Find the indicated real nth root(s) of a. n=3, a=27

The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.

A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.

For k=- 5, y=f(x) + k represents a vertical shift down.

For h=4, the horizontal shift left is y=f(x+h).

Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.

To know more about graph, visit:

https://brainly.com/question/17267403

#SPJ1

Answer:

D

Step-by-step explanation:

First take out a factor of 2:

2(1 - 25x^2)

Then factor the difference of squares:

2(1 -5x)(1+5x)

The correct expression for e (spring extension) is \(e=l_{1}+2Lcos\)θ.

To determine the correct expression for e, we need to understand the variables involved and their relationships.

Let's analyze the given expressions one by one:

\(e-2Lcos\)θ\(-l_{1}\):

This expression does not accurately represent the spring extension because the subtraction of \(l_{1}\) is incorrect. The correct relationship is that the spring extension is equal to \(2Lcos\)θ.

\(e-2Lsin0-L_{o}\):

This expression introduces variables \(O\) and \(L_{0}\) that are not mentioned or defined in the context of the problem. Without proper context or definition, it is not possible to determine the correctness of this expression.

\(e-l_{1} -2Lcos\)θ

This expression has the correct terms, but the subtraction of \(l_{1}\) is incorrect. The correct relationship is that the spring extension is equal to \(l_{1}\) plus the term \(2Lcos\)θ,  not minus.

\(e-h-2Lsin0\)

that are not mentioned or defined in the context of the problem. Without proper context or definition, it is not possible to determine the correctness of this expression.

Similar to expression 2, this expression introduces variables \(h\) and \(O\) that are not mentioned or defined in the context of the problem. Without proper context or definition, it is not possible to determine the correctness of this expression.

Among the four given expressions, the correct expression for e (spring extension) is \(e=l_{1}+2Lcos\)θ. This expression accurately represents the relationship between the spring extension \(e\), the arm length \(L\), and the angle θ.

To know more about spring visit

https://brainly.com/question/1968517

#SPJ11

Answer:

Step-by-step explanation:

Given:

x1 = -1

x2 = 6

y1 = 2

y2 = 3

Solution:

m = ( y2 - y1 ) / ( x2 - x1 )

m = ( 3 - 2 ) / ( 6 - -1 )

m = 1 / ( 6 + 1 )

m = 1/7

Then,

y - y1 = m ( x - x1 )

y - 2 = 1/7 ( x - -1)

y - 2 = 1/7 ( x + 1 )

y - 2 = 1/7x + 1/7

y = 1/7x + 1/7 + 2

y = 1/7x + 15/7

The length of CD is 6.32 units.

From the question, we have

CB / AB = DB / CB

CB / 14 = 10 / CB

CB² = 14 × 10

CB = √140

using the Pythagorean theorem,

AB² = CB² + AC²

14² = (√140)² + AC²

196 - 140 = AC²

AC = √56

Using the ratio of the similar triangle,

CD / AC = DB / CB

CD / √56 = 10 / √140

CD = (√56 × 10)/√140

CD = 6.32 units

the length of CD is 6.32 units.

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

To learn more about divide visit: https://brainly.com/question/15381501

#SPJ4

The appropriate statement for the null hypothesis is "the depression status and caffeinated coffee consumptions are independent."

The statement that is not appropriate for the null hypothesis according to hypothesis testing is "the levels of depression status and caffeinated coffee consumptions are equally likely."

This statement implies that there is an equal chance of having different levels of depression status and different levels of caffeinated coffee consumption, which is not a suitable assumption for the null hypothesis.

The null hypothesis should state that there is no significant relationship between the two variables, and the distribution of one variable does not depend on the distribution of the other variable.

Therefore, the appropriate statement for the null hypothesis is "the depression status and caffeinated coffee consumptions are independent."

Learn more about hypothesis testing

brainly.com/question/30588452

#SPJ11

When an item is reduced by a certain amount in percentages, the new value is equal to 100% subtracted by the given percentage. In this case the item had its price reduced by 25%, so the new value would be:

The value after the reduction is 75% of the original one. We can calculate this value as shown below:

The new value is $360. We need to find the percentage increase value that will make it equal to $480 again. To do that we need to do as shown below:

The increase in value must be equal to approximately 33.33%.

Answer:

The answer is H

Step-by-step explanation:

Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

By splitting the fraction, we can write the given expression as n²/(n+9)-8n/(n+9)+1/(n+9). Therefore, option E is the correct answer.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

The given expression is (n²-8n+1)÷(n+9).

By splitting the fraction, we get

n²/(n+9)-8n/(n+9)+1/(n+9)

Therefore, option E is the correct answer.

To learn more about the division visit:

https://brainly.com/question/1575906.

#SPJ1

Answer:

I believe the answer would be 30 people.

Step-by-step explanation:

To calculate the percentage out of a group of people or items, you just multiply the percent (in decimal form) by the amount of people you want it out of. For example: A 0.1% chance out of 1,000 people would be a chance and expectancy of 1 person out of those 1,000 people. In this case it's 3% for every person. 0.03 • 1,000 is 30.

The probability of winning a lottery game where the winning number is made up of three digits from 0 to 9 chosen at random and the numbers may repeat is 1/1000.

In the given problem, there are 10 digits from 0 to 9.If we are allowed to repeat the digits in the lottery number, then for each of the three digits, there are 10 possibilities.
Thus, the total number of possible lottery numbers = 10 × 10 × 10 = 1000.
Now, the player has only one winning number.
∴ The probability of winning the lottery = 1/1000\\

Thus, the probability of winning a lottery game where the winning number is made up of three digits from 0 to 9 chosen at random and the numbers may repeat is 1/1000.

To know more about probability, click here

https://brainly.com/question/29381779

#SPJ11

Answer:

C.

Step-by-step explanation:

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

To know more about "standard normal distribution" refer here:

https://brainly.com/question/29509087#

#SPJ11

The number of marbles that Leah has is: 48 marbles

Information about the problem:

To solve this problem we must establish the equation, isolate the variable following the rules of clearance and solve the operations:

Solving the equation we have:

1/3 x = 4/5 (x-28)

Simplifying the equation we have:

5(1x) = 3*[4*(x-28)]

5x = 12(x-28)

5x = 12x-336

336 = 12x-5x

7x = 336

x = 336/7

x = 48

Leah = x

Leah = 48

Dan = x - 28

Dan = 48-28

Dan = 20

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

Learn more about equation at: brainly.com/question/2972832 and brainly.com/question/27815607

#SPJ4

Answer:

Below

Step-by-step explanation:

12 C 2  = 12! / ( 10! 2!) = 66 ways

Answer: 81,000

Step-by-step explanation:

We can solve this by using the formula given.

If f(1)=1000x3^1, then 1,000x3=3,000

If f(2)=1000x3^2, then 3^2=9 and 1000x9=9000,

and so on,

Now, f(4) will equal 1000x3^4, and 3^4 is 3x3x3x3, which is 9x9 or 9^2, which would be equal to 81, and 81x1000=81,000

To complete the table of values for the exponential function f(x) = 1000*3^x, we can evaluate the function for x = 0, 1, 2, 3, and 4, since we are interested in the number of bacteria on the phone after 4 hours.

x f(x)

0 1000

1 3000

2 9000

3 27,000

4 81,000

Therefore, after 4 hours, there will be 81,000 bacteria on the surface of the phone, assuming the number of bacteria triples every hour and can be described by the exponential function f(x) = 1000*3^x.

#SPJ1

To convert the rectangular equation y = 9x to polar form, we can use the relationships between Cartesian and polar coordinates:

x = r cos(θ)

y = r sin(θ)

Substituting these equations into the given rectangular equation:

r sin(θ) = 9(r cos(θ))

Simplifying the equation:

r sin(θ) = 9r cos(θ)

Dividing both sides by r and rearranging:

tan(θ) = 9 cos(θ)

This is the polar form of the equation y = 9x.

To find the length of the graph of r = 1 + sin(θ) over the interval 0 ≤ θ ≤ 2π, we can use the arc length formula for polar curves:

L = ∫(θ1 to θ2) √(r^2 + (dr/dθ)^2) dθ

In this case, r = 1 + sin(θ), so we need to find (dr/dθ).

Taking the derivative of r with respect to θ:

dr/dθ = d/dθ (1 + sin(θ))

= cos(θ)

Now, we can substitute the values into the arc length formula:

L = ∫(0 to 2π) √((1 + sin(θ))^2 + cos^2(θ)) dθ

This integral may be challenging to evaluate analytically. You can use numerical methods or a calculator to approximate the value of the integral and find the length of the graph

To know more about rectangular refer here:

https://brainly.com/question/32444543#

#SPJ11

Answer:

It should be 42%

Step-by-step explanation:

Hence, there are 725,760 ways to seat the ten people together in a row, taking into account the two individuals who insist on sitting side-by-side.

If two of the ten people insist on sitting side-by-side, we can consider them as a single entity or a pair. So, essentially, we have nine entities (including the pair) to be seated in a row.

The number of ways to arrange these nine entities in a row is 9!, which is the factorial of 9.

However, within the pair, the two individuals can be arranged in 2! = 2 ways.

Therefore, the total number of ways to seat the ten people together, considering the pair as one entity, is 9! * 2!.

Simplifying this expression:

9! * 2! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 2 = 725,760

To know more about ways to seat,

https://brainly.com/question/31464578

#SPJ11

Answer:

No - Range is Max - Min = 6-0 = 6

The range is 6

Answer:

No, Madison did not find the range correctly.

Step-by-step explanation:

To find the range of any data set, take the smallest and the largest numbers and subtract them. The largest number in this data set is 6 and the smallest is 0, so

6 - 0 = 6

the range is 6.

Have a nice day!

Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

The Solution of the 9x⁴ – 2x² – 7 = 0 is x = ±1, ±i √(7/9)

What are the quadratic equations?

A quadratic equation is a type of polynomial equation with degree 2 (the highest power of the variable is 2). Quadratic equations have the general form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.

9x⁴ – 2x² – 7 = 0

Let's say that u = x²:

9u² – 2u – 7 = 0

Factor:

(u – 1) (9u + 7) = 0

u = 1, -7/9

Since u = x²:

x² = 1, -7/9

x = ±1, ±i √(7/9)

To learn more about quadratic equations, Visit

https://brainly.com/question/1214333

#SPJ4

The percentage of oil that has leaked​ from the tank is 14.29%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.

Given that,

The capacity of the tank = 49 litres.

Total litres of oil leaked = 7 litres.

Mathematically, the percentage for the amount of oil leakage in this tank is given by this formula:

Percentage = oil leakage/tank capacity *100

Substituting the given parameters into the formula, we have:

Percentage = 7/49 *100 =  14.29%

Thus, The percentage of oil that has leaked​ from the tank is 14.29%.

To know more about percentage visit: brainly.com/question/16797504

#SPJ4

Answer:

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

Find prime factors of 1265.

We see it is divisible by 5 since ends with 5:

253 is not divisible by 3 or 9 since the sum of digits is not divisible by 3 or 9. It is not divisible by 7 (since 25 - 3*2 = 19 is not divisible by 7) but divisible by 11, since the sum of digits in odd places is same as the digit in the even place (recall divisibility by 11):

23 is a prime number so no more factors.

Hence the prime factorization of 1265 is:

One possible solution to this puzzle is:

A=9, B=8, C=7, D=6, E=5, X=2

So the equation would look like:

58,746 X 4 = 23,494

This means that if you substitute the values I provided for the letters in the original equation, it would result in the equation 58,746 X 4 = 23,494 being true.

To find this solution, I used a process of elimination and logic.

First, I knew that the result of the multiplication must start with a 2, since 4 times any single-digit number results in a number between 40 and 36. Therefore, X must be either 2 or 3.

Next, I focused on the fact that the two middle digits of the result are the same, which means that either A and E are the same or B and D are the same.

If A and E are the same, they must be either 4 or 5, since they must be less than X.

However, if A and E are the same, then C must also be 4 or 5, since it cannot be higher than A or E. This means that there would be a repeated digit in the equation, which is not allowed.

Therefore, A and E cannot be the same, and B and D must be the same.

Using this information, I continued to eliminate possibilities until I found a solution that worked.

For example, since B and D must be the same and cannot be 4 or 5, they must be either 6, 7, 8, or 9.

However, if they were 6 or 7, then C would have to be 6 or 7 as well, which is not allowed. If they were 8 or 9, then A and E would have to be 4 or 5, which is also not allowed.

Therefore, B and D must be 8 or 9.

From there, I tried different combinations until I found one that worked. This process involved a lot of trial and error, but by using logic and the constraints of the puzzle, I was able to narrow down the possibilities and eventually arrive at a solution.

Read more about puzzles here:

https://brainly.com/question/28994707

#SPJ1

Answer:

Solution,

X=-2

y=4

Now,

3x+4y

\( = 3 \times ( - 2) + 4 \times 4 \\ = - 6 + 16 \\ = 10\)

hope this helps...

Good luck on your assignment..

Answer:

Ok,you just need substitute the x for the value given\

=3x+4y

=3(-2)+4(4)  Multiple the values

=-6+16        Just add the values  

=10             So,this is the answer

I hope this help you :)

If you need some help more just let me know...

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

To learn more about equations refer to:

https://brainly.com/question/2972832

#SPJ1

Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:

nile blue should be the correct answer

Step-by-step explanation: