Ateacher gives a test to a large group of students. the results are closely approximated by a normal curve. the mean is 74 with a standard deviation of 6. the teacher wishes to give a's to the top 8% of the students and f's to the bottom 8%. a grade of b is given to the next 15%, with d's given similarly. all other students get c's. find the bottom cutoff (rounded to the nearest whole number) for a b. (hint: use a table of areas under the standard normal curve to find z-scores from known a-values.) the bottom cutoff for a b is ?

82.46

Step-by-step explanation:

Given that the results of a test to a large group given by a teacher (X)

is normal with mean = 74 and std dev =6

X: N(74,6)

Hence

" alt="\frac{x-74}{6}" />" /> is N(0,1)

WE have to find out the bottom cut off for grade B.

B is between 8 and 23%

From std normal distribution we find Z values such that

P(Z>c1) = 0.08 and P(Z>c2) =0.23

c1=1.41: c2=0.74

Corresponding x values are

74+6(1.41) and 84+6(0.74)

i.e. 82.46 and 88.74

Thus bottom cut off for a B is 82.46

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.