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alexandr1967 [171]

2 years ago

15

) A coin is tossed 13 times. a) How many different outcomes are possible? 2^8 b) How many different outcomes have exactly 4 head

s? 70 c) How many different outcomes have at least 2 heads ? 247 d) How many different outcomes have at most 4 heads? 163

1 answer:

Svetradugi [14.3K]2 years ago

3 0

Answer:

Explanation:

a) A coin has two sides, therefore the total outcome possible when a coin is tossed is 2 i.e Head (H) and Tail (T)

outcome of two coins will be 4 i.e 2^2

Outcome of three coins will be 8 i.e 2^3 and so on. Since its following a trend, the outcome when 'n' coins is tossed will be 2^n.

Using the general formula, the possible outcome when a coin is tossed 13 times will be "2^13"

b)

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Aloop of wire of area 71 cm^2 is placed with its plane parallel to a 16 mt magnetic field. the loop is then rotated so that its

kkurt [141]

Answer:

Approximately 1.62 × 10⁻⁴ V.

Explanation:

The average EMF in the coil is equal to

$\displaystyle \frac{\text{Final Magnetic Flux} - \text{Initial Magnetic Flux}}{2}$ ,

Why does this formula work?

By Faraday's Law of Induction, the EMF $\epsilon$ induced in a coil (one loop) is equal to the rate of change in the magnetic flux $\Phi$ through the coil.

$\displaystyle \epsilon(t) = \frac{d}{dt}(\Phi(t))$ .

Finding the average EMF in the coil is similar to finding the average velocity.

$\displaystyle \text{Average}\; \epsilon = \frac{1}{t}\int_0^t \epsilon(t)\cdot dt$ .

However, by the Fundamental Theorem of Calculus, integration reverts the action of differentiation. That is:

$\displaystyle \int_0^{t} \epsilon(t)\cdot dt = \int_0^{t} \frac{d}{dt}\Phi(t)\cdot dt = \Phi(t) - \Phi(0)$ .

Hence the equation

$\displaystyle \text{Average}\; \epsilon = \frac{1}{t}\int_0^t \epsilon(t)\cdot dt = \frac{\Phi(t)- \Phi(0)}{t}$ .

Note that information about the constant term in the original function will be lost. However, since this integral is a definite one, the constant term in $\Phi(t)$ won't matter.

Apply this formula to this question. Note that $\Phi$ , the magnetic flux through the coil, can be calculated with the equation

$\Phi = B \cdot A \cdot N \; \sin{\theta}$ .

For this question,

$B = \rm 16\; mT = 16\times 10^{-3}\; T$ is the strength of the magnetic field.
$A = \rm 71\; cm^{2} = 71\times \left(10^{-2}\right)^2 \; m^{2}$ is the area of the coil.
$N = 1$ is the number of loops in the coil.
$\theta$ is the angle between the field lines and the coil.
At $\rm 0\;s$ , the field lines are parallel to the coil, $\theta = 0^{\circ}$ .
At $\rm 0.7\; s$ , the field lines are perpendicular to the coil, $\displaystyle \theta = 90^{\circ}$ .

Initial flux: $\Phi(0)= 0$ .

Final flux: $\Phi(0.7) = \rm 1.1136\times 10^{-4}\; Wb$ .

Average EMF, which is the same as the average rate of change in flux:

$\displaystyle \frac{\Phi(0.7) - \Phi(0)}{0.7} \approx\rm 1.62\times 10^{-4}\; V$ .

8 0

3 years ago

6. Draw a velocity-time graph for an object originally traveling at -3 m/s. The object

faltersainse [42]

See the graph in attachment

Explanation:

In this problem we have to draw a velocity-time graph for an object travelling initially at -3 m/s, then slowing down and turning around.

In the graph, we see that the initial velocity at time t = 0 is

$v_0 = -3 m/s$

and it is negative, so below the x-axis.

Later, the object slows down: this means that the magnitude of its velocity increases, therefore (since the velocity is negative) the curve must go upward, approaching and reaching the x-axis (which corresponds to zero velocity).

After that, the object's velocity keep increasing, but now it is positive: this means that the object is travelling in a direction opposite to the initial direction, so it has turned around.

Learn more about velocity:

brainly.com/question/5248528

#LearnwithBrainly

4 0

2 years ago

3 A 100 g steel ball falls from a height of 1.8 m on to a metal plate and rebounds to a height of 1.25 m.

BigorU [14]

Given values:

Mass of the steel ball, m = 100 g = 0.1 kg

Height of the steel ball, h1 = 1.8 m

Rebound height, h2 = 1.25 m

a. PE= mgh

0.1 x 9.8 x 1.8 =

1.764 Joules

b. KE = PE ->

1.764 Joules

c. KE= 1/2 mv square

so v = square root 2ke/m

square root 2 x 1.764/ 0.1

= 5.93 m/s

d. KE=PE=mgh square

0.1 x 9.8 x 1.21 =

1.186 joules

velocity of rebond is square root 2x 1.186/ 0.1 = 4.87 m/s

6 0

3 years ago

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The wheel on an upside-down bicycle moves through 18.0 rad in 5.39 s. What is the wheel’s angular acceleration if its initial an

Elden [556K]

Explanation:

Formula to calculate angular acceleration is as follows.

$\Delta (\theta) = \frac{1}{2} \alpha \Delta t^{2} + \omega_{1} \Delta t$

or, $\alpha = \frac{2(\Delta (\theta) - \omega_{1} \Delta t)}{\Delta t^{2}}$

Putting the given values into the above formula as follows.

$\alpha = \frac{2(\Delta (\theta) - \omega_{1} \Delta t)}{\Delta t^{2}}$

= $\frac{2(18.0 rad - 2.5 rad/s \times 5.30 s)}{(5.39)^{2}}$

= 0.326 $rad/s^{2}$

Thus, we can conclude that the wheel’s angular acceleration if its initial angular speed is 2.5 rad/s is 0.326 $rad/s^{2}$ .

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3 years ago

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umka2103 [35]

In my school, a student who refuses to wear their uniform gets suspended.

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3 years ago