What is the probability that a point chosen at random in the given figure will be inside the smaller square?

Find the angle between u = (8.- 3) and v = (-3,- 8) Round to the nearest tenth of a degree.

Nimfa-mama [501]

Answer:

Step-by-step explanation:

First you must calculate the module or the magnitude of both vectors

The module of u is:

$|u|=\sqrt{(8)^2 + (-3)^2} \\\\|u|=\sqrt{64 + 9}\\\\|u|=8.544$

The module of v is:

$|v|=\sqrt{(-3)^2 + (-8)^2} \\\\|u|=\sqrt{9 + 64}\\\\|u|=8.544$

Now we calculate the scalar product between both vectors

$u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0$

Finally we know that the scalar product of two vectors is equal to:

$u*v = |u||v|*cos(\theta)$

Where $\theta$ is the angle between the vectors u and v. Now we solve the equation for $\theta$

$0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°$

the answer is 90°

Whenever the scalar product of two vectors is equals to zero it means that the angle between them is 90 °

5 0

3 years ago

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Fifteen telephones have just been received at an authorized service center. Five of these telephones are cellular, five are cord

viktelen [127]

Answer:

a) The probability of getting all (ﬁve) cordless phones among the ﬁrst 10 is 0.0839.

b) The probability of having exactly two types in the last five is 0.24975.

c) To pick a sample of size 6 which contains two of each type of phone. The probability of selecting 2 phones from each type is 0.199800.

Step-by-step explanation:

a) The ﬁrst ten serviced (without regard to order within the ﬁrst ten) constitute a random sample without replacement of size 10 from 15 phones.

So, such samples are: (Using Combination "C")

(15C10) $=3003\\$

We now regard the phones as of just two types: cordless or not-cordless. The not-cordless phones are the cellular and regular phones, and there are 10 such phones.

So, The number of ways to pick 5 cordless and 5 non-cordless is

(5C5) $*\\$ (10C5) $=252$

Thus the probability of getting all (ﬁve) cordless phones among the ﬁrst 10 is

$\frac{252}{3003} =0.0839$

b) Regard the last 5 phones (without regard to order within the last 5) as a sample with replacement from the 15 phones.There are (15C5) such samples.

Thus

There are (3C2)= 3 ways to choose the two types. For each such choice there are (10C5)= 252 possible ways to get a sample of size 5 from only these two types of phones.

also as the 2 of these samples contain all phones of same type so,

252-2 = 250

250 ways are to pick from these two types, having both type restricted.

then the probability will be

$\frac{3*(250)}{15C5} =0.249756$

c) We want to the ﬁnd the probability that two phones of each type are among the ﬁrst six serviced. The ﬁrst six serviced can be regarded, when ignoring the order among the ﬁrst 6, as an unordered sample of size 6 from 15 objects. so, there are (15C6) samples.

And there are $(15C2)^3$ ways to pick from each 3 types of phones.

Thus the probability of selecting such a sample is

$\frac{(15C2)^2}{(15C6)}=0.199800$

7 0

3 years ago

I need help understanding this please

valentinak56 [21]

Answer:

Alma needs $35.28 to purchase the lace for her pillow.

Step-by-step explanation:

If it is a square, the length and the width would be the same. You have to take the square root of the area, so the square root of 324 is 18. Now, we know that the length is 18 cm and the width is also 18 cm. If she's selling every 2 centimeters for 98 cents, you have to find the total amount of centimeters the pillow has, so 18*4 (the 4 comes from the number of sides on the pillow)=72.

Now divide that answer by the 2 lace centimeters she will get. (72/2=36 cm).

Now multiply that by 98 cents, the cost. (36*0.98=35.28).

So Alma needs $35.28 to purchase the lace for her pillow.

6 0

3 years ago

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Find the volume of the cylinder

Marta_Voda [28]

Answer:

500π m^3

Step-by-step explanation:

The question is not complete

Cylinders are described with dimensions as

Diameter and Height

Say the diameter is

D= 10m

and Height is

H=20

Hence the radius is

R= D/2= 10/2= 5 m

Therefore the volume is gotten as

V= πr^2h

V= π*5^2* 20

V= π*25*20

V= 500π m^3

Hence the volume is 500π m^3

4 0

3 years ago

How do i classify a triangle?

Alexxx [7]

Step-by-step explanation:

There are always 3 sides, angles, and verticies on a triangle

Hope this helps!!!

Brady

4 0

3 years ago

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