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3 years ago

Caroline flips a coin 3 times. According to the tree diagram, how many possible outcomes exist?

Mathematics

2 answers:

nadya68 [22]3 years ago

8 0

Tossing a coin n times or tossing n coins simultaneously are same things.
AND the no. of outcomes are 2^n.

Here the answer is 2³ = 8

wariber [46]3 years ago

3 0

I believe the answer is D.8

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Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

3 years ago

En una reunión de 40 viejos piratas, 1/5 tenían una pata de palo y los 3/4 de ellos habían navegado en El Corsario. ¿Cuántos pir

Serga [27]

Answer:

spanish

Step-by-step explanation:

4 0

3 years ago

of the students in Ms. Danver's class, 6 walk to school. This represents 30% of her students.How many students are in Ms. Danver

Andrews [41]

21 students because if 6 represents 30% u add 6 two more time which equals 18 and 90% then u add 3 more because it is half of 6. when u add 3 more u will get 21 and 100%

8 0

3 years ago

Read 2 more answers

The display gives the result of performing a quadratic regression on a data set where the inputs are speeds in miles per hour an

alina1380 [7]

Y = a x² + b x + c
y = 0.0473809524 · 20² + 2.221428571 · 20 - 0.005952381 =
= 18.95236 + 44.42875 - 0.05952381 = 63.374978 ≈ 63.4
Answer: C ) 63.4 ft.

7 0

3 years ago

May I please receive help?

liq [111]

Answer:

Circumference: 12.56 yd
Area: 12.56 yd²

Step-by-step explanation:

The circumference is given by ...

C = πd

C = (3.14)(4 yd) = 12.56 yd

The area is given in terms of diameter by ...

A = (π/4)d²

A = (3.14/4)(4 yd)² = 12.56 yd²

3 0

3 years ago