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Ludmilka [50]
3 years ago
12

How does multiplying a vector by a scalar value of -pi / 4 change the vector?

Mathematics
1 answer:
makvit [3.9K]3 years ago
8 0

Answer:

The vector will change in direction and decrease in magnitude

Step-by-step explanation:

Given:

vector multiplication by -π/4

-π/4= -0.785

Due to the negative sign "-", the, vector will change/reverse its direction.

And as of the magnitude, 0.785<1 hence the magnitude of vector will be decreased by this factor !

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"6. A brand name has a 40% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small s
statuscvo [17]

Answer:

(a) The probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b) The probability that all of the selected consumers recognize the brand name is 0.0041.

(c) The probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d) The events of 5 customers recognizing the brand name is unusual.

Step-by-step explanation:

Let <em>X</em> = number of consumer's who recognize the brand.

The probability of the random variable <em>X</em> is, P (X) = <em>p</em> = 0.40.

A random sample of size, <em>n</em> = 6 consumers are selected.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> and <em>p</em>.

The probability mass function of <em>X</em> is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...

(a)

Compute the value of P (X = 5) as follows:

P(X=5)={6\choose 5}0.40^{5}(1-0.40)^{6-5}\\=6\times0.01024\times0.60\\=0.036864\\\approx0.0369

Thus, the probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b)

Compute the value of P (X = 6) as follows:

P(X=6)={6\choose 6}0.40^{6}(1-0.40)^{6-6}\\=1\times 0.004096\times1\\=0.004096\\\approx0.0041

Thus, the probability that all of the selected consumers recognize the brand name is 0.0041.

(c)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = P (X = 5) + P (X = 6)

              = 0.0369 + 0.0041

              = 0.041

Thus, the probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d)

An event is considered unusual if the probability of its occurrence is less than 0.05.

The probability of 5 customers recognizing the brand name is 0.0369.

This probability value is less than 0.05.

Thus, the events of 5 customers recognizing the brand name is unusual.

8 0
3 years ago
which of the following are the building blocks of geometry, according to hilbert? ray line angle point plane
statuscvo [17]
The building blocks of geometry would be point line and plane. 
8 0
2 years ago
Read 2 more answers
Hiran invests 20 000 rupees in an account for 3 years at 1.5% per year compound interest.
svp [43]

Answer:

There will be 20 914 rupees in the amount at the end of 3 years.

Step-by-step explanation:

The amount of rupes after t years in compound interest is given by:

A(t) = A(0)(1+r)^{t}

In which A(0) is the initial amount and r is the interest rate, as a decimal.

Hiran invests 20 000 rupees in an account for 3 years at 1.5% per year compound interest.

This means that A(0) = 20000, r = 0.015. So

A(t) = A(0)(1+r)^{t}

A(t) = 20000(1+0.015)^{t}

A(t) = 20000(1.015)^{t}

Work out the total amount of money in the account at the end of 3 years.

This is A(3). So

A(3) = 20000(1.015)^{3} = 20913.6

Rounding to the nearest rupee.

There will be 20 914 rupees in the amount at the end of 3 years.

8 0
2 years ago
Madelyn is knitting a scarf for a holiday gift. So far, it's 4.5 centimeters long. She plans to
olchik [2.2K]

In order to make the question true the length should be 45cm not 4.5 cm , Solving accordingly

  • Let nights be x
  • Rate of change=5cm

The equation is

  • y=45-5x

As 45 is base amount we used it as y intercect

7 0
2 years ago
The square represents a scale model that was created by using a factor of 4. A square with sides lengths of 8 feet. Which is tru
alexandr402 [8]

The answer should be 1/4

3 0
3 years ago
Read 2 more answers
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