Find the maximums and minimums, and where they reach of the function f(x,y) = x² + y² + xy, in {(x, y) = x2 + y² ≤ 1} a Locals b Absolutes c) Identify critical points inside the disk (not at the border) if there is any. say if they are extreme? what type? if they are saddle point, or we can not know using

it will take approximately 15.71 years for the money to double at a 4 1/2% interest rate compounded quarterly.

To determine how long it will take for money to double at a 4 1/2% interest rate compounded quarterly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = final amount (double the initial amount)
P = principal amount (initial amount)
r = interest rate (converted to decimal form)
n = number of compounding periods per year
t = time (in years)

Since we want the money to double, the final amount A will be 2 times the initial amount P. Let's substitute the given values into the formula:

2P = P(1 + 0.045/4)^(4t)

Simplifying the equation:

2 = (1 + 0.01125)^(4t)

Taking the natural logarithm of both sides to isolate the exponent:

ln(2) = ln((1 + 0.01125)^(4t))

Using the logarithmic property:

ln(2) = 4t * ln(1 + 0.01125)

Solving for t:

t = ln(2) / (4 * ln(1.01125))

Using a calculator, we can find the / value of t. Plugging in the values, we get:

t ≈ 15.71 years

Therefore, it will take approximately 15.71 years for the money to double at a 4 1/2% interest rate compounded quarterly.

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The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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The number line shows the yards gained or lost by a team during a football game.

To find the difference in yards between the third down and first down, we need to look at the positions of the markers for these downs on the number line. If we assume that the team started at the 0 yard line, we can use the number line to determine the yards gained or lost on each play. For example, if the team gains 5 yards on first down, the marker would move to the right 5 units on the number line. If they lose 3 yards on second down, the marker would move 3 units to the left. We can continue this process until we reach the marker for the third down. Then, we can calculate the difference in yards between the third down and first down by subtracting the position of the third down marker from the position of the first down marker. This difference will be the number of yards gained or lost by the team during these downs. It is difficult to provide a specific answer without a visual representation of the number line and the positions of the markers, but this method can be used to find the difference in yards between any two downs.

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The correct missing statement and the reason is NP = NO + OP by Segment Addition Property

Given: MONP

Prove: MN = OP

The Segment Addition Property states that,

When three locations A, B, and C are on the same line and point B is located between points A and C, the length of the line segment AC is equal to the sum of the lengths of the three line segments AB and BC.

In mathematical notation, this property can be represented as:

AB + BC = AC

Statements                                                  Reasons

1. MO = NP                                                     1. Given

2. MO = MN+ NO                                     2. Segment Addition Property

3. NP = NO + OP                                      3. Segment Addition Property

4. MN+NO = NO+ OP                              4. Substitution Property

5. MN = OP                                              5. Subtraction Property of Equality

Hence the correct option is 2nd.

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Answer:

hope this answer helps you dear....take care!

Answer:

\(total \: angleof \: a \: triangle = 180 \\ then \\ x + 3x - 1 + x - 19 = 180 \\ 5x - 20 = 180 \\ 5x = 180 + 20 \\ 5x = 200 \\ x = \frac{200}{5} \\ x = 40 \\ thank \: you\)

Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

Given that,

The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.

We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:

C + Z = 1287

3.1 C + 2.5 Z = 3601.5

By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.

3.1 C + 2.5 Z =  3601.5

-2.5 C -  2.5 Z = -3217.5

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

0.6 C              =    384      

Divide both sides by .6.

C = 640        

Subtract 640 from 1287.

Z = 647

Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.

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Answer: x = 7°

Explanation:

We know that sum of angles of a quadilateral is = 360°

Therefore ATQ

⇒ (12x-4)+(18x+4)+(15x+10)+(5x) = 360

⇒ (12x + 18x + 15x + 5x) + (-4+4+10) = 360

⇒ 50x + 10 = 360

⇒ 50x = 360-10

⇒ 50x = 350

⇒ x = 350/50

⇒ x = 7

Therefore value of x is 7°

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Step-by-step explanation:

your answer would be the second light blue one

(2h+1)(h+3) x=-1/2,-5

For polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) after dilation the vertices will be

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem, for r = 1/4 we have

preimage                                     image

A (-4, 6)   → (1/4 * -4, 1/4 * 6) →   A' (-1, 3/2)

B (−2, 2)   → (1/4 * -2, 1/4 * 2) →  B' (-1/2, 1/2)

C (4, −2)  → (1/4 * 4, 1/4 * -2) →   C' (1, -1/2)

D (4, 4)   → (1/4 * 4, 1/4 * 4)   →  D' (1, 1)

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Answer:

Third Answer Choice....A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

Step-by-step explanation:

1/4 = 0.25

Multiply by every number

A' = ( -1, 1.5 )
B' = ( -0.5, 0.5 )
C' = ( 1, -0.5)
D' = (1, 1)

If it says its wrong i dont even know whys that, because this is the only way i know that everyone can solve easily

Answer:

the store sold 2,750 video games.

Step-by-step explanation:

you can multiply 12.5 by 8 to get 100, so using that logic, you would multily 550 by  8 to get your answer.

Answer:

Cheena has 6 pieces of fabric.

Step-by-step explanation:

3/4 yard of fabric also means 6/8 yard of fabric.

(6/8) / (1/8) = 6

Or

6/8 yard = 6  1/8 yard pieces

Answer:

0.02, 0.2, 2, 20, 200, 2000

Step-by-step explanation:

As I write this Reiner is standing at my side. He knows this is a love letter but he’s still sneaking glances. Honestly it’s no wonder the creep is still single.

That said, he did give me his word that he’d deliver this letter to you. He says he owes me for the time I doubled back to save him.

I’m sorry about that. I never would have imagined myself choosing those two over you.

I’m gonna die soon,

but I’ll die without regrets.

Or that’s what I’d like to say.

Truth is, I do have one.

It's that I never got to marry you...

With love, Ymir.

also nice nene pfp

The answer to the equation A=h(B+b) is 4

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation

From the given question

A=h(B+b);

when A=60, B=8, b=7

substituting the values into the equation

60= h(8+7)

60=h(15)

Expanding the bracket

60=15h

dividing both sides by 15

h=60/15

h=4

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Before we can solve the length of the missing sides and measure of the missing angles, it is important to note some properties of a parallelogram.

1. The opposite angles are congruent. (∠A≅∠C, ∠B≅∠D)

2. The consecutive angles are supplementary. (∠A + ∠D = 180, ∠A + ∠B = 180, etc.)

3. The opposite sides of a parallelogram are parallel and congruent. (AD = BC, AB = DC)

4. Diagonals bisect each other. (AE = EC, DE = EB)

Based on the 2nd property, we know that ∠A + ∠D = 180°. In the question, ∠A = 120° hence, ∠D = 180° - 120° = 60°.

In the diagram, we can see that ∠D = ∠ADB + ∠BDC and the measure of ∠ADB is 43°. Let's solve for the measure of ∠BDC.

Hence, the measure of ∠BDC is 17°. Since ∠BDC and ∠ABD are alternating interior angles, the measure of ∠ABD is also 17°.

Lastly, based on the 4th property which states that diagonal bisect each other, the measure of AE is equal to the measure of EC. Since EC is 7 units, AE is also 7 units.

Answer:

they are 10km 32 degrees far from each other

Step-by-step explanation:

scott - 100km - 30 degrees

spork - 110km - 62 degrees

how far = difference between them

as spork's distance and degrees are greater than scott we substract Scott's from spork's

110 - 100 = 10 km

62 - 30 = 32 degrees

they are 10km 32 degrees far from each other

Answer:

24.4 km

Step-by-step explanation:

The Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse of the triangle, and a and b are the legs. Plugging in your values, we get:

20^2 + 14^2 = c^2

Simplify: 400 + 196 = c^2

Simplify again: 596 = c^2

Square root both sides to cancel out the exponent on the right: 24.4131=c

Round: 24.4

Answer:

A) \({2s + 5t = 49.50\\\\s = 2t\)

B) Keegan paid $5.50 for each t-shirt and $11 for each short.

Step-by-step explanation:

A)

⭐ What is a system of equations?

We are asked to create a system of equations for Keegan's situation.

Let s = the price for every short

Let t = the price for every t-shirt

So, if Keegan buys 2 shorts and 5 t-shirts, his cost will be $49.50.

As an equation, this situation would be:

\(2s + 5t = 49.50\)

It's given that the cost of 1 short is twice the cost of 1 t-shirt.

As an equation, this situation would be:

\(s = 2t\)

B)

⭐How can we solve a system of equations?

For this problem, the best way to solve this system of equations is through substitution. I will demonstrate how to use substitution for this problem.

Using the equations \(2s + 5t = 49.50\) and \(s = 2t\), we will literally substitute a variable from one equation into another equation to solve for the other variable.

Given that \(s = 2t\):

\(2s + 5t = 49.50\)

\(2(2t) + 5t = 49.50\)

\(4t + 5t = 49.50\)

\(9t = 49.50\)

\(t = 5.50\)

∴ It costs Keegan $5.50 for one t-shirt.

Now, we can substitute the value of t into the same equation to solve for the value of s.

Given that \(t = 5.50\):

\(2s + 5(5.50) = 49.50\)

\(2s + 27.5 = 49.50\)

\(2s = 22\)

\(s = 11\)

∴ It costs Keegan $11 for one short.

The interquartile range for the data set are

Andre

Interquartile Range: = 2

For Lin

Interquartile Range = 8

For Noah

Interquartile Range = 8

For Andre

Min: 25 the minimum number

Q1: 27 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 30 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 27 = 2

For Lin

Min: 20 the minimum number

Q1: 21 (the third position)

Median: 28 (the sixth position)

Q3: 29 (the 9th position)

Max: 32 (the maximum number)

Interquartile Range: Q3 - Q1 = 29 - 21 = 8

For Noah

Min: 13 the minimum number

Q1: 15 (the third position)

Median: 20 (the sixth position)

Q3: 23 (the 9th position)

Max: 25 (the maximum number)

Interquartile Range: Q3 - Q1 = 23 - 15 = 8

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The average change of C with respect to t over each time interval is given below:a. [1.0, 2.0]


Average change in C with respect to t is -0.1. It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.16-0.35)/(2-1)]b. [1.5, 2.0]:
Average change in C with respect to t is -0.08. It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.16-0.22)/(2-1.5)]c. [2.0, 2.5]:Average change in C with respect to t is -0.02.
It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.1-0.16)/(2.5-2.0)]d. [2.0, 3.0]:Average change in C with respect to t is -0.005. It is found by subtracting C(t1) from C(t2) and then dividing the result by the difference in the corresponding times [(0.09-0.1)/(3.0-2.0)]


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       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

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Answer:

Step-by-step explanation:

35+12*x ; where x = amount of months

The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

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Solving the provided question, we can say that The quadratic equation we have is -  \(p^2 + 2p - (q+1)(1-1)\) => p = \(\sqrt{-2p}\)

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

The quadratic equation we have is -

\(p^2 + 2p - (q+1)(1-1)\)

\(p^2 + 2p - (q+1)*0\)

\(p^2 + 2p = 0\)

\(p^2 = -2p\)

p = \(\sqrt{-2p}\)

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The prοbability οf getting 4 green οutcοmes and 1 οrange οutcοme in 5 rοlls οf the number cube is 803/1000 οr 0.803 as a decimal.

Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.

The prοbability οf rοlling a green side is 5/6, and the prοbability οf rοlling an οrange side is 1/6.

Tο find the prοbability οf getting 4 green οutcοmes and 1 οrange οutcοme in 5 rοlls, we can use the binοmial prοbability fοrmula:

P(4 green, 1 οrange) = (5 chοοse 4) * \((1/6)^1 * (5/6)^4\)

where (5 chοοse 4) represents the number οf ways tο chοοse 4 rοlls οut οf 5 tο be green.

(5 chοοse 4) = 5! / (4! * 1!) = 5

Substituting this value intο the fοrmula:

P(4 green, 1 οrange) \(= 5 * (1/6)^1 * (5/6)^4\)

= 5 * (1/6) * (625/1296)

= 3125/3888

= 0.803

Therefοre, the prοbability οf getting 4 green οutcοmes and 1 οrange οutcοme in 5 rοlls οf the number cube is 803/1000 οr 0.803 as a decimal.

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Answer: the answer is c

Step-by-step explanation: your welcome

Answer:

204,335,880 way's

Step-by-step explanation:

590 ways for the 1 st contestant

589 ways for the 1 st contestant

588ways for the 1 st contestant

590×589×588

204,335,880 way's

The solution for the system is (0,3) as line a meets the y-axis at (0, -3) and the Intersection point of a and b is (3,0). This makes it obvious that the solution for x will be 0 when the solution for y is 3

Given that the number graph ranges from negative eight to eight on the x-axis and negative eight to eight on the y-axis.

Two lines that are perpendicular to each other intersect at (three, zero). The line with a positive slope is labeled a, and the line with a negative slope is labeled b.

The system is given byx – y = 3 (line a)x + y = 3 (line b)We know that both the lines a and b pass through (3,0).

Let's first find the points of intersection of the line a with the x-axis and the y-axis.

To find the point of intersection of the line a with the x-axis, put y = 0 in the equation x - y = 3x - 0 = 3x = 3So, the point of intersection of line a with the x-axis is (3,0).

To find the point of intersection of the line a with the y-axis, put x = 0 in the equation x - y = 3 0 - y = 3y = -3So, the point of intersection of line a with the y-axis is (0,-3).

Similarly, let's find the points of intersection of the line b with the x-axis and the y-axis.

To find the point of intersection of the line b with the x-axis, put y = 0 in the equation x + y = 3x + 0 = 3x = -3So, the point of intersection of line b with the x-axis is (-3,0).

To find the point of intersection of the line b with the y-axis, put x = 0 in the equation x + y = 3 0 + y = 3y = 3So, the point of intersection of line b with the y-axis is (0,3).

Now, we can plot the graph of the two lines a and b and then find the points of intersection as follows:

Therefore, the solution for the system is (0,3) as line a meets the y-axis at (0, -3) and the intersection point of a and b is (3,0). This makes it obvious that the solution for x will be 0 when the solution for y is 3.

Hence, the answer is (0, 3).Option B. (0, 3)

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