1. Differentiate with respect to x:
​

Answer:

20 minutes

Step-by-step explanation:

80% of 480 is 384

480 x .80 = 384

4.8 x 20 = 96

a. If 1% of the shells are actually defective and we assume Independence, the probability of 0 defective shells in the sample is 82%,

b. if 1% of the shells are actually defective and we assume independence, the probability of 1 defective shell in the sample is 16% and

c. If 1% of the shells are actually defective and we assume Independence, the probability of more than 1 defective shell in the sample is 1.58%.

Given batch = 350 shells

sample = 20 shells

Given 1%10 f shells are defective = 0.01

That is 99% are non detective = 0.99

Using binomial theorem,

1. P(zero defective shells) = 20c0 (0.01)^0(0.99)^20

= 0.82

= 82%

2. P(One defective shells) = 20c1(0.01)(0.99)^19

= 0.16

= 16%

3. P(two defective shells) = 20c2(0.01)^2(0.99)^18

= 0.0158

= 1.58%

Hence the a. If 1% of the shells are actually defective and we assume Independence, the probability of 0 defective shells in the sample is 82%, b. if 1% of the shells are actually defective and we assume independence, the probability of 1 defective shell in the sample is 16% and c. If 1% of the shells are actually defective and we assume Independence, the probability of more than 1 defective shell in the sample is 1.58%.

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The distance between the rock and the surface is 827.20 cm.

Given data,

There is a robot on Mars' surface. 13.33 degrees of depression can be seen between a camera in the robot and a boulder on the surface of Mars. 196.0 cm is how high the camera is from the ground.

How far is the rock from the camera?

From the given data,

tan c = AB/BC

tan 13.33° = 196/BC

BC = 196/tan 13.33°

BC = 827.20 cm

Hence, the distance between the rock and the surface is 827.20 cm.

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Answer:Sample response: I set up an equation to show that the number of bracelets multiplied by the cost of each bracelet minus the commission is equal to the total, 6(x – 1.25) = 16.50. I divided each side by 6, then added 1.25 to each side with a result of x = 4. Hyo-Jim sold each bracelet for $4.

                                       just at least take out a few things and paraphrase it hope this is usefull

Answer:

Sample response: I set up an equation to show that the number of bracelets multiplied by the cost of each bracelet minus the commission is equal to the total, 6(x – 1.25) = 16.50. I divided each side by 6, then added 1.25 to each side with a result of x = 4. Hyo-Jim sold each bracelet for $4.

Step-by-step explanation:

I got if off the question.

Answer:

\( \red{\bold {7x - 9y - 39 = 0}} \)

Step-by-step explanation:

Line passes through the points

\( (3, \: - 2) =(x_1, \: y_1) \:\&\: (-6,\: - 9)= (x_2, \: y_2)\)

Equation of line in two point form is given as:

\( \frac{y-y_1}{y_1-y_2} = \frac{x-x_1}{x_1-x_2} \\\\

\frac{y-(-2)}{-2-(-9)} = \frac{x-3}{3-(-6)} \\\\

\frac{y+2}{-2+9} = \frac{x-3}{3+6} \\\\

\frac{y+2}{7} = \frac{x-3}{9} \\\\

9(y+2) = 7 (x - 3)\\\\

9y + 18 = 7x - 21\\\\

7x - 9y - 21 - 18 = 0\\\\

\huge \purple {\boxed {7x - 9y - 39 = 0}} \)

Answer:

the inequality, b ≤ 0 has interval Notation of -∞,0

Step-by-step explanation:

the inequality, b ≤ 0 has interval Notation of -∞,0

After each guess, your opponent has to tell you if your number is too high or too low. each guess is considered fifth attempt the last guess.

Let's dive deeper into the game and understand it from a mathematical perspective. You are given five chances to guess the number your opponent has written down. In each turn, you can guess a number, and your opponent will tell you if the number you guessed is too high or too low. This information is crucial because it helps you to narrow down the possibilities of what the actual number could be.

Now, let's consider the game in mathematical terms. Suppose the number your opponent has written down is called "X." Your goal is to guess X in five attempts. Let's call these attempts "A1, A2, A3, A4, and A5." After each attempt, your opponent will give you a clue that the number you guessed is either too high or too low. Based on this feedback, you can eliminate some possibilities of what the number X could be.

As you can see, with each guess, you are narrowing down the possibilities of what the number X could be. The game is all about using logical reasoning and deduction to guess the number X correctly in five attempts. If you guess the number correctly before your fifth attempt, you win the game.

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The Jackson family averaged 22.71 miles per gallon on their trip.

To find out the average miles per gallon used by the Jackson family on their trip, the distance they covered and the amount of fuel they consumed are both necessary information.

They started their trip with an odometer reading of 18,649.3 miles, and the odometer reading at the end of the trip was 20,630.5.

The distance covered, therefore, is:20,630.5 - 18,649.3 = 1,981.2 miles

Next, to determine the average miles per gallon, divide the total distance covered by the amount of fuel consumed:1,981.2 miles ÷ 87.3 gallons

= 22.71 miles per gallon.

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(a) The point with spherical coordinates (5, π/3, π/6) can be represented in rectangular coordinates as (√(75)/2, (5√3)/2, 5/2).To plot this point, we start by considering the first value, which represents the radial distance from the origin.

In this case, the radial distance is 5 units. The second value, π/3, represents the polar angle (θ), which is measured from the positive z-axis. The third value, π/6, represents the azimuthal angle (φ), which is measured from the positive x-axis.

To convert the spherical coordinates to rectangular coordinates, we use the following formulas:

x = r sinθ cosφ

y = r sinθ sinφ

z = r cosθ

Substituting the given values into the formulas, we find that x = (√(75)/2), y = (5√3)/2, and z = 5/2. Therefore, the rectangular coordinates of the point are (√(75)/2, (5√3)/2, 5/2).

(b) The point with spherical coordinates (9, π/2, 3π/4) can be represented in rectangular coordinates as (0, 9cos(π/2), 9sin(π/2)), which simplifies to (0, 0, 9).

Since the polar angle is π/2, the point lies on the positive z-axis. The azimuthal angle is 3π/4, which indicates a rotation from the positive x-axis in the xy-plane. The radial distance is 9 units, which determines the distance from the origin.Using the conversion formulas, we find that the x-coordinate is 0, the y-coordinate is 0, and the z-coordinate is 9. Therefore, the rectangular coordinates of the point are (0, 0, 9).

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The phrase "He went to get milk but never came back" is often used as a humorous way to explain someone's absence or to imply that someone is unreliable or untrustworthy.

The phrase likely originates from a common experience where a child's parent, often their father, promises to go out to get something, like milk, but never returns. This can be a source of disappointment and confusion for the child, and the phrase has since been used in a joking manner to explain someone's failure to show up or fulfill a promise.

However, it is important to recognize that this experience can also be a source of trauma and should not be used to make light of someone's pain or loss.

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The integral is to zero for a symmetric nonsingular positive semi-definite matrix A, and the expression is

∫ x∈\(R^n\) exp\((-1/2 x^T A x - x^T b - c) dx\) = 0.

The integral ∫ x∈R^n exp(-1/2 x^T A x - x^T b - c) dx, where A is a symmetric nonsingular positive semi-definite matrix, b ∈ R^n, and c ∈ R, can be evaluated.

To evaluate this integral, we can make use of the Gaussian integral formula for multi-dimensional integrals. The formula states that:

∫ exp\((-1/2 x^T C x) dx = ((2π)^(n/2)) / sqrt(det(C)),\)

where C is a positive definite matrix.

In our case, A is a symmetric positive semi-definite matrix. Since A is positive semi-definite, we can write it as A = Q^T D Q, where Q is an orthogonal matrix and D is a diagonal matrix with non-negative eigenvalues. As A is symmetric and positive semi-definite, its eigenvalues are non-negative.

Now, we can rewrite the integral as:

∫ exp\((-1/2 x^T A x - x^T b - c) dx = exp(-c) ∫ exp(-1/2 x^T A x - x^T b) dx.\)

Let's complete the square inside the exponent to further simplify the integral. We can rewrite the exponent as:

\(-1/2 x^T A x - x^T b = -1/2 (x^T A x + 2 x^T (A^-1 b)),\)

where A^-1 is the inverse of A.

Now, let's substitute y = x + A^-1 b. We have dy = dx, and the integral becomes:

exp(-c) ∫ exp(-1/2 y^T A y) dy.

At this point, we can apply the Gaussian integral formula mentioned earlier, with C = A. Therefore, the integral becomes:

exp(-c) ((2π)^(n/2)) / sqrt(det(A)).

Since A is positive semi-definite, its determinant is non-negative. So, we have sqrt(det(A)) = sqrt(0) = 0 for a positive semi-definite matrix A.

Therefore, the integral evaluates to zero for a symmetric nonsingular positive semi-definite matrix A, and the expression becomes:

∫ x∈R^n exp(-1/2 x^T A x - x^T b - c) dx = 0.

Thus, the integral is equal to zero.

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Answer:

--------------------------

Since the x-coordinates are same, the distance between the given points is the difference of the y-coordinates:

Correct choice is D.

Answer:

37 units

Step-by-step explanation:

We can use the below formula to find the distance between two coordinates.

\(\sf Distance=\sqrt{[x_2-x_1]^2+[y_2-y_1]^2}\)

Given that,

( 7, - 15 ) ⇒ ( x₁ , y₁ )

( 7, 22 ) ⇒ ( x₂ , y₂ )

Let us find it now.

\(\sf Distance=\sqrt{[x_2-x_1]^2+[y_2-y_1]^2}\\\\\sf Distance=\sqrt{[7-7]^2+[22-(-15)]^2}\\\\\sf Distance=\sqrt{[0]^2+[22+15]^2}\\\\\sf Distance=\sqrt{[0]+[37]^2}\\\\\sf Distance=\sqrt{[37]^2}\\\\\sf Distance=37\:units\)

Answer:

D

Step-by-step explanation:

Since all the points were shifted the same way, I'll just use point A and point A'.

Point A starts at (3,5) and A' is at (5,2)

If the subract the x coordinates: 5-3=2

Then subtract the y coordinates: 2-5=-3

The 2 is positive, so it is 2 units to the right (the positive x direction) and -3 is negative so 3 units down (negative y direction)

Although increasing the sample size can improve the accuracy of the estimate, there are some problems that may arise with very large samples.

The following are the problems that can occur:

Difficulty in obtaining a very large sample: It may be difficult to obtain a large sample that is representative of the population and has a low bias.

Cost of sampling: Collecting data from a very large sample can be time-consuming and expensive.

None of these: This is not a problem that can arise with very large samples.

Increase in standard error: As the sample size increases, the standard error of the estimate tends to decrease, but after a certain point, increasing the sample size further may not lead to a significant reduction in the standard error, and may even increase it due to other factors such as measurement errors or non-random sampling. This is called the "law of diminishing returns".

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The graphs of the absolute value function y = 2|x + 2| - 6 and the horizontal line y = -2 are given on the image at the end of the answer.

The definition of the absolute value function is given as follows:

y = |x - h| + k.

In which the coordinates of the vertex are (h,k), representing the turning point of the graph of the absolute value function, the point in which the function makes the "V".

In this problem, the definition of the function is:

y = 2|x + 2| - 6.

Hence the coordinates of the vertex are:

(-2, -6).

The multiplication by 2 represents a vertical stretch but is not related to the vertex of the function.

y = -2 is a horizontal line, and the graph with these two functions is given by the image at the end of the answer.

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The exact value of the circumference of the circle is 2×10⁶π cm and the approximate value is 6.28×10⁶cm

The circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.

The circumference of a circle is expressed as ;

C = πd

for exact value

C = 2×10⁶πcm, since 1km =1×10⁶cm

for the approximated value

C = 2×10⁶ × 3.14

C = 6.28×10⁶cm

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Answer:

x = -3

Step-by-step explanation:

\(y\geq -\frac{2}{3} x-3\\ y\leq 3x+8\)

\(-\frac{2}{3} x-3=3x+8\)

Add 2/3 x to both sides:  \(-3=\frac{11}{3}x+8\)

Subtract 8 from both sides: \(-11=\frac{11}{3}x\)

Multiply both sides by 3:  \(-33=11x\)

Divide both sides by 11:  \(x=-3\)

Therefore, point of intersection between both lines is at point (-3, -1)

The circumference of the circle in terms of pi is 16π yards.

The circumference of a circle is the distance around the edge or perimeter of the circle. It is the length of a closed curve and can be measured by using a flexible measuring tape or a string to wrap around the circle. The formula for the circumference of a circle is C = 2πr, where C is the circumference, r is the radius of the circle, and π is the mathematical constant pi (approximately equal to 3.14159). The circumference of a circle is proportional to its radius and increases as the radius increases. Therefore, if we know the radius of a circle, we can use the formula to find its circumference, and if we know the circumference, we can use the formula to find the radius. The circumference is an important concept in geometry and is used in many real-world applications, such as calculating the length of a fence needed to enclose a circular garden or the distance traveled by a car moving around a circular racetrack.

Substituting the given value of the radius, we get:

C = 2π(8) = 16π

Therefore, the circumference of the circle in terms of pi is 16π yards.

So the answer is 16pi yards.

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the approximate area of the base of the paint can is 53.5 square centimeters.by using Volume formula is Base Area × Height

To find the approximate area of the base of the paint can, we can use the formula for the volume of a cylinder:

Volume = Base Area × Height

We are given the volume (535 cubic centimeters) and the height (10 cm). We need to solve for the Base Area. Rearranging the formula to solve for Base Area, we get:

Base Area = Volume ÷ Height

Now, substitute the given values:

Base Area = 535 cubic centimeters ÷ 10 cm

Base Area ≈ 53.5 square centimeters

So, the approximate area of the base of the paint can is 53.5 square centimeters.

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The approximate area of the base of the can is 53.5 square centimeters

From the question, we have the following parameters that can be used in our computation:

Volume = 535 cubic centimeters of paint

Height of container = 10 cm

The area of the base of the can is calculated as

Base area = Volume/Height

Substitute the known values in the above equation, so, we have the following representation

Base area = 535/10

Evaluate

Base area = 53.5

Hence, the base area is 53.5 square centimeters

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Answer:

5

Step-by-step explanation:

-7X - 3X + 8X = -8 -2

-2X= -10

=> X = 5

Answer:

wouldnt it be. 4 × x+7

Step-by-step explanation:

because x and 7 equal the whole top and 4 is the side

Answer:

10-94-109.   sorry ihave not done this in like 4 years im probley like not eaven close. sorry for the late responts.

Answer:

ji aap ka answer number (B) wala hai

hope it's help you (^0^)

The composite function G(F(x)) = 4√x is for the functions when F(x) = √x and G(x) = 4x.

Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).

h(x) is called the composite function.

Given that, the composite function is,

G(F(x)) = 4√x

We have to find the functions G(X) and F(x).

We know that,

G(F(x)) is the function G(x) when x is changed to F(x).

Let G(x) = 4x

In G(F(x)), x will be replaced by F(x).

In order to get 4√x, x is replaced by √x.

So, F(x) = √x

Hence G(x) = 4x and F(x) = √x.

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By rewriting a relation we will see that there are 0.5 fluid ounces in a tablespoon.

We know the relation between the different units:

1 fluid ounce = 2 tablespoons.

To see how many fluid ounces are in a tablespoon, we just need to work with the relation above and write "1 tablespoon" on the right side.

So if we take our relation:

1 fluid ounce = 2 tablespoons.

And we divide both sides by 2 then we will get:

1/2 fluid ounce = 2/2 tablespoons.

0.5 fluid ounces = 1 tablespoon.

then we can conclude that there is 0.5 fluid ounces in a tablespoon.

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Answer:

yes because it is odd

Step-by-step explanation:

Answer:

7 is a rational number. Rational numbers are numbers that result when two integers are divided. For example, two integers whose quotient is equal to 7 are 14 and 2. When you divide 14 by 2, the result is 7, and this validates 7 as a rational number.

Answer:

A=False

B=True

C=True

Step-by-step explanation:

To calculate J₁(x₁) and μ₁(x₁), we need to evaluate the Bellman equation for all possible values of x₁ and μ₁. Then, we select the minimum cost and the corresponding optimal input as the solution.

a) State space \(s_{k}\) for k = 1, 2:

For k = 1, we have:

State x₁: It represents the state at time k = 1.

Input μ₁: It represents the control input at time k = 1.

Disturbance w₁: It represents the disturbance at time k = 1.

For k = 2, we have:

State x₂: It represents the state at time k = 2.

Input μ₂: It represents the control input at time k = 2.

Disturbance w₂: It represents the disturbance at time k = 2.

b) Calculation of optimal cost-to-go J₁(x₁) and optimal policy μ₁(x₁) for k = 1:

Given the system and cost function, we can use dynamic programming and the Bellman equation to calculate the optimal cost-to-go J₁(x₁) and optimal policy μ₁(x₁)for k = 1.

The Bellman equation for k = 1 is given by:

J₁(x₁) = min{c(x₁, μ₁, w₁) + J₂(f(x₁, μ₁, w₁))}

Where:

c(x₁, μ₁, w₁) represents the cost at state x₁, input μ₁, and disturbance w₁.

f(x₁, μ₁, w₁) represents the state transition function.

J₂ represents the cost-to-go function at k = 2.

To calculate J₁(x₁) and μ₁(x₁), we need to evaluate the Bellman equation for all possible values of x₁ and μ₁. Then, we select the minimum cost and the corresponding optimal input as the solution.

c) Effect of adding the term x²₀; to the cost function:

If we add the term x²₀; to the cost function, it will introduce an additional cost or penalty for having a non-zero value for x²₀; in the state.

The effect on the optimal cost-to-go J₁(x₁) and optimal policy μ₁(x₁) depends on the specific value and weight of the term x²₀;. If the weight is significant, the optimal policy may try to minimize the value of x²₀; in order to reduce the overall cost. This can result in a different optimal policy compared to the case without the term x²₀;.

In general, the addition of the term x²₀; to the cost function can modify the trade-off between minimizing the initial cost and minimizing the effect of the state variable x²₀; on the overall cost. It provides a mechanism to incorporate the importance of x²₀; into the optimization problem and can lead to different decisions and policies.

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The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.


The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Answer:

im not sure if this is what you're looking for but g=x^4 and the y intercept is g(0)=0

Step-by-step explanation: