MATHEMATICS COLLEGE

GUESS!147 - One digit is right but in the
wrong place
189 - One digit is right and in its
Place
964- Two digits are correct but both
are in the wrong place
523 - All digits are wrong
286 - One digit is right but in the
wrong place
What
are
the three numbers !

Answers

Answer 1

Answer:

The three numbers are 6, 7 and 9

Explanation:

First of all exclude the numbers which aren't correct.

From the 4th data,We can conclude the digit 5, 2 and 3 are wrong.

Now,

147 - One digit is right but wrong placed
189 - One digit is right and placed correctly
964 - Two digits are correct but at wrong place
523 - All digits are wrong
286 - One digit is right but in the wrong place

We've to find the three digits :

From case 4: 5, 2 and 3 are wrong

So, remove 5, 2 and 3 from all the cases

The numbers are:

147 - One digit is right but wrong placed
189 - One digit is right and placed correctly
964 - Two digits are correct but at wrong place
_86 - one digit is right but in the wrong place

From 1st and 3rd we can say that: 4 is present in both the case but wrongly placed.

Now the digits become:

1_7 - One digit is right but wrong placed
189 - One digit is right and placed correctly
96_ - Two digits are correct but at wrong place
_86 - one digit is right but in the wrong place

From 3rd and 4th case we can say that: 9 and 6 are correct but wrongly placed, 8 is not the number and 6 is placed at first

So, the two numbers of a 3 digit number are 6 and 9

From 2nd, 3rd and 4th case, the position of 6 and 9 are:

6 _ 9

From 1st case, 7 is the digit but wrongly placed. So, the 3 digit number becomes:

6 7 9

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Answers

Answer:

Step-by-step explanation:

speed=distance/time

20 minutes=1/3 hours

=3*3/1

=1miles/hour

Top answer is wrong it is
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Professors often attempt to determine if the submissions by the students are genuine or copied off the web sources. The program that performs this task is only 95 % accurate in correctly identifying a genuine submission and 80% accurate in correctly identifying copies. Based on the past statistics, 15% of the student turned in copied work. If a work is identified as a copy by the program, what is the probability that it is indeed a sample of copied work.

Answers

Answer:

0.7385 = 73.85% probability that it is indeed a sample of copied work.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = (P(A \cap B))/(P(A))$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Identified as a copy

Event B: Is a copy

Probability of being identified as a copy:

80% of 15%(copy)

100 - 95 = 5% of 100 - 15 = 85%(not a copy). So

$P(A) = 0.8*0.15 + 0.05*0.85 = 0.1625$

Probability of being identified as a copy and being a copy.

80% of 15%. So

$P(A \cap B) = 0.8*0.15 = 0.12$

What is the probability that it is indeed a sample of copied work?

$P(B|A) = (P(A \cap B))/(P(A)) = (0.12)/(0.1625) = 0.7385$

0.7385 = 73.85% probability that it is indeed a sample of copied work.

Evaluate ∫C ysin(z)ds, where C is the circular helix given by the equations x = cos(t), y = sin(t), z = t, 0 ≤ t ≤ 2π. SOLUTION The formula for a line integral in space gives the following. ∫y sin(z)ds = sin2(t) dt = (sin(t))2√ (cos(t))2 + (sin(t))2 + 1dt = 1 2 (1 - cos(2t))dt = √2 2 =

Answers

The line integral is

$\displaystyle\int_Cy\sin z\,\mathrm ds=\int_0^(2\pi)y(t)\sin z(t)\,\sqrt{\left((\mathrm dx)/(\mathrm dt)\right)^2+\left((\mathrm dy)/(\mathrm dt)\right)^2+\left((\mathrm dz)/(\mathrm dt)\right)^2}\,\mathrm dt$

We have

$x=\cos t\implies(\mathrm dx)/(\mathrm dt)=-\sin t$

$y=\sin t\implies(\mathrm dy)/(\mathrm dt)=\cos t$

$z=t\implies(\mathrm dz)/(\mathrm dt)=1$

so the integral reduces to

$\displaystyle\int_0^(2\pi)\sin^2t√((-\sin t)^2+\cos^2t+1^2)\,\mathrm dt=\frac{\sqrt2}2\int_0^(2\pi)(1-\cos2t)\,\mathrm dt=\boxed{\frac\pi{\sqrt2}}$

The line integral ∫C ysin(z) ds over the circular helix C, parametrized by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, evaluates to π√2.

To evaluate the line integral ∫C ysin(z) ds over the circular helix C given by x = cos(t), y = sin(t), z = t for 0 ≤ t ≤ 2π, we follow these steps:

1. Parameterize the curve: C is already parameterized as x = cos(t), y = sin(t), z = t.

2. Find the differential ds: ds = √(dx² + dy² + dz²) = √(sin²(t) + cos²(t) + 1)dt = √(1 + 1)dt = √2 dt.

3. Evaluate the integral: ∫C ysin(z) ds = ∫[0, 2π] sin(t) * sin(t) * √2 dt = ∫[0, 2π] sin²(t) * √2 dt.

Now, we'll integrate sin²(t) * √2 with respect to t:

∫ sin²(t) * √2 dt = (1/2) * ∫ (1 - cos(2t)) * √2 dt.

Using the power rule for integration, we get:

(1/2) * [(t - (1/2) * sin(2t)) * √2] | [0, 2π].

Plugging in the limits:

(1/2) * [(2π - (1/2) * sin(4π) - (0 - (1/2) * sin(0))) * √2].

Since sin(4π) = sin(0) = 0:

(1/2) * [(2π - 0 - 0) * √2] = π√2.

So, ∫C ysin(z) ds = π√2.

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When you have finished, use your Whisper voice to read each number out loud in bothunit and word form. How much does each number need to change for a ten
For 1 hundred?

Answers

The required numbers should be changed only by a unit, as proceeding from ten to 1 hundred.

Given that,
To determine how much each number needs to change for a ten for 1 hundred.

What is a number system?

A numbersystem is described as a technique of composing to represent digits. It is the mathematicalinscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmeticstructure.

Here,
According to the question,
The number from ten to 1 hundred,
10, 11, ......,99, 100.
From the above series, it can be concluded that each number is greater than by unity from the previous number.

Thus, hte required numbers should be changed only by a unit, as proceeding from ten to 1 hundred.

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100- 10 is 90 if that’s the question
So 90 or ninety
If you mean place value it’s tenths

Find the measure of <8

Answers

I’m pretty sure it’d be 72 degrees because they are alternate exterior angles

Please help me put thanks

Answers

Hence, x=-2 and y=4 are the answers to the system of equations.

Why do people utilise coordinate geometry?

For the purpose of connecting algebra and geometry with the aid of line and curve graphs, coordinate geometry is necessary. Finding points on a plane is a crucial component of mathematics. It also has a number of uses in other scientific fields such dimensional geometry, calculus, and trigonometry. Use y=-2x in place of x in the first equation:

5x - 9(-2x) = -46

Simplify and find x's value:

5x + 18x = -46

23x = -46

x = -2

We can use the second equation to get y now that we know the value of x:

y = -2x = -2(-2) = 4

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