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3 years ago

14. A pitcher contains quart of lemonade.

Mathematics

1 answer:

Sergio039 [100]3 years ago

3 0

Answer:

1/9 quart in each glass

Step-by-step explanation:

2/3) / 6

(2/3) * (1/6) = 2/18 = 1/9 quart in each glass

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1. Calculate the sum of the infinite series S. = 16+4+1+....

Mariana [72]

Answer:

yes

Step-by-step explanation:

8 0

3 years ago

A game consists of tossing three coins. If all three coins land on heads, then the player wins $75. If all three coins land on t

emmainna [20.7K]

Answer:

On average, a player should expect to win $15.

Step-by-step explanation:

The expected value in an event with outcomes:

x₁, x₂, ..., xₙ

Each with probability:

p₁, ..., pₙ

is given by:

Ev = x₁*p₁ + ... +xₙ*pₙ

In this case we have 3 outcomes:

player wins $75 = x₁

player wins $45 = x₂

player does not win = x₃

Let's find the probabilities of these events.

player wins $75)

Here we must have the 3 coins landing on heads, so there is only one possible outcome to win $75

While the total number of outcomes for tossing 3 coins, is the product between the number of outcomes for each individual event (where the individual events are tossing each individual coin, each one with 2 outcomes)

Then the number total of outcomes is:

C = 2*2*2 = 8

Then the probability of winning $75 is the quotient between the number of outcomes to win (only one) and the total number of outcomes (8)

p₁ = 1/8

Win $45:

This happens if the 3 coins land on tails, so is exactly equal to the case above, and the probability is the same:

p₂ = 1/8

Not wining:

Remember that:

p₁ + p₂ + ... + pₙ = 1

Then for this case, we must have:

p₁ + p₂ + p₃ = 1

1/8 + 1/8 + p₃ = 1

p₃ = 1 - 1/8 - 1/8

p₃ = 6/8

Then the expected value will be:

Ev = $75*1/8 + $45*1/8 + $0*6/8 = $15

On average, a player should expect to win $15.

7 0

3 years ago

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 − 2x, (0

raketka [301]

Answer:

$f(0)=-2\\f(1)=e-1$

Step-by-step explanation:

According to intermediate value theorem, if a function is continuous on an interval $[a,b]$ , and if $k$ is any number between $f(a)$ and $f(b)$ , then there exists a value, $x=m$ , where $a$ , such that $f(m)=k$

In the given question,

Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.

Here,

$f(x)=e^x-3+2x$

Put $x=0$

$f(0)=e^0-3+2(0)=1-3+0=-2$

Put $x=1$

$f(1)=e^1-3+2(1)=e-3+2=e-1$

3 0

3 years ago

Write the following equation in the general form Ax+ By+ C:

Mrac [35]

C the answer hehehehehehehwhw

8 0

4 years ago

Here is a tunnel for a toy train.

jonny [76]

The <em>total</em> area of all six faces of the tunnel is $614.197\pi$ square centimeters.

<h2>Procedure - Surface area of a tunnel for a toy train</h2>

The surface area of the solid ( $A$ ) used to represent the tunnel for a toy train is the sum of its six faces (two <em>semicircular</em> sections, inner <em>semicircular</em> arc section, outer <em>semicircular</em> arc section, two rectangles).

<h3>Determination of the surface area of the tunnel based on information of the diagram</h3>

We calculate the surface area as following:

$A = 2\cdot \frac{\pi}{2} \cdot [(10\,cm)^{2}-(8\,cm)^{2}] + \pi\cdot (8\,cm)\cdot (30\,cm) + \pi\cdot (10\,cm)\cdot (30\,cm) + 2\cdot (2\,cm)\cdot (30\,cm)$

$A = 614.197\pi\,cm^{2}$

The <em>total</em> area of all six faces of the tunnel is $614.197\pi$ square centimeters. $\blacksquare$

To learn more on surface areas, we kindly invite to check this verified question: brainly.com/question/2835293

5 0

2 years ago