USE FOR MASTERY Number of attempts allowed: 1 Write two rational numbers a/b and c/d, where a, b, c, and d are the digits 2, 3, 4, or 5, such that no digit can be used more than once and that the two rational numbers are the greatest distance apart on the number line. Explain how you got this answer.

The transformation graph is attached

The domain of the function y =  e^(x + 2) - 3 is: all real number

The range of the function y =  e^(x + 2) - 3 is: y > -3

The transformation from y =  e^x  to y =  e^(x + 2) - 3 is as follows:

The range of the function: y =  e^(x + 2) - 3

y =  e^(x + 2) - 3

y + 3 = e^(x + 2)

x + 2 = ㏑ (y + 3)

x = ㏑ (y + 3) - 2

hence y > -3

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(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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The range of numbers in the data series that controls the minimum, maximum, and incremental values on the value axis is referred to as the "axis scale" or "axis range."

It determines the span of values displayed on the value axis of a graph or chart. The axis scale is typically set based on the minimum and maximum values present in the data series, and the incremental values (tick marks) are placed at regular intervals within that range.

It represents the span of values that will be displayed on the value axis of a graph or chart. The data range determines the scale and divisions of the axis, allowing the viewer to interpret the data accurately and understand the relative magnitude of the values being presented.

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SOLUTION:

We want to construct the augmented matrix for these equations;

We start by writing the equations with variables on the right and constants on the left; multiplying equation 1 by 3, we have;

Expanding equation 2 and collecting like terms, we have;

Expanding equation 3 and collecting like terms, we have;

Writing the 3 equations, we have;

Putting this in augmented matrix form we have;

Which is the final answer

Answer:

It should be 356 acres that don't have crops

In contrast to quantitative research, sampling may not always produce the same results in qualitative data analysis.  The analysis will depend on the more complicated themes.

The researcher must seek for saturation in order to set a sample size restriction. The ideal in qualitative research is saturation. It serves as a tool to make sure sufficient, high-quality data are gathered to support the investigation.

Quantitative research is a method of gathering and analyzing data that uses numerical and statistical techniques. It is a systematic and objective approach that involves the collection of numerical data through surveys, experiments, or other forms of measurement, which is then analyzed using statistical tools. The goal of quantitative research is to generate and test theories, hypotheses, and models that can be generalized to a larger population.

Quantitative research often involves the use of large samples, which allow researchers to draw statistically significant conclusions about the population being studied. It also involves the use of standardized measures and data collection methods to ensure that the data collected is reliable and valid. Quantitative research is widely used in fields such as social sciences, education, psychology, and market research to study a variety of phenomena, including attitudes, behaviors, opinions, and trends.

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Complete Question:-

Which statement about sample size in qualitative research is true?

A. Sampling for qualitative studies should stop before information becomes redundant.

B. If the quality of data being collected is exceptionally good, a smaller sample may suffice than when data are of mediocre quality.

C. New researchers who have a fresh eye on phenomena can rely on smaller samples than more experienced researchers.

D. Typical case sampling requires more participants than maximum variation sampling.

In the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units.

In the best-case scenario analysis for Automatic Transmissions, Inc.'s new gear assembly project, the company assumes the upper limit of the ±15 percent range for its estimates. For the price per unit, they take a 15 percent increase, resulting in a value of $1081. Similarly, the variable cost per unit is increased by 15 percent to $391. The fixed costs are also adjusted upwards by 15 percent, reaching $3.91 million. Finally, the quantity is decreased by 15 percent, leading to a value of 45,050 units.

On the other hand, in the worst-case scenario analysis, the company assumes the lower limit of the ±15 percent range for its estimates. The price per unit is decreased by 15 percent, resulting in $799. The variable cost per unit is decreased to $289. The fixed costs are adjusted downwards to $2.89 million. Lastly, the quantity is increased by 15 percent to 60,950 units.

Therefore, in the worst-case scenario, the company should use the following values: price = $799 per unit, variable cost = $289 per unit, fixed costs = $2.89 million, and quantity = 60,950 units

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Answer:

x=6

Step-by-step explanation:

1. First, distribute the numerator. That leaves you with:

\(\frac{6x-12}{12} =\frac{2x+2}{7}\)

2. Now, cross multiply. You should have:

\(7(6x-12)=12(2x+2)\)

3. Next, simplify and solve the equation for x. You should have:

\(7(6x-12)=12(2x+2)\)

\(42x-84=24x+24\\42x=24x+108\\18x=108x=6\)

The number of surveyed nurses that were health club members or were smokers is 227.

Let the total number of nurses be 800 nurses

n(U) = 800

Let H be health club members, n(H) = 564

Let S be smokers, n(S) = 430

If 325 of the health club members were smokers, then n(HnS) = 325 members.

The number of surveyed nurses that were health club members or were smokers = 800 - [( 564 - 430) + (564-325)].

The number of surveyed nurses that were health club members or were smokers = 600 - (134+239) = 600 - 373 = 227

The number of surveyed nurses that were health club members or were smokers is 227.

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Answer:

3/2 o 1 entero 1/2

Step-by-step explanation:

150% es igual a 150 sobre 100= 150/100

(% este simbolo significa que el numero será divido por 100)

simplificas y te va a salir 3/2

Answer:

First number is 20, second is 25

Step-by-step explanation:

x + y = 5 + 2x = 45

solve for x first

5 + 2x = 45

x = 20

then solve for y

20 + y = 45

y = 25

hope this helps

The relationship between CE and AD is that, AD is one-fourth the length of CE

From the Circle given :

CD is half the length of CE

AD is half the length of CD

Combining the relationships,

Therefore, the correct option is B.

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Answer:

i think its G cause 25% but you don't have the time listed

Step-by-step explanation:

Answer:

I agree with the other person who answer 25% I thinking it's either H or G but im not sure

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The graph is not attached.

But as per description this is a direct relationship.

The formula:

Point (0, 0) is the start point when both the domain and range are equal to zero.

Correct option is A

The mean of the reading scores is 11.67, and the standard deviation is 2.97. The mean of a set of numbers is found by adding up all the values and dividing by the total number of values.

In this case, the sum of the reading scores is 140, and since there are 12 students, the mean is 140/12 = 11.67.

The standard deviation measures the variability or spread of the data from the mean. To find the standard deviation, we need to calculate the deviations of each score from the mean, square them, find their sum, divide by the total number of scores, and then take the square root of that value. The deviations from the mean for this set of scores are: -4.67, -4.67, 2.33, 1.33, -0.67, 2.33, -1.67, -0.67, -2.67, 1.33, 3.33, and 3.33. Squaring these deviations, we get: 21.69, 21.69, 5.43, 1.78, 0.45, 5.43, 2.78, 0.45, 7.12, 1.78, 11.09, and 11.09. Summing up these squared deviations gives us 89.79. Dividing by the total number of scores (12), we get 89.79/12 = 7.48. Finally, taking the square root of this value gives us the standard deviation of 2.97.

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Answer:

3.62

Step-by-step explanation:

AC=\(\sqrt{(CD)(BC)}\)

AC= \(\sqrt{2.3 * 5.7}\)

AC = \(\sqrt{13.11}\)

AC= 3.62

Answer:

66 percentage of people are on the sand.

a)  The direction in which you should walk to descend fastest is: (-12, -16)

b) The slope of your path is: -88

c) The direction of the greatest increase in temperature at the point (−2, 2) is: (-4, 4)

The maximum rate of change is: 4√2

d) The direction of the greatest decrease is: (4, -4).

The most negative rate of change is: 4√2

(a) The equation on the surface is:

z = 15 - (3x² + 2y²)

The gradient of this surface will be the partial derivatives of the equation. Thus:

Gradient of the surface z:

∇z = (-6x, -4y)

Since you are standing above the point (2,4), then the direction to descend fastest is:

∇z(2,4) = (-6(2), -4(4))

∇z(2,4) = (-12, -16)

That gives us the direction to descend fastest is in the direction.

(b) If you start to move in the direction (-12, -16) above, then slope of your path (rate of descent) is given by the dot product expressed as:

Slope = ∇z(2,4) · (-12, -16)

= (2)(-12) + (4)(-16)

= -24 - 64

= -88

(c) We want to find the direction of the greatest increase in temperature at the point (−2,2).

Thus, the gradient of T(x,y) is given by:

∇T = (2x, 2y).

The direction is:

∇T(-2, 2) = (2(-2), 2(2))

∇T(-2,2) = (-4, 4)

The maximum rate of change is:

∇T(-2,2) = √((-4)² + 4²)

= √(16 + 16)

= √(32)

= 4√2

(d) The direction of the greatest decrease is:

(-∇T(-2, 2)) = (-(-4), -4)

= (4, -4).

The most negative rate of change is:

∇T(-2, 2) = √(4² + (-4)²)

= √(16 + 16)

= √(32)

= 4√2

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Answer:

\(hey \: its \: easy\)

(1) Square of 5 = 5 × 5 = 25

(2) Square of 10 = 10 × 10 = 100

(3) Square of 16 = 16 × 16 = 256

(4) Square of 25 = 25 × 25 = 625

(5) Square of 110 = 110 × 110 = 12100

like this you can also find it

hope it helps

pls mark as brainliest

Answer:

Step-by-step explanation:

You have to figure out what has to multiply by itself to get to that number.

So for example, 121. The square root is more than 10 because 10 times 10 equals 100. It's less than 15 because 15 times 15 is a little over 200. If you have your multiplication tables memorized, you'd know that 11 multiplied by itself is 121. Therefore, the square root to 121 is 11. Hope this helps! (:

The expected number of times one needs to flip a fair coin to get two consecutive heads is 6.

To find the expected number of times one needs to flip a fair coin to get two consecutive heads, we can use the concept of conditional probability.

Let E be the expected number of flips needed to get two consecutive heads.

On the first flip, there is a probability of 1/4 of getting two consecutive heads. If this does not happen, we have to start over and flip the coin again.

On the second flip, there is a probability of 1/4 of getting two consecutive heads, but we have already used one flip, so the expected number of additional flips needed is E.

Therefore, we can write the following equation:

E = (1/4)2 + (1/2)(E+1) + (1/4)(E+2)

E = (1/2)( 1 + E + 1 + E/2 + 1)

E = (1/2)(3 + 3E/2)

E = 3/2 + 3E/4

E/4 = 3/2

E = 6

Therefore, the expected number of times one needs to flip a fair coin to get two consecutive heads is 6.

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Answer:

155625 is the answer.

Step-by-step explanation:

add astre#6666 on discord for the step by step

Answer:

Get natural log on both sides and subtract 8 to subject the unknown x.

Step-by-step explanation:

                        \(\begin{aligned}\\e^{x+8} &= 15\\\\ln(e^{x+8}) &=\small ln(15)\\\\(x+8) ln(e)&=\small ln(15)\\\\x+8&=\small ln(15) \cdots\cdots\cdots[ ln(e) = 1]\\\\x&=\small ln(15) -8\end{aligned}\)

Answer:

x = -5.29

Step-by-step explanation:

e^(x+8) = 15

==> take log of both sides

log(e) * (x+8) = log(15)

==> divide both sides by log e (log(15)/log(e) = 2.70805)

x + 8 = 2.70805

==> subtract both sides by 8

x = -5.29 (rounded to the nearest tenth)

The value(s) of k that make the limit of f(x) exist as x approaches 1 are k = -8 and k = 1.

To find the value(s) of k in the piecewise function such that the limit of f(x) exists as x approaches 1, we need to ensure that the left-hand limit and right-hand limit are equal at x = 1.

Let's first evaluate the left-hand limit (LHL) as x approaches 1:

LHL = lim(x→1-)〖(7x² - k²x)〗

To find the limit, we substitute x = 1 into the expression:

LHL = 7(1)² - k²(1) = 7 - k²

Now, let's evaluate the right-hand limit (RHL) as x approaches 1:

RHL = lim(x→1+)⁡〖(15 + 8kx² + k cos(1-x))〗

Substituting x = 1 into the expression:

RHL = 15 + 8k(1)² + k cos(1-1) = 15 + 8k + k = 15 + 9k

For the limit to exist, the LHL and RHL should be equal:

LHL = RHL

7 - k² = 15 + 9k

Simplifying the equation:

k² + 9k - 8 = 0

Now we solve this quadratic equation for k. We can factor the equation as:

(k + 8)(k - 1) = 0

Setting each factor equal to zero gives us two possible values for k:

k + 8 = 0 ↔ k = -8

k - 1 = 0 ↔ k = 1

Therefore, the value(s) of k that make the limit of f(x) exist as x approaches 1 are k = -8 and k = 1.

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Complete question =

Find the value(s) of k such that limx→1 f(x) exist where:

f(x) = {7x² - k²x, if x < 1

15 + 8kx² + k cos(1-x), if x > 1}

The function is \(e^{(x^3)}\) whose Maclaurin expansion is 1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

The Maclaurin series of a given function is represented as a sum of terms with increasing powers of x and decreasing factorials. The Maclaurin series you provided is:

1 + \(x^3\) + \((x^6)\)/2! + \((x^9)\)/3! + \((x^{12} )\)/4! + ...

This series can be rewritten as:

∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

This expansion resembles the Maclaurin series for \(e^x\), which is:

\(e^x\) = ∑ \(x^n\)/n! for n=0 to infinity.

However, in the given series, the powers of x are in multiples of 3. To adjust the standard exponential function to match the provided series, you can use the substitution \(x^3\) = u:

\(e^u\) = ∑ \(u^n\)/n! for n=0 to infinity.

Now, substitute \(x^3\) back for u:

\(e^{(x^3)}\) = ∑ \((x^{(3n)} )/n!\) for n=0 to infinity.

Therefore, the function whose Maclaurin expansion matches the given series is f(x) = \(e^{(x^3)}\).

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Answer:

84degrees

Step-by-step explanation:

First we need to get the measure of arcCA;

arcCA + arcAB+arcBC =  360

arcCA  + 104 + 88 = 360

arcCA + 192 = 360

arcCA = 360 - 192

arc CA =  168degrees

Also since m<ABC = 1/2 arcCA

m<ABC = 1/2 * 168

m<ABC = 84degrees

Hence the measure m<ABC is 84degrees

Answer:

84°

Step-by-step explanation:

According to the information, the 7 gold medals that Australia won in the Olympics correspond to 20% of the medals that this country won.

To find the percentage of gold medals that Australia won in the Olympic games, we must take into account the available information and perform the following mathematical operation:

Rule of three

According to the above, the 7 gold medals won by Australia in the Olympic Games are equivalent to 20% of the medals won by this country.

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Therefore, the function f is decreasing on the interval (- [infinity], -1].

A. (- [infinity], -1] only

We can use the first derivative test to determine where a function is increasing or decreasing. The first derivative test states that if the derivative of a function is positive, then the function is increasing, and if the derivative is negative, then the function is decreasing.

For this problem, the derivative of the function f is f'(x) = x^2 - 2/x.

We can see that for x < 0, the derivative is negative, so the function is decreasing on that interval. For x > 0, the derivative is positive, so the function is increasing on that interval.

Therefore, the function f is decreasing on the interval (- [infinity], -1].

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Answer:

x=-1/2

Step-by-step explanation:

hope it helps you

have a great day:)

The solution for system of equation provided as per the given question will be x = -19 and y = 55 or (-19,55).

It is given that the equations are:

y = –3x – 2

Simplifying it further, we get:

y + 3x = -2 (equation 1)

5x + 2y = 15 (equation 2)

Multiplying y + 3x = -2 by 2 and subtracting from 5x + 2y = 15, we get:

2y - 2y + 5x -6x = 15 + 4

-x = 19

x = -19

Plugging the value of x in the equation y + 3x = -2, we get:

y + 3 × - 19 = -2

y - 57 = -2

y = -2 + 57

y = 55

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