Are the two events independent or dependent ? Toss a penny and a nickel . Dependent or independent.

The cubes can be represented by the equation x³, where x represents the length of one side of the cube.

The vectors on the number line can be represented by the equation y = x, where x represents the position on the number line and y represents the magnitude of the vector.

So, to complete both equations, we can assign values to x and see the resulting values for y:

For the cubes:

For the vectors:

So, both the cubes and vectors can be represented on the number line, with the cubes represented as points with their x and y values being the length of one side and the volume of the cube, respectively, and the vectors represented as lines with their x and y values representing the position on the number line and the magnitude of the vector, respectively.

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Memoization is a technique used in programming to store the results of expensive function calls and return the cached result when the same inputs occur again. This approach can significantly improve the performance of recursive functions, such as the Legendre polynomials.

To define a recursive function L using memoization, we can create a dictionary or map that stores the previously calculated values of L(n, x). We can then check if the requested value of L(n, x) is already in the dictionary and return it if it is. If not, we can calculate the value using the recursive definition and store it in the dictionary for future use.

Here is an implementation of the memoized L function in Python:

```
memo = {}
def L(n, x):
   if n == 0:
       return 1
   elif n == 1:
       return x
   elif (n, x) in memo:
       return memo[(n, x)]
   else:
       result = ((2*n - 1)*L(n-1, x) - (n - 1)*L(n-2, x))/n
       memo[(n, x)] = result
       return result
```

In this implementation, we first check if n is 0 or 1 and return the appropriate base case values. If the requested value is already in the memoization cache, we return it directly. Otherwise, we calculate the value recursively using the provided formula and store it in the cache before returning it.

Using memoization, we can avoid recalculating the same values of L(n, x) multiple times and greatly speed up our computation.

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The square root of 13 in decimal form is an non-terminating non-recurring decimal

A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal.

Such decimals are irrational numbers since they cannot be expressed as fractions.

Examples. Pi is a decimal that doesn't end or repeat.

Since the square root of 13 will result to infinite number the number cannot fully reach the required value but an approximate

Because of this the decimal form of he square root of 13 will lack accuracy

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The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

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a) The divergence of f = \(e^{xy\) i - cosy j + sin z²k is y \(e^{xy\) + sin y + 2z cos z², and the curl is 0.

b) The divergence of f = xi + yj - zk is 1, and the curl is 0.

a) To find the divergence and curl of the vector field f = \(e^{xy\) i - cosy j + sin z²k:

Divergence:

The divergence of a vector field f = P i + Q j + R k is given by the formula:

div(f) = ∇ · f = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Given f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the divergence as follows:

∂P/∂x = ∂/∂x(\(e^{xy\)) = y \(e^{xy\)

∂Q/∂y = ∂/∂y(-cosy) = sin y

∂R/∂z = ∂/∂z(sin z²) = 2z cos z²

Therefore, the divergence of f is:

div(f) = y \(e^{xy\) + sin y + 2z cos z²

Curl:

The curl of a vector field f = P i + Q j + R k is given by the formula:

curl(f) = ∇ × f = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k

Using the vector field f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the curl as follows:

∂P/∂y = ∂/∂y(\(e^{xy\)) = x \(e^{xy\)

∂Q/∂z = ∂/∂z(-cosy) = 0

∂R/∂x = ∂/∂x(sin z²) = 0

∂R/∂y = ∂/∂y(sin z²) = 0

∂Q/∂x = ∂/∂x(-cosy) = 0

∂P/∂z = ∂/∂z(\(e^{xy\)) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

b) To find the divergence and curl of the vector field f = xi + yj - zk:

Divergence:

∂P/∂x = ∂/∂x(x) = 1

∂Q/∂y = ∂/∂y(y) = 1

∂R/∂z = ∂/∂z(-z) = -1

Therefore, the divergence of f function is:

div(f) = ∇ · f = 1 + 1 - 1 = 1

Curl:

∂P/∂y = ∂/∂y(x) = 0

∂Q/∂z = ∂/∂z(y) = 0

∂R/∂x = ∂/∂x(-z) = 0

∂R/∂y = ∂/∂y(-z) = 0

∂Q/∂x = ∂/∂x(y) = 0

∂P/∂z = ∂/∂z(x) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

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Answer:

n = -8 , n = -12

Step-by-step explanation:

First we factorise the quadratic using the factorisation method :

n²+8n+12n+96 = 0

n(n+8)+12(n+8) = 0

(n+12)(n+8) = 0

Now we equate each bracket to 0 :

Either

n + 12 = 0  

n = -12

OR

n + 8 = 0

n = -8

So the real solutions for that equation is

n = -8 , n = -12

The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.

Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.

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Athlete would have the best running economy Runner B: VO2 of 42 ml/kg/min at 7.5. Option B

To calculate exercise intensity in METs (metabolic equivalents), we need to know the resting metabolic rate (RMR) of an individual. Without the RMR information, we cannot determine the exercise intensity in METs for the 45-year-old male exercising at 2.26 L/min. Therefore, the exercise intensity in METs cannot be determined, and the correct answer is "Not enough information."

Regarding the question about which athlete has the best running economy, we can compare the VO2 values at the given running speeds.

Runner A: VO2 of 44 ml/kg/min at 8 mph

Runner B: VO2 of 42 ml/kg/min at 7.5 mph

Runner C: VO2 of 46 ml/kg/min at 9 mph

Running economy refers to the energy cost or oxygen consumption required to maintain a given running speed. In this case, a lower VO2 value indicates better running economy.

Comparing the given VO2 values, we can see that Runner B has the lowest VO2 of 42 ml/kg/min at 7.5 mph. This means Runner B has the best running economy among the three athletes. Option B

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It can be noted that the volume of the ball which is a sphere will be 5572.45 cm³.

From the information given, the soccer ball has a radius of 11 cm. This will be calculated by using the volume of a sphere.

Volume = 4/3πr³

= 4/3 × 3.14 × 11³

= 5572.45 cm³

In conclusion, the correct option is 5572.45 cm³.

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Answer:

C

Step-by-step explanation:

You add .3 km to the first day (tuesday)

then .6 then next day (wedneday)

next you add .9 on the next day (thursday)

finally you add 1.2 km on Friday

2.3+0.6+0.9+1.2=4 km

The value of  tan(45°+Θ) after using trigonometric ratio is  

1+tanΘ/ 1-tanΘ.

What is trigonometric ratios?

   There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given,

=> tan(45°+Θ)

Now using formula ,

=> tan(a+b) = \(\frac{tan a+tan b}{1-tan a*tanb}\)

=> tan(45°+Θ)= (tan 45°+tanΘ)/(1-tan45°*tanΘ)

We know that tan 45°=1 then ,

=> tan (45°+Θ)= 1+tanΘ/ 1-tanΘ

Hence the formula for  tan (45°+Θ) is  1+tanΘ/ 1-tanΘ.

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Answer:

The only correct choice is the third one: BH

Step-by-step explanation:

Shapes and Solids

We are given the image of a solid and are required to determine all the lines that are parallel to GD.

We don't have enough evidence to say what lines are parallel or perpendicular to others. We can only guess by construction.

Line GD forms a parallelogram with BH, thus this line is parallel to GD.

Also, CJ looks parallel to GC and so does LE. There are no more candidate lines to be parallel to GD.

Thus, the complete answer is: BH, CJ, and LE are parallel to GD. There is no choice to take them all.

The only correct choice is the third one: BH

Answer:

16x^3+16x^2+30

Step-by-step explanation:

Answer:

a) 23 and 24

b) see step-by-step

c) 23.2

Step-by-step explanation:

a)  find the greatest square number below 540?

    find the smallest square number above 540?

23² = 529   and   24² = 576

    529 < 540 < 576

⇒ √529 < √540 < √576

⇒ 23 < √540 < 24

Hence, √540 lies between 23 and 24

b) **I'm not sure how accurate they want this, so I've added several options**

√540 = 23.23790008...

23.23790008... - 23 = 0.2379000772...

0.2379000772... = 2,379,000,772 / 10,000,000,000

Therefore, √540 = 23 and 2,379,000,772 / 10,000,000,000

Or 23 and 2,379 / 10,000

Or 23 and 24/100 = 23 and 6/25

Or 23 and 2/10 = 23 and 1/5

c) (√540)² = 540

So we are looking for a number whose square is 540.

We know that √540 lies between 23 and 24 (from part a), so let's start with 23.5:

   23.5² = 552.25

552.25 > 540 so try a smaller number

   23.3² = 542.89

542.89 > 540 so try a smaller number

  23.2² = 538.24

538.24 < 540

  23.24² = 540.0976

540.0976 > 540

So √540 lies between 23.2 and 23.24, therefore, the decimal approximation is 23.2 to the nearest tenth place

The maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

Acceleration is directly proportional to the force acting on an object. In simple terms, if the force on an object is greater, then it will undergo more acceleration. However, there are limitations to the acceleration that can be tolerated by the human body. At about 5 g (49.0 m/s2) for more than a few seconds, an average person starts to lose consciousness. Let's use this information to answer the given question.

Let the maximum burn rate |ΔM/Δt| that the engine could reach before the ship's acceleration exceeded 5 g be x.

Let the mass of the spaceship be m and the exhaust speed of the engine be v.

Using the formula for the thrust of a rocket,

T = (mv)e

After substituting the given values into the formula for thrust, we get:

T = (3.00 × 104)(2.50 × 103) = 7.50 × 107 N

Therefore, the acceleration produced by the engine, a is given by the formula below:

F = ma

Therefore,

a = F/m= 7.50 × 107/3.00 × 104= 2.50 × 103 m/s²

The maximum burn rate that the engine could reach before the ship's acceleration exceeded 5 g is equal to the acceleration that would be produced by a maximum burn rate. Therefore,

x = a/5g= 2.50 × 103/(5 × 9.8)≈ 51.0 kg/s

Therefore, the maximum burn rate ∣ΔM/Δt∣ that the engine could reach before the ship's acceleration exceeded 5 g and its human occupants began to lose consciousness is approximately 51.0 kg/s.

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The distance between N and PS is 3.2.

What is the midpoint of the segment?

Take the distance between the two endpoints and divide it by two. This distance from either end is the line's midpoint. Alternatively, add the endpoints' x coordinates and divide by 2. Repeat for the y coordinates.

From the below figure,

N is the intersection of the red and blue circles.

I’ve drawn PQRS as the square (0,0), (4,0), (4,4), and (0,4).

Then the formula for the red circle is:

             (x-2)² + (y-4)² = 4.

The formula for the blue circle is

                  x² + y²- 16 = 0.

Solving for x and y yields intersections

               (0, 4) and (3.2, 2.4),

the first being S and the latter being N.

Hence, the distance between N and PS is 3.2.

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A 90° rotation around the origin characterised the transition.

A logical principle that specifies the circumstances in which one assertion can be legitimately inferred from one or more other statements, particularly in codified languages.

(x, y)(x, y) is the formula for a reflection over the x-axis.

Triangle ABC was changed utilizing the (x, y) rule (–y, x). The triangles' vertices are displayed. A (–1, 1) B (1, 1) C (1, 4) (1, 4) A' (–1, –1) (–1, –1) B' (–1, 1) C' (–4, 1) (–4, 1) Which phrase best sums up the change? A 90° rotation around the origin characterised the transition. A 180° rotation of the origin occurred during the transformation.  The transformation was a 270° rotation about the origin. The transformation was a 360° rotation about the origin.

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Answer: A reflection over the y-axis justifies ∆ABC ≅ ∆A'B'C'.

Step-by-step explanation: Took the test, no thanks neeeded :)

Answer:

h= 2/3d

Step-by-step explanation:

slope is the change of y value on the change of x value

4/6 = 2/3

Answer:

-5

Step-by-step explanation:

Cube root of -125 has to be -5

The correct Answer is 1/2

Answer:

40

Step-by-step explanation:

4 times 10 equals 40

i news more sownfjdhe

According to Pascal's principle, pressure is transmitted through a friction-less closed hydraulic system without a change in velocity. This principle states that the pressure applied to a fluid in such a system is uniformly transmitted throughout the fluid without causing a change in the velocity of the fluid particles.

Pascal's principle, formulated by Blaise Pascal, describes the behavior of pressure in a closed hydraulic system. According to Pascal's principle, pressure applied to a fluid in a confined space is transmitted uniformly in all directions and to all parts of the fluid.

In a friction-less closed hydraulic system, such as a hydraulic jack or brake system, the pressure applied to one part of the fluid is transmitted undiminished to other parts of the system. This means that the pressure remains the same throughout the system.

The statement that there is no change in velocity refers to the fact that the fluid particles in the hydraulic system do not experience a change in their speed or velocity. The pressure transmitted through the fluid does not cause the fluid particles to accelerate or change their velocity.

Other options listed in the question:

- Change in temperature: Pascal's principle does not address changes in temperature. It specifically focuses on the transmission of pressure in a closed hydraulic system.

- Loss: Pascal's principle assumes that there are no losses in the transmission of pressure within a friction-less closed hydraulic system.

- Change in heat energy: Pascal's principle does not involve the transfer of heat energy. It solely deals with the transmission of pressure in a closed hydraulic system.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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The choice which defines same arithmatic sequence using a Recursive Formula and an Explicit formula is (A) which is \(a_1= -23, a_n = a_{n-1}+ 12,a_n=-23 +12(n-1)\)

If first term of a arithmatic sequence is a₁ and the common difference is d then,

By Explicit Formula, the n-th term of the sequence is given by,

\(a_n=a_1+(n-1)d\)

By Recursive Formula,

\(a_n=a_{n - 1}+d\)

In the first choice: a₁ = -23 and

\(a_n=a_{n-1}+12\)

Then by recursive formula, it suggests arithmatic sequence with first term -23 and common difference 12.

and

\(a_n=-23+12(n-1)\)

So by explicit formula it also suggests arithmatic sequence with first term -23 and common difference 12.

So it is one correct choice.

In second choice: a₁ = -100 and

\(a_n=a_{n-1}+1\)

By recursive formula, it suggests arithmatic sequence with first term -100 and common difference 1.

\(a_n=100-1(n-1)\)

By explicit formula, it suggests arithmatic sequence with first term 100 and common difference -1.

So it is not the correct choice.

In third choice: a₁ = -41 and

\(a_n=a_{n-1}+12\)

By recursive formula, it suggests arithmatic sequence with first term -41 and common difference 12.

\(a_n=12-41(n-1)\)

By explicit formula, it suggests arithmatic sequence with first term 12 and common difference -41.

So it is not the correct choice.

In fourth choice: a₁ = 50 and

\(a_n=a_{n-1}-4\)

By recursive formula, it suggests arithmatic sequence with first term 50 and common difference -4.

\(a_n=50+4(n-1)\)

By explicit formula, it suggests arithmatic sequence with first term 50 and common difference 4.

So it is not the correct choice.

Hence the option (A), the first choice is correct.

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An SAT-M score in the 98th percentile is approximately 734.55 or higher.

According to the College Board website,

The scores on the math part of the SAT (SAT-M) in a recent year had a mean of 507 and a standard deviation of 111. Assume that SAT-M scores follow a normal distribution. To gain admission to a particular engineering school, a requirement is to obtain an SAT-M score in the 98th percentile, indicating that the score is among the top 2% of scores.

For getting the actual SAT-M score, we need to find the corresponding z-score for the 98th percentile.

Using the Inverse Normal Distribution Calculator, we get a z-score of 2.05 for the 98th percentile.

So, the formula for finding an actual SAT-M score is:

x = μ + zσ

Where x is the actual SAT-M score,

μ is the mean = 507,

z is the z-score = 2.05,

σ is the standard deviation = 111

x = 507 + (2.05)(111)

x = 507 + 227.55

x = 734.55

The actual SAT-M score for the 98th percentile is approximately 734.55 (rounded to the nearest hundredth).

Therefore, an SAT-M score of 734.55 or higher is required for admission to the engineering school.

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The incenter plays a crucial role in geometry problems and is used to solve many problems. The incenter of a triangle is the intersection point of the bisectors is b) angle.

The incenter of a triangle is the intersection point of the bisectors. When talking about the incenter, we need to know that it is the point where the bisectors of a triangle intersect. The angle bisectors are the lines that divide an angle into two equal parts.

Thus, the incenter is the intersection of the angle bisectors of a triangle.Let's take a look at the given options:

a) Circumcenter: It is the point where the perpendicular bisectors of a triangle intersect

b) Angle: The bisectors intersect at the incenter, which is not an angle

c) Perpendicular: The perpendicular bisectors of a triangle intersect at the circumcenter.

d) Midpoint: It is a point that is halfway between two endpoints.

Likewise, none of the options fit in for the given question except for option

b) angle.

Therefore, the correct option is

b) angle.

A brief explanation of incenter and its significance:

The incenter of a triangle is equidistant from all three sides of the triangle. In addition, the incenter is also the center of the incircle of a triangle. The incircle of a triangle is the largest circle that fits inside the triangle and touches all three sides. Also, The incenter plays a crucial role in geometry problems and is used to solve many problems.

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To find the critical numbers of the function \(\(g(y) = \frac{{y-1}}{{y^2-y+1}}\)\), we need to first find the derivative of \(\(g(y)\)\) and then solve for \(\(y\)\) when the derivative is equal to zero. The critical numbers correspond to these values of \(\(y\).\)

Let's find the derivative of \(\(g(y)\)\) using the quotient rule:

\(\[g'(y) = \frac{{(y^2-y+1)(1) - (y-1)(2y-1)}}{{(y^2-y+1)^2}}\]\)

Simplifying the numerator:

\(\[g'(y) = \frac{{y^2-y+1 - (2y^2 - 3y + 1)}}{{(y^2-y+1)^2}} = \frac{{-y^2 + 2y}}{{(y^2-y+1)^2}}\]\)

To find the critical numbers, we set the derivative equal to zero and solve for \(\(y\):\)

\(\[\frac{{-y^2 + 2y}}{{(y^2-y+1)^2}} = 0\]\)

Since the numerator can never be zero, the only way for the fraction to be zero is if the denominator is zero:

\(\[y^2-y+1 = 0\]\)

To solve this quadratic equation, we can use the quadratic formula:

\(\[y = \frac{{-b \pm \sqrt{{b^2-4ac}}}}{{2a}}\]\)

In this case, \(\(a = 1\), \(b = -1\), and \(c = 1\)\). Substituting these values into the quadratic formula, we get:

\(\[y = \frac{{1 \pm \sqrt{{(-1)^2 - 4(1)(1)}}}}{{2(1)}}\]\)

Simplifying:

\(\[y = \frac{{1 \pm \sqrt{{1-4}}}}{{2}} = \frac{{1 \pm \sqrt{{-3}}}}{{2}}\]\)

Since the discriminant is negative, the square root of -3 is imaginary. Therefore, there are no real solutions to the quadratic equation \(\(y^2-y+1=0\).\)

Hence, the function \(\(g(y)\)\) has no critical numbers.

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Answer:

So 12 of 15 free throws is 80% so she would have to make at least 13 of 15 free throws to at least get over 85% cause 13 of 15 is 86.6% repeated

Step-by-step explanation:

Answer:

the square root of 145

Step-by-step explanation:

D= square root[(y2-y1)^2 + (x2-x1)^2]

D=square root[(5+4)^2 + (5+3)^2]

D=square root[(9)^2 + (8)^2]

D=square root[81 + 64]

D=square root[145]