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This relationship shows that the diameter of the central circle (2R) is twice the diameter of each outer circle (2r).

In this configuration, four outer circles are placed around a central circle, such that they are all tangent to the central circle and tangent to each other.
To determine the relationship between the diameter of the outer circles and the diameter of the inner circle, follow these steps:
1. Let the radius of the outer circles be r and the radius of the central circle be R.
2. In this arrangement, the distance between the centers of any two adjacent outer circles is equal to the sum of their radii, which is 2r.
3. Now, draw a straight line connecting the centers of these two adjacent outer circles.

This line will pass through the center of the central circle.
4. The length of this line is the sum of the radii of the outer circle, the central circle, and another outer circle, which is

r + R + r = 2r + R.
5. Observe that the line connecting the centers of the two adjacent outer circles, along with the radii connecting the center of the central circle to the points of tangency, forms a right-angled isosceles triangle.
6. Since it is an isosceles triangle, the length of the line connecting the centers of the two adjacent outer circles (2r + R) is also the length of the other side of the triangle, which is equal to the diameter of the outer circle (2r).
7. Therefore, the relationship between the diameter of the outer circles and the diameter of the inner circle is:

2r = 2r + R.
8. Simplify the equation to find the relationship: R = 2r.

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The below list represents the years from driest to wettest

2012, 2011, 2009, 2008, 2010  

The average rainfall in Phoenix is 8.29 inches per year

The table shows recent data on the difference in annual rainfall from the average.  

Phoenix Annual Total Rainfall  Year compared to average yearly rainfall

2008     +6.57 inches

2009   –2.68 inches

2010     +12.26 inches

2011      –4.38 inches

2012     –4.46 inches

Driest   –4.46 inches       2012

Then  –4.38 inches in 2011    

–2.68 inches                    2009

+6.57 inches                    2008

+12.26 inches    Wettest  2010

The below list represents the years from driest to wettest

2012, 2011, 2009, 2008, 2010  

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We multiply the base's area by the prism's height to get the volume of the structure. In this case, the height of the prism is also 9 feet. Therefore, the volume of the triangular prism is 162 cubic feet.

By dividing the base's area by the prism's height, one can determine the volume of a triangular prism. The area of the triangular base can be calculated by using the formula

area of a triangle = [tex]\frac{1}{2}[/tex] × base × height.

In this case, the base of the triangular prism is 4 feet and the height is 9 feet. Hence, the triangle's base's area is:

[tex]\frac{1}{2}[/tex] × 4 ft × 9 ft = 18 square feet

Multiplying the area of the base by the height of the prism gives us the volume of the triangular prism:

Volume = Area of triangle × height of the triangle

18 sq ft × 9 ft = 162 cubic feet

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The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

To calculate the mean value, we add up all the values and divide by the

number of values:

(990 + 1030 + 950 + 1050 + 1000 + 980) / 6 = 1000

So the mean value is 1000 rpm.

To calculate the standard deviation, we need to first calculate the

variance:

Variance =[tex][(990 - 1000)^2 + (1030 - 1000)^2 + (950 - 1000)^2 + (1050 - 1000)^2 + (1000 - 1000)^2 + (980 - 1000)^2] / 6[/tex]

Variance = 12000 / 6 = 2000

So the variance is [tex]2000 (rpm)^2[/tex].

The standard deviation is the square root of the variance:

Standard deviation = √(2000) = 44.7 rpm

The best estimate of the true value for this data set is the mean value, which is 1000 rpm.

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Flying with the wind, a small plane flew 338 mi in 2 h. flying against the wind, the plane could fly only 312 mi in the same amount of time. So, the rate of the plane in calm air is 162.5 mph, and the rate of the wind is 6.5 mph.

Let's use variables to represent the unknowns in this problem:

- Let p represent the rate of the plane in calm air (in miles per hour).
- Let w represent the rate of the wind (in miles per hour).

When the plane is flying with the wind, the combined speed (plane + wind) is (p + w) mph. It flies 338 miles in 2 hours, so we have:

1. (p + w) * 2 = 338

When flying against the wind, the net speed (plane - wind) is (p - w) mph. It flies 312 miles in 2 hours, so we have:

2. (p - w) * 2 = 312

Now, we'll solve the two equations simultaneously. First, divide both sides of each equation by 2:

1. p + w = 169
2. p - w = 156

Next, add the two equations together to eliminate the w variable:

(p + w) + (p - w) = 169 + 156
2p = 325

Now, divide by 2 to find the rate of the plane in calm air:

p = 325 / 2
p = 162.5 mph

Now that we have the rate of the plane, we can find the rate of the wind by substituting the value of p back into either equation 1 or 2. Let's use equation 1:

162.5 + w = 169

Subtract 162.5 from both sides to find w:

w = 169 - 162.5
w = 6.5 mph

So, the rate of the plane in calm air is 162.5 mph, and the rate of the wind is 6.5 mph.

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Answer:

Step-by-step explanation:

x = 7

It is not reasonable to use the least-squares regression model to predict attendance per game for 0 wins because it involves extrapolation beyond the range of the observed data

Using the least-squares regression model to predict attendance per game for 0 wins is not reasonable because it would involve extrapolating the regression line beyond the range of the data.

In other words, the least-squares regression model is designed to capture the relationship between two variables within the range of the observed data. If we attempt to use this model to make predictions outside of this range, the results may not be reliable or accurate.

For example, if we were to use a least-squares regression model to predict attendance per game based on the number of wins a sports team had, and the range of wins in our data set was from 10 to 80, then any predictions we make for 0 wins (which is outside of this range) would be extrapolations rather than interpolations.

Extrapolation can be risky because it assumes that the relationship between the two variables continues beyond the range of the data. However, this assumption may not hold true in reality, and therefore the predictions made using extrapolation may not be accurate.

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In order to print out a deck of 52 cards, and each card having its suit and value displayed on the same line, 13 columns were used for each of the  card.

In Illustration 3, assuming that the deck contains 52 cards, each card in the deck was printed using 13 columns. This is because a standard deck of playing cards contains four suits (clubs, diamonds, hearts, and spades), and each suit has 13 cards (Ace, 2-10, Jack, Queen, King).

Therefore, to print out a deck of 52 cards, with each card having its suit and value displayed on the same line, 13 columns were used for each card.

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The complete question is :

In Illustration 3, a deck of cards was shuffled and printed out. Line 35 shuffles the deck. How many columns were used for each card in the deck, assuming that the deck contains 52 cards?

Answer:

-20p - 3.8

Step-by-step explanation:

Sure!

1.) Since you have a number outside of a parenthesis, you can distribute it to the parenthesis by multiplying it to each term in the parenthesis. You would get .2 +(-4)*5p + (-4) * 1.

2.) Now, by multiplying these together, you would get .2-20p-4.

3.) Finally, since you can further simplify by adding together like terms. .2 and -4 are both constants (numbers), so you can add them together.

4.) .2 + (-4) is equal to -3.8, so your final expression is -20p - 3.8.

Answer:

3=0

Step-by-step explanation:

The length of each leg of a right triangle given that one angle is 22° and the length of the hypotenuse is 10 inches are 3.75 and 9.27 inches respectively.

In order to determine the length of the opposite side and adjacent side, we would apply both the cosine and sine trigonometry ratio because the given side lengths represent the hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

By substituting the parameters into the sine trigonometry ratio formula, we have the following;

sin(θ) = Opp/Hyp

sin(22) = y/10

y = 10sin(22)

y = 3.75 inches.

For the adjacent side, we have:

cos(θ) = Adj/Hyp

cos(22) = x/10

x = 10cos(22)

x = 9.27 inches.

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The level of significance in a hypothesis test is the maximum allowable probability of a Type I error. A Type I error occurs when you reject a null hypothesis that is actually true.

The level of significance is usually denoted by the symbol α (alpha) and is expressed as a percentage or a decimal value, such as 5% or 0.05. This means that if the level of significance is set at 5%, there is a 5% chance of making a Type I error when the null hypothesis is true.
To answer the student question, the level of significance is not the same as the confidence coefficient or the p-value. The confidence coefficient is related to the confidence interval, which is a range of values within which the true population parameter is likely to fall. The confidence coefficient (1 - α) represents the probability that the true population parameter lies within the confidence interval.
The p-value, on the other hand, is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is less than or equal to the level of significance, you reject the null hypothesis and accept the alternative hypothesis.
Lastly, the maximum allowable probability of a Type II error (denoted by β) is not the same as the level of significance. A Type II error occurs when you fail to reject a null hypothesis that is actually false. The power of a test is defined as (1 - β) and represents the probability of correctly rejecting a false null hypothesis.

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The value of three times the number plus 17 - that same number is found to be 7.

It is provided that if twice a number is equal to that number minus then we have to find what is three times that number plus 17 minus that number.

Let's say that the number we are talking about his x.

From the given condition we can write at the twice of x will equal to x minus x - 5.

2x = x-5

Solving this simple algebraic equation.

x = -5.

Now, to find the answer,

3x + 17 - x

Putting values,

= 3(-5) + 17 -(-5)

= -15 + 17 + 5

= 7.

So, the value of thrice the number added to number minus from 17 is 7.

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From the given coordinates geometry function will be y=-3x+1.

Plotting points on a coordinate plane will provide the graph of the function y = -3x + 1. To accomplish this, we can select various x values, enter them into the equation, and then solve for y. As an illustration, if x = 0, then y = -3(0) + 1 = 1. We now get the graph's point (0, 1) thanks to this. Similar to the previous case, if we select x = 1, then y = -3(1) + 1 = -2. This results in the graph's point (1, -2) for us. By repeating this procedure, we can identify more points, which we can then join with a straight line to create the function's graph. A straight line with a slope of -3 and the point appears on the graph as a result (0, 1).

from graph we can write coordinates ,

(-1,4),(0,1),(1,-2),(2,-5)

so from these coordinates ,function will be

y=-3x+1.

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When graphed on a scatter plot, the data has a generally decreasing trend. Therefore, the basketball coach was correct in thinking that his players are not scoring as many points as they were in the previous weeks.

Based on the scatter plot, we can observe the trend that the number of game points decreases as the week progresses.

The points on the scatter plot are generally trending downwards, indicating a decrease in the number of points scored over time.

Therefore, the basketball coach was correct in his observation that his players are not scoring as many points as they were in the previous weeks.

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Radians are a unit of measurement for angles used in mathematics and physics. They are defined as the ratio between the length of an arc of a circle and the radius of that circle.

One of the most important benefits of using radians to measure angles is that they simplify calculations involving angles, making them easier to work with.

Additionally, they allow for a more elegant and unified approach to mathematical and physical problems involving angles. So, in short, the word "radian" might be associated with concepts such as circles, arcs, and the measurement of angles in mathematics and physics.

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Answer: 13/100

Step-by-step explanation:

The f(x) = 2x^2 + 4, so f(4) = 2(4)^2 + 4 = 36.

To find (Fog)(0), we first need to find g(0) and then plug that value into f(x).

We have g(x) = -3x + 4, so g(0) = -3(0) + 4 = 4.

Now we have (Fog)(0) = f(g(0)) = f(4).

We have f(x) = 2x^2 + 4, so f(4) = 2(4)^2 + 4 = 36.

Therefore, (Fog)(0) = 36.

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A has 156 cards, B has 39 cards, and J has 312 cards.

To find out how many cards A, B, and J have, follow these steps:

Let the number of cards B has be represented by the variable 'b'.

A has four times as many cards as B, so the number of cards A has can be represented as '4b'.

J has twice as many cards as A, so the number of cards J has can be represented as '2(4b)' or '8b'.

Together, A and J have 468 cards. Therefore, the equation can be written as 4b + 8b = 468.

Combine the like terms: 12b = 468.

Divide both sides of the equation by 12 to find the value of 'b': b = 468 / 12, which results in b = 39.

Now that we have the value of 'b', we can find the number of cards A and J have:

- A has 4 times as many cards as B: A = 4 × 39 = 156 cards.

- J has twice as many cards as A: J = 2 × 156 = 312 cards.

So, A has 156 cards, B has 39 cards, and J has 312 cards.

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Step-by-step explanation:

4x^2 + 16x -4       factor out a '4'

4 ( x^2 + 4x -1)     Done.  

                  There isn't anything else you can factor out of the three terms

Craig is accurate in that the supplied number line reflects the value of 1/3 since in the situation at hand, the red dot represents the value of 1/3.

Once someone outlines their solution and how they approached the challenge, clarifying questions should be asked.

List the parallels and differences between several approaches to solving the issue.

Find the mistake in a wrong response, and then provide proof to support your claim.

Create strong arguments and evaluate other people's reasoning.

What It Means: When kids can give us the right answer and explain how they arrived at it, we know they fully understand a topic.

So, in the given situation the red dot represents the value of 1/3, and thus Craig is correct that the given number line represents the value of 1/3.

Therefore, Craig is accurate in that the supplied number line reflects the value of 1/3 since in the situation at hand, the red dot represents the value of 1/3.

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Answer:

Step-by-step explanation:

There are 92 observations that are less than or equal to 50.

To calculate the cumulative frequency, we need to add up the frequencies of all the bins up to and including the bin in question. This can be calculated by adding up the frequency values for the bins that include values less than or equal to 50:

4 (from bin 15) + 62 (from bin 20) + 101 (from bin 25) + 70 (from bin 30) + 83 (from bin 35) + 20 (from bin 40) + 45 (from bin 45) + 9 (from bin 50) = 394

So, the cumulative percentage for the bin containing 50 is 92.71%. Therefore, the number of observations less than or equal to 50 is approximately 92.

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Answer:

3.25

With 3.254, rule A applies and 3.254 rounded to the nearest hundredth is: 3.25

AND

107.7

Rounded to the nearest 0.1 or

the Tenths Place.

107.747

You rounded to the nearest tenths place. The 7 in the tenths place rounds down to 7, or stays the same, because the digit to the right in the hundredths place is 4.

107.7

When the digit to the right is less than 5 we round toward 0.

107.747 was rounded down toward zero to 107.7

Answer:

5

Step-by-step explanation:

The solution of the  expression 6 × [tex]\frac{1}{4}[/tex] × (12 - 3) using order of operations rule BODMAS/PEMDAS is 13.5.

What is BODMAS?

BODMAS is acronym for B is for Bracket, O is for Of, D is for Division, M is for Multiplication, A is for Addition, and S is for Subtraction. This rule is used to explain the order of operation of a mathematical expression and solve the expression in case it has more than one operational signs. BODMAS is same as PEDMAS which i acronym for P-Parentheses, E-Exponents, D-Division, M-Multiplication, A-Addition, and S-Subtraction.

Here the expression is:

6 × [tex]\frac{1}{4}[/tex] × (12 - 3)= 6 × [tex]\frac{1}{4}[/tex] × (9) {solving the brackets}

                      = 54 × [tex]\frac{1}{4}[/tex]

                      = 13.5

The value of given expression is 13.5

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The solution of the  expression is using order of operations rule BODMAS/PEMDAS is 13.5.

BODMAS stands for Bracket, Of, D, Multiplication, Multiplication by One, Addition by One, and Subtraction by One. This rule is used to specify the order of operations in a mathematical equation as well as to solve expressions with multiple operational signs. P-Parentheses, E-Exponents, D-Division, M-Multiplication, A-Addition, & S-Subtraction are collectively referred to as PEDMAS. BODMAS stands for the same thing.

The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems.

Here the expression is:

6 × 1/4 × (12 - 3)= 6 × 1/4 × (9) {solving the brackets}

                     = 54 × 1/4

                     = 13.5

The value of given expression is 13.5

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Answer:

Base of the bottle = 15 cm

Step-by-step explanation:

Let's start by using the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * Base Area * Height

We know that the volume of the bottle is 140 cm³ and the height of the pyramid is 7 cm. We need to find the width of the base of the pyramid.

Let's first find the area of the rectangular base:

Base Area = Length * Width

We know that the length of the base is 4 cm, but we don't know the width. Let's call the width "w".

Base Area = 4 * w

Base Area = 4w

Now we can substitute the values we know into the formula for the volume of a pyramid:

Volume of a pyramid = (1/3) * Base Area * Height

140 = (1/3) * (4w) * 7

Simplifying the equation:

140 = (4/3) * 7w

140 = 9.333w

w = 15

Therefore, the width of the base of the bottle is 15 cm.

Answer:

diameter = 2× radius

circumference = [tex]2\pi r[/tex]

Area = [tex]\pi r^{2}[/tex]

use this formulas and put the given values and you will get the answers

Step-by-step explanation: