(-7i)(3+3i)(a) Write the trigonometric forms of the complex numbers. (Let0 ≤ theta < 2pi.)(-7i) =(3+31) =(b) Perform the indicated operation using the trigonometric forms. (Let0 ≤ theta< 2pi.)(c) Perform the indicated operation using the standard forms, and check your result with that of part (b).

According to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.

Given :

Blood pressure readings are normally distributed with a mean of 125 and a standard deviation of 8.

The formula of z-score is used to determine the probability that their mean blood pressure will be less than 127. The formula of z score is given by:

[tex]z = \frac{\frac{x - m}{\alpha } }{\sqrt{n} }[/tex]

Now, substitute the values of known terms in the above equation.

[tex]z = \frac{\frac{127 - 125}{8} }{\sqrt{100} }[/tex]

[tex]z = \frac{\frac{2}{8} }{10} }[/tex]

Further, simplify the above expression.

z = 2.5

P(z < 2.5) = 0.9938

So, the probability is 99.38%.

Therefore, according to the normal distribution table, the probability that their mean blood pressure will be less than 127 is 99.38%.

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The starting number of Michael's thought is 96

From the question, the given parameters are:

The above sequence of statements can be represented as

x * (100÷8) + 6.50 = 1206.5

Where x represents the number

So, we have

x * (100÷8) + 6.50 = 1206.5

Evaluate the quotient

x * 12.5 + 6.50 = 1206.5

Subtract 6.50 from both sides

x * 12.5 = 1200

Divide both sides by 12.5

x = 96

Hence, the initial number is 96

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The value of x in the given equation is 24.

Given equation:

(2/3)x + 4 = (5/6)x

We have to find the value of x by eliminating the fraction.

Fraction

Fraction is  termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.

LCM (3,6) = 6

Multiplying the whole equation by 6, we get:-

(2/3)x*6 + 4*6 = (5/6)x*6

4x + 24 = 5x

5x - 4x = 24

x = 24

Hence, the value of x is 24.

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SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The sum of interior angles of a polygon is:

CONCLUSION:

The final answer is:

The system of equations has one solution, so it is consistent and independent, the correct option is C.

Here we have the system of equations:

x = 5

y = 6

-x - y + z = 0

By replacing the first and second equations into the third one, we get:

-5 - 6 + z = 0

-11 + z = 0

z = 11

So the solution is (5, 6, 11)

So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).

Then the correct option is C.

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As per the concept of division, they sold 271 cookies boxes per day and there are 6 cookies are remained.

Division:

Division means splitting of a large group into smaller groups such that every group will have an equal number of items.

There are four parts of the division, which are dividend, divisor, quotient, and remainder.

Given,

The Tasty Cookies Factory has a new robotic oven that produces 3,258 cookies each day. They sell the cookies in boxes of 12 cookies each.

Here we need to find the number of boxes sold per day.

Through the given question we know that,

Number of cookies per day = 3,258

Number of cookies in one box = 12

So, the dividend is 3,258 and the divisor is 12.

So, the number of boxes per day is illustrated using the following diagram.

Based on these, there are 271 boxes are sold per day with 6 remaining cookies.

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Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;

The red graph represents x + y =<20

The blue graph represents 5x +8y =>120

Observe that the region where the blue and red are "mixed" together represent the solution region.

Option A (4, 15)

Option B (5, 12) and

Option C (10, 9) are possible solutions

Answer: [tex]\angle 2=83^{\circ}[/tex]

Step-by-step explanation:

By the alternate interior angles theorem,

[tex]5x+2=3x+40\\\\2x=38\\\\x=19[/tex]

This means that [tex]5x+2=3x+40=97[/tex].

Since [tex]\angle 2[/tex] and the [tex]97^{\circ}[/tex] form a linear pair, they add to 180 degrees. So, [tex]\angle 2=83^{\circ}[/tex]

Answer:

Angle VSR + Angle SRU = 180° (corresponding angles, sum of angles on a straight line = 180°)

(5x + 4) + (44 + x) = 180

6x + 48 = 180

6x = 132

x = 22

The next three terms for the pattern will be 12, 48, 192 and 768.

It is important to note that a pattern is used to show the sequence of events.

In this case, the first term of a pattern is 12 and the pattern follows the rule "multiply by 4."

This will be:

First term = 12

Second term = 12 × 4 = 48

Third term = 48 × 4 = 192

Fourth term = 768

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Answer:

no solutions

Step-by-step explanation:

2x - y = 3 → (1)

- 4x + 2y = 5 → (2)

multiply (1) by 2 and add to (2)

4x - 2y = 6 → (3)

add (2) and (3) term by term

0 + 0 = 11

0 = 11 ← not possible

this indicates the system has no solution

Answer:

y = 1/2x - 5

Step-by-step explanation:

The y intercept is negative 5. The line slowly goes one point up and two points to the right, staying positive. This makes it 1/2.

Answer:

Step-by-step explanation:  

So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!

The largest possible value in the list is 35.

What is mean, median and mode?

Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.

Given: There is a list of 11 positive integers.

Has a mean of 10, a median of 9 and a unique mode of 8.

Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).

If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.

The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.

The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.

Therefore, the largest possible value of an integer in the list is, 35.

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Answer:

24

Step-by-step explanation:

-6*(-4)

The negative signs cancel:

6*4

24

Given the system of equations:

x + y - z = 4 eq.(1)

3x + 2y + 4z = 17 eq.(2)

-x + 5y + z = 8 eq.(3)

Add the equations 1 and 3

so,

x + y - z + ( -x + 5y + z ) = 4 + 8

x + y - z - x + 5y + z = 12

6y = 12

y = 12/6 = 2

Substitute with y at eq. (1)

So,

x + 2 - z = 4

x - z = 4 - 2

x - z = 2 eq. (4)

Substitute with y at eq.(2)

3x + 2 * 2 + 4z = 17

3x + 4 + 4z = 17

3x + 4z = 17 - 4

3x + 4z = 13 eq.(5)

solve the equations (4) and (5) together

x - z = 2

3x + 4z = 13

Multiply [ x - z = 2 ] by 4

4x - 4z = 8

3x + 4z = 13

Add the last two equations

4x - 4z + 3x + 4z = 8 + 13

7x = 21

Divide both sides by 7

x = 21/7 = 3

So, x = 3 and y = 2

Substitute with the values of x and y at the equation [ -x + 5y + z = 8 ]

So,

-3 + 5 * 2 + z = 8

solve for z

-3 + 10 + z = 8

z = 8 + 3 - 10

z = 11 - 10 = 1

So,

x = 3 , y = 2 and z = 1

Answer:

The total T can be described as

[tex]T = (B+(B*.15))+1[/tex]

My first step is to draw a picture

We know that the length is 2 times the width

L = 2w

We are given a width of 4.6 yards

L = 2(4.6) = 9.2 yards

We can find the area by using the formula

A = l*w

A = 9.2 * 4.6

A =42.32 yd^2

ANSWER:

STEP-BY-STEP EXPLANATION:

In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people

solving for x:

a. The decrease road line verified by given function while increase in the highway The function representing the railroad miles has a negative​ slope, indicating a decrease. The function representing the highway miles has a positive​ slope, indicating an increase.

b. It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.

Given

The function y =-1518x + 144.068 represents the railroad miles.

While the function y =-360.5x + 155.18models the number of highway miles.

For each function, x is the number of years after 1995.

The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.

Therefore,

-1518x + 144.068=  -360.5x + 155.18

-1518x+360.5x = 155.18-144.068

1157.5x             = 11.112

                x      = 9

Then,

1995 - 9 = 1986

It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.

A mile, sometimes an international mile or base mile to distinguish it from other miles, is an imperial unit in the United Kingdom and a standard unit of distance in the United States. both are based on the older English unit of length, which is 5280 English feet or 1760 yards. The legal mile was standardized by an international agreement between the Commonwealth of Great Britain and the United States in 1959, when it was officially redefined in SI units to exactly 1609.3 meters.

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Answer: Solve 5x=(2x+3)

Step-by-step explanation:

We need to convert 40 degrees to radians:

Then, we need to use the next equation:

Solve it:

Hence, 40 degrees is equal to 2/9π radians.

The measure of the angle PRS is given as follows:

m<PRS = 45º.

As stated in this problem, these following angles are given:

MRQ and and QRN form a ray, hence they are supplementary angles.

For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:

142 + x = 180

x = 180 - 142

x = 38º.

The entire diagram forms an angle of 360º, hence:

142 + 38 + 90 + m<MRS = 360º.

270 + m<MRS = 360º

m<MRS = 90º.

The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:

The diagram is given by the image at the end of the answer.

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When 2 to the power of hundred is divided by 5 it show s remainder of 1

2 to the 100th power is solved as follows

2 ^ 100 = 1.2676506 * 10^30

This is solved using a calculator and the solution means that

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2...............2   (2 multiplying itself till the number of 2's are up to 100)

This gives the value = 1.2676506 * 10^30

Division of the  2^100, by 5

2^100 / 5

2^1 / 5 remainder =2

2^2 / 5 remainder = 4

2^3 / 5 remainder = 3

2^4 / 5 remainder = 1

2^5 / 5 remainder = 2

2^6 / 5 remainder = 4

2^7 / 5 remainder = 3

2^8 / 5 remainder = 1

2^9 / 5 remainder = 2

2^10 / 5 remainder = 4

2^11 / 5 remainder = 3

It can be seen that it generates a pattern which is

The pattern counts in 4's. If we follow the pattern and count to 2^30

= 100 / 4

= 25 ⇒ this is a multiple of 4 and multiples of 4 goes with remainder 1

This is to say

2^97 / 5 remainder = 2

2^98 / 5 remainder = 4

2^99 / 5 remainder = 3

2^100 / 5 remainder = 1

Hence 2^100 divided by 5 will give a remainder of 1

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Answer: Undefined

Step-by-step explanation:

There is not enough information to complete the task.

Answer:

Jonathan and Seth

Step-by-step explanation:

multiple the laps by 2 youll get the minutes

Answer: the answer is -4280

Step-by-step explanation:

The line given passes through two points. These are (-6,0) and (0,-8).

Remember that two lines are perpendicular if the product of their slopes is -1. So, the first thing we're going to do is to find the slope of the line given.

The slope between two points (x1,y1) and (x2,y2) can be found using the formula:

If we replace our values:

To find other perpendicular line to this one, we have to find a number which multiplication with -4/3 is -1.

This number is clearly 3/4. Because

Therefore, the slope of the perpendicular line must be 3/4, and the original slope is -4/3.

If we graph this:

Answer: 26

Step-by-step explanation:

[tex]f(-2)=-2(-2)^2 -(-2)+3=13\\\\2f(-2)=2(13)=26[/tex]