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2 years ago

Ignore the answer selected

Mathematics

2 answers:

Masteriza [31]2 years ago

6 0

Answer:

Option B is correct.

Step-by-step explanation:

$=6(cos270+isin270)\\\\=6(0-i)\\\\=6(-i)\\\\=-6i$

stich3 [128]2 years ago

6 0

$\sf - 6i$

The modulus r, of a pure imaginary number bi, b<0, equals |b| and its argument θ equals $\frac{3\pi}{2}$

$\sf \: r = 6 \\ \sf \theta = \frac{3\pi}{2}$

Substitute the given values into the formula r(cos(θ)+i×sin(θ))

$\sf6( \cos( \frac{3\pi}{2} ) + i \times \sin( \frac{3\pi}{2} ) )$

Since, The value of 3π/2 is 270°.. Put it in the equation

$\boxed{ \tt6( \cos270 + i \times \sin270) }$

<em>Thus, Option B is the correct choice!!~</em>

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Last Monday local mail carriers delivered 1,344 pieces of mail. Of all the deliveries they made, 1 / 6 were magazines, 1 / 12 we

Brut [27]

Answer: 1008 letters

Step-by-step explanation:

From the question, last Monday, a local mail carriers delivered 1,344 pieces of mail and of all the deliveries they made, 1 / 6 were magazines, 1 / 12 were packages, and the rest were letters. The fraction of letters will be:

= 1 - (1/6 + 1/12)

= 1 - (3/12)

= 9/12 = 3/4

We will now multiply 3/4 by 1344 to get the number of letters delivered.

= 3/4 × 1344

= 1008 letters

6 0

3 years ago

The annual rainfall (in inches) in a certain region is normally distributed with = 40 and = 4. What is the probability that star

sdas [7]

Answer:

0.93970

Step-by-step explanation:

Solution:-

- Denote a random variable "X" The annual rainfall (in inches) in a certain region . The random variable follows a normal distribution with parameters mean ( μ ) and standard deviation ( σ ) as follows:

X ~ Norm ( μ , σ^2 )

X ~ Norm ( 40 , 4^2 ).

- The probability that it rains more than 50 inches in that certain region is defined by:

P ( X > 50 )

- We will standardize our test value and compute the Z-score:

P ( Z > ( x - μ ) / σ )

Where, x : The test value

P ( Z > ( 50 - 40 ) / 4 )

P ( Z > 2.5 )

- Then use the Z-standardize tables for the following probability:

P ( Z < 2.5 ) = 0.0062

Therefore, P ( X > 50 ) = 0.0062

- The probability that it rains in a certain region above 50 inches annually. is defined by:

q = 0.0062 ,

- The probability that it rains in a certain region rains below 50 inches annually. is defined by:

1 - q = 0.9938

n = 10 years ..... Sample of n years taken

- The random variable "Y" follows binomial distribution for the number of years t it takes to rain over 50 inches.

Y ~ Bin ( 0.9938 , 0.0062 )

- The probability that it takes t = 10 years for it to rain:

= 10C10* ( 0.9938 )^10 * ( 0.0062 )^0

= ( 0.9938 )^10

= 0.93970

3 0

3 years ago

If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.

Lelechka [254]

Answer:

$\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }$

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

$f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)$

So we can say that

$a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}$

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

$(x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab$

and we can notice that

$a^2+b^2=(a+b)^2-2ab$ so

$(x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab$

it comes

$x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}$

multiply by 3

$3x^2-20x+2*16+5=3x^2-20x+37$

4 0

3 years ago

An equivalent expression for sin x is?<br><br>(please answer with steps)

Anestetic [448]

Answer:

Step-by-step explanation:

Using the trigonometric identity

sin2x = 2sinxcosx

That is the angle on the right side is half the angle on the left, thus

sinΘ = 2sin( $\frac{1}{2}$ Θ )cos( $\frac{1}{2}$ Θ ) → b

5 0

2 years ago

A line intersects the points (-4,6) and (-2,5). what is the slope intercept equation for this line

kompoz [17]

First find the slope of the line connecting these two points:

6-5

m = ------------ = -1/2

-4+2

Substitute this slope into y = mx + b: y = (-1/2)x + b.

Next, subst. 5 for y and -2 for x, and find b:

5 = (-1/2)(-2) + b, or 5-1=b. Then b = 4, and

the equation of the line is y = (-1/2)x + 4.

7 0

3 years ago

Read 2 more answers