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.

The expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.

According to the task content, it follows that the given expression in the task content is; x⁴z⁵/(xz)⁶.

Hence, the expression can be simplified by means of the laws of indices as follows;

x^(4-6) z^(5-6)

= x-²z-¹

= 1/x²z.

Ultimately, the expression which represents the simplified form of the given expression; x to the 4 power x z to the 5 power over xz to the 6 power as in the task content is; 1/x²z.

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[tex]s(t) = 17699(1 .066) {}^{t} [/tex]

[tex]s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73[/tex]

[tex]s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699[/tex]

[tex]17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years[/tex]

Answer:

The milk would be 60 ml and the topping would be 30 ml

Step-by-step explanation:

If there are 2 parts milk and 1 part toppings that would be a total of 3 (2+1 =3)  So we are looking for 2/3 of 90 and 1/3 of 90.

Answer:its (-2,1), (-6,-15)

Step-by-step explanation:

The absolute value equation that satisfies the solution set shown on the number line is given by:

|x| = 1/2

The absolute value function is defined by:

[tex]|x| = x, x \geq 0[/tex]

[tex]|x| = -x, x < 0[/tex]

It measures the distance from a point x to the origin at x = 0. In this problem, the solution set has a distance to the origin of [tex]\frac{1}{2}[/tex], as |-0.5 - 0| = |0.5 - 0| = 0.5, hence the equation is:

|x| = 1/2

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The savings plan balance after 18 months is $3,730.38

What is an ordinary annuity?

An ordinary annuity means that periodic savings are made at the end of each period unlike an annuity due where payments are made at the beginning of each period.

To determine the savings plan balance after 18 months, we need to make use of the future value formula of an ordinary annuity provided below:

FV=monthly payment*(1+r)^N-1/r

FV=future value after 18 months=unknown

monthly payment=$200

r=monthly interest rate=5%/12=0.00416666666666667

N=number of monthly payments in 18 months=18

FV=$200*(1+0.00416666666666667)^18-1/0.00416666666666667

FV=$200*(1.00416666666666667)^18-1/0.00416666666666667

FV=$200*(1.07771621094479000-1)/0.00416666666666667

FV=$200*0.07771621094479000/0.00416666666666667

FV=$3,730.38

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(a) g(- 4) ≈ - 20.566, g(0) = - 8, g(4) = 4, g(6) = 0, g(8) = - 4

(b) g(x) is increasing in the interval [- 4, 2] and decreasing in the interval [4, 8].

(c) There is an up concavity and a decreasing behavior in the interval [2, 6].

(d) The points x = 2 and x = 6 are points of inflection of g(x).

(e) The equation of the line tangent to g(x) at x = 6 is y = - 4 · x + 24.

(f) The range of g(x) is [- 20.566, 4].

(g) The graph of g(x) is shown in the picture attached below.

In this problem we have a piecewise defined function formed by four functions, a circle-like function and three lines, whose integral has to be analyzed in all its characteristics. (a) The integral is described graphically by the area below the curve, where g(2) = 0 and the following properties of the integral are used:

g(- 4) = g(2) - [F(2) - F(- 4)]

g(- 4) = 0 - 0.25π · 4² - 4 · 2

g(- 4) ≈ - 20.566

g(0) = g(2) - [F(2) - F(0)]

g(0) = 0 - 4 · 2

g(0) = - 8

g(4) = g(2) + [F(4) - F(2)]

g(4) = 0 + 0.5 · (2) · (4)

g(4) = 4

g(6) = g(2) + [F(6) - F(2)]

g(6) = 0 + 0.5 · (2) · (4)  - 0.5 · (2) · (4)

g(6) = 0

g(8) = g(2) + [F(8) - F(2)]

g(8) = 0 + 0.5 · (2) · (4) - (2) · (4)

g(8) = - 4

(b) An interval of g(x) is increasing when f(x) > 0 and decreasing when f(x) < 0. Thus, g(x) is increasing in the interval [- 4, 2] and decreasing in the interval [4, 8].

(c) There is an up concavity and a decreasing behavior in the interval [2, 6].

(d) There are points of inflection for values of x such that f'(x) do not exists. The points x = 2 and x = 6 are points of inflection of g(x).

(e) We need to determine the slope and the intercept of the tangent line to determine the equation of the line:

Slope

m = f(6)

m = - 4

Intercept (x = 6, g(x) = 0)

b = g(x) - m · x

b = 0 - (- 4) · 6

b = 24

The equation of the line tangent to g(x) at x = 6 is y = - 4 · x + 24.

(f) The range of g(x) corresponds to the set of values of y that exists in the function. In accordance with the information given in (a), the range of g(x) is [- 20.566, 4].

(g) The graph of g(x) is shown in the picture attached below.

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Using the z-distribution, the 95% confidence interval for the proportion is given as follows:

(0.4576, 0.5824).

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The other parameters for the interval are given as follows:

[tex]n = 246, \pi = 0.52[/tex].

The lower and upper bound of the interval, respectively, are given by:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 - 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.4576[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.52 + 1.96\sqrt{\frac{0.52(0.48)}{246}} = 0.5824[/tex]

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Using translation concepts, the trigonometric graph is given by:

y = sin(x) + 1 = 1sin(1x) + 1.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent function given in this problem is:

y = sin(x).

The dashed line is a shift up one unit of the parent function, hence the definition is:

y = sin(x) + 1 = 1sin(1x) + 1.

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Answer:

45°

Step-by-step explanation:

it is an inverted angle within a circle

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

Explanation:

Minor arc AD is the shortest path from A to D along the circle's edge. This is 90 degrees. Minor arc AD combines with DC  to get arc ADC

Arc ADC is a semicircle because of the diameter AC. Any semicircle has a measure of 180 degrees.

So,

(minor arc AD) + (minor arc DC) = arc ADC

(minor arc AD) + (minor arc DC) = 180

(90) + (minor arc DC) = 180

minor arc DC = 180 - 90

minor arc DC = 90

AD and DC are 90 degrees each.

Then notice that inscribed angle DAC subtends minor arc DC. Use the inscribed angle theorem to determine angle DAC is 90/2 = 45 degrees

The correct option regarding whether the relation is a function is:

B. The relation is a function. Each input value is paired with one output value.

A relation represent a function if each value of the input is paired with one value of the output.

In this problem, when the input - output mappings are given by:

{(–2, 3), (–1, 3), (0, 2), (1, 4), (5, 5)}.

Which means that yes, each input value is paired with one output value, hence the relation is a function and option B is correct.

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The total product cost per unit.

TPC= $33

This is further explained below.

Generally, The direct materials cost per unit, the direct labor cost per unit, the variable overhead cost per unit, and the fixed overhead cost per unit make up the total product cost per unit.

The total costs of the product may be calculated by adding up the costs of all of the direct materials, all of the direct labor and all of the overhead expenses of the production process. 1 Information such as the cost of manufacturing on a per-unit basis may assist a company in determining an acceptable selling price for the final product.

Generally, the equation for total product cost per unit. is  mathematically given as

TPC= 20 + 10 + 2 + 1

TPC= $33

In conclusion, the total product cost per unit.

TPC= $33

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Answer:

$33

Step-by-step explanation:

Part A - The average value of v(t) over the interval  (0, π/2) is 6/π

Part B -  The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

The average value of a function f(t) over the interval (a,b) is

[tex]f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx[/tex]

So, since  velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval  (0, π/2) is given by

[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt[/tex]

Since v(t) = 3cost, we have

[tex]v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}[/tex]

So, the average value of v(t) over the interval  (0, π/2) is 6/π

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

The total distance the yo-yo travels from time t = 0 to time t = π is given by

[tex]x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6[/tex]

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

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Answer: -4.73, -1.27

Step-by-step explanation:

[tex](x+3)^2 =3\\\\x+3=\pm \sqrt3\\\\\\x=-3 \pm \sqrt3\\\\x \approx -4.73, -1.27[/tex]

By changing the central angle, ∠CAB, the inscribed angle, ∠CDB has the following data sets:

m∠BAC (β)                                m∠BDC (α)

42°                                               84°

40°                                               80°

45°                                               90°

35°                                               70°

52°                                               104°

A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

In Geometry, a circle is considered to be a conic section which is formed by a plane intersecting a double-napped cone that is perpendicular to a fixed point (central axis) because it forms an angle of 90° with the central axis.

The inscribed angle theorem states that the measure of an inscribed angle is one-half the measure of the intercepted arc in a circle. Thus, this is given by this mathematical expression:

m∠BDC = ½ × m∠BAC.

For this exercise, we would change the central angle, ∠CAB, so that the inscribed angle, ∠CDB can have the following data sets:

m∠BAC (β)                                m∠BDC (α)

42°                                               84°

40°                                               80°

45°                                               90°

35°                                               70°

52°                                               104°

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Answer:

plato

Step-by-step explanation:

m∠BAC m∠BDC

50° 25°

70° 35°

90° 45°

125° 62.5°

150° 75°

Answer:

59

Step-by-step explanation:

Suppose, The number of seats in each row = z

Number of rows = number of seats in each row 7 z

So, the total plants = z×z=z^2

As per question,

z^2=3481

z=59

So the seats in each row = 59.

-0.81 has negative direction and o.81 is the magnitude, 0.40 has  positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude

A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

-0.81

Minus zero point eight one has negative direction and o.81 is the magnitude

0.40

zero point four zero has positive direction and 0.40 is the magnitude

0.15

Zero point one five has positive direction and 0.15 is the magnitude

-0.08

Minus zero point zero eight has negative direction and 0.08 is the magnitude

0.29

Zero point two nine has positive direction and 0.29 is the magnitude

Hence -0.81 has negative negative direction and o.81 is the magnitude, 0.40 has  positive direction and 0.40 is the magnitude, 0.15 positive direction and 0.15 is the magnitude, -0.08 has negative direction and 0.08 is the magnitude and 0.29 has positive direction and 0.29 is the magnitude

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Answer:

Zachary weights 95.7 pounds

Answer: [tex]48\pi[/tex]

Step-by-step explanation:

[tex](2 \times 24)\pi=48\pi[/tex]

Answer: 0

Step-by-step explanation:

Substituting in x=0, we get

[tex]\frac{0(0-2)}{2-2e^{2}(0)}=0[/tex]

The function f(x) = x² then the required function exists g(x) = -x²- 4.

The function exists described as y = f(x).

In mathematics, a function from a set X to a set Y allocates to each element of X exactly one element of Y. The set X exists named the domain of the function and the set Y exists named the codomain of the function. Functions stood originally for the idealization of how a variable quantity relies on another quantity.

For every x there exists a certain value of y.

From the graph g(x) exists reflection of f(x) at y = -4.

So g(x) = -f(x) - 4, the negative sign for reflection.

g(x) = -x² - 4

The required function exists g(x) = -x² - 4.

Therefore, the correct answer is option D. g(x) = -x² - 4.

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The complete question is:

F(x) = x². What is g(x)?

A. g(x) = x² - 4

B. g(x) = x² + 4

C. g(x) = -4x²

D. g(x) = -x² - 4

Answer:

  459

Step-by-step explanation:

The "long division method" algorithm for square root makes use of the relation described by the square of a binomial.

  (a +b)² = a² +2ab +b² = a² +b(2a +b)

The value for which the root is desired is written with digits marked off in pairs either side of the decimal point.

The initial digit of the root is the integer part of the square root of the most-significant pair. Here that is floor(√21) = 4. This is shown in the "quotient" spot above the leftmost pair. The square of this value is subtracted, and the next pair brought down for consideration. Here, that means the next "dividend" is 506.

The next "divisor" will be 2 times the "quotient" so far, with space left for a least-significant digit. Here, that means 506 will be divided by 80 + some digits. As in regular long division, determining the missing digit involves a certain amount of "guess and check." We find that the greatest value 'b' that will give b(80+b) ≤ 506 is b=5. This is the next "quotient" digit and is placed above the "dividend" pair 06. The product 5(85) = 425 is subtracted from 506, and the next "dividend" pair is appended to the result. This makes the next "dividend" equal to 8181.

As in the previous step, the next "divisor is 2 times the quotient so far: 2×45 = 90, with space left for the least significant digit. 8181 will be divided by 900-something with a "quotient" of 9. So, we subtract the product 9(909) = 8181 from the "dividend" 8181 to get the next "dividend." That result is zero, so we're finished.

The root found here is 459.

__

Additional comment

In practice, roots are often computed using iterative methods, with some function providing a "starter value" for the iteration. Some iterative methods can nearly double the number of good significant digits in the root at each iteration.

Using this "long division method," each "iteration" adds a single significant digit to the root. Its advantage is that it always works, and is generally suitable for finding roots by hand. Once the number of root digits begins to get large, the "divisor" starts to be unwieldy.

Answer:

hcf is 2*5=10

lcm is 2*2*2*5*3*7*3

Answer:

35,000 - 8000=27,000 altitude

Answer:

- [tex]\sqrt{2}[/tex]

Step-by-step explanation:

cos90° - 2sin45° + 2tan180°

= 0 - ( 2 × [tex]\frac{\sqrt{2} }{2}[/tex] ) + 2(0)

= 0 - [tex]\sqrt{2}[/tex] + 0

= - [tex]\sqrt{2}[/tex]

Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.

Given the data in the question;

To determine the bundle of steel required, let y represent the bundle.

Since;

1 bundle = 8 piece

y bundle = 98 piece

We cross multiply

y bundle × 8 piece = 1 bundle × 98 piece

y = ( 1 bundle × 98 piece ) / ( bundle ×  8 piece  )

y = 98 pieces / 8 piece

y = 12.25 ≈ 13

Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.

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The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².

In this problem we have a quadratic equation in standard form, whose form is defined by f(x) = a · x² + b · x + c, where a, b, c are real coefficients, and we need to transform it into vertex form, defined as:

f(x) - k = C · (x - h)²       (1)

Where:

This latter form can be found by algebraic handling. If we know that f(x) = 2 · x² - 20 · x + 8, then its vertex form is:

f(x) = 2 · x² - 20 · x + 8

f(x) = 2 · (x² - 10 · x + 4)

f(x) + 2 · 25 = 2 · (x² - 10 · x + 25)

f(x) + 75 = 2 · (x - 5)²

The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².

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Answer:

below

Step-by-step explanation:

1) 4 < 7

28 < 49

168 < 294

1680 < 2940

2) 11 > -2

16 > 3

19 > 6

15 > 2

3) -4 < -2

-10 < -8

-18 < -16

-20 < -18

4) -8 < 8

2 > -2

-1 < 1

5) When you multiply by a negative number, the inequality sign flips.

The probability that the mean fill is more than 84.8 ounces is 0.39358

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (84.8 - 84.5)/1.1

Evaluate the difference of 84.8 and 84.5

z = 0.3/1.1

Evaluate the quotient of 0.3 and 1.1

z = 0.27

The probability that the mean fill is more than 84.8 ounces is then calculated as:

P(x > 84.8) = P(z > 0.27)

From the z table of probabilities, we have;

P(x > 84.8) = 0.39358

Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358

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