This is quite a nice little problem. It takes a minute or three to figure out the answer, and when you do, you will be certain that you have been tricked. It is a little like the egg of Columbus.

Solution

The Base of Triangle ABN is AB

The Base of Triangle CDM is CD

The height of both given triangles is h. That is the distance between the two parallel lines.

Area ABN = 1/2*AB * h = 23 cm^2

Area CDM = 1/2*CD * h = 18 cm^2

Now the Area of the trapezoid is

Area_Trapezoid = 1/2 * h (AB + CD) Using the distributive property Remove the brackets.

Area_Trapezoid = 1/2*AB*h + 1/2*CD*h Did you notice something? Those terms are just the area of the triangles (written above.)

Area Trapezoid = 23 + 18 = 41 cm^2 <<<< Answer

6 0

3 years ago

Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op

Mashcka [7]

Answer:

a) P(X<50)=0.9827

b) P(X>47)=0.4321

c) P(-1.5<z<1.5)=0.8664

Step-by-step explanation:

We will calculate the probability based on a random sample of one moped out of the population, normally distributed with mean 46.7 and standard deviation 1.75.

a) This means we have to calculate P(x<50).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{50-46.7}{1.75}=\dfrac{3.7}{1.75}=2.114\\\\\\P(X$

b) We have to calculatee P(x>47).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

$z=\dfrac{X-\mu}{\sigma}=\dfrac{47-46.7}{1.75}=\dfrac{0.3}{1.75}=0.171\\\\\\P(X>47)=P(z>0.171)=0.4321$

c) If the value differs 1.5 standard deviations from the mean value, we have a z-score of z=1.5

$z=\dfrac{(\mu+1.5\sigma)-\mu}{\sigma}=\dfrac{1.5\sigma}{\sigma}=1.5$

So the probability that maximum speed differs from the mean value by at most 1.5 standard deviations is P(-1.5<z<1.5):

$P(-1.5$

3 0

3 years ago

Complementary angles equal 90 degrees true or false

barxatty [35]

False, Complementary angles equal to 180 degrees and Supplementary angles equal to 360 degrees

7 0

3 years ago

Vhich expression is equivalent to 16^3

LenKa [72]

Answer:16×16×16

Step-by-step explanaution:

16 ^3 so that means you need to but 16 3 times

6 0

3 years ago