The number of employees is 91.
According to the statement
Given that the standard deviation = 24.5
The width in the question = 13
We solve for the margin of error E.
E = width / 2
E= 13/2 = 6.5
At 90%
Alpha = 1-0.90
= 0.1
Alpha/2 = 0.1/2 = 0.05
Z 0.05 = 1.576
Now find the Sample size n
= ((1.576x24.5)/2)²
= 90.8
= 91
So, The number of employees is 91.
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With the information given we can wirte down 2 different equations where:
x = How many Fictoon books there are
A nd y = How many non-fiction books there are :
#1) x + y = 312
( The total of the books is 312 )
#2) x = 11y
(He has 11 times as many firction books as he has non-ficton books)
Now what we need to do is to isolate one the variables ( x or y ) , get its value and apply to one the equations to get the other variable's value:
We can do that by the property of substitution:
If x = 11y
then x + y = (11y) + y = 12y
If x + y = 312
and x + y = 12y
then 12y = 312
Now with the equation 12y = 312 , we can isolate y by dividing both sides of the equation by 12 :
12/12y = 312/12
y = 26
What that means : Mark has 26 non-fictional books.
Now that we have the value of y , we can find the value of x by plugging y to one of the equations :
x + y = 312
or
x = 7y
( I will do both , but you dont need to )
x + y = 312
Plugin 26 for y :
x + 26 = 312
Shift 26 to the other side of the equation by subtracting both sides of the equation by 26:
x + 26 - 26 = 312 - 26
26 - 26 cancel out , so we end up with :
x = 286
Second Equation :
x = 11y
Plugin 26 for y:
x = 11 × 26
x = 286
Awnser : Mark has 286 fictoon books and 26 non-fiction !
I hope you understood my brief explanation. And please consider marking this awnser as Branliest. Thank you ! :)
Answer:
Part 1)
Projection of vector A on vector B equals 19 units
Part 2)
Projection of vector B' on vector A' equals 35 units
Step-by-step explanation:
For 2 vectors A and B the projection of A on B is given by the vector dot product of vector A and B
Given
Similarly vector B is written as
Thus the vector dot product of the 2 vectors is obtained as
Part 2)
Given vector A' as
Similarly vector B' is written as
Thus the vector dot product of the 2 vectors is obtained as
It would be 6 because the other short side is 6 so it should be 6 units
Solution:
Equation of line perpendicular to , x=4 is
y +k=0
As, keep in mind , the equation of line perpendicular to , ax + by +c=0 is b x - a y +c=0
As, given the line perpendicular to, x =4, passes through the point (5,7).
So, y+k =0, passes through (5,7).
→ 7 +k=0
→ k= -7
So, line perpendicular to x=4, which passes through the point (5,7) is →y-7=0 that is y=7.
Option (C) →y=7
