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3 years ago

What is the image of the point (4, -8) after a rotation of 270° counterclockwise

Mathematics

1 answer:

iVinArrow [24]3 years ago

7 0

Answer:

point (-8,-4)

Step-by-step explanation:

You can plot that coordinate and rotate the graph to figure out this point.

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A student is given that point P(a, b) lies on the terminal ray of angle Theta, which is between StartFraction 3 pi Over 2 EndFra

Harman [31]

Answer:

A.

The student made an error in step 3 because a is positive in Quadrant IV; therefore,

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

Step-by-step explanation:

Given

$P\ (a,b)$

$r = \± \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{-a}{\sqrt{a^2 + b^2}} = -\frac{\sqrt{a^2 + b^2}}{a^2 + b^2}$

Required

Where and which error did the student make

Given that the angle is in the 4th quadrant;

The value of r is positive, a is positive but b is negative;

Hence;

$r = \sqrt{(a)^2 + (b)^2}$

Since a belongs to the x axis and b belongs to the y axis;

$cos\theta$ is calculated as thus

$cos\theta = \frac{a}{r}$

Substitute $r = \sqrt{(a)^2 + (b)^2}$

$cos\theta = \frac{a}{\sqrt{(a)^2 + (b)^2}}$

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}}$

Rationalize the denominator

$cos\theta = \frac{a}{\sqrt{a^2 + b^2}} * \frac{\sqrt{a^2 + b^2}}{\sqrt{a^2 + b^2}}$

$cos\theta = \frac{a\sqrt{a^2 + b^2}}{a^2 + b^2}$

So, from the list of given options;

The student's mistake is that a is positive in quadrant iv and his error is in step 3

3 0

3 years ago

Suppose that the rate of return on stocks is normally dis-tributed with mean of 9% and a standard deviation of 3%. If I pick fiv

alisha [4.7K]

Answer:

The probability that at least two stocks will have a return of more than 12% is 0.1810.

Step-by-step explanation:

Let X = rate of return on stocks.

The random variable X follows a Normal distribution, N (9, 3²).

Compute the probability that a stock has rate of return more than 12% as follows:

$P(X\geq 12)=1-P(X$

**Use the z table for the probability.

The probability of a stock having rate of return more than 12% is 0.1587.

Now define a random variable Y as the number of stocks that has rate of return more than 12%.

The sample size of stocks selected is, n = 5.

The random variable Y follows a Binomial distribution.

The probability of a Binomial distribution is:

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

Compute the value of P (X ≥ 2) as follows:

P (X ≥ 2) = 1 - P (X < 2)

= 1 - P (X = 0) - P (X = 1)

$=1-{5\choose 0}(0.1587)^{0}(1-0.1587)^{5-0}-{5\choose 1}(0.1587)^{1}(1-0.1587)^{5-1}\\=1-0.4215-0.3975\\=0.1810$

Thus, the probability that at least two stocks will have a return of more than 12% is 0.1810.

6 0

3 years ago

If 9 x 0 + 4 = 4 had parenthesis where would they go?

Bingel [31]

Answer:

(9 x 0) + 4=4

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

a bag contains Stephanie five marbles, some red some blue. The ratio of red marbles to blue ones is 3:2. how many red marbles ar

Nikolay [14]

Answer:

There are 3 red marbles.

Step-by-step explanation:

The ratio of red marbles to blue marbles is 3:2, so for every two blue marbles there are three red marbles. This means that there are three red marbles for every four marbles in the bag. Therefore, if there are five marbles in the bag, there must be three red marbles and two blue marbles.

7 0

2 years ago

Help please!!!!:::_))

sleet_krkn [62]

Answer with Step-by-step explanation:

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5 0

2 years ago