Ernie earned $121.50 more than Kaylin. Tria earned $35 less than 3 times the amount Kaylin earned. Ernie, Tria, and Kaylin earned $579 in all. How much did Tria earn?
$98.50
$220.00
$260.50
$330.50

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Answer:

10/3

Step-by-step explanation:

Keep, change, flip

Keep the first fraction in the equation, change the division symbol to multiplying, and then multiply the first fraction by the reciprocal (opposite) of the second fraction (14/3)

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Answer:

that is spanish for "hello, i like mathimatics"

Step-by-step explanation:

it is

Answer: Do you want a translation? If you do, it says, "Hello, I like Mathematics."

Step-by-step explanation: I know spanish.

Answer:

Step-by-step explanation:

7 blue cars out of 38 cars.

To find the percentage you just divide using your calculator and you should get something like this :

\(\frac{7}{38}\) = 0.1842105263

Then you just round that to the nearest hundredth.

If you round 0.184 to the nearest hundredth, it will be 0.18 (You have to round down since the number 4 in the thousandth place is smaller than 5)

Answer:

I think this should be your answer look at attachment

Step-by-step explanation:

hope this helps

The graph of the given situation is required.

The required graph is attached.

Let x be the cost of each seat

and y be the cost of additional snack.

Cost of seat = $20

Cost of snack = $5

Total cost = $400

The linear equation will be

\(20x+5y=400\)

Finding two points

\(x=0\)

\(5y=400\\\Rightarrow y=\dfrac{400}{5}=80\)

\((0,80)\)

\(y=0\)

\(20x=400\\\Rightarrow x=\dfrac{400}{20}\\\Rightarrow x=20\)

\((20,0)\)

Join the points and the graph representing the situation is obtained.

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The value of x is equal to 1.5.

It is required to find x.

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power. The quadratic formula to solve a quadratic equation ax2 + bx + c = 0 is x = [-b ± √(b2 - 4ac)]/2a.

Given that:

So for the triangle, the perimeter would be:

\((x^{2} +x+3)+(x^{2} +2x-2)+(x^{2} +2x-9)=4\)

By solving in above equation, we get

\((x^{2} +x+3)+(x^{2} +2x-2)+(x^{2} +2x-9)=4\\\\\\\2x^{2}+5x-8=4\\\\2x^{2}+5x-12=0\\\\2(x + 4)(x - 1.5)=0\\\\ x=-4\\\\ x=1.5\)

So, we take x= 1.5 and neglect -4 because we can't take negative roots of the quadratic equation.

Hence, the value of x is equal to 1.5.

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Answer:

i think you need to find the squar rout and you can just do that with a caulator.

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

The distance that you will travel if you will drive at given speed for the following situations are 120 km, 330km, 69km, 60km, and 234km respectively.

Calculating distance involves using the formula:

distance = rate x time

Where "rate" is the speed at which you're traveling, measured in units of distance per unit of time (such as kilometers per hour or miles per minute), and "time" is the duration of your travel in those units of time (such as hours or minutes).

To find the distance, simply multiply the rate by the time. For example, if you're traveling at 60 kilometers per hour for 2 hours, your distance would be:

distance = 60 km/h x 2 h = 120 km

So in this case, you would travel 120 kilometers.

Similarly,

Distance = (Speed) x (Time) = 55 km/h x 6 h = 330 km

Distance = (Speed) x (Time) = 46 km/h x 1.5 h = 69 km

Distance = (Speed) x (Time) = 80 km/h x (45 min/60 min) = 60 km

Distance = (Speed) x (Time) = 78 km/h x 3 h = 234 km

Thus, the distances are 120 km, 330km, 69km, 60km, and 234km respectively.

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Calculate the distance that you will travel is you will

drive for the following situations. Write your answers on a separate sheet of

paper.

1. 3 hours at 40km/h

2. 6 hours at 55km/h

3. 1.5 hours at 46km/h

4. 45 minutes at 80km/h

5. 3 hours at 78km/h​

Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

Mean reversion refers to the tendency of asset prices or economic variables to move back to their average or mean level over time. The mean-reverting level, x1, for a time series can be calculated using statistical methods like moving averages or exponential smoothing. These techniques estimate the average value or trend of the data.



The interpretation of x1 depends on the context. If the current value is above x1, it suggests a potential future decrease, reverting back to x1. Conversely, if the current value is below x1, it indicates a potential future increase, also reverting back to x1. The deviation from x1 provides insights into the strength or speed of the mean reversion process.



Therefore, Mean reversion is the tendency of prices or variables to return to their average level. The mean-reverting level, x1, is calculated using statistical methods and indicates potential future decreases or increases.

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To show that quadrilateral ABCD is a parallelogram, we need to show that both pairs of opposite sides are parallel. Additionally, we could also show that both pairs of opposite angles are congruent or that the diagonals bisect each other.

To show that quadrilateral ABCD is a parallelogram, you need at least one of the following pieces of information:

1. Both pairs of opposite sides are parallel (AB || CD and BC || AD).
2. Both pairs of opposite sides are congruent (AB ≅ CD and BC ≅ AD).
3. One pair of opposite sides are both parallel and congruent (e.g., AB || CD and AB ≅ CD).
4. Both pairs of opposite angles are congruent (angle A ≅ angle C and angle B ≅ angle D).
5. The diagonals bisect each other (AC and BD intersect at their midpoints).

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The number of books published by a small publishing company is 3240.

Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of books be x.

With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.

That is, 44,714+11.50x

With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.

That is, 17,174+20x

Now, the number of books produced will the costs from the two methods be the same.

So, 44,714+11.50x=17,174+20x

⇒ 44,714-17,174=20x-11.50x

⇒ 8.5x = 27540

⇒ x=3,240

Therefore, the number of books published by a small publishing company is 3240.

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This model of federalism ensures that both the national and state governments are equal and that neither has the power to override the other.

The form of federalism favored by Chief Justice Roger Taney was a dual-sovereignty system, in which the national and state governments are seen as distinct entities, providing separate services and limiting the power of the national government.

Taney argued that each government should remain supreme within its own sphere, and that there should be a strict division of authority between the two levels of government.

He argued that the Constitution was a compact between states, each of which had the right to govern itself without interference from the other, and that the Constitution created the federal government only to manage matters that could not be handled by the states.

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Answer:

Step-by-step explanation:

To check for 6 - Number should be Divisible by 2 and 3

4186650 is divisible by 2 % 3

To check for 8 - Las Three digits should be taken as a number and be checked if its divisible my 8

4186650 / 4 = 165.5

So the number is not divisible by 8

To check for 11 - we need to add the odd places and the even places and then subtract them both. if the answer is 11 or 0 then its divisible

4 + 8 + 6 + 0 = 19

1 + 6 + 5 = 12

19 - 12 = 7

So the number is not divisible by 11

Hope you are clear

Answer:

Hey! I believe this is your answer:

4 glasses

Hope this helped!

Step-by-step explanation:

Answer:

k=2

Step-by-step explanation:

Answer:

k=3/4

Step-by-step explanation:

-8k+6=-10k+10k

-8k+6=0

6=8k

8k=6

k=6/8

k=3/4

Answer:

$7.5

Step-by-step explanation:

you just divide 37.50 by 5 to get the price of an individual senior ticket price

The probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

µ = p

The standard deviation of this sampling distribution of sample proportion is:

σ = √p(1-p)/n

The information provided is:

p = 0.14

n = 41

As the sample size is large, i.e n = 411 > 30. the central limit theorem can be used to approximate the sampling distribution of sampling proportion.

Compute the values of P(p^ - p >0.04) as follows:

P(p^ - p < 0.04) = P(p^-p/σ > 0.04/√0.14(1-0.14)/411

= P(Z>2.33)

= 0.990

Thus the probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990

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Answer: yes

Step-by-step explanation: think about it

The appropriate simulation applet to calculate an approximate p-value is 0.0077.

The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.

Delay or no delay, answer: the number of words remembered

The mean distance between words remembered with and without delay over time is null, or zero.

Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.

Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.

The mean distance in words remembered is 1.85.

1)0.0077 as the p-value

2)Strong data suggests that a brief delay impairs memorization.

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Answer:

\(20x^{2} + 12x\)

Step-by-step explanation:

We can expand this equation:

(4x * 5x) + (4x * 3)

= \(20x^{2} + 12x\)

If simplified/factored further, we can take out the common variable, x, as well as 4, which is a common number shared between 20 and 12:

4x(5x + 3)

Answer:

nonlinear

Step-by-step explanation:

It isn't a straight line

Answer:

C. 10 and 3

Step-by-step explanation:

Answer:

\(\triangle ABC \cong \triangle DCB\) by AAS

Step-by-step explanation:

According to the following two triangles, \(\triangle ABC\) and \(\triangle DCB\) are congruent by Angle-Angle-Side (AAS), because there are two angles shown and share a side, which is in the middle between triangles.

Answer: There is 37.7 inches of cone and the cone can hold approximately 37.7 inches of ice cream.

Step-by-step explanation:

V = (π · r² · h) ÷ 3

d = 2r

r = 3

h = 4

(π · 3² · 4) ÷ 3 = 37.69911 (approximately 37.7)

There is 37.7 inches of cone and the cone can hold approximately 37.7 inches of ice cream.

The correct statement proves that parallelogram KLMN is a rhombus.

The slope of KM is 1 and the slope of NL is –1.

A rhombus is a parallelogram whose all sides are equal. Its diagonals perpendicularly bisect each other.

If one line is perpendicular to the other lines then the product of its slope should be -1.

The slope of the KM is;

\(\rm Slope = \dfrac{7-1}{7-1}\\\\Slope=\dfrac{6}{6}\\\\Slope=1\)

The slope of the KM is 1.

And the slope of NL is;

\(\rm Slope =\dfrac{5-3}{3-5}\\\\Slope=\dfrac{2}{-2}\\\\Slope=-1\)

The slope of NL is -1.

Hence, The slope of KM is 1 and the slope of NL is –1.

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Answer:

The correct statement proves that parallelogram KLMN is a rhombus.

The slope of KM is 1 and the slope of NL is –1.

Step-by-step explanation:

Answer:

mQR= 70°

Step-by-step explanation:

\(m\angle \: QPR = \cfrac{QP}{2} \)

\(11x + 2 = \cfrac{24x - 2}{2} = 12x - 1\)

\(12x -11 = 2 + 1\)

\(x = 1\)

Now, let's find the measure of arc QR....

\(mQR = 24x - 2\)

\(24(3) - 2\)

\(=70\)

Therefore, the measure of arc QR is 70°.

Hope this answers your question!