Given: Triangle ABC is similar to triangle DEF, side BC = 19, angle ABC = 48, angle BCA = 73.
If the side DF = 15, then AB - EF = ?

The C program for RK 4th order .

C program,

#include<stdio.h>

//differential equation "dy/dx = (y-2*x*y)"

float f(float x, float y)

{

return(y-2*x*y);

}

int main()

{

// Finds value of y for a given x using step size h

int i,n;

float x0,y0,x,h,k1,k2,k3,k4;

printf("Enter the value of x:");

scanf("%f",&x);

//initial value y0 at x0.

printf("Enter the initial value of x & y:");

scanf("%f%f",&x0,&y0);

//step size

printf("Enter the value of h:");

scanf("%f",&h);

//prints the initial value of y at x and step size.

printf("x0=%f\t yo=%f\t h=%f\n",x0,y0,h);

//Count number of iterations using step size or

//step height h

n=(x-x0)/h;

// Iterate for number of iterations

for(i=1;i<=n;i++)

{

//Apply Runge Kutta Formulas to find

//next value of y

k1 = h*f(x0,y0);

k2 = h*f(x0+h/2,y0+k1/2);

k3 = h*f(x0+h/2,y0+k2/2);

k4 = h*f(x0+h,y0+k3);

//Update next value of y

y0 = y0+(k1+2*k2+2*k3+k4)/6;

//Update next value of x

x0=x0+h;

}

//print the value of y at entered value of x.

printf("at x=%f\t,y=%f\n",x,y0);

return 0;

}

Solution of DE,

y' = y - 2xy, y(0) = 1

The task is to find value of unknown function y at a given point x.

Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h.

Here h is step height and xn+1 = x0 + h

\(K_{1} = h f(x_{n} ,y_{n} )\)

\(K_{2} = hf( x_{n} + h/2 , y_{n} + K_{1}/2 )\)

Thus,

\(y_{n+1} = y_{n} + K_{1} / 6 + K_{2} / 3 + K_{3} / 3 + K_{4} / 6 +O(h^{5} )\)

Know more about C program,

https://brainly.com/question/30905580?referrer=searchResults

#SPJ4

For f'(a) is given by f'(a) = 6a + 2 and equation of the line tangent to the graph is y = -10x - 12.

f(x) = 3x² + 2x

f'(x) = 6x + 2

So f'(a) = f'(-2) = -12+2 = -10

In order to find tangent line , we need a slope and a point. We have the x-co-ordinate for our point, so we can plug that in to find Y-coordinate.

F(-2) = 8

The slope of tangent line is the derivative at this point  , f'(-2) = -10

Equation of line tangent,

y - 8 = -10(x - (-2))

y = -10x - 12.

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

To learn more about Limits:

brainly.com/question/282767

#SPJ4

Answer:

0.53 hours

Step-by-step explanation:

D = (r)(t), Where

‘D’ is the distance covered

‘r’ is the approach rate

‘t’ is the total time spent

Distance covered, ‘D’ = 4 miles

Approach rate, “r” = 3.5mph + 4mph

r = 7.5mph.

t is unknown

Solving for t,

D = (r)(t)

4 = 7.5t

t = 4/7.5

t = 0.53 hours (to the nearest hundredth)

Therefore, it will take Amanda and Alexis 0.53 hours to meet

Answer:

Hi, there the answer is -1

Step-by-step explanation:

Answer:

black

black

Step-by-step explanation:

The transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

The rule that describes the transformation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

To understand this, let's apply the transformation rule to each vertex of the original parallelogram ABCD:

Point A (2, 5) becomes A' (-5, 2).

Point B (5, 4) becomes B' (-4, 5).

Point C (5, 2) becomes C' (-2, 5).

Point D (2, 3) becomes D' (-3, 2).

By applying the transformation rule, we observe that the x-coordinate of each point becomes the negative of the original y-coordinate, and the y-coordinate becomes the original x-coordinate.

This transformation is a 90-degree counterclockwise rotation about the origin (0, 0) on the coordinate plane. The image parallelogram A'B'C'D' is obtained by rotating the original parallelogram ABCD by 90 degrees counterclockwise.

Visually, this transformation can be seen as the original parallelogram being rotated around the origin, where the x-axis becomes the y-axis, and the y-axis becomes the negative x-axis.

Therefore, the transformation rule that describes the rotation from the original parallelogram ABCD to the image parallelogram A'B'C'D' is (x, y) → (–y, x).

For more such questions on parallelogram visit:

https://brainly.com/question/970600

#SPJ8

Answer:

(a.) 27^4/3 = 81, (b.) 36^3/2 = 216, (c.) (1/8)^2/3 = 1/4, (d.) 128^5/7 = 32

Step-by-step explanation:

All these expressions can be converted in square roots.

In order to do this, we can picture the fractional exponents as exponent / index

(a.) So for this first problem, we would have the cube root of \(27^{\frac{4}{3} }\) or

\(\sqrt[3]{(27)^{4} }\).

We must do the equation inside the radical first (i.e., \((27)^{4}\)) to get \(\sqrt[3]{531,441}\) = 81

We can follow these same steps for the remaining equations:  

(b.) \(36^{\frac{3}{2} }\) = \(\sqrt{(36)^3}\) = \(\sqrt{46,656}\) = 216

(c.) \((\frac{1}{8})^\frac{2}{3}\) = \(\sqrt[3]{(\frac{1}{8})^{2} }\) = \(\sqrt[3]{(\frac{1^2}{8^2}) }\) = \(\sqrt[3]{(\frac{1}{64}) }\) = \(\frac{1}{4}\)

(d.) \(128^{\frac{5}{7} }\) = \(\sqrt[7]{(128)^{5} }\) = 32

The probability that 49 randomly selected laptops will have a mean replacement time of 2.9 years or less can be calculated using the z-score and the standard normal distribution.

To find the probability, we first calculate the z-score using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean (2.9 years), μ is the population mean (3.1 years), σ is the population standard deviation (0.5 years), and n is the sample size (49 laptops).

Plugging in the values, we have:

z = (2.9 - 3.1) / (0.5 / √49)

z = -0.2 / (0.5 / 7)

z = -0.2 / 0.0714

z ≈ -2.80

Next, we use a standard normal distribution table or calculator to find the probability corresponding to the z-score of -2.80. The probability can be found as the area under the curve to the left of the z-score.

By calculating the z-score, we standardize the sample mean with respect to the population mean and standard deviation. This allows us to compare the sample mean to the population distribution.

The negative z-score indicates that the sample mean of 2.9 years is below the population mean of 3.1 years. By looking up the corresponding probability from the standard normal distribution, we find that it is very unlikely to obtain a sample mean of 2.9 years or less by chance alone.

To know more about z-scores , refer here:

https://brainly.com/question/31871890#

#SPJ11

Answer:

A, -11

Step-by-step explanation:

f(x)=-3x(-2)+1

=-3(4)+1

=-12+1

=-11

Step-by-step explanation:

f(x)=3x²+1

f(-2)=3(-2)²+1

= -12+1

=-13 ans

Answer:

B

Step-by-step explanation:

The probability that a child is not allergic to nuts is 0.986, or 98.6%.

The probability that a child is not allergic to nuts can be calculated by subtracting the probability of being allergic to nuts from 1.

Given the probabilities of a child being allergic to nuts, dairy, and gluten, we are interested in finding the probability that a child is not allergic to nuts.

The probability of being allergic to nuts is given as 0.014.

To find the probability that a child is not allergic to nuts, we subtract this value from 1.

P(Not allergic to nuts) = 1 - P(Allergic to nuts) = 1 - 0.014 = 0.986

Therefore, the probability that a child is not allergic to nuts is 0.986, or 98.6%.

This calculation is based on the assumption that being allergic to nuts and being allergic to other foods are independent events.

Learn more about Probability here:

brainly.com/question/15052059

#SPJ11

Answer: The salesperson must sell 20 memberships to make the same amount of money under both plans.

Step-by-step explanation:

Let x be the number of memberships.

In first plan,

Weekly salary of $300 plus a commission of $15 for each membership sold.

i.e. Earning (weekly) = 300+15x

In second plan,

The other plan offers no salary but pays $30 commission on each membership sold.

i.e. earning = 30x

According to the question, when \(300+15x=30x\)

\(\Rightarrow\ 300=30x-15x\\\\\Rightarrow\ 300=15x\\\\\Rightarrow\ x=\dfrac{300}{15}\\\\\Rightarrow\ x=20\)

Hence, the salesperson must sell 20 memberships to make the same amount of money under both plans.

Answer:

\(x=\frac{2}{7}\)

Step-by-step explanation:

\(x^{2}=\frac{4}{49}\)

\(\sqrt{x^2}=\sqrt{\frac{4}{49}\)

\(x=\pm\frac{2}{7}\)

Since we only want the positive value, then \(x=\frac{2}{7}\) is correct.

Answer:

Halfway between x = 2 and x = 4 is x =3 , and halfway between y = 8 and

y = 6 is at y =7, so the midpoint is (3, 7) .

Step-by-step explanation:

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.

This is because the sample means would be expected to be centered around the population mean.

The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

standard deviation of sample means = standard deviation of population / square root of sample size

In this case, the standard deviation of sample means would be:

6 / square root of 4 = 3

So the answer is 3.

So, the mean of the distribution of the sample means would be 3. Your answer: 3.

To learn more about mean : brainly.com/question/31101410

#SPJ11

Answer:

A. Obtuse triangle

B,C,D. Acute

Step-by-step explanation:

According to the empirical rule of IQ scores no higher than 125 and less than 77, the percentage is found to be 97.5%.

From the above data, we can determine the mean (U) and standard deviation (p), which are respectively 101 and 12.

And we're looking for the percentage that isn't greater than 125. We can utilise the calculation for the z score, which is as follows: z = X-U/p X is the percentage,

And by using the value provided, we obtained: z = (125-101)/12

z = 2.

According to the empirical rule, 95% of the values fall between two standard deviations, while 5% fall in the tails.

As a result the percentage is required to be less than the 2 standard deviation but above the mean which is equal to (100-2.5)=97.5%.

To know more about standard deviation and mean, visit,

https://brainly.com/question/24298037

#SPJ4

Answer:

3 times 12 equals 36. 36-4=32. The answer is 32

Step-by-step explanation:

Answer:

Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars each.

Answer:

Percent questions can be estimated using models by dividing the given number by the total number of parts in the model. For example, if there are ten students in a classroom and 30 candy bars, then each student would get three candy bars. Another example would be if there are ten students in a classroom and 30 candy bars, and one student takes five candy bars, then the remaining nine students would get two candy bars eac

Step-by-step explanation:

The rate constant of inactivation is -0.6538 \(s^{-1}\).

To determine the rate constant of inactivation using the Chick-Watson model, we need to plot the natural logarithm of the surviving fraction of the virus (N/N₀) against time (t) and fit a linear regression to the data. The Chick-Watson model is given by the equation:

ln(N/N₀) = -kt

Where:

N₀ is the initial number of viruses (\(10^{6}\))

N is the number of viruses at time t

k is the rate constant of inactivation

Let's calculate the surviving fraction (N/N₀) and perform the linear regression:

Time (s) | N/N₀ | ln(N/N₀)

0 | 1.0 | 0.0

2 | 0.2 | -1.61

4 | 0.01 | -4.60

6 | 0.0015 | -6.50

8 | 0.0001 | -9.21

Using the given data, we can perform linear regression on the ln(N/N₀) values against time (t) values to determine the rate constant (k).

Let's calculate the rate constant (k) using linear regression:

Sum of ln(N/N₀) = -21.92

Sum of t = 20

Sum of (\(t^{2}\)) = 120

Mean of ln(N/N₀) = (-21.92) / 5 = -4.384

Mean of t = 20 / 5 = 4

Mean of (\(t^{2}\)) = 120 / 5 = 24

Sum of [(t - mean(t)) * (ln(N/N₀) - mean(ln(N/N₀)))] = -52.304

Sum of \((t-mean(t))^{2}\) = 80

Using the linear regression formula:

k = [Sum of [(t - mean(t)) * (ln(N/N₀) - mean(ln(N/N₀)))]] / [Sum of  \((t-mean(t))^{2}\) ]

k = -52.304 / 80 = -0.6538

Therefore, the rate constant of inactivation for NH2Cl disinfection of MS2 bacteriophage at a concentration of 2 mg/L is approximately -0.6538 \(s^{-1}\).

Correct Question :

The data for NH2Cl disinfection of MS2 bacteriophage at a concentration of 2 mg/L is shown below. The temperature was 20 °C, the pH was 6.0. Determine the rate constant of inactivation assuming the Chick-Watson model applies with an n value of 1.0.

Time (s) 0 2 4 6 8

Number of virus \(10^{6}\) 0.2*\(10^{6}\) 0.1*\(10^{5}\) 0.15*\(10^{4}\) 0.1*\(10^{3}\)

To learn more about rate constant here:

https://brainly.com/question/31197553

#SPJ4

Answer: we need to get the values of x and y

x=(4y+3)/5

y=(5x-3)/4

Step-by-step explanation:

let us consider the quation 5x-4y=3

then on adding 4y on both sides it becomes:

     5x=3+4y

 this equation is in standard form

divide by 5 on both sides

 it becomes

                                x=(3+4y)/5

in the similar way subtract 5x on both sides

then we get -4y=3-5x

  it becomes: 4y=5x-3

                                     y=(5x-3)/4                                                

The total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.

First, let us understand the variables:

Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.

Let x and y be the quantity of shorts.

x is the number of attempts at the free throw line.

y is the quantity of two-point attempts.

According to the question, we have;

x + 2y = 20 ............equation 1

x + y = 13    ............equation 2

From equation 2 we can take out the value of x;

x = 13 - y     ............equation 3

substituting the value of x in equation 1, we will get;

(13 - y) + 2y = 20

13 - y + 2y = 20

13 + y = 20

y = 20 - 13

y = 7

putting the value of y in equation 3, we will get

x = 13 - 7

x = 6

Thus, the total number of free throws shots Jason made was 6 and the total number of two point shots Jason made was 7.

To learn more about variables visit:

https://brainly.com/question/28248724

#SPJ1

Answer:

60 and 100 degrees.

Step-by-step explanation:

Sum of the other 2 angles = 180-20 = 160 degrees.

3 + 5 = 8

160 / 8 = 20

- so the other 2 angles are:

3*20 = 60 and

5*20 = 100 degrees.

The quiz scores of Rich Borne's Chemistry 101 students are as follows: 24, 31, 47, 29, 31, 16, 48, 41, 50, 54, 37, 22, 54, 38, 7, and 16.the performance of Rich Borne's Chemistry 101 students on the quiz

To analyze this data, we can calculate various descriptive statistics such as the mean, median, mode, range, and standard deviation. The mean (average) score can be obtained by summing up all the scores and dividing by the total number of scores. The median represents the middle value when the scores are arranged in ascending order. The mode refers to the most frequently occurring score. The range is the difference between the highest and lowest scores, indicating the spread of the data. The standard deviation measures the variability or dispersion of the scores around the mean.

By calculating these descriptive statistics, we can gain insights into the performance of Rich Borne's Chemistry 101 students on the quiz and understand the central tendency and variability of their scores.

know more about descriptive statistics :brainly.com/question/30764358

#SPJ11

Answer:

A

Step-by-step explanation:

3/5th of a pound each. This is common knowledge but its 100% A

The correct answer is A because everyone will get 3/5 of it

Rewrite the equation in slope-intercept form::

\(y-5=12(x+9)\\y-5=12x+108\\y=12x+108-5\\y=12x+103\)

According to the slope-intercept form of the line equation, slope of the equation is \(m_1=12\).

Because another line is perpendicular to \(y=12x+103\), the slope of another line:

\(m_1 \times m_2=-1\\12\times m_2=-1\\m_2=-\frac{1}{12}\)

Substitute \(m_2=-\frac{1}{12}\) and  the point \((-1,-1)\) into the equation form:

\(y-y_1=m_2(x-x_1)\\y-(-1)=-\frac{1}{12}(x-(-1))\\y+1=-\frac{1}{12}(x+1)\\------------\times12\\12y+12=-(x+1)\\12y+12=-x-1\\x+12y+12+1=0\\x+12y+13=0\)

Hence the equation of the line is \(x+12y+13=0\).

Learn more about the equation of a line here: https://brainly.com/question/28695475

#SPJ1

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

Learn more about null hypothesis here:

https://brainly.com/question/29387900

#SPJ11