What type of number is 1/3?

Select each correct answer.

real
rational
natural
whole
integer
irrational

I see you use the TeX command "\binom" for binomial coefficient, but I think you meant to use "\frac" to write a fraction, namely,

[tex]\dfrac{\sin(\alpha)+\sin(2\alpha)}{1+\cos(\alpha)+\cos(2\alpha)}=\tan(\alpha)[/tex]

and I assume you're supposed to establish an identity.

Recall the double angle identities for cos and sin :

cos(2α) = cos²(α) - sin²(α) = 2 cos²(α) - 1

sin(2α) = 2 sin(α) cos(α)

Now expand the left side as

(sin(α) + sin(2α)) / (1 + cos(α) + cos(2α)) = (sin(α) + 2 sin(α) cos(α)) / (1 + cos(α) + 2 cos²(α) - 1)

Factor sin(α) from the numerator, and after canceling the 1s in the denominator and factor cos(α) :

… = [sin(α) (1 + 2 cos(α))] / [cos(α) (1 + 2 cos(α))]

Cancel the factors of 1 + 2 cos(α) :

… = sin(α) / cos(α)

which is equivalent to

… = tan(α)

by definition of tan.

Answer:

JK, NK

Step-by-step explanation:

both start at a point and extend through an arrow

Answer:

3,5

Step-by-step explanation:

Answer:

C 0.60km

I hope this answer helps if you have any questions just ask

Answer:

if u just scan that with photo math it will give u answer and explanation :) hope that helped i am sorry i don't know the anwswer

Step-by-step explanation:

Answer:

k=9

..............................

Answer:

∠CDE = 76

Explanation:

1) Find ∠CED

- 180 - 116 = 64

2) Find y

- 4y + 7y + 6 + 64 = 180

- 11y + 70 = 180

- 11y = 110

- y = 10

3) Substitute 10 for y

- 7y + 6

- 7(10) + 6

- 70 + 6

= 76

Answer:

if you pit the shape in a straight line it would be 180 degrees now take 180 take 130 and 100 and subtract those add that to the other 30 then take 180 divided by 60

Answer:

x = 50°

Step-by-step explanation:

sum of exterior angles is always equal to 360°

so, we can add all the given numbers and set them equal to 360° to find x:

130° + 30° + 100° + x° + x° = 360°

260° + 2x = 360°

2x = 100°

x = 50°

Answer:

D. 0-69

Step-by-step explanation:

I'm not quite 100% sure but I believe it is D. This is because the spread means the range, and the range is the lowest value to between the highest value so it makes sense that the spread is 0-69

apologize of its wrong

Answer:

62.5%

Step-by-step explanation:

There are a total of 8 people on the data plot.

5 of them got 15 questions or more correct, meaning 5/8 people got 15 or more questions correct.

5/8 = 5 ÷ 8

5 ÷ 8 = 0.625

0.625 = 62.5%

Answer:

its 125

Step-by-step explanation:

5x5x5

Answer:

Volume = [tex]length * width * height.[/tex]

Step-by-step explanation:

[tex]V=a^{3}[/tex]  that is the formula

So the volume of this cube is 125 cm

Answer:

AD = 13

Step-by-step explanation:

Area of trapezoid ABCD

[tex] = \frac{1}{2} (AB + AD) \times AB \\ \\ 525= \frac{1}{2} (37+ AD) \times21\\ \\ 525 \times 2= (37+ AD) \times21 \\ \\ 1050 = 21 \times 37 + 21AD \\ \\ 1050 = 777+ 21AD \\ \\ 21AD = 1050 - 777 \\ \\ 21AD = 273 \\ \\ AD = \frac{273}{21} \\ \\ AD = 13[/tex]

Answer:

A sample of 2017 people should be taken.

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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

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

Suppose a 95% confidence level:

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

Preliminary estimate of the proportion who smoke of .30.

This means that [tex]\pi = 0.3[/tex]

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)

This is n for which M = 0.02. So

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

[tex]0.02 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.02}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.02})^2[/tex]

[tex]n = 2016.84[/tex]

To the nearest whole number, 2017.

A sample of 2017 people should be taken.

5 1/2 feet is the base of window.

Answer:

area of parllelogram =base×height

25 2/3=base×4 2/3

77/3=base×14/3

77/3×3/14=base

base=77/14=11/2=5 1/2feet

Answer:

x = 39.5

Step-by-step explanation:

2(x-10) = 59

x - 10 = 29.5

x = 39.5

Answer:

x=39.5 or 79/2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Prism

Step-by-step explanation:

Answer:

–2 and 2      8 and –8                                                                                                         Which pairs of numbers are opposites? Check all that apply.

–6 and –6

–2 and 2

4 and 4

8 and –8

10 and 0

Step-by-step explanation:

Answer: 12 INCHES

Step-by-step explanation:

Answer:

no hablo espanol papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas papas fritas

Step-by-step explanation:

Answer:

1. 336

2. 9

3. 14

Step-by-step explanation:

He wraps 42 gifts/3hours

24 hours is 8 "3 hours"

42 hours per 3 gifts * 8 "3 hours" = 336 gifts

126 gifts is 3 "42 gifts"

3 hours per 42 gifts * 3 "42 gifts" = 9 hours

He wraps 42 gifts/3hours

divide these values by 3 and you get  14 gifts/one hour

14 gifts every one hour

Answer:

4 × 10²

Step-by-step explanation:

16 x 10^5 ÷ 4 x 10³ = 4 × 10²

4 * 10² is the number when multiplied to 4 * 10³ gives 16 * 10⁵

To divide exponents (or powers) with the same base, subtract the exponents.

Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.

The given expression is

4 * 10³ multplies with   ____ =   16 * 10⁵

We have to solve this ,

Let the number be x

4 * 10³ multplies with   __x__ =   16 * 10⁵

x = (16 * 10⁵ )/(4 * 10³)

x= ( 4²  * 10⁵ )/(4 * 10³)

Therefore the numerator and denominator has the same base so

[tex]\rm 4^{2-1} \times 10^{5-3}\\\\\\4^{1} \times 10^{2}\\\\\\4\times 10^{2}[/tex]is the number that when multiplied to   4 * 10³  gives  16 * 10⁵

To know more about Exponent Theorem

https://brainly.com/question/6532227

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Answer:

105/4 ft^2

Step-by-step explanation:

Multiply length and width: 7*15/4 = 105/4 ft^2

Answer:

Slope is 3/-7

Step-by-step explanation:

[tex]slope = \frac{6 - 3}{ - 5 - 2} = \frac{3}{ - 7} [/tex]

Answer:

h=43/2 = 21 1/2 = 21.5

Step-by-step explanation:

h−6.5=15

Add 6.5 to both sides.

h=15+6.5

Add 15 and 6.5 to get 21.5.

h=21.5