MATHEMATICS COLLEGE

Mary has a bag with 80 pieces of candy. She gives ¼ of her candy to John and 10% to Lisa. How much more candy did she give to John then Lisa?

Answers

Answer 1

Answer:

Answer:

12 pieces

Step-by-step explanation:

80 pieces of candy

1/4 is 25% or 20 pieces of candy

10% would be 8 pieces of candy

subtract the two. Your answer is 12

Answer 2

Answer:

He had 14 more pieces

Step-by-step explanation:

So 80/4 is 20 pieces. So we know John has 20. Now she has 60 left since 80-20 is 60. Now 10 percent of 60 would be 6 pieces. We can subtract 6 from 20 to find out how many more pieces John had. 20-6 is 14. So John had 14 more than Lisa

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We know that if the probability of an event happening is 100%, then the event is a certainty. Can it be concluded that if there is a 50% chance of contracting a communicable disease through contact with an infected person, there would be a 100% chance of contracting the disease if 2 contacts were made with the infected person

Answers

Answer:

The correct answer to the following question will be "No". The further explanation is given below.

Step-by-step explanation:

Probability (Keeping the disease out of 1 contact)

= $0.5$

Probability (not keeping the disease out of 1 contact)

= $1-0.5$

= $0.5$

Now,

Probability (not keeping the disease out of 2 contact)

= Keeping the disease out of 1 contact × not keeping the disease out of 1 contact

On putting the estimated values, we get

= $0.5* 0.5$

= $0.25$

So that,

Probability (Keeping the disease out of 2 contact)

= $1-0.25$

= $0.75 \ i.e., 75 \ percent$

∴ Not 100%

What is the system of checks and balances designed to ensure?

Answers

Answer:

ensure that no single branch of government would have too much power

Step-by-step explanation:

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.

For more such questions on Line Integral :

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There are twelve signs of the zodiac. How many people must be present for there to be at least a 50% chance that two or more of them were born under the same sign

Answers

Answer:

Step-by-step explanation:

Given that each zodiac sign occupies 1/12 of a year.

Then the minimum number of persons for Y[all different signs] < 0.5,

The probability of at least two having the same sign is 1 minus the probability of all having different signs.

This can be represented as A [at least 2 person share the same sign] = 1 - Y[all different signs] must be > 0.5

Therefore we have 1 - 12/12 *11/12 * 10/12 *9/12 *8/12 = 0.38

This implies that the lowest number will be found to be 5

Hence, the correct answer is 5.

Final answer:

To have at least a 50% chance that two or more people share the same Zodiac sign, there must be 13 people. This is based on the Pigeonhole Principle in probability theory.

Explanation:

This question is related to the field of probability theory. It can be solved using the principle of the Pigeonhole Principle, which states that if there are more items than containers, at least one container must hold more than one item.

Let's visualize each Zodiac sign as a container. If we have 12 people (items), each one can occupy a different Zodiac sign (container), without any sign repeating. Therefore, the probability of two people sharing a zodiac sign would be less than 50% at this point.

However, once we introduce the 13th person, regardless of their Zodiac sign, they would have to 'share' a container (be born under a sign that at least one other person was born under) since there are only 12 Zodiac signs. Therefore, for there to be a 50% chance that two or more people share a Zodiac sign, there would need to be 13 people.

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Can someone help me?

Answers

Answer:

..................................

WILL MARK BRAINLIEST PLEASE HELP

Answers

Answer:

1) h = -1/2t^2 +10t

2) h = -1/2(t -10)^2 +72

3) domain: [0, 20]; range: [0, 50]

Step-by-step explanation:

1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...

h = a(t -10)^2 +50

To find the value of "a", we must use another point on the graph. (0, 0) works nicely:

0 = a(0 -10)^2 +50

-100a = 50 . . . . . . subtract 100a

a = -1/2 . . . . . . . . . divide by -100

Then the standard-form equation is ...

h = (-1/2)(t^2 -20t +100) +50

h = -1/2t^2 +10t

2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.

h = -1/2(t -10)^2 +72

3.) The horizontal extent of the graph for Firework 1 is ...

domain: 0 ≤ t ≤ 20

The vertical extent of the graph for Firework 1 is ...

range: 0 ≤ h ≤ 50

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