All categories

3 years ago

DE has a length of 5 cm. What is the length of the image of DE after applying the composition rx degrees R0.-270degrees?

Mathematics

1 answer:

oee [108]3 years ago

7 0

Answer:

B. 5 cm

Step-by-step explanation:

We are given that,

Length of the segment DE = 5 cm

Now, the transformation applied to DE is $R_{x-axis}\circ R_{0,-270}$ .

That is, the segment DE is,

Rotated by 270° about the origin counter-clockwise and then reflected across x-axis.

It is required to find the length of the segment which is the image of DE.

Since, we know,

The only transformation which changes the measurements of the figure is 'dilation'.

Thus, rotation and reflection will not change the shape and size of the segment DE.

Hence, the length of the image of DE will be same as that of DE i.e. 5 cm.

You might be interested in

(Uniform) Suppose X follows a continuous uniform distribution from 3 to 9. (a) Write down the PDF of X. (b) Find P(X ≤ 6). Round

defon

Answer:

a) P(x) = {0.1667 for x in (3,9) , 0 otherwise}

b) P(x≤6) = 0.5

c) P(4 < x ≤ 6) = 0.3333

d) P(X > 4 | X ≤ 6) = 0.3333 or 1 *see below*

Step-by-step explanation:

Since it is a uniform distribution you can imagine it as a rectangle which extends from a = 3 to b = 9 and whose total area is 1.

Therefore the height must be equal to the inverse of the side:

P(X) = 1/(b-a) = 1/(9-3)= 1/6 for every x in (3,9) and 0 otherwise

P(X) = 0.1667

To find this probability we must find the area of the rectangle which extends from 3 to 6 and whose height is equal to P(x)

That is:

P(X ≤ 6) = (6-3)/(9-3) = 3/6 = 1/2 = 0.5

That make sense since 6 is half way between 3 and 9

Similar to b) but now we consider tha base of the rectangle from 4 to 6:

P(4 < X ≤ 6) = (6-4)/(9-3) = 2/6 = 1/3 = 0.3333

If '' | '' means " or ", the probability is one, since every number in the range (3,9) is either higher than 4 or less than 6.

If " | " means " and " the answer is the same as in c , that is because 4<x≤6 is the set of numbers which are higher than 4 and at most 6 which can be expressed as x>4 and x≤6

7 0

3 years ago

Yvette is considering taking out a loan with a principal of $16,200 from one of two banks. Bank F charges an interest rate of 5.

umka21 [38]

Hi there
First find the monthly payment of each offer to see which monthly payment is lower
The formula of the present value of annuity ordinary is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv present value
PMT monthly payment
R interest rate
K compounded monthly 12
N time
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]

Bank F
PMT=16,200÷((1−(1+0.057÷12)^(
−12×8))÷(0.057÷12))
=210.53

Bank G
PMT=16,200÷((1−(1+0.062÷12)^(
−12×7))÷(0.062÷12))
=238.21

From the above the monthly payment of bank f is lower than the bank g
And since the lifetime of bank g is lower than bank f the answer is
b. Yvette should choose Bank F’s loan if she cares more about lower monthly payments, and she should choose Bank G’s loan if she cares more about the lowest lifetime cost.

Good luck!

6 0

3 years ago

g Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 12. Use the empirical rul

Galina-37 [17]

Answer:

a) 95% of people has an IQ score between 76 and 124.

b) 0.3% of people has an IQ score less than 64 or greater than 136.

c) 0.15% of people has an IQ score greater than 136

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 100

Standard deviation = 12

(a) What percentage of people has an IQ score between 76 and 124? 

76 = 100 - 2*12

124 = 100 + 2*12

So within 2 standard deviations of the mean, and the percentage is 95%.

(b) What percentage of people has an IQ score less than 64 or greater than 136?

64 = 100 - 3*12

136 = 100 + 3*12

99.7% of people has scores between 64 and 136. So 100 - 99.7 = 0.3% of people has an IQ score less than 64 or greater than 136.

(c) What percentage of people has an IQ score greater than 136?

0.3% of people has an IQ score less than 64 or greater than 136.

Since the normal distribution is symmetric, 0.3%/2 = 0.15% are below 64 are 0.15% are above 136.

5 0

3 years ago

The mass of 3 washers, when converted to kg is

spayn [35]

Answer:

Step-by-step explanation:

272.155 kg

3 0

3 years ago

Read 2 more answers

Is -77 a integer? Anyone help pls

maria [59]

Step-by-step explanation:

yeah -77 is an integer

A whole numbers with + or - sign is an integer

3 0

3 years ago

Read 2 more answers