Polar coordinates: which is not the same?

Polar Coordinates: Which Is Not The Same?

Answers

Answer 1

Answer:

The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.

Step-by-step explanation:

Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.

Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.

Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)

We know that :

7.518 - 1.236 = 6.282 = ( About ) 2π

5.047 + 1.236 = 6.283 = ( About ) 2π

1.236 + 1.906 = 3.142 = ( About ) 2π

Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).


Related Questions

isted below are amounts​ (in millions of​ dollars) collected from parking meters by a security service company and other companies during similar time periods. Do the limited data listed here show evidence of stealing by the security service​ company's employees? Security Service Company: 1.5 1.7 1.6 1.4 1.7 1.5 1.8 1.4 1.4 1.5 Other Companies: 1.8 1.9 1.6 1.7 1.8 1.9 1.6 1.5 1.7 1.8 Find the coefficient of variation for each of the two​ samples, then compare the variation. The coefficient of variation for the amount collected by the security service company is nothing​%. ​(Round to one decimal place as​ needed.)

Answers

Answer:

Means:

1.55

1.73

Standard Deviation:

0.1434

0.1338

Coefficient of variation:

9.2

7.7

the limited data listed here shows evidence of stealing by the security service​ company's employees.

Step-by-step explanation:

Given data:

security Service Company          Other Companies    

               x                                                 x

               1.5                                              1.8

               1.7                                               1.9

               1.6                                               1.6

               1.4                                                1.7

               1.7                                                 1.8

               1.5                                                 1.9

               1.8                                                 1.6

               1.4                                                  1.5

               1.4                                                  1.7

               1.5                                                  1.8

      n₁ = 10                                                 n₂ = 10

To find:

coefficient of variation for each of the two​ samples

Solution:

The formula for calculating coefficient of variation of sample is:

Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100%

Calculate Mean for Security Service Company data:

Mean =  (Σ x₁) / n₁

         = (1.5 + 1.7 + 1.6 + 1.4 + 1.7 + 1.5 + 1.8 + 1.4 + 1.4 + 1.5) / 10

         = 15.5 / 10

Mean = 1.55

Calculate Standard Deviation for Security Service Company data:

Standard Deviation = √∑(x₁ - Mean)²/n₁-1

                                = √∑(1.5-1.55)² + (1.7-1.55)² + (1.6-1.55)² + (1.4-1.55)² + (1.7-1.55)² + (1.5-1.55)² + (1.8-1.55)² + (1.4-1.55)² + (1.4-1.55)² + (1.5-1.55)² / 10-1

=√∑ (−0.05)² + (0.15)² + (0.05)² + (−0.15)² + (0.15)² + (−0.05)² + (0.25)² +  (−0.15)² +  (−0.15)² +  (−0.05)² / 10 - 1

= √∑0.0025 + 0.0225 + 0.0025 + 0.0225 + 0.0225 + 0.0025 + 0.0625 +        0.0225 + 0.0225 + 0.0025 / 9

= √0.185 / 9

= √0.020555555555556

= 0.14337208778404

= 0.143374

Standard Deviation = 0.143374

Coefficient of Variation for Security Service Company:

CV = (Standard Deviation / Mean) * 100%

     = (0.143374 /  1.55) * 100

     = 0.09249935 * 100

     = 9.249935

CV  = 9.2

CV  = 9.2%

Calculate Mean for Other Companies data:

Mean =  (Σ x₂) / n₂

          =  (1.8 + 1.9 + 1.6 + 1.7 + 1.8 + 1.9 + 1.6 + 1.5 + 1.7 + 1.8) / 10

          =   17.3 / 10

Mean  = 1.73

Calculate Standard Deviation for Other Companies data:

Standard Deviation = √∑(x₂-Mean)²/n₂-1

                                = √∑[(1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.7-1.73)² + (1.8-1.73)² + (1.9-1.73)² + (1.6-1.73)² + (1.5-1.73)² + (1.7-1.73)² + (1.8-1.73)²] / 10 - 1

                                = √∑ [(0.07)² + (0.17)² + (-0.13)² + (-0.03)² + (0.07)² + (0.17)² + (-0.13)² + (-0.23)² + (-0.03)² + (0.07)²] / 9

                                = √∑ (0.0049 + 0.0289 + 0.0169 + 0.0009 + 0.0049 + 0.0289 + 0.0169 + 0.0529 + 0.0009 + 0.0049) / 9

                                = √(0.161 / 9)

                                = √0.017888888888889                                

                                = 0.13374935098493

                                =  0.13375

Standard Deviation = 0.13375

Coefficient of Variation for Other Companies:

CV = (Standard Deviation / Mean) * 100%

     = (0.13375 / 1.73) * 100

     = 0.077312 * 100

     = 7.7312

CV = 7.7

CV = 7.7%

Yes, the limited data listed here shows evidence of stealing by the security service​ company's employees because there is a significant difference in the variation.

Explain how to solve the inequality (x + 1)(x – 2) ∙ (x – 3) > 0. Explain in your own words, each step necessary to solve the inequality, making sure to follow the proper order of operations. Is this inequality accurate? Explain why or why not.

Answers

Answer:

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

Step-by-step explanation:

Given

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Required

Solve; with steps

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Start by splitting the inequality as follows

[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or  [tex]x - 3 > 0[/tex]

Solve the inequalities one after the other

Solving: [tex]x + 1 > 0[/tex]

Subtract 1 from both sides

[tex]x + 1 - 1 > 0 - 1[/tex]

[tex]x > -1[/tex]

Solving: [tex]x - 2 > 0[/tex]

Add 2 to both sides

[tex]x - 2 +2 > 0 +2[/tex]

[tex]x > 2[/tex]

Solving: [tex]x - 3 > 0[/tex]

Add 3 to both sides

[tex]x - 3 +3> 0+3[/tex]

[tex]x > 3[/tex]

Hence, the solution to the inequality is

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

for the functions f(x) = 4x^4+4x^3-8x^2-13x-5 and g(x) = x+1, find (f/g)(x) and (f/g)(2)

Answers

Answer:

(f/g)(x) = 4x³ - 8x - 5

(f/g)(2) = 11

Step-by-step explanation:

f(x) = 4x⁴ + 4x³ - 8x² - 13x - 5

g(x) = x + 1

To find (f/g)(2) first find (f/g)(x)

To find (f/g)(x) factorize f(x) first

That's

f(x) = 4x⁴ + 4x³ - 8x² - 13x - 5

f(x) = ( x + 1)( 4x³ - 8x - 5)

So we have

[tex] (f/g)(x) = \frac{( x + 1)( 4x³ - 8x - 5)}{x + 1} [/tex]

Simplify

We have

(f/g)(x) = 4x³ - 8x - 5

To find (f/g)(2) substitute 2 into (f/g)(x)

That's

(f/g)(2) = 4(2)³ - 8(2) - 5

= 4(8) - 16 - 5

= 32 - 16 - 5

= 11

(f/g)(2) = 11

Hope this helps you

During April of 2013, Gallup randomly surveyed 500 adults in the US, and 47% said that they were happy, and without a lot of stress." Calculate and interpret a 95% confidence interval for the proportion of U.S. adults who considered themselves happy at that time. 1 How many successes and failures are there in the sample? Are the criteria for approximate normality satisfied for a confidence interval?
A What is the sample proportion?
B compute the margin of error for a 95% confidence interval.
C Interpret the margin of error you calculated in Question 1
C. Give the lower and upper limits of the 95% confidence interval for the population proportion (p), of U.S. adults who considered themselves happy in April, 2013.
D Give an interpretation of this interval.
E. Based on this interval, is it reasonably likely that a majority of U.S. adults were happy at that time?
H If someone claimed that only about 1/3 of U.S. adults were happy, would our result support this?

Answers

Answer:

number of successes

                 [tex]k = 235[/tex]

number of failure

                 [tex]y = 265[/tex]

The   criteria are met    

A

    The sample proportion is  [tex]\r p = 0.47[/tex]

B

    [tex]E =4.4 \%[/tex]

C

What this mean is that for N number of times the survey is carried out that the which sample proportion obtain will differ from  the true population proportion will not  more than 4.4%

Ci  

   [tex]r = 0.514 = 51.4 \%[/tex]

 [tex]v = 0.426 = 42.6 \%[/tex]

D

   This 95% confidence interval  mean that the the chance of the true    population proportion of those that are happy to be exist within the upper   and the lower limit  is  95%

E

  Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

F

 Yes our result would support the claim because

            [tex]\frac{1}{3 } \ of N < \frac{1}{2} (50\%) \ of \ N , \ Where\ N \ is \ the \ population\ size[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 500[/tex]

     The sample proportion is  [tex]\r p = 0.47[/tex]

 

Generally the number of successes is mathematical represented as

             [tex]k = n * \r p[/tex]

substituting values

             [tex]k = 500 * 0.47[/tex]

            [tex]k = 235[/tex]

Generally the number of failure  is mathematical represented as

           [tex]y = n * (1 -\r p )[/tex]

substituting values

           [tex]y = 500 * (1 - 0.47 )[/tex]

           [tex]y = 265[/tex]

for approximate normality for a confidence interval  criteria to be satisfied

          [tex]np > 5 \ and \ n(1- p ) \ >5[/tex]

Given that the above is true for this survey then we can say that the criteria are met

  Given that the confidence level is  95%  then the level of confidence is mathematically evaluated as

                       [tex]\alpha = 100 - 95[/tex]

                        [tex]\alpha = 5 \%[/tex]

                        [tex]\alpha =0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is

                 [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as  

                [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p}{n} }[/tex]

substituting values

                 [tex]E = 1.96 * \sqrt{ \frac{0.47 (1- 0.47}{500} }[/tex]

                 [tex]E = 0.044[/tex]

=>               [tex]E =4.4 \%[/tex]

What this mean is that for N number of times the survey is carried out that the proportion obtain will differ from  the true population proportion of those that are happy by more than 4.4%

The 95% confidence interval is mathematically represented as

          [tex]\r p - E < p < \r p + E[/tex]

substituting values

        [tex]0.47 - 0.044 < p < 0.47 + 0.044[/tex]

         [tex]0.426 < p < 0.514[/tex]

The upper limit of the 95% confidence interval is  [tex]r = 0.514 = 51.4 \%[/tex]

The lower limit of the   95% confidence interval is  [tex]v = 0.426 = 42.6 \%[/tex]

This 95% confidence interval  mean that the the chance of the true population proportion of those that are happy to be exist within the upper and the lower limit  is  95%

Given that 50% of the population proportion  lie with the 95% confidence interval  the it correct to say that it is reasonably likely that a majority of U.S. adults were happy at that time

Yes our result would support the claim because

            [tex]\frac{1}{3 } < \frac{1}{2} (50\%)[/tex]

 

You have 9kg of oats and cup scales that gears of 50g and 200g. How − in three weighings− can you measure 2kg of the oats?

Answers

Answer: You will need 8 cup scales

Step-by-step explanation:

kg=1000 grams

2000/250=8

Translate this sentence into an equation. 43 is the sum of 11 and Carlos age. Use the variable c to represent Carlos age.

Answers

Answer:

c + 11 = 43

Step-by-step explanation:

C = Carlos age

11 = The number added

43 = The number added plus carlos' age

c +11 = 43

c = 43 - 11

c = 32

Carlos' age is 32 years.

Answer:

C+11=43

Step-by-step explanation:

C= Carlos age

11= added number

43= Carlos age +added number

C+11=43

C=43-11

C=32

Age of Carlos 32.  :)

Varia is studying abroad in Europe. She is required pay $3,500 (in US dollars) per year to the university; however, she must pay in euros. How many euros can Varia expect to pay per month to the university?

Answers

Answer: 247.92 euros

Step-by-step explanation:

Given:  Varia is required pay $3,500 (in US dollars) per year to the university.

So, [tex]$3500\div 12 \approx\$291.67[/tex]

i.e. She will pay $ 291.67 per month.

Recent currency value: 1 US dollar = 0.85 euro

∴ $291.67 = ( 0.85 ×291.67) euros

= 247.92 euros  [Round to the nearest cent]

She can expect 247.92 euros to pay per month to the university.

Kyle buys $30,000 of company XYZ's shares, at a share price of $50. A year later, XYZ's share price is $55, and Kyle sells all his shares. How many dollars did Kyle's investment gain

Answers

Answer:

$3,000

Step-by-step explanation:

Given that the shares are $50 per share and that Kyle buys $30,000 worth of shares,

Number of shares bought = total price of shares ÷ price per share

= $30,000 ÷ $50

= 600 shares

We are also give that a year later, the shares are worth $55

Total value of shares 1 year later = Price per share one year later x number of shares

= $55 x 600

= $33,000

Hence the investment gained $33,000 - $30,000 = $3,000

Answer:

10%

Step-by-step explanation:

x - amount of shares bought

x * 50[$] = 30000[$]

x = 30000/50 = 600

if he bought 600 shares then he sold earning in total:

600 * 55[$] = 33000[$]

that means investmant gain can be calculate as:

return on investment =  (gain from investment – cost of investment) / cost of investment

return on investment = (33000 - 30000) / 30000 = 3000/30000 =0.1 = 10%

Is 1.45 times 10 to the -7 power a scientific notation

Answers

Answer:

Yes.

It is 1.45 x 10^-7 or 0.000000145

Hope it helps!

Answer:

It is 1.45 x 10^-7 or 0.000000145

Step-by-step explanation:

i will rate you brainliest

Answers

Answer:

(3x+11)/ (5x-9)

Step-by-step explanation:

The numerator is what is on the top of the bar in the middle

(3x+11)/ (5x-9)

Answer:

[tex]\large \boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

The numerator of a fraction is the top section of the fraction.

the terms in this sequence increase by the same amount each time. _19_ _ 34_ a) work out the missing terms.

Answers

Answer:

The sequence is 14, 19, 24, 29, 34, 39.

Step-by-step explanation:

Let's call the common difference (the difference between two consecutive terms) as d. We see that the second term is 19 and the 5th term is 34 and since 5 - 2 = 3, we add d 3 times to 19 to get 34 so therefore:

19 + 3d = 34

3d = 15

d = 5 so the first term is 19 - 5 = 14, the third would be 19 + 5 = 24, the fourth would be 24 + 5 = 29 and the sixth would be 34 + 5 = 39.

Find all solutions to the equation. 2sin theta - squareroot 3 = 0
Write your answer in radians in terms of pi, and use the "or" button as necessary.
Example: theta = pi/5 + 2 k pi, k element Z or theta = pi/7 + k pi, k element Z

Answers

Answer:

[tex]\theta[/tex] =2mπ + π/3 for m ∈ Z.

Step-by-step explanation:

Given the equation [tex]2sin\theta - \sqrt{3} = 0[/tex], we are to find all the values of [tex]\theta[/tex] that satisfies the equation.

[tex]2sin\theta - \sqrt{3} = 0\\\\2sin\theta = \sqrt{3} \\\\sin\theta = \sqrt{3}/2 \\\\\theta = sin{-1} \sqrt{3}/2 \\\\\theta = 60^0[/tex]

General solution for sin[tex]\theta[/tex] is [tex]\theta[/tex] = nπ + (-1)ⁿ ∝, where n ∈ Z.

If n is an even number say 2m, then [tex]\theta[/tex] = (2m)π + ∝ where ∝ = 60° = π/3

Hence, the general solution to the equation will be [tex]\theta[/tex] = 2mπ + π/3 for m ∈ Z.

WILL GIVE BRAINLYEST AND 30 POINTS Which of the followeing can be qritten as a fraction of integers? CHECK ALL THAT APPLY 25, square root of 14, -1.25, square root 16, pi, 0.6

Answers

Answer:

25 CAN be written as a fraction.

=> 250/10 = 25

Square root of 14 is 3.74165738677

It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION,  but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION

=> 374/100

-1.25 CAN be written as a fraction.

=> -5/4 = -1.25

Square root of 16 CAN also be written as a fraction.

=> sqr root of 16 = 4.

4 can be written as a fraction.

=> 4 = 8/2

Pi = 3.14.........

It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION

=> 314/100

.6 CAN be written as a fraction.

=> 6/10 = .6

"Julien is trying to determine his variable type in order to select the proper statistical tests. He is measuring the height of a part. What type of variable is this"

Answers

Answer:

Quantitative

Step-by-step explanation: Quantitative or numerical variable are statistical or measured variables which involves numbers. Numerical variables allows for mathematical operations such as addition, subtraction and so on to be performed in them. Quantitative variables include height, age, weight, population and other measured variable with have numerical attributes. They can be measured on either ordinal, ratio or interval scales. Hence, since Julien is trying to determine height, the variable is a quantitative or numeric variable.

Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−2x3+x2−32x−240

Answers

Answer:

[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]

Step-by-step explanation:

Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).

[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]

The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.

[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]

We identify the coefficients for the like terms, it comes

a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].

[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]

The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.

[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]

And we can write in [tex]\mathbb{C}[/tex]

[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

HELP PLEASE!! (math)

Answers

Answer:

Hey there!

We can write: -2+9=7.

Let me know if this helps :)

Answer:

[tex]\large \boxed{{-2+9=7}}[/tex]

Step-by-step explanation:

-2 is also 0-2

The arrow goes from 0 to -2.

-2 + 9 = 7

The arrow goes from -2 to 7.

what is the difference between growth and development

Answers

Answer:

growth is usually reffered to as physical growth happening in size while development happens more gradually and happens mentally.

Step-by-step explanation:

idk if u meant pyscologically or not but that is my understanding.

BRAINLIEST IF CORRECT!!! and 15 points solve for z -cz + 6z = tz + 83

Answers

Answer:

z = 83/( -c+6-t)

Step-by-step explanation:

-cz + 6z = tz + 83

Subtract tz from each side

-cz + 6z -tz= tz-tz + 83

-cz + 6z - tz = 83

Factor out z

z( -c+6-t) = 83

Divide each side by ( -c+6-t)

z( -c+6-t)/( -c+6-t)  = 83/( -c+6-t)

z = 83/( -c+6-t)

Question 1 (5 points)
The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale
factor 2/3 about the origin. Find the endpoints of the dilated line segment.
OA) (-2, 4), (6,8)
B) (2, 4). (6,8)
OC) (4, -2), (6,8)
OD) (-2,4), (8,6)​

Answers

Answer: A) (-2, 4), (6,8)

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).

Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor [tex]\dfrac23[/tex] about the origin.

Let A' and B' b the endpoints of the dilated line segment.

Then, [tex]A'(\dfrac{2}{3}(-3), \dfrac23(6))=A'(-2,4)[/tex]

[tex]B'(\dfrac{2}{3}(9), \dfrac23(12))=B'(6,8)[/tex]

Hence, the correct option is A) (-2, 4), (6,8)

Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps

west and finally 50 steps on a bearing of 3150

.

i. Sketch Musah’s movement

ii. How far west is Musah’s final point from the centre?
iii. How far north is Musah’s final point from the centre?

iv. Describe how you would guide a JHS student to find the bearing and distance of

Musah’s final point from the centre. ​

Answers

Answer:

ii. 75 steps

iii. 75 steps

iv. 106 steps, and [tex]315^{0}[/tex]

Step-by-step explanation:

Let Musah's starting point be A, his waiting point after taking 50 steps northward and 25 steps westward be B, and his stopping point be C.

ii. From the second attachment, Musah's distance due west from A to C (AD) can be determined as;

bearing at B = [tex]315^{0}[/tex], therefore <BCD = [tex]45^{0}[/tex]

To determine distance AB,

[tex]/AB/^{2}[/tex] = [tex]/50/^{2}[/tex]   +  [tex]/25/^{2}[/tex]

          = 25000 + 625

          = 3125

AB = [tex]\sqrt{3125}[/tex]

     = 55.90

AB ≅ 56 steps

Thus, AC = 50 steps + 56 steps

               = 106 steps

From ΔACD,

Sin [tex]45^{0}[/tex] = [tex]\frac{x}{106}[/tex]

⇒ x = 106 × Sin [tex]45^{0}[/tex]

      = 74.9533

     ≅ 75 steps

Musah's distance west from centre to final point is 75 steps

iii. From the secon attachment, Musah's distance north, y, can be determined by;

Cos [tex]45^{0}[/tex] = [tex]\frac{y}{106}[/tex]

⇒ y = 106 × Cos [tex]45^{0}[/tex]

      = 74.9533

      ≅ 75 steps

Musah's distance north from centre to final point is 75 steps.

iv. Musah's distance from centre to final point is AC = AB + BC

                                     = 50 steps + 56 steps

                                     = 106 steps

From ΔACD,

Tan θ = [tex]\frac{75}{75}[/tex]

          = 1.0

θ = [tex]Tan^{-1}[/tex]  1.0

 = [tex]45^{0}[/tex]

Musah's bearing from centre to final point = [tex]45^{0}[/tex] + [tex]270^{0}[/tex]

                                                           =  [tex]315^{0}[/tex]

This expression represents the average cost per game, in dollars, at a bowling alley, where n represents the number of games:

3n+7/n


What is the average cost per game if James bowls 4 games?

Answers

Answer:

13.75 dollars

Step-by-step explanation:

n=4

3n+7/n =3(4) + 7/4

=12 + 1.75

=$13.75

Answer: A) 4.75

Step-by-step explanation:

How many g of amino acids are in a 2,000mL total parenteral nutrition of 4.25% travesol (amino acids and 20%dextrose?

Answers

Answer:

The  mass of  amino acid present is  85 g

Step-by-step explanation:

From the question we are told that

   The  volume of the total  parenteral nutrition is  [tex]V = 2000 mL[/tex]

   

Generally the volume of the amino acid present is  

                [tex]V_a = 0.0425 * 2000[/tex]

                [tex]V_a = 85 mL[/tex]

Generally  

               [tex]mass \ \ \alpha \ \ volume[/tex]

So the mass of amino acid present is 85g

A ladder 10 ft long leans against a vertical wall. If the lower end is being moved away from the wall at the rate of 6 ​ft/sec, how fast is the height of the top changing​ (this will be a negative​ rate) when the lower end is 6 feet from the​ wall?

Answers

Answer:

-4.5ft per sec

Step-by-step explanation:

Assume that vertical wall has a distance of y and the horizontal floor is x (6 ft).

This forms a triangle with the ladder as the hypothenus of length 10ft

We have dy/dt = 6ft per sec

According to Pythagoras law the relationship between x and y is

(x^2) + (y^2) = (hypothenus ^2) = 10^2

When we differentiate both sides of the equation

2x(dx/dt) + 2y(dy/dt) = 0

dy/dt = (x/y) * (dx/dt)

y= √(10^2) - (6^2) = 8ft

So dy/dt = (6/8)* (6/1)= -4.5 ft per sec

It is a negative rate

1) Dada a função, em reais, definida por f(x)=3.x-5. calcule :

a) f(2)=
b) f(-1)=

Answers

Answer:

f(x)= 3x-5

f(2) = 3(2)-5 = 6-5= 1

f(-1)= 3(-1)-5= -3-5= -8

Hope this helps

if u have question let me know in comments ^°^

will give 5 stars and thanks for correct answer Richard starts high school every day at 7:45 A.M.. How many seconds is Richard in school each day of school dismissed at 2:15 P.M.

Answers

Richard spends 21,600 seconds at school each day.

Write 8:18 as a fraction in simplest form.

Ratio as a Fraction:

Fraction in Simplest Form:

Answers

Answer:

[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]

[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]

Step-by-step explanation:

Part 1: Writing a ratio as a fraction

A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,

Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).

Therefore, 8:18 as a fraction is 8/18.

Part 2: Fraction in simplest form

To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.

8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.

Instead, if both numbers are even, divide by 2.

8/2 = 4

18/2 = 9

Check to see if the new numerator and denominator can reduce any further.

4/9 = 4/9

The fraction in simplest form is 4/9.

how many solutions are there to this non-linear systems/graph a. one solution,b.two solutions,c.no solutions

Answers

Photo of the graph?

Write the equations, after translating the graph of y = |x+2|: one unit up,

Answers

Answer:

y = |x + 2| + 1

Step-by-step explanation:

Parent Graph: f(x) = a|bx + c| + k

a is vertical stretch/shrink

b is horizontal stretch/shrink

c is horizontal movement left/right

k is vertical movement up/down

Since we are given an equation and we want to move it 1 unit up (vertical movement up), we only manipulate k:

y = |x + 2| + k

k = 1

y = |x + 2| + 1

Answer:

y = |x+2| + 1

Step-by-step explanation:

The equation will be y = |x+2| + 1.

By translating the graph one unit up, the equation will simply change by adding +1 to the graph, outside of the absolute value part.

nd the measure of angle m
2. Find the length of sie
m
18.2m
61°
15:1m
х
105mm

Answers

Answer:

1). m° = 56.1°

2). X= 91.8 mm

Step-by-step explanation:

For angle m°

Using the sine rule

15.1/sin m= 18.2/sin 90

But Sin 90= 1

15.1/sin m= 18.2

15.1= 18.2*sin m

Sin m = 15.1/18.2

Sin m=0.8297

m= sin^-1(0.8297)

m= 56.06°

m° = 56.1°

For length of side x

Using sine rule

X/sin 61= 105/sin 90

But sin 90= 1

X/sin 61= 105

X = sin61 *105

X=0.8746*105

X= 91.833 mm

X= 91.8 mm

The scores for all the Algebra 1 students at Miller High on a test are normally distributed with a mean of 82 and a standard deviation of 7. What percent of students made scores above 89?

Answers

Answer:

15.7% of students made above an 89.

Step-by-step explanation:

If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%

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