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3 years ago

A can of soda is 6 inches tall and has a diameter 3 inches how much soda does the can hold in terms of pi

Mathematics

1 answer:

Leno4ka [110]3 years ago

6 0

Answer:

diameter / 2 = radius

3 / 2 = 1.5

radius x radius x height x pi = volume

1.5 x 1.5 x 6 = 13.5

We don't multiply by Pi because it is already included

Hope this helps

Step-by-step explanation:

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In ΔFGH, the measure of ∠H=90°, FH = 39, GF = 89, and HG = 80. What ratio represents the cotangent of ∠G?

hoa [83]

Given:

In ΔFGH, the measure of ∠H=90°, FH = 39, GF = 89, and HG = 80.

To find:

The ratio which represents the cotangent of ∠G.

Solution:

In a right angle triangle, the ratio of the cotangent of an angle is

$\cot \theta =\dfrac{Base}{Perpendicular}$

It is also written as

$\cot \theta =\dfrac{Adjacent}{Opposite}$

In ΔFGH, the measure of ∠H=90°. So,

$\cot G =\dfrac{HG}{FH}$

$\cot G =\dfrac{80}{39}$

Therefore, the ratio for the cotangent of ∠G is $\cot G=\dfrac{80}{39}$ .

6 0

3 years ago

I need help on this question plz

devlian [24]

Answer is "Nothing, they are equal". The central angle = its associated arc.

Other things to remember:

Tangent Angle= 1/2 Arc

Inscribed angle= 1/2 Arc

The central angle is the only one that equals its arc.

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3 years ago

Suppose that Y has density function

zvonat [6]

I'm assuming

$f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}$

(a) f(x) is a valid probability density function if its integral over the support is 1:

$\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1$

Compute the integral:

$\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16$

So we have

k / 6 = 1 → k = 6

(b) By definition of conditional probability,

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)

P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)

It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).

We have

$\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y$

Then

P(Y ≤ 0.4) = F (0.4) = 0.352

P(Y ≤ 0.8) = F (0.8) = 0.896

and so

P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393

(c) The 0.95 quantile is the value φ such that

P(Y ≤ φ) = 0.95

In terms of the integral definition of the CDF, we have solve for φ such that

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95$

We have

$\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95$

which reduces to the cubic

3φ² - 2φ³ = 0.95

Use a calculator to solve this and find that φ ≈ 0.865.

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3 years ago

When heated and metal barn creases in line from 1.25 m to 1.262 m calculate percentage increase the correct one decimal place. C

Misha Larkins [42]

Answer:

0.96%

Step-by-step explanation:

Well the easy way to do this is

1.262

- - - - - - - x 100 = 100.96%

1.25

( this is just saying, now the thing is 100.96% of it original size)

So now they are asking the increase, so just simply take

100.96 - 100

= 0.96%

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2 years ago

A store sells 12 cans of nuts for $27. How much would it cost u to buy 7 cans of nuts

rusak2 [61]

Cross multiply and solve for x

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3 years ago

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