this as a decimali if you respond for first you will have
the brainlest answer​

This As A Decimali If You Respond For First You Will Have The Brainlest Answer

Answers

Answer 1

Answer:

8.525

Step-by-step explanation:


Related Questions

What’s the difference between the polynomials ?

Whats the difference between the polynomials ?

Answers

Answer:

7x^2-4x+3y^2      ( the ^ means the exponent EX: 5^2 is 5 squared. )

Step-by-step explanation:

Remove the parenthesis (a) = a

12x^2-11y^2-13x- (5x^2-14y^2-9x)

-(5x^2 - 14y^2 - 9x)

Distribute parenthesis

-(5x^2) - (14y^2) - (-9x)

Apply minus - plus rules

-5x^2 + 14y^2 + 9x

= 12x^2 - 11y^2 - 13x - 5x^2 + 14y^2 + 9x

Simplify

12x^2-11y^2-13x-5x^2+14y^2+9x

Group like terms

12x^2-5x^2-13x+9x-11y^2+14y^2

Add similar elements

7x^2-13x+9x-11y^2+14y^2

Add similar elements ( - 13x + 9x = -4x )

7x^2-4x-11y^2+14y^2

Add similar elements 11y^2 + 14y^2 = 3y^2

7x^2-4x+3y^2

The length of a rectangle is twice its width. Find its lenght and width, if its perimeter is 7 1/3 cm.

Answers

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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what are the similarities and differences in linear and exponential in intercepts?

what are the similarities and differences in linear and exponential in domain and range?

what are the similarities and differences in linear and exponential in asymptotes?

what are the similarities and differences in linear and exponential in misc.?

Answers

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?

Answers

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

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2. 7 cm In triangle ABC, AC = 7 cm, BC = 10 cm, angle ACB = 73° C 73° 10 cm Calculate the length of AB Give your answer correct to 3 significant figures. Diagram NOT accurately drawn B (Total 3 marks​

2. 7 cm In triangle ABC, AC = 7 cm, BC = 10 cm, angle ACB = 73 C 73 10 cm Calculate the length of AB

Answers

Answer:

AB = 10.398

Step-by-step explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398

A rectangle is divided into 25 equal parts. How many of these parts must be shaded in order to cover three fifths of the rectangle?​

Answers

Answer:

15 parts must be shaded

Step-by-step explanation:

3/5 × 25 = 15

15/25 = 3/5

Have a great day.

15 parts must be shaded in order to cover three fifths of the rectangle.

What is a rectangle?

"A rectangle has two pairs of equal opposite parallel sides, four right angles and two diagonals. The diagonals of a rectangle are congruent.

They also bisect each other. Each diagonal divides the rectangle into two congruent right triangles."

Given

A rectangle is divided into 25 equal parts.

Number of parts must be shaded in order to cover three fifths of the rectangle

= \(\frac{3}{5}\) × \(25\)

= 15

Checking whether the 15 parts must be shaded in order to cover three fifths of the rectangle

= \(\frac{15}{25}\)

= \(\frac{3}{5}\)

Hence, 15 parts must be shaded in order to cover three fifths of the rectangle.

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Paul writes newspaper articles. He earns a base rate of $500 per month and an additional $100 per article he writes. Last month he earned $2000.

Write an equation to determine the number of articles (a) he sold last month.

Answers

Answer:

Total earning last month with x articles is:

x*100 + 500

This is same amount as 2000

The equation is:

100x + 500 = 2000

Please answer this question

Please answer this question

Answers

Answer:

$40.00 is the answer

Step-by-step explanation:

also can you mark me as a brainlist if you get a chance

Answer: $40.00

Step-by-step explanation:

12 is 30% of 40

x+2y=5
4x+8y=20
I need help asap

Answers

Answer:

(x, -1/2x + 5/2) or infinitely many solutions

Step-by-step explanation:

We can solve the system of equations using substitution.  We can start by isolating x in the first equation.  Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:

Isolating:

x = -2y + 5

Plugging in and solving for y:

4(-2y + 5) + 8y = 20

-8y + 20 + 8y = 20

20 = 20

We see that we get a constant equal to another constant.  Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:

y = -1/2x + 5/2

Thus, the general rule for the solution to the system of equations is

(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions

You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation.  Let's try 4 for x and 0 for x:

4 for x in first equation:

4 + 2(-1/2(4) + 5/2) = 5

4 + 2(0.5) = 5

4 + 1 = 5

5 = 5

4 for x in the second equation

4(4) + 8(-1/2(4) + 5/2) = 20

16 + 8(0.5) = 20

16 +4 = 20

20 = 20

0 for x in the first equation:

0 + 2(-1/2(0) + 5/2) = 5

0 + 2(2.5) = 5

5 = 5

0 for x in the second equation:

4(0) + 8(-1/2(0) + 5/2) = 20

0 + 8(2.5) = 20

20 = 20

I need help with this question

I need help with this question

Answers

Look at image for explanation and answer


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I need help with this question

Given the following table of values for the function f(x), determine f^-1(4)

Given the following table of values for the function f(x), determine f^-1(4)

Answers

Using the inverse of the function from the table, the value of f⁻¹(4) is 107/3

What is the inverse of a function?

The inverse of a function is a new function that "undoes" the original function. It reverses the mapping of inputs and outputs, allowing you to find the original input value when you know the output value.

In this problem, we have to use the table to find the original function which is f(x) and use it to find the inverse of the function;

Taking two points from the table;

m = y₂ - y₁ / x₂ - x₁

m = 0 - (-3) / -9 - (-11)

m = 3 / 20

Using the slope and one point on the table;

y = mx + x

-3 = 3/20(-11) + c

-3 = -1.65 + c

c = -3 + 1.65

c = -1.35

Putting the slope and y - intercept together;

y = 3/20x - 1.35

y = 3/20x - 27/20

f(x) = 3/20x - 27/20

Taking the inverse of the function;

f⁻¹(x) = (20x + 27)/3

To find the value of f⁻¹(4), we just need to substituting the value of x in the function;

f⁻¹(4) = (20(4) + 27)/3

f⁻¹(4) = 107/3

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Select the correct answer.
Which function is the inverse of f(x)=x^3–6x^2+12x-8

Answers

Answer: (x-2)^3

Step-by-step explanation:

Frist step; (((x3) -  (2•3x^2)) +  12x) -  8

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

second step; x^3-6x^2+12x-8  is not a perfect cube

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

third step; Factoring:  x^3-6x^2+12x-8

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  x^3-8

Group 2:  -6x^2+12x

Pull out from each group separately :

Group 1:   (x^3-8) • (1)

Group 2:   (x-2) • (-6x)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

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

step four;

Find roots (zeroes) of :       F(x) = x^3-6x^2+12x-8

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -8.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,8

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -27.00    

     -2       1        -2.00        -64.00    

     -4       1        -4.00        -216.00    

     -8       1        -8.00       -1000.00    

     1       1        1.00        -1.00    

     2       1        2.00        0.00      x-2

     4       1        4.00        8.00    

     8       1        8.00        216.00    

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

  x^3-6x^2+12x-8

can be divided with  x-2

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

Step 5; Polynomial Long Division

Dividing :  x^3-6x^2+12x-8

                             ("Dividend")

By         :    x-2    ("Divisor")

dividend     x3  -  6x2  +  12x  -  8

- divisor  * x^2     x^3  -  2x^2        

remainder      -  4x^2 + 12x  - 8

- divisor  * -4x^1      -  4x^2 + 8x    

remainder             4x - 8

- divisor  * 4x^0             4x - 8

remainder                0

Quotient :  x^2-4x+4  Remainder:  0

Graph the cubic using its end behavior and a few selected points.

Falls to the left and rises to the right

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

stp6;

Factoring  x2-4x+4

The first term is,  x2  its coefficient is  1 .

The middle term is,  -4x  its coefficient is  -4 .

The last term, "the constant", is  +4

Step-1 : Multiply the coefficient of the first term by the constant   1 • 4 = 4

Step-2 : Find two factors of  4  whose sum equals the coefficient of the middle term, which is   -4 .

     -4    +    -1    =    -5

     -2    +    -2    =    -4    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  -2

                    x2 - 2x - 2x - 4

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-2)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-2)

Step-5 : Add up the four terms of step 4 :

                   (x-2)  •  (x-2)

            Which is the desired factorization

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

2.6    Multiply  (x-2)  by  (x-2)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x-2)  and the exponents are :

         1 , as  (x-2)  is the same number as  (x-2)1

and   1 , as  (x-2)  is the same number as  (x-2)1

The product is therefore,  (x-2)(1+1) = (x-2)2

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

Multiply  (x-2)2   by  (x-2)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (x-2)  and the exponents are :

         2

and   1 , as  (x-2)  is the same number as  (x-2)1

The product is therefore,  (x-2)(2+1) = (x-2)3

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

Answer; (x - 2)^3

Select the correct answer.Which function is the inverse of f(x)=x^36x^2+12x-8
Select the correct answer.Which function is the inverse of f(x)=x^36x^2+12x-8

How do I type in exponents

Answers

Answer:

on what

Step-by-step explanation: normaly you have a button that you can have certain characters

Water is 2parts of hydrogen and 1 part of oxygen. For one molecule of water, each atom has the atomic mass unit of u, shown. What percent of the mass of a water molecule is hydrogen

Oxygen=16.00u
Hydrogen = 1.01u

Answers

11.2% of the mass of a water molecule is hydrogen

How to solve for the percentage

As water is composed of two parts hydrogen and one part oxygen, the total mass of a single molecule may be determined by ascertaining the following:

The Total Mass of Water = (2 x Mass of Hydrogen) + (1 x Mass of Oxygen)

Total Mass of Water = (2 x 1.01u) + (1 x 16.00u)

Total Mass of Water = 18.02u

Consequently, the overall mass of one molecule of water is determined to be 18.02 atomic mass units (u).

% mass of hydrogen = (mass of hydrogen / total mass of water) × 100

% mass of hydrogen = (2.02u / 18.02u) × 100

% mass of hydrogen = 11.2%

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8x + 3y + 6z = 43
-3x + 5y + 2z = 32
5x – 2y + 5z = 24

Answers

Answer:

Why do you want us to do??

Step-by-step explanation:

A 128-ounce carton of milk states that there are 20 servings. How many ounces are in a serving?

Answers

Answer:water

Step-by-step explanation:

Answer:

6.4

Step-by-step explanation:

Maury and his mom painted the rectangular wall in Maury room Maury painted 1/6 of the wall and his mom painted 1/4 of the wall How much of the wall is still left to paint

Answers

Answer: 7/12

Step-by-step explanation:

1- 1/6 - 1/4

5/6 - 1/4

10/12 - 3/12

7/12 left

The makers of a soft drink want to identify the average age of its consumers. A sample of 25 consumers was taken. The average age in the sample was 31 years with a standard deviation of 3.8 years.The Margin of error of the 99% confidence interval for the average age of the consumers is a.1.90 years b.2.13 years c.4.10 years d.1.65 years

Answers

Answer:

a.1.90 years

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1-0.99}{2} = 0.005\)

Now, we have to find z in the Ztable as such z has a pvalue of \(1-\alpha\).

So it is z with a pvalue of \(1-0.005 = 0.995\), so \(z = 2.575\)

Now, find the margin of error M as such

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

In this question:

\(n = 25, \sigma = 3.8\)

So

\(M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90\)

So the correct answer is:

a.1.90 years

If the numbers below were ordered from least to greatest, which number could you use to replace the ____?
1/8, ____ 3/10, 0.6, 3/4

A. 1/5
B. 0.33
C. 2/5
D. 0.8

Answers

The answer is 2/8 or 1/4 have a good day:)

Siegell's Locksmith Shop is taking out a mortgage on a new building. It is going to be an interest-only, 12-year balloon mortgage for $350,000. The APR is 3.35%. The last payment will be the balloon payment of the full principal.
a. Find the total number of monthly payments, not including the final balloon payment.
b. Find the amount of each monthly payment if the payments are interest-only. Round to the nearest cent.
c. Find the difference between the regular monthly payment and the balloon payment, to the nearest hundred dollars.
d. If the mortgage was not a balloon mortgage, what would be the amount of the monthly payment, rounded to the nearest cent?

Answers

Total number of monthly payments, not including the final balloon payment is $1,195.77

How to solve the problem?

The monthly payment is the sum that must be paid each month for the duration of the loan to cover the principal balance. When a loan is taken out, not only the principal—the amount that was initially loaned out—but also the interest—which accrues—must be repaid.

Step1

M = 350,000(0.071/12)(1+0.071/12)² /(1+0.071/12)¹² =3,618.02

M = P(r/12) (1+r/12)¹²×n/(1+r/12)¹²×n -1

Step2:

3,618.02 × 12 × 12 = 520,994.88

The total paid is the product of the monthly payment and the number of payments.

520,994.88 - 350,000 = 170,994.88

= 170,994.88÷143

= 1,195.77

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The formula,Time traveled=Distance traveled/Rateor speed traveled is used to find the time traveled. The formula can be written in symbol as T=D/R. Solve the formula for D

Answers

Starting with the formula T = D/R, we want to isolate the variable D on one side of the equation.

To do this, we can multiply both sides of the equation by R:

T * R = D

Alternatively, we can write it as:

D = R * T

Therefore, the formula for distance traveled is D = R * T.

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Apples are on sale at the local fruit stand at 4 lbs. for $2.60. Which equation can be used to find the cost, c, of n pounds of apples?


c = 4

c = 8n

c = .65n

c = 2.60n

Answers

The answer is c=.65n

A company produces and sells solar panels for $520. The company's daily profit, P(x), can be modeled by the function P(x) = −6x2 + 156x + 1,000, where x is the number of $5 price increases for each solar panel. Use the graph to answer the questions. Graph of function p of x equals negative 6 x squared plus 156 x plus 1,000. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 1000), increases to the vertex at about (13, 2014), and decreases through about (31, 0). Part A: Identify the approximate value of the y-intercept. Explain what the y-intercept means in terms of the problem scenario. (3 points) Part B: Identify the approximate value of the x-intercept. Explain what the x-intercept means in terms of the problem scenario. (3 points) Part C: Identify the approximate value of the maximum of the function. Explain what the maximum of the function means in terms of the problem scenario. (4 points)

Answers

The maximum daily profit the company can earn is $2,350.

It is a set of points in a coordinate plane that represents the values of the function for different inputs.

The function P(x) = −6x² + 156x + 1,000 models the daily profit of the company, where x is the number of $5 price increases for each solar panel. The graph of the function has a vertex at approximately (15, 2350), which represents the maximum point on the graph.

Therefore, the maximum daily profit the company can earn is $2,350.

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How do I find the possible degree(s) of a function from the graph alone?

Answers

Answer:

To determine the possible degree(s) of a function from the graph alone, you need to examine the behavior of the graph at the extremes (far left and far right) and consider the number of turning points or changes in direction. Here's a step-by-step approach:

Look at the far left side of the graph: Determine the behavior of the graph as it approaches negative infinity. Does the graph approach a specific value, such as a horizontal line (asymptote) or the x-axis? If the graph approaches a horizontal line, it suggests a polynomial function of even degree. If the graph approaches the x-axis, it indicates a polynomial function of odd degree or possibly a function with a root of multiplicity greater than one.

Look at the far right side of the graph: Determine the behavior of the graph as it approaches positive infinity. Similar to step 1, observe if the graph approaches a specific value or a horizontal line. The behavior at the far right side should be consistent with the behavior at the far left side. This can help you identify if the function is even or odd degree.

Examine the number of turning points or changes in direction: Count the number of times the graph changes direction. These points are where the slope of the graph changes from positive to negative or vice versa. The number of turning points can provide an indication of the degree of the polynomial. For example, if there are two turning points, it suggests a polynomial function of degree 3.

Remember that this method provides potential degrees, but it may not definitively determine the exact degree of the function. Additional information or analysis might be required for a more accurate determination.

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!

Answers

A. The area of the triangle is 108 mm².

B. The area of parallelogram is 286√2 in²

How to find the area of each parallelogram of triangle?

A. Area of a triangle (A) = 1/2 * Base (b) * Height (h)

We have:

b = 18 mm

h = 12 mm

Thus:

A = 1/2 * 18 * 12

A = 108 mm²

B. The area of parallelogram is given by:

A = b * h

where b is the base and h is the height

We have:

b = 26 in

Using trig.:

sin 45 = h/22

h = 22 * sin 45

h = 11√2 in

Thus,

A = 26 * 11√2

A = 286√2 in²

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Tessa is training for her town's annual fun run. Today, she plans to run along a 1.55-mile loop trail in a nearby park. If Tessa wants to run a total of 3.1 miles, how many loops should she do?​

Answers

Answer:

2 loops

Step-by-step explanation:

If Tessa wants to run a total of 3.1 miles, then she has to complete 2 loops.

What is division?

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Tessa is training for her town's annual fun run.

Today, she plans to run along a 1.55-mile loop trail in a nearby park.

If Tessa wants to run a total of 3.1 miles.

Then the number of the loop will be

\(\rightarrow \dfrac{3.1}{1.55}\\\\\rightarrow 2\)

Then the total number of the loops is 2.

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use distributive property to rewrite this problem: -2(n-7)

Answers

Answer: -2n + 14

To rewrite the expression -2(n-7) using the distributive property, we need to distribute the -2 to both terms inside the parentheses. The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

Applying this property to the given expression:

-2(n-7) = -2 * n + (-2) * (-7)

Simplifying further:

-2(n-7) = -2n + 14

Therefore, the rewritten expression is -2n + 14.

What is the value of i4?

Answers

Answer:

  1

Step-by-step explanation:

You want to know the value of i^4.

Powers of i

The fourth power of i, √(-1), can be found the same way the value of any fourth power can be found: carry out the multiplication.

  i^4 = i·i·i·i = -1·i·i = -i·i = -(-1) = 1

The fourth power of i is 1.

__

Additional comment

As you can see from the evaluation process, ...

  i¹ = i

  i² = -1 . . . . . definition of i

  i³ = -i

  i⁴ = 1

The sequence repeats for higher powers.

Look at the picture below! WILL GIVE BRAINILEST TO CORRECT ANSWER!!!

Look at the picture below! WILL GIVE BRAINILEST TO CORRECT ANSWER!!!

Answers

Answer:

3/5

Step-by-step explanation:

A machine that manufactures automobile pistons is estimated to produce a defective piston 3% of the time. Suppose that this estimate is correct and that a random sample of 80 pistons produced by this machine is taken.
(a) Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable).
Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution.
Round your response to at least three decimal places

Answers

(a) The mean of the relevant distribution is 2.4 defective pistons.

(b) The standard deviation of the distribution is 1.539.

The mean of the relevant distribution is the expected number of defective pistons that we would expect to get from a sample of 80 pistons produced by this machine. The mean is calculated by multiplying the probability of a defective piston (3%) with the number of pistons in the sample (80). In this case, the mean is 2.4 defective pistons. The standard deviation of the distribution quantifies the uncertainty of our estimate. It is calculated by taking the square root of the variance, which is the expected value of the squared differences between the number of defective pistons in the sample and the mean. In this case, the standard deviation is 1.539. This means that, in theory, we would expect 68% of the samples to contain between 0.861 and 4.139 defective pistons.

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