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3 years ago

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You are handed two boxes. you cannot see what is inside but you have reliable information that one of the boxes contains two gre

en and ten red balls and the other contains eight green and four red balls. you select a ball from one of the boxes at random and take it out. it is red. which of the two boxes is it more like to have come from? what is that probability

1 answer:

Pavel [41]3 years ago

4 0

The probability of the first box with 2 green and 10 yellow is 1:5
the probability of the second box with 8 green and 4 red us 1:2.
The red ball most likly came from the first box.

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A buoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. Its displacement d fro

Mrac [35]

Answer:

The equation of the displacement $d$ as a function of time $t$ is :

$d(t)=8sin(\pi t+\pi )$

Step-by-step explanation:

Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple $sin$ or $cos$ terms.

Thus,

$d(t) = Asin(wt+c)$

is the general form of displacement of a SHM.

where,

<em> $d(t)$ is the displacement with respect to the mean position at any time $t$ </em>
<em> $A$ is amplitude </em>
<em> $w$ is the natural frequency of oscillation ( $rads^{-1}$ )</em>
<em> $c$ is the phase angle which indicates the initial position of the object in SHM ( $rad$ )</em>

given,

Time period ( $T$ ) = $2s$
$A=8$
The natural frequency ( $w$ ) and time period ( $T$ ) is :

$w=\frac{2\pi} {T}$

∴

$w$ = $\frac{2\pi }{2} = \pi$ $rads^{-1}$

∴

the equation :

<em>⇒ $d(t)=8sin(\pi t+c)$ </em> ------1

since $d=0$ when $t=o$ ,

<em>⇒ $0=8sinc\\c=n\pi$ ------2</em>

where n is an integer ;

<u>⇒since the bouy immediately moves in the negative direction , $x$ must be negative or c must be an odd multiple of $\pi$ .</u>

<em>⇒ $d(t) = 8sin(\pi t+(2k+1)\pi )$ ------3</em>

where k is also an integer ;

the least value of $k=0$ ;

thus ,

the equation is :

$d(t)=8sin(\pi t+\pi )$

<em></em>

7 0

3 years ago

Use two different methods to find an explain the formula for the area of a trapezoid that has parallel sides of length a and B a

evablogger [386]

Answer:

Formula of Trapezoid:

A = (a + b) × h / 2

The formula can be derived in different ways. for now, we have discussed two ways:

1. By using the formula of a triangle

2. By dividing into different sections

Step-by-step explanation:

1. By using the formula of a triangle

One of the ways to explain a formula for an area of a trapezoid using a formula for a triangle can be as follows.

Assume a trapezoid PQRS with lower base SR and upper base PQ (they are parallel) and sides PS and QR.

The image is attached below.

Connect vertices P and R with a diagonal.

Consider triangle ΔPQR as having a base PQ and an altitude from vertex R down to point M on base PQ (RM⊥PQ).

Its area is

S1= $\frac{1}{2} *PQ*RM$

Consider triangle ΔPRS as having a base SR and an altitude from vertex P up to point N on-base SR (PN⊥SR).

Its area is

S2= $\frac{1}{2} *SR*PN$

Altitudes RM and PN are equal and constitute the distance between two parallel bases PQ and SR.

They both are equal to the altitude of the trapezoid h.

Therefore, we can represent areas of our two triangles as

S1= $\frac{1}{2}*PQ*h$

S2= $\frac{1}{2}*SR*h$

Adding them together, we get the area of the whole trapezoid:

S=S1+S2= $\frac{1}{2} (PQ+SR)h,$

which is usually represented in words as "half-sum of the bases times the altitude".

2. By dividing into different sections

Trapezoid PQRS is shown below, with PQ parallel to RS.

Figure 1 - Trapezoid PQRS with PQ parallel to RS(image is attached below.)

We are going to derive the area of a trapezoid by dividing it into different sections.

If we drop another line from Q, then we will have two altitudes namely PT and QU.

Figure 2 - Trapezoid PQRS divided into two triangles and a rectangle. (image is attached below.)

From Figure 2, it is clear that Area of PQRS = Area of PST + Area of PQUT + Area of QRU. We have learned that the area of a triangle is the product of its base and altitude divided by 2, and the area of a rectangle is the product of its length and width. Hence, we can easily compute the area of PQRS. It is clear that

=> $A_{PQRS} = (\frac{ah}{2}) + b_{1}h + \frac{ch}{2}$

Simplifying, we have

=> $A= \frac{ah+2b_{1+C} }{2}$

Factoring we have,

=> $A_{PQRS} = (a+ 2b_{1} + c)\frac{h}{2} \\= > {(a+ b_{1} + c) + b_{1} }\frac{h}{2}$

But, $a+ b_{1} + c$ is equal to $b_{2}$ , the longer base of our trapezoid.

Hence, $A_{PQRS}= (b_{1} + b_{2} )\frac{h}{2}$

We have discussed two ways by which we can derive area of a trapezoid.

Read to know more about Trapezoid

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5 0

2 years ago

from a window 24 feet above the ground, the angle of elevation to the top of another building is 38 degrees. The distance betwee

Snowcat [4.5K]

Answer:

The height of the building is $73.2\ ft$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

$tan(38\°)=\frac{BC}{AB}$

we have

$AB=63\ ft$

substitute and solve for BC

$tan(38\°)=\frac{BC}{63}$

$BC=(63)tan(38\°)=49.2\ ft$

Find the height of the building

The height of the building (h) is equal to

$h=BC+24=49.2+24=73.2\ ft$

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4 years ago

What the ratio to 7 to 1 written in 3 different ways

Sholpan [36]

Answer: 14:2, 35:5, 21:3

Step-by-step explanation:

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3 years ago

Read 2 more answers

Bao saved $179 a month. He saved $145 less than Ada each month. How much would Ada save in three and a half years?

RSB [31]

Bao saved 179 dollars a month
Ada saved 145 dollars more than Bao a month
Let B = Bao
let A = Ada
=> B = 179 dollars
=> A = b + 145 dollars or 179 + 145
Now, find the total amount will ada save in 3 years and half
=> 3 years and half = (12 x 3) + 6 = 42 months
=> A = 179 + 145 x 42
=> a = 324 x 42
=> A = 13 608 dollars in 3 years and half.

4 0

3 years ago

Read 2 more answers