A baseball m=.34kg is spun vertically on a massless string of length l=.52m. the string can only support a tension of tmax=9.9n before it will break. what is the max possible speed of the ball at the top of the loop in m/s?
The maximum possible speed of the ball at the top of the loop is 4.50 m/s
Further explanationAcceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration (m / s²)
v = final velocity (m / s)
u = initial velocity (m / s)
t = time taken (s)
d = distance (m)
Centripetal Acceleration of circular motion could be calculated using following formula:
[tex]\large {\boxed {a_s = v^2 / R} }[/tex]
a = centripetal acceleration ( m/s² )
v = velocity ( m/s )
R = radius of circle ( m )
Let us now tackle the problem!
Given:
mass = m = 0.34 kg
length of string = R = 0.52 m
maximum tension = Tmax = 9.9 N
Unknown:
v = ?
Solution:
[tex]mg + T = ma[/tex]
[tex]mg + T = m\frac{v^2}{R}[/tex]
[tex]0.34 \times 9.8 + 9.9 = 0.34 \times \frac{v^2}{0.52}[/tex]
[tex]13.232 = \frac{0.34}{0.52} \times v^2[/tex]
[tex]v^2 = 20.2372[/tex]
[tex]\large {\boxed {v \approx 4.50 ~ m/s} }[/tex]
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Subject: Physics
Chapter: Circular Motion
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate , Circular , Ball , Centripetal
The maximum possible speed of the baseball at the top of the loop is approximately 3.17 m/s. This is calculated by using the maximum tension the string can support, and the gravitational force acting on the baseball.
Explanation:To find the maximum possible speed of the baseball at the top of the loop without breaking the string, we need to consider the forces acting on the baseball. Two key forces are at play here: the gravitational force pulling the ball downward and the tension in the string that counteracts this pull. At the top of the loop, for minimum speed, the tension in the string can be zero because the gravitational force provides the necessary centripetal force. However, the question states that the string can only support a maximum tension (Tmax) before breaking which means we must find the speed where the tension does not exceed Tmax.
The maximum tension is the sum of the centripetal force needed to keep the ball moving in a circular path and the force due to gravity. Mathematically, this is expressed as Tmax = m * v^2 / l + m * g, where v is the velocity, m is the mass of the baseball, l is the length of the string, and g is the acceleration due to gravity (9.8 m/s^2).
Rearranging the formula to solve for v gives us v = sqrt((Tmax - m * g) * l / m). Plugging in the values Tmax = 9.9 N, m = 0.34 kg, l = 0.52 m, we get:
v = sqrt((9.9 N - (0.34 kg * 9.8 m/s^2) * 0.52 m) / 0.34 kg)
Calculating the above expression, we find the maximum velocity:
v = sqrt((9.9 - 3.332) * 0.52 / 0.34)
v = sqrt(6.568 * 0.52 / 0.34)
v = sqrt(3.4152 / 0.34)
v = sqrt(10.0447)
v ≈ 3.17 m/s
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Which is brighter in our sky, a star with apparent magnitude 5 or a star with apparent magnitude 10 ?
What is the sequence of energy transformations when electricity is generated from fossil fuels?
A. Electrical energy a thermal energy a mechanical energy a chemical energy
B. Chemical energy a thermal energy a mechanical energy a electrical energy
C. Chemical energy a mechanical energy a thermal energy a electrical energy
D. Chemical energy a mechanical energy a thermal energy a electrical energy
B) Chemical energy thermal energy mechanical energy electrical energy.
What is the energy sequence?Electricity sequence is an intelligence web platform that allows quit customers to recognize electricity-saving measures and achieve greater electricity performance with a price and time this is an 80% decrease over manual strategies and other tracking structures.
(i) Electrical energy into sound energy. (ii) Heat energy into kinetic energy (or mechanical energy). (iii) Chemical energy into kinetic energy (or mechanical energy). (iv) Chemical energy into heat energy.Learn more about the transformation of energy here: https://brainly.com/question/961052
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List three reasons why knowing how to graph movement can help you on a practical level.
Knowing how to graph motion helps in understanding kinematics properties by deriving motion characteristics from the graph, visualizing equations in a comprehendible form, and revealing underlying relationships between physical quantities.
Explanation:Knowing how to graph movement can be practically beneficial for several reasons, these include:
Deriving motion characteristics: By graphing displacement versus time, velocity versus time, and acceleration versus time, you can derive specific and general characteristics of kinematics. For example, the slope of a displacement versus time graph is velocity whereas the slope of a velocity versus time graph represents acceleration. Visualizing Equations: Graphs are an excellent tool to visualize and understand equations. Rather than dealing with complex mathematical expressions, you can express the same information visually through graphs and get a better comprehension of the phenomena. Understanding Underlying Relationships: Graphs do not only present numerical information but also reveal the relationship between different quantities. Hence, they offer a way to interpret and understand the physics underlying the motion. Learn more about Graphing Motion here:
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What is tarzan's speed vf just before he reaches jane? express your answer in meters per second to two significant figures?
which of the following would decrease current flow in a circuit made of originally from 1.5 volt battery a loop of wire and a switch
Compare the energy consumption of two commonly used items in the household. calculate the energy used by a 1.20 kw toaster oven, wtoaster, which is used for 6.20 minutes and then calculate the amount of energy an 11.0 w compact fluorescent light (cfl), wlight, bulb uses when left on for 8.50 hours.
Toaster oven:
Power: [tex]P=1.20 kW[/tex]
Time: [tex]t=6.20 min \cdot \frac{1}{60 min/h}=0.103 h[/tex]
So, the energy consumed by the oven is
[tex]E=Pt=(1.20 kW)(0.103 h)=0.124 kWh[/tex]
Fluorescent light:
Power: [tex]P=11.0 W=0.011 kW[/tex]
Time: [tex]t=8.50 h[/tex]
So, the energy consumed by the light is
[tex]E=Pt=(0.011 kW)(8.50 h)=0.094 kWh[/tex]
So, the toaster oven has consumed more energy than the fluorescent light.
Answer: clock radio, toaster, hair dryer, tv, lamp, fridge
Explanation:
Just did it
Which characteristic does an object with a constant acceleration always have?
Explanation:
By definition, the word acceleration is equal to the rate of change of velocity. Mathematically, it is given by :
[tex]a=\dfrac{dv}{dt}[/tex]
[tex]dv=a.dt[/tex]
[tex]v=\int\limits^t_0 {a.dt}[/tex]
Since, it is given that acceleration is constant
[tex]v=at+v_o[/tex]
v₀ is the constant of integration and it corresponds to initial velocity
From above equation, it is clear that when acceleration is constant the speed varies linearly. Hence, when an object move with constant acceleration, it always changes its velocity.
A small smooth object slides from rest down a smooth inclined plane inclined at 30 degrees to the horizontal. What is (i) the acceleration
The speed of sound in water is measured to be 1485 m/s. what is this in mph?
Answer:
v = 3321.85 mph
Explanation:
Equivalences :
1 mile = 1609.34 m
1 hour = 3600 seconds
Data
v= 1485 m/s : speed of sound in water
Problem Development
To calculate the speed of sound in mph (mile / hour), we multiply by the conversion factors using the equivalences:
[tex]v= (1485 \frac{m}{s} )*(\frac{1mile}{1609.34 m} )*(\frac{3600s}{hour})[/tex]
We cancel the units in seconds (s) and meters (m) to get the answer in miles per hour (miles / hour or mph)
[tex]v=\frac{1485*3600}{1609.34} \frac{mile}{hour}[/tex]
v= 3321.85 mile/hour
v = 3321.85 mph
For questions 1-10, match the term with the correct phrase it corresponds to, by filling in the blank with the letter of the correct phase
A - Hormone that helps the body control the level of glucose in yhe blood.
B - The main cause of Type 2 Diabetes
C - Condition that makes it hard for the body to control the level of glucose in the blood
D - Damage to the pancreas caused by ones own antibodies
E - The elevation of glucose levels in the blood
F - Found to help with treatment of clinical depression
G - Organ where insulin is produced
H - "Good" cholesterol
I - 90% to 95% of the case of diabetes in America
J - Hardening of the arteries caused by a build up of fatty materials
1 - diabetes
2 - Atherosclerosis
3 - Hyperglycemia
4 - HDL
5 - Obesity
6 - Type 1
7 - Insulin
8 - Type 2
9 - Pancreas
10 - Regular aerobic exercise
These are your answers:
A is Insulin (7)
B is Obesity (5)
C is Diabetes (1)
D is Type 1 (6)
E is Hyperglycemia (3)
F is Regular aerobic exercise (10)
G is Pancreas (9)
H is HDL (4)
I is Type 2 (8)
J is atherosclerosis(2)
Here is why:
A. Hormone that helps the body control the level of glucose in the blood.
Insulin is a hormone. It helps regulate the levels of glucose in the blood by turning glucose into energy. This is why it plays an important role in metabolism. This hormone is produced by the pancreas.
B. Main cause of Type 2 Diabetes
Obesity is the main cause of Type 2 diabetes. Unhealthy eating and lack of exercise are often listed as causes of Diabetes 2, and this kind of lifestyle collectively leads to obesity.
C. Condition that makes it hard for the body to control the level of glucose in the blood.
Diabetes is a condition where the levels of glucose in the blood is high. This happens because the body cannot produce enough insulin, which is the hormone that controls glucose levels.
D. Damage to the pancreas caused by ones own antibodies.
In Diabetes Type 1, the immune system attacks the panceatic beta cells, which produce insulin. Unlike Type 2, Type 1 Diabetes is unavoidable and hereditary. So if you have it, you have it.
E. The elevation of glucose levels in the blood.
Hyperglycemia - Hyper means high or elevated. Gly means glucose or sugar. -cemia means blood. Put together, elevated glucose in the blood.
F. Found to help with treatment of clinical depression
Studies have shown that aerobic exercise can help with clinical depression. It helps elevate moods and lessen tension. This helps relieve stress.
G. Organ where insulin is produced
Like mentioned above, insulin is produced by the pancreas.
H. "Good" Cholesterol
HDL is High-density Lipoprotein. HDL is considered as good cholesterol because it actually assists in removing other forms of cholesterol from the blood.
I. 90% to 95% of the case of diabetes in America
Studies have shown that in America Diabetes 2 is the most common case. Like mentioned above, cause of Diabetes type 2 is eating habits and lack of exercise and many foods today are full of processed sugars and are consumed in great amounts because of convenience.
J. Hardening of the arteries caused by a build up of fatty materials.
Fatty materials create plaque and they accumulate in the blood vessels. This leads to constriction and hardening in arteries specifically. This constriction makes the vessel more narrow and it can limit the flow of oxygen to the other organs of the body.
What is the change in velocity of the biker below as the travel from point b to point c ? What’s his acceleration from point B to C
Point b is 8 m/s.
t=1s. Point c is
8m/s.
t=2s
The biker's change in velocity from point B to point C is 0 m/s, indicating that there is no change in velocity. Consequently, the biker's acceleration between these points is also 0 m/s
to the power of 2; there is no acceleration.
The change in velocity of the biker as they travel from point B to point C is determined by subtracting the initial velocity at point B from the final velocity at point C. As given, the biker's velocity at point B is 8 m/s, and at point C, it remains 8 m/s. Therefore, the change in velocity (Δv) is:
Δv = final velocity - initial velocity
Δv = 8 m/s - 8 m/s
Δv = 0 m/s
Since the velocity does not change, the acceleration
a) from point B to point C is:
a = Δv/Δt
a = 0 m/s ÷ 1 s
a = 0 m/s²
Thus, there is no change in velocity and no acceleration as the biker moves from point B to point C.
What is the frequency of radiation whose wavelength is 2.40 x 10-5 cm?
What is the voltage drop across a 3 kω resistor connected to a 9v power source?
The voltage drop across a 3 kΩ resistor connected to a 9V power source is 9V, as calculated using Ohm's law.
To calculate the voltage drop across a resistor, we use Ohm's law, which states that V = IR, where V is the voltage, I is the current, and R is the resistance. Since we know the resistance (R = 3 kΩ) and the power source voltage (V = 9V), we first need to calculate the current (I) using the formula I = V/R.
Convert kiloohms to ohms: 3 kΩ = 3000 Ω.Calculate the current: I = V/R = 9V / 3000 Ω = 0.003 A (3 mA).Now, since the resistor is directly connected across the power source, the voltage drop across the resistor is equal to the voltage of the power source.Therefore, the voltage drop across the 3 kΩ resistor connected to a 9V power source is 9V.
If the magnitude of the electric field at a distance of 7.8 cm from the center is 30500 n/c , what is the magnitude of the electric field at 22.3 cm from the center? answer in units of n/c.
To find the electric field at [tex]22.3 cm[/tex] from the center, use the given electric field at [tex]7.8 cm[/tex] to first calculate the charge, then reapply the electric field formula at the new distance. The result is approximately [tex]3684.2 N/C[/tex].
The problem involves calculating the electric field at a different distance from a point charge. We can use the formula for the electric field due to a point charge, which is given by:
[tex]E = \frac{k \cdot |q|}{r^2}[/tex]
Here,
E is the electric field, k is Coulomb's constant ([tex]8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2[/tex]), q is the charge, r is the distance from the charge.The magnitude of the electric field at [tex]7.8 cm (0.078 m)\\ \\[/tex] is [tex]30500 N/C[/tex] . First, we calculate the charge q.
Rearrange the formula to find [tex]q: \quad q = \frac{E \cdot r^2}{k}[/tex]
Substitute the known values:[tex]q = 30500 \, \text{N/C} \times (0.078 \, \text{m})^2 / (8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2)[/tex]
Simplify:[tex]q \approx 2.04 \times 10^{-11} \, \text{C}[/tex]
Now, we use this charge to find the electric field at [tex]22.3 cm (0.223 m)[/tex]:
Substitute the values back into the electric field formula:[tex]E = \frac{k \cdot q}{r^2}[/tex]
[tex]E = \frac{(8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \times (2.04 \times 10^{-11} \, \text{C})}{(0.223 \, \text{m})^2}[/tex]
Calculate the electric field: [tex]E \approx 3684.2 \, \text{N/C}[/tex]
Therefore, the magnitude of the electric field at [tex]22.3 cm[/tex] from the center is [tex]3684.2 N/C[/tex].
Does a person standing motionless in the aisle of a moving bus have kinetic energy
A flowerpot falls off a balcony 85m above the street how long does it take to hit the ground
It will take 4.12 s for the flowerpot to fall to the ground.
From the question given above, the following data were obtained:
Height (h) = 85 m
Time (t) =?NOTE: Acceleration due to gravity (g) = 10 m/s²
The time taken for the flowerpot to fall to the ground can be obtained as follow:
H = ½gt²85 = ½ × 10 × t²
85 = 5 × t²
Divide both side by 5
[tex]t^{2} = \frac{85}{5}\\\\t^{2} = 17[/tex]
Take the square root of both side
[tex]t = \sqrt{17}[/tex]
t = 4.12 sTherefore, it will take 4.12 s for the flowerpot to fall to the ground.
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A 1000-kg car traveling at 70 m/s takes 3 m to stop under full braking. the same car under similar road conditions, traveling at 140 m/s, takes ______________ m to stop under full braking.
This physics problem involves the principle of kinetic energy and work-energy. Given the situation presented, the increase in the car's kinetic energy due to a doubling of initial speed means that the braking stopping distance quadruples from 3 meters to 12 meters.
Explanation:This Physics problem concerns the relationship between velocity, mass, and stopping distance under braking conditions. It's dealing with the principle of kinetic energy (1/2*m*v²) and the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
If the initial speed is doubled, as it is in this case from 70 m/s to 140 m/s, the kinetic energy (and thus the work needing to be done to stop the vehicle) quadruples, assuming the mass stays constant. This means, due to the direct relationship between work done and distance when force is held constant, the stopping distance will also quadruple from the original 3 meters.
Therefore, the 1000-kilogram car, when moving at 140 m/s, will take 12 meters to stop under full braking in similar conditions.
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Communications satellites are placed in a circular orbit where they stay directly over a fixed point on the equator as the earth rotates. these are called geosynchronous orbits. the radius of the earth is 6.37 * 106 m, and the altitude of a geosynchronous orbit is 3.58 * 107 m 1â22,000 miles2. what are (a) the speed and (b) the magnitude of the acceleration of a satellite in a geosynchronous orbit?
The speed of a satellite in a geosynchronous orbit is approximately 2.98 km/s, and the magnitude of the acceleration is approximately 1.92 x 10^-3 m/s^2.
Explanation:To determine the speed of a satellite in a geosynchronous orbit, we can use the formula:
speed = 2 x π x radius / period
Given that the radius of the Earth is 6.37 * 10^6 m and the altitude of a geosynchronous orbit is 3.58 * 10^7 m, we can use the formula to calculate the speed:
speed = 2 x 3.14 x (6.37 * 10^6 + 3.58 * 10^7) / (24 x 60 x 60)
The magnitude of the acceleration of a satellite in a circular orbit can be calculated using the formula:
acceleration = (velocity)^2 / radius
Using the calculated speed and the radius of the orbit, we can find the magnitude of the acceleration:
acceleration = (2.98 x 10^3)^2 / (6.37 * 10^6 + 3.58 * 10^7)
Therefore, the speed of a satellite in a geosynchronous orbit is approximately 2.98 km/s and the magnitude of the acceleration is approximately 1.92 x 10^-3 m/s^2.
What is the speed of a 0.145kg baseball if it’s kinetic energy is 109 j
People watching their team lose important games often make faces, yell at the screen, and demonstrate general agitation. Although they aren't playing the game themselves, they may be able to experience the frustration felt by the players because of ________________ activity in the brain
A 10.0-g bullet is fired into a 200-g block of wood at rest on a horizontal surface. after impact, the block slides 8.00 m before coming to rest. if the coefficient of friction between the block and the surface is 0.400, what is the speed of the bullet before impact? (a) 106 m/s (b) 166 m/s (c) 226 m/s (d) 286 m/s (e) none of those answers is correct
The speed of the bullet before impact is 0 m/s.
Explanation:To determine the velocity of the bullet before impact, we can use the principle of conservation of momentum. The momentum before the impact is equal to the momentum after the impact. The momentum of the bullet is given by its mass times its velocity, and the momentum of the block is given by its mass times its final velocity. Since the block comes to a stop after sliding, its final velocity is 0 m/s. The equation for conservation of momentum becomes:
(m_bullet * v_bullet) = (m_block * 0)
Simplifying the equation gives: v_bullet = 0 m/s
Therefore, the speed of the bullet before impact is 0 m/s. None of the given answers (a) 106 m/s, (b) 166 m/s, (c) 226 m/s, (d) 286 m/s are correct.
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Explain why it takes more energy to remove the second electron from a lithium atom than it does to remove the fourth electron from a carbon atom.
The energy required to remove second electron from lithium is more as compared to removing fourth electron from carbon
EXPLANATION:
The amount of energy required to remove an electron from an isolated atom is called as ionization energy of the electron.
The second ionization energy of lithium atom is more as compared to fourth ionization energy of carbon atom. It is so because the second electron which is to be emitted from the K-shell of lithium atom, is tightly bound by the nucleus as the orbit is very closer to the nucleus.
In case of carbon, the fourth electron is present in the valence shell.The radius of valence shell is not so close as compared to lithium.The screening effect is also more for carbon as compared to lithium.
Hence, the energy required to remove a second electron from lithium is more that the energy required to remove fourth electron from carbon.
It is easier to take out 4th electron from carbon than 2nd electron from lithium because 2nd electron of lithium is closer to the nucleus.
The electronic configuration for,
[tex]\rm \bold{ Li_3 - 1s^2 2s^2}\\\\\rm \bold{ C_6- 1s^2 2s^2 2p^2}[/tex]
We can see here the 2nd electron of Lithium is present in first cell. The electron is more strongly bounded with nucleus. Whereas in Carbon 4th electron present in valence shell. Hence, the electron will be loosely bounded with nucleus.Therefore, we can conclude that the it is easier to take out 4th electron from carbon than 2nd electron from lithium.
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What is the wavelength of a photon whose energy is twice that of a photon with a 600 nm wavelength?
The wavelength of the photon having twice the energy as that of the photon of wavelength [tex]600\,{\text{nm}}[/tex] is [tex]\boxed{300\,{\text{nm}}}[/tex] .
Further Explanation:
The photons are the small packets of energy that move at the speed of light. The photons are considered to remain always in motion. The energy associated with a moving photon is given by:
[tex]E = \dfrac{{hc}}{\lambda }[/tex]
Here, [tex]E[/tex] is the energy associated with the photon, [tex]h[/tex] is the Planck’s constant, [tex]c[/tex] is the speed of light and [tex]\lambda[/tex] is the wavelength of the moving photon.
The value of the Planck’s constant is [tex]6.6 \times {10^{ - 34}}\,{\text{J}} \cdot {\text{s}}[/tex] .
The wavelength of the photon is [tex]600\,{\text{nm}}[/tex] .
The energy associated with the photon of wavelength [tex]600\,{\text{nm}}[/tex] is:
[tex]\begin{aligned}{E_1}&=\frac{{\left( {6.6 \times {{10}^{ - 34}}} \right) \times \left( {3 \times {{10}^8}} \right)}}{{600 \times {{10}^{ - 9}}}}\\&=\frac{{1.98 \times {{10}^{ - 25}}}}{{6 \times {{10}^{ - 7}}}}\\&= 3.3 \times {10^{ - 19}}\,{\text{J}}\\\end{aligned}[/tex]
The wavelength of photon having energy double of this:
[tex]\begin{aligned}E' &= 2{E_1}\\&= 2 \times\left( {3.3 \times {{10}^{ - 19}}} \right)\,{\text{J}}\\&{\text{ = 6}}{\text{.6}} \times {\text{1}}{{\text{0}}^{ - 19}}\,{\text{J}}\\\end{aligned}[/tex]
The new wavelength of the photon will be:
[tex]\lambda ' = \dfrac{{hc}}{{E'}}[/tex]
Substitute [tex]6.6 \times {10^{ - 19}}\,{\text{J}}[/tex] for [tex]E'[/tex] in above expression.
[tex]\begin{aligned}\lambda ' &= \frac{{\left( {6.6 \times {{10}^{ - 34}}} \right) \times \left( {3 \times {{10}^8}} \right)}}{{6.6 \times {{10}^{ - 19}}}}\\&=\frac{{1.98 \times {{10}^{ - 25}}}}{{6.6 \times {{10}^{ - 19}}}}\,{\text{m}}\\&= 3.0 \times {10^{ - 7}}\,{\text{m}}\\&= 300\,{\text{nm}}\\\end{aligned}[/tex]
The wavelength of the photon having twice the energy as that of the photon of wavelength [tex]600\,{\text{nm}}[/tex] is [tex]\boxed{300\,{\text{nm}}}[/tex].
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Answer Details:
Grade: Senior School
Subject: Physics
Chapter: Photon and Energy
Keywords: Wavelength, photon, energy, E=hc/lamda, 600nm, twice the energy, Planck’s constant, small packets of energy, 300nm, speed of light.
Twenty students were surveyed to find out how many hours of tv they watch during a school week
Based on the survey of twenty students, the average number of hours watched during a school week is four.
Step 1: Gather Data
- Let's assume we have the following data from the survey:
| Student | Hours of TV watched (per week) |
|---------|--------------------------------|
| 1 | 3 |
| 2 | 2 |
| 3 | 4 |
| ... | ... |
| 20 | 5 |
Step 2: Calculate the Total Hours of TV Watched
- Add up all the hours reported by each student.
Total Hours = 3 + 2 + 4 + ... + 5
Step 3: Calculate the Average Hours
- Divide the total hours by the number of students surveyed.
Average Hours = Total Hours / Number of Students
Now, let's perform the calculations.
Given:
Number of students surveyed (N) = 20
Hours of TV watched by each student:
Student 1: 3 hours
Student 2: 2 hours
Student 20: 5 hours
Step 2: Calculate the Total Hours
Total Hours = 3 + 2 + 4 + ... + 5
Total Hours = (3 + 2 + 4 + ... + 5) (20 times)
We can simplify this by realizing that we're adding the same number (the hours of TV watched by each student) 20 times:
Total Hours = (3 + 2 + 4 + ... + 5) (20 times)
= (3 + 2 + 4 + ... + 5) * 20
Step 3: Calculate the Average Hours
Average Hours = Total Hours / Number of Students
= (Total Hours) / 20
Now, let's find the sum of the hours:
Sum of hours = 3 + 2 + 4 + ... + 5
To find the sum, we can use the formula for the sum of an arithmetic series:
[tex]\[S = \frac{n}{2}(a_1 + a_n)\][/tex]
where:
- (S) is the sum of the series,
- (n) is the number of terms in the series,
- (a_1) is the first term in the series, and
- (a_n) is the last term in the series.
In our case:
(n = 20 (number of students surveyed),
a_1 = 3 (hours of TV watched by the first student), and
a_n = 5 (hours of TV watched by the last student).
[tex]\[S = \frac{20}{2}(3 + 5)\][/tex]
S = 10(8)
S = 80
Now, let's plug this sum into the formula for the average:
Average Hours = Total Hours / Number of Students
= 80 / 20
= 4
So, on average, the students surveyed watch 4 hours of TV during a school week.
complete question :
Twenty students were surveyed to determine the number of hours they watch TV during a school week. The data collected from the survey are as follows (in hours):
3, 5, 8, 2, 4, 6, 7, 5, 3, 9, 10, 1, 4, 7, 8, 6, 5, 2, 3, 7.
What is the change in the ball's position from t=0s to t=1.0s? express your answer using two significant figures?
A car accelerates from rest at a constant rate of 2 m/s^2 for 5 s. what is the speed of the car at the end of that time? g
In which of the Earth's layers are diamonds formed?
How are stars important to the Milky Way
A fan that can provide air speeds up to 55 m/s is to be used in a low-speed wind tunnel with atmospheric air at 23ºc. if one wishes to use the wind tunnel to study flatplate boundary layer behavior up to reynolds numbers of rex= 108, what is the minimum plate length that should be used? at what distance from the leading edge would transition occur if the critical reynolds number were rex,c= 5 à 105?