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2 years ago

What is the ordered pair of C' after point C (1, 2) is rotated 90° clockwise?

Mathematics

2 answers:

fiasKO [112]2 years ago

8 0

Answer:

option D

Step-by-step explanation:

C (1, 2) is rotated 90° clockwise

When (x,y) is rotated 90 degree clockwise then

(x,y) becomes (y,-x)

Interchange the value of x and y and multiply the x value by negative sign

C (1, 2) becomes (2,-1) that is C'

So , C (1, 2) is rotated 90° clockwise is C' (2,-1)

Anna [14]2 years ago

5 0

Answer:

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ), thus

C(1, 2 ) → C'(2, - 1 ) → D

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Find the inverse of the function. y = 2x2 –4

Alex73 [517]

Answer:

The inverse function is $y=\sqrt{\frac{x+4}{2}}$

Step-by-step explanation:

The given function is $y=2x^2-4$ .

This function is only invertible on the interval, $x\ge 0$ .

To find the inverse on this interval, we interchange $x$ and $y$ .

$x=2y^2-4$

We now make $y$ the subject to get,

$x+4=2y^2$

$\Rightarrow \frac{x+4}{2}=y^2$

$\Rightarrow \pm \sqrt{\frac{x+4}{2}}=y$

But the given interval is $x\geq 0$ , This implies that, $y\geq 0$ .

$y=\sqrt{\frac{x+4}{2}}$

4 0

2 years ago

Read 2 more answers

Charlize wants to measure the depth of an empty well. She drops a ball from a height of 3 feet into the well

pentagon [3]

Answer:

about 151 feet

Step-by-step explanation:

The height of the ball at a time of 3.1 seconds is given by Charlize's equation as ...

h(3.1) = -16(3.1)^2 +3 = -150.76 . . . feet

The well is about 151 feet deep.

_____

<em>Comment on this measurement</em>

The speed of sound is sufficiently slow that it will make a difference in the time Charlize records. She would get a more accurate measurement if she were able to <em>see</em> the ball hit bottom.

5 0

2 years ago

Two-digit natural numbers are formed, with replacement, from the digits 0 through 9.

alexdok [17]

Answer:

The first digit of a two digit number can be any of digits 1 - 9. It cannot be 0 though. Therefore there are 9 possible digits for the first place.

There are 5 possible digits for the second position. The two digit number has to be odd and therefore the final digit must be 1,3,5,7 or 9

Therefore for each and every one of the nine first digits there are 5 digits that the second can be.

Therefore ANSWER = 9 * 5 = 45 possible permutations.

2. The largest two digit number = 99

Subtract 57 and you get 42

ANSWER = 42

The forty two numbers are 58 ,59, 60, 61......98, 99

7 0

2 years ago

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A survey of 2690 musicians showed that 368 of them are left-handed. Find a point estimate for p, the population proportion of mu

makkiz [27]

Answer: 0.137.

Step-by-step explanation:

Let p be the population proportion of musicians that are left-handed.

Given: Sample size : n= 2690 [subset of population]

Number of musicians that are left-handed: x= 368

Then the sample proportion: $\hat{p}=\dfrac{368}{2690}\approx0.137$

Since sample proportion is the best point estimate of the population proportion.

Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.

7 0

2 years ago

The time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes

klio [65]

Answer:

a) The mean is 10 and the variance is 0.0625.

b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.

c) 10.58 minutes.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.

This means that $\mu = 10, \sigma = 2$

Suppose 64 visitors independently view the site.

This means that $n = 64, = \frac{2}{\sqrt{64}} = 0.25$

a. The expected value and the variance of the mean time of the visitors.

Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.

b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.

15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.

X = 10.25

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$