a pile of 4 pairs of different shoes (i.e., 4 left shoes and 4 right shoes that make a total of 8 shoes) are present . in how many total ways can i choose 4 shoes from the pile?

Answer:

Step-by-step explanation:

y - 9 = 3(x - 0)

y - 9 = 3x - 0

y = 3x + 9

The Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

To solve the ODE using the Euler method, we divide the interval into smaller steps and approximate the derivative with a difference quotient. Given that the step size is h = 0.5, we will perform three steps to obtain the numerical solution.

we calculate the initial condition: y(0) = -2.

1. we evaluate the derivative at t = 0 and y = -2:

y' = 3(0) - 10(-2)² = -40

Next, we update the values using the Euler method:

t₁ = 0 + 0.5 = 0.5

y₁ = -2 + (-40) * 0.5 = -22

2. y' = 3(0.5) - 10(-22)² = -14,860

Updating the values:

t₂ = 0.5 + 0.5 = 1

y₂ = -22 + (-14,860) * 0.5 = -7492

3. y' = 3(1) - 10(-7492)² ≈ -2.2395 x 10^9

Updating the values:

t₃ = 1 + 0.5 = 1.5

y₃ = -7492 + (-2.2395 x 10^9) * 0.5 = -1.1198 x 10^9

Therefore, after performing three steps of the Euler method with a step size of h = 0.5, the approximate numerical solution for the ODE is y(1.5) ≈ -1.1198 x 10^9.

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The length of the movie screen at the local cinema is 37188552  feet.

Let's assume the width of the rectangle movie screen is represented by 'w' feet. According to the given information, the length of the screen is 303030 feet longer than the width. Therefore, the length can be expressed as 'w + 303030' feet.

The perimeter of a rectangle is given by the formula: 2(length + width). In this case, the perimeter of the movie screen is 148148148 feet. We can set up the equation as follows:

2(w + (w + 303030)) = 148148148.

Simplifying the equation, we have:

2(2w + 303030) = 148148148.

4w + 606060 = 148148148.

4w = 147542088.

Dividing both sides by 4, we get:

w = 36885522.

Therefore, the width of the screen is 36885522 feet. Since the length is 303030 feet longer than the width, we can calculate the length as:

Length = Width + 303030 = 36885522 + 303030 = 37188552 feet.

Hence, the length of the movie screen is 37188552  feet.

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The length of the side is 10 units.

To solve word problems, we try to assign variables to the quantities involved and use the given information to interpret the situation as a mathematical equation. Mathematical equations can then be solved using various techniques, so we get a solution which is then reinterpreted into the situation.

Now, According to the question:

Let the length of the side is 'L'

The area of a square is numerically 60 more than the perimeter.

Then, P = perimeter = 4L

A = area = \(L^2\)

A = P + 60 ⇒

\(L^2\) = 4L + 60

\(L^2\) - 4L - 60 = 0

(L - 10)(L + 6) = 0

L = 10 or -6

L must be positive,

Since s can't be negative, L = 10 units.

Hence, The length of the side is 10 units.

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The rhombus' diagonals form a right angle cut across one another. The expression that can be used to symbolize AD in a rhombus ABCD is,

AD = \(\frac{1}{2} \sqrt{(2n+5)^{2} + (4n-3)^{2} }\)

What is property of diagonals of rhombus?

The diagonals of the rhombus bisect each other at right angle.

Given,

The length of the one diagonal of the rhombus is,

AC = (2n+5)

The length of the another diagonal of the rhombus is,

BD = (4n−3)

Let the center point of the rhombus is O as shown in the figure.

In ΔAOD the ∠AOD is the right angle triangle. Thus by the Pythagoras theorem,

AD² =AO² + DO²

Suppose the above equation as equation number 1.

As the diagonals of the rhombus bisect each other thus,

AO = 1/2 AC

DO = 1/2 BD

Put the values in equation 1,

AD² = ( 1/2AC)² + (1/2BD)²

Put the values,

AD² = [\(\frac{1}{2}(2n+5)\)]² + [\(\frac{1}{2}(4n-3)\)]²

AD²= [1/4 (2n+5)²+(4n−3)²]

AD² = √1/4 [ (2n+5)²+(4n−3)²]

AD²= 1/2√[ (2n+5)²+(4n−3)²]

Hence the expression in terms of  can be used to represent AD in rhombus ABCD is,

AD²= 1/2√[ (2n+5)²+(4n−3)²]

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Let x = 1st even integer

Let x + 2 = 2nd even integer

Let x + 4 = 3rd even integer

Now look at words and translate    Three times the sum of first and third is 24 greater than 4 times the second

                                                           3(        x   + x + 4)               =      24     +           4(x + 2)  now simplify

                                                           3(2x + 4)                            =       24       +         4(x + 2)  distribute

                                                                   6x + 12                       =      24         +       4x + 8  combine

                                                                                         6x + 12 = 32 + 4x       subtract 4x from each side

                                                                                        -4x                  -4x

                                                                                        2x +12   = 32         subtract 12 from each side

                                                                                              -12     -12

                                                                                                2x = 20      divide both sides by 2

                                                                                                   x = 10

This tells us that the first even number is 10, the second is 12, and the third is 14.

CHECK

3(10 + 14) = 24 + 4(12)

3(24)        = 24 + 48

     72      =  72√

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

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Answer: 20 (Option C)

Step-by-step explanation: Since B is the midpoint, Just set 5x and 3x+4 congruent to eachother. After you find out x ( which is 2) just plug it in and add them to get AC.

Answer: \(\displaystyle d=\sqrt{1 7}\;\text{or about 4.123 units}\)

Step-by-step explanation:

     We can use the distance formula to solve. Let (4, 6) be point one and (5, 2) be point two.

     \(\displaystyle d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2}\)

     \(\displaystyle d=\sqrt{(5-4)^2 +(2-6)^2}\)

     \(\displaystyle d=\sqrt{(1)^2 +(-4)^2}\)

     \(\displaystyle d=\sqrt{1 +16}\)

     \(\displaystyle d=\sqrt{1 7}\)

Answer:

(-3,4)

Step-by-step explanation:

So we have the quadratic function:

\(f(x)=x^2+6x+13\)

The formula for the x-coordinate of the vertex is:

\(x=-b/2a\)

From the function, we can determine that a is 1, b is 6, and c is 13. Thus:

\(x=-(6)/2(1)\)

Multiply:

\(x=-6/2\)

Divide:

\(x=-3\)

Now, substitute this back into the function to solve for the y-coordinate:

\(f(-3)=(-3)^2+6(-3)+13\)

Square and multiply:

\(f(-3)=9-18+13\)

Add:

\(f(-3)=4\)

So, the vertex is (-3,4)

And we're done!

Answer:

ok

Step-by-step explanation:

Answer:

57

Step-by-step explanation:

45,45,48,54,60,64,65,70

find middle

Answer:

57

Step-by-step explanation:

First put the points in order.

45 45 48 54 60 64 65 70.

Then find the middle number(s).

54 and 60

Find the middle of that.

54+60=114/2=57

Answer:

Force= Mass×Accelaraion

F=m×a

But as The unit of accelaration is given miles per hour and the SI is meters per second sqaure we have to convert 10mph to m/s²

Thus, we have 10mph = 4.47 meters per second square. (i converted using scientific calculator)

So now we have,

2000N= m×4.47m/s²

= 2000/4.47m/s²=m

= 447.42

Thus the mass of the object is 447.42 (i am not sure of units)

Answer:

Force= Mass×Accelaraion

F=m×a

The unit of accelaration is given miles per hour and the SI is meters per second sqaure we have to convert 10mph to m/s²

we have 10mph = 4.47 meters per second square

2000N= m×4.47m/s²

= 2000/4.47m/s²=m

= 447.42

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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Answer:

Concept:

Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!

The values are given below as

The image below shows how to calculate the mean

By substituting values, we will have

Hence,

The mean = 10

To calculate the variance, we will use the formula below

Hence

The variance = 21

To calculate the standard deviation,

Hence,

The standard deviation is = 4.58

The space matrix is a strategic management tool that helps organizations analyze their internal dimensions by plotting their financial strength and competitive advantage on the axes. This analysis enables decision-makers to determine appropriate growth strategies and allocate resources effectively.

The two internal dimensions represented on the axes of the space matrix are technology and market diversity. This is determined by plotting the company's position on each dimension using a scale of one to six, with one being low and six being high. The space matrix then combines these two dimensions with two external dimensions (industry attractiveness and business strength) to create a visual representation of the company's position in the market. In summary, the space matrix assesses a company's competitive position and strategic choices by evaluating these four dimensions in a three-by-three matrix.

Financial Strength (FS): This axis represents the organization's financial position, which can include factors like revenue, profitability, and access to capital. A strong financial position allows a company to invest in new projects and face competition effectively. Competitive Advantage (CA): This axis represents the unique capabilities, resources, or attributes that give an organization an edge over its competitors. These can include aspects like superior products, strong brand recognition, and efficient supply chain management. A sustainable competitive advantage enables a company to maintain or improve its market position.

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Answer:

A & C

Step-by-step explanation:

AB is the shortest segment in ABC

AC = 2AB

Since ABCD is an isosceles trapezoid, we know that AB = CD. Additionally, we know that AD = BC. Therefore, we can set up two equations:

AB = CD

AD = BC

Using the fact that B = x + 10 and C = 2x - 30, we can substitute those values into the equations:

AB = CD

x + 10 + AD = 2x - 30 + BC

Since AD = BC, we can simplify the second equation to:

x + 10 + AD = 2x - 30 + AD

x + 10 = 2x - 30

x = 40

Now that we know x, we can find the measures of angles B and C:

B = x + 10 = 50

C = 2x - 30 = 50

Since ABCD is an isosceles trapezoid, we know that angles B and C are congruent. Therefore, each of them measures 50 degrees. Since the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation:

A + B + C + D = 360

Substituting in the values we have:

A + 50 + 50 + D = 360

Simplifying the equation:

A + D = 260

Since ABCD is an isosceles trapezoid, we know that angles A and D are congruent. Therefore, we can set up the equation:

A + D = 2D

Substituting in the value we have:

2D = 260

Simplifying the equation:

D = 130

Therefore, the measure of angle D is 130 degrees.

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The probability of the spinner landing on 2 reds is P ( 2 Reds ) = 1/8

Given data ,

To find the probability of spinning two reds, we need to calculate the probability of spinning a red on the first spin and then multiply it by the probability of spinning a red on the second spin.

The probability of spinning a red on the first spin is 1/4 since there is one red section out of four equal sections.

Now , the value of P ( R ) = 1/4

when the spinner is spun twice ,

P ( A ) = P ( R ) P ( R )

P ( A ) = 1/4 ( 1/4 )

On simplifying , we get

P ( A ) = 1/8

Hence , the probability is P ( A ) = 1/8.

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As there are three players, the game will be played in cycles of 3 rounds. After each cycle is completed, the round after will be the round where every single player has 1 token less than they did at the beginning of the previous cycle.

After the first round of the game, player one will have 12 tokens, player two will have 15 and player three will have 14 left. Looking at this sequence, it is evident that player one will finish first.

Go a few rounds to establish the pattern:

Beginning chips: A B C

15 14 13

1st round:

12 15 14

2nd round: 13 12 15

3rd round: 14 13 12

So after 3 rounds and successive 3 rounds each player has one less than he started with at the beginning of the 3 round series.

So after 36 rounds each will be down 12 from the beginning:

                                            A B C

                                             3 2 1

On the 37 round A will give up his 3 to end at 0

37

For more clear understanding:

As player has one token less at the beginning of a new cycle than he/she had at the beginning of the previous cycle we go (12∗3)+1=37(12∗3)+1=37 to see how many turns it will take them to reach zero.

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Answer:

12.5 months

Step-by-step explanation:

Let x be the number of months

Let f(n) be the money saved by person n

we know that f(J)=300+20m

we also know that f(T)=400+12m

we want f(J)=f(T) so we have 300+20m=400+12m. solving we get 8m=100 and so m=12.5. Thus in 12.5 months they will have the same amount.

Step-by-step explanation:

q/8=5/4

q = 5/4 × 8

q = 5×2

q= 10

Answer:

the answer for this. question q is equal to 10

Answer:7 pens per second

Step-by-step explanation: 35/5=7

Answer: 7 Pens Per second

Step-by-step explanation:

35/5 = 7

The probability of a 6-card hand with three hearts and three spades is 0.001862, or 1/535

Probability is the mathematics of chance; it is the study of calculating the likelihood of certain outcomes in any given situation.

Here we have to find the probability of a particular 6-card hand consisting of three hearts and three spades is determined first by the fact that there are 13 hearts and 13 spades in a standard deck of 52 cards.

To calculate the probability of a 6-card hand consisting of three hearts and three spades, one must first consider that the order of the cards in a hand does not matter.

The total number of combinations of three hearts and three spades that can be drawn from a standard deck of cards is

=> 4,824.

This number can be calculated by an equation that uses the number of hearts, spades, and cards in a standard deck

=> (13 x 13 x 52).

Then the probability of a 6-card hand consisting of three hearts and three spades is calculated by dividing the number of combinations of three hearts and three spades

=>  (4,824) / (2,598,960).

This equation yields a probability of 0.001862, or a 1 in 535 chance of getting a 6-card hand with three hearts and three spades.

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The smaller of the two acute angles is approximately 36.87 degrees, and the larger acute angle is approximately 53.13 degrees.

We can use the trigonometric ratios of sine, cosine, and tangent to find the measures of the acute angles of a right triangle. For a triangle with legs of length 3 and 4, we can use the ratios:

sin θ = opposite/hypotenuse = 3/5

cos θ = adjacent/hypotenuse = 4/5

tan θ = opposite/adjacent = 3/4

Using inverse trigonometric functions, we can find the measure of the smaller acute angle θ₁:

θ₁ = sin^-1(3/5) ≈ 36.87°

To find the measure of the larger acute angle θ₂, we can use the fact that the sum of the measures of the acute angles of a right triangle is 90°:

θ₂ = 90° - θ1 ≈ 53.13°

Note that the angles can also be expressed as exact values using inverse trigonometric functions, but the problem asks for at least one digit beyond the decimal point.

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The truck is propelled forward by force D of 2.769 * 10⁴ N and acceleration of 0.78 m/s2.

The definition of force is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

Given, Mass of the truck = 5000 kg

Mass of car = 1600 kg

Force applied = 25000 N

As we know Force (F)  =m.a

Where m = mass of the body

a = acceleration of the body

25000 = (5000  + 1600) * a

a = 25000/ 6600 = 3.7878.

a = 3.79 m/s²

According to diagram D = ma

m = 27000 + 8500 = 35500 kg

a = 0.78 m/s²

so D = 35500 * 0.78 = 27690N

Therefore, Force D that moves the truck forward is 2.769 * 10⁴ N, and acceleration is  0.78 m/s².

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