Marina's bill for dinner totals 38.65, including tax. She leaves a 20% tip . If she pays with a 100$ bill, how much change will Marina recieve

Answer:

No

Step-by-step explanation:

A function can have only  output for each input.  The input 3 has two outputs 3 and 5.  

The input 4 has two outputs 4 and 6.

Answer:

This correlation simply means that, in every twin whether identical or fraternal twins, there is a relation between their IQ scores and when they are raised together.

Regarding to the test carried out, it showed that, when an identical twin is raised together, their IQ score tends to be higher in direct comparison with a fraternal twin that was raised together. That is, if the fraternal twin IQ is 100, then, the identical twin IQ is going to be above 100 (probably around 120)

Step-by-step explanation:

The independent variable for Scenario A is given as follows:

a. The employee benefits package.

In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:

In the context of this problem, we have that the input and the output of the relation are given as follows:

Hence the independent variable for Scenario A is given as follows:

a. The employee benefits package.

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Answer:

\( {5}^{2} \)

Step-by-step explanation:

\(\frac{5^6}{5^4}=5^{6-4}=5^2\)

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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The coordinates of X that partitions XY in the ratio 5 to 4 include the following: X (-1.6, -7).

In this scenario, line ratio would be used to determine the coordinates of the point X on the directed line segment AB that partitions the segment into a ratio of 5 to 4.

In Mathematics and Geometry, line ratio can be used to determine the coordinates of X and this is modeled by this mathematical equation:

M(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

By substituting the given parameters into the formula for line ratio, we have;

M(x, y) = [(5(2) + 4(-6))/(5 + 4)],  [(5(-11) + 4(-2))/(5 + 4)]

M(x, y) = [(10 - 24)/(9)],  [(-55 - 8)/9]

M(x, y) = [-14/9],  [(-63)/9]

M(x, y) = (-1.6, -7)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

a) In standard form, the simplified expression is 1.176 x \(10^{6}\). b) The solution to the simultaneous equations is x = 2 and y = 11. c) The solution to the double inequality -5 < 2x + 3 < 7 is -4 < x < 2.

a) To simplify the expression (2.8 x \(10^{3}\)) x (4.2 x \(10^{2}\)), we can multiply the coefficients and add the exponents.

(2.8 x \(10^{3}\)) x (4.2 x \(10^{2}\)) = (2.8 x 4.2) x (\(10^{3}\) x \(10^{2}\))

= 11.76 x \(10^{3+2}\)

= 11.76 x \(10^{5}\)

In standard form, the simplified expression is 1.176 x \(10^{6}\).

b) To solve the pair of simultaneous equations:

{8x - 2y = -6

{3x + y = 17

We can use the method of substitution or elimination to find the solution.

Let's use the elimination method by multiplying the second equation by 2 to eliminate the y variable:

{8x - 2y = -6

{6x + 2y = 34

Adding the two equations together, we get:

14x = 28

Dividing both sides by 14, we find:

x = 2

Substituting the value of x into the second equation:

3(2) + y = 17

6 + y = 17

Subtracting 6 from both sides, we have:

y = 11

Therefore, the solution to the simultaneous equations is x = 2 and y = 11.

c) To solve the double inequality:

-5 < 2x + 3 < 7

We can solve it by treating it as two separate inequalities:

-5 < 2x + 3 and 2x + 3 < 7

Solving the first inequality:

-5 - 3 < 2x

-8 < 2x

Dividing both sides by 2 (since the coefficient is positive), we get:

-4 < x

For the second inequality:

2x + 3 < 7

Subtracting 3 from both sides, we have:

2x < 4

Dividing both sides by 2 (since the coefficient is positive), we find:

x < 2

Therefore, the solution to the double inequality -5 < 2x + 3 < 7 is -4 < x < 2.

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Step-by-step explanation:

We would do multiplication first, because of order of operations.

2x3=6

Now we add.

6+4=10

hope it helps! :3

Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

The directional derivative of f at point (3,4) in the direction of the unit vector determined by the angle θ = 2π/5 is approximately -29.13

To find the directional derivative of f(x,y) = -2x^2 + 4y^2 at point (3,4) in the direction of the unit vector determined by the angle θ = 2π/5, we need to first find the unit vector u in the direction of θ.

The unit vector u can be found as:

u = (cos θ, sin θ) = (cos (2π/5), sin (2π/5))

Using the formula for directional derivative, the directional derivative of f at point (3,4) in the direction of u can be calculated as:

D_u f(3,4) = ∇f(3,4) · u

where ∇f(3,4) is the gradient of f at point (3,4), which can be found as:

∇f(x,y) = (-4x, 8y)

So, ∇f(3,4) = (-12, 32)

Substituting these values, we get:

D_u f(3,4) = (-12, 32) · (cos (2π/5), sin (2π/5))

Using a calculator, we can evaluate this dot product as:

D_u f(3,4) ≈ -29.13

Therefore, the directional derivative of f at point (3,4) in the direction of the unit vector determined by the angle θ = 2π/5 is approximately -29.13

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Answer:

Using point-slope form we get:

y - 6 = 1/3(x + 6)

y - 6 = 1/3x + 2

y = 1/3x + 8

Answer:

Function B

Step-by-step explanation:

Your question is incomplete but Function B is a linear equation. The equation would be f(x)=\(\frac{5}{3}\)x

the slope is always rise over run (difference of y / difference of x).

Your second question is incomplete.

The solution of the given linear system of equations is x = 2, y = 1 and z = 2.

Given that the linear system of equations is

2x + 4y + 2z = 16-2x - 3y + z = -52x + 2y - 3z = -3

To solve the system of equations by Cramer's rule method, arrange them in the form of Ax = B as below:

A = [2, 4, 2; -2, -3, 1; 2, 2, -3], x = [x, y, z] and B = [16, -5, -3]

To find the inverse of the coefficient matrix A⁻¹, first, find the determinant of A as below:

|A| = 2[-3 - 2] - 4[-2 + 2] + 2[-8 + 1] = -12

The determinant is non-zero, hence A is invertible

A⁻¹ = 1/|A| [adj A]

where adj A is the transpose of the cofactor matrix [C] of A:

adj A = [C]T

So, we find [C] by replacing each element of A with its cofactor and taking its transpose matrix as below:

C = [5, 2, 6; 2, -2, 2; -4, -4, -4]

Then [C]T = [5, 2, -4; 2, -2, -4; 6, 2, -4]So, A⁻¹ = 1/|A| [adj A] = 1/(-12) [5, 2, -4; 2, -2, -4; 6, 2, -4] = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2]

To solve the system of equations, we have x = A⁻¹B as below:

x = [-5/6, -1/2, 1/2; -1/6, 1/2, 1/2; 1/2, 1/2, 1/2][16; -5; -3] = [2; 1; 2]

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9514 1404 393

Answer:

  1. B, E

  2. A, E

  16. B'(1, 5)

Step-by-step explanation:

Lines p and r are parallel, as are lines a and b. Either of the lines in one parallel pair is perpendicular to the lines in the other parallel pair. Line q has no necessary relation to anything, so can be ignored. (No answer containing q can be correct.)

__

1.  p ⊥ b

  r ⊥ a

__

2.  r║p

  a║b

__

16. Point B(3, 2) translated (right, up) = (-2, 3) will be ...

  B' = B + (-2, 3) = (3, 2) +(-2, 3) = (3 -2, 2 +3)

  B' = (1, 5)

Note: (x, y) coordinates are (right, up). So, in translation problems it is important to pay attention. Often, the up/down translation is listed before the left/right translation. If you're not paying attention, you may inadvertently reverse the numbers that need to be added to the coordinates to do the translation.

Answer:

i already solved the step by step explanation, ask someone else to draw the graph for u

Step-by-step explanation:

• y = cos(Θ) + sin(Θ)

Prediction: The graph of this equation will be a sinusoidal wave with an amplitude of √2 and a period of 2π. It will intersect the y-axis at y = √2 and have a minimum value of -√2 at Θ = 3π/4 and a maximum value of √2 at Θ = π/4.

Graph:

Graph of y=cos(Θ) + sin(Θ)

The graph confirms our prediction.

• y = cos2(Θ)

Prediction: The graph of this equation will be a cosine wave squared, which means it will have the same period as the cosine function but its amplitude will be squared. It will intersect the y-axis at y = 1 and have a minimum value of 0 at Θ = π/2 and Θ = 3π/2.

Graph:

Graph of y=cos2(Θ)

The graph confirms our prediction.

• y = sin2(Θ)

Prediction: The graph of this equation will be a sine wave squared, which means it will have the same period as the sine function but its amplitude will be squared. It will intersect the y-axis at y = 0 and have a minimum value of -1 at Θ = π/2 and a maximum value of 1 at Θ = 3π/2.

Graph:

Graph of y=sin2(Θ)

The graph confirms our prediction.

• y = cos2(Θ) + sin2(Θ)

Prediction: This equation represents the identity cos2(Θ) + sin2(Θ) = 1, so the graph of this equation will simply be a horizontal line at y = 1.

Graph:

Graph of y=cos2(Θ) + sin2(Θ)

The graph confirms our prediction.

The best answer would be 213.

Assuming that the sign denotes summation, we are adding from k=4 to k=9.

To get, we change k=4 to k=9.

We simplify obtaining,

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

Summarizing mainly entails entering the values k=4, 5, 6, 7, 8, and 9 into the formula section 5K+3 and adding them all together.

So, the result is:

(5(4)+3)+(5(5) + 3) + (5(6) + 3) + (5(7) +3) + (5(8) + 3) + (5(9) + 3) 23+28+33 +38+43 + 48

= 213

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Answer:

1

Step-by-step explanation:

logic

There are a total of 2626 permutations of the 26 letters. We need to subtract the number of permutations that contain the sequences ROCK, STONE, PLUG, FIT, or HAY.

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Answer:

-5

Step-by-step explanation:

\(\frac{12}{6} + 5 - 4(6) + 12 = -5\)

Have a great day :)

Alisha can choose either shop based on personal preference or other factors like turnaround time or quality of service, as both options have the same charge for her order of 120 T-shirts.

Let's define the variables for the two print shops:

- For Smith's T-Shirt Shop:

 - Let x be the number of T-shirts ordered.

 - Let S(x) be the total charge from Smith's T-Shirt Shop.

- For Brilliant Print Shop:

 - Let y be the number of T-shirts ordered.

 - Let B(y) be the total charge from Brilliant Print Shop.

Now let's write the functions for the total charges:

For Smith's T-Shirt Shop:

- For 0 ≤ x ≤ 100: S(x) = 12x

- For 101 ≤ x ≤ 200: S(x) = 10x

- For x ≥ 201: S(x) = 8x

For Brilliant Print Shop:

- For 1 ≤ y ≤ 100: B(y) = 200 + 14y

- For 101 ≤ y ≤ 200: B(y) = 10y

- For y ≥ 201: B(y) = 8y

To compare the two options, let's evaluate the charges for Alisha's order of 120 T-shirts:

For Smith's T-Shirt Shop:

- For 101 ≤ x ≤ 200: S(120) = 10 * 120 = $1,200

For Brilliant Print Shop:

- For 101 ≤ y ≤ 200: B(120) = 10 * 120 = $1,200

Both shops charge the same amount for 120 T-shirts, which is $1,200. Therefore, Alisha can choose either shop.

Now let's compare the key features of the graphs of the functions for both shops:

Smith's T-Shirt Shop:

- Initial Value: The total charge starts at $0 when no T-shirts are ordered.

- End Behavior: As the number of T-shirts ordered increases, the total charge decreases. The rate of decrease changes at 100 and 200 T-shirts.

Brilliant Print Shop:

- Initial Value: The total charge has a flat fee of $200 when ordering 1-100 T-shirts.

- End Behavior: As the number of T-shirts ordered increases, the total charge decreases. The rate of decrease changes at 100 and 200 T-shirts.

Both shops have different pricing structures, but they both decrease the total charge as the number of T-shirts ordered increases. Smith's T-Shirt Shop has a tiered pricing structure, while Brilliant Print Shop has different rates for different ranges. The key difference is that Brilliant Print Shop has a flat fee for the first range of T-shirts (1-100).

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Answer:  1.166666... the 6s go on forever

When rounded to say four decimal places, then we'd get 1.1667

We can write that as  \(1.166666\ldots = 1.1\overline{6}\)

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

Explanation:

The quick way to get the answer is to type 7/6 into your calculator, or 7÷6, and you should get 1.1667 approximately. The reality is that the "6"s go on forever. But at some point, we have to round.

When writing \(1.166666\ldots = 1.1\overline{6}\) the horizontal bar tells us which digit goes on forever.

If you want to do this by long division, then check out the work shown below.

Let u = 3√3 and v = 4√3. Since u and v are fixed, a triangle can only exist if we find a line segment that is less than the sum of u and v and greater than the difference of u and v.

The triangle inequality is defined by the formula that states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let w be the third leg of the triangle, which is not fixed. The inequality is as follows:

w + u > vw + v > uw + w > u - v > -v - u > -u - w > -v - w

Because we know that angle W is 30 degrees, we may utilize the law of cosines, which is defined as:

a² = b² + c² - 2bc cos(A)

We may use the law of cosines to solve for a given angle or side in the triangle. The angle opposite u is W, thus:

a² = u² + v² - 2uv cos(W)a² = (3√3)² + (4√3)² - 2(3√3)(4√3) cos(30)a² = 36 + 48 - 72a² = 12a = 2√3We can use the law of sines to determine the remaining side of the triangle, as follows:

a/sin(A) = b/sin(B) = c/sin(C)A = 30°, B = C = 75°a/sin(30) = b/sin(75) = c/sin(75)a = (2√3) / (1/2) = 4√3b = (4√3) / sin(75) = 4√3 / ( √6 + √2 ) = (√6 - √2) 4c = (4√3) / sin(75) = 4√3 / ( √6 + √2 ) = (√6 - √2) 4

The only triangle that can exist is the one that has sides 2√3, 4√3/(√6 + √2), and 4√3/(√6 - √2). This triangle has angles of 30 degrees, 75 degrees, and 75 degrees, which is not a right triangle.

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Answer:

Graph in the image above

Step-by-step explanation:

Answer: The answer is C. ( 6, -5)

Step-by-step explanation:

Check the picture below.

so the area of it, is really the area of a 16x16 square and four triangles with a base of 16 and a height of 15.

\(\stackrel{ \textit{\LARGE Areas}}{\stackrel{ square }{(16)(16)}~~ + ~~\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(16)(15) \right]}}\implies 256~~ + ~~480\implies \text{\LARGE 736}~cm^2\)

Answer:

elevation of –200 feet  

below sea level

Step-by-step explanation

600-800=-200

The z-scores that bound the middle 66% of the area under the standard normal curve are -0.43 and 0.43.

To find the z-scores that bound the middle 66% of the area under the standard normal curve using the TI-84 Plus calculator, you can follow these steps:

1. Turn on the calculator and press the "2nd" button, followed by "Vars" to access the DISTR menu.

2. Scroll down to "2: normalcdf(" and press enter.

3. Enter the lower bound of the middle 66% (left tail) as 0.17 (since 50% - 33% = 17%) and press comma ",".

4. Enter the upper bound of the middle 66% (right tail) as 0.83 (since 50% + 33% = 83%) and press comma ",".

5. Enter 0 for the mean and 1 for the standard deviation (since we are working with the standard normal distribution) and press enter.

The calculator will calculate the area under the standard normal curve between the given z-scores.

The z-scores that bound the middle 66% of the area under the standard normal curve are approximately -0.43 and 0.43 (rounded to two decimal places).

Therefore,To find the z-scores that bound the middle 66% of the area under the standard normal curve using the TI-84 Plus calculator, you can follow these steps:

1. Turn on the calculator and press the "2nd" button, followed by "Vars" to access the DISTR menu.

2. Scroll down to "2: normalcdf(" and press enter.

3. Enter the lower bound of the middle 66% (left tail) as 0.17 (since 50% - 33% = 17%) and press comma ",".

4. Enter the upper bound of the middle 66% (right tail) as 0.83 (since 50% + 33% = 83%) and press comma ",".

5. Enter 0 for the mean and 1 for the standard deviation (since we are working with the standard normal distribution) and press enter.

The calculator will calculate the area under the standard normal curve between the given z-scores.

The z-scores that bound the middle 66% of the area under the standard normal curve are approximately -0.43 and 0.43 (rounded to two decimal places).

Therefore, the z-scores that bound the middle 66% of the area under the standard normal curve are -0.43 and 0.43.

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