Select the total number of possible permutations.

On a separate piece of paper, draw tree diagrams to show all possible outcomes if you match the letters in box 1 to the numbers in box 2.

The centripetal acceleration of the wooden block is 0.32 m/s^2.

The centripetal acceleration of an object moving in a circle with radius r and angular velocity ω (in radians per second) is given by the formula:

a = rω^2

In this problem, the wooden block is on the end of a string with a radius of 0.7 meters, and it makes 14 rotations in 20.7 seconds. The angular velocity ω can be calculated by dividing the number of rotations by the time:

ω = (14 rotations) / (20.7 seconds) = 0.676 radians/second

Plugging in the values for r and ω, we get:

a = (0.7 meters) × (0.676 radians/second)^2 = 0.32 m/s^2

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The given question is incomplete, the complete question is:

A group of students observes that a wooden block (m = 0.40 kg) on the end of a string with a radius of 0.7 meters makes 14 rotations in 20.7 seconds when twirled. Part A Calculate the centripetal acceleration of the wooden block?

Answer: The side of the square is 20 miles

Step-by-step explanation:

Since the area of square= side *side

given, area =400 square miles

400 = side *side

400= side²

√400=side

20 miles=side

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The measures in the parallelogram are given as follows:

In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.

The angles of 12x + 3 and 7x - 13 are consecutive, meaning that the value of x is given as follows:

12x + 3 + 7x - 13 = 180

19x = 190

x = 190/19

x = 10.

Then the angle measures are given as follows:

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The domain and range of the function  f(x) = 3/x + 2 are  (-∞, 0) ∪ (0, ∞) and  (-∞, 2) ∪ (2, ∞). The vertical and horizontal asymptotes are x = 0 and y = 2 respectively

In mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.

To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.

The function f(x) = 3/x + 2

The domain of the function is (-∞, 0) ∪ (0, ∞)

The range of the function is (-∞, 2) ∪ (2, ∞)

The x - intercept is (-3/2, 0)

The y - intercept does not exist

The vertical asymptotes is x = 0

The horizontal asymptotes is y = 2

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To find the expression for the nth term of the sequence, we need to first find the common difference.

The common difference is the difference between any two consecutive terms in the sequence. We can see that the difference between each pair of consecutive terms is 6. Therefore, the common difference is 6.

To find the nth term, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

Substituting the values we have:

a1 = 5

d = 6

So the expression for the nth term of the sequence is:

an = 5 + (n - 1)6

Simplifying:

an = 6n - 1

Answer:

x=14, and value of second one would be 7

Step-by-step explanation:

  tanθ   = √3 are the values of cos and tan in Trigonometric Ratios .

How are trigonometric ratios defined?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Sinθ =  -√3/2

  cosθ = √1 - sin²θ

        = √1 - (-√3/2)²

       = √ 1 - 3/4

       = √4-3/4

     = √1/4

 cosθ = 1/2

since π<θ<3π/2 in third quadrant.

 We know, cosθ in third quadrant is negative.

   cosθ = -1/2

  tanθ = sinθ/cosθ

     tanθ = -√3/2/-1/2

       tanθ   = √3

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The number can be said to be a multiple of 4 if the last two digits of the number is a multiple of 4

Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder

Given data ,

Let the number be represented as n

Now , the number can be said to be a multiple of 4 if the last two digits of the number is a multiple of 4

Let the value of the number n be n = 3240

Now , the last two digits of the number is 40

And , the number 40 is a multiple of 4 , so the number 3240 is also a multiple of 4

where n / 4 = 810

Hence , the factors of the number 4 is a multiple of 4

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Answer:

Step-by-step explanation:

The rate of change is dy/dx=-1025

The answer is 4 times the cube of the first number minus the sum of the second number and two times the third number. That is the result of the calculation is -6.

To calculate this, first, we multiply the first number by itself twice to get the cube of the first number. Then, we subtract the sum of the second and third numbers multiplied by two from the cube of the first number. This result is our answer.

For example, let's say we have the numbers 2, 3, and 4. We first calculate the cube of 2, which is 8. Then, we subtract the sum of 3 and 4 multiplied by two, which is 14. So, the final answer is 8 - 14 = -6.

We can also show the stepwise calculation as follows:

= 2³ - (3 + 2 × 4)

= 8 - 14

= -6

Therefore, the result of the calculation is -6.

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It can't because 15 + 8=23 and the sum of the first 2 sides have to be greater than the third side
So the answer is 18

Answer:

I'm going to assume it's a right triangle, but if you're looking for the hypotenuse with the side lengths 5 and 8, then the answer is 9.434

You can write a check for the full amount of $303.12 right away because you currently owe $378.12 on your credit card.

aggregating attempting to quantify the number, maximum count, or time needed. The sum in front of you or being contemplated about is quite active. the overall verdict, its impact, or its import. three accountings: initial, interest, and indeed the third. Word equivalents include amounts, amounting, and amount. supple noun How much something is, how many you have, what you're using, or even how much you get is its quantity. He needs as much cash to get by.

given

owe $378.12 on your credit card

past due charge of $25

limit fee of $50

$378.12- ($25 + $50 )

= $378.12 - $75

= $303.12

You can write a check for the full amount of $303.12 right away because you currently owe $378.12 on your credit card.

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Answer: (2,1.6)

y=1.6

Step-by-step explanation:

you have the x coordinate, so that means x=2.

Plug in values for x:

5(2) + 5y = 18

10 + 5y = 18

Solve for y.

Answer:

The missing coordinate is 1.6.

Step-by-step explanation:

A coordinate is two points, x value and y value, on a graph. Ex: 1, 4. 1 is on the x axis, and 4 is on the y axis. In some Math problems, the point in the x value will be replaced with x.

5x + 5y = 18

5(2) + 5y = 18

10 + 5y = 18

10 - 10 + 5y = 18 - 10

5y = 8

5y/5 = 8/5

y = 1.6

To check this, we need to input 2 and 1.6 into the original problem.

5(2) + 5(1.6) = 18

10 + 5(1.6) = 18

10 + 8 = 18

18 = 18

This is true, so we know 1.6 is correct.

Answer:

Step-by-step explanation:

To determine the number of water tables set up for the Bridge Run, we need to divide the total length of the run by the distance between the water tables.

The total length of the run is given as 12 km.

The distance between the water tables is 600 meters.

To convert the units, we can express the total length of the run in meters:

12 km = 12,000 meters

Now we can divide the total length of the run by the distance between the water tables:

12,000 meters ÷ 600 meters = 20

So there are 20 water tables set up for the Bridge Run.

Answer:

Step-by-step explanation:

up to beyond hald a milimeter in length

2mm

The factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.

The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.

The given polynomial is:

x² - x - 42 = 0

Expand the quadratic equation:

x² + 6x - 7x - 42 = 0

Take the common terms out from the equation:

x(x + 6) - 7(x + 6) = 0

(x - 7)(x + 6) = 0

Hence, the factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.

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The given sequence is

[tex]z_n = log(1 + (θ/(α + {i*cos(π/2) - i*sin(π/2)}))^n)[/tex]

First, we need to simplify the expression inside the log. The term [tex]{i*cos(π/2) - i*sin(π/2)}[/tex] can be simplified to 0, since cos(π/2) = 0 and sin(π/2) = 1.

Therefore, the expression inside the log becomes [tex](1 + (\theta/\alpha)^n)[/tex].

Now, we need to find the limit of this sequence as n approaches ∞.

If θ/α is less than 1, then (θ/α)^n will approach 0 as n approaches infinity, and the limit of the sequence will be log(1) = 0.

If θ/α is greater than 1, then (θ/α)^n will approach infinity as n approaches infinity, and the limit of the sequence will be log(infinity) = infinity.

If θ/α is equal to 1, then (θ/α)^n will always be 1, and the limit of the sequence will be log(2).

Therefore, the limit of the sequence depends on the values of θ and α. If θ/α < 1, the limit is 0. If θ/α > 1, the limit is infinity. If θ/α = 1, the limit is log(2).

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Two polygons are similar if and only if all corresponding angles are congruent and all corresponding sides are proportional. The solution has been obtained by using concept of similar quadrilaterals.

What are similar quadrilaterals?

Two quadrilaterals are considered to be similar when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).

Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.

Hence, the corresponding angles need to be congruent.

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A graph of the points (-3, 8) and (5, -8) is shown on the plane below.

The slope-intercept form of the equation of the line through these points is y = -2x + 2.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (-3, 8), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - 8 = (-8 - 8)/(5 + 3)(x + 3)

y - 8 = -16/8(x + 3)

y = -2(x + 3) + 8

y = -2x - 6 + 8

y = -2x + 2

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The total price of the sofa is £3000.

To calculate this, multiply the given amount by "0.2", which equals "20%".

[tex]2500*0.2=500[/tex]

[tex]2500+500=3000[/tex]

The total price of the sofa is £3000.

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

So if we want to add 20% of any amount to said amount, we may multiply it by (1+0.2), which equals "1.20", and it'll give us the result immediately:

[tex]2500*(1+0.2)\\ \\2500*1.2=3000[/tex]

Now, working on the opposite way, let's say we want to reduce that same number (2500) by 25%, maybe because there's a discount on the product. In that case, we must multiply by (1-0.25), which equals 0.75:

[tex]2500*(1-0.25)\\ \\2500*(0.75)=1875.[/tex]

Given :-

To Find:-

Solution:-

Here we are given that Ryan purchases a sofa for £2500 . In order to find the cost of sofa after VAT , find 20% of the price of the sofa,

20% of £2500

20/100 * £2500

£500

Now add this to the original price of the sofa,

£2500 + £500

£3000

Hence the cost of the sofa after VAT is £3000 .

The probability that he will make both free throws is 0.84.

What exactly is the meaning of probability?

Probability expresses the possibility of an event. This branch of mathematics studies the occurrence of a random event. The value ranges between 0 and 1. Probability is used in mathematics to anticipate the possibility of events occurring.

Probability refers to the likelihood of something occurring. This fundamental premise of probability theory is used by the probability distribution. We must first know the entire number of possibilities before we can assess the possibility of an event occurring.

P(E) is the probability of an event occurring divided by the total number of outcomes.

Now,

Given that player makes 92% of freethrows

that means p(making free throws)=92/100

=23/25

so making two free throws probability will be =23*23/25*25

=529/625

=0.84

Hence,

           The probability that he will make both free throws is 0.84.

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The width of the olen river is 16 yards

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

ABC, ~ EDC

The above means tha the triangles are similar triangles

Using the above as a guide, we have the following:

x : 32 = 20 : 40

Express as fraction

x/32 = 20/40

So, we have

x = 32 * 20/40

Evaluate

x = 16

Hence, the length is 16 yards

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The required value of the given expression of limit is 1/2.

In mathematics, a limit is a fundamental concept that describes the behavior of a function as its input approaches a certain value or point. In particular, the limit of a function at a point is the value that the function approaches as its input gets arbitrarily close to that point, whether from the left or the right.

Here,
Given expression,
[tex]=\lim_{x \to \\ \pi /3} sin(3\sqrt{2}x/\pi - sec(3x/4) + \pi/6)[/tex]

Put x = π/3
= sin (3√2 × π/3 × 1/π - sec (3/4 × π / 3) + π /6)
= sin(√2 - sec(π/4) + π/6)
= sin(√2 - √2 + π/6)
= sin(π/6)
= 1/2

Thus, the required value of the given expression of limit is 1/2.

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Answer: Approximately 34.17%.

Step-by-step explanation: Let's divide 41 by 120. Doing so, we get 0.3466666 looping forever. We can simplify that to .3417, and then turn that into a percentage giving us 34.17%

Answer: |x + 4| = 3

Step-by-step explanation:

Answer:

graph linked

Step-by-step explanation:

The value of the indicated trigonometric ratio cosβ is equal to 11/12.

From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:

In order to determine the magnitude of cosβ, we would apply the law of cosine because the given side lengths represent the adjacent side and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

Therefore, we have the following cosine trigonometric function:

cosβ = 22/24

cosβ = 11/12

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