

In this case, since we want to find the area of one loop, we can integrate over the interval [0, π/6] (or any interval that covers one complete loop).

A = (1/2\(\int\limits^0_{\pi/6}\) (sin(6θ))² dθ

Simplifying the integral and evaluating it, we get

A = (1/2) \(\int\limits^0_{\pi/6}\) (1 - cos(12θ))/2 dθ

A = (1/4) \(\int\limits^0_{\pi/6}\) (1 - cos(12θ)) dθ

To evaluate this integral, we can use the antiderivative of (1 - cos(12θ)), which is θ - (1/12)sin(12θ). Applying the Fundamental Theorem of Calculus, we have

A = (1/4)[θ - (1/12)sin(12θ)] evaluated from 0 to π/6

Plugging in the limits, we get

A = (1/4)[(π/6) - (1/12)sin(2π)]

Simplifying further, we have

A = (1/4)(π/6) = π/24

Therefore, the area enclosed is π/24.

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--The given question is incomplete, the complete question is given below " find the area of the region enclosed by one loop of the curve.  r = sin(6θ) "--

Out of the given options, (a) and (d) are examples of time series while (b) and (c) are not.

A time series is a set of data points collected at regular intervals of time, with the aim of analyzing trends, patterns, and changes over time. In other words, it's a sequence of data points recorded at successive intervals of time. Here's a detailed explanation of each option:

a) The number of daily visitors to Niagara Falls during the month of April: This is an example of a time series. It shows the number of visitors to Niagara Falls every day in the month of April. The data points are collected at regular intervals of time (daily) and can be used to analyze patterns, trends, and changes in the number of visitors over time.

b) The recorded exam scores of students in a class: This is not an example of a time series. The data points represent a one-time measurement of exam scores and do not change over time.

c) The sales prices of single-family homes sold last month in Florida: This is not an example of a time series. The data points represent a one-time measurement of sales prices and do not change over time.

d) The current average prices of regular gasoline in different states of the U.S.: This is an example of a time series. The data points represent the current average prices of regular gasoline in different states of the U.S. The data points are collected at regular intervals of time and can be used to analyze patterns, trends, and changes in gasoline prices over time.

Therefore, Out of the given options, (a) and (d) are examples of time series while (b) and (c) are not.

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The solutions to the equation f(x) = g(x) are the values of x that make f(x) and g(x) equal. Looking at the table, we can see that f(x) = g(x) for x = 7 and x = 5. Therefore, the solutions to the equation f(x) = g(x) are C. 5 and D. 9. Answer choices A. 1 and F. 10 are not solutions to the equation as f(1) ≠ g(1) and f(10) is not given in the table. Answer choice B. 3 is also not a solution as f(3) ≠ g(3).

Answer:

O North Atlantic Treaty Organization

Step-by-step explanation:

In estimating a population mean, an interval estimate is more likely to be correct than a point estimate. An interval estimate provides a range of values within which the true population mean is likely to fall, while a point estimate provides only a single value.

When estimating a population mean, using an interval estimate is more likely to be correct because it accounts for the uncertainty associated with the estimate. A point estimate, on the other hand, provides a single value that is assumed to represent the true population mean. However, due to sampling variability and potential errors in measurement, a point estimate is prone to error and may not accurately reflect the true population mean.

By using an interval estimate, which includes a range of values, we have a measure of uncertainty. The range is typically constructed based on a certain level of confidence, such as a 95% confidence interval. This means that if we were to repeat the sampling and estimation process many times, the true population mean would be expected to fall within the estimated interval in 95% of those repetitions.

The interval estimate takes into account the variability in the data and provides a more realistic representation of the true population mean. It provides a margin of error and acknowledges that the point estimate is just one possible value among many that could have been obtained through sampling.

Therefore, when estimating a population mean, an interval estimate is preferred because it not only provides a point estimate but also quantifies the uncertainty associated with that estimate, leading to a higher likelihood of being correct.

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The result of applying the square root property of equality to this equation is x = (-b ± √(b² - 4ac)) / (2a)

If we apply the square root property of equality to the equation (x + (b/2a))² = (-4ac + b²)/(4a²), we get:

x + (b/2a) = ±√[(-4ac + b²)/(4a²)]

Next, we can simplify the expression under the square root:

√[(-4ac + b²)/(4a²)] = √(-4ac + b²)/2a

Now, we can substitute this expression back into our original equation:

x + (b/2a) = ±√(-4ac + b²)/2a

Finally, we can isolate x by subtracting (b/2a) from both sides:

x = (-b ± √(b² - 4ac)) / (2a)

This is the quadratic formula, which gives us the solutions for the quadratic equation ax² + bx + c = 0. By completing the square, we have derived this formula from the original quadratic equation.

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Complete question is:

In the derivation of the quadratic formula by completing the square, the equation (x+ (b/2a))² =(-4ac+b²)/(4a²) is created by forming a perfect square trinomial What is the result of applying the square root property of equality to this equation?

When a point falls outside of control limits in statistical process control, the probability is quite high that the process is experiencing special cause variation.

In statistical process control (SPC), control limits are used to define the range within which a process is expected to operate under normal or common cause variation. Common cause variation refers to the inherent variability of a process that is predictable and expected.

On the other hand, special cause variation, also known as assignable cause variation, refers to factors or events that are not part of the normal process variation. These are typically sporadic, non-random events that have a significant impact on the process, leading to points falling outside of control limits.

When a point falls outside of control limits, it indicates that the process is exhibiting a level of variation that cannot be attributed to common causes alone. Instead, it suggests the presence of specific, identifiable causes that are influencing the process. These causes may include equipment malfunctions, operator errors, material defects, or other significant factors that introduce variability into the process.

Therefore, when a point falls outside of control limits in statistical process control, it is highly likely that the process is experiencing special cause variation, which requires investigation and corrective action to identify and address the underlying factors responsible for the out-of-control situation.

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Answer: m=3

Step-by-step explanation:

ABCD ~ QRST

Therefore m=3 as QT is also 3.

The speed of the man in the question is: 6 km/hr

The formula to find the average speed when given distance and time is expressed as:

Average Speed = Distance/Time

Let the speed of the man be x.

At this speed(X), the total time he takes to travel 108km is 108/X.

Now, If he had travelled 2km/hour faster, his speed would have been X + 2 km/hour.

At this speed, he could have arrived at the destination 4.5 hours earlier.

This means that the time taken to travel would have been (108/x) - 4.5 hours if his speed had been (X + 2) km/hour.

So, according to the question, we have:

(108/X) - 4.5 = 108/ (X + 2) ----------- (1)

Solving this equation, we get X = 6 or -4. So, his speed is 6km/hour.

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A. A real-world problem for the division will be how many rods can be cut from a rod that's 8 3/8cm long of each rod is 1/4 each.

B. A model or write an equation for the division will be 8 3/8 ÷ 1/4

C The quotient for the real-world problem is 33 1/2.

From the information, the real-world problem for the division will be how many rods can be cut from a rod that's 8 3/8cm.long of each rod is 1/4 each.

Therefore, the model will be:

8 3/8 ÷ 1/4

The quotient will be:

= 8 3/8 ÷ 1/4

= 8.375 ÷ 0.25

= 33.5 or 33 1/2.

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An advantage of stem-and-leaf plots compared to most frequency distributions is that provide more information about the distribution of the data.

Stem-and-leaf plots offer several advantages over most frequency distributions.

One advantage is that stem-and-leaf plots provide a more detailed representation of the data than frequency distributions.

They allow you to see the individual data values and their magnitudes, which can provide more information about the distribution, such as the spread, central tendency, and outliers.

Additionally, stem-and-leaf plots can be easier to read and interpret than frequency distributions, especially for small data sets.

They can reveal patterns and trends in the data that might not be apparent in a frequency distribution.

Finally, stem-and-leaf plots can be used to compare different data sets or to identify similarities or differences within a single data set.

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Answer:

$8.85

Step-by-step explanation:

$59 x 0.15 = $8.85

Answer:

30.

Step-by-step explanation:

First, we have to split up the equation:

(7 x 4) + (10 ÷ 5)

Now, we simplify:

(7 x 4) + (10 ÷ 5)

28 + 2

28 + 2 = 30.

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Answer:

$32  

Step-by-step explanation:

If a 10 pound sack costs $8, we know that the sacks must cost $8 for 10 pounds.

With this knowledge, we have to multiply 4 and 8.

Multiply

4x8=32

32

Answer:

the probability is 5/12  or 0.416 or 41%

Step-by-step explanation:

Hope I helped!

The correct equation is b) C2+2e−⇒2C2. This equation represents the reduction of carbon (C) where two electrons (2e-) are gained, resulting in the formation of two carbon atoms (2C). The arrow pointing to the right (⇒) indicates the direction of the reaction.

In chemical reactions, electrons can be gained or lost, leading to oxidation or reduction processes. The equation b) C2+2e−⇒2C2 represents a reduction reaction, where C2 (a diatomic carbon molecule) gains two electrons (2e-) to form two separate carbon atoms (2C).

The equation a) F2+2e=>2F1- represents the reduction of fluorine (F2) to form two negatively charged fluorine ions (F1-). This equation is incorrect because fluorine does not form positive ions.

The equation c) S+3e=S3- represents the reduction of sulfur (S) where three electrons (3e-) are gained, resulting in the formation of a negatively charged sulfur ion (S3-). This equation is incorrect because sulfur typically forms sulfide ions (S2-) rather than S3-.

The equation d)  P+2e−>P3-  represents the reduction of phosphorus (P) where two electrons (2e-) are gained, forming a negatively charged phosphide ion (P3-). This equation is incorrect because phosphorus typically forms phosphide ions with a charge of -3 (P3-) or -2 (P2-), not P3-.

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Mixing is a physical reaction, which does not change any chemical properties of elements and molecules because it does not change the number of protons.

It is the number of protons that determine the unique properties of each element (hence why the periodic table sorts elements by increasing the number of protons).

The probability that John will roll more than 4 times until the dice roll sums to 8 three times is 4 times = 1 - (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

To find the probability that John will roll more than 4 times until the dice sum to 8 three times, we need to calculate the probability of him rolling 4 or fewer times and subtract it from 1.

Let's calculate the probability of John rolling 4 or fewer times. To do this, we need to find the probability of him rolling the sum of 8 three times or more within 4 rolls.

First, let's find the total number of possible outcomes for rolling two dice, which is 36 (6 possibilities for each dice).

Next, let's find the number of favourable outcomes for rolling the sum of 8 three times or more within 4 rolls.

We can use combinations to calculate this. For the first roll, the possible combinations that result in a sum of 8 are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). So, there are 5 favourable outcomes for the first roll.

For the second roll, we need to find favourable outcomes given that the first roll was not a favourable outcome. We need to subtract the outcomes that were already counted.

So, there are 4 favourable outcomes for the second roll. Similarly, for the third roll, we subtract the outcomes that were already counted and find 3 favourable outcomes.

Finally, for the fourth roll, we subtract the outcomes that were already counted and find 2 favourable outcomes.

To find the probability, we divide the number of favourable outcomes by the total number of possible outcomes. Probability of rolling the sum of 8 three times or more within

4 rolls = (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

Now, we can find the probability of rolling more than 4 times by subtracting this probability from 1.

Probability of rolling more than

4 times = 1 - (5 * 4 * 3 * 2) / (36 * 36 * 36 * 36)

The probability that John will roll more than 4 times until the dice roll sums to 8 three times is the result obtained in the calculation above.

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Answer:

The 3rd option

Step-by-step explanation:

The pattern is every 2 hours is $15 so 4 hours would be equal to $30

Since 4 hours would equal 30 and we need 12 hours multiplying both numbers by 3 would get you the answer

4x3=12

30x3=90

Making it equal

Answer:

20 percent

40 percent

20 percent

20(.008) percent

Step-by-step explanation:

6) 54 - 45 = 9

45 / 9 = 5

100 / 5 = 20

20 percent

7) 60 - 36 = 24

60 / 24 = 2.5

100 / 2.5 = 40

40 percent

8) 30 - 24 = 6

30 / 6 = 5

100 / 5 = 20

20 percent

9) 24.99 - 19.99 = 5

24.99 / 5 = 4.998

100 / 4.998 approx. = 20.008

20.008 percent (or rounded 20 percent)

Answer:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

point form : (-2 , -1)

equation form : x = -2 , y = -1

Step-by-step explanation:

( 5x + 9 = -2x - 5)

for y = 5x + 9 (substitute x = -2)

y = 5(-2) + 9 = -1