Se le dieron ocho esferas doradas a un rey, pero una de ellas era falsa, por lo que llamó al mejor matemático para demostrar que tenía razón. Dijo: te daré el balance, pero solo puedes usarlo dos veces. Si encuentras la esfera falsa, te doy el doble de recompensa.

The correct answer is not listed among the given options. None of the listed options is a CSS3 2D transformation function that resizes an object by a factor of x horizontally.

Here are brief explanations of the given options:

a. scaleY(y) - This function scales an object vertically by a factor of y.

b. rotate(angleY) - This function rotates an object around the y-axis by the specified angle.

c. translateY(offY) - This function translates an object vertically by the specified offset.

d. skewY(angleY) - This function skews an object along the y-axis by the specified angle.

To resize an object horizontally by a factor of x, you can use the scaleX(x) function. This function scales an object horizontally by a factor of x.

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To determine if a distribution is normal, you can employ several methods:

Histogram: Plot the data on a histogram and visually inspect its shape. A normal distribution typically has a symmetric bell-shaped curve, with the majority of the data points concentrated around the mean.

Quantile-Quantile (Q-Q) Plot: A Q-Q plot compares the quantiles of your data to the quantiles of a theoretical normal distribution. If the points on the plot roughly follow a straight line, it suggests that the data is normally distributed.

Skewness and Kurtosis: Calculate the skewness and kurtosis of the data. For a normal distribution, the skewness should be close to zero and the kurtosis should be close to three. Deviations from these values indicate departures from normality.

Shapiro-Wilk Test: Conduct a statistical test, such as the Shapiro-Wilk test, which tests the null hypothesis that the data comes from a normal distribution. If the p-value is above a predetermined significance level (e.g., 0.05), you fail to reject the null hypothesis and conclude that the data is normally distributed.

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Answer:

2 percent of 40 is 0.8.

To calculate 2 percent of 40, we can use the following formula:

(percent) / 100 * total = amount

In this case, the percent is 2, the total is 40, and the amount is equal to:

(2) / 100 * 40 = 0.8

Therefore, 2 percent of 40 is 0.8.

Step-by-step explanation:

Answer:

$19,000

Step-by-step explanation:

Let's start by finding the sum of the prices of all 80 mobile phones:

80 × 30,000 = 2,400,000

Next, we can find the sum of the prices of the remaining 78 mobile phones by multiplying the new average by 78:

78 × 29,500 = 2,301,000

We know that the highest price is $80,000. Let's assume that the lowest price is x dollars. We can set up an equation to solve for x:

2,400,000 - 80,000 - x = 2,301,000

Simplifying the equation:

2,320,000 - x = 2,301,000

Subtracting 2,301,000 from both sides:

19,000 = x

Therefore, the lowest price of the mobile phone is $19,000.

To determine the correct option, we need to check if the rates and times given in each option satisfy the condition of being inversely proportional.

Option A: 4 mph for 2.25 hours and 6 mph for 1.5 hours.

The product of the rate and time is not consistent: (4 mph) × (2.25 hours) = 9 and (6 mph) × (1.5 hours) = 9. Therefore, this option does not satisfy the condition.

Option B: 6 mph for 1.5 hours and 5 mph for 1.25 hours.

The product of the rate and time is not consistent: (6 mph) × (1.5 hours) = 9 and (5 mph) × (1.25 hours) = 6.25. Therefore, this option does not satisfy the condition.

Option C: 5 mph for 2 hours and 4 mph for 3 hours.

The product of the rate and time is consistent: (5 mph) × (2 hours) = 10 and (4 mph) × (3 hours) = 12. Therefore, this option satisfies the condition.

Option D: 4.5 mph for 3 hours and 6 mph for 4 hours.

The product of the rate and time is consistent: (4.5 mph) × (3 hours) = 13.5 and (6 mph) × (4 hours) = 24. Therefore, this option satisfies the condition.

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[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{2}\\ o=\stackrel{opposite}{9} \end{cases} \\\\\\ c=\sqrt{ 2^2 + 9^2}\implies c=\sqrt{ 4 + 81 } \implies c=\sqrt{ 85 }\implies c\approx 9.2[/tex]

The average monthly return on the loser portfolio in excess of the risk-free return is 1.26 percent, the standard deviation of its monthly excess returns is 8.7 percent, the monthly Sharpe ratio is 0.145, the annualized Sharpe ratio is 0.5, and the annualized Sharpe ratio of the overall market index is 0.54.

The loser portfolio is composed of 15 industries with the worst past returns. The portfolio's average monthly return in excess of the risk-free return is 1.26 percent, while its standard deviation of monthly excess returns is 8.7 percent. The monthly Sharpe ratio is 0.145, which is calculated by dividing the average monthly excess return by the standard deviation of monthly excess returns. The annualized Sharpe ratio is 0.5, which is the monthly Sharpe ratio multiplied by the square root of 12. The annualized Sharpe ratio of the overall market index is 0.54.

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If Jason follows the given condition in the given data question then answer will be Jason had 4 nickels.

Let's assume the number of nickels Jason had is represented by the variable 'n.' Since the problem states that there were 3 times as many dimes as nickels, the number of dimes can be represented as 3n. Additionally, the problem states that there were twice as many quarters as dimes, so the number of quarters can be represented as 2(3n) or 6n.

Now, we can create an equation based on the total value of the coins: 5n (nickels) + 10(3n) (dimes) + 25(6n) (quarters) = 37 (total value in cents).

Simplifying the equation, we have 5n + 30n + 150n = 37.

Combining like terms, we get 185n = 37.

Dividing both sides by 185, we find n = 0.2.

Since we can't have a fraction of a nickel, we round down to the nearest whole number.

Therefore, Jason had 4 nickels.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{4}}x+2\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ \cfrac{7}{4}} ~\hfill \stackrel{reciprocal}{\cfrac{4}{7}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{4}{7} }}[/tex]

so we're really looking for the equation of a line whose slope is -4/7 and it passes through (2 , -2)

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{7} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{- \cfrac{4}{7}}(x-\stackrel{x_1}{2}) \implies y +2 = - \cfrac{4}{7} ( x -2) \\\\\\ y+2=- \cfrac{4}{7}x+\cfrac{8}{7}\implies y=- \cfrac{4}{7}x+\cfrac{8}{7}-2\implies {\Large \begin{array}{llll} y=- \cfrac{4}{7}x-\cfrac{6}{7} \end{array}}[/tex]

The sprinter's speed before he increased it was 8.2 miles per hour.

To find the sprinter's speed before he increased it, we can use the following steps:
Step 1: Identify the final speed and the increase in speed.
The sprinter's top speed is 23 miles per hour, and he increased his speed by 14.8 miles per hour.
Step 2: Subtract the increase in speed from the final speed.
We can determine the sprinter's initial speed by subtracting the increase in speed (14.8 miles per hour) from the final speed (23 miles per hour).
Initial speed = Final speed - Increase in speed
Initial speed = 23 miles per hour - 14.8 miles per hour
Step 3: Calculate the initial speed.
Now, we can perform the subtraction:
Initial speed = 8.2 miles per hour
So, the sprinter's speed before he increased it was 8.2 miles per hour.

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The sprinter's speed before he increased his speed was approximately 8.2 miles per hour. The correct option is D

We need to subtract the increase in speed from his top speed.

Assume that "x" miles per hour represents the sprinter's initial speed (before to the increase).

The sprinter improved his speed by 14.8 miles per hour, as indicated by the information, to reach a top speed of 23 miles per hour. This can be said as follows:

x + 14.8 = 23

To find the value of "x," we can solve this equation:

x = 23 - 14.8

x ≈ 8.2

Therefore, the sprinter's speed before he increased his speed was approximately 8.2 miles per hour.

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Answer:

he needs 9 cans

Step-by-step explanation:

first,

43L/5L

= 8.6 cans

8.6 cans is not logical therefore u need to round up to 9 cans

Answer: c

Step-by-step explanation:

Answer:

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

Simplify in steps:

Point A is between the 7th and 8th tick marks. Once you zoom in, you can see that the decimal would be 7.4. So the number could be represented by the expression 7.4 times 10 to the 11th power.

In Geometry and Mathematics, a number line refers to a type of graph that is usually composed of a graduated straight line, which typically comprises both negative and positive numerical values (numbers) that are located at equal intervals along its length.

In this scenario and exercise, we would determine the numerical value (number) that is represented by point A by solving as follows;

10¹² × 7/10 = 7 × 10¹¹

10¹² × 4/10 = 4 × 10¹¹

By adding the numbers, we have:

7 × 10¹¹ + 4/10 × 10¹¹ = 7.4 × 10¹¹

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

To find the area of the whole mosaic, we need to multiply the length by the width. In this case, the mosaic is a 7 x 7 array of square tiles, and each tile is 1 ft long.

Area = Length × Width

Area = 7 ft × 7 ft

Area = 49 square feet

So, the area of the whole mosaic is 49 square feet.

2. The conversions are as follows: a. (11/9)π, b. -80°/9, and c. 3.5 remains in degrees.

3. The trigonometric functions are: a. - (√2)/2, b. - (√2)/2, and c. -1

4. The possible values of θ between 0° and 360° are 210° and 330°.

5. The possible values of θ between 0° and 2π are 45° and 315°.

2. Converting angles:

(a) 220° to radians:

To convert degrees to radians, multiply the degree measure by π/180.

220° x (π/180) = (22/18)π = (11/9)π

(b) -4π/9 to degrees:

To convert radians to degrees, multiply the radian measure by 180/π.

-4π/9 * (180/π) = -80°/9

(c) 3.5 remains in degrees.

3. Evaluating trigonometric functions:

(a) sin(-225°):

Since sine is an odd function, sin(-θ) = -sin(θ).

sin(-225°) = -sin(225°)

To find the exact value of sin(225°), use the reference angle of 45° in the second quadrant:

sin(225°) = -sin(180° + 45°) = -sin(45°)

sin(45°) = (√2)/2

Therefore, sin(-225°) = - (√2)/2

(b) cos(5π/4):

To find the exact value of cos(5π/4), use the reference angle of π/4 in the third quadrant:

cos(5π/4) = -cos(π/4)

cos(π/4) = (√2)/2

Therefore, cos(5π/4) = - (√2)/2

(c) tan(3π/4):

To find the exact value of tan(3π/4), use the reference angle of π/4 in the second quadrant:

tan(3π/4) = -tan(π/4)

tan(π/4) = 1

Therefore, tan(3π/4) = -1

4. Finding possible values of θ for sin θ = - ¹/₂:

Given that sin θ = - ¹/₂ is true for θ in the third and fourth quadrants.

In the third quadrant, the reference angle is 30°, so θ = 180° + 30° = 210°.

In the fourth quadrant, the reference angle is also 30°, so θ = 360° - 30° = 330°.

Therefore, the possible values of θ between 0° and 360° are 210° and 330°.

5. Finding possible values of θ for cos θ = (√2)/2:

Given that cos θ = (√2)/2 is true for θ in the first and fourth quadrants.

In the first quadrant, the reference angle is 45°, so θ = 45°.

In the fourth quadrant, the reference angle is also 45°, so θ = 360° - 45° = 315°.

Therefore, the possible values of θ between 0° and 2π are 45° and 315°.

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The difference is that tropical rainforests are near the equator while temperate rainforests are found further north near coastal areas. The Option A is correct.

The tropical rainforests are located near equator and spans across regions such as the Amazon Basin in South America, the Congo Basin in Africa and parts of Southeast Asia. These rainforests are characterized by high temperatures and humidity throughout the year with no distinct seasons.

The temperate rainforests are found further north, primarily in coastal areas of temperate regions. Examples include the Pacific Northwest in North America which experience milder temperatures compared to tropical rainforests and have distinct seasonal variations.

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The angle of depression that each chain makes with the ceiling are approximately 67° and 56°.

To solve the problem, use trigonometry. Let's call the angle of depression that the first chain makes with the ceiling x, and the angle of depression that the second chain makes with the ceiling y. Then:

In triangle ABC, where A is one of the hooks, B is the other hook, and C is the point where the chains meet:

AC = 1.9 m

BC = 2.2 m

angle BAC = 86°

Find angle BCA, which is the angle of depression that chain AC makes with the ceiling. Use the law of sines to find this angle:

sin BCA / AC = sin BAC / BC

sin BCA = AC sin BAC / BC

sin BCA = 1.9 sin 86° / 2.2

sin BCA ≈ 0.925

BCA ≈ 67.3°

So the angle of depression that chain AC makes with the ceiling is approximately 67 degrees.

Similarly, find the angle of depression that chain BD makes with the ceiling by considering triangle ABD:

AD = 2.8 m

BD = 2.2 m

angle ADB = 86°

Using the law of sines:

sin ADB / BD = sin BAD / AD

sin ADB = BD sin BAD / AD

sin ADB = 2.2 sin 86° / 2.8

sin ADB ≈ 0.836

ADB ≈ 56.4°

So the angle of depression that chain BD makes with the ceiling is approximately 56 degrees.

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The dilation of △JKP is centered at P(3, 2) and has a scale factor of 2.

A coordinate rule to represent the dilation is (x, y)  →  (2(x - 3) + 3, 2(y - 2) + 2).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would determine scale factor that was used to dilate △JKP as follows;

Scale factor = side length of image/side length of pre-image

Scale factor = J'K'/JK

Scale factor = 4/2

Scale factor = 2

Now, we can write the coordinate rule that represent the dilation by using a scale factor of 2 centered at the point P (3, 2) by using this mathematical equation:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

(x, y)  →  (2(x - 3) + 3, 2(y - 2) + 2)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The magnitude and direction of the vectors is 12.65 and 161.6⁰ respectively.

The magnitude and direction of the vectors is calculated as follows;

The given vector, u = 2, v = 4

when the vectors are multiplied by 2 and 3 respectively, we will have;

2u = 2 x 2 = 4

3v = 3 x 4 = 12

The components of the vectors is calculated as follows;

2u (y component) = 4 x sin(90) = 4

2u (x component) = 4 x cos (90) = 0

3v (y component) = 12 x sin(180) = 0

3v (x component) = 12 x cos(180) = -12

sum of x and y component of the vectors is calculated as;

∑x = 0 -12 = -12

∑y = 4 + 0 = 4

The magnitude of the vectors is calculated as;

2u + 3v = √( (-12)² + 4²) = 12.65

The direction of the vectors is calculated as follows;

θ = arc tan (y/x)

θ = arc tan (4/-12)

θ = -18.4⁰ = 161.6⁰

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Answer:

It will take him 9 hours to mow 12 lawns.

Step-by-step explanation:

We can use a proportion. We see that the answer choices are in hours, so let's first convert the given information to hours.

180 minutes × (1 hour)/(60 minutes) = 3 hours

180 minutes to mow 4 lawns = 3 hours to mow 4 lawns

Proportion:

3 hours is to 4 lawns as x hours is to 12 lawns

3/4 = x/12

4x = 3 × 12

4x = 36

x = 9

Answer: It will take him 9 hours to mow 12 lawns.

Using the given mean and standard deviation, we can calculate the probability of a randomly selected high jumper having a personal best of no more than 230 cm. By using the normal distribution and the cumulative distribution function (CDF), we can find this probability.

To find the probability, we can standardize the value of 230 cm using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (230 - 221) / 11 = 0.818. This standardized value represents the number of standard deviations that 230 cm is away from the mean.

Next, we use a standard normal distribution table or a calculator to find the cumulative probability associated with the standardized value of 0.818. This probability represents the area under the normal curve to the left of 0.818. Using technology, we can find this probability to be approximately 0.7910.

Therefore, the probability that a randomly selected high jumper has a personal best of no more than 230 cm is 0.7910, or 79.10%.

This means that approximately 79.10% of the high jumpers in the nearby state have a personal best height of 230 cm or lower.

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Answer: 33.6

Step-by-step explanation:

Answer:

33.6

Step-by-step explanation:

First, let's multiply 8.4 by 100.

This gives us the number 840.

Next, divide 840 by 25.

That gives us 33.6, our final answer.

Answer:

Step-by-step explanation:

Both y = 5 and y = 5x - 4 are equations of straight lines in the Cartesian plane. The first equation, y = 5, represents a horizontal line passing through the y-axis at 5. The second equation, y = 5x - 4, represents a line with a slope of 5 and y-intercept of -4. These two lines are related in that the second equation is a linear function with a non-zero slope, while the first equation is a special case of the second equation where the slope is zero. Additionally, the second equation can be obtained from the first equation by adding a non-zero slope term.

The answer is 2.6825  cm, which is not one of the given options. Therefore, the correct answer is E. none of these.

The bulk modulus, B is defined as:

B = (P / ΔV / V), where P is the pressure applied, ΔV is the change in volume, and V is the original volume.

For a cube, the change in volume, ΔV is related to the change in length, ΔL by:

[tex]\sf \Delta V = \Delta L^3[/tex].

Given that the cube has 2.0 cm sides, the original volume, V is:

[tex]\sf V = (2.0 \ cm)^3 = 8.0 \ cm^3[/tex].

The pressure applied is [tex]\sf P = 2.0 \times 10^5[/tex] Pa and the bulk modulus is [tex]\sf B = 4.7 \times 10^5 \ N/m^2[/tex].

We can rearrange the bulk modulus formula to solve for ΔL as:

[tex]\sf \Delta L = \huge \text(\dfrac{P}{B} \huge \text) \times \dfrac{V}{3}[/tex].

Substituting the values, we get:

[tex]\sf \Delta L = (2.0 \times 10^5 \ \dfrac{Pa}{4.7} \times 10^5\ N/m^2) \times \dfrac{8.0 \ cm^3}{3} = 0.6825 \ cm[/tex]

Therefore, the final length of any side of the cube is:

[tex]\sf L = 2.0 \ cm + \Delta L = 2.0 \ cm + 0.6825 \ cm = 2.6825 \ cm[/tex]

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Complete Question:

A cube with 2.0-cm sides is made of material with a bulk modulus of4.7 × 10^5 N/m2. When it is subjected to a pressure of 2.0 × 10^5 Pa the length of its any of its sides is:

A. 0.85 cm

B. 1.15 cm

C. 1.66 cm

D. 2.0 cm

E. none of these

Answer:

No you cannot

Step-by-step explanation:

Triangle side length rule says the sum of any two sides must be greater than the remaining side

7 + 8   is NOT greater than 18 ....you cannot draw a triangle with these side lengths

No, we cannot form a triangle using side lengths 7, 8, and 18 units.

The Triangle Inequality Theorem can be used to determine if a triangle can be built with sides that are 7, 8, and 18 units long. The lengths of any two sides of a triangle with side lengths a, b, and c must add up to more than the length of the third side, according to the theorem.

Let's determine if this criterion is satisfied for the specified side lengths:

7 + 8 = 15

7 + 18 = 25

8 + 18 = 26

In this instance, the length of the third side (18) is greater than the total of the two shorter side lengths (7 and 8). This means that a triangle cannot be built using side lengths of 7, 8, and 18 units, according to the Triangle Inequality Theorem.

As a result, with side lengths of 7, 8, and 18 units, a triangle cannot be built according to the Triangle Inequality Theorem.

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To find the volume of the cube, we need to know the length of one side of the cube. However, since it is not provided in the question, we cannot calculate the exact volume.

We can use a formula to relate the volume of the cube to its surface area. The formula is:

Surface Area = 6 * (side)^2

Given that the surface area of the cube is 294 cm², we can set up the equation:

294 = 6 * (side)^2

Divide both sides of the equation by 6:

49 = (side)^2

Take the square root of both sides:

side = √49

side = 7 cm

Now that we know the length of one side of the cube is 7 cm, we can calculate the volume using the formula:

Volume = side^3

Volume = 7^3

Volume = 343 cm³

Therefore, the volume of the cube is 343 cm³.

[tex]\begin{array}{cllll} -6x+5y&=&34\\ -6x-10y&=&4 \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{ \textit{using elimination method} }{\begin{array}{cllll} \text{\LARGE -1}(-6x+5y&=&34)\\ -6x-10y&=&4 \end{array}}\implies \begin{array}{clclll} 6x ~~ -5y&=&-34\\ -6x-10y&=&4\\\cline{1-3} 0 ~~ -15y&=&-30 \end{array} \\\\\\ -15y=-30\implies y=\cfrac{-30}{-15}\implies y=2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{substituting on the 1st equation}}{-6x+5(2)=34\implies} -6x+10=34\implies x=\cfrac{24}{-6}\implies x=-4 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-4~~,~~2)~\hfill[/tex]

Assuming that the size of the stack is constant, we would need to know the number of cans that can be stacked in order . Since the number of cans is evenly divisible by the number of cans per stack, there would be zero cans left over from the stack.

Assuming that the size of the stack is constant, we would need to know the number of cans that can be stacked in order to determine the answer. However, let's assume that a single stack can hold 10 cans. If Selene has 90 cans, then we can divide the total number of cans by the number of cans per stack to determine how many stacks are needed.

90 cans / 10 cans per stack = 9 stacks

Therefore, Selene would need 9 stacks to hold all 90 cans. However, there would be some cans left over from the last stack.

9 stacks x 10 cans per stack = 90 cans

90 cans - 90 cans = 0 cans

Since the number of cans is evenly divisible by the number of cans per stack, there would be zero cans left over from the stack.

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Answer:

Step-by-step explanation:

Here Is a Quick Explanation :)

To find the axis of symmetry and the vertex of the function, we can use the fact that the function is recursive, and we can write:

f(x) = f(x-1)² + 7

f(x-1) = f(x-2)² + 7

f(x-2) = f(x-3)² + 7

...

f(1) = f(0)² + 7

If we substitute the last equation into the previous one, we get:

f(x-1) = (f(0)² + 7)² + 7

f(x) = ((f(0)² + 7)² + 7)² + 7

This shows that the function depends only on the initial value f(0), and we can use this fact to find the axis of symmetry and the vertex.

To find the axis of symmetry, we need to find the value of x that makes f(x) equal to f(-x). We can write:

f(-x) = f(-(x-1))² + 7 = f(-x+1)² + 7

Now, if we substitute f(x) = f(x-1)² + 7 into the last equation, we get:

f(-x) = (f(x-1)² + 7)² + 7 = f(x)² + 7

This means that the axis of symmetry is the line x = 0, and not y = 7 as stated in option A.

To find the vertex, we need to find the maximum or minimum value of the function. Since f(x) = f(x-1)² + 7, the function is increasing if f(x-1) > -7, and decreasing if f(x-1) < -7. Since f(0) = 7, we can conclude that the function is increasing on the interval -∞ < x < 1, and decreasing on the interval x > 1. Therefore, the vertex is at x = 1, and the corresponding value is f(1) = 7.

Therefore, the correct statements are:

The axis of symmetry of f(x) is x = 0.

The vertex of the function is (1, 7).

f is increasing on the interval -∞ < x < 1.

f is decreasing on the interval x > 1.