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balandron [24]
2 years ago
7

Which rule describes the translation PQR --> P'Q'R'?

Mathematics
1 answer:
Ksenya-84 [330]2 years ago
5 0
The "Pre Image" is the image that we started with, so the pink triangle. 
The "Image" is the image that we ended with, so the blue triangle. 

To determine how far we went from the pre image to the image, we can focus on one point, let's say point "P". 

The pre image coordinates for point "P" are 2, 3. 
The image coordinates for point "P'" are -1, 0. 

To get from x value 2 to x value -3, we subtracted 3. 
To get from y value 3 to y value 0, we subtracted 3. 

So, our rule for this translation would be A, (x, y) ----> (x-3, y-3).
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A doctor gives a patient a 6060​% chance of surviving bypass surgery after a heart attack. if the patient survives the​ surgery,
DENIUS [597]
Let BS be the event that the patient survives bypass surgery. Let H be the event that the heart damage will heal. Then P(BS) = 0.60, and also we have a conditional probability: GIVEN that the patient survives, the probability that the heart damage will heal is 0.5, that is P(H|BS) = 0.5 We want to know P(BS and H). Using the formula of the conditional probability: P(H and BS) = P(H|BS)·P(BS) = (0.6)(0.5) = 0.3 
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2 years ago
What is slope between the points (-5,7) and (4,-8)?
WINSTONCH [101]
The slope can sometimes be called the gradient, and the equation for the gradient is (y2 - y1)/(x2 - x1). So therefore, you'd do: (-8 - 7)/(4 - -5) which is (-15)/9) which is -1 2/3 or -1.6 (recurring), which is your answer. I hope this helps! Let me know if I've confused you :)
3 0
3 years ago
Using f(x) = 4x + 6 with a domain of {-1, 0, 2 }, find the range.
lianna [129]

Answer:

{2, 6, 14}

Step-by-step explanation:

Using f(x) = 4x + 6 with a domain of {-1, 0, 2 }, find the range.

To get the range, we will substitute the values of the domain into the given function as shown;

when x = -1

f(-1) = 4(-1)+6

f(-1) = -4+6

f(-1) = 2

when x = 0

f(0) = 4(0)+6

f(0) = 0+6

f(0) = 6

when x = 2

f(2) = 4(2)+6

f(2) = 8+6

f(2) = 14

Hence the required range are {2, 6, 14}

6 0
3 years ago
A vector with magnitude 9 points in a direction 190 degrees counterclockwise from the positive x axis. Write in component form
Over [174]

Answer:

\vec{v}= \text{ or } \approx

Step-by-step explanation:

Component form of a vector is given by \vec{v}=, where i represents change in x-value and j represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector \vec{v}=, the magnitude is ||v||=\sqrt{i^2+j^2.

190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being i, one leg being j, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.

In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

\sin 10^{\circ}=\frac{j}{9},\\j=9\sin 10^{\circ}

To find the other leg, i, we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:

\cos 10^{\circ}=\frac{i}{9},\\i=9\cos 10^{\circ}

Verify that (9\sin 10^{\circ})^2+(9\cos 10^{\circ})^2=9^2\:\checkmark

Therefore, the component form of this vector is \vec{v}=\boxed{}\approx \boxed{}

6 0
3 years ago
A filling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces. forty jars filled
Lunna [17]
Let's attack this problem using the z-score concept.  The sample std. dev. here is (0.25 oz)/sqrt(40), or 0.040.  Thus, the z score representing 3.9 oz. is
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z = -------------- = -2.5
          0.040 

In one way or another we must find the area under the std. normal curve that lies to the left of z = -2.5.  Use a table of z-scores or a calculator with built-in statistics functions.  According to my TI-83 Plus calculator, that area is

0.006.  One way of interpreting this that with so small a standard deviation, most volumes of coffee put into the jars are very close to the mean, 4 oz.
4 0
3 years ago
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