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Ira Lisetskai [31]

2 years ago

13

What is the area of a circle with a circumference of 36.68 units

1 answer:

Lina20 [59]2 years ago

4 0

Answer:

radius = circumference / (2 * PI)

radius = 5.8378033126

Circle Area = PI * radius^2

Circle Area = PI * 5.8378033126^2

Circle Area = PI * 34.0799475167

Circle Area = 107.07 square units

Step-by-step explanation:

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32 percent of the customers of a fast food chain order the Whopper, French fries and a drink. A random sample of 10 cash registe

weqwewe [10]

Answer: 0.0023

Step-by-step explanation:

Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.

probability of success p = 32% = 0.32

Sample size : n= 10

Binomial probability function :

$P(X=x)= \ ^nC_xp^x(1-p)^{n-x}$

Now, the probability that eight receipts will show that the above three food items were ordered :

$P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023$

hence, the required probability = 0.0023

8 0

2 years ago

Add −2/3+2 3/8 . Write your answer as a mixed number in simplest form.

d1i1m1o1n [39]

Answer:

41/24 or 1 17/24

Step-by-step explanation:

2 3/8=19/8

-2/3+19/8

-16/24+57/24

41/24

5 0

1 year ago

Read 2 more answers

Please help me for the love of God if i fail I have to repeat the class

Elena-2011 [213]

$\theta$ is in quadrant I, so $\cos\theta>0$ .

$x$ is in quadrant II, so $\sin x>0$ .

Recall that for any angle $\alpha$ ,

$\sin^2\alpha+\cos^2\alpha=1$

Then with the conditions determined above, we get

$\cos\theta=\sqrt{1-\left(\dfrac45\right)^2}=\dfrac35$

and

$\sin x=\sqrt{1-\left(-\dfrac5{13}\right)^2}=\dfrac{12}{13}$

Now recall the compound angle formulas:

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

$\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$

$\sin2\alpha=2\sin\alpha\cos\alpha$

$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$

as well as the definition of tangent:

$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$

Then

1. $\sin(\theta+x)=\sin\theta\cos x+\cos\theta\sin x=\dfrac{16}{65}$

2. $\cos(\theta-x)=\cos\theta\cos x+\sin\theta\sin x=\dfrac{33}{65}$

3. $\tan(\theta+x)=\dfrac{\sin(\theta+x)}{\cos(\theta+x)}=-\dfrac{16}{63}$

4. $\sin2\theta=2\sin\theta\cos\theta=\dfrac{24}{25}$

5. $\cos2x=\cos^2x-\sin^2x=-\dfrac{119}{169}$

6. $\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}=-\dfrac{24}7$

7. A bit more work required here. Recall the half-angle identities:

$\cos^2\dfrac\alpha2=\dfrac{1+\cos\alpha}2$

$\sin^2\dfrac\alpha2=\dfrac{1-\cos\alpha}2$

$\implies\tan^2\dfrac\alpha2=\dfrac{1-\cos\alpha}{1+\cos\alpha}$

Because $x$ is in quadrant II, we know that $\dfrac x2$ is in quadrant I. Specifically, we know $\dfrac\pi2$ , so $\dfrac\pi4$ . In this quadrant, we have $\tan\dfrac x2>0$ , so

$\tan\dfrac x2=\sqrt{\dfrac{1-\cos x}{1+\cos x}}=\dfrac32$

8. $\sin3\theta=\sin(\theta+2\theta)=\dfrac{44}{125}$

6 0

2 years ago

Samantha works at a nursery where she pots plants. It takes her 112 hours to pot 12 plants. Question 1 Part A How many plants ca

PolarNik [594]

Answer:

9

Step-by-step explanation:

112/12= 9.3

3 0

2 years ago

A fair coin is flipped three times. What is the probability of getting two heads and then a tail?

Debora [2.8K]

2/3!

I hope this helped! Mark me Brainliest! :) -Raven❤️

3 0

2 years ago

Read 2 more answers