order the group of quadratic functions from widest to narrowest graph

Order The Group Of Quadratic Functions From Widest To Narrowest Graph

Answers

Answer 1

Answer:

"The coefficient with the largest absolute value is the most narrow graph."

y = ⅓x² → widest

y = -½x²

y = -9x² → narrowest


Related Questions

Determine the degree of the polynomial −65b+53x3y

Answers

Answer:

im pretty sure the degree is 4.

Step-by-step explanation:

Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor, but 3 days later 68 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)

Answers

Answer:

106 people.

Step-by-step explanation:

Logistic equation:

The logistic equation is given by:

[tex]P(t) = \frac{K}{1+Ae^{-kt}}[/tex]

In which

[tex]A = \frac{K - P_0}{P_0}[/tex]

K is the carrying capacity, k is the growth/decay rate, t is the time and P_0 is the initial value.

Suppose a rumor is going around a group of 191 people. Initially, only 38 members of the group have heard the rumor.

This means that [tex]K = 191, P_0 = 38[/tex], so:

[tex]A = \frac{191 - 38}{38} = 4.03[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

3 days later 68 people have heard it.

This means that [tex]P(3) = 68[/tex]. We use this to find k.

[tex]P(t) = \frac{191}{1+4.03e^{-kt}}[/tex]

[tex]68 = \frac{191}{1+4.03e^{-3k}}[/tex]

[tex]68 + 274.04e^{-3k} = 191[/tex]

[tex]e^{-3k} = \frac{191-68}{274.04}[/tex]

[tex]e^{-3k} = 0.4484[/tex]

[tex]\ln{e^{-3k}} = \ln{0.4484}[/tex]

[tex]-3k = \ln{0.4484}[/tex]

[tex]k = -\frac{\ln{0.4484}}{3}[/tex]

[tex]k = 0.2674[/tex]

Then

[tex]P(t) = \frac{191}{1+4.03e^{-0.2674t}}[/tex]

How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?

This is P(6). So

[tex]P(6) = \frac{191}{1+4.03e^{-0.2674*6}} = 105.52[/tex]

Rounding to the nearest whole number, 106 people.

Which property was used to simplify the expression 4(b+2)=4b+8

Answers

Answer: distributive property

Step-by-step explanation: the 4 is multiplied by everting in the parenthesis

The cost of producing a custom-made clock includes an initial set-up fee of $1,200 plus an additional $20 per unit made. Each clock sells for $60. Find the number of clocks that must be produced and sold for the costs to equal the revenue generated. (Enter a numerical value.)

Answers

Answer:

30 clocks

Step-by-step explanation:

Set up an equation:

Variable x = number of clocks

1200 + 20x = 60x

Isolate variable x:

1200 = 60x - 20x

1200 = 40x

Divide both sides by 40:

30 = x

Check your work:

1200 + 20(30) = 60(30)

1200 + 600 = 1800

1800 = 1800

Correct!

Seventeen individuals are scheduled to take a driving test at a particular DMV office on a certain day, nine of whom will be taking the test for the first time. Suppose that six of these individuals are randomly assigned to a particular examiner, and let X be the number among the six who are taking the test for the first time. (a) What kind of a distribution does X have (name and values of al parameters)? 17 hx;6, 9, 17) O h(x; 6,? 17 bx; 6, 9,17) (x; 6, 9, 17) 17 (b) Compute P(X = 4), P(X S 4), and P(X PLX = 4) 0.2851 PX S 4)-13946X RX24) -0.1096 X 4). (Round your answers to four decimal places.) (c) Calculaethe mean value and standard deviation of X. (Round your answers to three decimal places.)

Answers

Answer:  

a) h(x; 6, 9, 17).

b) P[X=2] = 0.2036

P[X ≤ 2] = 0.2466

P[X ≥ 2] = 0.9570.

c) Mean  = 3.176.

Variance = 1.028.

Standard deviation = 1.014.

Step-by-step explanation:

From the given details K=6, n=9, N=-17.

We conclude that it is the hypergeometric distribution:  

a) h(x; 6, 9, 17).

b)

[tex]P[X=2]=\frac{(^{g}C_{2})^{17-9}C_{6-2}}{^{17}C_{6}\textrm{}}[/tex]

P[X=2] = 0.2036

P[X ≤ 2] = P(x=0)+ P(x=1) + P(x=2)

P[X ≤ 2] = 0.2466

P[X ≥ 2] = 1-[P(x=0)+P(x=1)]

P[X ≥ 2] = 0.9570.

c)

Mean= [tex]n\frac{K}{N}[/tex]

            = 3.176.

Variance = [tex]n\frac{K}{N}( \frac{N-K}{N})(\frac{N-n}{n-1} )[/tex]

               = 2.824 x 0.6471 x 0.5625

               = 1.028.

Standard deviation = [tex]\sqrt{1.028}[/tex] = 1.014.


If the cost of a 2.5 meter cloth is $30.5. What will be the cost of 22 meters ?

Answers

Answer:

268.40

Step-by-step explanation:

We can write a ratio to solve

2.5 meters        22 meters

-----------------  = --------------

30.5 dollars       x dollars

Using cross products

2.5 * x = 30.5 * 22

2.5x =671

Divide each side by 2.5

2.5x / 2.5 = 671/2.5

x =268.4

What is the common difference between successive terms in the sequence?

0.36, 0.26, 0.16, 0.06, –0.04, –0.14,

Answers

The correct answer is: -0.10. Explanation: The common difference between successive terms in a sequence is the number you add to each term to find the next one.

Please help with this question

Answers

Answer:

im not too sure but try using a cartesuan plane and measure it precisely using a protractor then key in the measurements. Im not entirely sure its the correct method tho

On a coordinate plane, a curved line begins at point (negative 2, negative 3), crosses the y-axis at (0, negative .25), and the x-axis at (1, 0).
What is the domain of the function on the graph?

Answers

Answer:

Option D

Step-by-step explanation:

correct answer on edge :)

Answer:

D <3

Step-by-step explanation:

A wire 9 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a frame for a stained glass ornament, while the other piece is bent into a circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used for each: For the equilateral triangle:

Answers

The length of wire used for the equilateral triangle is approximately 5.61 meters.

The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.

Here,

To minimize the total area of both figures, we need to find the optimal cut point for the wire.

Let's assume the length of the wire used for the equilateral triangle is x meters, and the remaining length of the wire used for the circle is (9 - x) meters.

For the equilateral triangle:

An equilateral triangle has all three sides equal in length.

Let's call each side of the triangle s meters. Since the total length of the wire is x meters, each side will be x/3 meters.

The formula to find the area of an equilateral triangle with side length s is:

Area = (√(3)/4) * s²

Substitute s = x/3 into the area formula:

Area = (√(3)/4) * (x/3)²

Area = (√(3)/4) * (x²/9)

Now, for the circle:

The circumference (perimeter) of a circle is given by the formula:

Circumference = 2 * π * r

Since the remaining length of wire is (9 - x) meters, the circumference of the circle will be 2π(9 - x) meters.

The formula to find the area of a circle with radius r is:

Area = π * r²

To find the area of the circle, we need to find the radius.

Since the circumference is equal to 2πr, we can set up the equation:

2πr = 2π(9 - x)

Now, solve for r:

r = (9 - x)

Now, substitute r = (9 - x) into the area formula for the circle:

Area = π * (9 - x)²

Now, we want to minimize the total area, which is the sum of the areas of the triangle and the circle:

Total Area = (√(3)/4) * (x²/9) + π * (9 - x)²

To find the optimal value of x that minimizes the total area, we can take the derivative of the total area with respect to x, set it to zero, and solve for x.

d(Total Area)/dx = 0

Now, find the critical points and determine which one yields the minimum area.

Taking the derivative and setting it to zero:

d(Total Area)/dx = (√(3)/4) * (2x/9) - 2π * (9 - x)

Setting it to zero:

(√(3)/4) * (2x/9) - 2π * (9 - x) = 0

Now, solve for x:

(√(3)/4) * (2x/9) = 2π * (9 - x)

x/9 = (8π - 2πx) / (√(3))

Now, isolate x:

x = 9 * (8π - 2πx) / (√(3))

x(√(3)) = 9 * (8π - 2πx)

x(√(3) + 2π) = 9 * 8π

x = (9 * 8π) / (√(3) + 2π)

Now, we can calculate the value of x:

x ≈ 5.61 meters

So, the length of wire used for the equilateral triangle is approximately 5.61 meters.

The remaining length of wire used for the circle will be 9 - 5.61 ≈ 3.39 meters.

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[(2021-Y)-5]*X-X=XX cho biết X,Y,XX là gì?

Answers

nfbdjanckwochgducbenxikwks

i need help. i will give brainiest as soon as possible

Answers

Answer:

B

Step-by-step explanation:

Let me know if you need an explanation.

Answer:

B

Step-by-step explanation:

4x^3+x^2+5x+2

4x^3 cannot cancel with others= 4x^3

4x^2-3x^2= x^2

5x cannot cancel with others= 5x

-3+5= 2

4x^3+x^2+5x+2

Using f(x)=2x+7 and g(x)=x-3, find f(g(-2))

Answers

It’s 2x+1 sorry if it’s wrong

What is the area of the circle in terms of [tex]\pi[/tex]?

a. 3.4225[tex]\pi[/tex] m²
b. 6.845[tex]\pi[/tex] m²
c. 7.4[tex]\pi[/tex] m²
d. 13.69[tex]\pi[/tex] m²

Answers

[tex] \sf \: d \: = 3.7m \\ \sf \: r \: = \frac{3.7}{2} = 1.85 \: m\\ \\ \sf \: c \: = \pi {r}^{2} \\ \\ \sf \: c \: = \pi ({1.85})^{2} \\ \sf c = 1.85 \times 1.85 \times \pi \\ \sf \: c = \boxed {\underline{ \bf a. \: 3.4225\pi \: m ^{2} }}[/tex]

Anthony read 46 pages of a book in 23 minutes.

To find the unit rate, use
.
Anthony read
pages per minute.

Answers

Answer:

2 pages per minute

Step-by-step explanation:

Take the number of pages and divide by the number of minutes

46 pages / 23 minutes

2 pages per minute

Answer:

2 Pages per Minute

Solutions:

46 ÷ 23 = 2

Final Answer:

Anthony can read 2 pages per minute.

Please help with this question

Answers

9514 1404 393

Answer:

  (d)  -1/32

Step-by-step explanation:

It may be easier to rearrange the expression so it has positive exponents.

  [tex]\dfrac{1}{2^{-2}x^{-3}y^5}=\dfrac{2^2x^3}{y^5}=\dfrac{4(2)^3}{(-4)^5}=-\dfrac{4\cdot8}{1024}=\boxed{-\dfrac{1}{32}}[/tex]

At the Fidelity Credit Union, a mean of 3.5 customers arrive hourly at the drive-through window. What is the probability that, in any hour, more than 5 customers will arrive? Round your answer to four decimal places.

Answers

Answer:

0.1423 = 14.23% probability that, in any hour, more than 5 customers will arrive.

Step-by-step explanation:

We have the mean, which means that the Poisson distribution is used to solve this question.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A mean of 3.5 customers arrive hourly at the drive-through window.

This means that [tex]\mu = 3.5[/tex]

What is the probability that, in any hour, more than 5 customers will arrive?

This is:

[tex]P(X > 5) = 1 - P(X \leq 5)[/tex]

In which

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.5}*3.5^{0}}{(0)!} = 0.0302[/tex]

[tex]P(X = 1) = \frac{e^{-3.5}*3.5^{1}}{(1)!} = 0.1057[/tex]

[tex]P(X = 2) = \frac{e^{-3.5}*3.5^{2}}{(2)!} = 0.1850[/tex]

[tex]P(X = 3) = \frac{e^{-3.5}*3.5^{3}}{(3)!} = 0.2158[/tex]

[tex]P(X = 4) = \frac{e^{-3.5}*3.5^{4}}{(4)!} = 0.1888[/tex]

[tex]P(X = 5) = \frac{e^{-3.5}*3.5^{5}}{(5)!} = 0.1322[/tex]

Finally

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0302 + 0.1057 + 0.1850 + 0.2158 + 0.1888 + 0.1322 = 0.8577[/tex]

[tex]P(X > 5) = 1 - P(X \leq 5) = 1 - 0.8577 = 0.1423[/tex]

0.1423 = 14.23% probability that, in any hour, more than 5 customers will arrive.

To make a committee 4 men are chosen out of 6 candidates. What is the probability that 2 certain people will serve on that committee

Answers

Answer:

The probability that 2 certain people will serve on that committee is 11.11%.

Step-by-step explanation:

Since to make a committee 4 men are chosen out of 6 candidates, to determine what is the probability that 2 certain people will serve on that committee the following calculation must be performed:

4/6 = 2/3

1/3 x 1/3 = X

0.333 x 0.333 = X

0.1111 = X

Therefore, the probability that 2 certain people will serve on that committee is 11.11%.

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

6 groups, and 4 certain people

6

   C

        4

[tex]\frac{6!}{(6-2)!(2!)}[/tex]

1 × 2 × 3 × 4 × 5 × 6/1 × 2 × 3 × 4 × 1 × 2

1 × 2 × 3 × 4 × 5 × 6/1 × 2 × 3 × 4 × 1 × 2

5 × 6/ 1 × 2

30/2 = 15

15 possible combinations

4 people, and 2 specific ones

4

   C

        2

[tex]\frac{4!}{(4-2)!(2!)}[/tex]

1 × 2 × 3 × 4/1 × 2 × 1 × 2

1 × 2 × 3 × 4/1 × 2 × 1 × 2

12/2 = 6

[tex]\frac{6}{15}=\frac{\frac{6}{3} }{\frac{15}{3} } =\frac{2}{5}[/tex]

A chemist has three different acid solutions.

The first solution contains 25% acid, the second contains 35%acid, and the third contains 55% acid.
She created 120 liters of a 40% acid mixture, using all three solutions. The number of liters of 55% solution used is 3 times the number of liters of 35% solution used.

How many liters of each solution was used?

Answers

Let x, y, and z be the amounts (in liters, L) of the 25%, 35%, and 55% solutions that the chemist used.

She ended up with 120 L of solution, so

x + y + z = 120 … … … [1]

x L of 25% acid solution contains 0.25x L of acid. Similarly, y L of 35% solution contains 0.35y L of acid, and z L of 55% solution contains 0.55z L of acid. The concentration of the new solution is 40%, so that it contains 0.40 (120 L) = 48 L of acid, which means

0.25x + 0.35y + 0.55z = 48 … … … [2]

Lastly,

z = 3y … … … [3]

since the chemist used 3 times as much of the 55% solution as she did the 35% solution.

Substitute equation [3] into equations [1] and [2] to eliminate z :

x + y + 3y = 120

x + 4y = 120 … … … [4]

0.25x + 0.35y + 0.55 (3y) = 48

0.25x + 2y = 48 … … … [5]

Multiply through equation [5] by -2 and add that to [4] to eliminate y and solve for x :

(x + 4y) - 2 (0.25x + 2y) = 120 - 2 (48)

0.5x = 24

x = 48

Solve for y :

x + 4y = 120

4y = 72

y = 18

Solve for z :

z = 3y

z = 54

3.52 A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total number of heads on the 2 tosses. If the coin is unbalanced and a head has a 40% chance of occurring, find (a) the joint probability distribution of W and Z; (b) the marginal distribution of W; (c) the marginal distribution of Z

Answers

Answer:

a)  The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

b)  P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

c) P ( z = 0 ) = 0.6

  P ( z = 1 ) = 0.4

Step-by-step explanation:

Number of head on first toss = Z

Total Number of heads on 2 tosses = W

% of head occurring = 40%

% of tail occurring = 60%

P ( head ) = 2/5 ,    P( tail ) = 3/5

a) Determine the joint probability distribution of W and Z

P( W =0 |Z = 0 ) = 0.6         P( W = 0 | Z = 1 ) = 0

P( W = 1 | Z = 0 ) = 0.4        P( W = 1 | Z = 1 ) = 0.6

P( W = 1 | Z = 0 ) = 0           P( W = 2 | Z = 1 ) = 0.4

The joint probability distribution

P(0,0) = 0.36, P(1,0) = 0.24,   P(2,0) = 0,   P(0,1) = 0,  P(1,1) = 0.24,  P(2,1)= 0.16

B) Marginal distribution of W

P( W = 0 ) = 0.36,    P(W = 1 ) = 0.48,  P(W = 2 ) = 0.16

C) Marginal distribution of Z ( pmf of Z )

P ( z = 0 ) = 0.6

P ( z = 1 ) = 0.4

Part(a): The required joint probability of W and Z is ,

[tex]P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16[/tex]

Part(b): The pmf (marginal distribution) of W is,

[tex]P(w=0)=0.36,P(w=1)=0.48,P(w=2)=0.16[/tex]

Part(c): The pmf (marginal distribution) of Z is,

[tex]P(z=0)=0.6,P(z=1)=0.4[/tex]

Part(a):

The joint distribution is,

[tex]P(w=0\z=0)=0.6,P(w=1|z=0)=0.4,P(w=2|z=0)=0[/tex]

Also,

[tex]P(w=0\z=1)=0,P(w=1|z=1)=0.6,P(w=2|z=1)=0.4[/tex]

Therefore,

[tex]P(0,0)=0.36,P(1,0)=0.24,P(2,0)=0,P(0,1)=0,P(1,1)=0.24,\\\\P(2,1)=0.16[/tex]

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A medicine bottle contains 8 grams of medicine. One dose is 400 milligrams. How many milligrams does the bottle contain?

Answers

Answer:

8×1000 milligrams

8000 milligrams

How many subsets of at least one element does a set of seven elements have?

Answers

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

For each subset it can either contain or not contain an element. For each element, there are 2 possibilities. Multiplying these together we get 27 or 128 subsets. For generalisation the total number of subsets of a set containing n elements is 2 to the power n.

n=7 elemens

total subsets

2^n2⁷128

plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help i will give
brainliest

Answers

Answer:

55

Step-by-step explanation:

55 appears 3 times, which is the most repetition in the data set

Answer:

55

Step-by-step explanation:

Mode = number that appears most often

The number 55 appears 3 times which is the most out of the other numbers

Hence mode = 55

Simplify this expression 3^-3
ASAPPPP PLSSSS

Answers

Step-by-step explanation:

-27 okay 3^-3 its same as 3^3

Answer: A)

[tex]3^{-3}[/tex]

[tex]3^{-3}=\frac{1}{3^3}[/tex]

[tex]=\frac{1}{3^3}[/tex]

[tex]3^3=27[/tex]

[tex]=\frac{1}{27}[/tex]

OAmalOHopeO

HELP ASAP PLEASE! I tried inputting the numbers into the standard deviation equation but I did not get the right answer to find z. Can someone please help me? Thank you for your time!

Answers

Answer:

Z =  -1.60

it is low ... it appears that for this problem 2 standard deviations below must be reached to be considered "unusual"

Step-by-step explanation:

-28=7(x-7) what does x equal

Answers

Answer:

x=3

Step-by-step explanation:

7(x - 7) = -28

x - 7 = -4

x = 3

Answer:

x = 3

Step-by-step explanation:

Your goal is to isolate the x from the other numbers.

-28 = 7(x - 7)

Distribute the 7 to the (x - 7)

You will end up with:

-28 = 7x - 49

Add 49 to both sides of the equation to further isolate the x

21 = 7x

Finally, divide both sides by 7 so x is by itself

x = 3

(3) If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?

Show all your steps.

Answers

Answer:

3 meters.

Step-by-step explanation:

400 rev / minute = 400 × 60 rev / 60 minutes

= 24,000 rev / hour

24,000 × C = 72,000 m : C is the circumference

C = 3 meters

Answer:

3 meters

Step-by-step explanation:

72 km / hour * 1 hour/ 60 min  * 1000m/ 1 km

72000 meters /60 minute

1200 meters / minute

velocity = radius * w

Where w is 2*pi * the revolutions per minute

1200 = r * 2 * pi *400

1200 / 800 pi = r

1.5 /pi = r meters

We want to find the circumference

C = 2 * pi *r

C = 2* pi ( 1.5 / pi)

C = 3 meters

Hello, please help ASAP. Thank you!

Answers

Answer:

23) No

24) No

25) Yes

Step-by-step explanation:

Question 23)

We want to determine if a zero exists between 1 and 2 for the function:

[tex]f(x)=x^2-4x-5[/tex]

Find the zeros of the function. We can factor:

[tex]\displaystyle 0 = (x-5)(x+1)[/tex]

Zero Product Property:

[tex]x-5=0\text{ or } x+1=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle x = 5\text{ or } x=-1[/tex]

Therefore, our zeros are at x = 5 and x = -1.

In conclusion, a zero does not exist between 1 and 2.

Question 24)

We have the function:

[tex]f(x)=2x^2-7x+3[/tex]

And we want to determine if a zero exists between 1 and 2.

Factor. We want to find two numbers that multiply to (2)(3) = 6 and that add to -7.

-6 and -1 suffice. Hence:

[tex]\displaystyle \begin{aligned} 0 & = 2x^2-7x + 3 \\ & = 2x^2 -6x -x + 3 \\ &= 2x(x-3) - (x-3) \\ &= (2x-1)(x-3) \end{aligned}[/tex]

By the Zero Product Property:

[tex]2x-1=0\text{ or } x-3=0[/tex]

Solve for each case:

[tex]\displaystyle x=\frac{1}{2} \text{ or } x=3[/tex]

Therefore, our zeros are at x = 1/2 and x = 3.

In conclusion, a zero does not exist between 1 and 2.

Question 25)

We have the function:

[tex]f(x)=3x^2-2x-5[/tex]

And we want to determine if a zero exists between -2 and 3.

Factor. Again, we want to find two numbers that multiply to 3(-5) = -15 and that add to -2.

-5 and 3 works perfectly. Hence:

[tex]\displaystyle \begin{aligned} 0&= 3x^2 -2x -5 \\ &= 3x^2 +3x - 5x -5 \\ &= 3x(x+1)-5(x+1) \\ &= (3x-5)(x+1)\end{aligned}[/tex]

By the Zero Product Property:

[tex]\displaystyle 3x-5=0\text{ or } x+1=0[/tex]

Solve for each case:

[tex]\displaystyle x = \frac{5}{3}\text{ or } x=-1[/tex]

In conclusion, there indeed exists a zero between -2 and 3.

A bus driver makes roughly $3280 every month. How much does he make in one week at this rate.

Answers

Answer:

I think around $36

Hope it helps!

Answer:

It depends...

Step-by-step explanation:

It depends how much weeks are in the month if there are three weeks and no extra days then you would have an answer of about 1093 (exact: 1093.33333333). just divide the number of weeks by the number of money.

[tex]i^0 +i^1+i^2+i^3+............+i^{2021} = ?[/tex]

Include work.

Answers

Answer:

1+i

Step-by-step explanation:

I do believe i to be the imaginary unit.

Let's write out some partial sums from power=0 to power=7 or whatever we need to see a pattern.

i^0=1

i^0+i^1=1+i

i^0+i^1+i^2=1+i+-1=i

i^0+i^1+i^2+i^3=i+i^3=i+-i=0

i^0+i^1+i^2+i^3+i^4=0+i^4=0+1=1

Hmmm.... we might see 1+i, then i, then 0 again.... let's see.

i^0+i^1+i^2+i^3+i^4+i^5=1+i

Coolness so we should see a pattern

Sum from power=0 to power=multiples of 4 will give us 1.

Sum from power=0 to power=remainder of 1 when final power is divided by 4 gives us 1+i.

Sum from power=0 to power=remainder of 2 when final power is divided by 4 gives us i.

Sum from power=0 to power=remainder of 3 when final power is divided by 4 gives us 1

0.

So 2021 divided by 4....

Since 2020 is a multiple of 4, then 2021 has a remainder of 1 when divided by 4.

So the answer is 1+i.

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