draw a contour map of the function showing several level curves.
f(x,y) = x^3-y

Answer:

(10 + √-9) - (2 + √-25) = 10 - 3i - 2 + 5i

= 8 - 2i

The derivative of (sec(x)) / (1 + sec(x)) is [tan(x)] / [(1 + sec(x))^2].

To find the derivative of the given function, we can use the quotient rule:

Let u = sec(x) and v = 1 + sec(x).

Then, we have:

f(x) = u/v

Using the quotient rule, we have:

f'(x) = (v × u' - u × v') / v^2

where u' and v' are the derivatives of u and v with respect to x, respectively.

To find u' and v', we can use the chain rule:

u' = sec(x) × tan(x)

v' = sec(x) × tan(x)

Substituting u', v', u, and v into the quotient rule formula, we get:

f'(x) = [(1 + sec(x)) ×sec(x) × tan(x) - sec(x) × sec(x) × tan(x)] / (1 + sec(x))^2

Simplifying the numerator and denominator, we get:

f'(x) = [tan(x)] / [(1 + sec(x))^2]

Therefore, result of the derivative is [tan(x)] / [(1 + sec(x))^2]

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Answer:

hjkhj8008898

Step-by-step explanation:

a) y=-2780.85+1.447x

b) There are 142.09 voters estimated in the year 2012

Regression analysis is a group of statistical techniques used in statistical modelling to identify relationships between a dependent variable and one or more independent variables. The dependent variable is frequently referred to as the "outcome" or "response" variable, or a "label" in machine learning jargon (often referred to as "predictors," "covariates," "explanatory variables," or "features"). The line (or more complex linear combination) that most closely matches the data in terms of a specified mathematical criterion is found in linear regression, the most common type of regression analysis. For instance, the line (or hyperplane) that minimises the sum of squared differences between the real data and that line is determined when using the ordinary least squares approach (or hyperplane).

x = 11940 / 6 = 1990y = 593.8/6 = 98.9667

let the regression equation be y = a + bx

b = \(\frac{ ∑xy - nxy }{∑x^{2} -nx^{2} }\) = \(\frac{1182067 - 6 * 1990 * 98.9667}{23760880 - 6 * 1990^{2} }\) = 1.447

a = y - bx = 98.667  -  1.447 x 1990 = -2780.85

The regression equation is

x = 2020 in regression equation

substituting x=2020 in the regression equation

y = 142.09

There are 142.09 voters estimated in the year 2012

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The value of the length f is 6. 7

To determine the value, we have to know the different trigonometric identities.

These trigonometric identities are enumerated as;

To determine the length of f

Let us use the tangent identity, we have that;

tan θ = opposite/adjacent

substitute the values, we have;

tan 24 = f/15

Multiply the values, we get;

f = 0. 4452(15)

multiply the values

f = 6. 7

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Therefore,  f(g(0)) = 11 and g(f(0)) = -3. These values are obtained by substituting the appropriate values into the given functions f(x) = 3x - 1 and g(x) = 4 - 7x².

Let's calculate f(g(0)) and g(f(0)) step by step:

First, we evaluate g(0) by substituting x = 0 into the function g(x):

g(0) = 4 - 7(0)^2 = 4

Next, we substitute the result g(0) = 4 into the function f(x):

f(g(0)) = f(4) = 3(4) - 1 = 12 - 1 = 11

Now, we evaluate f(0) by substituting x = 0 into the function f(x):

f(0) = 3(0) - 1 = -1

Finally, we substitute the result f(0) = -1 into the function g(x):

g(f(0)) = g(-1) = 4 - 7(-1)^2 = 4 - 7 = -3

Therefore,  we have f(g(0)) = 11 and g(f(0)) = -3. These values are obtained by substituting the appropriate values into the given functions f(x) = 3x - 1 and g(x) = 4 - 7x².

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To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).

Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:

Loss Amount | Probability

$10 million | 0.5%

$1 million | 99.5%

To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.

The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.

The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.

Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:

VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)

VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)

VaR = $50,000 + $995,000

VaR = $1,045,000

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

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

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

point B

Step-by-step explanation:

isolate the x to solve for x:

=> x = 1 - \(\frac{3}{4}\)

=> x = \(\frac{1}{4}\)

point B=> the half of \(\frac{1}{2}\) is \(\frac{1}{4}\)=> \(\frac{1}{2}\) x \(\frac{1}{2}\) = \(\frac{1}{4}\)

Answer:

yes

Step-by-step explanation:

Explanation

To answer this given question, we will make use of the Empirical rule of normal distribution

The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

The image below helps gives a clearer understanding

So in our case, since the mean is 189 mg/dL and the standard deviation is 23

Then we will have the following values at

If I were required to survey Fresno City College students regarding their employment status, I would use a stratified random sampling technique.

Stratified random sampling involves dividing the population into subgroups, or strata, based on certain characteristics that are relevant to the survey. In this case, the relevant characteristic is employment status. The population consists of all Fresno City College students, and the two strata are employed and unemployed students.

Once the population has been divided into strata, a random sample is taken from each stratum. The sample size for each stratum is proportional to the size of the stratum in the population. For example, if 60% of Fresno City College students are employed, then 60% of the sample should consist of employed students.

Using a stratified random sampling technique ensures that the sample is representative of the population and that each subgroup is represented in the sample. It also reduces sampling error and increases the precision of the estimates.

Answer:

-113

Step-by-step explanation:

sub the values

x^3-2y^2-3x^3+z^4

(3)^3-2(5)^2-3(3)+(-3)^4

27-50-9-81

-113

Based on statistical inference from Casella and Berger, the given question's response is,

(a) P(Q(T, θ) ≤ q) = ∫{q': Q(R(q', θ), θ) ≤ q} g(R(q', θ)) * |dR(q', θ)/dq'| dq' ,

(b) \(P(T \leq F_0^{(-1)(u)})\) = u, for 0 ≤ u.

The term "inverse function" refers to an expression that reversed the implications of another function. More exactly, if f(x) is a function that converts every x value in its domain into a distinct value of y, then \(f^{(-1)}(y)\), which is its inverse function, converts every y value in its range into a distinct value of x.

We must demonstrate that the distribution of Q(T, 0) is independent of the unknown parameter θ in order to demonstrate that it is a pivot. By describing the distribution of Q(T, θ) in terms of the distribution of T and a recognised function, we can achieve this.

Q(t, θ) is known to have an inverse function since it is monotone in t for all values of. R(Q(t, θ), θ) = t if R is the inverse function of Q

with respect to.

Next, we have:

P(Q(T, θ) ≤ q) = P(T ≤ R(q, θ)) = ∫{t:Q(t, θ) ≤ q} f(t|θ) dt

Using the variable change t = R(q, θ) in the integral, we get:

P(Q(T, θ) ≤ q) = ∫{q': Q(R(q', θ), θ) ≤ q} f(R(q', θ)|θ) * |dR(q', θ)/dq'| dq'

We know that Q(t, θ) has a derivative θ with regard to t that is non-zero since Q(t, θ) is monotone in t for each value of. As a result, for

every value of, the inverse function R(q, θ) exists and is θ monotone in q. This implies that for all q' and, |dR(q', θ)/dq'| is non-zero.

We now have the following based on the fact that f(t|θ) can be stated in the form (9.2.11):

P(Q(T, θ) ≤ q) = ∫_{q': Q(R(q', θ), θ) ≤ q} g(R(q', θ)) * |dR(q', θ)/dq'| dq'

In terms of the distribution function of T, a known function g, and the inverse function R, this is the distribution function of Q(T, θ). We

can see that Q(T, θ) is a pivot because R is monotone in q and g is a known function.

(b)  Let g = 1 in (9.2.11), so that f(t|θ) = h(t) exp{θt - k(θ)}. Then we have:

\(F_0(t)\) = P(T ≤ t|θ = 0) = h(t) exp{0*t - k(0)} = h(t) exp{-k(0)}

Consequently, we can write:

\(F_0(t)\) = g(Q(t, 0)) = exp{-k(0)}

This results in the following when used in the expression for the distribution function of Q(T, θ) in part (a):

P(Q(T, θ) ≤ q) = ∫{q': Q(R(q', θ), θ) ≤ q} exp{-k(0)} * |dR(q', θ)/dq'| dq'

If we simplify, we get:

P(Q(T, θ) ≤ q) = exp{-k(0)} * ∫{q': Q(R(q', θ), θ) ≤ q} |dR(q', θ)/dq'| dq'

We can get the distribution of using the Probability Integral Transform that

\(F_0(T)\) is uniform on [0, 1]. Therefore, we have:

\(P(F_0(T)\leq u)\) = u, for 0 ≤ u ≤ 1

Using \(F_0\)'s inverse function, we obtain:

\(P(T\leq F_0^{(-1)}(u))\) = u, for 0 ≤ u.

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Answer:

85

Step-by-step explanation:

5×9=45

8×5=40

add it

85

Answer:

2x + 60 - 37.50

x = 6

Answer:

the SSS similarity theorem

Step-by-step explanation:

⇒ It cannot be the SAA similarity theorem as they only share a single common angle

⇒ It cannot be the HL similarity theorem, as the sides are not equal

⇒ It must be the SSS triangles

===========================================================

It states that :

If the lengths of the corresponding sides of two triangles are proportional, then the two triangles are similar.

============================================================

Let's take the sides in proportion :

⇒ 15/5 = 3 (Hypotenuses)

⇒ 6+3/3 = 9/3 = 3 (Heights)

⇒ 8+4/4 = 12/4 = 3 (Bases)

As the sides are in proportion, the triangles are similar by the SSS similarity theorem.

Answer:

34.77

Step-by-step explanation:

The statement "Increasing the step size h in Euler's method generally results in a less accurate estimate of the value y(t_end) that we are looking for" is (b) false because a smaller step size provides a more accurate estimate.

Increasing the step size h used in Euler's method can actually result in a less accurate estimate of the value y(t,end). This is because larger step sizes can lead to increased truncation error and instability in the method. It is generally recommended to use a smaller step size for a more accurate estimate in Euler's method.

A larger step size might not capture the finer details of the function's behavior, leading to more significant errors in the approximation. A smaller step size typically provides a more accurate estimate as it better represents the changes in the function over the interval.

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7 + 7 + 7 + 7 + 7​ means 7 is added 5 times

It could be written as

5(7)

7 x 5 and

7 . 5

But it can not be written as 7^5 because 7^5 means 7 x 7 x 7 x 7 x 7

Hence, 7^5 does not represent the expression 7 + 7 + 7 + 7 + 7​

This makes the correct option to be the third option. That is 7^5

Answer:

T = 4.0 s

Step-by-step explanation:

The period of a simple pendulum is given by

\(period = 2\pi \sqrt{ \frac{l}{g} } \)

where l = length of the pendulum

= 4 m

g = acceleration due to gravity

= 9.8 m/s^2

\(period = 2\pi \sqrt{ \frac{(4 \: m)}{(9.8 \: \frac{m}{ {s}^{2} } )} } = 4.0 \: s\)

Answer:

A. The lowest point of the hammock is at the point 1 meters above the ground and 3 meters from one end of the hammock

B. The two trees are 6 meters away from one another

Step-by-step explanation:

The given equation of the parabola representing the hammock is as follows;

y = 0.4·(x - 3)² + 1

The general equation of a parabola is a·(x - h)² + k;

Where the coordinates of the vertex point of the parabola, which is the lowest (or highest, furthest) point on the vertex is (h, k) = (3, 1)

Therefore, we have;

A, The coordinates of the lowest point on the hammock is (3, 1)

Therefore, the lowest point of the hammock is at 1 meters above the ground and 3 meters from one end of the hammock

B.  Given that the distance from one end is "x", we have;

The height at which the hammock is attached is given as the point where x = 0 as follows;

Given that the vertex of the parabola represents the axis of symmetry of the parabola, we have that the horizontal distance from one end of the hammock to the vertex point of the parabola that the hammock forms is (3 - 0) meters = 3 meters

Therefore, by the definition of symmetry, the distance from the vertex point to the other end of the parabola that the hammock forms is also 3 meters

From which we have, the distance the two trees are from one another is 3 meters + 3 meters = 6 meters.

Answer:

a = 11

Step-by-step explanation:

if A is 7 in the equation A + 4, the it could also be written as 7 + 4.

then it would just be simple addition, because you would add 7 + 4, which equals 11.

Hope this helps!

Answer:

11

Step-by-step explanation:

lest's substitute 7 for a

a + 4

= 7 + 4

= 11

Answer:

A and B

Step-by-step explanation:

-(5/3) = -1.67

-5/3 = -1.67

5/-3 = -1.67

5/3 ≠ -1.67

-5/-3 ≠ -1.67

-(-5/3) ≠ -1.67

The value of n in the global truncation error of the Runge-Kutta method can be determined by taking the number of steps required to reach a certain point.

As the local truncation error is of O(h3), it means that the error in each step is proportional to h3. Therefore, if we take n steps, the total error would be proportional to h3n. Since we are given that the global truncation error is of O(hn), we can conclude that n must be equal to 3.

Based on the information provided, the local truncation error in the Runge-Kutta method is given as O(h^3). The global truncation error is generally one order lower than the local truncation error. Therefore, in this case, the global truncation error in the Runge-Kutta method can be determined as O(h^2), where the value of n is 2.

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The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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The correct answer is b. On average, LinkedIn users would send between 5.48 and 8.72 total messages per year with the new algorithm.

The 95% confidence interval provided by Yue Bing suggests that the true difference in the average number of messages sent per year between the two groups of users (those using the new algorithm and those using the old algorithm) is likely to be between 5.48 and 8.72. This means that we can be 95% confident that the true difference in the average number of messages sent per year falls within this range. It does not necessarily mean that all LinkedIn users will send more or fewer messages with the new algorithm, but rather that the average number of messages sent by users using the new algorithm is likely to be within this range.
Your answer: d. On average, all LinkedIn users would send more messages with the new algorithm than with the old algorithm.

Explanation: Yue Bing computed a 95% confidence interval for the difference between the two parameters, which is (5.48, 8.72) messages per year. Since the entire interval is positive, this indicates that the new recommendation algorithm likely leads to an increase in the average number of messages sent by LinkedIn users compared to the old algorithm.

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Single Factor ANOVA focuses on a comparison of A. more than two population or treatment

The number of populations, or treatments, compared in Single Factor ANOVA is represented by the letter I.

The number of populations, or treatments, compared in Single Factor ANOVA is represented by the letter n_I.

x bar represents the overall mean

x bar i. represents the sample mean of treatment

X bar i,j represents the ith observation in the jth treatment group

Analysis of Variance (ANOVA) is a statistical technique that is used to compare the means of two or more groups. Single factor or one-way ANOVA is used when there is one categorical independent variable and one continuous dependent variable.

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Answer:

Both are correct

Step-by-step explanation:

Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

Given information:

Jared found that  for one equation and substituted  for y in the other equation.

Nicole found  for the one equation and substituted  for x in the other equation.

So, there are two equations. Based on the question, the equation should be,

and .

Now, Jared and Nicole have found the value of one variable from one equation and have put it in the other equation.

This method is the substitution method which is used to find the solution of the system of equations.

Therefore, Jared and Nicole both have found the correct value and will get the same solution to the system of equations.

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Answer: sqrt(61)

Step-by-step explanation:

For parts a) and c1), refer to the attached picture.

For part b), the distance formula is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Using x1 = -1, y1 = -4, x2 = -6, y2 = 2:

d = sqrt[(-6 + 1)^2 + (2 + 4)^2] = sqrt[25 + 36] = sqrt(61)

Part c2) Another way to find the length of AB without using the distance formula is by drawing the line and measuring it according to the scale.

Part d) This will only work as long as the graph paper is accurately made, and the scale computation is done correctly. However, this will only give approximations, and will not give an exact answer when radicals are involved.