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stephanwant to count number of objects have in space For a first measurement, they count the asteroids for 60 days and detect 1000 objects. Several months later, they start a second measurement: This time, they count for 80 days. How many asteroids will they detect during the second measurement? Explain why. we can consider that the asteroids are homogeneously distributed in their solar system.)

$$ \\ $$stephanwant to count number of objects have in space For a first measurement, they count the asteroids for 60 days and detect 1000 objects. Several months later, they start a second measurement: This time, they count for 80 days. How many asteroids will they detect during the second measurement? Explain why. we can consider that the asteroids are homogeneously distributed in their solar system.)

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Question Number 172099 Answers: 1 Comments: 0

The probability that Abiola will be late to office on a given day is(2/5) . in a given week of six days, find the 1) probability that he will be late of only 3 days 2) not be late in the week

$${The}\:{probability}\:{that}\:{Abiola}\:{will}\:{be} \\ $$$${late}\:{to}\:{office}\:{on}\:{a}\:{given}\:{day}\:{is}\frac{\mathrm{2}}{\mathrm{5}}\:.\:{in} \\ $$$${a}\:{given}\:{week}\:{of}\:{six}\:{days},\:{find}\:{the}\: \\ $$$$\left.\mathrm{1}\right)\:{probability}\:{that}\:{he}\:{will}\:{be}\:{late}\:{of} \\ $$$${only}\:\mathrm{3}\:{days} \\ $$$$\left.\mathrm{2}\right)\:{not}\:{be}\:{late}\:{in}\:{the}\:{week} \\ $$

Question Number 172014 Answers: 0 Comments: 2

using properties of determinats prove that [−yz y^2 +yz z^2 +yz] [x^2 +xz −xz z^2 +xy] =(xy+yz+zx)^2 x^2 +xy y^2 +xy −xy]

$${using}\:{properties}\:{of}\:{determinats} \\ $$$${prove}\:{that} \\ $$$$\left[−{yz}\:\:\:\:\:\:{y}^{\mathrm{2}} +{yz}\:\:\:\:\:\:\:{z}^{\mathrm{2}} +{yz}\right] \\ $$$$\left[{x}^{\mathrm{2}} +{xz}\:\:\:−{xz}\:\:\:\:\:\:\:\:\:\:{z}^{\mathrm{2}} +{xy}\right]\:=\left({xy}+{yz}+{zx}\right)^{\mathrm{2}} \\ $$$$ \\ $$$$\left.\:{x}^{\mathrm{2}} +{xy}\:\:\:\:\:{y}^{\mathrm{2}} +{xy}\:\:\:\:\:\:\:\:−{xy}\right] \\ $$

Question Number 171801 Answers: 1 Comments: 0

Two numbers are respectively 20% and 10% more than a third number. How much percent is the first number more than the second? Mastermind

$$\mathrm{Two}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{20\%}\:\mathrm{and} \\ $$$$\mathrm{10\%}\:\mathrm{more}\:\mathrm{than}\:\mathrm{a}\:\mathrm{third}\:\mathrm{number}.\:\mathrm{How}\: \\ $$$$\mathrm{much}\:\mathrm{percent}\:\mathrm{is}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{more} \\ $$$$\mathrm{than}\:\mathrm{the}\:\mathrm{second}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 171799 Answers: 0 Comments: 0

Two numbers are less than a third number by 30% and 37% respectively. how much percent is the second less than the first? Mastermind

$$\mathrm{Two}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{less}\:\mathrm{than}\:\mathrm{a}\:\mathrm{third}\: \\ $$$$\mathrm{number}\:\mathrm{by}\:\mathrm{30\%}\:\mathrm{and}\:\mathrm{37\%}\:\mathrm{respectively}. \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{percent}\:\mathrm{is}\:\mathrm{the}\:\mathrm{second}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{the}\:\mathrm{first}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 171798 Answers: 0 Comments: 0

Two numbers are respectively 60% and 20% more than a third number, second number expressed as a percentage of first is Mastermind

$$\mathrm{Two}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{60\%}\:\mathrm{and} \\ $$$$\mathrm{20\%}\:\mathrm{more}\:\mathrm{than}\:\mathrm{a}\:\mathrm{third}\:\mathrm{number},\:\mathrm{second} \\ $$$$\mathrm{number}\:\mathrm{expressed}\:\mathrm{as}\:\mathrm{a}\:\mathrm{percentage}\:\mathrm{of} \\ $$$$\mathrm{first}\:\mathrm{is}\: \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 171796 Answers: 0 Comments: 0

If the given two numbers are respec− tively 7% and 28% of a third number, then what percentage is the first of the second? Mastermind

$$\mathrm{If}\:\mathrm{the}\:\mathrm{given}\:\mathrm{two}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{respec}− \\ $$$$\mathrm{tively}\:\mathrm{7\%}\:\mathrm{and}\:\mathrm{28\%}\:\mathrm{of}\:\mathrm{a}\:\mathrm{third}\:\mathrm{number}, \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{percentage}\:\mathrm{is}\:\mathrm{the}\:\mathrm{first}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{second}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 171795 Answers: 0 Comments: 0

If A′s income is 25% less than that of B, then how much percent is B′s income more than that of A? Mastermind

$$\mathrm{If}\:\mathrm{A}'\mathrm{s}\:\mathrm{income}\:\mathrm{is}\:\mathrm{25\%}\:\mathrm{less}\:\mathrm{than}\:\mathrm{that}\:\mathrm{of}\:\mathrm{B}, \\ $$$$\mathrm{then}\:\mathrm{how}\:\mathrm{much}\:\mathrm{percent}\:\mathrm{is}\:\mathrm{B}'\mathrm{s}\:\mathrm{income} \\ $$$$\mathrm{more}\:\mathrm{than}\:\mathrm{that}\:\mathrm{of}\:\mathrm{A}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Question Number 171793 Answers: 0 Comments: 1

Question Number 171794 Answers: 0 Comments: 0

If a number is 20% more than the other, how much percent is the second number less than the first? Mastermind

$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:\mathrm{is}\:\mathrm{20\%}\:\mathrm{more}\:\mathrm{than}\:\mathrm{the}\:\mathrm{other}, \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{percent}\:\mathrm{is}\:\mathrm{the}\:\mathrm{second}\:\mathrm{number} \\ $$$$\mathrm{less}\:\mathrm{than}\:\mathrm{the}\:\mathrm{first}? \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

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Ω=∫_0 ^1 Log(((Log^2 (x))/x^(x^5 −x^4 +x^3 −x^2 +x−1) ))dx Anyone?

$$\Omega=\int_{\mathrm{0}} ^{\mathrm{1}} {Log}\left(\frac{{Log}^{\mathrm{2}} \left({x}\right)}{{x}^{{x}^{\mathrm{5}} −{x}^{\mathrm{4}} +{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +{x}−\mathrm{1}} }\right){dx} \\ $$$$ \\ $$$${Anyone}? \\ $$

Question Number 171627 Answers: 0 Comments: 5

A mass 10kg is placed at the foot of an inclined plane 13m long, whose upper end is 5m higher than the foot. The mass is connected by a light inextensible string, passing over a smooth pulley at the top of the plane, to another mass 10kg which hangs level with the top of the plane, 5m above the floor. If the coefficient of friction between the first mass and then plane is ½ and the system is released from rest, find the acceleration and tension In the string. [Take g = 9.8m/s²]

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