Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.

If (-1, -1) is an extremum of [tex]f[/tex], then both partial derivatives vanish at this point.

Compute the gradients and evaluate them at the given point.

[tex]\nabla f = \left\langle y - \dfrac1{x^2}, x - \dfrac1{y^2}\right\rangle \implies \nabla f (-1,-1) = \langle-2,-2\rangle \neq \langle0,0,\rangle[/tex]

[tex]\nabla f = \langle 2x+2,0\rangle \implies \nabla f(-1,-1) = \langle0,0\rangle[/tex]

[tex]\nabla f = \langle y, x-2y\rangle \implies \nabla f(-1,1) = \langle-1,1\rangle \neq\langle0,0\rangle[/tex]

[tex]\nabla f = \left\langle y + \frac1{x^2}, x + \frac1{y^2}\right\rangle \implies \nabla f(-1,1) = \langle0,0\rangle[/tex]

The first and third functions drop out.

The second function depends only on [tex]x[/tex]. Compute the second derivative and evaluate it at the critical point [tex]x=-1[/tex].

[tex]f(x,y) = x^2+2x \implies f'(x) = 2x + 2 \implies f''(x) = 2 > 0[/tex]

This indicates a minimum when [tex]x=-1[/tex]. In fact, since this function is independent of [tex]y[/tex], every point with this [tex]x[/tex] coordinate is a minimum. However,

[tex]x^2 + 2x = (x + 1)^2 - 1 \ge -1[/tex]

for all [tex]x[/tex], so (-1, 1) and all the other points [tex](-1,y)[/tex] are actually global minima.

For the fourth function, check the sign of the Hessian determinant at (-1, 1).

[tex]H(x,y) = \begin{bmatrix} f_{xx} & f_{xy} \\ f_{yx} & f_{yy} \end{bmatrix} = \begin{bmatrix} -2/x^3 & 1 \\ 1 & -2/y^3 \end{bmatrix} \implies \det H(-1,-1) = 3 > 0[/tex]

The second derivative with respect to [tex]x[/tex] is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.

The correct choice is the fourth function.

The solution of the given equation represented in the task content can be determined by first evaluating the LCM and hence is; y= 27.

The given equation is; (y-5)/2=(y+6)/3.

Hence, by multiplying the equation by 6, we have;

3(y-5) = 2(y+6)

3y -15 = 2y +12

y = 27.

Hence, it follows that the value of y which is a solution to the equation is; y = 27.

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Answer:

c

Step-by-step explanation:

Oblique Asymptotes

R(x) will have oblique asymptote if it can be represented in the form

1 / (Q)x

Answer:

The answer is B if the octagon has side lengths of 8

Answer:

(10,10)

Step-by-step explanation:

y = .5x + 5

If you put in 10 for x, we get 10 for y.

y = .5(10) + 5

y =5 + 5

y = 10

When x is 10, y is 10 (10,10)

Based on the given task content about the average hourly rate, Dominique's average hourly rate is $0.26.

Average hourly rate = Regular rate of Dominique's payment ÷ Number of hours worked

= $14 / 54 hours

= 0.25925925925925

Approximately,

Average hourly rate = $0.26

Therefore, Dominique's average hourly rate is $0.26

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Given that the graph shows P as a function of n, we have:

a. The more hot dogs that is sold, his profit increases.

b. Jimmy sells the hot dog for $1 each.

c. Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. He would make a profit of $7.

e. The number of hot dogs he needs to sell is: 20.

A linear  function is expressed as, y = mx + b, where y is a function of x, m is the unit rate, and b is the starting value or initial value of the function.

We are given that profit, P, is a function of the number of hot dogs sold, n.

a. The graph of the function slopes upwards, so this means that the more hot dogs that is sold, his profit increases.

b. Cost of 1 hot dog = Unit rate = change in y / change in x = 2 units/2 units

Cost of 1 hot dog = Unit rate = 1

Thus, Jimmy sells the hot dog for $1 each.

c. If you trace profit (P) on the graph when it is $8, the corresponding number of hot dogs, n, would be 16.

So, Jimmy needs to sell 16 hot dogs to recover the $8 he invested.

d. When n = 15, P, from the graph would be 7.

Thus, if Jimmy sells 15 hot dogs, he would make a profit of $7.

e. When P = 12, from the graph, the corresponding n value is 20.

Therefore for Jimmy to make $12, the number of hot dogs he needs to sell is: 20.

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Answer:

at least $500,000 in sales

Step-by-step explanation:

Answer:

40°

Step-by-step explanation:

Using external angle intercepted arcs calculation:

    50° = 1/2 (210-x)    shows x = 110°

then z = 360 - 210 -110 = 40°

Using the z-distribution, since the p-value of the test is less than 0.01, there is enough evidence to conclude that the claim is correct.

At the null hypothesis, it is tested if there is not enough evidence that the proportion is above 0.5, hence:

[tex]H_0: p \leq 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is above 0.5, hence:

[tex]H_1: p > 0.5[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]n = 825, \overline{p} = \frac{500}{825} = 0.606, p = 0.5[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.606 - 0.5}{\sqrt{0.5(0.5)}{825}}}[/tex]

z = 6.1.

We have a right-tailed test, as we are testing if the proportion is greater than a value. Using a z-distribution calculator, with z = 6.1, the p-value is of 0.

Since the p-value is less than 0.01, there is enough evidence to conclude that the claim is correct.

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Answer:

23 24

it is the answer it is answered

JD Scott I have no idea how to go but she is kind I don't really care about

Answer: a.

Step-by-step explanation:

46 is subtracted by n to get -21 so the equation is 46 - n = -21

Add n on both sides; 46 - n + n = -21 + n; 46 = -21 + n

Add 21 on both sides; 46 + 21 = -21 + n + 21; 67 = n

So n = 67

Answer:

  $152,419.36

Step-by-step explanation:

The future value of an ordinary annuity is given by the formula ...

  FV = P((1 +r/12)^(12t) -1)/(r/12)

where P is the monthly payment, r is the annual interest rate, and t is the number of years.

For P = 350, r = 0.021, and t = 27 (years to retirement age), the value is ...

  FV = 350((1 +0.021/12)^324 -1)/(0.021/12) ≈ $152,419.36

The value of Jolene's retirement account when she turns 60 will be $152,419.36.

Answer:

  20

Step-by-step explanation:

The sides of the 4-sided figure are the same length, so we can find the perimeter (sum of side lengths) by multiplying one side length by 4.

Points F(-2, -2) and G(-2, 3) lie on the same vertical line: x = -2. The distance between them is the difference of their y-coordinates:

  FG = (3 -(-2)) = 5

Each side is 5 units long.

The length of the four sides is ...

  P = 4s = 4(5) = 20

The perimeter of the rhombus is 20 units.

Answer:

18

Step-by-step explanation:

For this problem, you have to look at the ratios of the corresponding sides.

Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18

Step-by-step explanation:

pls make did make sense, darling!!

Answer: 55

Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.

Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.

Thus, we could label the points A, B, and C, and set up an algebraic expression.

Let A = 27, B = 98, and C = x.

A + B + C = 180°.

Substituting A, B, and C we get:

27 + 98 + x = 180°.

Adding, we get:

125 + x = 180°

Subtracting 125 by 180, we get:

x = 55°

Thus, the angle X is 55°.

We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.

The number of times that Greg is on time to class is 4

The given parameters are:

Probability that Greg is on time, p = 14%

The sample size, n = 30

The estimate of the number of times that Greg is on time to class is

E(x) = np

Substitute the known values in the above equation

E(x) = 30 * 13%

Evaluate the product

E(x) = 3.9

Approximate

E(x) = 4

Hence, the number of times that Greg is on time to class is 4

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Answer:

The equation is y=⅗x+⅘

Step-by-step explanation:

First,find the slope of the two pts.

Secondly, apply the equation formula Which is

So, we have to solve for b using one of the two points that are given let's just take the second point (2,2) and solve for b.

Finally, substitute all the values on y=mx+b

Thus, y=⅗x+⅘.

Applying the inscribed angle theorem, the measure of angle BAC is: 110°.

According to the inscribed angle theorem, the measure of angle BAC is half the measure of the intercepted arc, x + 50°.

x - 30 + x + 50 = 360

2x + 20 = 360

2x = 360 - 20

2x = 340

x = 170

m∠BAC = 1/2(x + 50)

Plug in the value of x

m∠BAC = 1/2(170 + 50)

m∠BAC = 110°

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The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.

According to the task content, the equation given; y = -3x +3 is to be written in function notation.

Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;

f(x) = -3x +3.

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(-4, 0)

(-0.667, 0)

(0.5, 0)

Answer:

8

Step-by-step explanation:

i think it's 8 but I'm not sure i will check it for you

Answer:

8

Step-by-step explanation:

because all the number is over 1

The Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².

Given: Physical Properties of the Brass rod exist

Length, L = 250 mm

Radius, R = Diameter / 2 = 25/2 mm

Load of 50 kN hanging on the brass rod which results in elongation of the rod to 0.3 mm.

To estimate the Young Modulus of the brass rod we will require Stress on the rod, Ratio of elongation to the total length.

To find the stress on the rod,

Stress(Pressure) = Force / Area

⇒ Stress = 50,000 / (Area of cross-section)

The rod exists shaped like a cylinder then the area of its cross-section will be πR² ( R = radius)

⇒ Stress = 50000 / (π (25/2 mm)² )

The force exists given in newton, then we must convert the unit of the area into m² to obtain the solution in pascal.

1 mm = 0.001 m

⇒ Stress = 50,000 / 22/7 ( 25/2 × 10⁻³ m)²

take, π = 22/7

⇒ Stress = 50000 / ( 22/7 × 625 / 4 × 10⁻⁶ )

⇒ Stress = 50000 / ( 11/14 × 625 × 10⁻6 )

⇒ Stress = 50000 × 14 × 10⁶ / 625×11

⇒ Stress = 80 × 14 × 10⁶ / 11

⇒ Stress = 1120/11 × 10⁶ Pa

Now, that we maintain Stressed, to estimate Strain (ratio of elongation to original length),

⇒ Strain = (Elongation) / (Original length)

⇒ Strain = 0.3 / 250

⇒ Strain = 3 / 2500

Therefore, Young Modulus, Y = Stress / Strain

⇒ Y = 1120/11 × 10⁶ / 3/2500

⇒ Y = 1120/11 × 2500/3 × 10⁶

⇒ Y = 101.8 × 833.3 × 10⁶

⇒ Y = 84829.94 × 10⁶

⇒ Y ≈ 8.5 × 10¹⁰ Pa

Therefore, the Young Modulus of the brass rod ≈ 8.5 × 10¹⁰ Pa or N/m².

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Answer:

isosceles trapezoind

Step-by-step explanation:

An isosceles trapezoid is a trapezoid with congruent base angles.

A negative slope can be illustrated when a line that is trending downward from left to right, has a negative value.

It should be noted that a negative slope implies that two variables are negatively related.

This implies that when x increases, y decreases, and also when x decreases, y increases.

Graphically, a negative slope implies that as the line on the line graph moves from left to right, the line will fall.

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Answer:

The correct answer is √2 (√√2)

Step-by-step explanation:

√8 = √(4.2) = 2 √2

√√8 = √(2√2) = √2 (√√2)

Answer:

2 √2 (C)

and to the second question the answer is..

1 (B)

9 (C)

Step-by-step explanation:

I answered it on ed 2022