When describing the results of an observational study, the mathematical relationship between the relative risk (RR) and the odds ratio (OR) is referred to as: a. The rare disease assumption b. The built-in bias c. The relative odds approach d. Effect modification e. All of the above
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Answer:

0.56

Step-by-step explanation:

The r-value that represents the most moderate correlation is 0.56

Correlation is represented with r.

And the range of values of r is:

-1 ≤ r ≤ 1

This means that r can take any value from -1 to 1

-1 and 1 are considered strong correlation

While values closer to 0.5 or - 0.5 are moderate

From the list of options,

0.56 is closer to 0.5 than others

Hence, the r-value that represents the most moderate correlation is 0.56

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The correct term to complete the sentence "A number, a variable, or a product of a number and one or more variables is called a(n)" is "expression."

In mathematics, an expression is a combination of one or more numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It can be a single term or a combination of multiple terms, and it can contain constants and variables.

A number, a variable, or a product of a number and one or more variables is called an expression.

For example, 5x, 3x + 2, and 4x² + 3xy are all expressions.

An expression can be evaluated by substituting the values of the variables into the expression and then performing the operations.

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Answer:

The small angle = 3

The larger angle = 29 * 3 = 87

Together they equal 90 as they should.

Step-by-step explanation:

Let the compliment = x

Let the other angle = 29*x

Complementary angles = 90

x + 29x = 90

30x = 90

30x/30 = 90/30

x = 3

Answer:The angle is 87 degrees and its complement is 3 degrees.

Step-by-step explanation ion enn kno i jus got it right so im givin u da answer

d) Tthe probability that there is a moving object given that both sensors detect motion is approximately 0.98.

(a) To find the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

A = Movement outside

B = Sensor V does not detect motion

C = Sensor L detects motion

We are given:

P(A) = 0.7 (probability of movement outside)

P(B|A) = 0.05 (probability of sensor V not detecting motion given movement outside)

P(C|A) = 0.8 (probability of sensor L detecting motion given movement outside)

We want to find P(C|A', B), where A' denotes the complement of event A.

Using Bayes' theorem:

P(C|A', B) = [P(A' | C, B) * P(C | B)] / P(A' | B)

We can calculate the values required:

P(A' | C, B) = 1 - P(A | C, B) = 1 - P(A ∩ C | B) / P(C | B) = 1 - [P(A ∩ C ∩ B) / P(C | B)]

             = 1 - [P(B | A ∩ C) * P(A ∩ C) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / P(C | B)]

             = 1 - [P(B | C) * P(A) * P(C | A) / [P(B | C) * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A')]]

P(B | C) = 0 (since sensor V does not detect motion when there is motion outside)

P(C | A') = 0 (since sensor L does not detect motion when there is no motion outside)

Substituting these values:

P(C | A', B) = 1 - [0 * P(A) * P(C | A) / (0 * P(A) * P(C | A) + P(B | C') * P(A') * P(C | A'))]

             = 1 - [0 / (0 + P(B | C') * P(A') * P(C | A'))]

             = 1 - 0

             = 1

Therefore, the probability that sensor L detects motion given that there is movement outside and sensor V does not detect motion is 1.

(b) To find the probability that the home security system alerts the police given that there is a moving object, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

M = There is a moving object

We need to calculate P(D | M). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | M) = P(D, V detects motion, L detects motion | M) + P(D, V does not detect motion, L detects motion | M)

We know:

P(D, V detects motion, L detects motion | M) = P(V detects motion | M) * P(L detects motion | M) = 0.95 * 0.8 = 0.76

P(D, V does not detect motion, L detects motion | M) = P(V does not detect motion | M) * P(L detects motion | M) = (1 - 0.95) * 0.8 = 0.04

Substituting

these values:

P(D | M) = 0.76 + 0.04

        = 0.8

Therefore, the probability that the home security system alerts the police given that there is a moving object is 0.8.

(c) To find the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, we need to consider the different combinations of sensor detections.

Let's denote the events as follows:

D = The home security system alerts the police

NM = There is no movement

We need to calculate P(D | NM). This can occur in two ways:

1. Both sensor V and sensor L detect motion.

2. Sensor L detects motion while sensor V does not.

Using the law of total probability:

P(D | NM) = P(D, V detects motion, L detects motion | NM) + P(D, V does not detect motion, L detects motion | NM)

We know:

P(D, V detects motion, L detects motion | NM) = P(V detects motion | NM) * P(L detects motion | NM) = 0.1 * 0.05 = 0.005

P(D, V does not detect motion, L detects motion | NM) = P(V does not detect motion | NM) * P(L detects motion | NM) = (1 - 0.1) * 0.05 = 0.045

Substituting these values:

P(D | NM) = 0.005 + 0.045

         = 0.05

Therefore, the probability of a false alarm, i.e., that there is no movement but the police are alerted anyway, is 0.05.

(d) To find the probability that there is a moving object given that both sensors detect motion, we can use Bayes' theorem.

Let's denote the events as follows:

M = There is a moving object

V = Sensor V detects motion

L = Sensor L detects motion

We want to find P(M | V, L).

Using Bayes' theorem:

P(M | V, L) = [P(V, L | M) * P(M)] / [P(V, L)]

We can calculate the values required:

P(V, L | M) = P(V | M) * P(L | M) = 0.95 * 0.8 = 0.76

P(M) = 0.7 (given probability of movement)

P(V, L) = P(V, L | M) * P(M) + P(V, L | M') * P(M')

        = 0.76 * 0.7 + 0.04 * 0.3

        = 0.532 + 0.012

        = 0.544

Substituting these values:

P(M | V, L) = (0.76 * 0.7) / 0.544

           ≈ 0.98

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By the radius-tangent theorem, the radius is equal to 39/10 units.

In Euclidean geometry, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

Since CB is tangent to OA at point C and line segment CB is perpendicular to line segment AC by the radius-tangent theorem, we would determine the radius by applying Pythagorean's theorem as follows;

r^2 + 8^2 = (r + 5)^2

r^2 + 64 = r^2 + 10r + 25

r^2 - r^2 = -10r + 64 - 25

10r = 39

r = 39/10 units.

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The length of the curve is 3√17/4.. to find the length of the curve defined by the equation x = 3 - (y/4) from y = 1 to y = 4, we can use the arc length formula for a curve in cartesian coordinates .

the arc length formula is given by:

l = ∫ √[1 + (dx/dy)²] dy

first, let's find dx/dy by differentiating x with respect to y:

dx/dy = -1/4

now we can substitute this into the arc length formula:

l = ∫ √[1 + (-1/4)²] dy

 = ∫ √[1 + 1/16] dy

 = ∫ √[17/16] dy

 = ∫ (√17/4) dy

 = (√17/4) ∫ dy

 = (√17/4) y + c

to find the length of the curve from y = 1 to y = 4, we evaluate the definite integral:

l = (√17/4) [y] from 1 to 4

 = (√17/4) (4 - 1)

 = (√17/4) (3)

 = 3√17/4

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Answer:

Step-by-step explanation:

6

The second term is 40.20. Let the mean term be x.Given, the two terms are 15 and 60.

Hence, x² = 15 × 60 ⇒ x = 30

Therefore, the mean term is 30.

16. Let the number of science books be x.

Therefore, the ratio of English books to Math books

= 1200/1800

= 2/3

The ratio of Math books to Science books

= 1800/x

Equating the two ratios,

we get:2/3

= 1800/x ⇒ x

= 2700

Thus, the number of Science books is 2700.17.

The four given numbers are 12, 15, 8, 10.

The possible proportions are:

12:15

= 4:512:8

= 3:212:10

= 6:515:8

= 15:815:10

= 3:220:8

= 5:220:10

= 2:118:10

= 9:5.18.

Let the first term be x.Common ratio, r

= (80/21)

= (120/80)

= (n/120) ⇒ n

= 180

Therefore, x

= 21/5

= 4.219.

Let the second term be x.Common ratio, r

= (27/15)

= (63/27)

= (81/x) ⇒ x

= 40.

The second term is 40.20. Let the mean term be x.Given, the two terms are 15 and 60.

Hence, x²

= 15 × 60 ⇒ x

= 30

Therefore, the mean term is 30.

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The rate of change of the volume is 1800 \(cm^3/s.\)

Since we now know that the volume of a cube is provided by the equation V = a, we can use this knowledge to obtain the equation connecting V and a cube edge.

where a stands for how long each edge is.

We obtain: dV/dt = 3 by taking the derivative of both sides with respect to time (t).

* da/dt

Given that the cube's edges are growing at a rate of 6 cm/s, we know that da/dt = 6 cm/s.

Substituting this value into the equation, we have:

dV/dt = \(3a^2 * 6\)

Simplifying further, we have:

dV/dt =\(18a^2\)

Now we need to find the rate of change of the volume when the length of each edge is 10 cm. Substituting a = 10 into the equation, we get:

dV/dt = 18 * \((10^2)\)

dV/dt = 18 * 100

dV/dt = 1800 \(cm^3/s\)

Therefore, the rate of change of the volume is 1800 \(cm^3/s.\)

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Answer: A

Step-by-step explanation: The question states that the change wasn't a positive one, it was a negative one as it states that the temperature changed an average of -2.250 Fahrenheit per hour. So, we multiply that by 3 to get -6.75. This is why A is correct.

Answer:

its c

Step-by-step explanation:

got it right on edge

Answer:

y=1/5x+2

Step-by-step explanation:

First, find the slope. 1-3/-5-5=-2/-10=1/5

Now find the y intercept.

y=1/5x+b

3=1/5(5)+b

3=1+b

Subtract 1 from both sides

2=b

y=1/5x+2

The range and the vertex is   4 ≤ y < [infinity] and  (5, 4).

To find the vertex, we can take the derivative of the function and set it equal to 0:

y' = |x − 5|' = 0

=> x − 5 = 0

=>  x = 5

Then, we can plug x = 5 into the original equation to find the y-value at the vertex:  

y = |x − 5| = |5 − 5| = |0| = 0

So, the vertex of y = |x − 5| is (5, 4).

To find the range, we need to consider the range of the absolute value function. The range of the absolute value function is:

−[infinity] < y < [infinity]. So, the range of y = |x − 5| is also −[infinity] < y < [infinity] (or 4 ≤ y < [infinity]).

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Answer:

F-1 (x)=1/6x-2/3

Step-by-step explanation:

Use substitution, Interchange the variables, Swap the sides, movthe constant to the right, Divide both sides, Use substitution, and youll find your solution. By the way the -1 is in scientific notation!

Answer:

y = .80x + 3 is the slope - intercept form.

80 cents, the fare, is determined by the number of times it's paid. 3 dollars is paid whether or not 80 cents is paid a number of times or at all.

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The sampling distribution of the sample mean will always have the same the mean of the original non-normal distribution, as the original distribution.

What is distribution?

Each of these samples contains a mean, and if we add up all of the means, we can construct a probability distribution that explains the distribution of the means. As long as we have sufficient samples, as will be discussed later, this distribution is always normal and is referred to as the sampling distribution of the sample mean.

Since the sample mean's sampling distribution is normal, we can naturally calculate the distribution's mean and standard deviation and utilise that information to analyse probability questions.

Here, The sample variance is equal to the population variance divided by the sample size if the population is infinite and the sampling is random, or if the population is finite but we are sampling with replacement.

So we need to use the mean of non-normal distribution.

Hence the answer will be the mean of the original non-normal distribution.

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The decay rate for the resale price of laser cutting tool will be -121000\(e^{-0.22t}\)

Let R is the resale value of a particular type of laser cutting tool after years

Where, R(t) = 550000\(e^{-0.22t}\)

Rate at which the resale value is changing will be dR/dt = 550000\(e^{-0.22t}\)(-0.22)= -121000\(e^{-0.22t}\)

Initial value of the laser cutting tool, at time ‘t’ =0 will be 550000\(e^{-0.22t}\)x0 = 550000

At time ‘t’ resale value is 550000 \(e^{-0.22t}\)

Therefore, the decay in resale price = 550000 - 550000 \(e^{-0.22t}\)

Therefore, the decay rate = (550000 - 550000 \(e^{-0.22t}\))/t = 550000(1-\(e^{-0.22t}\))/t

As we have dR/dt = R’ = -121000\(e^{-0.22t}\)

Therefore, R’(10) = -121000\(e^{-2.2}\) = -13407.18

Therefore, after 10 years the resale price will be -13407.18

R’(20) = -121000\(e^{-4.4}\)= -1485.55

Therefore, after 20 years the resale price will be -1485.55

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It can be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times

To prove that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times, follow these steps,

1. Choose an algorithm, Select any algorithm that can be applied to the Rubik's cube. For example, the R U R' U' algorithm.

2. Apply the algorithm repeatedly, Perform the chosen algorithm on the Rubik's cube multiple times. Keep track of the number of times the algorithm is applied.

3. Observe the cube's state, After each iteration, observe the state of the Rubik's cube to see if it returns to its original state.

4. Identify the cycle length, Eventually, the Rubik's cube will return to its original state after a certain number of repetitions of the algorithm. This number is the cycle length of the algorithm.

5. Generalize the proof, The proof holds true for any algorithm on the Rubik's cube, as every algorithm has a finite cycle length due to the finite number of possible configurations of the cube.

In conclusion, it can be proven that a Rubik's cube will return to its original state if you repeat any algorithm for a number of times, because every algorithm has a finite cycle length due to the finite number of possible configurations of the cube.

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Answer:

20 ducks

Step-by-step explanation:

4+5=9

4/9:x/45

9*5=45

4*5=20ducks

Answer:

doing really good

Step-by-step explanation:

brainiest please.

To find out how many more dollars the football team's total payroll is than the baseball team's total payroll, we need to subtract the baseball team's total payroll from the football team's total payroll.

The football team's total payroll is \(2.5 x 10^11\)dollars, and the baseball team's total payroll is \(2.34 x 10^9\)dollars.
To subtract these numbers, we can simply subtract the exponents and divide the larger number by the smaller number.
\(10^11\)divided by \(10^9\) is equal to \(10^2\).
So, the football team's total payroll is \(10^2\) times larger than the baseball team's total payroll.
To find the actual difference in dollars, we multiply the baseball team's total payroll by \(10^2\).
\(2.34 x 10^9\) dollars multiplied by 10^2 is equal to\(2.34 x 10^11\)dollars. , the football team's total payroll is\(2.34 x 10^11\) dollars more than the baseball team's total payroll.

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The problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

The problem can be solved using the simplex method, and verified using the graphical method. Here are the steps:

Convert the problem to standard form by introducing slack variables:
Min Z = -2X1 - 4X2 - 3X3 + 0S1 + 0S2 + 0S3
St. X1 + 3X2 + 2X3 + S1 = 30
X1 + X2 + X3 + S2 = 24
3X1 + 5X2 + 3X3 + S3 = 60
Xi, Si >= 0

Set up the initial simplex tableau:
| 1 3 2 1 0 0 30 |
| 1 1 1 0 1 0 24 |
| 3 5 3 0 0 1 60 |
| 2 4 3 0 0 0 0 |

Identify the entering variable (most negative coefficient in the objective row): X2

Identify the leaving variable (smallest ratio of RHS to coefficient of entering variable): S1

Pivot around the intersection of the entering and leaving variables to create a new tableau:
| 0 2 1 1 -1 0 6 |
| 1 0 0 -1 2 0 18 |
| 0 0 0 5 -5 1 30 |
| 2 0 1 -2 4 0 36 |

Repeat steps 3-5 until there are no more negative coefficients in the objective row. The final tableau is:
| 0 0 0 7/5 -3/5 0 18 |
| 1 0 0 -1/5 2/5 0 6 |
| 0 0 1 1/5 -1/5 0 6 |
| 0 0 0 -2 4 0 24 |

The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

To verify the solution using the graphical method, plot the constraints on a graph and find the feasible region. The optimal solution will be at one of the corner points of the feasible region. By checking the values of the objective function at each corner point, we can verify that the optimal solution found using the simplex method is correct.

In conclusion, the problem can be solved using the simplex method, and the solution can be verified using the graphical method. The optimal solution is X1 = 6, X2 = 0, X3 = 6, Z = 24.

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Answer:

f. 85

Step-by-step explanation:

All triangles add up to 180 degrees

BCE=25

then you need to find DBC, you can do that since ABD is isocilies that means all sides are equal in length and angle so 180 divided by 3 (number of side) is 60

isoceles triangle have 2 sides that are equiangular, cince we know BCA is 25 we also know BAC is 25, leaving angle ABC to be 130 (180-50=130)

we subtract angle ABD from angle ABC to get angle DBC, leaving angle DBC to equal 70 degrees

since 70 (angle DBC) + 25 (Angel BCA)= 95

we just subtrract 95 from 180 to get the answer 85 (:

Answer:

85 degrees

Step-by-step explanation:

if Δ ABD is equilateral  then the 3 sides and three angles are equal

sum of angles of Δ=180

180/3=60 degrees (∠A,∠B,∠D)

ΔBCA is isosceles then the two angles A and C are equal = 25

∠B=180-50=130

∠B in Δ BEC=130-60=70

∠E+∠B+∠C in Δ BEC=180

∠E= 180-70-25=85 degrees

Answer:

In 14,689, 14 is the thousands group, and 689 is the ones group.

The equation that can be represented by the number line is option D: -3 + (-1) = -4.

The equation that can be represented by the number line is option D: -3 + (-1) = -4.

Let's analyze each option:

A. -4 + 1 = -3: This equation does not represent the situation where we start from -4 and move 1 unit to the right on the number line, resulting in -3.

B. -3 + 4 = 1: This equation represents the situation where we start from -3 and move 4 units to the right on the number line, resulting in 1. However, this equation does not match the form of the equation in the options.

C. 3 + (-4) = -1: This equation represents the situation where we start from 3 and move 4 units to the left on the number line, resulting in -1. However, this equation does not match the form of the equation in the options.

D. -3 + (-1) = -4: This equation matches the form of the equation in the options, and it represents the situation where we start from -3 and move 1 unit to the left on the number line, resulting in -4.

Therefore, the equation that can be represented by the number line is option D: -3 + (-1) = -4.

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The equation that could be represented by the number line is  -3+ (-1) = -4 (option D)

Let us check each option and delve into their implications on the number line:

A. -4 + 1 = -3: This equation does not depict the scenario where we initiate from -4 and shift 1 unit towards the right on the number line, yielding -3.

B. -3 + 4 = 1: This equation represents the scenario where we commence from -3 and progress 4 units towards the right on the number line, culminating in 1. Nonetheless, this equation fails to conform to the prescribed structure specified in the options.

C. 3 + (-4) = -1: This equation portrays the scenario where we commence from 3 and proceed 4 units towards the left on the number line, resulting in -1. However, this equation does not align with the prescribed format presented in the options.

D. -3 + (-1) = -4: This equation adheres to the stipulated format outlined in the options, and it accurately represents the scenario where we initiate from -3 and traverse 1 unit towards the left on the number line, leading to -4.

There, the equation that can be aptly represented by the number line is option D: -3 + (-1) = -4.

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To find the surface area of a triangular prism, we need to add up the area of all the faces.

First, we need to find the area of the triangular bases. The formula for the area of a triangle is:

A = (1/2)bh

Where A is the area, b is the base, and h is the height.

Since the triangular base of the prism has a base of 8 and a height of 12, we can calculate its area as:

A = (1/2)(8)(12) = 48

Now we need to find the area of the three rectangular faces. The formula for the area of a rectangle is:

A = lw

Where A is the area, l is the length, and w is the width.

Since there are three rectangular faces, we need to calculate their areas separately.

The first rectangular face has a length of 12 and a height of 3:

A1 = (12)(3) = 36

The second rectangular face has a width of 8 and a height of 3:

A2 = (8)(3) = 24

The third rectangular face has a length of 12 and a width of 8:

A3 = (12)(8) = 96

Now we can add up all the areas to find the total surface area of the prism:

SA = A1 + A2 + A3 + 2A
SA = 36 + 24 + 96 + 2(48)
SA = 252

Therefore, the surface area of the triangular prism with length 12, width 8, and height 3 is 252 square units.

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(a) The standard error of the mean is 129. (b) The probability that the sample mean will be more than $27,175 is 0.50 (c) The probability that the sample mean will be within $1,000 of the population mean is 0.955. (d) The probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100 is 0.999.

(a) The standard error of the mean is the square root of the population standard deviation divided by the sample size, which in this case is 7,400/57 = 129.12. The value of the standard error of the mean is therefore 129 (rounded to the nearest whole number).

(b) To find the probability that the sample mean will be more than $27,175, you can use the Z-score formula. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175)/129 = 0. The probability that the sample mean will be more than $27,175 is 50%, since the probability of any Z-score of 0 is 0.50.

(c) To find the probability that the sample mean will be within $1,000 of the population mean, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/129 = ±7.8. The probability that the sample mean will be within $1,000 of the population mean is 95.5%, since the probability of any Z-score of ±7.8 is 0.955.

(d) To find the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100, you can use the Z-score formula again. The Z-score formula is (sample mean - population mean)/standard error of the mean. Therefore, the Z-score would be (27175-27175±1000)/74 = ±13.5. The probability that the sample mean will be within $1,000 of the population mean is 99.9%, since the probability of any Z-score of ±13.5 is 0.999.

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Answer:

The first Answer:

Step-by-step explanation:

The x-values are not the same on one line:

Image

The line connecting isn't perfect but see what I mean?

Answer:

The radius of the circle is 18.

Step-by-step explanation:

Since you have a right triangle, you can use Pythagorean Theorem.

a^2 + b^2 = c^2

or leg^2 + leg^2 = hypotenuse^2

One leg is r and the other leg is 24. The hypotenuse is r+12.

This gives us:

r^2 + 24^2 =(r+12)^2

r^2 + 576 = r^2+24r+144

I just squared the 24 on the left side of the equation. And squared r+12 on the right side of the equation.

subtract r^2 from both sides.

576 = 24r + 144

subtract 144

432 = 24r

divide by 24

18 = r

The radius r, of the circle is 18.