A carpet expert believes that 8% of Persian carpets are counterfeits. If the expert is accurate, what is the probability that the proportion of counterfeits in a sample of 827 Persian carpets would be greater than 7%

The factorized form of \(x^3 - (y - z)^3\ is \ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

The Factorization is derived from the application of a mathematical identity. As an AI language model, the information provided is generated based on existing knowledge and formulas.

The given expression is \(x^3 - (y - z)^3.\)To factorize it,  the difference of cubes, which states that a^3 - b^3 can be factorized as\((a - b)(a^2 + ab + b^2).\)

Applying this identity to our expression, we have:

\(x^3 - (y - z)^3 = (x - (y - z))((x - (y - z))^2 + (x - (y - z))(y - z) + (y - z)^2)\)

Simplifying further, we get:

\(= (x - y + z)(x^2 - 2xy + 2xz - y^2 + 2yz - z^2 + xy - y^2 + yz - z^2 + y^2 - 2yz + z^2)\\= (x - y + z)(x^2 - 2xy + xy + 2xz + yz - 2yz - y^2 + y^2 - y^2 + 2yz - 2z^2 + y^2 - z^2 + z^2)\\= (x - y + z)(x^2 - xy + 2xz + yz - 2z^2)\)

So, the factorized form of \(x^3 - (y - z)^3 \ is\ (x - y + z)(x^2 - xy + 2xz + yz - 2z^2).\)

the above factorization is derived from the application of a mathematical identity.

To know more about factorized .

https://brainly.com/question/14268870

#SPJ11

The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

To learn more about the geometric sequence visit:

https://brainly.com/question/11266123.

#SPJ1

❥\(\Large\pmb{ \underline {\tt Answer}}\)

#1

a + b • 3 = 3a + 3b

No

Actual equation formed:-

a + 3b = 3a + 3b

#2

Yes

#3

a + b • 3 = a + 3b

Yes

#4

a + 3b • 3= 3a + 6b

No

Actual equation formed:-

a + 9b

#5

a + 3b • 3 = a + 9b

Yes

Rule applies:-

BODMAS

B - brakets

O - on/off

D- divide

M - multiply

A - add

S - subtract

━━━━━━━━━━━━━━━━━━

Answer:

27

Step-by-step explanation:

angle adjacent to 163 = 27

x=27 by alternate angles equal principle.

Answer:

c. y = x^2 - 4

Step-by-step explanation:

If you graph both y = x^2 and y = x^2 - 4, you'll be able to see that the equation of function, y = x^2 - 4, is 4 units down from the equation of function y = x^2.

When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

For more questions on Function .

https://brainly.com/question/11624077

#SPJ8

Answer:

Step-by-step explanation:

$100x0.5x1=$5

The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .

Given :

the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .

Base case :

The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .

we know that ,

def func ( n ) :

     if   n == 0 :

return 1

Here the base case is clearly n = 0

Learn more about the solution here:

https://brainly.com/question/17429689

#SPJ4

Answer:

slope=7

Step-by-step explanation:

The slope of a line is always the coefficient of x.

Answer:

Slope m = 7

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = 7x

Step 2: Break Function

Identify Parts.

Slope m = 7

y-intercept b = 0

There would be a 68% chance that the average blood pressure would be between 193 to 197.

The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.

We know that,

                       E   =   z ( α / 2 )  ×  σ / √n          →  1

As per the given question,

For 68% confidence,

                                z ( α / 2 )   =   0.9944

Substitute the values in 1,

E   =   z ( α / 2 )  ×  σ / √n

     =   0.9944  ×  20 / √100

     =   0.9944  ×  20 / 10

     =   0.9944  ×  2

E    =   1.9888   ≅   1.99

Let us consider,

⇒   x  -  E     <     μ     <     x  +  E

⇒   195  -  1.99     <     μ     <     195  +  1.99

⇒   193.01     <     μ     <     196.99

⇒   193     <     μ     <     197          ( ∵  193.01 ≅ 193 and 196.99 ≅ 197 )

⇒   μ   =   ( 193 , 197 )

Therefore, A 68% chance that the average blood pressure lies between 193 to 197. Hence Option b is correct.

To know more about confidence interval problems refer to:

https://brainly.com/question/10126826

#SPJ4

The complete question is

Blood pressure in a population of very at risk people has an expected value of 195 and a standard deviation of 20. Suppose you take a random sample of 100 of these people. There would be a 68% chance that the average blood pressure would be between Select one:

a.) 155 to 235

b.) 193 to 197

c.) 175 to 215

d.) 191 to 199

e.) 200 to 230

Answer:

Thus, the equation of line for point (-1, 2)  is y = x + 3.

Step-by-step explanation:

Answer:

The equation of the line is y = x + 3.

Step-by-step explanation:

A line that is parallel to y=x+4 and passes through the point (-1,2) will have the same slope as y=x+4. The slope of y=x+4 is 1, so the equation of the line will be in the form y = mx + b, where m=1. To find b, we can plug in x = -1 and y = 2 into the equation and solve for b.

y = mx + b

y = 1 * -1 + b

y = -1 + b

b = y + 1

b = 2 + 1

b = 3

1. Find the graph of the parabola attached below

2. Vertex (-4, 2)   Focus (-7/2, 2)  Directrix (x = -9/2)  Endpoints (-7/2, 1) (-7/2, 3)

For the parabola,  x = 1/2(y-2)² - 4 we will use the equation x = 4p(y-k)² + h,

Vertex → (h, k)

In our given equation, (y - 2) → (y - k), so k = 2. The term on the rightmost side of our equation (-4) → h in the form, so we know h = -4. ∴  vertex (-4, 2).

focus → (h, k) = (-4, 2); P = 1/2

Parabola is symmetric around the x axis and so the focus lies a distance P, from the center, along the x axis.

∴  Focus is (-4 + p, 2)

(-4 + 1/2, 2) ⇒ (-7/2, 2)

directrix → x = d

Parabola is symmetric around the x axis and therefore the directrix is a line paralled to the y axis a distance away from the ceter (-4, 2) x coordinate.

∴ x = -4 - p   ⇒ x = -4 - 1/2

x = 9/2

focal chord endpoints →

The focus of the parabola is (-7/2, 2).

The y-coordinate of the focus is 2, so the y-coordinates of the endpoints of the focal chord are 2 + 1 and 2 - 1, → 3 and 1.

Therefore, the endpoints of the focal chord are:

(-7/2, 3) and (-7/2, 1).

Find more exercises on parabola;

https://brainly.com/question/11911877

#SPJ1

Sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.

What is Sampling variation?

The term "sampling variance" describes how much a sample estimate (a statistic) is likely to fluctuate from sample to sample due to the unique nature of each sample.

Sample Sizes and Variability are the factors which lead to sampling variation. As and when the sample size is changed i.e. either increased or decreased, the variability of samples fluctuates.

Since, Sam runs a large chain of car repair shops, this means he has large number of employees.

But his sample size is only of 10 employees whom he asks about their billable hours from which he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company.

Since, sampling variation is greatly affected by the sample size and variability, therefore it will have more impact on confidence interval.

Hence, sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.

Learn more about sampling variation from the given link:

https://brainly.com/question/28213657

#SPJ4

Since the options are missing in the question, here are the options from which answer is to be chosen

Answer:

88.4505 kilograms

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Answer:

191

Step-by-step explanation:

Answer:

1460

Step-by-step explanation:

rounding to the nearest ten, that is nearest to 1456 which would be 1460 (hope this helps! ) ♡

Answer:

1460

Step-by-step explanation:

Original number is 1 4 5 6

To round to the nearest ten, look at the digit in the 10's place and the digit immediately to the right of it

The digit in the tens place is 5

If the digit to the immediate right of this digit is 5 or greater, round the digit in the tens place up by one digit and set the immediate right digit to 0

So 5 rounds up to 6

The 6 to the immediate right(units place becomes 0)

1 4 5 6 rounded to nearest ten==> 1 4 6 0

Answer:

\(\frac{\pi }{2}\) m

Step-by-step explanation:

C = 2\(\pi\)(radius)

=2\(\pi\)(1/4)

=\(\frac{\pi }{2}\) m (meters)

\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)

\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)

\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)

\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)

\( \sf \longrightarrow \: \: 100n =20\\ \)

\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)

\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)

Answer:-

To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:

Step 1: Distribute the 5 on the left side:

\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)

Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:

\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)

\(\sf 5n = 1 \\\)

Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):

\(\sf \frac{5n}{5} = \frac{1}{5} \\\)

\(\sf n = \frac{1}{5} \\\)

Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Translate the word problem into a system of equations, with x representing true/false questions and y representing multiple choice questions:

(1) \(x+y=20\) <-- a test has 20 total questions

(2) \(4x+8y=100\) <-- the test is worth 100 total points

Now we have a system of two equations with two unknowns, which we can solve with the elimination method.

Let's multiply equation (1) by -4 so that we can eliminate x from the system:

\(-4x-4y=-80\)

Now, add this new equation to equation (2) to eliminate x so that we only have one variable left:

\(4y=20\)

Solve for y:

\(y=5\)

Now, substitute this value for y into either the original equation (1) or (2). I will do equation 1 for simplicity:

\(x+5=20\)

Solve for x:

\(x=15\\\)

Notice that we now have values for both x and y, so we are done. We now know that there are 15 true/false questions and 5 multiple choice questions on the test!

From the problem, we are given:

mean = 157 psi

standard deviation 3 psi

Since it is a non-normal distribution, given that n=64. We will use the following formula:

After 31 years the population will be the same. Their populations will be 2072 when they are the same.

Growth rates are calculated by dividing the difference between the ending and beginning values for the period under consideration by the starting value. The most common time periods for growth rates are annually, quarterly, monthly, and weekly.

The formula for the growth of the population is:

A = P(1+r)^n

A is the total number population after n years.

P is the initial number of population

r is rate of interest.

For town A,

The initial population is 700. The growth rate is 3.5% = 0.035.

The population of town A after t year is y = 700(1+0.035)^t

For town B,

The initial population is 1400. The growth rate is 1.25% = 0.0125.

The population of town A after t year is y = 1400(1+ 0.0125)^t

The system of equations is:

y = 700(1+0.035)^t

y = 1400(1+ 0.0125)^t

The intersection point is (31.537,2071.432).

After 31 years the populations will be the same.

their populations will be 2072 when they are the same

To learn more about point of intersection visit:

https://brainly.com/question/29188411

#SPJ1

Answer:

100% increase

Step-by-step explanation:

0.1 to 0.2

0.1 = 100% (original number)

0.2 - 0.1 = 0.1

0.1 = 100%

Answer:

B: rectangle JKLM ~ rectangle QRSP

Step-by-step explanation:

5/6=0.83

12.5=0.83

JK corresponds to QR

JM corresponds to PQ

rectangle JKLM ~ rectangle QRSP

Answer:

Step-by-step explanation: C is 100 X is 10 IV is 4 since the smaller number is in the front so you subtract instead of add

C=100 3X=30 IV=4

100+30+4=134

CXXXIV=134

It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

For more such information on: speed

https://brainly.com/question/24739297

#SPJ8

Step-by-step explanation:

To find the profit of the firm, we need to first determine the quantity Q that maximizes the profit, and then use that quantity to find the price and profit.

The profit function can be written as:

π(Q) = TR(Q) - TC(Q)

where TR(Q) is the total revenue function and TC(Q) is the total cost function. We can write TR(Q) as:

TR(Q) = P(Q) * Q

where P(Q) is the price function, which is given as:

P(Q) = 240 - 20Q

So, the profit function becomes:

π(Q) = (240 - 20Q) * Q - (120 + 45Q - Q^2 + 0.4Q^3)

Simplifying this expression, we get:

π(Q) = -0.4Q^3 + 24.6Q^2 - 195Q + 120

To maximize the profit, we take the derivative of the profit function with respect to Q and set it equal to zero:

π'(Q) = -1.2Q^2 + 49.2Q - 195 = 0

Solving for Q using the quadratic formula, we get:

Q = (49.2 ± sqrt(49.2^2 - 4*(-1.2)(-195))) / (2(-1.2))

Q = 21 or Q = 32.5

Since the coefficient of the Q^3 term in the profit function is negative, the profit function has a maximum at Q = 32.5. Therefore, the firm should produce and sell 32.5 units of output.

To find the price that the firm should charge, we substitute Q = 32.5 into the demand function:

P = 240 - 20Q

P = 240 - 20(32.5)

P = 160

Therefore, the firm should charge a price of $160 per unit.

To find the profit at the optimal level of output, we substitute Q = 32.5 and P = 160 into the profit function:

π(Q) = -0.4Q^3 + 24.6Q^2 - 195Q + 120

π(32.5) = -0.4(32.5)^3 + 24.6(32.5)^2 - 195(32.5) + 120

π(32.5) = $1,722.81

Therefore, the profit at the optimal level of output is $1,722.81