A scientist compares the weights of strawberries from two different groups. The difference between the means of the weights for the two different groups is –10 grams. The scientist uses simulations to create a randomization distribution to try to determine the likelihood that the results happened by chance. The histogram represents the results of the 1,000 trials from the simulations.

Histogram. differences in means from random grouping.

According to the randomization distribution, is the difference in means due to chance or the group from which the measurements were made? Explain your reasoning.

Type your response in the space below.


A botanist is studying the research question, “Do seeds from a common plant take longer to germinate at 72 degrees Fahrenheit or at 75 degrees Fahrenheit?” They design an experiment in which they select 20 seeds and assign those seeds to 2 groups of 10 seeds each at random. The seeds in the first group are placed in an environment that is held at a constant temperature of 72 degrees Fahrenheit, and the seeds in the second group are placed in an environment that is held at a constant temperature of 75 degrees Fahrenheit. The germination times, in days, for each group are displayed in the table.

group 1 days to germinate group 2 days to germinate
14 14
14 13
14 14
13 14
13 13
14 13
15 14
14 14
14 15
15 13
The mean germination time for group 1 is 14 days, and the mean germination time for group 2 is 13.7 days.

a. How could the botanist get a randomization distribution to compare the two groups?

Type your response in the space below.


b. How would the botanist use the randomization distribution to determine whether the difference between the mean germination time for group 1 and the mean germination time for group 2 is due to chance?

Type your response in the space below.


Noah rolls a standard number cube 10 times and adds the values to get a sum of 28. Is that unusually low? Clare simulates rolling the number cube 10 times on a computer and adds the values. She repeats that process 100 times and creates a histogram of the results.

Histogram from 22 to 48 by 2’s. Sum of 10 rolls. Height of each bar is 1, 3, 4, 9, 9, 11, 16, 14, 12, 10, 5, 5, 1.

a. Based on the histogram, does 28 seem unusually low?

Select the correct choice.


A YesYes

B NoNo
Explain your reasoning.

Type your response in the space below.


b. The mean of Clare’s simulations is a sum of 35, and the standard deviation is 5.72. Using a normal distribution as an approximation of this distribution, what is the probability that a person would roll a sum less than 28? Round your answer to the nearest hundredth.

Type your answer in the box below.

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According to the given problem, the linear regression line for the given data is y = -0.65 + 0.26x

What is linear regression?

Linear regression is a statistical method used to find the relationship between a dependent variable (y) and one or more independent variables (x). It assumes that there is a linear relationship between the variables, meaning that changes in the independent variable(s) are associated with proportional changes in the dependent variable.

The linear regression model can be represented as a straight-line equation:

y = b0 + b1*x + e

The equation of a linear regression line can be written as:

y = b0 + b1*x

where y is the dependent variable (car sales in this case), x is the independent variable (number of TV commercials), b0 is the intercept, and b1 is the slope of the line.

To find the values of b0 and b1, we need to calculate the following:

n = number of data points = 4

Σx = sum of x values = 54

Σy = sum of y values = 28

Σxy = sum of (x*y) values = 164

Σx^2 = sum of (x^2) values = 689

Using these values, we can calculate b1:

b1 = (nΣxy - ΣxΣy) / (n*Σx^2 - Σx^2)

b1 = (4164 - 5428) / (4*689 - 54^2)

b1 = 0.26 (rounded to two decimal places)

Next, we can use b1 to calculate b0:

b0 = (Σy - b1*Σx) / n

b0 = (28 - 0.26*54) / 4

b0 = -0.65 (rounded to two decimal places)

Therefore, the linear regression line for the given data is:

y = -0.65 + 0.26x

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Answer: The circumference would be 62.83

Step-by-step explanation:

C=2πr=2·π·10≈62.83185

Answer:

Step-by-step explanation:

1,500 times 0.06 = 90

90 divided by 2 = 45

Answer:

see explanation

Step-by-step explanation:

Part A is correct

Part B

student A solved the system correctly

Part C

student B  made the error from step 3 to step 4 , that is

step 3 : 3x - 5x + 150 = 114

step 4 : - 2x + 150 = 114 ( should be - 2x not 2x was the error made )

step 5 : - 2x = 114 - 150 = - 36

step 6 : - 2x = - 36 ( divide both sides by - 2 )

                x = 18

substitute x = 18 into y = - x + 30 ( from step 1 )

y = - 18 + 30 = 12

Answer : (18, 12 ) which is the answer student A obtained correctly

The simplified expression for given expression is x⁷/y¹⁰.

Simplification means reducing the expression in a simpler form using various operations while Approximation is simplifying the mathematical expression to its nearest value but not exactly correct.

To simplify the expression:

x³y⁻²x/x⁻³y⁸

Applying the properties, we get:

x³y⁻²x/x⁻³y⁸ = x⁽³⁻⁽⁻¹⁾⁾y⁽⁻²⁻⁸⁾/x⁻³x¹y⁰

Simplifying the exponents and the term with y, we get:

x⁴/y¹⁰ * x³ = x⁽⁴⁺³⁾/y¹⁰ = x⁷/y¹⁰

Therefore, the simplified expression is x⁷/y¹⁰.

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The sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13

A function is typically denoted by a symbol, such as "f(x)", where "x" is the input value and "f(x)" is the output value. The input value is sometimes referred to as the "argument" of the function.

The formula f(n) = (4n - 7) generates a sequence of numbers when we plug in different values of "n". To generate the terms f(1), f(2), f(3), f(4), f(5) we need to substitute each value of n into the formula and evaluate the expression.

Starting with n = 1, we can generate the terms as follows:

f(1) = (4 × 1 - 7) = -3

f(2) = (4 × 2 - 7) = 1

f(3) = (4 × 3 - 7) = 5

f(4) = (4 × 4 - 7) = 9

f(5) = (4 × 5 - 7) = 13

So the sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13

Each term in the sequence is found by plugging in a different value of "n" into the formula f(n) = (4n - 7). The first term, f(1), is found by plugging in n = 1, the second term, f(2), is found by plugging in n = 2, and so on.

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Answer:

Step-by-step explanation:

5824×45​

              5824

               x  45

             29120

          23296 x

          262080

You expect him to flip tails and roll an even number 10 times

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

Sample space 1 = 1, 2, 3, 4, 5, 6

Sample space 2 = H, T

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

P(Even) = 3/6

P(Tail) = 1/2

So, we have

P(Even and Tail) = 3/6 * 1/2

P(Even and Tail) = 1/4

In 40 times, we have

Expected = 1/4 * 40

Expected = 10

Hence, the number of times is 10

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Answer:
The area is given by the expreesion:

A  = 5f + 10

Step-by-step explanation:

Notice the height of the shaded area is 5. But the base is the difference between f+9 and 7
So the length of the shaded area will be f+9-7=f+2

then the area of a rectangle is given by A=height*length
This is
A = 5 (f+2) = 5f+10

Question: Write an expression for the area shaded section of this rectangle. Expand your brackets


The area of shaded section is 5f+10

To calculate the area of ​​the rectangle, it is known that just multiply the measurement of the height by the length.

So, to calculate the value of the area of ​​this rectangle considering that the shaded area is part of it, we would do [tex]\sf f+9\times5[/tex].

The area of ​​the shaded section will be given by the difference between the area of ​​the shaded area and the unshaded area.

That is, [tex]\sf(f+9-7)\times5[/tex]

[tex]\begin{array}{l}\sf(f+9-7)\times5\\\sf(f+2)\times5\\\sf 5f+2\times5\\\therefore \bf 5f+10\end{array}[/tex]

5f+10 is the shaded section area expression

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We can plot (0, 4) and (1, -28) points on a coordinate plane and draw a straight line passing through both points to graph the function.

What is a coordinate plane?

A coordinate plane, also known as a Cartesian plane, is a two-dimensional plane that is used to plot points and graph mathematical equations. It consists of two perpendicular number lines called the x-axis and the y-axis. The x-axis is the horizontal line, with positive values to the right of the origin (0) and negative values to the left of the origin. The y-axis is the vertical line, with positive values above the origin and negative values below the origin. The x-coordinate gives the horizontal position of the point, and the y-coordinate gives the vertical position of the point. By plotting points on a coordinate plane, we can graph lines, curves, and other mathematical functions. It is a fundamental tool in mathematics, science, and engineering for visualizing and analyzing relationships between variables.

To find two points on the line of the function r(x) = 4 - 32x, we can simply choose any two values of x and find the corresponding values of r(x).

For example, when x = 0:

r(0) = 4 - 32(0) = 4

So one point on the line is (0, 4).

When x = 1:

r(1) = 4 - 32(1) = -28

So another point on the line is (1, -28).

Therefore, we have two points on the line: (0, 4) and (1, -28).

We can plot these points on a coordinate plane and draw a straight line passing through both points to graph the function.

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Hence, in answering the stated question, we may say that We know, equation however, that r must be positive, therefore we take the positive square root: [tex]r(A) = -4 + square root(64 + 2A) /[/tex]

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to describe the relationship between the two sentences on opposite sides of a letter. In usually, the logo and the programme are the same. For instance, 2x - 4 equals 2.

Part a: Because the radius of a cylinder must be a positive real integer, the domain of A(r) is the set of all real numbers greater than zero.

As a result, the domain of A(r) is:

{r ∈ ℝ | r > 0}

Part b: To determine the inverse function r(A), solve the equation A = 2r2 + 16r for r expressed in terms of A.

To begin, we may simplify the equation by removing 2r:

A = 2πr(r + 8)

Hence, using the quadratic formula, we can find r:

[tex]r = (-16 \sqrt((16)2 - 4(2 )(-A)) / 2(2 )\\r = (-16 \sqrt(2562) + 8A) / 4 r = -4 \sqrt(64 + 2A) /[/tex]

We know, however, that r must be positive, therefore we take the positive square root:

[tex]r(A) = -4 + square root(64 + 2A) /[/tex]

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The radius is apprοximately 11.51 inches when the surface area is 300 square inches.

A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra.

Part a: The dοmain οf A(r) is the set οf all real numbers greater than οr equal tο zerο since the radius οf a cylinder cannοt be negative.

Dοmain οf A(r): r ≥ 0

Part b: Tο find the inverse functiοn r(A), we start with the equatiοn fοr A(r), set it equal tο A, and sοlve fοr r using the quadratic fοrmula:

[tex]2 \pi r^2 + 16 \pi r - A = 0[/tex]

[tex]r = [-16 \pi \± \sqrt{((16 \pi)^2 - 4(2 \pi)(-A))}] / 2(2 \pi)[/tex]

[tex]r = [-16\pi \± \sqrt{(256\pi^2 + 8 \pi A)}] / 4\pi[/tex]

Simplifying this expressiοn, we get:

[tex]r = (-4 \± \sqrt{(64 + 2A)}) / 2[/tex]

[tex]r(A) = -2 \± \sqrt{(32 + 0.5A)[/tex]

Since the radius οf a cylinder cannοt be negative, we take the pοsitive square rοοt:

[tex]r(A) = -2 + \sqrt{(32 + 0.5A)[/tex]

Part c: Tο find the radius when the surface area is 300 square inches, we plug in A = 300 intο the expressiοn fοr r(A) and simplify:

[tex]r(300) = -2 + \sqrt{(32 + 0.5(300))[/tex]

r(300) = -2 + sqrt(182)

r(300) ≈ 11.51

Therefοre, the radius is apprοximately 11.51 inches when the surface area is 300 square inches.

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Answer:

To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can use proportional reasoning.

Let X be the cost to supply 10%. Then:

The cost to supply 50% is 5 times the cost to supply 10%, so it is 5X.

The cost to supply 85% is 8.5 times the cost to supply 10%, so it is 8.5X.

The cost to supply 10% is X.

To find the cost of supplying bins to 10%, 50%, and 85% of the cost to supply 10%, we can substitute X = $1 and multiply by the appropriate percentages:

The cost to supply bins to 10% of the cost to supply 10% is 0.1 * X = 0.1 * $1 = $0.10.

The cost to supply bins to 50% of the cost to supply 10% is 0.5 * X = 0.5 * $1 = $0.50.

The cost to supply bins to 85% of the cost to supply 10% is 0.85 * X = 0.85 * $1 = $0.85.

Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are $0.10, $0.50, and $0.85, respectively.

Answer:

Let the cost to supply 10% of the bins be X dollars.

To find the cost of supplying bins to 50% of the cost to supply 10%, we can set up the following proportion:

10% of the cost = X dollars

50% of the cost = Y dollars

We know that the two costs are proportional, so we can set up the following equation:

10% / 50% = X / Y

Simplifying this equation, we get:

0.1 / 0.5 = X / Y

0.2 = X / Y

Multiplying both sides by Y, we get:

Y * 0.2 = X

Y = X / 0.2

Y = 5X

Therefore, the cost of supplying bins to 50% of the cost to supply 10% is 5 times the cost of supplying bins to 10%.

Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:

Y = 5X = 5(C/10) = C/2

So the cost of supplying bins to 50% of the cost to supply 10% is C/2 dollars.

To find the cost of supplying bins to 85% of the cost to supply 10%, we can set up a similar proportion:

10% of the cost = X dollars

85% of the cost = Z dollars

We know that the two costs are proportional, so we can set up the following equation:

10% / 85% = X / Z

Simplifying this equation, we get:

0.1 / 0.85 = X / Z

0.1176 = X / Z

Multiplying both sides by Z, we get:

Z * 0.1176 = X

Z = X / 0.1176

Z = 8.5X

Therefore, the cost of supplying bins to 85% of the cost to supply 10% is 8.5 times the cost of supplying bins to 10%.

Substituting X = C/10 (where C is the cost to supply 10% of the bins), we get:

Z = 8.5X = 8.5(C/10) = 0.85C

So the cost of supplying bins to 85% of the cost to supply 10% is 85% of the cost to supply 10%, or 0.85C dollars.

Therefore, the costs of supplying bins to 10%, 50%, and 85% of the cost to supply 10% are:

- 10% of the cost: X dollars = C/10 dollars

- 50% of the cost: Y dollars = C/2 dollars

- 85% of the cost: Z dollars = 0.85C dollars

Answer:

The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter

Step-by-step explanation:

The solution to the trigonometric expression is given as follows:

sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).

The trigonometric expression for this problem is defined as follows:

sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)).

The tangent and the cotangent are represented as follows:

Hence:

sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)[1 + sin(x)/cos(x)] + cos(x)[1 + cos(x)cot(x)]

sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = sin(x)+sin²(x)/cos(x) + cos(x) + cos²(x)/sin(x)

sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = [sin²(x)cos(x) + sin³(x) + sin(x)cos²(x) + cos³(x)]/(sin(x)cos(x))

sin(x)(1 + tan(x)) + cos(x)(1 + cot(x)) = csc(x) + sec(x).

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Option B. g(x)=(x-2)²is the equation of blue graph.

A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.

The red graph is represented by the function:

f(x)=x²

Also, we need the formula for the blue graph.

We can see that the blue graph is just the red graph with the horizontal axis moved 2 units to the right.

An example of a horizontal transition is:

f(x-h) where h is the quantity we shift (to the right).

h = 2 since we moved two units to the right.

Our new role will thus be:

g(x)=f(x-2)=(x-2)²

Therefore:

g(x)=(x-2)²

Our response is B.

Notes:

A denotes a downward vertical movement of two units.

C (assuming it is x²) denotes a two-unit vertical displacement upward.

And D (if you let h = -2, then f(x - (-2)) = f(x + 2) = (x + 2)²) is a horizontal shift of two units to the left.

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the complete question is:

The graphs below have the same shape. What is the equation of the blue

graph?

f(x) = x2

g(x) = ?

9(x) =

O A. g(x) = x² - 2

B. g(x) = (x - 2)2

c. g(x) = x + 2

D. Q(x) = (x + 2)2

Image is attached below;

The next three terms of the sequence 240,-120,60 are -30, 15 and -7.5

240, -120, 60

From observation, the second term is found by halving the first term and multiplying by negative

The third is found by halving the second term and multiplying by negative.

The fourth term = negative third term divided by half

= -(60/2)

= -30

The fifth term = negative fourth term divided by half

= -(-30/2)

= 15

The sixth term = negative fifth term divided by half

= -(15/2)

= -7.5

Hence, the next terms of 240, -120, 60 are -30, 15 and -7.5

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By answering the given question, we may state that We can apply the formula if we know the radius: C = 2πr where the radius r is.

In geometry, a circle's diameter is any straight line segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. The diameter of a sphere can be defined using either idea. The diameter is the length of the line perpendicular to the two points at either end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.

We must know the base's diameter or radius in order to calculate the circumference of the tin.

If we know the diameter, we can apply the following formula to determine the circle's circumference:

C = πd

where d is the diameter and C is the circumference.

We can apply the formula if we know the radius:

C = 2πr

where the radius r is.

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Answer:

to find are u need to do it this way: pie r sqare

Step-by-step explanation:

22/7x7x7

22/7 x49

cut 7 and 49

1 and 7

22/1x7

=22x7

=154

The number of particles in 9.89 moles of carbon is solved to be

To determine the number of particles in 9.89 moles of carbon, we can use Avogadro's constant, which is defined as the number of particles (atoms or molecules) in one mole of a substance.

Avogadro's constant is approximately 6.02 x 10^23 particles per mole.

So, the number of particles in 9.89 moles of carbon is:

= 9.89 moles x (6.02 x 10^23 particles/mole)

= 5.95 x 10^24 particles

Therefore, there are approximately 5.95 x 10^24 particles in 9.89 moles of carbon.

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Answer:

50¢/cookie, $1.00/lemonade

Step-by-step explanation:

Let l = cost of one lemonade

c = cost of one cookie

We have:

5l + 2c = 1.50 -------> 10l + 4c = 3.00

2l + 5c = 2.70 -------> 10l + 25c = 13.50

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

21c = 10.50

c = .50

5l + 2(.50) = 1.50

5l + 1.00 = 1.50

5l = 5, so l = 1.00

Each cookie costs 50¢, and each lemonade costs $1.00.

Answer: True

Step-by-step explanation: That was a complete guess. Did you forget to include an image? Am I missing something?

The probability that they do not like cats given that person does not like dogs: 13/51.

Total people : 324.

People like dogs D: 120

Probability P(D) = 120/324

Probability Not like dogs P(D') = 1 - 120/324 = 204/324

People like cats C: 150

Probability P(C) = 150/324

Probability who don't like digs but like cats:

P(C ∩ D') = 52/ 324

Probability that they do not like cats given that person does not like dogs:

P(C'/D') = 1  -  P(C ∩ D')/P(D')

P(C'/D') = 1 - (52/324) /(204/324)

P(C'/D') = 1 - 52/204

P(C'/D') = 152/204 = 13/51

Thus, the probability that they do not like cats given that person does not like dogs: 13/51.

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So the average rate of change of the function over the interval 0 ≤ x ≤ 15 is 4.4.

In mathematics, a function is a relationship between two sets of numbers, where each input in the first set (called the domain) corresponds to exactly one output in the second set (called the range). In other words, a function takes an input, performs a specific operation on it, and produces an output. A function is usually denoted by a symbol (often a letter) and is defined by a rule that specifies how to calculate the output value for any given input value.

Here,

To find the average rate of change of the function over the interval 0 ≤ x ≤ 15, we need to calculate the change in the function value divided by the change in x over the interval.

The change in the function value over the interval is f(15) - f(0), which is 159 - 93 = 66.

The change in x over the interval is 15 - 0 = 15.

Therefore, the average rate of change of the function over the interval 0 ≤ x ≤ 15 is:

average rate of change = change in f / change in x

= 66 / 15

= 4.4

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If Jayla makes her goal 80% of the time, we can say that she has a probability of 0.8 of achieving her goal on any given day.

The probability of Jayla making her goal every day for the next 10 days can be calculated by multiplying the probability of her achieving her goal on each day.

Assuming each day's result is independent of the previous day, the probability of Jayla making her goal every day for the next 10 days is:

0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 x 0.8 = 0.1073741824

So, there is approximately a 10.7% chance that Jayla will make her goal every day for the next 10 days.

Answer: -4 5/12

Step-by-step explanation: because -7 2/3+(-5 1/2)= -13 1/6

finally take -13 1/6 + 8 3/4= -4 5/12

Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.

Annual interest rate is the amοunt οf interest that is charged οn a lοan οr investment per year, expressed as a percentage οf the amοunt bοrrοwed οr invested.

Tο cοmplete the table, we can use the fοllοwing steps:

Fοr the first mοnth:

Priοr balance: $4900

Interest οn priοr balance: 1.75% οf $4900 = $85.75 (rοunded tο the nearest cent)

Mοnthly payment: $175

Ending balance: $4900 + $85.75 - $175 = $4710.75 (rοunded tο the nearest cent)

Fοr the secοnd mοnth:

Priοr balance: $4710.75

Interest οn priοr balance: 1.75% οf $4710.75 = $82.46 (rοunded tο the nearest cent)

Mοnthly payment: $175

Ending balance: $4710.75 + $82.46 - $175 = $4628.21 (rοunded tο the nearest cent)

Repeat the same prοcess fοr the next three mοnths:

Fοr the third mοnth, priοr balance is $4628.21, interest οn priοr balance is $80.89, mοnthly payment is $175, and ending balance is $4549.10.

Fοr the fοurth mοnth, priοr balance is $4549.10, interest οn priοr balance is $79.34, mοnthly payment is $175, and ending balance is $4469.69.

Fοr the fifth mοnth, priοr balance is $4469.69, interest οn priοr balance is $77.78, mοnthly payment is $175, and ending balance is $4389.72.

Mοnth    Priοr Balance      Interest              Mοnthly           Ending

                                              οn                  Payment          Balance

                                       Priοr Balance    

1                   $4900           $85.75                 $175          $4710.75

2                  $4710.75        $82.46                 $175          $4628.21

3                   $4628.21       $80.89                $175         $4549.10

4                  $4549.10        $79.34                 $175         $4469.69

5                  $4469.69       $77.78                 $175          $4389.72

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The required point's coordinates are (0,3).

A mathematical statement known as an equation consists of two algebraic expressions separated by equal signs (=) on either side.

It demonstrates the equality of the relationship between the printed statements on the left and right.

Left side equals right side in all formulas.

To find the values of unknowable variables, which stand in for unknowable quantities, you can solve equations.

A statement is not an equation if it lacks the equals sign. When two expressions have the same value, a mathematical statement known as an equation will include the symbol "equal to" between them.

Hence, The required point's coordinates are (0,3).

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Answer:

Given that

(5a+6 )°+90°+(7a)°=180°

(angles on a straight line sum up to 180°)

5a°+6°+90°+7a°=180°

5a°+7a°=(180-96)°

12a°=84°

Deviding both sides by 12° gives

a=84/12

a=7°

therefore the value of

a=7°

Answer:

r = 3

Step-by-step explanation:

Pythagoras' theorem states that for all right-angled triangles, 'The square on the hypotenuse is equal to the sum of the squares on the other two sides.

AO^2 = AB^2 + BO^2

(2 + r)^2 = 4^2 + r^2

r^2 + 4r + 4 = 16 + r^2

4r = 12

r = 12/4

r = 3