State the correct polar coordinate for the graph shown:

State The Correct Polar Coordinate For The Graph Shown:

Answers

Answer 1

Answer:

Solution : ( - 8, - 5π/3 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° ) . - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° ) . - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).


Related Questions

Suppose that you borrow $1000.00 from a friend and promise to pay back $1390.00 in 2 years. What simple interest rate will you pay?
The simple interest rate is % (Round to the nearest tenth as needed.)

Answers

Answer:

19.5%

Step-by-step explanation:

Use the formula I = prt, where I is the interest money, p is the starting amount of money, r is the interest rate, and t is the time that the money was borrowed.

Plug in the values and solve for r:

390 = (1000)(r)(2)

390 = 2000r

0.195 = r

r = 19.5%

Answer:

19.5%

Step-by-step explanation:

Simple Interest = Principal x Time x Rate in % / 100

SI = 1000 x 2 x a / 100

=> SI = 10 x 2 x a

=> SI = 20a

Total Amount = SI + Principal

=> 1390 = 20a + 1000

=> 1390 - 1000 = 20a +1000 - 1000

=> 390 = 20a

=> 390/20 = 20a/20

=> 19.5 = a

Let's recheck

=> 1000 x 2 x 19.5 /100

=> 10 x 2 x 19.5

=> 195 x 2

=> 390

1390 = 390 + 1000

=> 1390 = 1390

So, the interest rate is 19.5 %

What is the 25th term in the following arithmetic sequence? -7, -2, 3, 8, ...

Answers

Answer:

108.

Step-by-step explanation:

-7, -2, 3, 8 is an arithmetic sequence with a1 (first term) = -7 and common difference (d)  = 5.

The 24th term = a1 + (24 - 1)d

=  -7 + 23 * 5

= -7 + 115

= 108.

woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g

Answers

Answer: 24ways

Step-by-step explanation:

Given data:

No of men in the workplace = 7

No of women in the workplace = 1

How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.

Solution.

A group of 4 can carry out the project with one be a woman

This means there must be 3 males and 1 female in the group

= 4p3

= 24ways

The project can be carried out by 4 groups in 24 ways

Find the total area of all the shaded rectangles.
4
The total area of all the shaded rectangles is
(Simplify your answer. Type an expression using x as the variable​

Answers

Answer:

25x^2 + 40x + 16

Step-by-step explanation:

area = 5x * 5x + 5x * 4 + 5x * 4 + 4 * 4

area = 25x^2 + 40x + 16

25x² + 40x + 16 is the required equation in variable x.

What is mensuration ?

Mensuration is a branch of mathematics where we calculate length, width, area, volume, lateral surface area, total surface area.

The sum of the areas of the shaded rectangles is the total area.

By observation we can see that the four shaded rectangles together form a square.

We all know that the area of the square is (side)²

= (5x + 4)²

= 25x² + 40x + 16  this is the required equation.

learn more about mensuration here :

https://brainly.com/question/23877107

#SPJ2

Enclosing the Largest Area The owner of the Rancho Grande has 3,052 yd of fencing with which to enclose a rectangular piece of grazing land situated along the straight portion of a river. If fencing is not required along the river, what are the dimensions (in yd) of the largest area he can enclose

Answers

Answer:

the shorter side = 1526

the longer side = 763

area = 1164338

Step-by-step explanation:

lets say

a=length

b = width

a + 2b = 3052

this is the perimeter

such that

a = 3052 - 2b

the area of a rectangle is a*b

= (3052 - 2b)b

= 3052b - 2b²

we differentiate this to get:

= 3052 - 4b

such that

3052 = 4b

divide through by 4, to get b, the width

3052/4 = 763

b = 763

put the value of b into a

a = 3052 - 2b

a = 3052 - 2(763)

a = 3052 - 1526

a = 1526

therefore

the shorter side = 1526

the longer side = 763

area = a x b

area = 1526 x 763

area = 1526 x 763

= 1164338

2. Write the equation of the circle in general form. Show your work.

Answers

Answer:

[tex] {(x + 1)}^{2} + {(y - 1)}^{2} = 9[/tex]

[tex] {x} ^{2} + {y} ^{2} + 2x - 2y - 7 = 0 [/tex]

The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 35 36 39 43 37 35 34 30 36 34 30 39 37 40 38 33 31 28 39 35 35 36 41 24 36 How many classes would you recommend? What class interval would you suggest? (Round up your answer to the next whole number.) Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution. It is not symmetric. It is fairly symmetric, with most of the values between 24 and 43. It is not very symmetric, but most of the values lie between 24 and 43.

Answers

Answer:

It is not symmetric, but skewed left. Data appears more to be on the left side.

Step-by-step explanation:

The smallest value is 24 and the largest is 43 . The difference between these two values is 19 which can be divided into into intervals of 4.

19/4= 4.75 It will be rounded to 5.

The class interval can of 5. Starting from 20 we get class intervals and frequency distribution as

Class Intervals          Data                                        Frequency      

20-24                           24                                              1

25- 29                           28,                                            1

30-34                            34,30,34,30,33,31,                   6

35-39                         35,36,39,37,35,36,39,37,           14

                                         38,39,35,35,36,36

40-44                                43,40,41                                3

The class intervals are inclusive of both upper and lower limits. The difference between the lower limits of two consecutive classes or upper limits of two consecutive classes must be the same.

As we see the difference here is that of 5 between the two upper or lower limits of consecutive classes.

The histogram is attached which shows the class intervals along x- axis and data frequency along y- axis.

Joey’s pizza sells large cheese pizzas for $12.00. Each additional topping costs $0.50. Basketball Boosters bought 12 large pizzas, each with 3 toppings. There are 8 slices per pizza. How much does it cost per slice? Round to the nearest cent.

Answers

Answer:

So first you do $0.50 x 3 = 1.5

then you add that to $12.00

$12.00 + 1.5 = 13.5

13.5 is the cost of one pizza.

Since they bought 12:

The total cost of the 12 pizza is $162 <== not important

13.5 divided by 8 is 1.687

round 1.56875 to the nearest cent 1.7 = $2

so each slice costs $2

Billy has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy

Answers

Answer:

Charlie: 5 + xDanny: x - 8Eric: x × 3

the grasshopper population in Georgia is currently 4,000. It's growing by 2.3% each year. Write an equation that models the situation.

Answers

Answer:

[tex]4000(1.023)^t\\\\[/tex]

Step-by-step explanation:

Using this exponential growth equation we can get an equation that models the situation.

A= Principal Amount

R= Rate of Growth

T= Amount of time

[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]

[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]

What is the volume of a square pyramid whose length of one side of its base is 9cm and whose height is 15cm. Show your work

Answers

Answer:

The answer is 405cm³

Step-by-step explanation:

Volume of a pyramid is given by

[tex]V = \frac{1}{3} \times area \: of \: base \: \: \times height[/tex]

height = 15cm

From the question the pyramid is a square pyramid which means it's base is a square

Area of a square = l²

where l is the length of one side

l = 9cm

Area of square = 9² = 81cm²

So the volume of the pyramid is

[tex]V = \frac{1}{3} \times 81 \times 15[/tex]

[tex]V = 27 \times 15[/tex]

We have the final answer as

V = 405 cm³

Therefore the volume of the pyramid is

405cm³

Hope this helps you

A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you decide to collect data from a random sample of students to assess whether the publisher's claim is reasonable, and you find that in a random sample of 22 college students, the mean price of textbooks for the fall 2019 semester was $433.50 with a standard deviation of $86.92. At the 0.01 significance level, is there sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher?

Answers

Answer:

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom   n  - 1     df = 22 - 1     df = 21

As the question mentions " different " that means,  a two-tail test

At 0,01 significance level     α  = 0,01       α/2  =  0,005

and t(c)  = 2,831

Test Hypothesis

Null Hypothesis                      H₀          μ  =  μ₀

Alternative hypothesis           Hₐ          μ  ≠  μ₀

To calculate t(s)

t(s)  =  (  μ  -  μ₀ ) /σ/√n

t(s)  =  (  433,50 - 385 ) / 86,92 / √22

t(s)  =  2,6171

Comparing   t(c)   and t(s)

t(s) < t(c)

Then  t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim

Use the dot product to determine whether v and w are orthogonal.

v=-i-j, w=-i+j

Select the correct choice below and fill in the answer box to complete your choice.

O A. The vectors v and w are not orthogonal because their dot product is ___

O B. The vectors v and w are orthogonal because their dot product is ___

Answers

Answer:

B. The vectors v and w are orthogonal because their dot product is 0

Step-by-step explanation:

Given that :

v=  - i - j  

w= - i + j

Therefore;

vw = ( - i - j )  ( - i + j )

Taking each  set of integer of the vector into consideration:

vw = ( -1 × - 1) ( -1 × 1)

vw = 1 - 1

vw = 0

Hence, we can conclude that :

The vectors v and w are orthogonal because their dot product is 0  

Which phrase describes the algebraic expression 8f+7?
the product of 8 and 7 more than a number
the quotient of 8 and 7
8 times the sum of a number and 7
8 times a number plus 7​

Answers

Answer:

8 times a number plus 7

Step-by-step explanation:

Let the number be f.

Simply, 8 f+7 is the expression.

Thank you!

How long will it take $3800 to grow into $5700 if it’s invested at 6% interest compounded continuously?

Answers

Answer: 25 years

Step-by-step explanation:

t = I / Pr

t = 5700 / ( 3800 × 0.06 ) = 25

t = 25 years

The sum of 8 times a number and 7 equals 9!

Answers

Answer:

0.25*8+7=9

Step-by-step explanation:

8x+7=9

2/8=x

0.25=x

Rational equation of 3/x+1=2/x-3

Answers

Answer:

x = 11

Step-by-step explanation:

3/x+1=2/x-3

Solve by using cross products

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

Distribute

2x+2 = 3x-9

Subtract 2x

2x+2-2x = 3x-2x-9

2 = x-9

Add 9 to each side

2+9 =x-9+9

11 =c

logx-log(x-l)^2=2log(x-1)​

Answers

Answer:

  x = 1.00995066776

  x = 2.52925492433

Step-by-step explanation:

This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...

  [tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]

The attached graph shows zeros at

  x = 1.00995066776 and 2.52925492433

_____

Comment on the equation

Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068

Comment on the answer refinement

We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.

A quality control manager is concerned about variability of the net weight of his company’s individual yogurt cups. To check the consistency, he takes a random sample of sixteen 6-ounce yogurt cups and finds the mean of the sampled weights to be 5.85 ounces and the sample standard deviation to be 0.2 ounce.

Requried:
a. Test the hypotheses H0: µ ≥ 6 Ha: µ < 6 at the 5% level of significance. Assume the population of yogurt-cup net weights is approximately normally distributed.
b. Based on the results of the test, will the manager be satisfied that the company is not under-filling its cups?
c. State the decision rule, the test statistic, and the manager’s decision.

Answers

Answer:

a) We reject H₀

b) The manager won´t be satisfied with nominal filling its cup

c) See step-by-step explanation

Step-by-step explanation:

Normal distribution  n <  30, therefore, we should use t - student table

Sample size  n  =  16

degree of freedom  =   df =  n - 1     df = 15

Sample mean    μ  = 5,85 ou

Sample standard deviation  is    s = 0,2 ou

Hypothesis test

Null hypothesis                               H₀              μ   >=  μ₀

Alternative hypothesis                   Hₐ               μ   <   μ₀

CI  = 95 %    then   α = 5 %     α = 0,05     α/2  =  0,025

Then in t-student table we find  t(c) = 1,753

To calculate  t(s)

t(s) =  (   μ   -  μ₀  ) s/√n

t(s)  =   ( 5,85 -  6 ) / 0,2/√16

t(s)  =  -  0,15* 4 / 0,2

t(s)  =  -  3

To compare  t(s) and t(c)

|t(s)| > |t(c)|        3 > 1,753

Then t(s) is in the rejection region. We should reject H₀. Data indicate that at 95 % of CI μ seems to be smaller than 6 ou

b) The manager won´t be satisfied with nominal filling its cup

What is the equation of the parabola that has its vertex at (8,-1) and a y-intercept of (0,-17)?

Answers

y = a(x  + 1.5)^2 - 12.5

y intercept is (0,-8) so:-

-8 = a(0+1.5)^2 - 12.5

-8 = 2.25a - 12.5

a =  4.5/ 2.25 = 2

so we have  

y  = 2 ( x +1.5)^2 - 12.5

solving for x  when y = 0:-

(x + 1.5)^2 = 12.5/2 = 6.25

taking sqrt's  x + 1.5  = +/- 2.5

x =  -4,   1

so the x intercepts are (-4,0) and (1,0)

Answer:

y = –1∕4(x – 8)^2 – 1

Step-by-step explanation:

I took the exam and  got  it  right.

Combine like terms. What is a simpler form of each expression? 4c-4d+8c-3d

Answers

Answer:

12c-7d

Step-by-step explanation:

[tex]4c-4d+8c-3d=0\\4c+8c=3d+4d\\12c=7d\\12c-7d[/tex]

Answer: 12c-7d

===============================================

Explanation:

The terms 4c and 8c are one pair of like terms that combine to 4c+8c = 12c. We add 4 and 8 to get 12, then tack a 'c' at the end

The other pair of like terms are -4d and -3d. They combine to -7d for similar reasoning.

12c and -7d are not like terms, so we can't combine them and we stop here.

-----------

One way to think of combining like terms is consider simplifying 2c+3c. You could say that 2c represents having 2 cups while 3c is having 3 cups. Writing 2c+3c means we start with 2 cups and add on 3 more getting a total of 2+3 = 5 cups. Symbolically we would then write 5c. Therefore 2c+3c = 5c.

Identify the recursive formula for the sequence given by the explicit formula f(n) = 20 – 4(n − 1).

Answers

Answer:

[tex]\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]

Step-by-step explanation:

[tex]f(n)=20-4(n-1)=20+(n-1)(-4)\\\\\text{It's an explicit formula of an arithmetic sequence:}\\\\f(n)=a_1+(n-1)(d)\\\\a_1-\text{first term}\\d-\text{common difference}\\\\\text{Conclusion:}\\\text{Next term}=\text{previous one}\ -4\\\\\text{The recursive formula:}\\\\\huge\boxed{f(n)=\left\{\begin{array}{ccc}f(1)=20\\f(n)=f(n-1)-4\end{array}\right}[/tex]

Answer:

Step-by-step explanation:

someone answered already

Use the frequency distribution, which shows the number of American voters (in millions) according to age, to

find the probability that a voter chosen at random is in the 18 to 20 years old age range

Ages

18 to 20

21 to 24

25 to 34

35 to 44

45 to 64

65 and over

Frequency

4.2

7.8

20.8

23.7

50.1

28 2

Date

07/2

3:29

The probability that a voter chosen at random is in the 18 to 20 years old age range is 0.0311

(Round to three decimal places as needed.)

07/2

8:52

Question Viewer

07/1

8:03

07/1

5:46

>

07/1

12:2

07/1

5:39

07/1

2:42

Question is complete. Tap on the red indicators to see incorrect answers.

07/1

12:00

Answers

Answer:

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

Step-by-step explanation:

We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.

Ages                Frequency

18 to 20             4.2

21 to 24             7.8

25 to 34           20.8

35 to 44           23.7

45 to 64           50.1

65 and over       28.2

∑                        134.8

The probability of an event is given by the occurrence of an event by the total occurrences .

So

Here the occurrence of ages 18-20 is given by 4.2

and the total frequency is 134.8

The probability that a voter chosen at random is in the 18 to 20 years old age range is =  4.2/ 134.8= 0.0311572

If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?

Answers

Answer:

The probability that the box will contain less than the advertised weight of 453 g is 0.00034.

Step-by-step explanation:

Let X represent the weight (in grams) of cereal in a box of Lucky Charms.

It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.

Compute the probability that the box will contain less than the advertised weight of 453 g as follows:

[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]

                  [tex]=P(Z<-3.4)\\=0.00034[/tex]

*Use the z-table.

Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.

A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?

Answers

Answer:

Total expected amount = $0.04375

Step-by-step explanation:

We need to calculate probability of getting heads on every combination of coin tosses

HHH = 1/8 = 3 heads

HHT = 1/8 = 2 heads

HTH = 1/8 = 2 heads

HTT = 1/8 = 1 head

THH = 1/8 = 2 heads

THT = 1/8 = 1 head

TTH = 1/8 = 1 head

TTT = 1/8 = 0 head

So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175

Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225

Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375

Total expected amount = 0.00375 + 0.0225 + 0.0175

Total expected amount = $0.04375

If the sum of the daily unpaid balances is $7,812 over a 31-day billing cycle, what is the average daily balance?

Answers

Answer:

252

Step-by-step explanation:

Divide 7812 by 31 and we get the average daily answer... Hope this helps!!


Which of the following is the correct notation of the complex number?

Answers

Answer:

-84 + 10i

Step-by-step explanation:

Standard Complex Form: a + bi

Step 1: Evaluate

√-100 = √-1 x √100 = i x 10 = 10i

-84 = -84

Step 2: Combine

10i - 84

Step 3: Rearrange

-84 + 10i

Answer:

Last Option

Step-by-step explanation:

√-100 - 84

(√(100×-1)) - 84

(√100)(√-1)-84

√-1 = i

10i - 84 or -84 + 10i

a company should stop making a part internally and buy externally when

Answers

Answer:

Make-or-Buy Decision

Step-by-step explanation:

If the nth term is , then the (n+1)st is: Please make sure you check the image :)

Answers

Answer:

( n+1) /2 *( 3n+2)

Step-by-step explanation:

n/2 * ( 3n-1)

We want the n+1 term

Replace n with n+1

( n+1) /2 *( 3( n+1) -1)

Distribute

( n+1) /2 *( 3n+3 -1)

( n+1) /2 *( 3n+2)

Answer:

[tex]\large \boxed{\sf C. \ \frac{n+1}{2} (3n+2)}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{n}{2} (3n-1)[/tex]

To find the (n+1)st term, replace the n variable with n+1.

[tex]\displaystyle \frac{n+1}{2} (3(n+1)-1)[/tex]

Expand brackets.

[tex]\displaystyle \frac{n+1}{2} (3n+3-1)[/tex]

Subtract like terms in brackets.

[tex]\displaystyle \frac{n+1}{2} (3n+2)[/tex]

the bold answer is incorrect. what is the right answer?

Answers

Answer: first choice

Explanation:

A complementary angle are two angles add up to 90 degree

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