Find the slope of the curve y=x^3-3 at the point P(1,-2) by finding the limiting value of th slope of the secants through P.
B. Find an equation of the tangent line to the curve at P(1,-2).
A. The secant slope through P is ______? (An expression using h as the variable)
The slope of the curve y=x^3-3 at the point P(1,-2) is_______?
B. The equation is _________?

Answer:

YES 68 is the correct answer

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

3 times 25 = 75

Step-by-step explanation:

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There are 75 lasagna dinners are likely to be needed for a flight with 360 passengers.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

An airline food service finds that a recent flight of 120 passengers ordered dinner as depicted in the table to the right.

Here, Number of Lasagna for 120 passengers = 25

Hence, For 360 passengers number of lasagna is,

⇒ 120 / 35 = 360 / x

Where, x is umber of lasagna for 360 passengers

⇒ x = 360 × 25 / 120

⇒ x = 75

Thus, There are 75 lasagna dinners are likely to be needed for a flight with 360 passengers.

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Yes, Victor needs to have similar portion of the population in the sample.

What is population size?

The number of objects inside a geographical area that has been arbitrary assigned as the population size.

In a fair, unbiased poll

Population proportion plus random error equals sample proportion.

According to the Normal Approximation, the standard deviation of the distribution of these random mistakes across all feasible samples is

\(\sqrt{\frac{\text{Population proportion}(1-\text{Population proportion})}{n}}\)

The sample estimate's variance from the actual population value is known as the random error. Numerous alternative summaries, such as sample averages or discrepancies between two sample proportions or averages, are likewise consistent with the observation that random mistakes follow the normal curve.

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A) 54,912 B) 2,598,960 C)  15

A) The number of ways to produce three of a kind (Num3) is equal to the product of the number of ways to make each independent choice. Therefore,

Num3 = 13C1 * 12C2 * 4C3 * 4C1 * 4C1

Num3 = 13 * 66 * 4 * 4 * 4 = 54,912

B) First, we count the number of five-card hands that can be dealt from a standard deck of 52 cards. This is a combination problem. The number of combinations is n! / r!(n - r)!. We have 52 cards in the deck so n = 52. And we want to arrange them in unordered groups of 5, so r = 5. Thus, the number of combinations is:

52C5 = 52! / 5!(52 - 5)! = 52! / 5!47! = 2,598,960

Hence, there are 2,598,960 distinct poker hands.

C) 6 C 4 = 6! / 4! (6-4)!

= 6*5*4! / 4!*2!

= 30 / 2

= 15

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Answer:

Our calculator limits your interest deduction to the interest payment that would be paid on a $1,000,000 mortgage. Interest rate: Annual interest rate for this

Step-by-step explanation:

Answer:

106 cm

Step-by-step explanation:

Given that the rectangles are similar, therefore the ratio of their corresponding sides will be equal. So , we can say that;

53cm/100cm = x/200 cm

Simplify and solve for "x" , as ;

x = 53/100 *200 cm

x = 53*2 cm

x = 106 cm

Hence the value of x is 106cm .

Answer:

Let's assume the original shape was an equilateral triangle with vertices at (0,0), (1,2), (2,0).

After a translation 5 units right, the triangle's vertices will be at (5,0), (6,2), (7,0).

To explain, a translation is a transformation which moves a shape's location without rotating, reflecting, or resizing it. In this case, since the shape was translated 5 units right, each vertex moved 5 units right from its original position, so (0,0) became (5,0), (1,2) became (6,2), and (2,0) became (7,0).

Step-by-step explanation:

The two figures shown are made of unit squares. The positive difference of the perimeters, in units, is 8.

Perimeter is the total distance around the boundary of the shape. Since each square has a side length of 1 unit, the perimeter is equal to the number of sides.

1. Figure A: Counting the number of unit squares on the boundary of the shape, the perimeter of the first shape is:   8+4+4+4+4=24 units.

2. Figure B:Counting the number of unit squares on the boundary of the shape, the perimeter of the second shape is: 10+2+10+2=24 units.

The positive difference of the perimeters in units = |24 - 24| = 0 units. Therefore, the positive difference of the perimeters, in units is 0.

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Answer: The Slope is 20

Step-by-step explanation:

M A T H W A Y . C o M

The cyclist will pedal at given speed for minimum 1.25 and maximum 2.25 hours.

The relation between speed, distance and time is as follows -

Speed = distance ÷ time. The maximum and minimum number of hours will depend on the distance. The maximum number of hours will be spent when maximum distance is covered, and minimum number of hours will be spent when minimum distance is covered.

Maximum distance = 35 + 10

Maximum distance = 45 miles

Minimum distance = 35 - 10

Minimum distance = 25 miles

Maximum number of hours = 45 ÷ 20

Maximum number of hours = 2.25 hours

Minimum number of hours = 25 ÷ 20

Minimum number of hours = 1.25 hours

Thus, cyclist will pedal at given speed for minimum 1.25 and maximum 2.25 hours.

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The equivalent regular expression for the given DFA using Arden's theorem is (a+b)(a+bb+ba(a+b))*.

1. Start with the given DFA and its transition table:

  State | Input a | Input b

  ------|---------|---------

  1     | 3       | 2

  2     | 1       | 2

  3     | 2       | -

2. Apply Arden's theorem, which states that for a DFA with a single final state, the regular expression for that state can be obtained by substituting the regular expressions for the other states into the equation: R = S + RP, where R is the regular expression for the final state, S is the regular expression for the current state, and P is the regular expression for the next state.

3. Begin with state 1:

  - Substitute the regular expression for state 3 into the equation:

    1 = 3a + ε

  - Since state 3 has no outgoing transition for input b, it is represented as ε (empty string).

4. Move to state 2:

  - Substitute the regular expression for state 1 into the equation:

    2 = 1(a + b) + 2a + 3b

  - State 1 is represented as (a + b) from the previous step.

  - Note that 1 is substituted because it is the regular expression for the state itself.

5. Move to state 3:

  - Substitute the regular expression for state 2 into the equation:

    3 = 2b

  - State 2 is represented as b from the previous step.

6. Substitute the obtained regular expressions back into the previous equations until no new substitutions are made:

  - In this case, there are no new substitutions to be made.

7. The resulting regular expression for state 1 is (a + b)(a + bb + ba(a + b))*.

Therefore, the equivalent regular expression for the given DFA using Arden's theorem is (a + b)(a + bb + ba(a + b))*.

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Answer:

56.52m is the circumference. The area is 254.34\(m^{2}\)

Step-by-step explanation:

The equation for the circumference of a circle is c=2πr with r being the radius. So 2(3.14)(9)=56.52m. The area equation for a circle is A=π\(r^{2}\) so it would be (3.14)(9)^2 or (3.14)(81) which equals 254.34\(m^{2}\)

1. The interest rate for a present value of $260 is  4.86% 2. The interest rate for a present value of  $380 is 6.39%  3. The interest rate for a present value of $41,000 is 6.77%  4. The interest rate for a present value of $40,261 is 5.55.

1. The interest rate for a present value of $260, over a period of 3 years, resulting in a future value of $307. The interest rate can be found using the formula:

Future Value = Present Value * (1 + Interest Rate)^Years

Rearranging the formula to solve for the interest rate:

Interest Rate = ((Future Value / Present Value)^(1 / Years) - 1) * 100

Substituting the given values:

Interest Rate = ((307 / 260)^(1 / 3) - 1) * 100 ≈ 4.86%

2. For a present value of $380, a future value of $1,107, and a period of 17 years, we can use the same formula:

Interest Rate = ((Future Value / Present Value)^(1 / Years) - 1) * 100

Plugging in the values:

Interest Rate = ((1107 / 380)^(1 / 17) - 1) * 100 ≈ 6.39%

3. Considering a present value of $41,000, a future value of $185,586, and a period of 18 years:

Interest Rate = ((Future Value / Present Value)^(1 / Years) - 1) * 100

Using the given values:

Interest Rate = ((185586 / 41000)^(1 / 18) - 1) * 100 ≈ 6.77%

4. Lastly, for a present value of $40,261, a future value of $342,595, and a period of 20 years:

Interest Rate = ((Future Value / Present Value)^(1 / Years) - 1) * 100

Applying the values:

Interest Rate = ((342595 / 40261)^(1 / 20) - 1) * 100 ≈ 5.55%

In conclusion, the unknown interest rates for the given scenarios are approximately 4.86%, 6.39%, 6.77%, and 5.55%, respectively. These rates represent the annual percentage growth required for the present values to reach their corresponding future values over the given time periods.

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Answer:

160

Step-by-step explanation:

x = original price

x+ 25% x = 200

Change to decimal form

x + .25x = 200

1.25x = 200

Divide each side by 1.25

x = 200/1.25

x =160

The original price was 160

To solve the initial value problem by the method of undetermined coefficients \(y'' − 5y' + 6y = ex(2x−3), y(0) = 1, and y' (0) = 3\), we have to find the homogeneous solution and particular solution. The given differential equation can be rewritten as\(y'' − 2y' − 3y' + 6y = ex(2x−3).\)

The homogeneous solution is yh = C1e3x + C2e2x. To find the particular solution, let’s assume that yp = Aex(2x−3) + Bxex(2x−3).Differentiate yp to get y'p = (2A + B + 2Bx)ex(2x−3)Differentiate y'p to get y''p = (4A + 4Bx + 6B)ex(2x−3)Substitute the values in the given differential equation and solve it for A and B.Axex(2x-3) + Bxex(2x-3) - 10Aex(2x-3) - 10Bxex(2x-3) + 6Axex(2x-3) + 6Bxex(2x-3) = ex(2x-3)

Simplifying the above expression, we get -4A + 4Bx = 1So, A = 1/4 and B = 0.The particular solution is yp = (1/4)ex(2x-3).The general solution is y = yh + yp = C1e3x + C2e2x + (1/4)ex(2x-3).Substitute y(0) = 1 in the above equation.1 = C1 + C2 + 1/4Substitute y'(0) = 3 in the above equation.3 = 3C1 + 2C2 + (1/2)The solution of the initial value problem is y = e3x/2 - (1/4)e2x + (1/4)ex(2x-3).Therefore, the particular solution is y = e3x/2 - (1/4)e2x + (1/4)ex(2x-3).

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Answer:

square root of (l^2 + b^2)

The formula for the diagonal of a rectangle is given by the d = √(l² + w²).

What is the length of the diagonal of the rectangle?

We can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

The diagonal of a rectangle is a line segment connecting two opposite corners of the rectangle and passes through the interior of the rectangle.

The formula for the diagonal of a rectangle is given by the Pythagorean theorem:

d = √(l^2 + w^2)

Where,

d is the length of the diagonal,

l is the length of the rectangle,

and w is the width of the rectangle.

The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

In the case of a rectangle, the two shorter sides are the length and the width of the rectangle, and the longest side is the diagonal.

Therefore, the diagonal of a rectangle can be considered as the hypotenuse of a right triangle with sides equal to the length and width of the rectangle.

Hence, The formula for the diagonal of a rectangle is given by the d = √(l² + w²).

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Answer:

Step-by-step explanation:

\(Sin \ 39 = \dfrac{opposite \ side}{hypotenuse}\\\\0.63 = \dfrac{1.7}{x}\\\\0.63*x=1.7\\\\x= \dfrac{1.7}{0.63}\\\\\\x = 2.7\)

Answer:

x=12

Step-by-step explanation:

Solution of Square root,  x² = 30: x = √30 = √30² = 30, x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30: x = ∛30 = ∛30³ = 30, x = -∛30 = -∛30³ = -30

Given,

Square root x² = 30

Then, the value of:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

x = ∛30 = ∛30² = 3.107

x = -∛30 = -∛30² = -3.107

Now,

Cube root, x³ = 30

x = √30 = √30³ = 164.317

x = -√30 = -√30³ = -164.317

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

Therefore,

Solution of Square root,  x² = 30:

x = √30 = √30² = 30

x = -√30 = -√30² = 30

Solution of Cube root, x³ = 30:

x = ∛30 = ∛30³ = 30

x = -∛30 = -∛30³ = -30

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Answer:

93 years old

Step-by-step explanation:

We can set the equation up as 300 - 2x = 114 since reduce means subtraction, we do not know the age yet, and the difference is 114.

Since there are 130 people in the sport center and 121 people using any combination of facilities, we find that 130 - 121 = 9 people use exactly one of the facilities.

In the given sport center, there are 130 people utilizing various facilities. To determine how many people use exactly one of these facilities, we can use the principle of inclusion-exclusion.Total number of people using any facility: 61 (gym) + 68 (pool) + 60 (track)
However, this includes people who use multiple facilities, so we subtract the overlaps:Overlaps: 25 (gym & pool) + 30 (pool & track) + 19 (gym & track)
Now, we add back the people who use all three facilities, as they were subtracted twice: 6 (gym, pool, & track)
Combining these numbers, we get:(61 + 68 + 60) - (25 + 30 + 19) + 6 = 189 - 74 + 6 = 121.

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Answer:

11/306

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to  the  number of total outcome.

Given that  there are 4 red, 8 yellow, and 6 blue socks in a drawer where the  probability of  picking a red, yellow and blue socks be  p(r), p(y), and p(b) respectively.

The probability of reaching into the drawer without looking and drawing out 2 blue socks

= 6/(4 + 8 + 6) * 5/(4 + 8 + 5)

= 6/18 + 5/17

= 11/306

Answer: it be 85% i did this one to :)

Step-by-step explanation:

Answer: The answer is likely E/i

Step-by-step explanation:

1. Based by guesses here, multiply R on both sides, making it RI = E

2. Then, divide I on both sides, so RI/I = E/I

3. Becoming R = E/I

Answer:

B

Step-by-step explanation:

sana nakatulong mga lods