15 POINTS!!!!!NEED HELP ASAP!!!!

To transform the graph of f(x) = log8x into the graph of g(x) = -log8(x+5), we need to apply a horizontal and a vertical transformation. Firstly, we need to shift the graph horizontally by 5 units to the left, which means we need to replace x with x+5 in the argument of the logarithm.

This transformation is represented by the formula f(x) -> f(x+5). Secondly, we need to reflect the graph vertically across the x-axis, which means we need to take the negative of the function. This transformation is represented by the formula f(x) -> -f(x). Therefore, the transformation of f(x) that results in g(x) can be represented as g(x) = -log8(x+5).

To transform the graph of f(x) = log3x into the graph of g(x) = 1/3log6(x)+4, we need to apply a horizontal and a vertical transformation. Firstly, we need to compress the graph horizontally by a factor of 2, which means we need to replace x with 2x in the argument of the logarithm.

This transformation is represented by the formula f(x) -> f(2x). Secondly, we need to shift the graph vertically upward by 4 units, which means we need to add 4 to the function. This transformation is represented by the formula f(x) -> f(x) + 4. Therefore, the transformation of f(x) that results in g(x) can be represented as g(x) = 1/3log6(2x) + 4.

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By solving the given equations for the bolded variables, we have the following:

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In this exercise, you're required to describe the steps that should be taken to rearrange and make bolded variables the subject of formula. Therefore, the appropriate and required steps are listed as follows:

Z = sL

You should divide both sides by L, to make s the subject of formula:

s = L/Z

P = 2l + 2w

You should subtract 2l from both sides, to make w the subject of formula:

P = 2l + 2w

P - 2l = 2l + 2w - 2l

P - 2l = 2w

Rearranging the equation, we have:

2w = P - 2l

Dividing both sides by 2, we have:

w = (P - 2l)/2

I = V/R

You should cross-multiply, to make R the subject of formula:

IR = V

R = V/I

S = 3πr² + 2πrh

You should subtract 3πr² from both sides, to make h the subject of formula:

S - 3πr² = 3πr² + 2πrh - 3πr²

S - 3πr² = 2πrh

Rearranging the equation, we have:

2πrh = S - 3πr²

Dividing both sides by 2πr, we have:

h = (S - 3πr²)/2πr

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Answer:

9

Step-by-step explanation:

Pythagorean triples. 3, 4, 5. Multiply by 3 and get 9.

Answer:

See below for answers and explanations

Step-by-step explanation:

Find critical points

\(f(x)=2x^3+9x^2-24x\\f'(x)=6x^2+18x-24\\\\0=6x^2+18x-24\\0=x^2+3x-4\\0=(x-1)(x+4)\\x=1,-4\)

Use test points

\(f'(-5)=(-5-1)(-5+4)=6 > 0\\f'(-3)=(-3-1)(-3+4)=-4 < 0\\f'(0)=(0-1)(0+4)=-4 < 0\\f'(2)=(2-1)(2+4)=6 > 0\)

Therefore, by observing the value of the derivative around the critical points, the function increases over the intervals \((-\infty,-4)\) and \((1,\infty)\), and the function decreases over the interval \((-4,1)\).

The function f(x) = 2x3 + 9x2 – 24x is increasing on interval (-∞,-1),(4,∞). Function f(x) = 2x3 + 9x2 – 24x is decreasing on the interval (-1,4).Minimum value of f(x) is 13, and it occurs at x = -1 and maximum of f(x) is -112.

To find the intervals on which f(x) is increasing or decreasing, we need to find the intervals on which its derivative f'(x) is positive or negative. The derivative of f(x) is f'(x) = 6x(x + 4). f'(x) = 0 for x = -4, 0. Since f'(x) is a polynomial, it is defined for all real numbers. Therefore, the intervals on which f'(x) is positive are (-∞,-4) and (0,∞). The intervals on which f'(x) is negative are (-4,0).

The function f(x) is increasing on the intervals where f'(x) is positive, and it is decreasing on the intervals where f'(x) is negative. Therefore, f(x) is increasing on the interval (-∞,-1) and (4,∞). It is decreasing on the interval (-1,4).

To find the local minimum and maximum values of f(x), we need to find the critical points of f(x). The critical points of f(x) are the points where f'(x) = 0. The critical points of f(x) are x = -4 and x = 0.

To find the local minimum and maximum values of f(x), we need to evaluate f(x) at the critical points and at the endpoints of the intervals where f(x) is increasing or decreasing. The values of f(x) at the critical points and at the endpoints are as follows:

x | f(x)

---|---

-4 | 13

-1 | -112

0 | 0

4 | -112

The smallest value of f(x) is 13, and it occurs at x = -4. The largest value of f(x) is -112, and it occurs at x = 4. Therefore, the local minimum value of f(x) is 13, and it occurs at x = -4. The local maximum value of f(x) is -112, and it occurs at x = 4.

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To stop a 1200 kg car moving at 99 km/h in a straight path,

the work that must be done in Joules is 453750.

Step-by-step Given,

Mass of car, m = 1200 kg

Initial velocity, u = 99 km/h = 27.5 m/s

Final velocity, v = 0 m/s (as the car is brought to rest)

Initial kinetic energy, K.E1 = 1/2 m u²

Final kinetic energy, K.E2 = 1/2 m v²

Work done to bring the car to rest,

W = K.E1 - K.E2W

= 1/2 m u² - 1/2 m v²W

= 1/2 × 1200 × (27.5)² - 1/2 × 1200 × (0)²W

= 1/2 × 1200 × (27.5)²W

= 453750 J

Therefore, the work that must be done in Joules to stop the car is 453750.

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slope is 1

slope formula: y2-y1/x2-x1

4-3/0-(-1)

The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.

In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.

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Answer:

Yes

Step-by-step explanation: The explicit formula used: An = 1000(2)n - 1 is the correct formula. This is modeled as exponential growth with a common ratio of 2; which is correct based on the data given in the table.

The predicted population for year 50 is approximately \(1.1259\) x \(10^18\) wombats.

To predict the populations for years 6, 10, and 50 using the given explicit formula an = \(1000(2)^n\) – 1, we can substitute the respective values of n and calculate the population.

For year 6 (n = 6):

a6 =  \(1000(2)^6\) – 1

a6 = 1000(64) – 1

a6 = 64,000 – 1

a6 ≈ 63,999

The predicted population for year 6 is approximately 63,999 wombats.

For year 10 (n = 10):

a10 = \(1000(2)^ 10\)

a10 = 1000(1,024) – 1

a10 = 1,024,000 – 1

a10 = 1,023,999

The predicted population for year 10 is 1,023,999 wombats.

For year 50 (n = 50):

a50 = \(1000(2)^50\) – 1

a50 = 1000(1.1259 x 10¹⁵ ) – 1

a50 = 1.1259 x 10¹⁸ – 1

a50 ≈ 1.1259 x 10¹⁸

The predicted population for year 50 is approximately 1.1259 x 10^18 wombats.

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Answer:

Equation: 5b + 7 = 3

Step-by-step explanation:

Unknown number = b

5 times of number = 5b

Sum of 5b and 7 = 5b + 7

Equation;

5b + 7 = 3

The probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

To find the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur, we need to determine the individual probabilities of each event and then multiply them together since the events are independent.

Event A: The coin lands on heads

A fair coin has two equally likely outcomes, heads or tails. Since we are interested in the probability of heads, there is only one favorable outcome out of two possible outcomes.

P(A) = 1/2

Event B: The die is 5 or greater

A fair six-sided die has six equally likely outcomes, numbers 1 through 6. Out of these six outcomes, there are two favorable outcomes (5 and 6) for Event B.

P(B) = 2/6 = 1/3

To find the probability of both events occurring (A and B), we multiply the individual probabilities:

P(A and B) = P(A) * P(B) = (1/2) * (1/3) = 1/6

Therefore, the probability that both Event A (coin lands on heads) and Event B (die is 5 or greater) will occur is 1/6.

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Answer:

10x - 40 = 5x + 25

Dividing both sides by 5:

2x - 8 = x + 5

x = 13

Answer:

x=13

Step-by-step explanation:

10(x - 4) = 5x + 25

2x-8=X+5

x=13

Answer:

I'm guessing you're solving for X so

X=  17/2

Step-by-step explanation:

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃  = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

The function is nonlinear because: D. the rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

What is a nonlinear function?

A nonlinear function can be defined as a type of function whose rate of change (increase or decrease) are not the same i.e they are different.

The rate of change between 2 and 3 trees is given by:

R₂₃ = (180 - 120)/(3-2)

R₂₃ = 60.

Also, the rate of change between 3 and 5 trees is given by:

R₃₅ = (290 - 180)/(5-3)

R₃₅ = 110/2

R₃₅ = 55.

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Complete Question:

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear?

Answer:

18 tables: $143

t tables: $35 + $6t

Step-by-step explanation:

35 + 6t

35 + 6(18) = 35 + 108 = 143

Answer:

$14

Step-by-step explanation:

ok so since he is delivering groceries he gets $4.

now when he delivers he get $2 more, so for each house he delivers to he adds $2 to that $4.

so the easiest was to do this is 5x2.

5x2 is 10.

now $10 is how much more he gets on top of the $4, so now we need to add the $4 to the $10.

your answer is $14  

plz mark brainliest!

Step-by-step explanation:

the second equation gives us right away

y = 4 - 3x

we can use that now in the 3rd equation :

-2(4 - 3x) + 2z = 4

-8 + 6x + 2z = 4

6x + 2z = 12

3x + z = 6

z = 6 - 3x

now we use both in the 1st equation :

-2x + 3(4 - 3x) - (6 - 3x) = -2

-2x + 12 - 9x - 6 + 3x = -2

-8x + 6 = -2

-8x = -8

x = 1

y = 4 - 3x = 4 - 3×1 = 4 - 3 = 1

z = 6 - 3x = 6 - 3×1 = 6 - 3 = 3

so,

(1, 1, 3)

The empirical rule may be used to determine the percentage of data values that must be within only one, two, and three standard deviations of the mean for data having a bell-shaped distribution.

The 68 95 99 rule, commonly referred to as the empirical rule in statistics, asserts that given normal distributions, 68% of observed data points will fall within one standard deviation from the mean, 95% will fall between two standard deviations, and 99.7% will happen within three standard deviations.

Fairly anticipate that your data will resemble a normal distribution, the empirical rule, the mean, as well as the standard deviation become even more beneficial. Determine probabilities and percentages for many events just by knowing these two statistics.

The term "empirical rule" derives from empirical research, which relies on measurements and observations of actual results rather than theory. In other words, the term "empirical" denotes a foundation in actuality.

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Answer: (-1, 1)

Step-by-step explanation:

Since the graph is already given, we could directly refer to the intersecting point of the system of equations.

According to the graph, [ y = 2x + 3 ] and [ y = -x ] intersect at (-1, 1).

Therefore the solution is \(\Large\boxed{(-1,1)}\)

Given equation

1) y = 2x + 3

2) y = -x

Substitute the y value in the 1) equation by the 2)

(-x) = 2x + 3

Add x on both sides

-x + x = 2x + 3 + x

0 = 3x + 3

Subtract 3 on both sides

0 - 3 = 3x + 3 - 3

-3 = 3x

Divide 3 on both sides

-3 / 3 = 3x / 3

x = -1

Substitute the x value into one of the equations to find the y value

y = -x

y = - (-1)

y = 1

Therefore, the solution is \(\Large\boxed{(-1,1)}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It’s c

Step-by-step explanation:

I just did it in edg

The number of solutions the system of equations have is (a) no solution

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

y = 0.5x + 1

y = 0.5x + 3

Subtract the equations

So, we have

0 = -2

The above equation is false

This means that the number of solutions in the equation is 0

i.e. no solution

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Step-by-step explanation:

\( \frac{3( {s}^{2} )^{4} \times {s}^{ - 5} } {27 {s}^{3} } \)

\( \frac{3 {s}^{8} \times {s}^{ - 5} }{27 {s}^{3} } \)

\( \frac{3 {s}^{3} }{27 {s}^{3} } \)

\( \frac{1}{9} \)

Question:

Hailey ran a few laps. D(n), models the duration (in seconds) of the time it took for Hailey to run her nth lap. When did the lap duration increase faster?

A. Between the 3rd and 7th lap

B. Between the 7th and 9th lap

C. The lap duration increased at the same rate over both intervals

Answer:

B. Between the 7th and 9th lap

Step-by-step explanation:

Given

See attachment for table

Required

Determine when the lap increases faster

To do this, we simply calculate the rate of change between each lap.

From the attachment, we have:

\(D(3) = 85\)

\(D(7) = 99\)

\(D(9) = 110\)

Rate of change is calculated using:

\(Rate = \frac{D(b) - D(a)}{b - a}\)

For D(3) to D(7), the rate is:

\(Rate = \frac{D(7) - D(3)}{7 - 3}\)

\(Rate = \frac{99 - 85}{7 - 3}\)

\(Rate = \frac{14}{4}\)

\(Rate = 3.5\)

For D(7) to D(9), the rate is:

\(Rate = \frac{D(9) - D(7)}{9 - 7}\)

\(Rate = \frac{110 - 99}{9 - 7}\)

\(Rate = \frac{11}{2}\)

\(Rate = 5.5\)

The rate of change between the 7th and 9th lap  is greater than the rate of change between then 3rd and 7th lap .

Hence, (b) is correct

Answer:

B) Between the 7th lap and the 9th lap

Step-by-step explanation:

The image of point (8,4) after translation is (-6,0).

What is image of a point?

A transformation where a point is moved across a certain line, called the line of reflection, to appear at an equal distance.

Main Body:

Given point is (8,4)

Translation in the point is left 2 units, down 4 units.

so left- right translation is done on x-axis where moving left means subtracting is while up - down translation is done on y- axis where moving down means subtracting.

Which means 2 units will be subtracted from x-axis and 4 units from y-axis

New point = (8-2 ,4-4)

                 = (6,0)

Image of point (6,0) according to y-axis will be (-6,0).

Hence image point is (-6,0)

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Taking the square root of both sides, we finally get the Schwarz inequality: || ≤ ||f|| ||g||. And that's the proof for the Schwarz inequality.

The Schwarz in equality can be proved by taking the square root of the both sides.

To prove the Schwarz inequality, we can follow the hint provided. Let's consider the function F(a) = ||f + ag||^2, where ||g|| ≠ 0. F(a) is a second-degree polynomial in a, and it has no negative values since the square of a norm is always non-negative.

F(a) = ||f + ag||^2
=  + 2a + a^2

Now, let's examine the discriminant of this polynomial. The discriminant, Δ, is given by: Δ = B^2 - 4AC
Here, A = , B = 2, and C = . Substituting these values, we get: Δ = (2)^2 - 4

Since F(a) has no negative values, its discriminant must be non-positive, i.e., Δ ≤ 0. Thus, (2)^2 - 4 ≤ 0 (2)^2 ≤ 4

Dividing both sides by 4, we obtain: ()^2 ≤ .Taking the square root of both sides, we finally get the Schwarz inequality: || ≤ ||f|| ||g||. And that's the proof for the Schwarz inequality.

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Answer: 5

Step-by-step explanation:

Subtract 5 on both sides

3x = 15

Divide by 3 on both sides

x = 5

Answer:

y = 10.5

Step-by-step explanation:

Δ MOP and Δ MNQ are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{OP}{NQ}\) = \(\frac{MO}{MN}\) ( substitute values )

\(\frac{y}{7}\) = \(\frac{8+4}{8}\) = \(\frac{12}{8}\) ( cross- multiply )

8y = 84 ( divide both sides by 8 )

y = 10.5

The measurement of body temperature is a variable that makes use of numerical data.

Quantitative data refers to information that is expressed quantitatively, such as measurements or statistics. Body temperature is a variable that makes use of numerical data. A is used to record the precise temperature in degrees Fahrenheit or Celsius while keeping track of body . Quantitative data's precise number enables study and comparison with other temperature values. In the medical field, this kind of data is used to make judgements and choices, as when to check for fever or track a patient's progress. Monitoring local environmental changes, such as changes in ocean or air temperature, also makes use of quantitative data. Quantitative information is crucial.

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According to the statement, the new flavour received 3 votes for every vote received by the original flavour. Denoting:

• x = # of votes of the original flavour,

• n = # of votes of the new flavour.

We can write the following equation for the number of votes:

Now, according to the statement, the number of votes of the new flavour is n = 723, replacing this number in the equation above and solving for x, we get:

Answer

The original flavour received 241 votes.

The range in which 95% of the scores lie is between 75 and 95.

According to the Empirical Rule: For a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% of the data falls within 2 standard deviations of the mean, and approximately 99.7% of the data falls within 3 standard deviations of the mean.

So, about 95% of the scores lie between 75 and 95. T

This is because the mean score is 85 and one standard deviation is 5, so one standard deviation below the mean is 80 (85-5) and one standard deviation above the mean is 90 (85+5).

Two standard deviations below the mean are 75 (85-2*5) and two standard deviations above the mean is 95 (85+2*5).

Therefore, the range in which 95% of the scores lie is between 75 and 95.

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