When evaluated, which expression has a result that is a rational number?

Answer:

area of polygon : 120in²

Answer:

C) y = 2.50x + 10

Step-by-step explanation:

Equation C is saying:

total cost = 2.50(number of games) + $10 entery fee

Hope this helps :)

Answer:

Hence the area of the region bounded by all leaves of the rose is [tex]\pi[/tex].

Step-by-step explanation:

Here,

[tex]2 cos (3\Theta )=0\\\Rightarrow cos(3\Theta)=0\\\Rightarrow cos(3\Theta )=cos\left (\frac{\pi }{2} \right )\\\Rightarrow \Theta =\left (\frac{\pi }{6},-\frac{\pi }{6} \right )[/tex]

Now consider for one leaf of rose:-

[tex]Area = 3\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}}\frac{r^{2}}{2}d\Theta \\\\ = \frac{3}{2}\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}}4 cos^{2}\left ( 3\Theta \right ) d\Theta \\\\ = \frac{12}{2}\int_{-\frac{\pi }{6}}^{\frac{\pi }{6}} \frac{cos(6\Theta +1)}{2}d\Theta\\\\ =\frac{6}{2}\left [ \frac{sin(6\Theta +\Theta )}{6} \right ]_{-\frac{\pi }{6}}^{\frac{\pi }{6}}\\\\ =3\times \left [ \frac{\pi }{6}+\frac{\pi }{6} \right ]\\\\ =3\times \frac{2\pi }{6}\\\\ = \pi[/tex]

Answer:

a) The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).

b) The margin of error is of 0.05.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In a sample of 400 students, 60% of them prefer eBooks.

This means that [tex]n = 400, \pi = 0.6[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.054[/tex].

Margin of error -> Question b:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 2.054\sqrt{0.6*0.4}{400}}[/tex]

[tex]M = 0.05[/tex]

The margin of error is of 0.05.

A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.

Sample proportion plus/minus the margin of error.

0.6 - 0.05 = 0.55

0.6 + 0.05 = 0.65

The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).

9514 1404 393

Answer:

  k = 10

Step-by-step explanation:

The exterior angle is equal to the sum of the remote interior angles.

  115° = (4k +5)° +(6k +10)°

  115 = 10k +15 . . . . . . . . . . . divide by °, simplify

  100 = 10k . . . . . . . . . . . . subtract 15

  10 = k . . . . . . . . . . . . . . divide by 10

Answer:

2,160

Step-by-step explanation:

432-324=108 earnings based on sales

sales x 5%=108

sales=108/.05

sales=2,160

Answer:

Five

Step-by-step explanation:

Just look at the point where x=-6

Answer:20, 40, 40,100

Step-by-step explanation:

5x+2x+2x=180 9x=180 x=20

Answer:

(6,80)

Step-by-step explanation:

To check

Substitute (6,80) for x & y value

Y = 10x + 20

80 = 10(6) + 20

80 = 60 + 20

80 = 80

Y = 5x + 50

80 = 5(6) + 50

80 = 30 + 50

80 = 80

Answer:

(6.80) is the correct answer

Answer:

g(-1)=-1

Step-by-step explanation:

g(-1)=[tex](-1)^{3} + (-1)^{2} - (-1) -2[/tex]=- 1

g(2) = [tex]2^{3} + 2^{2} -2-2=8[/tex]

g(1) =[tex]1^{3} +1^{2} -1-2=-1[/tex]

⇒g(2)+g(1)=8+(-1)=7

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\sqrt{34}[/tex]

»»————-　★　————-««  

Here’s why:

⸻⸻⸻⸻

[tex]\text{\underline{The distance formula is:}}\\\\d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer....}}\\\\d = \sqrt{(1-6)^2+(0-(-3))^2}\\--------------\\\rightarrow d = \sqrt{(-5)^2+(3)^2}\\\\\rightarrow d = \sqrt{(25+9)}\\\\\rightarrow d =\boxed{ \sqrt{34} }[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.

9514 1404 393

Answer:

Step-by-step explanation:

The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where the annual interest rate is r for t years on loan value P.

Filling in the given information, we find the monthly payment to be ...

  A = $28000(0.05/12)/(1 -(1 +0.05/12)^(-12·5)) ≈ $528.39

The monthly payment is $528.39.

__

The total amount repaid is ...

  ($528.39/mo)(60 mo) = $31,703.40

The interest paid is the difference between this and the loan amount:

  interest paid = $31,703.40 -28,000 = $3,703.40

The total interest paid is $3,703.40.

Answer:

1.) A = (1/2bh) 4 + lxw

= 1/2 x 7 x 13 x 4 + 7 x 7

182 + 49 = 231cm2

l think u can use the formula to find the area of the other pyramids

Answer:

indeed

Step-by-step explanation:

just carry the one when adding

Step-by-step explanation:

1 = 1

41 – 40 = 61 – 60

16 + 25 – 40 = 36 + 25 – 60

4² + 5² – 2 * 4 * 5 = 6² + 5² – 2 * 6 * 5

(4 – 5)² = (6 – 5)²

4 – 5 = 6 – 5

4 = 6

2 = 3

1 + 1 = 3…proved

Answer:

202 m

Step-by-step explanation:

Given :

Angle of depression, θ = 36°45' ; 45/60 = 0.75 = 36 + 0.75 = 36.75°

The height, h = 270

The distance of park bench from the building, d is given by :

Tan θ = opposite / Adjacent

Tan 36.75 = d / 270

d = 270 * Tan 36.75

d = 201.61856

d, distance of Park bench from building is 202 m

Answer:

The rate of change is 13 new participants every year.

Step-by-step explanation:

y=13x+50

This is in the form y = mx+b  where m is the slope and b is the y intercept

x is the number of years so for every year increase we gain 13 new participants

Answer:

D. Square root of 16

Step-by-step explanation:

Rational numbers are numbers that have simple answers. It is also considered as fractions, Integers, and possible square roots.

- If you chose the square root of 2 = 1.41

- Pi has a value of 3.14, It's not a fraction nor an integer so it's an Irrational number

- Square root of 10 is 3.16

- So Square root of 16 is 4 which is a regular number and a possible square root.

Thank you!

Answer:

last option- square root of 16 is a rational number

Answer: 3.333333333333% as a percent 3.25 as a decimal

Answer:

x = -30

Step-by-step explanation:

Use the direct variation equation, y = kx

Plug in 2 as y and -12 as x, and solve for k:

y = kx

2 = k(-12)

-1/6 = k

So, the equation is y = -1/6x

Plug in 5 as y and solve for x:

y = -1/6x

5 = -1/6x

-30 = x

So, when y = 5, x = -30

The exponential growth function to model represents as P = 236,000 (1+ 0.04)⁹ and 335,902 people in 2009.

The exponential growth function is given by:-

y = A(1 +r)ⁿ

where r is the rate of growth and A is the initial amount and n is the time period.

Let t represent the number of years since 2000 and P represent the population.

The population of a city is increasing at a rate of 4% each year. In 2000, there were 236,000 people in the city.

Put A = 236,000 , r = 0.04 and t = 9, we get

P = 236,000 (1+ 0.04)⁹

P = 335,902

Hence, the exponential growth function to model represents P = 236,000 (1+ 0.04)⁹ and 335,902 people in 2009.

Learn more about exponential growth and decay here:

brainly.com/question/2193820

#SPJ6

ln(20) + ln(5) = 2 ln(x)

ln(20×5) = ln(x ²)

ln(100) = ln(x ²)

100 = x ²

x = 10

Answer:

20 is it's right answer I think ok

4

Hope this helps! :)

______________

Answer:

the last one is correct.............

Answer:

Option A: [tex]5\frac{1}{4} *4\frac{1}{5}[/tex]

Step-by-step explanation:

Area of a parallelogram is base times height so in this case it would be 5 1/4 times 4 1/5. 5 1/4 being the base and 4 1/5 being the height.

Answer:

X+(X+1)+X+2)=30

Step-by-step explanation: