If Professor Wilson found that the test scores of his students had a variance of 4.4, what is the standard deviation? Type a numerical answer in the space provided. Round your answer to the nearest tenth.

(a) For the equation r(t) = e^(-t), 2t^2, 3tan(t), the first derivative is r'(t) = -e^(-t), 4t, 3sec^2(t). (b) The second derivative is r''(t) = e^(-t), 4, 6tan(t)sec^2(t). (c) The dot product of r'(t) and r''(t) is (-e^(-t))(e^(-t)) + (4t)(4) + (3sec^2(t))(6tan(t)sec^2(t)) = -e^(-2t) + 16t + 18tan(t)sec^4(t).

(a) For the equation r(t) = 3cos(t)i + 3sin(t)j, the first derivative is r'(t) = -3sin(t)i + 3cos(t)j.

(b) The second derivative is r''(t) = -3cos(t)i - 3sin(t)j.

(c) The dot product of r'(t) and r''(t) is (-3sin(t))(-3cos(t)) + (3cos(t))(3sin(t)) = 0, which means that the vectors r'(t) and r''(t) are orthogonal or perpendicular to each other.

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Answer:

77bb

Step-by-step explanation:

Vertices (-4, 4) and (12, 4), foci (-6, 4) and (14, 4) is given by: (x - h)² / a² - (y - k)² / b² = 1.

Since the given vertices (-4, 4) and (12, 4) are located on the transverse axis of the hyperbola, the length of the transverse axis is 16 (the distance between the vertices), and thus,

2a = 16, or a = 8.

Also, since the distance between the foci (-6, 4) and (14, 4) is 20, we have 2c = 20,

or c = 10,

where c is the distance from the center of the hyperbola to each focus.

Since the hyperbola is symmetric with respect to the y-axis, the center is given by (h, k) = (4, 4).

Thus, b² = c² - a²

= 100 - 64

= 36,

and b = ±6.

So, the equation in standard form is (x - 4)² / 64 - (y - 4)² / 36 = 1.

The exact values of the following functions are given by: a) sin(a - B)Let's draw the points P(a, b) and Q(a, -b) on the unit circle, where

a = -15/17 and

b = 8/17.

Now, sin a = -b = -8/17 and

cos a = a

= -15/17, and similarly,

sin B = b

= 5/13 and

cos B = a

= 12/13.

Using the formula for sin(a - B), we get:

sin(a - B) = sin a cos B - cos a

sin B= -8/17 × 12/13 - (-15/17) × 5/13

= -96/221 - (-75/221)

= -21/221

b) cos(a + B) Using the formula for cos(a + B), we get:

cos(a + B)

= cos a cos B - sin a

sin B= -15/17 × 12/13 - (-8/17) × 5/13

= -180/221 + 40/221

= -140/221

c) tan(a + B) Using the formula for tan(a + B), we get: tan(a + B) = (tan a + tan B) / (1 - tan a tan B)

= (-8/15 + 5/12) / (1 - (-8/15) × (5/12))

= (-32/60) / (169/180)

= -16/169

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Answer:   (^-^)    2

Step-by-step explanation:

2+7 is 9 you divided 18 by 9 which it is 2

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Composite function fog To find the composite function fog, first we need to substitute g(x) into f(x) in place of x.So,

f(g(x))=f(√x) = (√x)² - 5(√x) + 1= x - 5√x + 1.

Domain of fog Since the domain of g(x) is all real numbers, x ≥ 0 (i.e., non-negative), the domain of fog is x ≥ 0 or [0,∞).

Range of fog We can use the function graph to find the range of fog. The range of f(x) is (-∞, ∞), but when restricted to the domain of fog, the range is [1, ∞).Therefore, the range of fog is [1,∞).b) Composite function gof To find the composite function gof, we substitute f(x) into g(x) in place of x.So, g(f(x)) = g(7°) = log (7°)² = log 49° = 1.69°Domain of gof The domain of f(x) is all real numbers, but when restricted to the domain of gof, the domain is restricted to 7° only.So, the domain of gof is {7°}.

Range of gof Since the range of f(x) is [0, ∞), the range of gof is [log 49°, ∞) or (1.69°, ∞).c) Composite function fog To find the composite function fog, we substitute g(x) into f(x) in place of x.So, f(g(x))= f(sin x) = sin² x - 5 sin x + 1 Domain of fog Since the domain of g(x) is all real numbers, the domain of fog is also all real numbers or (-∞, ∞).Range of fogWe can use the function graph to find the range of fog. The range of f(x) is [-1, 1], and since the function is quadratic, the range is restricted to [1 - (5²)/4, ∞) or [-6.25, ∞) when x is restricted to [-5/2, 5/2].Therefore, the range of fog is [-6.25, ∞).

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We are given the relationship:

a. It's required to find a relationship where r is a function of t. To do that, we need to solve the equation for r.

Subtract 4t:

Divide by 7:

b. We use the function found in part a and evaluate it for t=-7:

Thus, f(-7) = 6

c. Solve f(t) = 18

Again, we use the function from part a and solve the equation:

Multiplying by 7:

Subtract 14 and then divide by -4:

t = -28

(a) There is no extreme value of A subject to the given constraint,

(b) For x = 0, y + z² ≤ 16.

y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.

For x = ±y, z = 4 - y².

y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.

When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.

Therefore, one should exclude the value of zero from the domain of the function or expression.

In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.

Let's find the partial derivatives of A with respect to x, y, and z.

∂A/∂x = 3

∂A/∂y = 2y - 2 = 2(y - 1)

∂A/∂z = 0

Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.

\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)

Substituting the values of the partial derivatives, we get:

\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)

The second and third equations are contradictory. So, under the given constraint, A has no extreme value.

In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.

Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.

We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.

2x = λ(2x),

2y = λ(1),

2z = λ(2z).

Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.

Substituting the values of x and λ from the first and second equations into the third equation, we get:

z = 4 - y² or z = 0.

Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:

Case 1: x = 0, y + z² ≤ 16.

So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.

Case 2: x = ±y, z = 4 - y².

So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.

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Answer:

Yes

Step-by-step explanation:

Hypothesis: If two angles are congruent.

Conclusion: Then they have the same measure.

The hypothesis states that if two angles are congruent, which means they are identical in shape and size, then the conclusion is that they have the same measure. In other words, when two angles are congruent, their measures are equal.

Angles are typically measured in degrees or radians. When we say that two angles are congruent, it implies that the measures of those angles are the same. This can be understood through the transitive property of congruence, which states that if two angles are congruent to a third angle, then they are congruent to each other.

For example, if angle A is congruent to angle B, and angle B is congruent to angle C, then it follows that angle A is congruent to angle C. This implies that the measures of angle A and angle C are equal, as congruent angles have the same measure.

In conclusion, the hypothesis that if two angles are congruent implies that they have the same measure is valid and supported by the principles of congruence and the transitive property.

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The fraud triangle is a model that describes the three key factors that must be present for fraud to occur: opportunity, rationalization, and pressure.

These factors are often represented as the three sides of a triangle, with fraud being the result at the center.

Opportunity refers to the ability of an individual to commit fraud, either due to a lack of internal controls or the ability to override existing controls. Rationalization refers to the mental process by which an individual justifies the fraudulent behavior to themselves, often by convincing themselves that it is not really wrong or that they have a valid reason for doing it. Pressure refers to the external factors that motivate an individual to commit fraud, such as financial difficulties, job insecurity, or a desire to meet performance targets.

In summary, the fraud triangle indicates that all three conditions of opportunity, rationalization, and pressure must be present for fraud to be perpetrated.

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Answer:

480

Step-by-step explanation:

25-13=12

12 x 80=960

960 divided by 2=480

We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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Answer:

3

Step-by-step explanation:

18/6 = 3

The probability of getting heads is 3/8.

Probability:

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. Probability is a number between 0 and 1, with 0 generally indicating impossibility and 1 indicating certainty. that an event will occur. A simple example is tossing a fair (unbiased) coin. Since the coin is fair, the two outcomes (heads and tails) are equally likely. The probability of heads is the same as the probability of tails. Since no other outcome is possible, the probability of heads or tails is 1/2 (also written as 0.5 or 50%).

Since 3 is a small number, let's list out all possible combinations.

H represents a head while T represents a tail.

3 Heads

HHH

2 Heads

HHT

HTH

THH

1 Head

HTT

THT

TTH

0 Head

TTT

The answer is

3/1+3+3+1=3/8

                                            OR

In general, we will find that the list resembles a particular row of the pascal's triangle.

If you want to know the probability of getting r heads (or tails) from n flips, it is the sum of the rth  elements in the n + 1 line. All elements of the series n+1.

\(\left[\begin{array}{ccc}N\\\\R\end{array}\right]\)/ 2ⁿ = \(\frac{n!}{r! * (n - r)!* 2^{n} }\)

n this case,

N =3andR= 2

   3!/ 2!×1! × 2³

= 6/ 2× 1 × 8

= 3/8

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The maximum monthly rent that Yasmine should pay is approximately $619.58.

To calculate the maximum monthly rent that Yasmine should pay, we need to determine her monthly income and then find 30% of that amount.

Yasmine's hourly  = $11.75

Hours worked per week = 35

Weekly income = Hourly wage * Hours worked per week

             = $11.75 * 35

             = $411.25

Monthly income = Weekly income * Number of weeks in a month

              = $411.25 * 4

              = $1645

Now, let's calculate 30% of her monthly income:

Rent limit = 30% of Monthly income

          = 0.30 * $1645

          = $493.50

Therefore, the maximum monthly rent that Yasmine should pay is

To determine the maximum monthly rent that Yasmine can afford, we first calculate her monthly income. Since she earns $11.75 per hour and works 35 hours per week, we multiply her hourly wage by the number of hours worked per week to find her weekly income.

Next, we multiply her weekly income by the number of weeks in a month (which we assume to be 4) to obtain her monthly income.

Finally, we calculate 30% of her monthly income by multiplying it by 0.30, which represents 30% as a decimal.

The result, rounded to two decimal places, is the maximum monthly rent that Yasmine should pay. In this case, the maximum monthly rent is $493.50.

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The given system of equations has no solution. The correct option is  "There are no solutions to the given system of equations."

The given system of equations is:x² + y² = 6, andx² – y = 6

The solution(s) of the given system of equations are to be determined. The given system of equations can be solved by the substitution method.

For this purpose, the value of y² in the first equation can be substituted by 6 - x² obtained from the second equation. Then the resulting equation can be solved for x.

x² + y² = 6 ...(1)

x² – y = 6 ...(2)

y² = 6 – x² ...(3)

Substituting (3) in (1), we get:x² + (6 – x²) = 6⇒ 6 = 6

This implies that the given system of equations has no solution.

Therefore, the correct option is: "There are no solutions to the given system of equations."

Note: If we graph the two equations of the given system, we find that the graph of x² + y² = 6 is a circle with the center at the origin and radius 2√3, while the graph of x² – y = 6 is a hyperbola that opens upwards and downwards.

Since the two graphs do not intersect, there are no solutions to the given system.

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The area of the rectangle with vertices I(-6, 4), J(0, -4), K(4, -1), L(-2, 7), obtained from the formula for the area of a rectangle is 50 square units

Please find attached the plot of the points of the rectangle, created using MS Excel.

A rectangle is a quadrilateral that has four 90 degrees interior angles.

The coordinates of the vertices of the rectangle are; I(-6, 4), J(0, -4), K(4, -1), L(-2, 7)

Please find attached the graph of the points rectangle created with MS Excel

The lengths of the segments of the rectangle indicates that we get;

The length of IJ = √((-6 - 0)² + (4 - (-4))²) = 10

Length of JK = √((4 - 0)² + (-1 - (-4))²) = 5

Length of KL = √((4 - (-2))² + (-1 - 7)²) = 10

Length of IL = √((-6 - (-2))² + (4 - 7)²) = 5

The area of the rectangle = 10 × 5 = 50

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Answer:

8 bags

7 green marbles and 3 yellow marbles

Step-by-step explanation:

Find the GCF of 24 and 56

24 = 4 x 6

= 2 x 2 x 2 x 3

56 = 7 x 8

= 7 x 4 x 2

= 7 x 2 x 2 x 2

The common factors are - 2 x 2 x 2, which is 8.

So the greatest number of bags they can make is 8

Divide the amount of marbles by the number of bags

24 yellow marbles and 8 bags, so 24/8 is 3

56 green marbles and 8 bags, so 56/8 is 7

Hope this helps, let me know if you have any questions

Answer:

im 1000000000900

Step-by-step explanation:

Answer:

T (2, -9)

Step-by-step explanation:

The specific function that will be called by the function call square(23.4) cannot be determined without knowing the definitions of the four functions.

The answer depends on the function signatures and parameter types of the defined functions.

To determine which function will be called, we need to consider the parameter types and function signatures of the four defined functions. If one of the functions has a parameter that matches the type of the argument passed (in this case, 23.4), that function will be called.

The function definition must explicitly state a parameter of the appropriate type to match the argument. Without knowledge of the function definitions and their parameter types, it is not possible to determine which specific function will be called by the function call square(23.4).

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Answer:

\( - 6 \frac{1}{3} \)

Step-by-step explanation:

\( \frac{10}{3} - \frac{1}{3} - \frac{29}{3} - ( - \frac{1}{3} ) \\ \\ = \frac{10}{3} - \frac{1}{3} - \frac{29}{3} + \frac{1}{3} \\ \\ = \frac{10}{3} - \frac{29}{3} - \frac{1}{3} + \frac{1}{3} \\ \\ = \frac{10 - 29}{3} \\ \\ = \frac{ - 19}{3} \\ \\ = - 6 \frac{1}{3} \)

Answer:

Total amount = R41 337.50

Step-by-step explanation:

The value of the deposit is 15% of the total purchase price:

Deposit = 15/100 x R35 000

Deposit = R5 250

To calculate the balance that Claire will have to pay off, we need to subtract the deposit from the total purchase price:

Balance = Total purchase price - Deposit

Balance = R35 000 - R5 250

Balance = R29 750

To calculate the interest that Claire will have to pay on the balance, we can use the formula:

Interest = Principal x Rate x Time

where:

Principal is the amount of the balance

Rate is the annual interest rate (13%)

Time is the duration of the loan in years (3)

So, the interest that Claire will have to pay is:

Interest = R29 750 x 0.13 x 3

Interest = R11 587.50

Therefore, the total amount that Claire will have to pay back over the 3-year period is:

Total amount = Balance + Interest

Total amount = R29 750 + R11 587.50

Total amount = R41 337.50

Note that this assumes that the interest is calculated annually and added to the balance at the end of each year. In reality, the interest may be calculated differently depending on the terms of the hire purchase agreement.

Answer:

6 \(\frac{3}{20}\) is your answer. Hope it helps!

Answer:

Volume = 261.8 cm³

Surface area = 254.2 cm²

Step-by-step explanation:

To calculate the volume of the cone, we have to use the following formula:

\(\boxed{V = \frac{1}{3} \pi r^2 h}\),

where:

V ⇒ volume

r ⇒ radius = 5 cm

h ⇒ height = 10 cm

Using the above formula and the provided measures, we get:

V = \(\frac{1}{3}\) × π × (5)² × 10

    = \(\frac{1}{3}\) × π × 25 × 10

      = 261.8 cm³

In order to calculate the surface area of the cone, we have to use the following formula:

\(\boxed{SA = \pi r^2 + \pi r l}\)

where:

SA ⇒ surface area

r ⇒ radius = 5 cm

l ⇒ slant length = \(\sqrt{r^2+h^2}\) = \(\sqrt{5^2+10^2}\) = 5√5 cm

Using the formula,

SA = π × (5)² + π × 5 × 5√5

     = π × 25 + π × 25√5

     = 254.2 cm²

David, Jeff, and Paula have (7d)/3 books.

To find out how many books David, Jeff, and Paula have altogether in terms of d, we can use the given information as follows:

1. David has d books.
2. David has 3 times as many books as Jeff, so Jeff has d/3 books.
3. David has the same number of books as Paula, so Paula also has d books.

Now, to find the total number of books for all three of them, we simply add the number of books each person has:

Total books = David's books + Jeff's books + Paula's books
Total books = d + d/3 + d

To combine these terms, we can find a common denominator (in this case, 3):
Total books = (3d + d + 3d) / 3

Now, we can simplify the expression:
Total books = (7d) / 3

So, altogether, David, Jeff, and Paula have (7d)/3 books in terms of d.

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-33 is the value of f(-3) if the equation is If f(x)=x³- x²- x .

Explain what a linear equation is.

f(x)=x³- x²- x

f(-3) = ( - 3)³ - ( -3)² - ( -3)

      =  - 27 - 9 + 3

      =  - 36 + 3 = -33

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Answer:14

Step-by-step explanation:

14

Answer:

18

Step-by-step explanation:

addition is always before subtraction so you add 8 plus 5 is 13 then 4 minus 2 is 2 so add all together and its 18

There is no error, the calculation of Dwight is correct.

Standard Deviation:

Standard deviation is a measure of the amount of variation or spread in a set of values. A low standard deviation indicates that the values ​​tend to be closer to the mean (also called mean) of the set, while a high standard deviation indicates that the values ​​are more spread out.

According to the Question:

Given that mean {x} = 2

x = 2.

\(x_i\) from i = 1 to 4 is x₁ = 1 , x₂ = 2, x₃ = 1 and x₄ = 4.

​

Since each deviation is the difference between each data point (1, 2, 1, 4) and 2

So ,\((x_i - X)^2 = (1 - 1)^2 + (2 - 2)^2 + (1 - 2)^2 + (4 - 2)^2\)

This is divided by  N -1 = 4 - 1 = 3

Therefore,

There is no error in Dwight's standard deviation formula.

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Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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