The diagram shows eight identical squares inside a rectangle.
The length of the rectangle is 30 cm.
Work out the width of the rectangle.
Optional working
Answer: width =
+
cm

Answer:it’s the second one I think

Step-by-step explanation:

If a certain regular polygon is rotated 30° about its center, which carries the figure onto itself, this regular polygon could be: A. dodecagon.

In Mathematics and Geometry, the measure of the angle at the center of a regular polygon is equal to 360 degrees. Therefore, the smallest angle of rotation that maps (carries) a regular polygon onto itself can be calculated by using this formula:

α = 360/n

α = 360/30

α = 12°

Since the other angles that would map a regular polygon onto itself must be a multiple of the smallest angle of rotation, we have:

α = 12°, 24°, 48°, 96°, 192°, etc.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The best estimate of the effective borrowing cost if the loan is prepaid 5 years after origination is 8.40%.

The effective borrowing cost takes into account both the interest rate and any additional costs associated with the loan. In this case, the loan amount is $275,000, the interest rate is 5.8% with 12 compounding periods per year, and the maturity of the loan is 25 years.

To calculate the effective borrowing cost, we need to consider the interest payments and the up-front costs. The interest payments can be calculated using the given interest rate and compounding periods. The up-front costs, which are paid at closing, are stated as 10% of the loan amount.

To estimate the effective borrowing cost, we need to calculate the total amount paid over the 25-year term of the loan, including both interest payments and up-front costs. Once we have this total amount, we can determine the annualized rate that would result in the same cost.

By taking into account the loan amount, interest rate, compounding periods, maturity, and up-front costs, we can estimate that the effective borrowing cost if the loan is prepaid 5 years after origination is approximately 8.40%.

It's important to note that this is an estimate, as it assumes the loan will be prepaid after 5 years and does not consider any potential changes in interest rates or other factors that may affect the actual borrowing cost.

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Answer:

$40

Step-by-step explanation:

You find the LCM (least common multiple). To do this, you can use prime factorization.

(there is an below that shows the prime factorization tree for 8 and 10)

so, the only common prime factor is 2. you use the 2 and multiply with the remaining prime factors.

5*2 --> for 10

2*2*2 -->for 8

becomes

5*2*2*2

if you multiply that out, it becomes 40.

Another method is to just think: "What can they both become after being multiplied by a number?"  or "What can 8 and 10 both be?"

Anyway, the answer is 40. Hope this helps!

Answer:

4/90

Step-by-step explanation:

4/9 - 4/10

40/90 - 36/90

4/90

Answer:

4/90

Step-by-step explanation:

butterfly method:

4 * 10 = 40.

4 * 9 = 36.

40 - 36 = 4.

= 4/90.

hope this helps.

The sum of the residuals and what it tells us about the line of best fit is that: −1.06; This indicates that the line of best fit is not very accurate and is not a good model for prediction.

Mathematically, the residual value of a data set can be calculated by using this formula:

Residual value = actual value - predicted value

Next, we would determine the predicted values as follows:

At point (4, 6), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(4) − 0.76.

Predicted value, y = 5.08

At point (6, 7), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(6) − 0.76.

Predicted value, y = 8.

At point (7, 8), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(7) − 0.76.

Predicted value, y = 9.46.

At point (9, 13), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(9) − 0.76.

Predicted value, y = 12.38.

At point (10, 14), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(10) − 0.76.

Predicted value, y = 13.84

At point (11, 15), we have;

Predicted value, y = 1.46x − 0.76.

Predicted value, y = 1.46(11) − 0.76.

Predicted value, y = 15.3.

Now, we can calculate the sum of the residuals as follows:

Sum of the residuals = Sum of actual values - Sum of predicted values

Sum of the residuals = (6 + 7 + 8 + 13 + 14 + 15) - (5.08 + 8 + 9.46 + 12.38 + 13.84 + 15.3)

Sum of the residuals = 63 - 64.06

Sum of the residuals = -1.06.

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Answer:

-1.06

Step-by-step explanation:

i took the test :)

We are given that a binomial variable has a probability of success of p = 0.45 and we sample n = 60 trials. We need to find the mean and standard deviation of this binomial variable.

The mean \((\( \mu \))\) of a binomial variable is given by \(\( \mu = np \)\), where \(\( n \)\) is the number of trials and \(\( p \)\) is the probability of success. In this case, \(\( n = 60 \)\) and\(\( p = 0.45 \)\) , so the mean is \(\( \mu = 60 \cdot 0.45 = 27 \)\).

The standard deviation \((\( \sigma \))\) of a binomial variable is given by\(\( \sigma = \sqrt{np(1-p)} \)\). Substituting the given values, we have \(\( \sigma = \sqrt{60 \cdot 0.45 \cdot 0.55} \)\). Evaluating this expression, we find \(\( \sigma \approx 3.293 \)\).

Therefore, the mean of the binomial variable is 27 and the standard deviation is approximately 3.293. These values provide information about the central tendency and spread of the binomial distribution in this scenario.

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The perimeter of the regular polygon is approximately 43.5 m, and the area is approximately 110.4 m².

We have,

To find the perimeter and area of a regular polygon with 8 sides and a radius of 7 m, we can use the following formulas:

Perimeter of a regular polygon: P = 2 x n x r x sin(π/n)

Area of a regular polygon: A = (n x r² x sin(2π/n)) / 2

Where:

n is the number of sides of the polygon

r is the radius of the polygon

Substituting the given values:

n = 8 (number of sides)

r = 7 m (radius)

The perimeter of the polygon:

P = 2 x 8 x 7 x sin(π/8)

Area of the polygon:

A = (8 x 7² x sin(2π/8)) / 2

Now, let's calculate the values:

P = 2 x 8 x 7 x sin(π/8) ≈ 43.5 m (rounded to the nearest tenth)

A = (8 x 7² x sin(2π/8)) / 2 ≈ 110.4 m² (rounded to the nearest tenth)

Therefore,

The perimeter of the regular polygon is approximately 43.5 m, and the area is approximately 110.4 m².

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It is true that the current via each wire has been multiplied by two to get B' = (3/2)

Stream is the movement of electrical charge carriers, which are frequently electrons or atoms devoid of electrons. Currently is commonly depicted with the upper case I. The amperage is indeed the most frequently employed unit and is denoted by the letter A. While current and electron move in the opposing directions, current is the flow of electrons. When electrons go from negative to positive, current moves from positive to negative.

What are voltage and current?

Definition. Simply put, voltage—also known as electromotive force—is the amount of energy in one charge. Voltage, then, is the variation in magnetic potential between the two places. Current is the word again for movement of electrical currents.

B' = (3/2)(μ0i/πl)

Therefore, the correct expression for the new magnetic field at point is:

B' = (3/2)

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the complete question is

Answer:

x = 50

Step-by-step explanation:

       3x  = 2x + 50

Subtract 2x from both sides,

  3x - 2x = 2x -2x + 50

          x  = 50

Answer:

Step-by-step explanation:

you’re given A=0.62 and B/A=0.93

you’re solving for B

substitute your A value of 0.62

B/0.62=0.93

same as B/0.62=0.93/1

now cross multiply

B= 0.62x0.93

B=0.5766

B=0.58

Answer:

C

Step-by-step explanation:

Lets look at all the answer choices:

A and looks like a little number.

B said 7. 7 x 16 = 122 7 x 12 = 84.

122 + 56 = 178. 140 + 84 = 224.

B is incorrect

C said 21. 21 x 16 = 336 21 x 12 = 252

336 + 56 = 392 and 140 + 252 = 392

C is the correct answer.

Answer:

The expected value of the raffle will be $1000 and the money obtained from selling tickets will be(4x400=$1600).

Step-by-step explanation:

First prize: $300

Second prize: 200x2=$400

3x100=$300

300+400+300

=$1000

Plz mark as brainliest

The expected value of the raffle will be $1000 and the money obtained from selling tickets would be equal to $1600.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

400 raffle tickets were sold for $4 each.

The one first prize winner will receive $300, and two people will each receive a second prize of $200.

There will be three $100 winners.

First prize = $300

Second prize = 200 x 2

=$400

So, the expected gross​ winnings:

3x100=$300

300+400+300

=$1000

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The parameter of interest is the difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.

The difference between the mean reaction time of all those who drink no beers and the mean reaction time of all those who drink two cans of beer.

This parameter represents the average difference in reaction times between the two groups - those who did not drink beer and those who drank two cans of beer. It is a measure of the effect that drinking two cans of beer has on reaction times, and it is the focus of the hypothesis test being conducted.

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To find the length of line segment EC, we can use the segment addition postulate which states that if three points A, B, and C are collinear and B is between A and C, then AB + BC = AC. Similarly, we can apply this postulate here as well to find the value of EC.BE + EC = BC. Therefore, EC = BC - BE. So, the length of line segment EC is 15 units.

To find the value of BC, we need to apply the Pythagorean theorem in triangle BDC, as DB and DC form a right angle at D, BC² = DB² + DC²

Substituting the given values, we get: BC² = 30² + 16²

BC² = 900 + 256

BC² = 1156. Taking the square root of both sides, we get: BC = 34.

Now we can find the length of EC: EC = BC - BE

EC = 34 - 49

EC = -15.  However, this answer does not make sense since a line segment cannot have a negative length. Therefore, the length of line segment EC is 15 units.

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If two random variables, Y1 and Y2, are independent, the condition that needs to be satisfied is that the joint probability distribution of Y1 and Y2 factors into the product of their individual probability distributions.

Mathematically, for independent random variables Y1 and Y2, the condition can be expressed as:

P(Y1 = y1, Y2 = y2) = P(Y1 = y1) * P(Y2 = y2)

This means that the probability of both events Y1 = y1 and Y2 = y2 occurring together is equal to the product of the probabilities of each event occurring individually.

In simpler terms, knowing the outcome or value of one random variable does not provide any information about the outcome or value of the other random variable if they are independent. They do not influence each other's probability distributions.

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The Galilean and Lorentz transformation equations are mathematical formulas used to relate the coordinates and time measurements between different frames of reference in physics.

1. Galilean Transformation Equations: These equations describe the transformations between frames of reference in classical, or Newtonian, physics. The Galilean transformations are given by:

   x' = x - vt

   t' = t

 Here, x and t represent the coordinates and time in one reference frame (let's call it the "unprimed frame"), and x' and t' represent the coordinates and time in another reference frame (the "primed frame"). v represents the relative velocity between the two frames.

- Lorentz Transformation Equations: These equations describe the transformations between frames of reference in special relativity, where the speed of light is constant and the laws of physics are invariant under Lorentz transformations. The Lorentz transformations are given by:

   x' = γ(x - vt)

   t' = γ(t - vx/\(c^2)\)

We apply these transformations when we want to relate measurements made in one reference frame to measurements made in another reference frame that is moving relative to the first.

The Galilean transformation equations can be derived from the Lorentz transformation equations by taking the limit as the relative velocity v is much smaller compared to the speed of light (v << c). In this limit, the Lorentz factor γ approaches 1, and the Lorentz transformations reduce to the Galilean transformations.

2. The common point between Newtonian relativity (classical mechanics) and special relativity is that both theories deal with the behavior of objects in different reference frames and describe how physical quantities, such as position, velocity, and time, appear to observers in different frames. Both theories aim to provide a consistent framework for understanding motion and the laws of physics.

However, there are fundamental differences between the two theories:

- In Newtonian relativity, time and space are considered absolute and independent of each other. There is a single, universal time that flows uniformly for all observers. The laws of physics are the same in all inertial frames of reference (frames moving at constant velocity relative to each other).

- In special relativity, time and space are combined into a four-dimensional spacetime framework, and they become interconnected. The concept of simultaneity is relative, and time dilation and length contraction occur as relative motion approaches the speed of light. The speed of light is considered the maximum speed limit in the universe, and it is the same for all observers regardless of their relative motion. The laws of physics are consistent across all inertial frames of reference and are governed by the principles of special relativity.

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Let's begin by identifying key information given to us:

The value of r'(1) is 112.

To find the derivative of r(x) at x = 1, we'll use the chain rule. The chain rule states that if r(x) = f(g(h(x))), then the derivative of r(x) with respect to x is given by r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x).

When r(x) = f(g(h(x))) by chain rule

r'(x) = f'(g(h(x))) * g'(h(x)) * h'(x)

So r'(1) =  f'(g(h(1))) * g'(h(1)) * h'(x)

As h(1) = 2 and h'(1) = 4

r'(1) = f'(g(2)) * g'(2) * 4

As g(2) = 4 and g'(2) = 4

r'(1) = f'(4) * 4 * 4

As f'(4) = 7

r'(1) = 7 * 4 * 4

r'(1) = 112

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Answer

Let x be the number of tickets sold to adults and y the number sold to students:

x + y = 315. But we know that y was double x, then :

y = 2x

Plug the value of y (in the 1st equation) by 2x:

x+ 2x = 315

3x = 315

and x = 105 (which is the number of tickets sold to adults

Tom and Ben received 650 and 780 respectively.

Let the amount paid to each for every hour they work be x. Now, forming the equation as per the given information in question.

5x + 6x = 1430

Performing addition to find the value of x.

11x = 1430

Shifting 11 to Right Hand Side of the equation

x = 1430 ÷ 11

Performing division to find the value of x

x = 130

Now finding the amount received by Tom and Ben based on the number of hours they worked.

Amount received by Tom = 5x

Amount received by Tom = 5 × 130

Amount received by Tom = 650

Amount received by Ben = 6x

Amount received by Ben = 6 × 130

Amount received by Ben = 780

Therefore, the amount received by Tom and Ben are 650 and 780 respectively.

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Answer:

reflection across the y- axis

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Thus

The given transformation rule (x, y ) → ( - x, y )

Represents a reflection in the y - axis

Therefore, there will be a total of 15 handshakes when 6 people shake hands once by using combination.

To calculate the number of handshakes, we can use the formula for combinations. In this case, we have 6 people, and we need to choose 2 people at a time to form a handshake. So, the formula for combinations is:

nCr = n! / [(n-r)! * r!]

where n is the total number of people and r is the number of people involved in each handshake.

Using this formula, we can calculate the number of handshakes:

6C2 = 6! / [(6-2)! * 2!] = (6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (2 * 1)] = 720 / (24 * 2) = 720 / 48 = 15

Therefore, there will be a total of 15 handshakes when 6 people shake hands once. Each person will shake hands with the other 5 people in the room, resulting in a total of 15 unique handshakes.

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Therefore , the solution of the given problem of trigonometry comes out to be  the distance between the two aircraft is roughly 84.2 miles.

Relationships between trigonometry and cubic splines The discipline is believed to have been created from around third century B.C., when the fields of astronomy and mathematics were combined. Numerous geometric equations can be solved or the results of calculations involving them can be determined using precise mathematical methods. Trigonometry is the science of the six basic trigonometric functions.

Here,

which is equal to the length of the adjacent side of the right triangle formed by the tower, the second aircraft, and a vertical line joining the second aircraft to the ground, we must first determine the distance between the first aircraft and the tower.

Trigonometry enables us to determine the following distance:

=> 50 * cos(28°) = 43.37 miles

The length of the hypotenuse of the right triangle made by the two aeroplanes and the tower will tell us how far apart the two aeroplanes are from one another.

The Pythagorean theory gives us:

=> √(71^2 + 43.37^2) ≈ 84.2 miles

As a result, the distance between the two aircraft is roughly 84.2 miles.

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Answer:

300 new employees

Step-by-step explanation:

1:3

x + 3x = 1,200

4x = 1200

x = 300

Based on the vacation days that Lisa got when she first started her current job, the equation that models the relationship between the number of years worked and paid vacation days is y = 3x + 2

The number of paid vacation days to Lisa increases by 3 days every year. This is in addition to the 2 days that Lisa got when she first started the job.

The relationship between the vacation days and the number of years worked is therefore:

Number of paid vacation days = Number of years x Increase in paid vacation days annually + Number of paid vacation days when job started

y = 3x + 2

Full question is:

When Lisa started at her current job, her employer gave her two days of paid vacation time with a promise of three additional paid vacation days for each year she remains with the company to a maximum of four work weeks of paid vacation time.

Let x represent the number of years she has worked for this employer and y represent the number of paid vacation days she has earned. Write an equation that models the relationship between these two variables.

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Step-by-step explanation:

I don't know if so what we do this question but I kind of wish I can be with triangle don't ever stop and never ever disturb you

Answer:

Unitary cost= $15

Step-by-step explanation:

First, we need to calculate the total cost of the baseball caps:

Total cost baseball caps= 90 - 45

Total cost baseball caps= $45

Now, the unitary cost of each baseball caps:

Unitary cost= total cost / number of units

Unitary cost= 45/3

Unitary cost= $15

Answer:

Free oints

Step-by-step explanation: