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What will be the remainder when (265)4081+9 is divided by 266?
To find the remainder when ( (265)_{4081} + 9 ) is divided by 266, we first need to convert ( (265)_{4081} ) from base 4081 to decimal.The number ( (265)_{4081} ) means:[2 cdot 4081^2 + 6 cdot 4081^1 + 5 cdot 4081^0]Calculating each term:[2 cdot 4081^2 + 6 cdot 4081 + 5 = 2 cdot 16656061 + 24486 + 5Read more
To find the remainder when ( (265)_{4081} + 9 ) is divided by 266, we first need to convert ( (265)_{4081} ) from base 4081 to decimal.
The number ( (265)_{4081} ) means:
[
2 cdot 4081^2 + 6 cdot 4081^1 + 5 cdot 4081^0
]
Calculating each term:
[
2 cdot 4081^2 + 6 cdot 4081 + 5 = 2 cdot 16656061 + 24486 + 5 = 33312122 + 24486 + 5
]
[
= 33336513
]
Now we add 9 to this decimal value:
[
33336513 + 9 = 33336522
]
Next, we will find the remainder when ( 33336522 ) is divided by 266:
[
33336522 mod 266
]
Calculating:
[
33336522 div 266 approx 125194.5 text{ (we take the integer part, 125194)}
]
Multiplying back:
[
125194 cdot 266 = 33336484
]
Now, subtract from ( 33336522 ):
[
33336522 –
See lessTwo runners, Sony and Mony, start running on a circular track of length 200 m at speeds of 18 and 24 km/h, respectively, in the same direction. After how much time from the start will they meet again at the starting point?
To determine when the two runners, Sony and Mony, will meet at the starting point again, we can follow these steps: 1. Convert the speeds from km/h to m/s:- Sony's speed: ( 18 , text{km/h} = frac{18 times 1000}{3600} = 5 , text{m/s} )- Mony's speed: ( 24 , text{km/h} = frac{24 times 1000}{3600} = frRead more
To determine when the two runners, Sony and Mony, will meet at the starting point again, we can follow these steps:
1. Convert the speeds from km/h to m/s:
– Sony’s speed: ( 18 , text{km/h} = frac{18 times 1000}{3600} = 5 , text{m/s} )
– Mony’s speed: ( 24 , text{km/h} = frac{24 times 1000}{3600} = frac{24000}{3600} = frac{20}{3} = 6.67 , text{m/s} )
2. Calculate the relative speed:
– The relative speed when both are running in the same direction:
[ text{Relative speed} = text{Speed of Mony} – text{Speed of Sony} = 6.67 , text{m/s} – 5 , text{m/s} = 1.67 , text{m/s} ]
3. Determine the time taken to meet again at the starting point:
– The time taken for the faster runner (Mony) to gain a complete lap over the slower runner (Sony) can be calculated using the track length and the relative speed:
[ text{Time} =
See lessA local telephone network is an example of a _______ network
A local telephone network is an example of a circuit-switched network.
A local telephone network is an example of a circuit-switched network.
See lessIf the four numbers, 39, 117, 17 and y are in proportion, then find the value of y.
To determine the value of (y) such that the numbers 39, 117, 17, and (y) are in proportion, we can set up the proportion as follows:[frac{39}{117} = frac{17}{y}]To solve for (y), we can cross-multiply:[39y = 117 times 17]Calculating (117 times 17):[117 times 17 = 1989]Now substituting back:[39y = 19Read more
To determine the value of (y) such that the numbers 39, 117, 17, and (y) are in proportion, we can set up the proportion as follows:
[
frac{39}{117} = frac{17}{y}
]
To solve for (y), we can cross-multiply:
[
39y = 117 times 17
]
Calculating (117 times 17):
[
117 times 17 = 1989
]
Now substituting back:
[
39y = 1989
]
Next, we’ll solve for (y) by dividing both sides by 39:
[
y = frac{1989}{39}
]
Calculating (frac{1989}{39}):
[
y = 51
]
Thus, the value of (y) is (51).
See lessA man, a boy and a woman can finish a work in 10 days, 15 days and 30 days, respectively. In how many days can the work be finished by a man, a woman and a boy when all of them work together?
To determine how long it takes for a man, a woman, and a boy to complete the work together, we first need to find their individual work rates.- The man's work rate is ( frac{1}{10} ) of the work per day.- The boy's work rate is ( frac{1}{15} ) of the work per day.- The woman's work rate is ( frac{1}Read more
To determine how long it takes for a man, a woman, and a boy to complete the work together, we first need to find their individual work rates.
– The man’s work rate is ( frac{1}{10} ) of the work per day.
– The boy’s work rate is ( frac{1}{15} ) of the work per day.
– The woman’s work rate is ( frac{1}{30} ) of the work per day.
Now, we add their work rates together:
[
text{Total work rate} = frac{1}{10} + frac{1}{15} + frac{1}{30}
]
To add these fractions, we need a common denominator, which in this case is 30.
[
frac{1}{10} = frac{3}{30}, quad frac{1}{15} = frac{2}{30}, quad frac{1}{30} = frac{1}{30}
]
Now, we can add them up:
[
text{Total work rate} = frac{3}{30} + frac{2}{30} + frac{1}{30} = frac{6}{30} = frac{1}{5}
]
This means that together, they complete ( frac{1}{5} ) of the work in one day. Therefore,
See lessIn what time will ₹10,000 at 4% per annum, produce the same interest as ₹8,000 does in 4 years at 5% simple interest?
To solve this, we first need to find the interest earned by ₹8,000 at 5% simple interest over 4 years.The formula for simple interest is:[ text{Interest} = frac{P times R times T}{100} ]Where:- ( P = 8000 ) (Principal)- ( R = 5 ) (Rate of interest)- ( T = 4 ) (Time in years)Calculating the interest:Read more
To solve this, we first need to find the interest earned by ₹8,000 at 5% simple interest over 4 years.
The formula for simple interest is:
[ text{Interest} = frac{P times R times T}{100} ]
Where:
– ( P = 8000 ) (Principal)
– ( R = 5 ) (Rate of interest)
– ( T = 4 ) (Time in years)
Calculating the interest:
[ text{Interest} = frac{8000 times 5 times 4}{100} ]
[ text{Interest} = frac{80000}{100} ]
[ text{Interest} = 800 ]
So, ₹8,000 at 5% over 4 years produces ₹800 in interest.
Now, we need to find out how much time it will take for ₹10,000 at 4% per annum to produce the same ₹800 in interest.
Using the simple interest formula again:
Let ( T ) be the time in years for ₹10,000 at 4% to produce ₹800 interest.
[ 800 = frac{10000 times 4 times T}{100} ]
[ 800 = 10000 times 0.04 times T ]
[ 800 = 400 times T ]
Now, solving for ( T ):
[ T
See lessWhich protocol is a signalling communication protocol used for controlling multimedia communication sessions?
The protocol used for controlling multimedia communication sessions is called SIP (Session Initiation Protocol).
The protocol used for controlling multimedia communication sessions is called SIP (Session Initiation Protocol).
See lessMultiplexing technique that shifts each signal to a different carrier frequency
The multiplexing technique that shifts each signal to a different carrier frequency is called Frequency Division Multiplexing (FDM).
The multiplexing technique that shifts each signal to a different carrier frequency is called Frequency Division Multiplexing (FDM).
See lessMultiplexing technique that shifts each signal to a different carrier frequency
Frequency Division Multiplexing (FDM)
Frequency Division Multiplexing (FDM)
See lessIn TDM, the transmission rate of the multiplexed path is usually _______ the sum of the transmission rates of the signal sources.
In TDM, the transmission rate of the multiplexed path is usually equal to the sum of the transmission rates of the signal sources.
In TDM, the transmission rate of the multiplexed path is usually equal to the sum of the transmission rates of the signal sources.
See less