Which theorem correctly justifies why the lines m and n are parallel when cut by a transversal k

Answer:

The total number of nails in Susan's box is 660 nails

Step-by-step explanation:

The given parameters are;

The number of small nails in John's box = 65

The number of medium nails in John's box = 40

The number of large nails in John's box = 45

The number of medium nails in Susan's box = 176

The ratio of the nails in John's box  is given as follows;

The ratio of small nails in John's box = 65/(65 + 40 + 45) = 13/30

The ratio of medium nails in John's box = 40/(65 + 40 + 45) = 4/15 = 8/30

The ratio of large nails  in John's box = 45/(65 + 40 + 45) = 3/10 = 9/30

Given that the proportion of the nails in John's box and Susan's box are the same, we have;

The ratio of medium nails in Susan's box =  8/30

Therefore;

Where the total number of nails in Susan's box = X, we have;

8/30 × X = 176

X = 176 × 30/8 = 660 nails

The total number of nails in Susan's box = 660 nails.

Using proportions, it is found that the total number of nails in Susan's box was 660.

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

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

Since the proportions are equal:

\(\frac{40}{150} = \frac{176}{x}\)

\(40x = 150\times176\)

\(x = \frac{150\times176}{40}\)

\(x = 660\)

The total number of nails in Susan's box was 660.

A similar problem is given at https://brainly.com/question/19905617

Answer:

ur welcoem

Step-by-step explanation:

The value of\(e^3\) is approximately 20.09, so x ≈ 20.09 - 1 = 19.09. Therefore, the correct option is a) 19.09.

Given, ln(x + 1) = 3

To solve for x, we need to follow the following steps:

Step 1: Express the given logarithmic equation as an exponential equation, using the definition of the natural logarithm.The natural logarithm is defined as follows:ln a = b\(=> e^b = a\)

So, we can write the given logarithmic equation as e^3 = x + 1.

Step 2: Simplify and solve for x

Subtracting 1 from both sides, we get:x = \(e^3\) - 1

The value of e^3 is approximately 20.09. So,x ≈ 20.09 - 1 = 19.09Therefore, the correct option is a) 19.09.

To solve the given logarithmic equation ln(x + 1) = 3, first express it as an exponential equation using the definition of natural logarithm. The natural logarithm states that if ln a = b, then\(e^b\)= a. S

o, using this definition, the given logarithmic equation can be written as e^3 = x + 1. By subtracting 1 from both sides, we can solve for x.

To know more about value visit:

brainly.com/question/32584187

#SPJ11

Answer:

a). To find the median from a set of numbers, you need to arrange them from ascending order (smallest to biggest), and then you need to find the number in the middle

b). 32

Step-by-step explanation:

b). Smallest to biggest

29, 30, 31, 32, 33, 34, 37

From the set of numbers given, we can clearly see that 32 is in the middle.

Answer:

350m

Step-by-step explanation:

Vi = 15 m/s

A = 4 m/s^2

delta t = 10s

delta x = ?

delta x = (Vi)(delta t) + 1/2(A)(delta t)^2

delta x = (15m/s)(10s) + 1/2(4m/s^2)(10s)^2

delta x = 350 m

Answer:

x=4

Step-by-step explanation:

they are the same

what you do is take 4x+23 and make it equal to 10x-1

4x+23=10x-1

+1              +1

4x+24=10x

-4x      -4x

24=6x

/6    /6

x=4

The interest earned by Mrs Grey over the 7 years is R5670. The cost of the television set 5 years ago was R20,600.

4.1.1 To calculate the interest earned by Mrs Grey over 7 years, we use the formula for simple interest: Interest = Principal x Rate x Time. Mrs Grey's principal is R18,000 and the rate is 4.5% per annum. The time is 7 years. Using the formula, we can calculate the interest as follows:

Interest = R18,000 x 0.045 x 7 = R5670. Therefore, Mrs Grey has earned R5670 in interest over the 7 years.

4.1.2 To calculate the cost of the television set 5 years ago, we need to account for the inflation rate. The cost of the television set now is R27,660. The average rate of inflation over the last 5 years is 6.7% per annum. We can use the formula for compound interest to calculate the original cost of the television set:

Cost 5 years ago = Cost now / (1 + Inflation rate)^Time

Cost 5 years ago = R27,660 / (1 + 0.067)^5 = R20,600. Therefore, the cost of the television set 5 years ago was R20,600.

4.1.3 To determine the rate of simple interest Mrs Grey should have invested her money at 7 years ago, we can use the formula for interest: Interest = Principal x Rate x Time. We know the principal is R18,000, the time is 7 years, and the interest earned is R5670. Rearranging the formula, we can solve for the rate:

Rate = Interest / (Principal x Time)

Rate = R5670 / (R18,000 x 7) ≈ 0.0448 or 4.48% per annum. Therefore, Mrs Grey should have invested her money at a rate of approximately 4.48% per annum to have earned enough interest to purchase the television set using only her original investment and the interest earned over the 7 years.

Learn more about simple interest here:

brainly.com/question/30964674

#SPJ11

The probability that Xeres arrives first AND Regina arrives last is 3.33%.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

Here The number of possible arrangements of n elements is given by:

\(A_n=n!\)

In this problem:

6 people are invited, so the number of ways they can arrive is T = \(6!\)

Xeres first and Regina last, for the middle 4 there are  way D= 4! ways

Then the probability is P = \(\frac{D}{T}=\frac{4!}{6!}\) =  0.0333 = 3.33%

To learn more about probability refer the below link

https://brainly.com/question/13604758

#SPJ1

Answer:

Step-by-step explanation:

The answer is h(x) = ^2 + 12 and g (x) = ^2

The probability that the dog is still lost at the end of the second day is 0.41

To solve this problem, we can use Bayes' theorem, which allows us to update the probability of an event based on new information.

Let A be the event that the dog is in forest A, and B be the event that the dog is in forest B. Let F be the event that the dog is found within two days.

We want to calculate P(F'), the probability that the dog is still lost at the end of the second day. We can use the law of total probability to express this as

P(F') = P(F'|A) × P(A) + P(F'|B) × P(B)

where P(F'|A) is the probability of not finding the dog within two days given that the dog is in forest A, P(F'|B) is the probability of not finding the dog within two days given that the dog is in forest B, and P(A) and P(B) are the prior probabilities of the dog being in forest A and forest B, respectively.

Using the information given in the problem, we can calculate

P(F'|A) = 1 - 0.5 = 0.5 (the probability of not finding the dog in forest A within two days is 1 - 0.5 = 0.5)

P(F'|B) = 1 - 0.8 = 0.2 (the probability of not finding the dog in forest B within two days is 1 - 0.8 = 0.2)

P(A) = 0.7 (the prior probability of the dog being in forest A)

P(B) = 0.3 (the prior probability of the dog being in forest B)

Plugging these values into the formula above, we get

P(F') = 0.5 × 0.7 + 0.2 × 0.3 = 0.41

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The given question is incomplete, the complete question is:

Oscar has lost his dog; there is a 70% probability it is in forest A and a 30% chance it is forest B. If the dog is in forest A and Oscar looks there for a day, he has a 50% change of finding the dog. If the dog is in forest B and Oscar looks there for a day, he has an 80% chance of finding the dog. what is the probability that the dog is still lost at the end of the second day?

Answer:

Step-by-step explanation:

If the multiplication of two numbers has the zero at the end, one of them will have a factor of 2 and the other number will have the factor of 5.

Example: Multiplication of 25 and 8.

                Factors of 25 = 5 × 5 [5 is a factor of 25]

                Factors of 8 = 2 × 2 × 2 [2 is a factor of 8]

Multiplication of 8 × 25 = 200 [Zero at the end]

Two numbers are 459 and 885.

Factors of 459 = 3 × 3 × 3 × 17

Factors of 885 = 3 × 5 × 59

[Since, 2 is not a factor in both the numbers multiplication of the numbers will not have 0 at the end]

459 × 885 = 406215

The height of the cone is the same as the radius of the circular sheet of paper, which is 2 cm. The slant height of the cone is the hypotenuse of a right triangle with legs equal to the radius and the circumference of the sector.

The circumference of the sector is 2 * pi * 2 cm = 4 pi cm.

The slant height of the cone is therefore sqrt(2^2 + 4 pi^2) = sqrt(4 + 16 pi^2) = 2 * sqrt(1 + 4 pi^2) in simplest radical form.

Therefore, the height of the cone is 2 cm and the slant height of the cone is 2 * sqrt(1 + 4 pi^2) cm.

The radius of the cone is the same as the radius of the circle, which is 2 cm. The slant height of the cone is the hypotenuse of a right triangle with legs equal to the radius and the circumference of the sector.

The circumference of the sector is 2 * pi * 2 cm = 4 pi cm.

In general, different refrigerants should not be mixed or recovered into the same cylinder.

Different refrigerants have unique chemical compositions and properties that make them incompatible with one another. Mixing different refrigerants can lead to unpredictable reactions, loss of refrigerant performance, and potential safety hazards. Therefore, it is generally recommended to avoid recovering different refrigerants into the same cylinder.

When recovering refrigerants, it is important to use separate recovery cylinders or tanks for each specific refrigerant type. This ensures that the refrigerants can be properly identified, stored, and recycled or disposed of in accordance with regulations and environmental guidelines.

The refrigerant recovery process involves capturing and removing refrigerant from a system, storing it temporarily in dedicated containers, and then transferring it to a proper recovery or recycling facility. Proper identification and segregation of refrigerants during the recovery process help maintain the integrity of each refrigerant type and prevent contamination or cross-contamination.

To maintain the integrity and safety of different refrigerants, it is best practice to recover each refrigerant into separate cylinders. Mixing different refrigerants in the same cylinder can lead to complications and should be avoided. Following proper refrigerant recovery procedures and guidelines helps ensure the efficient and environmentally responsible management of refrigerants.

To know more about cylinder visit:

https://brainly.com/question/30390407

#SPJ11

The number of different refrigerants that may be recovered into the same cylinder is zero.

When it comes to refrigerants, it is important to understand that different refrigerants should not be mixed together. Each refrigerant has its own unique properties and should be handled and stored separately. mixing refrigerants can lead to chemical reactions and potential safety hazards.

The recovery process involves removing refrigerants from a system and storing them in a cylinder for proper disposal or reuse. During the recovery process, it is crucial to ensure that only one type of refrigerant is being recovered into a cylinder to avoid contamination or mixing.

Therefore, the number of different refrigerants that may be recovered into the same cylinder is zero. It is essential to keep different refrigerants separate to maintain their integrity and prevent any adverse reactions.

Learn more:

About refrigerants here:

https://brainly.com/question/13002119

#SPJ11

The largest interval I over which the solution is defined is:

I = (9 - ∞, 9 + ∞)

To solve the given initial-value problem, we need to rearrange the equation and separate the variables. The equation can be rearranged as follows:

y dx = (3y^2 + x) dy

Next, we need to separate the variables and integrate both sides of the equation:

∫y dx = ∫(3y^2 + x) dy

∫y dx = y^3 + xy + C

Now, we can use the initial condition x(9) = 1 to solve for C:

1 = 9^3 + 9(1) + C

C = -729

Therefore, the solution to the initial-value problem is:

y^3 + xy = 729

To find the largest interval I over which the solution is defined, we need to determine the values of x and y that make the equation true. Since the equation is a cubic equation, there are potentially three solutions for y. However, since we are looking for the largest interval, we only need to find the smallest and largest values of y that satisfy the equation. These values will be the endpoints of the interval I.

The smallest value of y occurs when x is at its largest value, which is infinity. Plugging in x = ∞ and solving for y gives us:

y^3 + ∞y = 729

y^3 = 729 - ∞y

y = 729^(1/3) - ∞^(1/3)

y = 9 - ∞

The largest value of y occurs when x is at its smallest value, which is negative infinity. Plugging in x = -∞ and solving for y gives us:

y^3 - ∞y = 729

y^3 = 729 + ∞y

y = 729^(1/3) + ∞^(1/3)

y = 9 + ∞

Therefore, the largest interval I over which the solution is defined is:

I = (9 - ∞, 9 + ∞)

For more similar questions on interval:

brainly.com/question/17373970

#SPJ11

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

Read more about domain at

https://brainly.com/question/31900115

#SPJ1

For the function f(x,y)=x3−3x+3xy2,

(0,0) - a critical point of undetermined nature

(0,1) - a saddle point

(0,-1) - a saddle point

and there are no local maxima or local minima.

To find the local maximum and minimum values and saddle points of the function f(x,y)=x3−3x+3xy2, we need to first find its critical points.

To find the critical points of f(x,y), we need to solve the system of equations given by setting the partial derivatives of f(x,y) with respect to x and y equal to zero:

∂f/∂x = 3x2 - 3 + 3y2 = 0

∂f/∂y = 6xy = 0

From the second equation, we get either x=0 or y=0.

If x=0, then the first equation becomes 3y^2-3=0, which gives y=±1. Substituting these values of x and y back into f(x,y), we get the critical points (0,1) and (0,-1).

If y=0, then the second equation becomes x=0. Substituting this value of x back into f(x,y), we get the critical point (0,0).

So, we have three critical points: (0,0), (0,1), and (0,-1).

Now, we need to classify these critical points as local maxima, local minima, or saddle points. To do this, we can use the second partial derivative test.

The Hessian matrix of f(x,y) is given by:

H(x,y) =

[6x 6y]

[6y 6x+6]

At the critical point (0,0), we have H(0,0) =

[0 0]

[0 6]

The determinant of H(0,0) is 0, and the eigenvalues are 0 and 6. Since the determinant is 0, we cannot conclude whether (0,0) is a local maximum, local minimum, or saddle point using the second partial derivative test. Instead, we can use other methods to determine the nature of this critical point.

At the critical point (0,1), we have H(0,1) =

[0 6]

[6 6]

The determinant of H(0,1) is -36, and the eigenvalues are approximately -4.59 and 10.59. Since the determinant is negative and the eigenvalues have opposite signs, we can conclude that (0,1) is a saddle point.

At the critical point (0,-1), we have H(0,-1) =

[0 -6]

[-6 6]

The determinant of H(0,-1) is 36, and the eigenvalues are approximately -10.59 and 4.59. Since the determinant is positive and the eigenvalues have opposite signs, we can conclude that (0,-1) is also a saddle point.

Therefore, the critical points of f(x,y) are:

(0,0) - a critical point of undetermined nature

(0,1) - a saddle point

(0,-1) - a saddle point

So, there are no local maxima or local minima for the function f(x,y)=x3−3x+3xy2.

For more such questions on Functions.

https://brainly.com/question/31402672#

#SPJ11

No supply function given, assuming linear function, need more information to find equilibrium price and consumers' surplus for demand function \(D(q) = (9q + 5)^2\) at equilibrium q = 7.

The demand function for a particular beverage is given by \(D(q) = (9q + 5)^2\), and the supply and demand are in equilibrium at q = 7. We can find the consumers' surplus by first finding the equilibrium price, and then using the formula for consumers' surplus.

At equilibrium, the quantity demanded is equal to the quantity supplied. Since the demand function is given by \(D(q) = (9q + 5)^2\), we have\(D(7) = (9(7) + 5)^2 = 6561\) as the equilibrium quantity.

To find the equilibrium price, we need to use the supply function. However, the supply function is not given in the problem statement. Therefore, we need more information to determine the equilibrium price.

Assuming that the supply function is linear and takes the form S(q) = mq + b, where m is the slope and b is the intercept, we can use the equilibrium condition to solve for m and b. At equilibrium, D(q) = S(q), so we have \((9q + 5)^2 = mq + b\). Evaluating this equation at q = 7, we get \(6561 = 7m + b\).

Without additional information, we cannot solve for m and b, and hence we cannot find the equilibrium price or the consumers' surplus.

In summary, to find the consumers' surplus for a particular beverage with demand function \(D(q) = (9q + 5)^2\) and equilibrium quantity q = 7, we need to know the supply function to determine the equilibrium price. Without additional information, we cannot find the consumers' surplus.

To know more about equilibrium price refer here:

https://brainly.com/question/30797941#

#SPJ11

Answer:

after paying all expenses Ron will have $10 leftover each month.

Answer:

10 on edge

Step-by-step explanation:

Answer:

8/17 is correct because cosine = adjacent/hypotenuse, and since angle A is theta, or the reference angle, the adjacent of A would be 8, and the hypotenuse is always across the right angle.

15/17 would be sine instead of cosine

Answer:

196

Step-by-step explanation:

196 is the perfect square number, because its square root is 14.

\( \sqrt{196} = 14\)

The volume of the resulting solid is \(150.85 cm^3\)

Given radius of ball = \(r_1\) = 10cm

hole radius = \(r_2\) = 8cm

volume of remaining solid = volume of ball - volume of hole

volume of remaining solid = \(\frac{4 \pi }{3} r_1^{2} - \frac{4 \pi }{3} r_2^{2}\)

volume of remaining solid = \(\frac{4 \pi }{3} 10^{2} - \frac{4 \pi }{3} 8^{2}\) = \(\frac{4 \pi }{3} (100 - 64)\)

volume of remaining solid = 150.85 \(cm^3\)

To learn more about volume with the given link

https://brainly.com/question/13338592

#SPJ4

The recursive formula for the number of regions created by n lines, where every pair of lines cross and no three lines cross at the same point, is Rn = Rn-1 + (n - 1).

Let n be a natural number representing the number of lines drawn in the plane such that every pair of lines cross and no three lines cross at the same point. Suppose we wish to determine the number of regions in the plane, including some unbounded regions rn. For instance, in the picture below, there are 5 regions in the plane, including two unbounded regions.In order to find a recursive formula for the number of regions created by n lines, we can start with the base case where n = 1. If there is only one line, there will be two regions: one bounded and one unbounded. Next, we can find a recursive formula for n lines by adding one more line and counting the number of regions it creates. When we add a new line, it will intersect every existing line once and create new intersection points. By connecting these points, we can see that the new line will divide each existing region it passes through into two parts. Additionally, it will create a new region bounded by the new line and the previous lines. Therefore, the number of regions created by adding one more line is equal to the number of regions created by the previous (n - 1) lines, plus the number of intersection points created by the new line. The number of intersection points created by the new line is equal to the number of existing lines it intersects, or (n - 1). Thus, we obtain the recursive formula:Rn = Rn-1 + (n - 1)where Rn represents the number of regions created by n lines and Rn-1 represents the number of regions created by the previous n - 1 lines.To justify why this recursion is correct, we can use mathematical induction. The base case is when n = 1, which we have already established as true. Now, assume that the recursion is true for some n = k. Then, we have:Rk = Rk-1 + (k - 1)Next, consider the case where n = k + 1. By adding one more line, we obtain the formula:Rk+1 = Rk + kWe can substitute our expression for Rk into this equation to obtain:Rk+1 = Rk-1 + (k - 1) + k = Rk + (k - 1) + k = Rk + kNow, we can see that this is the same as our formula for Rk+1, which is:Rk+1 = Rk + kTherefore, the formula is true for n = k + 1. By the principle of mathematical induction, it follows that the formula is true for all natural numbers n ≥ 1.

To know more about natural number, visit:

https://brainly.com/question/32686617

#SPJ11

The Length of the conjugate axis is equal to 2b. The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola.

In a hyperbola, the name of the green segment is called the transverse axis. The transverse axis is the longest distance between any two points on the hyperbola, and it passes through the center of the hyperbola. It divides the hyperbola into two separate parts called branches.

The transverse axis of a hyperbola lies along the major axis, which is perpendicular to the minor axis. Therefore, it is also sometimes called the major axis.

The other axis of a hyperbola is called the conjugate axis or minor axis. It is perpendicular to the transverse axis and passes through the center of the hyperbola. The length of the conjugate axis is usually shorter than the transverse axis.In the hyperbola above, the green segment is the transverse axis, and it is represented by the letters "2a". Therefore, the length of the transverse axis is equal to 2a.

The blue segment is the conjugate axis, and it is represented by the letters "2b".

Therefore, the length of the conjugate axis is equal to 2b.The transverse axis is an essential feature of a hyperbola, as it determines the overall shape of the hyperbola. In particular, the distance between the two branches of the hyperbola is determined by the length of the transverse axis.

If the transverse axis is longer, then the branches of the hyperbola will be further apart, and the hyperbola will look more stretched out. Conversely, if the transverse axis is shorter, then the branches of the hyperbola will be closer together, and the hyperbola will look more compressed.

For more questions on Length .

https://brainly.com/question/28322552

#SPJ8

Final Answer: \(f = -7\)

Steps/Reasons/Explanation:

Question: Solve \(f - 4 = -11\).

Step 1: Add 4 to both sides.

\(f =-11 + 4\)

Step 2: Simplify \(-11 + 4\) to \(-7\).

\(f = -7\)

~I hope I helped you :)~

Answer:

i know the answer

Step-by-step explanation:

Answer:

Three consecutive multiples are 110,121 and 132 which has the sum of 363. 33C = 363; C = 33, By substituting C = 33 in numbers 11C, 11(C – 1) and 11(C + 1) we get values 110, 121, 132.

The zeros of r with the given restrictions are 0, π/6, π/3, π/2, 2π/3, 5π/6, π, 7π/6, 4π/3, 3π/2, 5π/3, and 11π/6.

Equation is a mathematical statement that shows the equality of two expressions on either side of an equal sign. It is used to express relationships between unknown variables and is fundamental to algebra, calculus, and other branches of mathematics. Equations can be used to model real-world problems, uncover trends, and make predictions. Solving equations involves isolating a variable on one side of the equation and determining its value.

The equation r = 3 cos(6theta) is a trigonometric equation representing a rose curve. A rose curve is a graph of a polar equation which can look like a rose flower. In this equation, r is the radius of the curve and theta is the angle. The equation r = 3 cos(6theta) is a type of rose curve with 6 petals, hence 6 zeros. The equation can be simplified to cos(6theta) = 0, and the zeros of the equation can be found by solving cos(6theta) = 0. This equation has 6 solutions which are 0, π/6, π/3, π/2, 2π/3, 5π/6.

The given restrictions 0 ≤ r ≤ 2 limit the zeros of r to 0, π/6, π/3, π/2, 2π/3, 5π/6, π, 7π/6, 4π/3, 3π/2, 5π/3, and 11π/6. This is because the radius of the curve at those angles is between 0 and 2. Therefore, the zeros of r with the given restrictions are 0, π/6, π/3, π/2, 2π/3, 5π/6, π, 7π/6, 4π/3, 3π/2, 5π/3, and 11π/6.

To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1

The required answer is  {±1, ±2, ±4, ±5, ±10, ±20}.

To find the set of possible rational roots for the polynomial x^3 + 5x^2 - 8x - 20, use the rational root theorem.

According to the theorem, the possible rational roots are of the form p/q, where p is a factor of the constant term (in this case, -20) and q is a factor of the leading coefficient (in this case, 1).

The factors of -20 are ±1, ±2, ±4, ±5, ±10, and ±20. The factors of 1 are ±1.

Therefore, the set of possible rational roots for the polynomial are:
{±1, ±2, ±4, ±5, ±10, ±20}.

this set represents the possible rational roots, but not all of them may be actual roots of the polynomial.

To know about polynomial. To click the link.

https://brainly.com/question/11536910.

#SPJ11