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4 years ago

Write the translation

Mathematics

1 answer:

tatiyna4 years ago

8 0

Translate 5 units to the right, and 2 units down

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Find the point P that is 2/5 of the way from A to B on the directed line segment AB

Kruka [31]

The point P(–4, 4) that is $\frac{2}{5}$ of the way from A to B on the directed line segment AB.

Solution:

The points of the line segment are A(–8, –2) and B(6, 19).

P is the point that bisect the line segment in $\frac{2}{5}$ .

So, m = 2 and n = 5.

$x_1=-8, y_1=-2, x_2=6, y_2=19$

By section formula:

$$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)$

$$P(x, y)=\left(\frac{2\times 6+5\times (-8)}{2+5}, \frac{2\times 19+5\times (-2)}{2+5}\right)$

$$P(x, y)=\left(\frac{12-40}{7}, \frac{38-10}{7}\right)$

$$P(x, y)=\left(\frac{-28}{7}, \frac{28}{7}\right)$

P(x, y) = (–4, 4)

Hence the point P(–4, 4) that is $\frac{2}{5}$ of the way from A to B on the directed line segment AB.

4 0

3 years ago

The waking time of a student under common conditions is normally distributed with mean of 30 hours and a standard deviation of 5

Elina [12.6K]

Answer:

If the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 30 hours

Standard Deviation, σ = 5 hours

We are given that the distribution of waking time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.95

$P( X < x) = P( z < \displaystyle\frac{x - 30}{5})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 30}{5} = 1.645\\\\x = 38.225$

Thus, if the walking time is greater than or equal to 38.225 hours, than it exceeds 95% probability that is lie in top 5%.

4 0

3 years ago

Quadrilateral RUST has a vertex at R(2,3). What are the coordinates of R' after dilation by a scale factor of 3, centered at the

coldgirl [10]

Concept of this answer is (3,5) in the y(x)=-3

6 0

3 years ago

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A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digita

dusya [7]

Answer:

a) uniform

b) 1/2

c) 1/1000

Step-by-step explanation:

a) "numbers with equal probability" have a uniform distribution.

b) Even numbers make up 1/2 of all numbers.

c) There are ten such numbers in the range, so the probability is ...

10/10000 = 1/1000

7 0

3 years ago

What is the whole number 11 minus the number 3 4/12 show your work

olga2289 [7]

1.) 11 - 3 4/12

2.) 11 - 3 1/3

3.) 11/1 - 3 1/3

4.) 33/3 - 10/3

5.) 23/3 or 7.7 or 7 2/3 is your answer, depending on how you want it

7 0

3 years ago

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