The M&M jar has a square base with a length and width of 7 cm and a height of 6.5 cm. What would be the most reasonable lower limit for the number of M&M`s in the jar of the choices below?

A.10
B.100
C.1,000
D.10,000

Answer:

10

Step-by-step explanation:

20/2=10

Answer:10

Step-by-step explanation:

Answer:

The system of equations is

[tex]f=4n[/tex]  and  [tex]f=n+27[/tex]

Fred's age is 36 years old and Nathan's age is 9 years old

Step-by-step explanation:

Let

f -----> Fred's age

n ----> Nathan's age

we know that

[tex]f=4n[/tex]-----> equation A

[tex]f=n+27[/tex] ----> equation B

equate the equations and solve for n

[tex]4n=n+27\\4n-n=27\\3n=27\\n=9[/tex]

Find the value of f

[tex]f=4(9)=36[/tex]

therefore

Fred's age is 36 years old and Nathan's age is 9 years old

Answer:

The system of equations is f=4n  and  f=n+27

Step-by-step explanation:

Answer:

width = 23 inches

length = 57 inches

Step-by-step explanation:

Let x inches be the width of the rectangular solar panel.

So,

width = x inches

3 times the width = 3x inches

12 inches shorter than 3 times the width = 3x - 12 inches

length = 3x - 12 inches

The perimeter of the rectangle is

[tex]P=2(\text{Width}+\text{Length})[/tex]

Hence,

[tex]160=2(x+3x-12)\\ \\160=2(4x-12)\\ \\80=4x-12\ [\text{Divided by 2}]\\ \\4x=80+12\\ \\4x=92\\ \\x=23\ inches\\ \\3x-12=3\cdot 23-12=69-12=57\ inches[/tex]

Answer:

The answer to your question is below

Step-by-step explanation:

I think it will easy to understand if we graph this information but let's explain it without the graph.

According to the information given, we know that f(x) represents the number of baskets and x the number of players at the practice.

So, if we have the point (12, 36) we can conclude that during practice there were 12 players and there were 36 baskets.

For me, it makes sense.

Answer: Yes. The input and output are both possible

Step-by-step explanation:

The reason why is because f(x) stands for y and in parenthe this is how it looks like(x,y) and if you put the numbers in you have (12,36) 12 stands for the number of players and f(x) or y stands for the number of baskets made.

Answer:

  40.56 ft

Step-by-step explanation:

The perimeter is the sum of the lengths of the "sides" of this figure. Starting from the left side and working clockwise, the sum is ...

  P = left side (8 ft) + top side (10 ft) + semicircle (1/2×8 ft×π) + bottom side (10 ft)

  = 28 ft + 4π ft

  = (28 +12.56) ft

  P = 40.56 ft

Answer:

Top part lenght= 24 ft.

Middle part= 72 ft.

Bottom part = 144 ft.

Step-by-step explanation:

First we assign varibales to each rocket part

top part length= x;

middle part length= y;

bottom part length= z;

Then from the reading we can write the next equations:

X=1/6 Z; (1)

Y=1/2 Z; (2)

X + Y +Z = 240 (3)

Then solving, we replace x and y, in the equation (3)

1/6 z + 1/2 z + z = 240

Multiply by 6 both sides:

6/6 z + 6/2 z + 6 z = 1440

z + 3 z + 6 z = 1440

Then grouping similar terms

10 z = 1440

z= 144

Then replacing in (1) and (2)

Y=1/2 *144=72

X=1/6*144= 24

Answer:

Last year, the average cost of a traditional Thanksgiving dinner was $48.91.

Step-by-step explanation:

If this year the cost of a traditional Thanksgiving dinner was decreased by 1.76% compared to last year, then

last year cosr - 100%

this year cost - 100%-1.76%=98.24%

So,

$x - 100%

$48.05 - 98.24%

Write a proportion:

[tex]\dfrac{x}{48.05}=\dfrac{100}{98.24}[/tex]

Cross multiply:

[tex]98.24x=48.05\cdot 100\\ \\98.24x=4,805\\ \\x\approx 48.91[/tex]

Last year, the average cost of a traditional Thanksgiving dinner was $48.91.

Final answer:

The average cost of a traditional Thanksgiving dinner in the last year was approximately $48.91, calculated by dividing this year's cost of $48.05 by the percentage decrease converted to a decimal (1 - 0.0176).

Explanation:

To calculate the average cost of a traditional Thanksgiving dinner in the last year, given this year's average cost and the percentage decrease, we can use the formula original price = discounted price / (1 - discount rate). The discount rate in this case is the percentage decrease in cost, expressed as a decimal. Given that this year's average cost is $48.05 and the decrease is 1.76%, we first convert the percentage to a decimal by dividing by 100, which gives us 0.0176.

The formula becomes:

original price = $48.05 / (1 - 0.0176)

original price = $48.05 / 0.9824

original price = $48.91 approximately

Therefore, the average cost of a traditional Thanksgiving dinner in the last year was about $48.91.

Answer:

[tex]dAB=10\ units[/tex]

Step-by-step explanation:

we know that

The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points

The formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

A(1, 1) and B(7, −7)

Let

(x1,y1)=A(1, 1)

(x2,y2)=B(7, −7)

substitute the given values in the formula

[tex]dAB=\sqrt{(-7-1)^{2}+(7-1)^{2}}[/tex]

[tex]dAB=\sqrt{(-8)^{2}+(6)^{2}}[/tex]

[tex]dAB=\sqrt{64+36}[/tex]

[tex]dAB=\sqrt{100}[/tex]

[tex]dAB=10\ units[/tex]

Answer:  The required distance between the points between A(1, 1) and B(7, −7) is 10 units.

Step-by-step explanation:  We are given to explain the distance formula. Also, to calculate the distance between A(1, 1) and B(7, −7).

Distance formula :  The distance between any two two points with co-ordinates (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points A(1, 1) and B(7, −7) is given by

[tex]D\\\\=\sqrt{(7-1)^2+(-7-1)^2}\\\\=\sqrt{36+64}\\\\=\sqrt{100}\\\\=10.[/tex]

Thus, the required distance between the points between A(1, 1) and B(7, −7) is 10 units.

Answer:

The answer to your question is:  7.00 x 10⁶

Step-by-step explanation:

- Write a number with a non-zero digit                           7

- Six place values away from the decimal point             7 000 000.00

-Write this number in scientific notation                          7.00 x 10⁶

An example of a number with its first non-zero digit six places away from the decimal is 0.000001, which is written in scientific notation as 1 × 10^-6 by moving the decimal six places to the right.

An example of a number with its first non-zero digit six place values away from the decimal point is 0.000001. To write this number in scientific notation, we follow the standard convention: moving the decimal point such that there is only one non-zero digit to the left of the decimal point and counting the number of places the decimal point has moved to determine the power of 10.

In this case, we move the decimal point six places to the right, which gives us 1 × 10^-6. This means that 0.000001 in scientific notation is expressed as 1 × 10^-6 .

Answer:

I am trying on this but I can solve you the 10th question

Answer:

12.4 miles, N84.4°E

Step-by-step explanation:

Split the translation over the components parallel to the direction S>N and W>E, then calculate the sum of both components, and get magnitude and direction of the movement. Here's my calculation, double check them regardless.

For the first hour, it travels [tex] 8.5 cos 37.5 [/tex] north and [tex] 8.5 sin 37.5 [/tex] east. Once the wind changes, it flies [tex] 6*1.5 cos (180-52.5) = 9 cos 127.5 [/tex] "north" ( the actual movement is southbound, which will appear calculating the cosine and getting a negative number) and [tex]6*1.5 sin (180-52.5) = 9 sin 127.5 [/tex]. The complete movement is 1.2 miles N and 12.3 miles E. The total movement is, with the Pythagorean theorem, 12.4 miles total, and the angle it forms with the north direction is the [tex]tan^{-1} \frac{12.3}{1.2} = 84.4°[/tex].

Answer:

Step-by-step explanation:

The radius is half the diameter, so is ...

  r = d/2 = 15 cm/2 = 7.5 cm

The area formula is ...

  A = πr²

Filling in the radius, we have ...

  A = π·(7.5 cm)² = 56.25π cm² ≈ 176.7 cm² . . . area

__

The circumference formula is ...

  C = πd

Filling in the diameter, we have ...

  C = π·(15 cm) = 15π cm ≈ 47.1 cm . . . circumference

Answer:

Here's ur answer

Step-by-step explanation:

Answer:

(-37+43)-44=x

Step-by-step explanation:

i put the parentheses only because of PEMDAS. it's a pretty straightfoward question. To put it in an expression however, I'm not sure. Best of luck!

Answer:

31 emails, but I can't do a # number line.

Step-by-step explanation:

Answer: There are 31 emails left in her inbox.

Step-by-step explanation:

Since we have given that

Number of emails in her inbox = 78

Number of emails she deleted = 47

We need to find the number of emails that are left in her inbox.

So, for left we would use "Subtraction operator"

So, Number of emails left in her inbox = Number of emails in her inbox - Number of emails she deleted.

[tex]=78-47\\\\=31[/tex]

Hence, there are 31 emails left in her inbox.

Answer:

A

Step-by-step explanation:

from the graph you can tell that there is a vertical asymp. at -3.

In the anwers A is the only one with vertical asymp. at -3.

Answer:

A f(x)=[tex]\frac{x}{x+3}[/tex]

Step-by-step explanation:

To answer this question, to identify which rational function relates to that graph we must at first look for Rational Function in this form:

[tex]P(x)=\frac{Q(x)}{R(x)}[/tex]

Where P(x)= Polynomial Quotient, Q(x)=Quotient, R(x)=Remainder. Q(x) and R(x) are Polynomial Functions.

So exclude B, then C, for they do not fit as Polynomial Functions.

Then rather than setting the graph, the second step would be looking for the vertical asymptote, given by the equation on the denominator. We must detach it from the original function then solve it.

x+3=0 ∴ x=-3

Answer:

Area = length * width

11.25 sq ft = 4.5 ft * width

width = 11.25 / 4.5

width = 2.5 feet

5/2 feet = 2.5 feet

answer is D

Step-by-step explanation:

Answer:

program status word

Step-by-step explanation:

The acronym for PSW is Program Status Word. The Program Status Word or the PSW consists of  status bits which shows the present Central Processing Unit state.

                    The PSW or Program Status Word is IBM System/360 architecture which means it is an independent model architecture for S/360 series of computers developed by IBM.

The status register contains all the information about the processor.

Thus the answer is program status word.

Answer:

a.[tex]P(E_1/A)=0.0789[/tex]

b.[tex]P(E_2/A)=0.395[/tex]\

c.[tex]P(E_3/A)=0.526[/tex]

Step-by-step explanation:

Let [tex]E_1,E_2,E_3[/tex] are the events that denotes the good drive, medium drive and poor risk driver.

[tex]P(E_1)=0.30,P(E_2)=0.50,P(E_3)=0.20[/tex]

Let A be the event that denotes an accident.

[tex]P(A/E_1)=0.01[/tex]

[tex]P(A/E_2=0.03[/tex]

[tex]P(A/E_3)=0.10[/tex]

The company sells Mr. Brophyan insurance policy and he has an accident.

a.We have to find the probability Mr.Brophy is a good driver

Bayes theorem,[tex]P(E_i/A)=\frac{P(A/E_i)\cdot P(E_1)}{\sum_{i=1}^{i=n}P(A/E_i)\cdot P(E_i)}[/tex]

We have to find [tex]P(E_1/A)[/tex]

Using the Bayes theorem

[tex]P(E_1/A)=\frac{P(A/E_1)\cdot P(E_1)}{P(E_1)\cdot P(A/E_1)+P(E_2)P(A/E_2)+P(E_3)P(A/E_3)}[/tex]

Substitute the values then we get

[tex]P(E_1/A)=\frac{0.30\times 0.01}{0.01\times 0.30+0.50\times 0.03+0.20\times 0.10}[/tex]

[tex]P(E_1/A)=0.0789[/tex]

b.We have to find the probability Mr.Brophy is a medium driver

[tex]P(E_2/A)=\frac{0.03\times 0.50}{0.038}=0.395[/tex]

c.We have to find the probability Mr.Brophy is a poor driver

[tex]P(E_3/A)=\frac{0.20\times 0.10}{0.038}=0.526[/tex]

Final answer:

The probability that Mr. Brophy is a good, medium, and poor risk driver given he has had an accident is approximately 0.079, 0.395, and 0.526 respectively, as calculated using Bayes' theorem.

Explanation:

Using Bayes' theorem, we can find out the probability that Mr. Brophy is a good, medium, or poor risk driver given that he has had an accident:

Let's denote A as the event of having an accident and Gi, Mi, Pi as the events of Mr. Brophy being a good, medium, or poor risk driver respectively.

The total probability of an accident, P(A), is given by:

P(A) = P(A|Gi)P(Gi) + P(A|Mi)P(Mi) + P(A|Pi)P(Pi)

P(A) = (0.01)(0.30) + (0.03)(0.50) + (0.10)(0.20) = 0.003 + 0.015 + 0.02 = 0.038

The probability of Mr. Brophy being a good driver given he had an accident, P(Gi|A), is:

P(Gi|A) = (P(A|Gi)P(Gi)) / P(A) = (0.01)(0.30) / 0.038 ≈ 0.079

The probability of Mr. Brophy being a medium risk driver given he had an accident, P(Mi|A), is:

P(Mi|A) = (P(A|Mi)P(Mi)) / P(A) = (0.03)(0.50) / 0.038 ≈ 0.395

The probability of Mr. Brophy being a poor risk driver given he had an accident, P(Pi|A), is:

P(Pi|A) = (P(A|Pi)P(Pi)) / P(A) = (0.10)(0.20) / 0.038 ≈ 0.526

Answer:

n=2/5 or 0.4

Step-by-step explanation:

thx mate brainliest plzz

Answer:

The answer is 10

Step-by-step explanation:

The side length cannot be negative, hence the side length of the patio will be 10 feet

Give the expression that represents the statement given as:

[tex](s+4)^2 = 196[/tex]

We need to get the length of the side of the patio "s"

[tex](s+4)^2 = 196\\s+4 = \pm\sqrt{196}\\s+4=\pm14[/tex]

Subtract 4 from both sides

[tex]s+4-4=14-4\\s=14-4\\s =10ft[/tex]

Since the side length cannot be negative, hence the side length of the patio will be 10 feet

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Answer: 12.56 inches

Step-by-step explanation: First, when know the following:

A clock is a circle, so the total movement, from 12 to 12 is 360° or 2π.

It is also know that a circle circunference (The total size of the circle on a straight line) is 2π * Radius

The minute hand does a circle on its travel, that circle radius is equal to 6 inches.

The movement from 12 to 4 is a third (4/12 = 1/3). Knowing this:

120° = (1/3) * 360° = (1/3) * 2π = (2/3) * π

So the travel from 12 to 4 is (2/3)π

To know the distance on inches, we multiply the distance on radians per the radius.

Total distance = 6 * (2/3)π

Total distance = 4π inches

Total distance = 12.56 inches

Final Answer:

The tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.

Explanation:

To solve this problem, we will consider the movement of the minute hand as an arc on a circle. The distance that the tip of the minute hand moves is the length of the arc that it traces as it moves from 12 o'clock to 4 o'clock. Here's how we'll calculate it:
Step 1: Determine the angle of movement in degrees.
The clock is divided into 12 hours, so each hour represents an angle of 360 degrees / 12 = 30 degrees. Since the minute hand moves from 12 o'clock to 4 o'clock, it covers 4 hours. Thus, the angle covered is 4 hours * 30 degrees/hour = 120 degrees.

Step 2: Convert the angle from degrees to radians.
To find the arc length, it is convenient to work with radians rather than degrees. The conversion from degrees to radians is performed using the factor π radians = 180 degrees.

[tex]\( \text{Angle in radians} = \text{Angle in degrees} \times \frac{\pi}{180} \)[/tex]

So, for our angle:

[tex]\( \text{Angle in radians} = 120 \times \frac{\pi}{180} \\\\\( \text{Angle in radians} = \frac{2}{3} \pi \)[/tex]

Step 3: Use the arc length formula.
The arc length (s) on a circle can be calculated using the formula s = r * θ, where r is the radius (length) of the circle (in this case, the length of the minute hand), and θ is the angle in radians.

[tex]\( s = r * \theta \\\\\( s = 6 \text{ inches} * \frac{2}{3} \pi \\\\\( s = 4 \pi \text{ inches} \)[/tex]

So, the distance the tip of the minute hand moves is [tex]\( 4 \pi \)[/tex] inches.

Step 4: Calculate the numerical value of the arc length.
To find the numerical value, we will approximate [tex]\( \pi \)[/tex] to 3.14159.

[tex]\( s \approx 4 * 3.14159 \\\\\( s \approx 12.56636 \text{ inches} \)[/tex]
Step 5: Round the numerical value to two decimal places.
[tex]\( s \approx 12.57 \text{ inches} \)[/tex]
Therefore, the tip of the minute hand moves approximately 12.57 inches from 12 o'clock to 4 o'clock.

Answer:

OPTION A.

OPTION D.

OPTION E.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the  slope and "b" is the y-intercept.

The  Standard form of the equation of the line is:

[tex]Ax + By = C[/tex]

Where "A" is a positive integer, and "B" and "C" are integers.

Choose two points from the table and find the slope with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Points:

[tex](1,27)\\\\(4,24)[/tex]

So we get that the slope is:

[tex]m=\frac{24-27}{4-1}=-1[/tex]

Let's substitute the slope and the coordinates of the point (1,27) into  [tex]y=mx+b[/tex] and then solve for "b":

[tex]27=(-1)(1)+b\\\\27+1=b\\\\b=28[/tex]

Then, we get that the equation of the line in Slope-Intercept form is:

[tex]y=-x+28[/tex] or [tex]28-x=y[/tex]

In order to write it in Standard form, we can add "x" to both sides of the equation:

[tex]y+x=-x+28+x\\\\x+y=28[/tex]

We can solve for "x" by subtracting "y" from both sides of the equation:

[tex]x+y-y=28-y\\x=28-y\\\\28-y=x[/tex]

Answer:

A,D, and E

Step-by-step explanation:

Answer: 380

Step-by-step explanation: Did you mean to ask how much time it took him? If he’s doing 4 races each being 95 miles it would simply be 95 x 4 = 380

The total distance driven by Walt is calculated by multiplying the length of each race (95 miles) by the number of races (4), giving a total of 380 miles.

Walt averages 98 miles per hour, each race is 95 miles long, and he completed 4 races. To find the total distance driven by Walt, we only need to know how long each race is and how many races Walt completed because the speed at which Walt drives does not affect the total distance he covered in the race. Therefore, to get the total distance, we simply multiply the length of each race by the number of races. In this case, Walt drove 95 miles x 4 = 380 miles in total.

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Answer:

408.6 meters.

Step-by-step explanation:

Let x be the height from the base of the building to the 86th floor,

∵ the total height of the building is another 124 meters above the 86th floor,

So, the total height of the building = ( x + 124 ) meters,

Now, the angle of elevation from the point on the ground to 86th floor = 82°,

Also, the distance from the point to the base of the building = 41 meters,

Thus, by trigonometric ratio,

[tex]tan 82^{\circ}=\frac{x}{41}[/tex]

[tex]\implies x = 41\times tan 82^{\circ}=284.614788895\approx 284.6\text{ meters}[/tex]

Hence, the height of the building = ( 284.6 + 124 ) = 408.6 meters.

The height of the building in consideration is given approximately as 408.61 meters

You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.

Consider the figure attached for the given situation as described in the problem.

The person watching the building's 86th floor is at A.

The 86th floor is at C, the base of the building is at B.
The total height of the building is at D.

Using the tangent ratio to find the height of the building, we get:

[tex]\tan(82^\circ) = \dfrac{x}{41} \\\\x = \tan(82^\circ) \times 41\\x \approx 284.61 \: \rm meters[/tex] (from calculator).

Thus, the height of the building is length of AD

= |AD| = x + 124 ≈ 284.61 + 124 = 408.61 meters

Thus, the height of the building in consideration is given approximately as 408.61 meters

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Answer: 0.3061.

Step-by-step explanation:

Given : The temperature reading from a thermocouple placed in a constant-temperature medium is normally distributed with mean [tex]\mu[/tex], the actual temperature of the medium, and standard deviation [tex]\sigma[/tex].

Let X be the random variable that represents the reading of the thermometer.

Confidence level : [tex]=95\%[/tex]

We know that the z-value for 95% confidence interval is 1.96.

Then, we have

[tex]-1.96<\dfrac{X-\mu}{\sigma}<1.96[/tex]      [tex]z=\dfrac{X-\mu}{\sigma}[/tex]

[tex]\Rightarrow\ -1.96\sigma<X-\mu<1.96\sigma[/tex]  

But all readings are within 0.6° of [tex]\mu[/tex].

So, [tex]1.96\sigma=0.6[/tex]  

[tex]\Rightarrow\ \sigma=\dfrac{0.6}{1.96}=0.30612244898\approx0.3061[/tex]

Hence, the required standard deviation will be  

The confidence level is 95% in normal distribution then The value of standard deviation is 0.3061.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

Given

The temperature reading from a thermocouple placed in a constant temperature medium is normally distributed with mean μ, the actual temperature of the medium, and standard deviation σ.

Let x be the random variable that represents the reading of the thermometer.

The confidence level is 95%. Then the z-value for 95% confidence level interval is 1.96.

Then we have

[tex]-\ \ 1.96 \ < \dfrac{x- \mu}{\sigma} < 1.96\\-1.96 \sigma < x- \mu \ < 1.96 \sigma[/tex]

But all the readings are within 0.6° of μ. Then

[tex]1.96 \sigma = 0.6\\[/tex]

On solving

[tex]\sigma = \dfrac{0.6}{1.96}\\\\\sigma = 0.306122 \approx 3061[/tex]

Thus, the standard deviation is 0.3061.

More about the normal distribution link is given below.

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Answer:

This study will be identified as : exempt review

Step-by-step explanation:

A student is conducting a research project that involves using a survey. The survey asks subjects about their political affiliation and their favorite politicians.

No identifiable information will be collected.

This study will be identified as : exempt review

To qualify for a review at the exempt level, the research should be less than the minimal risk defined.

Answer:

3rd graph

Step-by-step explanation:

Hi, the answer would be the 3rd graph because each given set is shown on that coordinate relation.

Hope this helps, I attached the graph in case my explanation was confusing.

Third graph represents the set B = (1, 2), (2, 1), (3, 0), (4, -1).

Here, Set of points given as,

B = (1, 2), (2, 1), (3, 0), (4, -1).

We have to check the graph which represents the given set.

How to show points on graph?

Points are identified by stating their coordinates in the form of (x, y).

Where x is coordinate of x - axis and y is coordinate of y - axis.

Now,

Set of points given as,

B = (1, 2), (2, 1), (3, 0), (4, -1).

⇒ Third graph represents the set B = (1, 2), (2, 1), (3, 0), (4, -1).

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[tex]\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}] [/tex]

[tex]\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}][/tex]

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

   [tex] \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}][/tex]

The solutions are[tex]\( z = 5e^{i(\frac{9\pi}{4})} \), \( z = 5e^{i(\frac{17\pi}{4})} \), \( z = 5e^{i(\frac{25\pi}{4})} \), and \( z = 5e^{i(\frac{33\pi}{4})} \).[/tex]

To find the solutions of the equation [tex]\( z^4 = -625 \) in the given range of argument, we first rewrite the equation in polar form. Let \( z = re^{i\theta} \), where \( r \) is the magnitude of \( z \) and \( \theta \) is its argument.[/tex]

The equation becomes:

[tex]\[ (re^{i\theta})^4 = -625 \]\[ r^4e^{4i\theta} = -625 \]Now, since the right side is a negative real number, we can express it in polar form as \( -625 = 625e^{i\pi} \). So we have:\[ r^4e^{4i\theta} = 625e^{i\pi} \][/tex]

Comparing the magnitudes and arguments on both sides, we get:

[tex]\[ r^4 = 625 \]\[ 4\theta = \pi \]Solving for \( r \) and \( \theta \):\[ r = \sqrt[4]{625} = 5 \]\[ \theta = \frac{\pi}{4} \][/tex]

However, we need solutions in the given range of argument, which is between [tex]\( 270^\circ \) and \( 360^\circ \). Since \( \frac{\pi}{4} \) is approximately \( 45^\circ \) or \( \frac{\pi}{4} \), we need to add multiples of \( 2\pi \) to this angle to get solutions within the desired range.[/tex]

The solutions are:

[tex]\[ z_1 = 5e^{i(\frac{\pi}{4} + 2\pi)} \]\[ z_2 = 5e^{i(\frac{\pi}{4} + 4\pi)} \]\[ z_3 = 5e^{i(\frac{\pi}{4} + 6\pi)} \]\[ z_4 = 5e^{i(\frac{\pi}{4} + 8\pi)} \]Simplifying the angles:\[ z_1 = 5e^{i(\frac{9\pi}{4})} \]\[ z_2 = 5e^{i(\frac{17\pi}{4})} \]\[ z_3 = 5e^{i(\frac{25\pi}{4})} \]\[ z_4 = 5e^{i(\frac{33\pi}{4})} \][/tex]

Finally, we can convert these back to rectangular form if needed:

[tex]\[ z_1 = 5\left(\cos\frac{9\pi}{4} + i\sin\frac{9\pi}{4}\right) \]\[ z_2 = 5\left(\cos\frac{17\pi}{4} + i\sin\frac{17\pi}{4}\right) \]\[ z_3 = 5\left(\cos\frac{25\pi}{4} + i\sin\frac{25\pi}{4}\right) \]\[ z_4 = 5\left(\cos\frac{33\pi}{4} + i\sin\frac{33\pi}{4}\right) \][/tex]

You can compute the approximate values of these complex numbers and round them to the nearest thousandth if necessary.

Complete Question;

Find the solution of the following equation whose argument is strictly between [tex]$270^\circ$[/tex] , degree and [tex]$360^\circ$[/tex] , degree. Round your answer to the nearest thousandth.  [tex]\[z^4 = -625z\][/tex]

Answer:

  CD = 40

Step-by-step explanation:

Since D is the midpoint, the entire length CE is twice the length of CD, so we have ...

  2×CD = CE

  2×(5x) = 9x +8

  x = 8 . . . . . . . . subtract 9x and simplify

Then the length of CD is ...

  CD = 5x = 5·8 = 40

Answer:

Step-by-step explan 3x+2x+20+4x-20=180. 9x=180 X=180÷9. X=20