The line AB has a midpoint of (2,5). A has coordinates (1,7). find the coordinates of B

The length of JK would be given as  14.48

From the question we would have a circle that passes through the triangle ABC.

In the triangle we have

1/2 Ac* BC = 1/2 AB * cd

= 20 x 21 = 29 x CB

CB = 14.48

The angle that is to have the arc is at 90 degrees. Opposite the 90 degree angle we have the diameter

Then JK = CB

Then JK would be given as  14.48

Read more on tangent to an angle here:https://brainly.com/question/3685164

#SPJ1

Answer: 3 games to win

Step-by-step explanation:

8 teams each; assuming 1 game moves team forward.  

After 1 win, 4 teams left; after 2 wins, 2 teams left; after 3 wins = championship

The hottest temperature on the edge of the elliptical plate is approximately 98.66 degrees, and the coldest temperature is also approximately 98.66 degrees.

The constraint equation is the equation of the ellipse, which is x² + y² + xy = 16.

The method of Lagrange multipliers in two variables can be used to find the maximum and minimum values of the temperature function subject to the constraint equation. We introduce a Lagrange multiplier λ and set up the following equations:

∇T(x,y) = λ ∇g(x,y)

where g(x,y) is the constraint equation. This gives us:

<18x, 18y+xλ> = <2λx+y, 2λy+x>

Equating the x and y components separately, we get:

18x = 2λx + y (1)

18y = 2λy + x (2)

We also have the constraint equation:

x² + y² + xy = 16 (3)

Solving equations (1) and (2) simultaneously, we get:

λ = 9

y = 36/7 x

Substituting these values into equation (3), we get:

x² + (36/7 x)² + x(36/7 x) = 16

Simplifying this equation, we get:

85x² = 784

Solving for x, we get:

x = ± 8/√85

Substituting this value into the equation for y, we get:

y = ± 288/85√85

Now we can evaluate the temperature function at these points to find the hottest and coldest temperatures:

T(x,y) = 9(x² + y²)

For the point (8/√85, 288/85√85), we have:

T(8/√85, 288/85√85) ≈ 98.66 degrees

For the point (-8/√85, -288/85√85), we have:

T(-8/√85, -288/85√85) ≈ 98.66 degrees

Therefore, the hottest temperature on the edge of the elliptical plate is approximately 98.66 degrees, and the coldest temperature is also approximately 98.66 degrees.

Learn more about elliptical plate,

https://brainly.com/question/28281835

#SPJ4

Answer:El mínimo común múltiplo (mcm) es el número más pequeño que es múltiplo de dos o más números. Por ejemplo, el mcm de 4 y 6 es 12, ya que 12 es el número más pequeño que es múltiplo tanto de 4 como de 6.

El máximo común divisor (mcd) es el número más grande que divide exactamente dos o más números. Por ejemplo, el mcd de 12 y 18 es 6, ya que 6 es el número más grande que divide exactamente tanto a 12 como a 18.

Step-by-step explanation:

Answer: B 0.50

Step-by-step explanation:The probability P(number greater than 4) is (b) 0.50

How to determine the probability P(number greater than 4).

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

A fair, eight-sided number cube

This means that

Sample size = 8

Numbers greater than 4 = 4

The probability

The exponential function that models the total amount of medication m after t hours is [tex]m(t) = 150 e^{(-0.35t)[/tex].

What is exponential function?

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant and x is the independent variable.

Let the initial amount of medication be M = 150 mg and the decay rate be r = 35% = 0.35 per hour.

Then, the amount of medication remaining after t hours can be modeled by the exponential function:

[tex]m(t) = Me^{(-rt)[/tex]

Substituting the given values, we get:

[tex]m(t) = 150 e^{(-0.35t)[/tex]

Therefore, the exponential function that models the total amount of medication m after t hours is m(t) = 150 e^(-0.35t).

To learn more about exponential function visit:

https://brainly.com/question/2456547

#SPJ1

an exponential function that models  is [tex]m = 150 * e^{-0.35t}[/tex])

To model the total amount of medication m after t hours, we can use the formula for exponential decay:

[tex]m = m0 * e^{-rt}[/tex]

where m0 is the initial dose of the medication that was given to the cat—in this instance, 150 mg—r is the decay rate—in this instance, 35 percent, or 0.35 percent—and t is the time since the medication was given to the cat.

Substituting in the values, we get:

[tex]m = 150 * e^{-0.35t}[/tex]

This function tells us how much flea medication is in the cat's bloodstream at any given time, and the decay rate causes the amount to decrease exponentially over time.

Therefore, the exponential function that models the total amount of medication m after t hours is:

[tex]m = 150 * e^{-0.35t}[/tex]

know more about exponential function visit :

https://brainly.com/question/3127939

#SPJ1

The average value of the function y(t) = 2.04(1.03)^t for 0 ≤ t ≤ 30 is approximately 2.62.

For more such question on function

https://brainly.com/question/11624077

#SPJ11

Answer:

Step-by-step explanation:

6.5

Answer: Exact Form:

13/2

Decimal Form:

6.5

Mixed Number Form:

6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

The LCM of 8 and 10 is 40. To find the least common multiple of 8 and 10, we need to find the multiples of 8 and 10 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 8 and 10, i.e., 40.

True, all three parts of a whole, parts of a set, and division meanings of fractions involve the idea of partitioning.

Partitioning is a method of splitting numbers into smaller parts to make work easy. An example of Partitioning is when the child is taught to recognize that the number 54 represents 5 tens and 4 ones, which shows how the number can be partitioned into 50 and 4.

A fraction is defined as a part of the whole thing in mathematics, for example, when we say "1/2 of the pizza", we are partitioning the whole pizza into two equal parts and taking one of those parts. Types of Fractions are Proper Fractions, Improper Fractions, Mixed fractions, Like fractions, Unlike fractions, and Equivalent fractions

To learn more about Fractions:

https://brainly.com/question/78672

#SPJ4

The greatest common divisor (gcd) of 108 and 134 using Extended Euclidean Algorithm is 2 = s * 108 + t * 134.

The Extended Euclidean Algorithm is a method for finding the greatest common divisor (gcd) of two integers and expressing it as a linear combination of the two integers. The algorithm also finds the coefficients of this linear combination.

To find the gcd of 108 and 134, we can use the following steps:

Divide 134 by 108 and find the remainder: 134 = 108 * 1 + 26

Divide 108 by 26 and find the remainder: 108 = 26 * 4 + 4

Divide 26 by 4 and find the remainder: 26 = 4 * 6 + 2

Divide 4 by 2 and find the remainder: 4 = 2 * 2 + 0

Since the remainder is 0, the last divisor (2) is the gcd of 108 and 134.

To express the gcd as a linear combination of 108 and 134, we can use the coefficients obtained during the Extended Euclidean Algorithm. Starting from the bottom, we have:

4 = 26 - 4 * 6

2 = 26 - 4 * 6 - 2 * (108 - 4 * 26) = -1 * 108 + 5 * 26

1 = 108 - 4 * 26 = 108 - 4 * (134 - 108) = 5 * 108 - 4 * 134

Therefore, we can express the gcd of 108 and 134 as:

2 = (-1) * 108 + 5 * 26 = (-1) * 108 + 5 * (134 - 108)

or

2 = 5 * 108 - 4 * 134 = 5 * (108 - 134) - 6 * 134

Using any of the above expressions, we can write:

2 = s * 108 + t * 134

where s and t are the coefficients of 108 and 134, respectively. The values of s and t depend on the expression we choose.

For expression A, we have:

2 = (-1) * 108 + 5 * (134 - 108) = 5 * 134 - 6 * 108

Therefore, we have:

s = 25

t = -31

For expression B, we have:

2 = 5 * 108 - 4 * 134 = (-4) * 108 + 5 * 134

Therefore, we have:

s = -31

t = 25

For expression C, we have:

2 = 5 * (108 - 134) - 6 * 134 = (-31) * 108 + 22 * 134

Therefore, we have:

s = 22

t = -6

For expression D, we have:

2 = (-6) * 108 + 5 * (134 - 108) = (-6) * 108 + 5 * 26

Therefore, we have:

s = -6

t = 22

Know more about greatest common divisor (gcd) here:

https://brainly.com/question/5252620

#SPJ11

To solve for p in the inequality -9p ≥ 40.5, we need to isolate p on one side of the inequality sign.

We can start by dividing both sides of the inequality by -9. However, when we multiply or divide both sides of an inequality by a negative number, we must reverse the direction of the inequality sign.

So, dividing both sides by -9 and reversing the direction of the inequality, we get:

p ≤ -40.5 ÷ (-9)

Simplifying the right side, we have:

p ≤ 4.5

Therefore, the solution for p is p ≤ 4.5.

It's True

*IG: whis.sama_ent*

False. A univariate data set is a set of data that only has one variable or category.

In this case, the running times for 500 runners would have multiple variables - the time each runner takes to complete the race. Therefore, it would be a multivariate data set.

Additionally, the term "group starts" suggests that the runners may have been grouped by certain categories or factors, further adding to the complexity of the data set.

To know more sbout unvariate data set  click on below link :

https://brainly.com/question/13415579#

#SPJ11

The data given 259,283,317,328,330,345,362,392 represents the number of students in 8 schools, after the changes in the central-tendency due to change in data,

a)Median:It stays the same.

b)Mean:Decreases by 10

What is central-tendency?

A single number that shows data to characterise a set by assessing the central position within that collection of data is referred to as a measure of central tendency. Measures of central location or summary statistics are other names for measures of central tendency. You are probably most familiar with the mean or average as a measure of central tendency, but there are more options, including the median and the mode. The mean, median, and mode are all indicators of central tendency, but under various circumstances, some indicators are more useful than others.

Given data of 8 schools:

a)Original observations:259,283,317,328,330,345,362,392

Median:mean of 4th & 5th observations

Median=[tex]\frac{328+330}{2}[/tex]

Median=329

On changing 259 to 179,

New observation:179,283,317,328,330,345,362,392

Median:mean of 4th & 5th observations

Median=[tex]\frac{328+330}{2}[/tex]

Median=329

Median:remains same

b)Mean of original observations=[tex]\frac{sum of all observations}{number of observations}[/tex]

           =[tex]\frac{259+283+317+328+330+345+362+392}{8}[/tex]

           =[tex]\frac{2616}{8}[/tex]

           =327

Mean of new observations=[tex]\frac{sum of all observations}{number of observations}[/tex]

              =[tex]\frac{179+283+317+328+330+345+362+392}{8}[/tex]

              =[tex]\frac{2536}{8}[/tex]

              =317

Mean:Decreases by 10

To know more about central-tendency, visit:

https://brainly.com/question/30218735

#SPJ1

The statement "Within any group of 50 persons, there must be at least 6 who were born in the same month" is True. The Pigeonhole Principle is a fundamental principle in combinatorics that states that if there are more pigeons than pigeonholes.

According to the Pigeonhole Principle, which is a basic principle of combinatorial mathematics, if there are more items (or "pigeons") than there are available places to put them (or "pigeonholes"), then at least one of the pigeonholes must contain more than one item. In the context of the question, there are 12 months in a year, and only 50 persons in the group. Since there are more persons than there are months, by the Pigeonhole Principle, there must be at least one month with more than one person born in it.

Therefore, there must be at least 6 persons who were born in the same month in any group of 50 persons.

To learn more about Pigeonhole Principle here:

brainly.com/question/30322724#

#SPJ11

The  volume of each solid figure are (3)   52h³  (4) 1530h³ and (5) 1348 h³

A cuboid is a convex polyhedron bounded by six rectangular faces with eight vertices and twelve edges, also known as a hexahedron

The volume of a cuboid can be calculated using the formula Volume of a cuboid = Length × Width × Height Cubic units

The volume of each of the cuboids is the volume of the larger one + the volume of the small one

(3) Volume = LWH  + lwh

Volume = (7*1*4) + (4*2*3)

Volume = 28 + 24

The volume is = 52h³

(4) Volume = LWH  + lwh

Volume= (10*16*9) + (6*5*3)

Volume= 1440 + 90

Volume= 1530h³

5)  Volume = LWH  + lwh

Volume=  (13*10*10) + (3*4*4)

Volume=  1300 + 48

Volume=  1348 h³

Learn more about volume of cuboid on https://brainly.com/question/29568631

#SPJ1

The chance that five minutes or more passes between two hits is equal to e(-5), where is the rate of hits per minute.

The chance that 5 or more minutes pass between two hits can be calculated using the exponential distribution formula. Let λ be the rate of hits per minute. The probability that no hits occur in a time interval of length t is given by e^(-λt). Therefore, the probability that at least one hit occurs in a time interval of length t is 1-e^(-λt).

To find the probability that 5 or more minutes pass between two hits, we need to calculate the probability that no hits occur in a time interval of length 5 or greater. This is given by e^(-5λ). Therefore, the probability that at least one hit occurs within 5 minutes is 1-e^(-5λ).

So, the chance that 5 or more minutes pass between two hits is simply the complement of this probability:

P(5 or more minutes pass between two hits) = 1 - (1-e^(-5λ))

Simplifying this expression, we get:

P(5 or more minutes pass between two hits) = e^(-5λ)

Thus, the chance that 5 or more minutes pass between two hits is equal to e^(-5λ), where λ is the rate of hits per minute.
visit here to learn more about exponential distribution:

brainly.com/question/22692312

#SPJ11

The slope of a line can be positive, negative, zero or undefined.the slope of the line is [tex]1/6[/tex] .

The given information provides three points on the line:   [tex](-3,2), (3,3),[/tex] and  [tex](3,)[/tex] .

To find the slope of the line, we need to calculate the rise (change in y) over the run (change in x) between any two of these points. Let's choose (-3,2) and (3,3):

rise = change in [tex]y = 3 - 2 = 1[/tex]

run = change in [tex]x = 3 - (-3) = 6[/tex]

slope = rise/run [tex]= 1/6[/tex]

Therefore, the slope of the line is [tex]1/6[/tex] .

Learn more about slope here:

brainly.com/question/3605446

#SPJ1

The unit normal vector of the function f(x,y)=x^3 at point P(5,3,125) is ⟨1, 0, 0⟩.

To find a unit normal vector at point P(5,3,125) for the function f(x,y) = x^3, we need to find the gradient vector of f and normalize it to obtain a unit vector.

The gradient of f is given by

∇f = ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩ = ⟨3x^2, 0, 0⟩

At point P(5,3,125), the gradient vector is

∇f(P) = ⟨75, 0, 0⟩

To obtain a unit normal vector, we need to normalize ∇f(P) by dividing it by its magnitude

||∇f(P)|| = √(75^2 + 0^2 + 0^2) = 75

So the unit normal vector at point P is

n = ∇f(P) / ||∇f(P)|| = ⟨75/75, 0/75, 0/75⟩ = ⟨1, 0, 0⟩

Therefore, the unit normal vector for the function at the point P is ⟨1, 0, 0⟩.

To know more about normal vector:

https://brainly.com/question/29050578

#SPJ4

Answer:

Step-by-step explanation:

The function f(x) = 1/x is not defined for x = 0 since division by zero is undefined. Therefore, f(x) is not a function from R to R since it does not assign a unique value to every element in the domain.

To find the coordinate vector of A relative to the basis S = {A1, A2, A3, A4}, express A as a linear combination of the basis vectors and then write the coefficients as a column vector.

A = 4A1 + 2A2 - 14A3 + 20A4
= 4(1,0,0,0) + 2(0,1,0,0) - 14(0,0,1,0) + 20(0,0,0,1)
= (4,2,-14,20)

Therefore, the coordinate vector of A relative to the basis S is:

[A]s =
[4]
[2]
[-14]
[20]

This means that A can be expressed as a linear combination of the basis vectors with coefficients 4, 2, -14, and 20 respectively. This representation is unique to the basis S.

Learn more about coordinate vector: https://brainly.com/question/31427002

#SPJ11

Since the graph of the parent function f(x) = x would be stretched horizontally by a factor of 2 and reflected over the y-axis, f(x) is replaced by this transformation: (A) -2f(x).

In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate (y-axis) while the sign of the x-coordinate (x-axis) would change from positive to negative or negative to positive.

Since the graph of the parent function f(x) = x would be stretched horizontally by a scale factor of 2, followed by a reflection over or across the y-axis or line x = 0, f(x) should be replaced by this transformation rule -2f(x).

Read more on reflection here: brainly.com/question/27912791

#SPJ1

(a) The probability that the sample mean will weigh between 0.048 and 0.053 ounces is approximately 0.6181.

(b) The probability that a package of 100 almonds will weigh between 4.8 and 5.3 ounces is essentially 0.

To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with a finite mean and standard deviation is approximately a normal distribution, as the sample size increases.

(a) We want to find the probability that the sample mean will weigh between 0.048 and 0.053 ounces. We can standardize the sample mean using the formula

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get

z = (0.048 - 0.05) / (0.015 / √100) = -0.67

z = (0.053 - 0.05) / (0.015 / √100) = 0.67

Using a standard normal distribution table or a calculator, we can find that the probability of z being between -0.67 and 0.67 is approximately 0.6181.

Therefore, the probability that the sample mean will weigh between 0.048 and 0.053 ounces is approximately 0.6181.

(b) We want to find the probability that a package of 100 almonds will weigh between 4.8 and 5.3 ounces. We can use the fact that the sample mean is normally distributed with a mean of 0.05 ounces and a standard deviation of 0.015 / √100 = 0.0015 ounces.

Then, we can standardize the values using the formula

z = (x - μ) / σ

where x is the weight of the package of almonds.

Substituting the given values, we get

z = (4.8 - 5) / 0.0015 = -133.33

z = (5.3 - 5) / 0.0015 = 133.33

Since the distribution is symmetric, we can find the probability of z being less than -133.33 and add it to the probability of z being greater than 133.33 to get the total probability.

Using a standard normal distribution table or a calculator, we can find that the probability of z being less than -133.33 is essentially 0, and the probability of z being greater than 133.33 is also essentially 0.

Learn more about probability here

brainly.com/question/11234923

#SPJ4

(a) The natural logarithm of the moment generating function (MGF) of 3X at t=0.75 is ln(ϕ_3X(0.75)).

(b) The expectation of 3X is E(3X) = 3E(X).

(c) The natural logarithm of the MGF of 3X+8 at t=0.75 is ln(ϕ_(3X+8)(0.75)).

(a) First, find the MGF of 3X: ϕ_3X(t) = ϕ_X(3t) = (0.21[tex]e^3^t[/tex] + 1 - 0.21)⁷. Next, evaluate at t=0.75: ϕ_3X(0.75) = ([tex]0.21e^2^.^2^5[/tex] + 1 - 0.21)⁷. Finally, find the natural logarithm: ln(ϕ_3X(0.75)).

(b) To find the expectation of 3X, first find the expectation of X: E(X) = ϕ'_X(0). Differentiate the MGF of X w.r.t t: ϕ'_X(t) = 7(0.21[tex]e^t[/tex])(0.21[tex]e^t[/tex] + 1 - 0.21)⁶. Evaluate at t=0: E(X) = 7(0.21)(1)⁶ = 1.47. Then, E(3X) = 3E(X) = 3 * 1.47 = 4.41.

(c) The MGF of 3X+8 is ϕ_(3X+8)(t) = [tex]e^8^t[/tex]ϕ_3X(t). Evaluate at t=0.75: ϕ_(3X+8)(0.75) = e⁶ * ([tex]0.21e^2^.^2^5[/tex] + 1 - 0.21)⁷. Find the natural logarithm: ln(ϕ_(3X+8)(0.75)).

To know more about natural logarithm click on below link:

https://brainly.com/question/30085872#

#SPJ11

If you rejecting the null hypothesis can lead to either a correct decision or to an error, either a type I error or a type II error. (option a).

A correct decision occurs when we reject the null hypothesis and the alternative hypothesis is actually true.

A type I error, also known as a false positive, occurs when we reject the null hypothesis when it is actually true. In other words, we conclude that there is a significant difference between two groups or that a certain parameter is different from what was assumed in the null hypothesis, when in reality, there is no difference. Type I errors can occur due to random chance, or if the sample size is too small, or if the significance level is too high.

A type II error, also known as a false negative, occurs when we fail to reject the null hypothesis when it is actually false. This means that we conclude that there is no significant difference between two groups or that a certain parameter is equal to the value assumed in the null hypothesis, when in reality, there is a difference. Type II errors can occur if the sample size is too small or if the significance level is too low.

Therefore, option (a) is the right one.

To know more about hypothesis here

https://brainly.com/question/29576929

#SPJ4

However, it is in dynamic equilibrium because the net force acting on the object is zero, as the centripetal force is balanced by the object's inertia.

Static equilibrium refers to a state where an object is at rest and all the forces acting on it are balanced, so the object remains stationary. In contrast, an object moving on a circular path at a constant speed is in dynamic equilibrium, where the object is moving at a constant speed but the direction of its velocity is changing continuously.

In this case, there is a centripetal force acting on the object that keeps it moving in a circular path. The force is directed towards the center of the circle and is proportional to the mass of the object, the speed at which it is moving, and the radius of the circular path.

Therefore, the object is not at rest and there is a force acting on it, so it is not in static equilibrium. However, it is in dynamic equilibrium because the net force acting on the object is zero, as the centripetal force is balanced by the object's inertia.

To learn more about equilibrium visit:

https://brainly.com/question/30807709

#SPJ11

Mary's HLV is $2,215,773.95.

Mary's HLV if she works until 70 is $1,611,008.23.

Mary's COE if she works until 75 is $5,130,372.40.

Mary's COE if she works until 70 is $2,985,308.60.

To calculate the Human Life Value insurance (HLV) of Mary, we need to determine the present value of her future income stream.

Annual after-tax earnings = $55,000 x (1 - 0.15) = $46,750

Total after-tax earnings over working life = $46,750 x (1 + 0.03)^(75-35) = $3,382,820.33

Total personal consumption = 27% x $3,382,820.33 = $914,073.89

Calculate Mary's HLV:

= $3,382,820.33 - (1 + 0.05)^(-1) x $914,073.89

= $2,215,773.95

Therefore, Mary's HLV is $2,215,773.95.

If Mary works until 70 total after-tax  = $46,750 x (1 + 0.03)^(70-35) = $2,124,182.09

Mary's HLV if she works until 70 is $1,611,008.23.

To calculate the Capitalization of Earnings (COE) method. Here's how we can calculate it:

Calculate Mary's expected earnings in her final year of work:

Expected earnings in final year = $55,000 x (1 + 0.03)^(75-35) = $256,518.62

Apply a capitalization rate to the expected earnings:

COE = expected earnings in final year / capitalization rate

= $256,518.62 / 0.05

= $5,130,372.40

Therefore, Mary's COE if she works until 75 is $5,130,372.40.

If Mary works until 70, her expected earnings in her final year of work would be:

Expected earnings in final year = $55,000 x (1 + 0.03)^(70-35) = $149,265.43

Mary's COE if she works until 70 is $2,985,308.60.

Learn more about insurance

brainly.com/question/8664299

#SPJ11

To construct E from the given ciphertext xhBBpWdotCf!uJE, we need to use the given numbers as the key to decrypt the message. The numbers represent the positions of the letters in the alphabet, where A=1, B=2, C=3, and so on.

Starting with the first number 24, we look for the 24th letter in the alphabet which is X. Similarly, we decrypt the remaining numbers and get the following letters: h, B, B, p, W, d, o, t, C, f, !, u, J, and E.

Therefore, the decrypted message E can be constructed from the given ciphertext xhBBpWdotCf!uJE.

To do this, follow these steps:

1. Write down the given ciphertext: xhBBpWdotCf!uJE
2. Write down the given series of numbers: 24 2 -16 -4 -20 -6 -21 -8 2 23 29 3 28 10
3. For each character in the ciphertext, find its corresponding ASCII value.
4. Add the corresponding number from the series to the ASCII value of each character.
5. Convert the resulting ASCII values back to characters.
6. Combine the characters to form the plaintext (E).

Following these steps, you'll be able to construct the plaintext E from the given ciphertext and the series of numbers.

Learn more about ciphertext on: brainly.com/question/30143645

#SPJ11