find the t-value such that the area under the t distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (d f).

The answer of the given question based on finding the missing length of a triangle the answer is , None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

In geometry,  triangle is  two-dimensional polygon with three straight sides and three angles. It is one of  basic shapes in geometry and can be defined as  closed figure with three line segments as its sides, where each side is connected to two endpoints called vertices. The sum of  interior angles of  triangle are 180° degrees.

Triangles are classified based on length of their sides and  measure of their angles. A triangle can be equilateral, isosceles, or scalene based on whether all sides are equal, two sides are equal, or all sides are different, respectively.

To find the missing length indicated, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs (the sides adjacent to the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this triangle, we can see that the two legs have lengths of 9 and 16, and the hypotenuse has length X. So we can write:

9²+ 16² = X²

Simplifying the left-hand side:

81 + 256 = X²

337 = X²

Taking the square root of both sides (and remembering that X must be positive, since it is a length):

X = sqrt(337)

X ≈ 18.3575

So the missing length indicated is approximately 18.3575. None of the answer choices match this value exactly, but the closest one is D) 15. Therefore, the answer is D) 15.

To know more about Pythagorean theorem visit:

https://brainly.com/question/14930619

#SPJ1

The description of the ensembles would be: 1. Students who attend both recitals, 2. Students who attend one of the two recitals, 3. students who attend both recitals, 4.The difference between the set P and U, that is, 3 students.

To graph the information in a Venn diagram we must take into account the information in the statement. In this case we must place 6 students outside the circles because there are 6 who do not attend any activity.

So, there would be 34 remaining students, of which 20 go to the piano recital and 23 to the voice recital. So, we can establish that 20 go to both recitals, 3 go to the voice recital, and 1 go to the piano recital.

Learn more about Venn diagram in: https://brainly.com/question/29301560

#SPJ1

Answer:

Step-by-step explanation:

Since they are traveling in the same direction, the distance between them increases at a rate of the difference of their speeds.

The relative speed of train A with respect to train B is:

105 kmph - 87 kmph = 18 kmph

In three hours, the distance between them will be:

Distance = Speed x Time

Distance = 18 kmph x 3 hours

Distance = 54 km

Therefore, the two trains will be 54 kilometers apart after three hours.

The resultant force is equal to F1, which is {-300i + 170j + 190k}N, and the couple moment acting at point 0 is  (-0.19i - 0.34j + 0.15k) N.m.

To determine the resultant force acting at point O, we can add all the forces acting at point O. In this case, we have only one force F1 = {-300i + 170j + 190k}N. Therefore, the resultant force acting at point O is F1 itself.

To determine the couple moment acting at point O, we can use the formula:

M = r x F

where r is the position vector from point O to any point on the line of action of force F.

Since we don’t know the position vector r, we can choose any arbitrary point on the line of action of force F. Let’s say we choose point A which lies on the line of action of force F and is perpendicular to it.

Therefore, r = OA where OA is the position vector from point O to point A. We can find OA by subtracting position vectors of points O and A i.e., OA = A - O.

Now, let’s calculate M using M = r x F.

M = (OA) x F1

M = (A - O) x {-300i + 170j + 190k}N M

= (-0.19i - 0.34j + 0.15k) N.m

To know more about resultant force, refer:

https://brainly.com/question/29753501

#SPJ4

Complete question is:

Replace the loading system by an equivalent resultant force and couple moment acting at point o. Assume F1 = {-300i + 170j + 190k}N

Part A Determine the resultant force. Enter the 2, y and a components of the resultant force separated by commas.

Part B Determine the couple moment acting at point 0. Enter the x, y and 2 components of the couple moment separated by commas.

Functions of these are algebraic expression (f+g)(x) = x² + x-2 and             (f-g)(x) = x² + 5x - 14.  

In mathematics, a functiοn is a rule οr mapping that assοciates each element x in a set (called the dοmain) with a unique element f(x) in anοther set (called the range οr cοdοmain).Fοr example  functiοn f(x) = x² + 3x - 8.

An algebraic expressiοn is a cοntains οf variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, and expοnentiatiοn. It cantains  parentheses and οther grοuping symbοls tο indicate the οrder in which the οperatiοns shοuld be perfοrmed.

In the given question ,

To find (f+g)(x),

we simply add the two functions f(x) and g(x) term by term:

(f+g)(x) = f(x) + g(x)

= (x² + 3x - 8) + (-2x + 6)

= x²  + (3x - 2x) + (-8 + 6)

= x² + x - 2  

Therefore, (f+g)(x) = x² + x - 2.

To find (f-g)(x), we subtract g(x) from f(x) term by term:

(f-g)(x) = f(x) - g(x)

= (x²  + 3x - 8) - (-2x + 6)

= x²  + (3x + 2x) + (-8 - 6)

= x²  + 5x - 14  

Therefore, (f-g)(x) = x²  + 5x - 14.

To know more about codomain, visit:

brainly.com/question/17513079

#SPJ1

Part A :  the probability that a randomly chosen recipient served in the army, navy, or marines is 0.993. Part : the probability that a randomly chosen recipient served in the Air Force is 0.0038.

Probability is a branch of mathematics that deals with the study of chance or randomness. It involves the measurement of the likelihood or chance of an event occurring. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and it landing on heads is 0.5 or 50%, assuming a fair coin.

The total number of recipients in the pie chart is the sum of all the values: 2393 + 743 + 296 + 13 + 8 + 1 = 3454.

Part A: The number of recipients who served in the army, navy, or marines is 2393 + 743 + 296 = 3432. Therefore, the probability that a randomly chosen recipient served in the army, navy, or marines is:

P(Army or Navy or Marines) = (2393 + 743 + 296) / 3454 ≈ 0.993

Part B: The number of recipients who were civilians is 8. Therefore, the probability that a randomly chosen recipient was a civilian is:

P(Civilian) = 8 / 3454 ≈ 0.0023

Therefore, the probability that a randomly chosen recipient served in the Air Force is:

P(Air Force) = 13 / 3454 ≈ 0.0038.

To know more about chart visit:

https://brainly.com/question/25796636

#SPJ1

The formula for the  temperature (T), number of gas molecules (n), volume (V), and pressure (P)  is found as: nR = 0.224 / 275.

While dealing with gas, a popular equation was utilized to relate the various components necessary to solve a gas problem. This same Ideal Gas Equation is the name given to this formula. We have always understood that there is no such thing as an ideal. Two well-known presumptions must have been made in this case in advance:

Those four gas variables are: temperature (T), number of gas molecules (n), volume (V), and pressure (P) . Last but not least, the following equation's constant, R, or the gas constant, will be covered in more detail later:

PV = nRT

PV/T = nR

Given data:

Putting the value;

nR = PV/T

nR = 10*0.0224 / 275

nR = 0.224 / 275

Thus, the formula for the  temperature (T), number of gas molecules (n), volume (V), and pressure (P)  is found as: nR = 0.224 / 275.

Know more about the universe gas law

https://brainly.com/question/27870704

#SPJ1

The graph's function limit at x=4 is 6.

In mathematics, the limit of a function is the value that the function approaches as the input approaches a certain value or as the input approaches infinity or negative infinity. A function may or may not have a limit at a given point or as the input goes to infinity or negative infinity.

The formal definition of the limit of a function f(x) as x approaches a value a is as follows:

For every positive number ε (epsilon), there exists a corresponding positive number δ (delta) such that if 0 < |x-a| < δ, then |f(x)-L| < ε.

Limit f(x) at x tend to 4⁺ =6.

Limit f(x) at x tend to 4⁻ =6

Hence, the graph's function limit at x=4 is 6.

To know more about function, visit:

https://brainly.com/question/12431044

#SPJ1

Answer:

What is the Value of Tan 270 Degrees? The value of tan 270 degrees is undefined. Tan 270 degrees can also be expressed using the equivalent of the given angle (270 degrees) in radians (4.71238 . . .) ⇒ 270 degrees = 270° × (π/180°) rad = 3π/2 or 4.7123 . . .

please marke a a brainalist pls

Answer:

  (a, b)  -2

  (c) -1, -1.5, -2, -2.5

Step-by-step explanation:

You want the average and instantaneous rates of change at various times in year 3, given the money in the bank after t years is 180+3t-t².

The amount at the beginning of year 3 is ...

  180 +3t -t² = 180 +t(3 -t)

  180 +2(3 -2) = 182 . . . . . . t=2

The amount at the end of year 3 is ...

  180 +3(3 -3) = 180 . . . . . . t=3

The amount increased by 180 -182 = -2 thousand dollars.

This change occurred in one year, so the average rate of change is ...

  change/years = -2/1 = -2 thousand dollars per year

The derivative of the amount function will give its instantaneous rate of change:

  da/dt = 3 -2t

The values of t at the beginning of the quarters in year 3 are ...

  t = 2: da/dt = 3 -2·2 = -1 thousand per year at start of 1st quarter

  t = 2.25: da/dt = 3 -2(2.25) = -1.5 thousand per year at start of Q2

  t = 2.50: da/dt = 3 -2(2.50) = -2 thousand per year at start of Q3

  t = 2.75: da/dt = 3 -2(2.75) = -2.5 thousand per year at start of Q4

The sine function with the desired features is given as follows:

F(x) = sin(3.5π(x + π/2)) + 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are listed as follows:

The function has an amplitude of 1, hence the parameter A is given as follows:

A = 1.

The period is of 4/7, hence the coefficient B is given as follows:

2π/B = 4/7

4B = 14π

B = 3.5π.

The function contains the point (-π, 2), hence the phase shift and the vertical shift are given as follows:

Hence the function is:

F(x) = sin(3.5π(x + π/2)) + 1.

More can be learned about trigonometric functions at brainly.com/question/21558626

#SPJ1

The resulting three-dimensional figure is a cone with base radius of 17 inches.

A cone is a three-dimensional geometric shape that has a circular base and a curved surface that tapers to a point, called the apex. The base of the cone is a circle, and the height of the cone is the perpendicular distance from the apex to the center of the base. The surface of the cone is made up of all the points that are equidistant from the apex and lie on the base.

Consider an isosceles triangle with 82 inches of circumference and a leg length of 24 inches.

This means that 82 - 2(24) = 82 - 48 = 34 inches is the length of the other side.

The triangle is rotated along a line that passes through points B and D, with point D serving as the intersection of lines AC.

When this happens, a cone will be created in three dimensions with a base radius equal to the length of line AD (i.e. half of the length of line AC being the other side of the isosceles triangle).

The resulting cone's base radius is 1/2 (34) = 17 inches.

Hence, the resulting three-dimensional figure is a cone with base radius of 17 inches.

To know more about Cone visit :

brainly.com/question/16394302

#SPJ1

The expected value of a total of all 10 cards is 65.38 when the five players are dealt with 2 cards each without replacement.

The expected value of the sum of all 10 cards dealt without replacement can be calculated by multiplying the expected value of a single card by 10.

The expected value of a single card can be calculated by adding up all possible outcomes (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K) and dividing by the total number of cards in a deck (52).

= 52/13

This gives us an expected value of 6.5381.

Therefore, the expected value of the sum of all 10 cards is 65.38

To know more about the expected value, refer:

https://brainly.com/question/26996999

#SPJ4

Complete question is:

Five players are each dealt 2 cards without replacement.

What is the expected value of the sum of all 10 cards?

The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.

To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:

[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]

[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]

[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]

The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.

Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.

Learn more about standard here:

https://brainly.com/question/12972781

#SPJ1

The width of the top of the bookcase should be approximately 12.2 inches to give Bria's soap carving collection an area of 300 square inches.

Simply multiply the length and width measurements to get the area of your square or rectangular area in square inches.

Assume the bookcase's top is rectangular, with length "L" and width "b". Because the area of a rectangle is the product of its length and width, we get:

L * b = 300

To find "b," we can rearrange the equation as follows:

b = 300 / L

We don't have enough information to directly solve for "L," but we can make an educated guess based on the figure provided. Based on the illustration, the bookcase appears to be roughly twice as long as it is wide. So let us suppose:

L ≈ 2b

When we plug this into the equation above, we get:

b = 300 / (2b) (2b)

To simplify, we have:

b^2 = 150

When we take the square root of both sides, we get:

b ≈ 12.2

We have, rounded to the nearest tenth of an inch:

b ≈ 12.2 inches

As a result, the width of the top of the bookcase should be approximately 12.2 inches in order to give Bria's soap carving collection a 300-square-inch area.

To know more about Area of Square Inches visit:

https://brainly.com/question/7742557

#SPJ1

The value of (f • p)(-5) is 1885 when functions are given as f(s) = 3s + 2 and p(s) = s³+ 4s.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. It is often represented by an equation or formula, and can be visualized as a graph. Functions are widely used in various areas of mathematics, science, engineering, and other fields to model real-world phenomena and solve problems.

Here,

f(s) = 3s + 2

p(s) = s³+ 4s

To find (f • p)(-5), we need to first find f(-5) and p(-5), and then multiply them together. To find f(-5), we substitute -5 into the function f(s) and simplify:

f(-5) = 3(-5) + 2

= -13

To find p(-5), we substitute -5 into the function p(s) and simplify:

p(-5) = (-5)³ + 4(-5)

= -125 - 20

= -145

Now we can multiply f(-5) and p(-5) together to find (f • p)(-5):

(f • p)(-5) = f(-5) * p(-5)

= (-13) * (-145)

= 1885

To know more about function,

https://brainly.com/question/28193995

#SPJ1

The answers are a)the sample mean, which is $1,235. b) margin of error = $58.50. c)95% .d)the average monthly rent is at least $1,300.e)The z-score for a 92% confidence interval is 1.75.

a) The sample mean is the point estimate of the true mean monthly rent for one-bedroom apartments available for rent near BCIT, which is $1,235.

(b) At a 95% confidence level, the margin of error on the true mean monthly rent estimate is calculated as follows:

Margin of error = Z * (standard deviation / square root of sample size), where Z is the desired confidence level's z-score, which is 1.96 for a 95% confidence level.

Thus, the margin of error is equal to 1.96 * (150 / sqrt(36)) = $58.50.

(c) The 95% confidence interval for the true mean monthly rent is calculated as follows:

Lower value = point estimate minus margin of error = $1,235 minus $58.50 equals $1,176.50

Upper estimate + margin of error = $1,235 + $58.50 = $1,293.50.

(d) To see if the confidence interval supports the friend's claim that the average monthly rent for a one-bedroom apartment available for rent near BCIT is at least $1,300, we need to see if the lower limit of the confidence interval is greater than or equal to $1,300.

Given that the confidence interval is $1,176.50 $1,300, we can conclude that the confidence interval does not support the friend's claim that the

average monthly rent is at least $1,300. As a result, the answer is "No."

(e) A standard normal distribution table or calculator can be used to calculate the z-score corresponding to a 92% confidence interval.

A 92% confidence interval has a z-score of 1.75. (to two decimal places).

To know more about confidence interval visit:-

https://brainly.com/question/29680703

#SPJ1

The appropriate 0.5 adjusted formula for normal approximation is option (d) p(x > 8.5)

The appropriate 0.5 adjusted formula for normal approximation to approximate binomial probabilities when n is large is

P(Z > (x + 0.5 - np) / sqrt(np(1-p)))

where Z is the standard normal variable, x is the number of successes, n is the number of trials, and p is the probability of success in each trial.

To approximate binomial probability p(x > 8) when n is large, we need to use the continuity correction and find the appropriate 0.5 adjusted formula for normal approximation. Here, x = 8, n is large, and p is unknown. We first need to find the value of p.

Assuming a binomial distribution, the mean is np and the variance is np(1-p). Since n is large, we can use the following approximation

np = mean = 8, and

np(1-p) = variance = npq

8q = npq

q = 0.875

p = 1 - q = 0.125

Now, using the continuity correction, we adjust the inequality to p(x > 8) = p(x > 8.5 - 0.5)

P(Z > (8.5 - 0.5 - 8∙0.125) / sqrt(8∙0.125∙0.875))

= P(Z > 0.5 / 0.666)

= P(Z > 0.75)

Therefore, the correct option is (d) p(x > 8.5)

Learn more about binomial probability here

brainly.com/question/29350029

#SPJ4

The given question is incomplete, the complete question is:

To approximate binomial probability p(x > 8) when n is large, identify the appropriate 0.5 adjusted formula for normal approximation. a) p(x > 7.5) b)  p(x >= 9) c) p(x > 9) d) p(x > 8.5)

The product of the number 3/4 and 8 1/2 is 51/8.

A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.

The given numbers are 3/4 and 8 1/2.

Convert the mixed number to an improper fraction:

8 1/2 = (8 x 2 + 1) / 2 = 17/2

Then, we can multiply the fractions:

3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8

Hence, the product of 3/4 and 8 1/2 is 51/8.

Learn more about improper fraction here:

https://brainly.com/question/21449807

#SPJ1

Answer:

Integral

Step-by-step explanation:

explain integral calculus

After labeling with the corresponding boxes , The statements which describes Red pulp and white pulp are as follow:

1. Red pulp           2. Red Pulp        3. White Pulp        4. Red pulp    

5. White Pulp        6. White Pulp        7. Red Pulp.

Red Pulp:

The red pulp of the spleen is made up of connective tissue (also known as Bill Roth's cord) and numerous sinusoids of the spleen which appear red due to excess blood. Its main function is to filter antigens, microorganisms and defective or worn out red blood cells from the blood.

The spleen consists of red and white pulp, separated by the marginal zone; 76-79% of a normal spleen is made up of red pulp. Unlike white pulp, which contains mostly lymphocytes (such as T cells), red pulp is made up of several types of blood cells, including platelets, granulocytes, red blood cells, and plasma.

White Pulp:

White pulp is the histological name for the areas of the spleen (so called because they appear whiter in rough sections than the surrounding red pulp), which make up approximately 25% of the spleen. The white pulp is entirely composed of lymphoid tissue.

Specifically, the white pulp contains several regions with distinct functions:

The periarteriolar lymphatic sheaths (PALS) are usually associated with the arteriolar supply to the spleen; they contain T lymphocytes.

Lymphoid follicles with dividing B lymphocytes located between the PALS and the marginal zone bordering the red pulp. This region produces IgM and IgG2.

These molecules play a role in the opsonization of extracellular organisms, in particular encapsulated bacteria.

The marginal zone exists between the white pulp and the red pulp. It is located away from the central arterioles, close to the red pulp. It contains antigen-presenting cells (APCs), such as dendritic cells and macrophages. Some white pulp macrophages are of a special type called metallolipid macrophages.

Learn more about function:

https://brainly.com/question/23952628

#SPJ4

The vertex is frequently identified by the letter that appears in the middle, like the letter V. Angles are often measured in degrees, and degrees are used to characterize angles. Thus, option C is correct.

Angle 7 is perpendicular to angle 3, and angle 3 is supplementary to angle 8, therefore they both fall along a straight line. Hence, angle 8 is complementary to angle 7.

Since they form a straight line and are opposite angles, angles 5 and 7 are supplementary. Hence, angle 5 is complementary to angle 7.

The only angle in the figure that is not a support for angle 7 is angle 6. If angles 6 and 7 do not overlap but share a vertex and side, then they are considered neighbouring.

Because they do not go to a straight line, angles 6 and 7 are not extra in this case. The answer is therefore Angle 6.

Therefore, They are not always complementary, even if two nearby angles come together to create a straight line.

Learn more about angle here:

https://brainly.com/question/28451077

#SPJ1

Answer:y=x-5

Step-by-step explanation:this is the answer for sure

Answer:

[tex]y=x-5[/tex]

Step-by-step explanation:

Notice for every X you do increase your Y by 1, this is the slope must be 1, to check you can use the slope equation with any two points

[tex]m= \frac{-4-(-3)}{1-(2)} =-1[/tex]
The lets use one point and the line equation:

[tex]y-yo=m(x-xo)[/tex]
[tex]y+4=-1(x-1)[/tex]

Solving for Y you can obtain

[tex]y=x-5[/tex]

You can input any X value and check the Y value to be sure, for example, for X=3 you can check Y=3-5=-2. In the table for X=3 the Y value is -2, so this checks.

Answer:

D?

Step-by-step explanation:

I'm not completely sure, but there are 2 different 180 degree lines that y falls on. On one line (y+70=180) it is for sure 110 degrees

When measured on the other line it is (y+70+x=180) I'm not too familiar with this??

Therefore, the only statement that is true is: "The new area is 6 times the original area."

Area is a measure of the size or extent of a two-dimensional surface or region, such as the surface of a square, rectangle, circle, triangle, or any other shape. It is expressed in square units, such as square meters, square feet, or square centimeters.

Here,

If the side lengths of a square are tripled, the new side length will be 2 mm x 3 = 6 mm.

The original area of the square is:

Area = side length x side length = 2 mm x 2 mm = 4 mm²

The new area of the square with tripled side lengths will be:

New area = new side length x new side length = 6 mm x 6 mm = 36 mm²

Therefore, the new area of the square will be 36 mm².

To determine which of the following statements about its area will be true, we need to see which statements are true for the new area of 36 mm²:

A. The new area is 6 times the original area. This statement is true because 36 mm² is 6 times larger than 4 mm².

B. The new area is 3 times the original area. This statement is false because 36 mm² is 9 times larger than 4 mm², not 3 times larger.

C. The new area is equal to the original area. This statement is false because the new area of 36 mm² is much larger than the original area of 4 mm².

To know more about area,

https://brainly.com/question/22469440

#SPJ1

Complete question:

look at this square: 2 mm 2 mm if the side lengths are tripled, then which of the following statements about its area will be true?

The ratio of the new area to the old area will be 2:1

The ratio of the new area to the old area will be 6:1.

The ratio of the new area to the old area will be 1:2.

The ratio of the new area to the old area will be 4:1.

For a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.

L'Hospital's rule applies to limit expressions of the form 0/0 or infinity/infinity. Specifically, if we have a limit expression of form f(x)/g(x), where f(x) and g(x) both approach 0 or infinity as x approaches a certain value, then L'Hospital's rule may be applied to find the limit of the expression.

It is important to note that L'Hospital's rule can only be applied if the limit of the derivative of f(x) divided by the derivative of g(x) exists and is finite, or if the limit of the derivative of f(x) divided by the derivative of g(x) approaches infinity or negative infinity.

Therefore, for a limit expression to be solved using L'Hospital's rule, the expression must be in the form of 0/0 or infinity/infinity, and the derivatives of the numerator and denominator must exist and approach a finite limit or infinity/negative infinity at the point of evaluation.

Find out more about L'Hospital's rule

at brainly.com/question/30300388

#SPJ4

Answer: 3 cm

Step-by-step explanation:

The formula for the area of a circle is A = πr², where A is the area and r is the radius. We are given that the area of the circle is 28½ cm².

So, 28½ = πr²

We need to solve for r. Dividing both sides by π, we get:

r² = 28½/π

r² = 9

Taking the square root of both sides, we get:

r = 3√1 = 3 cm

Therefore, the radius of the circle is 3 cm.

Answer:

(15+x)÷4 = 80-x

by criss cross we'll get:

15+x = 4(80-x)

15+x = 320-4x

x+4x=320-15

5x = 305

x = 61