The cost price of 20 articles is the same as sellling price of 16 articles find the gain percent

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

If the person owes $252 and the interest rate is 1.5% , then the interest charge is $3.78 and the new balance will be $255.78  .

The interest charge can be calculated by multiplying the balance by the interest rate, expressed as a decimal ,

So , Interest charge = $252 × 0.015 ,

⇒ Interest charge = $3.78 ,

So , the interest charge will be = $3.78.

Now , to calculate the new balance, we need to add the interest charge to the original balance ,

⇒ New balance = $252 + $3.78 ,

⇒ New balance = $255.78

Therefore, the new balance will be = $255.78.

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The answer of the given question based on the code is , the output of the code will be: The root of x³ + 2x - 2 between 0 and 1 is 0.771

MATLAB code:
To show that `x³ + 2x - 2` has a root between 0 and 1 and,

to find the root to 3 significant digits using the Newton Raphson Method,

we can use the following MATLAB code:  

Defining the function

f = (x)x³ + 2*x - 2;

Plotting the function

f_plot (f, [0, 1]);

grid on;

Defining the derivative of the function

f_prime = (x)3*x² + 2;

Implementing the Newton Raphson Method x0 = 1;

Initial guesstol = 1e-4;

Tolerance for erroriter = 0; % Iteration counter_while (1)

Run the loop until the root is founditer = iter + 1;

x1 = x0 - f(x0)

f_prime(x0);

Calculate the next guesserr = abs(x1 - x0);

Calculate the error if err < tol

Check if the error is less than the tolerancebreak;

else x0 = x1;

Set the next guess as the current guessendend

Displaying the resultfprintf('The root of x³ + 2x - 2 between 0 and 1 is %0.3f\n', x1));

The output of the code will be: The root of x³ + 2x - 2 between 0 and 1 is 0.771

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When you run the above code in MATLAB, it will display the root of x^3 + 2x - 2 to 3 significant digits.

MATLAB code:

Show that x^3 + 2x - 2 has a root between 0 and 1:

Here is the code to show that x^3 + 2x - 2 has a root between 0 and 1.

x = 0:.1:1;y = x.^3+2*x-2;

plot(x,y);

xlabel('x');

ylabel('y');

title('Plot of x^3 + 2x - 2');grid on;

This will display the plot of x^3 + 2x - 2 from x = 0 to x = 1.

Find the root to 3 significant digits using the Newton Raphson Method:

To find the root of x^3 + 2x - 2 to 3 significant digits using the Newton Raphson Method, use the following code:

format longx = 0;fx = x^3 + 2*x - 2;dfdx = 3*x^2 + 2;

ea = 100;

es = 0.5*(10^(2-3));

while (ea > es)x1 = x - (fx/dfdx);

fx1 = x1^3 + 2*x1 - 2;

ea = abs((x1-x)/x1)*100;

x = x1;fx = fx1;

dfdx = 3*x^2 + 2;

enddisp(x)

When you run the above code in MATLAB, it will display the root of x^3 + 2x - 2 to 3 significant digits.

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The best data set that represents the histogram is (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42, option C is correct.

From the histogram, we can see that there were 3 data points in the interval 1-10, 3 data points in the interval 11-20, 7 data points in the interval 21-30, 4 data points in the interval 31-40, and 3 data points in the interval 41-50.

Therefore, the best data set that represents the histogram is the one that has 3 data points in the range 1-10, 3 data points in the range 11-20, 7 data points in the range 21-30, 4 data points in the range 31-40, and 3 data points in the range 41-50.

4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42 does not fit this pattern since it has more than 3 data points in some of the intervals.

4, 7, 10, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42 also does not fit the pattern since it has more than 3 data points in some of the intervals.

4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42 fits the pattern and has 3 data points in each interval. This is the correct answer.

4, 6, 9, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42 does not fit the pattern since it has more than 3 data points in some of the intervals.

Therefore, the best data set that represents the histogram is  (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42

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Answer:

2,188,180

Step-by-step explanation:

since 0 can't give anything to 8 the number would stay the same

Based on the time that you departed Seattle and the layovers in Dallas and Portland, you will arrive in Seattle at 6:45 am.

If you leave Seattle at 9:10 pm, you will arrive in Atlanta at 10:25 am .

If the leg from Dallas back to Atlanta is 2/3 of an hour longer then you will arrive at 11:05 am.

The hours you will spend going from Atlanta to Seattle including layover times is:

= 2.75 + 1.5 + 3.5 + 1.75 + 0.75

= 10 hours 15 minutes

The time you will arrive in Seattle is:

= 11:30 pm + 10 hours 15 minutes - 3 hour time difference

= 6:45 am

Your total flight time and layover time is 10 hours 15 minutes. You will therefore arrive in Atlanta at:

= 9:10 pm + 10 hours 15 minutes + 3 hour time difference

= 10:25 am

If the leg back to Atlanta took an additional 2/3 of an hour then you would arrive at:

= 10:25 + 40 minutes

= 11:05 am

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Answer: D. domain; x>-2; range: y>0; Yes, it is a function

Step-by-step explanation:

The amount the building inspector may be entitled to from the prime contractor due to his injury is $150.00.

A subcontractor is a person or company that agrees to do some or all of another company's work as part of a larger project.

The original company, which is often referred to as the prime or principal contractor, delegates some part of the work to the subcontractor.

Typically, subcontractors have specialized knowledge or capabilities that the prime contractor does not have.

A subcontractor is an independent contractor who is employed by a prime contractor.

Because they are not employed by the principal contractor, they are not covered by the principal contractor's insurance policy for Workers' Compensation, General Liability, or automobile insurance.

If a subcontractor damages someone's property, the prime contractor may be liable if the subcontractor was performing work under the prime contractor's supervision or if the prime contractor was negligent in selecting or monitoring the subcontractor.

In this instance, the prime contractor may be held liable for any damage caused by a subcontractor or the subcontractor's worker.

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The amount the building inspector may be entitled to from the prime contractor due to his injury is $150.00.What is a subcontractor?A subcontractor is a person or business hired by a general contractor to carry out specific tasks on a construction site.

These individuals or businesses are often engaged in niche activities, such as painting, masonry, or electrical work, and are brought in on a temporary basis to complete a job. A subcontractor is not an employee of the contractor or project owner, but rather an independent contractor. What is the independent contractor rule?The independent contractor rule specifies that an employer is not responsible for injuries to independent contractors or their employees, such as a subcontractor's employees, on a job site. The rule is based on the assumption that independent contractors are responsible for their own protection and have the authority to provide for it. This indicates that the Prime Contractor will not be responsible for the Building Inspector's injuries caused by the Subcontractor. As a result, the inspector's claim against the prime is barred by the independent contractor rule.What is the outcome?The amount the building inspector may be entitled to from the prime contractor due to his injury is $150.00.

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Answer:

y = -1/5x + 2

Step-by-step explanation:

I will assume the "-" is an equal sign. Solve for y.

x + 5y = 10

~Subtract x to both sides

5y = 10 - x

~Divide 5 to everything

y = 2 - 1/5x

~Reorder

y = -1/5x + 2

Best of Luck!

A measure of the dispersion of observations in a process distribution is called: range.

This is further explained below.

Generally, The range of a collection of data is the difference between the highest and smallest values in the set. This difference is calculated by subtracting the sample maximum and minimum from the sample size. It is written out using the same units that were used for the data.

In conclusion, The term "range" refers to a measure of the dispersion of observations included within a process distribution.

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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Answer:

y = 2.5 , x = 4

Step-by-step explanation:

5x - 4y = 10 ____eq1

x + 2y = 9 ____eq2

5x=10+4y

x = (10 +4y)/5 ____eq3

x = 9 -2y ____eq4

Using eq3 and eq 4 to solve simultaneously,

9 - 2y = (10 +4y)/5

45 -10y = 10 +4y

14y = 25

y =2.5

if y =2.5,

x = 9 -2y = 9 - 2(2.5) =4

The probability that a randomly chosen part is defective is 0.16, or 16%.

The probability that a randomly chosen part is defective, we need to use the law of total probability.

Let \($D$\) be the event that a part is defective and let \($M_i$\) be the event that the part came from machine \($i$\), for \($i = A, B, C$\).

Then we have:

\($P(D) = P(D|M_A)P(M_A) + P(D|M_B)P(M_B) + P(D|M_C)P(M_C)$\)

60% of the products come from machine A, 30% from machine B, and 10% from machine C.

Therefore:

\($P(M_A) = 0.6$\)

\($P(M_B) = 0.3$\)

\($P(M_C) = 0.1$\)

The probability of a part being defective is 10% if it comes from machine A, 30% if it comes from machine B, and 40% if it comes from machine C.

Therefore:

\($P(D|M_A) = 0.1$\)

\($P(D|M_B) = 0.3$\)

\($P(D|M_C) = 0.4$\)

Substituting these values into the law of total probability, we get:

\($P(D) = 0.1 \cdot 0.6 + 0.3 \cdot 0.3 + 0.4 \cdot 0.1 = 0.16$\)

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Given the diagram given where lines n and p are parallel, and transversals r and s are perpendicular, the measure of angle 1 is: \(\mathbf{1) 51^{\circ}}\)

The angle measure where two perpendicular lines intersect each other equals 90 degrees.

Therefore, the angle formed as shown in the figure attached, where transversals r and s meet = 90 degrees.

Since lines n and p are parallel lines, therefore:

\(m \angle 1 + 90 = 141\) (alternate interior angles are equal)

\(m \angle 1 = 141 - 90\\\\\mathbf{m \angle 1 = 51^{\circ}}\)

Therefore, given the diagram given where lines n and p are parallel, and transversals r and s are perpendicular, the measure of angle 1 is: \(\mathbf{1) 51^{\circ}}\)

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Answer:

1. The domain is (-2, -1, 0, 1) the rage is (4,2,0,2) 2. It is a function

Step-by-step explanation:

The domain in a pair is always the first number. The range is always the second number in the ordered pair.

Answer:

Domain: {−2,−1,0,1}

Range: {0,2,4}

Step-by-step explanation:

The domain is all the x-coordinates, but NEEDS TO BE ORDERED, which are {−2,−1,0,1} and you also need to include the curly brackets { }.

The range is all the y-coordinates and also NEEDS TO BE ORDERED, which are {0,2,4} and you also still need to include those curly brackets { }.

Hope this helps and answers your question! :)

Answer:

A = 27 cm²

Step-by-step explanation:

let 'w' = width

let '3w' = length

P = 2l + 2w

24 = 2(3w) + 2w

24 = 6w + 2w

24 = 8w

w = 3

l = 3(3) or 0

A = lw

A = 3(9)

A = 27

If three pencils, each measuring one foot in length, are laid end to end touching, the total distance covered by the row would be 3 feet.

Since each pencil is 1 foot long, when three pencils are laid end to end, they form a row that is 3 feet long. The key information here is that the pencils are touching, which means there are no gaps between them. Therefore, the row would extend for a total distance of 3 feet.

In this scenario, the correct answer is option a, 3 ft. The row would not extend beyond 3 feet because there are only three pencils, each measuring one foot in length. If there were more pencils or if they were not touching end to end, the total distance covered by the row would be different. However, based on the given information, the row formed by the three one-foot-long pencils would have a length of 3 feet.

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Answer:

y = (x-5)² - 3

Step-by-step explanation:

Given:

\(\displaystyle \large{f(x)=(x-1)^2+2}\)

Transformation:

\(\displaystyle \large{f(x-a)}\) is translation of a units to the right

\(\displaystyle \large{f(x)-b}\) is translation of b units down.

Therefore:

\(\displaystyle \large{g(x)=f(x-4)-5}\) is our new equation or transformation:

\(\displaystyle \large{g(x)=[(x-4)-1]^2+2-5}\\\displaystyle \large{g(x) = [x-4-1]^2-3}\\\displaystyle \large{g(x)=(x-5)^2-3}\)

Therefore, the new equation is y = (x-5)² - 3

Answer:

A. 4 7/24

Step-by-step explanation:

subtract 15 - 11 which equals 4

then do 5/15 - 1/8 =7/24

Answer:

The correct answer would be 8 root symbol 3

Step-by-step explanation:

because i chose it and got it right

The length of the line segment YX is \(8\sqrt{3}\) if the line XW is of 24 units.

It is a ratio of sides of a right angled triangle.

It can be seen that the diagonal is making a right angle triangle XWV so

we will use the trigonometric function to determine the value of WV which will then be equal to XY because it is a rectangle.

tan(30)=VW/XW

1/\(\sqrt{3}\)=VW/24

VW=24/\(\sqrt{3}\)

VW=8\(\sqrt{3}\) UNITS by multiplying and divide by root 3.

Hence the length of the side XY =8 root 3 units.

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The largest subset S on which the vector-valued function F is continuous is the interval (-3, ∞).

To find the largest subset S on which the given vector-valued function is continuous, we need to examine the individual component functions and identify any restrictions or conditions that could cause discontinuities.

Component 1: f1(t) = t/(9 + t^4)

This function is a rational function. It will be continuous for all real values of t except where the denominator equals zero: 9 + t^4 = 0. However, there are no real values of t that satisfy this equation, so f1(t) is continuous for all real values of t.

Component 2: f2(t) = 7t^2 - 7t + 1

This function is a polynomial function, and polynomial functions are continuous for all real values of t. Therefore, f2(t) is continuous for all real values of t.

Component 3: f3(t) = ln(t + 3)

The natural logarithm function is defined for the positive values of its argument. Therefore, t + 3 > 0, which implies t > -3. Hence, the function f3(t) is continuous for t > -3.

Taking all these considerations into account.The function is continuous for all values of t greater than -3.

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Answer:

it is linear

Step-by-step explanation:

Work Shown:

x = number of minutes

5x = amount of water added

5x+20 = total amount of water

Plug in x = 20 to find that:

5x+20 = 5*20+20 = 120 gallons of water is in the tank after 20 minutes.

The fraction of the peanut butter that Irfan used that was less than the amount he should have used was 1/10.

Irfan was meant to use 1/2 cups of peanut butter but instead used only 2/5.

The amount that he didn't use was therefore:

= 1/2 - 2/5

In decimals this is:

= 0.5 - 0.4

= 0.1

In fraction form this:

= 10/100

= 1/10

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Answer y = -2

Step 1.

In order to make an equation with 1 variable, substitute the right side of the first equation for x in the second equation for 3x + 5y = 20. In the example all instances of x in the second equation will be replaced by 10.

Rewrite the x so it will be 3 · 10.

3 · 10 + 5y = 20

Step 2.

Multiply 3 by 10.

3 × 10 = 30

Step 3.

Subtract 30 from both sides.

30 + 5y - 30 = 20 - 30

Step 4.

Simplify.

5y = -10

Step 5.

Divide both sides by 5.

1. Divide the numbers.

5 ÷ 5 = 1

= y

2. Simplify. \(\frac{-10}{5}\)

Apply the fraction rule. \(\frac{-x}{y} =-\frac{x}{y}\)

\(-\frac{10}{5}\)

3. Divide.

10 ÷ 5 = 2

Y = -2

The quota sampling produces the same advantages for convenience sampling that stratified random sampling produces for probability sampling.

Sampling:

Sampling is defined as the process in statistical analysis where researchers take a predetermined number of observations from a larger population.

Given,

Here we need to find the type of sampling that produces the same advantages for convenience sampling quota sampling.

Before, move on to the result, first we have to know the details about quota sampling and the probability sampling.

Probability sampling defined as the selection of a sample from a determined number of population, when this selection is based on the principle of randomization, that is, random selection or chance.

In contrast to probability sampling, Quota sampling means a non-probability sampling method in which researchers create a sample involving individuals that represent a population.

Based on these definition we have identified that the method that is best suitable answer for this one is stratified random sampling.

Because the stratified random sampling means, is a probability sampling technique in which the total population is divided into homogenous groups to complete the sampling process.

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Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the number =x

So, x*12*2=144

=12x=144/2

=12x=72

=x=72/12

=x=6

So the answer is 6 because 6*12=72 and doubling 72 gives us 144.

Have a great day!!!

The statement holds for k + 1. By the principle of mathematical induction, the original equation is proven for all positive integers n greater than or equal to 1.

To prove the given statement using mathematical induction, we first establish the base case. When n = 1, the equation becomes s(1) = 1 * 1! = 1. On the other hand, (1-1)! - 1 = 0 - 1 = -1. Since these values are not equal, the base case is invalid.

Next, we assume that the equation holds true for some positive integer k, denoted as s(k) = (k-1)! - 1. This is known as the induction hypothesis. Now we need to prove that the statement holds for k + 1.

Considering s(k+1), we can rewrite it as s(k+1) = (k+1) * (k+1)! and simplify it further.

s(k+1) = (k+1) * (k+1)!

= (k+1) * (k+1)! * k/k

= (k+1) * (k!) * k/k

= (k+1)! * k

= (k+1)! * (k+1 - 1)

= (k+1)! * k!

Now we can substitute the induction hypothesis into the equation:

s(k+1) = (k+1)! * k!

= (k+1 - 1)! - 1 (by induction hypothesis)

= k! - 1

Thus, the statement holds for k + 1. By the principle of mathematical induction, the original equation is proven for all positive integers n greater than or equal to 1.

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