Which of the following is equivalent to the complex number i^32

Answer:

Y = -½x

OR

y+4= -½(x-8)

Step-by-step explanation:

For perpendicular lines ,L1 and L2 ,the following relation hold;

Gradient of L1 × Gradient of L2= -1

i.e

Product of their gradients equal to one for perpendicular lines

GL1.GL2 =-1

from equation given

y=2x+ 13

it is in the form y =mx +c,where

m is the gradient and c is constant.

therefore the gradient of the line is

2, since 2 is in position of m

=> GL1 = 2

2 GL2 = -1

=> GL2 =-½

Since gradient is given by =

( change in y)/(change in X)

(y+4)/(x-8)=-½

=> -½x+4=y+4

=> y=-½x

therefore the equation is

y=-½x

Answer:

$38.08

Step-by-step explanation:

12% of 34.00 as an equation would be \(34*0.12\), \(34*0.12=4.08\) so we add 4.08 to the total of the lunch already. \(34.00+4.08=38.08\). So the answer is $38.08. Hope this helps :)

The height of the cylinderical can is approximately 1147.8 inches.

What is a cylinder?

A cylinder is a three-dimensional geometric object made up of two parallel and congruent circular bases that are joined by a curving lateral surface. The lateral surface has a uniform circular cross-section and is perpendicular to the bases. A cylinder's height is the perpendicular distance between its bases. Cans, tubes, and pipes are all instances of cylinders. The volume of a cylinder may be computed by multiplying its base area by its height, and the formula for the lateral surface area is 2πrh, where r is the radius of the base and h is the cylinder's height.

Now,

We can start by finding the radius of the can using the given diameter:

radius = diameter/2 = 5/2 = 2.5 inches

The surface area of the can is given by:

Surface area = 2πrh + 2πr²

where h is the height of the can, r is the radius, and π is the mathematical constant pi.

Substituting the given values, we get:

18064 = 2π(2.5)(h) + 2π(2.5)²

Simplifying and solving for h, we get:

18064 = 15.707h + 39.269

18064 - 39.269 = 15.707h

18024.731 = 15.707h

h = 18024.731/15.707

h ≈ 1147.8 inches

Therefore, the height of the can is approximately 1147.8 inches.

To know more about cylinder visit the link

brainly.com/question/16134180

#SPJ1

Answer:

Step-by-step explanation:

Given two points:

The distance between them is the difference of y- coordinates since x- coordinates are same:

The values of x is 6 and y is (-6).

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

-4x-5y=6............(1)

9x+7y=12..................(2)

Solving Equation (1) and (2) we get

-36 x  - 45y = 54

36x + 28y = 48

____________

         -17y= 102

              y= -6.

and, -4x -5y= 6

-4x - 5(-6) = 6

-4x + 30 = 6

-4x = 6-30

-4x = -24

x= 6

Learn more about Equation here:

https://brainly.com/question/1097748

#SPJ1

Answer:

324

Step-by-step explanation:

the answer 325

Answer:

\(\green{\rule{200pt}{555555pt}}\)

\(\green{\rule{200pt}{555555pt}}\)

\(\green{\rule{200pt}{555555pt}}\)

\(\green{\rule{200pt}{555555pt}}\)

\(\green{\rule{200pt}{555555p

Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

At least 3/4 of the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours.

Step-by-step explanation:

Chebyshev's Theorem states that:

1) at least 3/4 of the data lie within two standard deviations of the mean, that is, in the interval with endpoints x bar ±2s for samples and with endpoints μ±2σ for populations;

2) at least 8/9 of the data lie within three standard deviations of the mean, that is, in the interval with endpoints x bar ±3s for samples and with endpoints μ ± 3σ for populations;

3) at least 1−1/k² of the data lie within k standard deviations of the mean, that is, in the interval with endpoints x bar ± ks for samples and with endpoints μ ± kσ for populations, where k is any positive whole number that is greater than 1.

1) endpoints μ ± 2σ for populations;

μ = mean = 4

σ = standard deviation = 0.8

= 4 ± 2(0.8)

= 4 ± 1.6

= 4+ 1.6 = 5.6

= 4 - 1.6 = 2.4

Therefore, the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours is at least 3/4

Answer:

3/4

Step-by-step explanation:

Rounded to the nearest hundredth, the value of y at \(x = 7\) is approximately \(12.78\), according to the concept of linear regression line.

To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form \(y = mx + b\), where m represents the slope and b represents the y-intercept.

Using the provided data, the linear regression line equation is:

\(\[ y = 1.3642x + 3.2324 \]\)

To find the value of \(y\) at \(x = 7\), we substitute \(x = 7\) into the equation:

\(\[ y = 1.3642(7) + 3.2324 \]\)

Simplifying the equation, we get:

\(\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \]\)

In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is \(y = 1.3642x + 3.2324\). By substituting \(x = 7\) into the equation, we find that the estimated value of y is approximately \(12.78\). This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.

For more such questions on linear regression line:

https://brainly.com/question/30401933

#SPJ8

Answer:

-10 if you meant 1/4(8-4p)

-20 if you meant 1/4{(8-4p)+2p}

Step-by-step explanation:

Answer:

-10 if you meant 1/4(8-4p)

-20 if you meant 1/4{(8-4p)+2p}

Step-by-step explanation:

hope this helps have a great day.

Answer:

4/13 < 6/13

Step-by-step explanation:

= means equal

< means less than

> means greater than

Since 4/13 is less than 6/13 the correct answer is 4/13 < 6/13

Answer:

See below for answers and explanations

Step-by-step explanation:

Problem 1

Here, \(\frac{3}{4}v\) tells us that the vector \(v\) is impacted by a scale factor of \(\frac{3}{4}\), so we are doing scalar multiplication basically for both components of the vector. This only impacts the magnitude of the vector and not its direction. If we were to assume that \(v=\langle4,8\rangle\), then \(\frac{3}{4}v=\langle\frac{3}{4}(4),\frac{3}{4}(8)\rangle=\langle3,6\rangle\). Therefore, this matches vector \(u\), so D is the correct answer

Problem 2

Cannot be able to read as the text is too small

Problem 3

Cannot be able to read as the text is too small

Problem 4

\(-7u=\langle-7(8),-7(-4)\rangle=\langle-56,28\rangle=-56i+28j\), so A is correct. Remember to use scalar multiplication for each component.

Problem 5

\(r-s=\langle5-9,11-(-8)\rangle=\langle-4,19\rangle\), so B is correct. Remember to subtract the horizontal and vertical components seperately.

ANSWERS TO THE WHOLE QUIZ:

1. 13.23

2. 1/2

3. 0.25

4. 31.16

5. 76.50

Your Welcome and have a great day!

( I had to fail the quiz to give the answers)

The farmer can 9 days more than 31 days.

given,

farmer buy 1000 pounds of hay

if cow eats 25 pounds of hay per day .

here, 25 x 31 =775

which is less than 1000 ,so that the farmer can feed the cow more than 31 days

1000-775=225

225/25=9

therefore the farmer can 9 days more than 31 days.

There are four basic properties of numbers: commutative, associative, distributive, and identity. You should be familiar with each of these.

distributive property ;

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

The commutative property states that the change in the order of two numbers in an addition or multiplication operation does not change the sum or the product.

to know more about properties;

visit; brainly.com/question/11232266

#SPJ9

The hypotenuse of a right triangle will be $561$.

What is hypotenuse?

In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle.

Lengths of legs of a right triangle are given that are $264$ and $495$.

According to The Pythagorean Theorem,

\(hypotenuse^{2} = lenght^{2} + lenght^{2}\\hypotenuse^{2} = 264^{2} + 495^{2}\\\\hypotenuse^{2} = 69,696 + 245,025\\ hypotenuse^{2} = 314,721\\hypotenuse = 561\)

The hypotenuse of a right triangle will be $561$.

To learn more about right triangle visit : brainly.com/question/29285631

#SPJ4

Answer:

1.3 meters

Step-by-step explanation:

1/2 + 4/5 = 13/10

13/10 = 1 3/10

1 3/10 = 1.3

Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.

In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.

In the given question,

We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:

6/total candies = number of lemon candies/100

We can cross-multiply to solve for the number of lemon candies:

number of lemon candies = 6 x 100 / total candies

We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:

total candies = lemon + orange + grape + cherry

Using the information from the table, we can estimate the total number of candies:

total candies = 6 + 5 + 8 + 13 = 32

Therefore, the estimated number of lemon candies in the bag is:

number of lemon candies = 6 x 100 / 32 = 18.75

We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.

To know more about Ratio and proportion, visit:

https://brainly.com/question/29774220

#SPJ1

Answer:

a)9. b) 12

Step-by-step explanation:

a) | -6 -3 | .

-6-3 = -9

|-9| =9

b) | 0 - 12 |.

0-12=-12

|-12|=12

Answer:

No

Step-by-step explanation:

The table represents two sets of data

The values of x are repeated (3.45 appears twice)

Therefore it not a function as per definition of a function

The answer is no

The solution of the differentiated equation is dy/dx = -6x⁵

From the question, we have the following equations that can be used in our computation:

x = ⁶√t

y = 8 - t

To start with:

We need to make the variable t the subject of the formula in the equation x = ⁶√t

Make t the subject

So, we have

t = x⁶

Substitute t = x⁶ in the equation y = 8 - t

y = 8 - x⁶

The rule of first principle of differentiation is represented as

If y = axⁿ, then dy/dx = naxⁿ⁻¹

Using the above as a guide, we have

y = 8 - x⁶

dy/dx = 0 * 8x⁰⁻¹ - 6 * x⁶⁻¹

Evaluate the difference

So, we have

dy/dx = 0 * 8x⁻¹ - 6 * x⁵

Evaluate the products

So, we have

dy/dx = 0 - 6x⁵

Evaluate the sum

So, we have

dy/dx = -6x⁵

Hence, the equation result is dy/dx = -6x⁵

Read more about differentiation at

brainly.com/question/25081524

#SPJ1

Answer:

1.) inverse proportion : 1kx = y

2) direct proportion. y = kx

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
for more such questions on total amount

https://brainly.com/question/9879870

#SPJ8

Answer:

Maggie is 13 years old.

Step-by-step explanation:

The explanation is attached.

Answer:

volume is 8 times larger and surface area is about 2.7 times larger

Step-by-step explanation:

a)24 in³ b) 76 in² c) volume is 8 times larger and surface area is about 2.7 times larger.

Answer:

Please check the explanation.

Step-by-step explanation:

Given the function

\(f\left(x\right)=\sqrt{x^3-16x}\)

We know that the domain of the function is the set of input or arguments for which the function is real and defined.  

In other words,  

Now, determine non-negative values for radicals so that we can sort out the domain values for which the function can be defined.

\(x^3-16x\ge 0\)

as x³ - 16x ≥ 0

\(\left(x+4\right)\left(x-4\right)\ge \:0\)

Thus, identifying the intervals:

\(-4\le \:x\le \:0\quad \mathrm{or}\quad \:x\ge \:4\)

Thus,

The domain of the function f(x) is:

\(x\left(x+4\right)\left(x-4\right)\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-4\le \:x\le \:0\quad \mathrm{or}\quad \:x\ge \:4\:\\ \:\mathrm{Interval\:Notation:}&\:\left[-4,\:0\right]\cup \:[4,\:\infty \:)\end{bmatrix}\)

And the Least Value of the domain is -4.

Step-by-step explanation:

The coordinates and vertices

which reflected over the y- axis are

r(-2,0) , s(2,-3) , and t(2,3).

Given the arithmetic series below

To find the sum of the arithmetic series,

We find the last term, i.e 8th term of the series

The formula to find the last term/formula for the arithmetic progression is given below

The common difference, d, is

Where,

Substitute the values into the formula to find the 8th term

The formula to find the arithmetic series is

Where

Subtsitute the values into the formula to find the arithmetic series above

Hence, the sum of the arithmetic series is 104

-32/9 feet/min fast is the person's shadow on the wail changing in Length (in feet per minute) when the person is 25 feet from the wall. So the option a is correct.

In the given question, a 5 foot person walks at 40 feet per minute on a level path toward a vertical wall.

A light on the ground directly behind the person casts a shadow of the person on the wall.

The light is loo feet from the wall.

We have to find how fast the person's shadow on the wail changing in Length (in feet per minute) when the person is 25 feet from the wall.

From the diagram given below;

dx/dt = 40 feet/min

y/100 = 5/x

Multiply by 100 on both side, we get;

y = (5×100)/x

y = (500)/x

dy/dt = -500/x^2(dx/dt)

Now putting the value of dx/dt

dy/dt = -500/x^2 *40

dy/dt = -20000/x^2

from the diagram given below, x = 75 feet

Now putting the value of x

dy/dt = -20000/(75)^2

dy/dt = -32/9 feet/min

Hence, -32/9 feet/min fast is the person's shadow on the wail changing in Length (in feet per minute) when the person is 25 feet from the wall. So the option a is correct.

To learn more to find change in length link is here

brainly.com/question/13150044

#SPJ4