Write the following repeating decimal using a bar over the repeated digit(s).
0.355555555...

The rectangular form of z is √(2) + √(2)i.

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

In other words, a complex number is a number that combines both a real component (a) and an imaginary component (bi). The real component represents the position of the complex number on the real number line, while the imaginary component represents its position on the imaginary number line.

Complex numbers are used in many branches of mathematics, including algebra, geometry, calculus, and engineering. They are particularly useful for solving problems involving equations with roots that are not real numbers, and for modeling complex phenomena in physics and engineering, such as alternating current and electromagnetic waves.

The rectangular form of a complex number is defined as a + bi, where a is the real part and b is the imaginary part.

Given z = √(2) * [cos(-π/4) + i sin(-π/4)], we can find a and b as follows:

a = √(2) * cos(-π/4)

b = √(2) * sin(-π/4)

Using the identity cos(-x) = cos(x) and sin(-x) = -sin(x), we get:

a = √(2) * cos(π/4) = √(2) * √(2)/2 = √(2)

b = √(2) * sin(π/4) = √(2) * √(2)/2 = √(2)

So, the rectangular form of z is √(2) + √(2)i.

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According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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The answer to this Question is A we can use basic knowledge from linear equations to find the answer

What is Linear Equation?

Linear Equation is a equation in which degree of variables is 1 only

Yes the given case is possible only under some conditions that we can define as follows and as given in Linear Equations from Options

together cole and maggie have won 30 games and we are also given that  out of those 30 maggie has won 4 games

we should closely see at Linear Equations given in Options.

therefore cole has won 26 games which is more than 13

Hence the answer to the Question is Yes

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Answer:

4

Step-by-step explanation:

trust

The value of DA in parallelogram ABCD is 4 inches.

A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel to each other.

In parallelogram ABCD:

AB = DC, AD = BC

Hence:

8x - 5 = 3x + 10

5x = 15

x = 3 units

AB = 8(3) - 5 = 19 inches

Let y = AD = BC:

AB + BC + DC + AD = perimeter

19 + 19 + y + y = 46

y = 4 inches

The value of DA in parallelogram ABCD is 4 inches.

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The surface area of the rectangular prism is 396 square inches

He will need 504 tlles

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

The number of tiles is 7 * 12 * 6 = 504

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Question

wants to tile the surface of a rectangular storage case that is 7 inches​ long, 12 inches​ wide, and 6 inches tall. If he uses all green​ tiles, how many tiles will he​ need?

The solution of quadratic equation is,

a = 7 / 3

b = - 5/3

c = 2

We have to given that;

Equation is,  

y = ax² + bx + c  . (i)

And, Points are (- 1, 6), (2, 8) and (0, 2)

Now, We can simplify as;

Plug x = - 1, y = 6 in (i);

6 = a (- 1)² + b (- 1) + c

6 = a - b + c

Plug x = 2, y = 8

8 = a (2)² + b (2) + c

8 = 4a + 2b + c

Plug x = 0, y = 2;

c = 2

Simplify al the above equation we get;

a = 7 / 3

b = - 5/3

c = 2

Thus, The solution is,

a = 7 / 3

b = - 5/3

c = 2

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The values of a, b, and c that satisfy the equation y = ax² + bx + c and pass through the points (-1, 6), (2, 8), and (0, 2) are:

a = 7/3

b = -5/3

c = 2

We have,

To find the values of a, b, and c for the quadratic function y = ax² + bx + c that passes through the given points (-1, 6), (2, 8), and (0, 2), we can substitute the coordinates into the equation and form a system of equations to solve.

Let's substitute the x and y values of the three points into the equation:

Point (-1, 6):

6 = a(-1)² + b(-1) + c

6 = a - b + c ............(1)

Point (2, 8):

8 = a(2)² + b(2) + c

8 = 4a + 2b + c ............(2)

Point (0, 2):

2 = a(0)² + b(0) + c

2 = c ............(3)

Now we have a system of equations:

Equation (1): 6 = a - b + c

Equation (2): 8 = 4a + 2b + c

Equation (3): 2 = c

From Equation (3), we can determine that c = 2.

Substituting this value into Equations (1) and (2), we get:

Equation (1): 6 = a - b + 2

Equation (2): 8 = 4a + 2b + 2

Simplifying these equations:

Equation (1): a - b = 4 ............(4)

Equation (2): 4a + 2b = 6 ............(5)

Now we can solve this system of equations (4) and (5) to find the values of a and b.

Multiplying Equation (4) by 2, we get:

2a - 2b = 8 ............(6)

Adding Equation (6) and Equation (5):

(2a - 2b) + (4a + 2b) = 8 + 6

6a = 14

a = 14/6

a = 7/3

Substituting the value of a back into Equation (4):

(7/3) - b = 4

7 - 3b = 12

-3b = 12 - 7

-3b = 5

b = -5/3

Therefore,

The values of a, b, and c that satisfy the equation y = ax² + bx + c and pass through the points (-1, 6), (2, 8), and (0, 2) are:

a = 7/3

b = -5/3

c = 2

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)

\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)

Answer:

11.1803398875

Step-by-step explanation:

Answer:

y<5/3 I believe. sorry if I am wrong!

Answer:

To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.

Method 1: The fourth vertex is directly below the first vertex.

In this case, the coordinates of the fourth vertex are (5, 9), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . X

Method 2: The fourth vertex is directly to the right of the first vertex.

In this case, the coordinates of the fourth vertex are (1, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

X . . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Method 3: The fourth vertex is diagonal to the first vertex.

In this case, the coordinates of the fourth vertex are (5, 5), as shown below:

Y 9 8 7 6 5 4 3 2 1 0

X 1 2 3 4 5 6 7 8 9

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . X . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .

Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

The blanks in order for the bottom row are 8, 9. The blanks for the top row is 6.

Step-by-step explanation:

It is counting by 1's starting at 5 for the bottom row and starting at 0 counting by 1's in the top row.

Answer:

in order from left to right, 8, 9, 6

Step-by-step explanation:

Since he already wrote 5 pages and will write 1 more every hour, the top row (# of hours) + 5 will equal the bottom row (pages written). 3+5=8, 4+5=9, and 6+5=11, so from left to right, it's

8, 9, 6

Answer:

45, 90/2 equals 45. everytime you need to find it you do miles/hours

1.    in this exercise you  must substitute the value of  of x = 12  in the equation of the parable given, if the result is 10 then the ball pass through the hoop

2.    Y = (-.125)(12)^2+ (1.84)(12)+6 = -18+22.08+6 = 10.06≅10 , of  this form it is demonstrated, that the ball pass through the  hoop

Points A, B, and C are collinear then the possibility of AB will be equal to 4.7. Hence, option A is correct.

Points that are parallel to or within a single line are referred to as collinear points. In Euclidean space, two or more points have been shown to be collinear if they are situated on a line that is either close to or far from another.

As per the given information in the question,

The case is that when B is in between A and C, which means A, B, and C are collinear.

So,

AB + BC = AC

AB + 8.5 = 13.2

AB = 13.2 - 8.5

AB = 4.7

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Answer: 2300 kg.

Step-by-step explanation: The size and shape of the boat is irrelevant for this problem.

The mass of the water displaced by the boat is 2300kg.

The law of buoyancy states that buoyancy force on an object is equal to the weight of the fluid displaced by the object.

Buoyant force = weight of the fluid displaced by the object

The buoyant force acting on motorbot

= density of water(d) * gravitational acceleration(g) * Volume of the water displaced by the object(V)

We know that Buoyant force = weight of the body(motorboat)

\(dgV =2300g\)

\(dV=2300\)

So the mass of the displaced water =2300kg.

Hence, the mass of the water displaced by the boat is 2300kg.

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Answer:

(A)

Step-by-step explanation:

The survey follows of women's height a normal distribution.

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

The new height requirements would be 57.7 to 68.6 inches

The given parameters are:

\mathbf{\mu = 63.5}μ=63.5 --- mean

\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation

(a) Percentage of women between 58 and 80 inches

This means that: x = 58 and x = 80

When x = 58, the z-score is:

\mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

This gives

\mathbf{z_1= \frac{58 - 63.5}{2.5}}z

1

=

2.5

58−63.5

\mathbf{z_1= \frac{-5.5}{2.5}}z

1

=

2.5

−5.5

\mathbf{z_1= -2.2}z

1

=−2.2

When x = 80, the z-score is:

\mathbf{z_2= \frac{80 - 63.5}{2.5}}z

2

=

2.5

80−63.5

\mathbf{z_2= \frac{16.5}{2.5}}z

2

=

2.5

16.5

\mathbf{z_2= 6.6}z

2

=6.6

So, the percentage of women is:

\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z

2

)−P(z<z

1

)

Substitute known values

\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)

Using the p-value table, we have:

\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034

\mathbf{p = 0.9860948}p=0.9860948

Express as percentage

\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%

\mathbf{p = 98.60948\%}p=98.60948%

Approximate

\mathbf{p = 98.61\%}p=98.61%

This means that:

The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.

So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.

(b) Change of requirement

Shortest = 1%

Tallest = 2%

If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).

So, we have:

Shortest = 1% to 98%

This means that:

The p values are: 1% to 98%

Using the z-score table

When p = 1%, z = -2.32635

When p = 98%, z = 2.05375

Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

Substitute \mathbf{z = -2.32635}z=−2.32635

\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=

2.5

x−63.5

Multiply through by 2.5

\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5

Make x the subject

\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5

\mathbf{x = 57.684125}x=57.684125

Approximate

\mathbf{x = 57.7}x=57.7

Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=

σ

x−μ

\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=

2.5

x−63.5

Multiply through by 2.5

\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5

Make x the subject

\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5

\mathbf{x= 68.634375}x=68.634375

Approximate

\mathbf{x= 68.6}x=68.6

Hence, the new height requirements would be 57.7 to 68.6 inches

A) The prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.

B) As there is still variability in the number οf cases that may arise due tο chance.

Prοbability is the study οf the chances οf οccurrence οf a result, which are οbtained by the ratiο between favοrable cases and pοssible cases.

(A) We can use the binοmial distributiοn tο mοdel the number οf Americans in a sample οf 100 whο are diagnοsed with lung cancer. Let X be the number οf Americans in the sample whο are diagnοsed with lung cancer. Then X ~ Bin(100, 0.0625).

We want tο find P(X < 5). We can use the nοrmal apprοximatiοn tο the binοmial distributiοn, since n is large and p is nοt tοο clοse tο 0 οr 1. Using the cοntinuity cοrrectiοn, we have:

P(X < 5) = P(X < 5.5)

\(= P((X - np) \sqrt{(np(1-p))} < (5.5 - np)\sqrt{(np(1-p))})\)

\(= P(Z < (5.5 - 6.25100)\sqrt{(6.25100*(1-0.0625)))\)

= P(Z < -3.52)

= 0.0002 (frοm standard nοrmal table)

Therefοre, the prοbability that less than 5% οf Americans in a sample οf 100 will be diagnοsed with lung cancer is very small, οnly 0.02%.

(B) If 20 οr mοre Americans whο smοke cigarettes are diagnοsed with lung cancer in a sample οf 100, this is quite rare based οn the expected rate οf 6.25% in the general pοpulatiοn. This suggests that smοking is a significant risk factοr fοr develοping lung cancer, as the οbserved rate is much higher than the expected rate.

Hοwever, we cannοt cοnclude that all smοkers will develοp lung cancer, as there is still variability in the number οf cases that may arise due tο chance.

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Step-by-step explanation:

the inside expression of an absolute value expression can be positive or negative, but the result is only the positive one.

therefore, for our example here the negative case would be

2.5x - 6.8 = -12.9

which gives us

2.5x = -6.1

x = -6.1/2.5 = -2.44

and the positive case would be

2.5x - 6.8 = 12.9

and that gives us

2.5x = 19.7

x = 19.7/2.5 = 7.88

Probability = # of desired options / # of total options

Our desired option is blue and there are 9 blue marbles in the bag.

There are 32 total marbles (options) in the bag.

P(blue) = 9 / 32 = 0.28125 = 28.125%

Hope this helps!

Hi there!  

»»————-　★　————-««

I believe your answer is:  

"Isolate the variable  using inverse operations."

»»————-　★　————-««  

Here’s why:

To solve for a variable, we would have to isolate it on one side.

To isolate it, we would use inverse operations on both sides on the equation until the variable is isolated.

There are no like terms in the given equation.

⸻⸻⸻⸻

\(\boxed{\text{Solving for 'z'...}}\\\\\frac{z}{6} = 36\\-------------\\\rightarrow (\frac{z}{6})6 = (36)6\\\\\rightarrow \boxed{z = 216}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

First option: Isolate the variable using inverse operations

Step-by-step explanation:

z/6 = 36

Since we already have the equation set up and cannot simplify any further, we must try to isolate the variable, z, by using inverse operations.

The inverse operation of division is multiplication, so to isolate z, we multiply 6 on each side:

z/6 · 6 = 36 · 6

z = 216

Step-by-step explanation: To fill in the table, we will need to first count the number of times each wait time appears in the given data. We can then use these counts to fill in the Frequency column of the table. We will also need to calculate the relative frequency of each wait time, which is the number of times it appears in the data divided by the total number of data points. We can then use these relative frequencies to fill in the Relative Frequency column of the table, expressed as a percentage.

Here is the completed table:

Wait Time (minutes) Frequency Relative Frequency (%)

5                                     5                 11.36

10                                 4                  9.09

15                                 7                  15.91

20                                6                   13.64

25                                7                   15.91

30                                 4                   9.09

35                                5                    11.36

40                                3                    6.82

45                                 2                    4.55

50                                 1                    2.27

60                                  2                    4.55

75                                  1                       2.27

Note that the total number of data points is 44, so each relative frequency is calculated as the corresponding frequency divided by 44.

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

The following code is written in Python. It is a function that takes in the number of miles as an argument and returns the number of laps that those miles represents.

def miles_to_laps(miles):

   laps = miles / 0.25

   return laps

Answer:

depending on what it is I’ll try my best to help

Step-by-step explanation:

There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.

To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.

Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.

Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.

To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.

Therefore, there will be 12 slices of pizza left over.

To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.

If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.

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Answer: C=2πr

r Radius

Answer:

Step-by-step explanation:

Total sales = x

Correct choice is C

The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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The radius of the circle is determined as r = 5.

option B.

The radius of the circle is determined by applying the general formula for circle equation.

(x - h)² + (y - k)² = r²

where;

The given circle equation;

4x² + 4y² = 100

Simplify the equation by dividing through by 4;

x² + y² = 25

x² + y² = 5²

So from the equation above, the radius of the circle corresponds to 5.

r = 5

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