Differentiate implicitly to find dy/dx. Then find the slope of the curve at the given point. y^2 - x^3 = 28; (2, - 6) The slope of the graph at the given point is. (Type an integer or a simplified fraction.)

Answer:

18

Step-by-step explanation:

Answer:

18 pounds

Step-by-step explanation:

5x 3 3/5= 18

The value of the standard Deviation of Z rounded to the nearest tenth is 2.9.

Let's first find the mean of ZLet Z = 7X - 3Y

Therefore, E(Z) = E(7X - 3Y) = 7E(X) - 3E(Y)

We know that X ~ Uniform(5, 10) and Y ~ Uniform(3, 8)E(X) = (a + b) / 2 = (5 + 10) / 2 = 7.5E(Y) = (a + b) / 2 = (3 + 8) / 2 = 5.5Therefore,E(Z) = 7E(X) - 3E(Y) = 7(7.5) - 3(5.5) = 26

Now, let's find the variance of Z:Var(Z) = Var(7X - 3Y) = 49Var(X) + 9Var(Y)

(because X and Y are independent)We know that X ~ Uniform(5, 10) and Y ~ Uniform(3, 8)Var(X) = (b - a)^2 / 12 = (10 - 5)^2 / 12 = 25 / 12Var(Y) = (b - a)^2 / 12 = (8 - 3)^2 / 12 = 25 / 12

Therefore, Var(Z) = 49Var(X) + 9Var(Y) = 49(25 / 12) + 9(25 / 12) = 25(49 + 9) / 12 = 100Var(Z) = 100 / 12 = 25 / 3

Now, the standard deviation of Z = √(Var(Z))= √(25/3)= 5/√3 ≈ 2.89

Hence, the value of the standard deviation of Z rounded to the nearest tenth is 2.9.

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Step-by-step explanation:

21 ÷ 6 = $ 3. 50 each

I hope this answers your question

Answer:

The price for one comic book is $3.5

When the base, b, is greater than 1, the function y = a bˣ models exponential growth, while when the base, b, is between 0 and 1, the function models exponential decay

The function y = a.bˣ represents exponential growth or decay depending on the value of the base, b.

Exponential Growth:

When the base, b, is greater than 1 (b > 1), the function y = a.bˣ represents exponential growth. In this case, as x increases, the value of b^x also increases, resulting in a corresponding increase in y. The factor of b amplifies the growth, causing the function to grow at an accelerating rate.

For example, if b = 2, then y = a × 2^x represents exponential growth, where the function doubles with each unit increase in x. As x gets larger, the value of y grows at an increasing rate.

Exponential Decay:

When the base, b, is between 0 and 1 (0 < b < 1), the function y = a×bˣ represents exponential decay. In this case, as x increases, the value of bˣ decreases, resulting in a corresponding decrease in y. The factor of b causes the function to decay or decrease at a diminishing rate.

For example, if b = 0.5, then y = a × 0.5ˣ represents exponential decay, where the function halves with each unit increase in x. As x gets larger, the value of y decreases at a decreasing rate.

In summary, when the base, b, is greater than 1, the function y = a bˣ models exponential growth, while when the base, b, is between 0 and 1, the function models exponential decay.

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The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.

To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:

First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.

Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.

The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.

The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.

The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.

Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:

V = ∫[a, b] 2πrh dy

Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).

Substituting t

he values of r and h into the integral, we have:

V = ∫[0, 9] 2πy(y) dy

Simplifying, we get:

V = 2π ∫[0, 9] y^2 dy

Evaluating the integral, we have:

V = 2π [y^3/3] from 0 to 9

V = 2π [(9^3/3) - (0^3/3)]

V = 2π [(729/3) - 0]

V = 2π (243)

V = 486π

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This question is a simultaneous equation having a quadratiic equation above and a linear equation below.

substitute the value of y in equation 2 for y in equation 1

recall y = 2x + 10 ( equation 2 )

2x + 10 = x2 - 3x -4 ( since y = 2x + 10 )

Having gotten the two values of x, we see that -2 is in the x position in the options given to us but 7 was ignored. Therefore we shall use x = -2 to find the value of y in equation 2

Recall, y = 2x + 10 ( equation 2 )

thus, y = 2 ( -2 ) + 10 ( since x = -2 )

hence, y = -4 + 10 ( since 2 x -2 = _4 )

so, y = +6

finally, x = -2 and y = 6. the best coordinate is ( -2, 6 )

Answer:

y=7x, y=-5x, y=24x, y=-2x

Step-by-step explanation:

7. each of the Xs multiplied by 7 is the Y, so y=7x

8. the function is inverse, so we can assume that x is negative, and after we multiply the x by -1, we find that the rule is multiply by 5, so y=-5x

9.   looking again at the pattern, we can find that x * 24 is the y, so y=24x

10. again, the function is inverse so x is negative, and the pattern is multiplying by 2, so y=-2x

Answer:

Step-by-step explanation:

The loop will run an infinite number of times

The probability that a sample will contain 2 or fewer nonconforming units, using the Poisson distribution with an average of 1.6, is approximately 0.602.

To calculate the probability that a sample will contain 2 or fewer nonconforming units, we can use the Poisson distribution. The Poisson distribution is commonly used to model the probability of rare events occurring over a fixed interval or in a given sample.

The formula for the Poisson distribution is:

P(X = k) = (e^(-λ) * λ^k) / k!

where λ is the average number of

units.

In this case, the average number of nonconforming units is 1.6. We want to find the probability of having 2 or fewer nonconforming units, which means we need to calculate:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Using the Poisson distribution formula, we can substitute the values:

P(X ≤ 2) = (e^(-1.6) * 1.6^0) / 0! + (e^(-1.6) * 1.6^1) / 1! + (e^(-1.6) * 1.6^2) / 2!

Calculating this expression, we find:

P(X ≤ 2) ≈ 0.602

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Answer:

4(n-6)

Step-by-step explanation:

4(n-6)

n stands for number

quantity means you have to use parenthesis

Answer:

Answer is 5 inches on edg

Step-by-step explanation:

Answer:

The correct answer would be 5 inches.

Step-by-step explanation:

Answer:

Draw a line going down from the 300, with a break in the middle and finish it out at the 6 hr mark.

Step-by-step explanation:

Start at the 300 and draw that line down to the 180 mark lined up with the 2 hour dot. Then draw a horizontal line from there to the middle of the 2 and the 4. Then draw a line from where you ended the break with the same slope as the beginning.

Hope this helps!

Answer:

\(1 - {.32}^{5} = .9966 = 99.66\%\)

Answer:

Question 1 = 4.90

Question 3 = 9.28

Question 7 = 35.00

The price per unit that will yield maximum revenue is $67.04.

In order to find the price per unit that will yield maximum revenue, we have to follow the below-given steps:

Step 1: The revenue function for x units of a product is

R(x) = x * P(x),

where P(x) is the price per unit of the product.

Step 2: The demand function is

D(x) = 170e^(-0.04x)

Step 3: We are given that the 0 ≤ x ≤ 55, it means that we only need to consider this domain. Also, the price per unit of the product is unknown. Let's take it as P(x). Hence, the revenue function will be:

R(x) = P(x) * xR(x) = x * P(x)

Step 4: We need to find the price per unit that will yield maximum revenue. In order to do that, we have to differentiate the revenue function with respect to x and find its critical point. Let's differentiate the revenue function.

R'(x) = P(x) + x * P'(x)

Step 5: Now we will replace P(x) with D(x) / x from the demand function to obtain a function that depends on x only.

This will give us R(x) = x * (D(x) / x).

Simplifying this expression, we get R(x) = D(x).

Let's write it. R(x) = D(x)R'(x) = D'(x)

Step 6: Differentiate D(x) with respect to x, we get:

D'(x) = -6.8e^(-0.04x)

Step 7: To find the critical point of R(x), we will equate R'(x) to zero and solve for x.

R'(x) = 0D(x) + x * D'(x) = 0

Substitute D(x) and D'(x)D(x) + x * D'(x) = 170e^(-0.04x) - 6.8x * e^(-0.04x) = 0

Divide both sides by e^(-0.04x)x = 25

The critical point of R(x) is 25. It means that if the company sells 25 units of the product, then the company will receive maximum revenue.

Step 8: We need to find the price per unit that will yield maximum revenue. Let's substitute x = 25 in the demand function to find the price per unit of the product.

D(25) = 170e^(-0.04*25) = 67.04

Therefore, the price per unit that will yield maximum revenue is $67.04.

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5/x = x/ 9

Cross-multiply

x² =45

Take the square root of both-side

x = 3√5 or 6.7082039325

Answer: F

Step-by-step explanation:

Given that a card is drawn at random from a standard deck of cards. We are asked to find the probabilities of

1) A queen or a spade.

2) A black or a face card.

3) A red queen.

This can be seen below;

Explanation

The formula for the probability of an event is given as;

For a given deck of cards, the number of total possible outcomes is 52 different cards. Next, we find the number of events for each case

Therefore we can find the probability in each case. Recall that "or" in probability implies we will add the values of the probabilities we are comparing.

1) A queen or a spade

Answer

2) A black or a face card

Answer:

3) A red queen

Answer

Formula's:

solve:

\(\rightarrow \rm sin \ cot \ sec = 1\)

\(\rightarrow \rm sin \ \dfrac{cos}{sin} \ \dfrac{1}{cos} = 1\)

\(\rightarrow \rm \dfrac{sin \ cos}{sin \ cos} = 1\)

\(1 = 1\)

L.H.S = R.H.S

Hence both sides are equal and confirmed true. identify proved.

Answer:

Prove  \(sin(x)cot(x)sec(x)=1\)

Using the following trig identities:

\(cot(x)=\dfrac{1}{tan(x)}\)

\(sec(x)=\dfrac{1}{cos(x)}\)

\(\dfrac{sin(x)}{cos(x)}=tan(x)\)

\(\implies sin(x)cot(x)sec(x)=sin(x) \cdot \dfrac{1}{tan(x)} \cdot\dfrac{1}{cos(x)}\)

                                    \(= \dfrac{1}{tan(x)} \cdot\dfrac{sin(x)}{cos(x)}\)

                                    \(= \dfrac{1}{tan(x)} \cdot tan(x)\)

                                    \(= \dfrac{tan(x)}{tan(x)}\)

                                    \(=1\)

Hence \(sin(x)cot(x)sec(x)=1\)

Answer:

a = 120°

b = 60°

Step-by-step explanation:

Angle a and 60° are suplementary. The sum of supplementary angles is 180° (straight angle).

a + 60° = 180°

a = 180° - 60°

a = 120°

The sum of angles in the quadrilateral is 360°. Notice how two of the angles in the quadrilateral are marked as right angles (angles marked with a square). Each of them is 90°.

b + 90° + a + 90° = 360°

Substitute a with the value calculated in the previous step.

b + 90° + 120° + 90° = 360°

Solve for b.

b + 300° = 360°

b = 60°

Answer:

\(\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}\)

Step-by-step explanation:

We are given the equation:

\(2\cos^2(x)=\sin(x)+1\)

And we want to find all solutions for x.

First, we should put the equation into terms of only one trigonometric ratio.

Since we are given cos²(x), we can turn this into sine. Recall the Pythagorean Identity which states:

\(\sin^2(x)+\cos^2(x)=1\)

Therefore:

\(\cos^2(x)=1-\sin^2(x)\)

By substitution:

\(2(1-\sin^2(x))=\sin(x)+1\)

Distribute:

\(2-2\sin^2(x)=\sin(x)+1\)

Isolate the equation:

\(2\sin^2(x)+\sin(x)-1=0\)

We can factor:

\((2\sin(x)-1)(\sin(x)+1)=0\)

Zero Product Property:

\(2\sin(x)-1=0\text{ or } \sin(x)+1=0\)

Solve for each case:

\(\displaystyle \sin(x)=\frac{1}{2}\text{ or } \sin(x)=-1\)

We can use the unit circle.

sin(x) = 1/2 for every π/6 and 5π/6. So, it will continue every 2π.

sin(x) = -1 every 3π/2. And this will also continue every 2π.

Hence, our solutions are:

\(\displaystyle x=\left\{\frac{\pi}{6}+2n\pi, \frac{5\pi}{6}+2n\pi, \frac{3\pi}{2}+2n\pi\right\}, n\in\mathbb{Z}\)

Note:

If you only need the solutions within the interval [0, 2π), then it is:

\(\displaystyle x=\left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{3\pi}{2}\right\}\)

In determining whether a process is in statistical control, the R-chart should be analyzed first.

Given that, in determining whether a process is in statistical control, the _____ should be analyzed first.

A quality control technique called statistical process control uses statistical techniques to monitor and manage a process. This makes it possible to maintain an effective process that generates more products that meet specifications while using less trash.

When measuring small subgroups (n 10) from a process at regular intervals, an R-chart is a sort of control chart that is used to track the process variability (as the range). The value of a subgroup range is represented by each point on the chart.

Therefore, in determining whether a process is in statistical control, the R-chart should be analyzed first.

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Answer:

10.46

Step-by-step explanation:

Let the Number of additional pair = x

Ware house A :

855 + 92x - - - (1)

Warehouse B:

Initial cost per pair before 9

= 810 / 9 = $90

Additional 7% for pairs after 9

1.07 * 90 = 96.3

810 + 96.3x - - - (2)

810 + 96.3x = 855+ 92x

96.3x - 92x = 855 - 810

4.3x = 45

x = 45 / 4.3

x = 10.46

Additional pair be 10.46

5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

Naya's gross annual income is approximately $46,416.67.

To determine Naya's gross annual income, we need to reverse engineer the tax calculation based on the given information.

Let's denote Naya's gross annual income as G. We know that Naya's net annual income, after income tax, is 36,560. We also know that Naya pays income tax at the same rates and has the same annual tax credits as Emma.

Emma pays income tax on her taxable income at a rate of 20% on the first 35,300 and 40% on the balance. She has annual tax credits of 1,650.

Based on this information, we can set up the following equation:

G - (0.2 * 35,300) - (0.4 * (G - 35,300)) = 36,560 - 1,650

Let's solve this equation step by step:

G - 7,060 - 0.4G + 14,120 = 34,910

Combining like terms, we have:

0.6G + 7,060 = 34,910

Subtracting 7,060 from both sides:

0.6G = 27,850

Dividing both sides by 0.6:

G = 27,850 / 0.6

G ≈ 46,416.67

Therefore, Naya's gross annual income is approximately $46,416.67.

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The equation of line in slope intercept form is y = -0.5x -3.

What is slope intercept form?

The graph of the equation y = mx + b is a line with slope m and y-intercept b. The slope-intercept method is used to depict the linear equation, where m and b are real numbers.

We are given a line on the graph.

Taking two points as (2, -4) and (-2, -2), we get the slope as

⇒m = \(\frac{-2 +4 }{-2-2}\)

⇒m = \(\frac{2 }{-4}\)

⇒m = \(\frac{-1 }{2}\)

⇒m = -0.5

Similarly,

b = -3

We know that slope intercept form is given by

y = mx + b

On substituting, we get

y = -0.5x -3

Hence, the equation of line in slope intercept form is y = -0.5x -3.

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Answer:

use graphs

Step-by-step explanation:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

Answer: - radical 7 / 4

Step-by-step explanation:

draw a triangle in quadrant III

plug in correct terms

use Pythagorean theorem

to simplify down to find the opposite angle

b= rad 7

The sum of the squared lengths of the other two sides of a right triangle equals the square of the hypotenuse's length, which can be defined as follows:

\(\to \cos \theta =-\frac{3}{4}\)

\(\to \sin \theta =?\)

\(\sin \theta = \frac{opposite}{hypotenuse}\\\\\cos \theta =\frac{hypotenuse}{adjacent}\\\\\)

therefore

hypotenuse= -3

adjacent= 4

Using the Pythagorean theorem to find the opposite:

Hypotenuse²= Adjacent²+ Opposite²

\(-3^2= 4^2+x^2\\\\9=16+x^2\\\\x^2= -16+9\\\\x^2=-7\\\\x= -\sqrt{7}\\\\\)

Therefore the value of sin θ \(= \frac{\sqrt{7}}{-3}= \frac{\sqrt{7}}{3}\)

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