help pls i don’t understand and don’t know which option topick

1.     [tex]i^{23}[/tex] = - i

2.   [tex]\sqrt{-128}[/tex]  = 8i√2

Steps to simplify complex numbers:

1.  To simplify  [tex]i^{23}[/tex]

We can rewrite [tex]i^{23}[/tex] as [tex](i^{4)^{5} } (i^{2} . i )[/tex]

write [tex]i^{4}[/tex] as [tex](i^{2} )^{2}[/tex]

[tex](i^{4)^{5} } (i^{2} . i )[/tex]  = [tex]((i^{2} )^{2} )^{5} (i^{2} . i)[/tex]

we  know [tex]i^{2}[/tex] = -1

((-1²))⁵  [tex](i^{2} .i)[/tex]

we know that -1² = 1

= 1⁵ [tex](i^{2} .i)[/tex]

= 1 [tex](i^{2} .i)[/tex]

= [tex](i^{2} .i)[/tex]

here [tex]i^{2}[/tex] =-1

-1 . [tex]i^{}[/tex]

= - i

so [tex]i^{23}[/tex] is -i

2. To simplify [tex]\sqrt{-128}[/tex]

= [tex]\sqrt{(- 1) . (128)}[/tex]

= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{128}[/tex]

= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (64)}[/tex]

= [tex]\sqrt{-1}[/tex] x [tex]\sqrt{(2) . (8) . (8)}[/tex]

here [tex]}\sqrt{-1}[/tex]  = i

substituting i we get

= i . 8 √2

= 8i√2

To learn more about complex number refer to :

https://brainly.com/question/5564133

#SPJ13

The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.

If the probability of making a sale is 0.03 then the probability of not making a sale must be 1-0.03 which is 0.97.

So looking at contacting 100 prospects, you could say there are two general outcomes. Either the salesman makes no sales at all, or he makes at least one sale. There are no other possible outcomes, so the probability of those two outcomes must add up to 1.

So the probability of making of at least one sale is 1 minus the probability of making no sales.

The probability of making no sales in 100 tries is 0.97^100. That's equal to about 0.0476, so the probability of getting at least one sale is 0.9524. About 95%.

learn more about of probability here

https://brainly.com/question/16904657

#SPJ4

The linear function to model the amount of money in her checking account at any time t is 185 + 5.55t.

An interest simply means the extra amount that's borrowed when one borrows money or when one saves.

In this case, the checking account pays simple interest at 3% per year. She has $185 in her account.

The amount of money in the account at anytime will be:

= 185 + (PRT/100)

P = principal

R = rate

T = time

= 185 + [(185 × 3 × t)/100]

= 185 + 5.55t

The function is 185 + 5.55t.

Learn more about interest on:

brainly.com/question/25793394

#SPJ1

Step-by-step explanation:

Let's say first piece is x. First and third ratio is 1:4 so it would be

4x - x = 360

3x = 360

x = 120 Third piece is 120g. Now we just multiply the rest.

2 × 120 = 240g

4 × 120 = 480g, total 840g

Answer:

840 g

Step-by-step explanation:

  Ratio of weight of 3 pieces = 1 : 2 : 4

Weight of 3 pieces = x , 2x , 4x

Weight of third piece - weight of first piece = 360 g

           4x - x = 360

                3x = 360

Divide both sides by 3,

                  x = 360÷ 3

                 x = 120 g

Weight of first piece = x = 120 g

Weight of second piece = 2x = 2*120 = 240g

Weight of third piece = 4x = 4 *120 = 480 g

Weight of the whole cake = 120  + 240 + 480

                                          = 840 g

Answer: E. 2.24

Step-by-step explanation:

6720 - 6720 x 2/3

6720 - 4480

= 2,240

1 kilo = 1000 meters

2240 ÷ 1000

= 2.24

Answer:

[tex]\frac{14}{25}[/tex]

Step-by-step explanation:

per cent means 'out of 100 ' , then

56%

= [tex]\frac{56}{100}[/tex] ( divide numerator/ denominator by 4 )

= [tex]\frac{14}{25}[/tex] ← in simplest form

Slope of the line graph here is undefined.

When a line is vertical, its slope is ambiguous. A vertical line lacks the horizontal distance required for a positive, negative, or zero slop to exist. Since there is no horizontal change, there is no slope for vertical lines because 0 cannot be divided into any integer.

It is obvious that the x-coordinates are the same if we have a pair of coordinates, (x1, y1) and (x1, y2) through which a line passes. They are the same vertical line's points. As a result, the slope of such a line will be ambiguous.

Examples of undefined slope in real-world situations include elevators that only go up and down, and a mountain cliff that is vertical for a certain amount of height but impossible for climbers to scale.

To know more about undefined slope refer to the given link:

https://brainly.com/question/10633357?referrer=searchResults

#SPJ1

For 6 hours

Grace will pay = $11 + 6 x $4

= $11 + $24

= $35

for t hours

Grace will pay = $11 + t x $4

= $11 + $4t

= $( 11 + 4t )

Answer:

a) 78.75

b) 62.5

a) 2 minutes

b) 19 minutes

c) 24 minutes and 48 seconds

Answer:

A = 101250 meter²

Step-by-step explanation:

Answer:

Maximum area enclosed will be 101250 meter².

Step-by-step explanation:

Let the length of the rectangular plot is x meters and the width is y meters.

900 meters is the length of the fence which represents the length of the three sides of the plot.

Therefore,

x + 2y = 900

y =  meters

Now the area of the rectangular plot will be

A = Length × Width

  = (x)(y)

  = 

  = 450x - 

We know for the maximum area we will differentiate the area and equalize it t the zero.



= 450 - x

For the maximum area, 

Therefore, 450 - x = 0

x = 450

and y = 

y = 

y = 450 - 225

  = 225 meters

Now the area enclosed A = 450 × 225

A = 101250 meter²

Answer:

Coordinate A would be (12,3)

Coordinate B would be (12,7)

Coordinate C would be  (10,5)

Step-by-step explanation:

[tex]area \: of \: circle = \pi\:r^{2} \\ \pi \times6.5^{2} - \pi \times {2.3}^{2} = 36.96\pi = 116.113... {cm}^{2} [/tex]

Answer:

116.129 cm²

Step-by-step explanation:

       [tex]\boxed{\bf Area \ of \ circle = \pi r^2}[/tex]

Area of outer circle:

    R = 6.5 cm

   Area =3.142 * 6.5 * 6.5

             = 132.75 cm²

Area of inner circle:

 r = 2.3 cm

       Area of inner circle =3.142 * 2.3 *2.3

                                        = 16.621 cm²

Area of shaded area = area of outer circle - area of inner circle

                                    = 132.75 - 16.621

                                    =  116.129 cm²

Jonas have to repay $13888 after 4 years.

Given

Principle amount of loan (P) = $12,400

Rate of interest (R) = 3%

Time period (T) = 4 years

Also the interest is not compounded, hence it is simple interest.

The formula for simple interest is (PTR)/100

Where,

P = Principle amount

T = time period

R = rate of interest

By substituting the values in the formula we get,

Simple interest =  (12400 x 4 x 3) / 100

Simple interest = 1488

Hence adding this interest to Principle sum we get

12400 + 1488 = 13888

Jonas has to repay $13888 after 4 years.

Learn more about Simple interest at

https://brainly.com/question/25845758?referrer=searchResults

#SPJ1

The value of the quadratic equation given as -9- -8x^2= -209 is 5

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The quadratic equation is given as

-9- -8x^2= -209

Add 9 to all sides of the equation

So, we have

-8x^2= -200

Divide both sides of the equation by -8

x^2= 25

Take the square roots

x = 5

Hence, the solution of the equation is 5

Read more about quadratic equations at

https://brainly.com/question/1214333

#SPJ1

We have the following:

We must apply the simple interest formula which is the following:

Where, P is the principal 3000

r is the interest rate 0.12

t is time in years

A is the total value

replacing:

The answer is $3360 at the end of the 1 year period

Coplanar lines are referred to as parallel lines because they may be extended indefinitely without ever intersecting. || is the sign meaning "parallel to." If two lines are drawn, they don't have to be parallel, and a third line runs across them as seen in the diagram below. We may obtain eight distinct angles by drawing two parallel lines, and then drawing a transverse line through them.

Four pairs of matching angles will be created from all eight angles. One of the pairings is represented by angles F and B in the preceding diagram. If the two lines are parallel, corresponding angles are congruent.

To know more about lines refer to https://brainly.com/question/18831322

#SPJ1

Answer:

In second week there is percentage limit (-ve sign) of 20% in people traveling examine to first week.

In 0.33 week there is proportion increase of 50% in human beings traveling compare to 2nd week.

In fourth week there is share limit of 75% in humans visiting evaluate to 1/3 week.

The value of b for which the difference between the fractions

 (2b - 1) / 2 and  (1 + 5b) / 4 negative will be;

⇒ b < -3

What is Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Given that;

Two fractions are,

⇒ (2b - 1) / 2 and  (1 + 5b) / 4

Since, The difference between the fractions  (2b - 1) / 2 and  (1 + 5b) / 4 negative.

So, we can formulate;

⇒ (1 + 5b) / 4 - (2b - 1) / 2 < 0

Solve for b, as;

⇒ 1 + 5b - 2 (2b - 1) < 0 x 4

⇒ 1 + 5b - 4b + 2 < 0

⇒ b + 3 < 0

Subtract 3 both side;

⇒ b + 3 - 3 < 0 - 3

⇒ b < -3

Therefore, The value of b for which the difference between the fractions  (2b - 1) / 2 and  (1 + 5b) / 4 negative will be;

⇒ b < -3

Learn more about the fraction visit:

https://brainly.com/question/20712359

#SPJ1

Note the in such type of questions the term 'probability' and 'proportion' can be used in place of each other. It is because the probability gives the proportion of favorable outcomes to the total outcomes.

Let X be the random variable representing the number of data points greater than or equal to 22.

Given that the mean and standard deviation is 18.5 and 3.25, respectively.

Consider the formula for z-score as,

So the probability is calculated as,

From the Standard Normal Distribution Table,

Substitute this value,

Thus, there is 0.1401 or 14.01% probability that a data will be greater than or equal to 22.

So, the 14.01% of the data is expected to be 22 or greater.

Given

The table,

The sample size is 27.

To find:

The mean weight of these 27 babies.

Explanation:

It is given that,

That implies,

The mean weight of 27 babies is,

Hence, the mean weight of 27 babies is 6.1 pounds.

Percentage of the cupcakes that had sprinkles = 30 %

Percentage

Percentage, often referred to as percent, is a fraction of 100. Percentage means "per 100," and denotes part a total amount. For example, 45% represents 45 out of 100.

Proportion

The proportion formula is used to depict if two ratios or fractions are equal. We can find the missing value by dividing the given values. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The first step is to divide 12 by 40 to get the answer in decimal form:

12 / 40 = 0.3000

Then, we multiplied the answer from the first step by one hundred to get the answer as a percentage:

0.3000 * 100 = 30.00%

Percentage of the cupcakes that had sprinkles = 30 %

To learn more about Percentage visit:

brainly.com/question/28269290

#SPJ4

Answer:

y=3x+3

Step-by-step explanation:

i use point (-1,0) and (0,3) then 3-0/0-(-1)=3/1=3 so (0,3) 3 is the y intercept plug in so y=3x+3is the equation

Answer:

See below

Step-by-step explanation:

Find two convenient points to calculate the slope:

0,3   and   -1,0         slope =  m =  (3-0) / ( 0 - -1) = 3

  and the y axis intercept = 3   (from looking at graph)

line equation is   y = mx + b             ( where b is the y-axis intercept)

                     y = 3x + 3

The area in square inches of the tile is 9 / 4 t .

She makes rectangular kitchen tiles with an area of t square inches.

Therefore,

area of the rectangular kitchen tiles = lw

t = lw

l = t / w

w = t / l

Therefore, the tile is 3 / 4 as long and 3 times wide as her kitchen tiles.

Hence,

area of the tile = 3 / 4 t / w × 3(t / l)

area of the tile = 9 / 4 × t² / lw

where

lw = t

Hence,

area of the tile  = 9 / 4 × t² / t

area of the tile  = 9 / 4 × t

Therefore,

area of the tile  = 9 / 4 t

learn more on rectangle and area here: https://brainly.com/question/27919973

#SPJ1

P(A). P(Y)= 0.5*0.6=0.3

Probability: - Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.

Number of cases of A, N(A)= 250,

So,

     P(A)=250/500 =0.5

and

      N(Y)= 300, so P(Y)=300/500 =0.6

N(A and Y)= 175 so P(A and Y)= 175/500=0.35

A and Y are mutually exclusive implies A and Y donot have any elements in common, but here there are 175 people who are below 30 years and under the influence of alcohol, So they are not mutually exclusive!!

For A and Y to be independent, the Probability of A intersection Y should be equal to the product of their respective probabilities,

in this case P(A). P(Y)= 0.5*0.6=0.3 which is not equal to P( A intersection Y) (0.35)

So, A and Y are not mutually Independent also.

Learn more about Probability from the link

https://brainly.com/question/24756209

#SPJ4

Answer: 60 divided by 4

Step-by-step explanation:

Answer:

The average would be $15 for each shirt.

Step-by-step explanation:

divide the amount of money by the amount of shirts.