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2 years ago

14

Parallelogram ABCD is rotated to create image A'B'C'D'. On a coordinate plane, 2 parallelograms are shown. The first parallelogr

am has points A (2, 5), B (5, 4), C (5, 2), D (2, 3). The second parallelogram has points A prime (5, negative 2), B prime (4, negative 5), C prime (2, negative 5), D prime (3, negative 2). Which rule describes the transformation? (x, y) → (y, –x) (x, y) → (–y, x) (x, y) → (–x, –y) (x, y) → (x, –y)

2 answers:

maw [93]2 years ago

6 0

Answer:

(x,y) → (y,-x)

Step-by-step explanation:

We are given two parallelograms.

ABCD with coordinates

A=(2,5)

B=(5,4)

C=(5,2)

D=(2,3)

Another parallelogram A'B'C'D' with coordinates

A'=(5,-2)

B'=(4,-5)

C'=(2,-5)

D'=(3,-2)

Now, A is transformed to A' that is (2,5) is transformed to (5,-2)

We see that the y coordinate becomes the x-coordinate after transformation and the negative of x coordinates becomes y coordinate after transformation.

A similar pattern can be seen for the B, C and D.

Thus, the transformation is given by:

(x,y) → (y,-x)

Gala2k [10]2 years ago

4 0

Answer:

(x,y)→(y,-x)

Step-by-step explanation:

Parallelogram ABCD:

A(2,5)

B(5,4)

C(5,2)

D(2,3)

Parallelogram A'B'C'D':

A'(5,-4)

B'(4,-5)

C'(2,-5)

D'(3,-2)

Rule:

A(2,5)→A'(5,-2)

B(5,4)→B'(4,-5)

C(5,2)→C'(2,-5)

D(2,3)→D'(3,-2)

so the rule is

(x,y)→(y,-x)

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The probability that a grader will make a marking error on any particular question of a multiple-choice exam is 0.15. If there a

sashaice [31]

Answer:

$P(X=0)=(10C10)(0.15)^{0} (1-0.15)^{10-0}=0.1969$

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

$P(X=0)=(nCn)(p)^{0} (1-p)^{n-0}=(1-p)^n$

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

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.15)$

what is the probability that no errors are made?

For this case means that all the questions were correct so we want this probability:

$P(X=0)=(10C10)(0.15)^{0} (1-0.15)^{10-0}=0.1969$

what is the probability that at least one error made?

For this case we want this probability:

$P(X \geq 1)$

And we can use the complement rule:

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

If there are n questions and the probability of a marking error is p rather than 0.15, give expressions for the probabilities of no errors and at least one error

$P(X=0)=(nCn)(p)^{0} (1-p)^{n-0}=(1-p)^n$

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

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3 years ago

Two radar stations 5.5 miles apart are tracking an airplane. The straight line distance

Vesnalui [34]

Answer:

19°

Step-by-step explanation:

I have attached an image showing this elevation.

From the image, let's first find the angle A by using cosine rule.

Thus;

8.1² = 5.5² + 13.1² - 2(5.5 × 13.1)cos A

65.61 = 30.25 + 171.61 - 144.1cos A

144.1cos A = 171.61 + 30.25 - 65.61

144.1cosA = 136.25

cosA = 136.25/144.1

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A = cos^(-1) 0.9455

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5 0

2 years ago

For a data set of the pulse rates for a sample of adult? females, the lowest pulse rate is 39 beats per? minute, the mean of the

Zarrin [17]

Answer:

a) The difference is of 35 beats per minute.

b) So 3.07 standard deviations below the mean.

c) Z = -3.07.

Step-by-step explanation:

Z-score:

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.

In this question:

Mean $\mu = 74$ , standard deviation $\sigma = 11.4$

a. What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the? females?

39 - 74 = -35

The difference is of 35 beats per minute.

b. How many standard deviations is that? [the difference found in part? (a)?

|Z| when X = 39. So

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

$Z = \frac{39 - 74}{11.4}$

$Z = -3.07$

|Z| = 3.07

So 3.07 standard deviations below the mean.

c. Convert the pulse rate of 39 beats per minutes to a z score.

From item b. above, Z = -3.07.

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Neko [114]

Answer:

Given System of equation:

x-y =6 .....,[1]

2x-3z = 16 ......[2]

2y+z = 4 .......[3]

Rewrite the equation [1] as

y = x - 6 .......[4]

Substitute the value of [4] in [3], we get

$2(x-6)+z = 4$

Using distributive property on LHS ( i.e, $a \cdot (b+c) =a \cdot b+ b \cdot c$ )

then, we have

2x - 12 +z =4

Add 12 to both sides of an equation:

2x-12+z+12=4+12

Simplify:

2x +z = 16 .......[5]

On substituting equation [2] in [5] we get;

2x+z=2x -3z

or

z = -3z

Add 3z both sides of an equation:

z+3z = -3z+3z

4z = 0

Simplify:

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Substitute the value of z = 0 in [2] to solve for x;

$2x-3(0) = 16$

or

2x = 16

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$\frac{2x}{2} =\frac{16}{2}$

Simplify:

x= 8

Substitute the value of x =8 in equation [4] to solve for y;

y = 8-6 = 2

or

y = 2

Therefore, the solution for the given system of equation is; x = 8 , y = 2 and z =0

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