What complex number is represented by the expression 7i^5+9i^8

Answers

Answer 1

Answer:

[tex]9 + 7i[/tex]

Step-by-step explanation:

[tex]7i^5+9i^8[/tex]

[tex]i^5 = i\\ i^8 = 1[/tex]


Related Questions

An arch is in the form of a parabola given by the function h = -0.06d^2 + 120, where the origin is at ground level, d meters is the horizontal distance and h is the height of the arch in meters.
Graph this function on your graphing calculator then complete the following statements.
The height of the arch is: ------- m
The width to the nearest meter, at the base of the arch is ------ m

Answers

Answer:

See attachment for graph

The height of the arch is: 120 m

The width to the nearest meter, at the base of the arch is 22 m

Step-by-step explanation:

Given

[tex]h = -0.06d^2 + 120[/tex]

Solving (a): The graph

See attachment for graph

Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.

Solving (b): The height

The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,

Hence:

[tex]height = 120[/tex]

Solving (c): The width

The curve touches the horizontal axis at two different points.

[tex]x_1 = -11[/tex]

[tex]x_2 = 11[/tex]

The absolute difference of both points represents the width.

So:

[tex]Width = |x_2 - x_1|[/tex]

[tex]Width = |11 - -11|[/tex]

[tex]Width = |11 +11|[/tex]

[tex]Width = |22|[/tex]

Hence:

[tex]Width = 22[/tex]

The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?

Answers

Answer:

22608 mm³/s

Step-by-step explanation:

Applying chain rule,

dV/dt = (dV/dr)(dr/dt)............... Equation 1

Where dV/dr = rate at which the volume is increasing

But,

V = 4πr³/3

Therefore,

dV/dr = 4πr²............... Equation 2

Substitute equation 2 into equation 1

dV/dt = 4πr²(dr/dt).............. Equation 3

From the question,

Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm

Consatant: π = 3.14

Substitute these values into equation 3

dV/dt = 4×3.14×30²×2

dV/dt = 22608 mm³/s

The mean of a data set is observed to be very different from its median, representing a strong skewness. However, the 1.5 IQR rule reveals that there are no outliers. Which of the following is correct, if the sample size is 100?

a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.
b. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is not appropriate to use.
c. A normal quantile plot of the data follows a diagonal line, and the t-procedure is not appropriate to use.
d. A normal quantile plot of the data does not follow a diagonal line, and the t- procedure is appropriate to use.

Answers

Answer:

a. A normal quantile plot of the data follows a diagonal line, and the t-procedure is appropriate to use.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

Sample size of 100 > 30, which means that we use the Central Limit Theorem, and thus, the sampling distribution is approximately normal, following a diagonal line, and since the standard deviation of the population is not know, we use the t-procedure. Thus, the correct answer is given by option a.

A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost. (Let x represent the length of the sides of the square base and let y represent the height. Round your answers to two decimal places.) x

Answers

Answer:

Box dimensions:

x =  3.42 cm

y = 6.84 cm

C(min) = 14.04 $

Step-by-step explanation:

We need the surface area of the cube:

S(c)  =  2*S₁ ( surface area of top or base) +  4*S₂ ( surface lateral area)

S₁  = x²        2*S₁  = 2*x²

Surface lateral area is:

4*S₂  =  4*x*h                          V(c) =  80 cm³  =  x²*h          h  =  80/x²

4*S₂  = 4*80/x

4*S₂  = 320 / x

Costs

C (x)  =  0.2* 2*x²   +  0.1 * 320/x

Taking derivatives on both sides of the equation we get:

C´(x)  =    0.8*x   -  32/x²

C´(x)  =  0            0.8*x - 32/x²  = 0

0.8*x³  -  32  =  0            x³  =  32/0.8

x³  =  40  

x =  3.42 cm

h =  80/(3.42)²          h  = 6.84 cm

To find out if x = 3.42 brings a minimum value for C we go to the second derivative

C´´(x) =  64/x³       is always positive for  x > 0  

The C(min) = 0.4*(3.42)²  +  32/(3.42)

C(min)  =  4.68 +  9.36

C(min)  = 14.04 $

please help i guess on a

Answers

Answer:

A = (2, 2)

B = (3, -1)

C = (-1, 0)

Step-by-step explanation:

To translate a point, you have to translate each individual point. At the bottom it shows <-2,3>, therefore you have to translate x 2 units to the left (because it's negative meaning the number is going away from 0, and 3 units to the right because 3 is a positive number.)

First Point A:

x: 4 - 2 = 2; y: -1 + 3 = 2

Second Point B:

x: 5 - 2 = 3; y: -4 + 3 = -1

Lastly, Point C:

x: 1 - 2 = -1, y: -3 + 3 = 0

I hope this helps!

(a^2 - b^2)=???????????????????????????

Answers

[tex](a^2 - b^2) = (a + b)(a - b)[/tex]

Calculate the sample mean and sample variance for the following frequency distribution of hourly wages for a sample of pharmacy assistants. If necessary, round to one more decimal place than the largest number of decimal places given in the data. Hourly Wages (in Dollars) Class Frequency 10.01 - 11.50 44 11.51 - 13.00 27 13.01 - 14.50 38 14.51 - 16.00 33 16.01 - 17.50 40

Answers

Answer:

[tex]\bar x = 13.739[/tex]

[tex]\sigma^2 = 4.923[/tex]

Step-by-step explanation:

Given

[tex]\begin{array}{cc}{Class} & {Frequency} & 10.01 - 11.50 & 44 & 11.51 - 13.00 & 27 & 13.01 - 14.50 & 38 & 14.51 - 16.00 & 33 & 16.01 - 17.50 & 40 \ \end{array}[/tex]

Required

The sample mean and the sample variance

First, calculate the midpoints

[tex]x_1 = \frac{10.01 + 11.50}{2} = 10.755[/tex]

[tex]x_2 = \frac{11.51 + 13.00}{2} = 12.255[/tex]

And so on...

So, the table becomes:

[tex]\begin{array}{ccc}{Class} & {Frequency} & {x} & 10.01 - 11.50 & 44 & 10.755 & 11.51 - 13.00 & 27 & 12.255 & 13.01 - 14.50 & 38 & 13.755 & 14.51 - 16.00 & 33 & 15.255 & 16.01 - 17.50 & 40 & 16.755 \ \end{array}[/tex]

So, the sample mean is:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

[tex]\bar x = \frac{44 * 10.755 + 27 * 12.255 + 38 * 13.755 + 33 * 15.255 + 40 * 16.755}{44 + 27 + 38 + 33 + 40}[/tex]

[tex]\bar x = \frac{2500.41}{182}[/tex]

[tex]\bar x = 13.739[/tex]

The sample variance is:

[tex]\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}[/tex]

[tex]\sigma^2 = \frac{44 * (10.755 - 13.739)^2 + 27 * (12.255 - 13.739)^2+ 38 * (13.755 - 13.739)^2 + 33 * (15.255 - 13.739)^2+ 40 * (16.755- 13.739)^2}{44 + 27 + 38 + 33 + 40-1}[/tex]

[tex]\sigma^2 = \frac{890.950592}{181}[/tex]

[tex]\sigma^2 = 4.923[/tex]

Find sin d, sin e, cos d, and cos e. Write each answer as a fraction in simplest form

Answers

Answer:

r= 17.73174

Step-by-step explanation:

calculations

Please help ASAP!!! Thank you!!!

Answers

Step-by-step explanation:

1) = Solution

(3x+2)(x-1) = 3x^2 - 3x+2x-2

= 3x^2 - x - 2

2) = (x-5)(2x+3)

= 2x^2 + 3x - 10x - 15

= 2x^2 - 7x - 15

3) = (2x+5)(3x-2)

= 6x^2 - 4x + 15x - 10

= 6x^2 + 11x - 10

(1) =(3x+2)(x-1) =3x(x-1)+2(x-1) =3x^-3x+2x-2 =3x^-x-2

(2) =(x-5) (2x+3) =x(2x+3)-5(2x+3) =2x^+3x-10x-15 =2x^-7x-15

(3) =(2x+5) (3x-2) =2x(3x-2)+5(3x-2) =6x^-4x+15x-10 =6x^+11x-10

An analysis of 99 Wall Street traders showed that 32 of their stock picks beat the market average. What is the estimate of the population proportion

Answers

Answer:

The estimate of the population proportion is 0.3232.

Step-by-step explanation:

Estimate of the population proportion:

The estimate is the sample proportion, which is the number of desired outcomes divided by the number of total outcomes.

In this question:

32 out of 99, so:

[tex]p = \frac{32}{99} = 0.3232[/tex]

The estimate of the population proportion is 0.3232.

Lia can rent a van for either $90 per day with unlimited mileage or $50 per day with 250 free miles and an extra 25¢ for each mile over 250. For what number of miles traveled in one day would the unlimited mileage plan save Lia money? (Show work)

Answers

Answer:

ok so 90 is 40 more dollars then 50 and there is 4 25 cents in each dollars so

4*40=160

so she would have to drive 161 miles to save money

Hope This Helps!!!

how much is -(3)(3)=

Answers

Answer:

-9

Step-by-step explanation:

Since the threes are in parenthesis, you multiply them first then apply the negative sign.

I hope this helps!

Answer:

-9

Step-by-step explanation:

Multiplying 3 by -3 will get you -9. You know it's negative because only one number is negative and 3*3=9.

The figure shown represents a roof truss
design. Based on the markings on the figure,
which of the triangles can you prove are
congruent?

Answers

OPTION C is the correct answer.

The ΔAFE ≅ ΔBHG  by the angle, side and angle theorem are congruent. Option (A) is correct.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

The figure shows models of a roof truss. Based on the markings, there is enough information to prove that

ΔAFE ≅ ΔBHG

∠EFA=∠GHB  (90 degrees )

EF = GH  (equal side)

EAF = GBH (the side opposite to the angle is equal)

ΔAFE ≅ ΔBHG  (ASA )

Thus, ΔAFE ≅ ΔBHG  by the angle, side and angle theorem are congruent.

Learn more about triangles here:

https://brainly.com/question/14366937

#SPJ2

ANSWER ASAP IM BEING TIMED
IF I GET AN A ON THIS I WILL DO ANOTHER POINT FREE DROP, PLEASE SHOW YOUR WORK

The side of a square measures (4x − 7) units.

Part A: What is the expression that represents the area of the square? Show your work to receive full credit. (4 points)

Part B: What are the degree and classification of the expression obtained in Part A? (3 points)

Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

(10 points)

Answers

Step-by-step explanation:

Area of a square = s x s

(4x-7)x(4x-7)

Open brackets

4x(4x-7)-7(4x-7)

16x^2-28-28x+49

16x^2-28x+21

Last year, each Capulet wrote 4 essays, each Montague wrote 6 essays, and both families wrote 100 essays in total.
This year, each Capulet wrote 8 essays, each Montague wrote 12 essays, and both families wrote 200 essays in total.
How many Capulets and Montagues are there?
Choose 1 answer:
A: There is not enough information to determine the exact number of Capulets and Montagues.
B: The given information describes an impossible situation.
C: There are 16 Capulets and 6 Montagues.
D: There are 6 Capulets and 16 Montagues

Answers

Answer: There are 16 Capulets and 6 Montaques.

Step-by-step explanation:Other choices were either less than or greater than 200 multiplied by each other. If we do 16x8 which is 128 for the Capulets. Also, if we do 12x6 which is 72 for the Montaques. 128+72=200 essays in total

How many students rank themselves as introverts? Demonstrate your work.

Answers

Answer:

36 introverts

Step-by-step explanation:

Total number of adults in the survey = 120

Ratio of introverts to extroverts = 3:7

Number of introverts = ratio number of introverts / ratio total × 120

Ratio number of introverts = 3

Ratio total = 3 + 7 = 10

Number of introverts = 3/10 × 120

= 36

I'm not sure how to do this so I'm just asking for help.

Answers

Answer:

C

Step-by-step explanation:

In ∆DEG, we are given that all the three angles are congruent.

This means that all the three angles have equal measure. Thus,

<D = <E = <F

An equilateral triangle has equal angle measure. ∆DEF is an equilateral triangle.

Since the sum of a triangle is 180°, therefore, each angle in ∆DEF = 60°

m<D = 60°

Find the size of angle XZY give your answer

Answers

The diagram or the shape

Answer:

yeah u forgot to add the picture ig

In 2019, 15.9% of Broadway actors were acting in their first role on Broadway. Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers. What are the mean and standard deviation for the sampling distribution of pÌ p^? 1. Mean: 0.159, Standard Deviation: 0.0592. Mean: 0.159, Standard Deviation: 0.36573. Mean: 0.184, Standard Deviation: 0.0634. Mean: 0.184, Standard Deviation: 0.0595. Mean: 0.159, Standard Deviation: 0.063In 2019 the CDC reported that 14.0% of US adults are smokers. Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.What is the mean and the standard deviation of the sampling distribution of pÌ p^ ?1. mean = 0.140, standard deviation = 0.0682. mean = 0.167, standard deviation = 0.0633. mean = 0.140, standard deviation = 0.0634. mean = 0.167, standard deviation = 0.068

Answers

Answer:

For the Broadway actors acting in their first role on Broadway, mean: 0.184, Standard Deviation: 0.063.

For the proportion of smokers, mean = 0.167, standard deviation = 0.068

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose we took a survey of 38 Broadway actors and found that 18.4% of the actors we surveyed were first-timers.

This means that [tex]p = 0.184, n = 38[/tex]

What are the mean and standard deviation for the sampling distribution of p^?

Mean:

[tex]\mu = p = 0.184[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.184*0.816}{38}} = 0.063[/tex]

Suppose you take a random sample of 30 smokers and find that the proportion of them who are current smokers is 16.7%.

This means that [tex]n = 30, p = 0.167[/tex]

What is the mean and the standard deviation of the sampling distribution of p^ ?

Mean:

[tex]\mu = p = 0.167[/tex]

Standard deviation:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.167*0.833}{30}} = 0.068[/tex]

Can someone help me out here please? I tried dividing and multiplying but still have not got the correct answer. How do I go about solving this problem and where do I start?

Answers

9514 1404 393

Answer:

  $4000

Step-by-step explanation:

The problem tells you the relation between commission (c) and stock value (v) is ...

  c = 10 + 0.025v . . . . $10 + .025 of the value traded

We want to find the value (v) for the given commission (c=110). We can put these numbers into the formula and solve for v:

  110 = 10 + 0.025v

  100 = 0.025v . . . . . . . subtract 10

  100/0.025 = v = 4000 . . . . divide by the coefficient of v

The value of stock traded was $4000.

_____

Additional comment

As always, you start by reading and comprehending the problem. You look for what is being asked for, what is being given, and any information that relates one to the other.

Here, the value of stock traded is asked for, the amount of commission is given, and a description of the relation of one to the other is provided. Translate that description to an equation, fill in the given value, and solve for the unknown. (That's what we did above.)

__

You can also work this in your head. The commission is $10 more than some fraction of the amount traded. Since the commission is $110, only $100 of that is the fraction of the amount traded. With a little experience, you can recognize the fraction 0.025 as being 1/40. That means $100 is 1/40 of the value traded, or the value traded is 40 × $100 = $4000.

What is the midpoint of AB?

Answers

Answer:

point G

Step-by-step explanation:

There's 14 marks between point A and B(counting point B). 14/2=7, the 7th mark is point G.

Please help ASAP!!!! Thank you !!

Answers

Answer:

Hereeeeeeeeeeeeeeeee

(1) =(x+4)(x+5) =x(x+5)+4(x+5) =x^+5x+4x+20 =x^+9x+20

(2) =(x+4)(x-5) =x(x-5)+4(x-5) =x^-5x+4x-20 =x^-x-20

(3) =(x-4)(x+5) =x(x+5)-4(x+5) =x^+5x-4x+20 =x^+x+20

(4) =(x-4)(x-5) =x(x-5)-4(x-5) =x^5x-4x+20 =x^-x+20

(5) =(x+7y)(x+7y) =x(x+7y)+7y(x+7y) =x^+7xy+7xy+49y^ =x^+14xy+49y^

It was very easy

A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=-16^2+104t+56 models the balls height above the ground,h(t),in feet, T seconds after it was thrown
what is the maximum height of ball.=
How many seconds did it take to hit the ground=
Please help!

Answers

Answer:

Part 1)

225 feet.

Part 2)

7 seconds.

Step-by-step explanation:

The height h(t) of the ball above the ground after t seconds is modeled by the function:

[tex]h(t)=-16t^2+104t+56[/tex]

Part 1)

We want to determine the maximum height of the ball.

Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.

The vertex of a parabola is given by:

[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = -16, b = 104, and c = 56.

Find the x- (or rather t-) coordinate of the vertex. So:

[tex]\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}[/tex]

In other words, the ball reaches its maximum height after 3.25 seconds.

To find the maximum height, substitute this value back into the function. Hence:

[tex]\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}[/tex]

The maximum height of the ball is 225 feet in the air.

Part 2)

We want to find the amount of time it took for the ball to hit the ground.

When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:

[tex]0=-16t^2+104t+56[/tex]

We can simplify a bit. Divide both sides by -8:

[tex]0=2t^2-13t-7[/tex]

We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.

-14 and 1 works! Therefore, split the second term into -14 and 1:

[tex]\displaystyle 0=2t^2-14t+t-7[/tex]

Factor out a 2t from the first two terms and group the last two terms:

[tex]0=2t(t-7)+(t-7)[/tex]

Factor by grouping:

[tex]0=(2t+1)(t-7)[/tex]

Zero Product Property:

[tex]2t+1=0\text{ or } t-7=0[/tex]

Solve for each case:

[tex]\displaystyle t=-0.5\text{ or } t=7[/tex]

Since time cannot be negative, we can ignore the first case.

Therefore, it takes seven seconds for the ball to hit the ground.

Can someone answer? Please I tried everything I don’t know how to do this.

Answers

Step-by-step explanation:

-7.2(x-15.6)= -9-7.2x+112.32= -9-7.2x= -9-112.32-7.2x= -121.32x= -121.32/ -7.2x=16.85

hope it helps.stay safe healthy and happy.

What is the value of x in the figure below? If necessary, round your answer to
the nearest tenth of a unit.
X
15
D 4 B
A. 7.7
B. 3.8
O C. 15
D. 4

Answers

Answer:

Step-by-step explanation:

Blank DVD's are sold in packages of 50 for $17.95 if your company will need 2700 blank divide these next year how much money must your budget for blank dvd's

Answers

Answer:

Step-by-step explanation:

50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.

There are 10 students on the track team who compete in sprinting events. They make up 25% of the track team. How many students are on the track team?

Answers

Answer:

40

Step-by-step explanation:

10/x = 25/100

Cross multiply 10 and 100 = 1000.

Then, divide 1000 by 25 = 40.

10/40 = 0.25 = 25%

The level of significance is the a. same as the p-value. b. maximum allowable probability of Type I error. c. same as the confidence coefficient. d. maximum allowable probability of Type II error.

Answers

Answer:

The level of significance is the

b. maximum allowable probability of Type I error.

Step-by-step explanation:

The significance level provides the maximum probability of rejecting the null hypothesis when it is true.  It is the same as a type I error (also known as false-positive).  This error occurs when a researcher or investigator rejects a true null hypothesis that is supposed to be accepted.  It is the opposite of a type II error (false-negative), which occurs when the researcher fails to reject a false null hypothesis.

Identify an equation in point-slope from for the line perpendicular to y=-4x-1 that passes through (-2, 4)​

Answers

Answer:

y - 4 = ¼(x + 2)

Step-by-step explanation:

Point-slope form equation is given as y - b = m(x - a). Where,

(a, b) = a point on the line = (-2, 4)

m = slope = ¼ (sleep of the line perpendicular to y = -4x - 1 is the negative reciprocal of its slope value, -4 which is ¼)

✔️To write the equation, substitute (a, b) = (-2, 4), and m = ¼ into the point-slope equation, y - b = m(x - a).

y - 4 = ¼(x - (-2))

y - 4 = ¼(x + 2)

None of the options are correct

What is the lcd for 3/6 and 2/9

Answers

9514 1404 393

Answer:

  LCD = 18

Step-by-step explanation:

6 and 9 have a common factor of 3, so the LCD is ...

  (6×9)/3 = 18

Then the fractions can be written as ...

  3/6 = 9/18

  2/9 = 4/18

Other Questions
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