Answer:
2nd option
Step-by-step explanation:
If AB is a tangent to the circle then ∠ B is right angle
Using the converse of Pythagoras' identity.
If the square of the longest side is equal to the sum of the squares on the other 2 sides, then the triangle is right
longest side = 52 and 52² = 2704
48² + (10 + 10)² = 48² + 20² = 2304 + 400 = 2704
Then AB is a tangent to the circle since ∠ B is a right angle
area of first figure=444
area of second figure=57
area of third figure=132
Explanation
The first figure
has 9 faces, 2 triangular and 7 rectangular.
bottom face-rectangle
length=16
breadth=5
area=l*b=16*5=80(1)
two similar rectangular faces
length=16
breadth=4
area=l*b=16*4=64
area of two faces=2*64=128(2)
two similar rectangular faces
length=5
breadth=4
area=5*4=20
area of two faces=2*20=40(3)
two top slant faces-rectangular
length=10
breadth=5
area=10*5=50
area of two faces=2*50=100(4)
two triangular top faces
base=16
height=6
area=1/2 bh=1/2 *16*6=48
area of two faces=2*48=96(5)
total area of the structure=(1)+(2)+(3)+(4)+(5)=80+128+40+100+96=444
The second figure
It has two triangles
triangle 1
length=7
breadth=3
area1=l*b=21
triangle 2
length=9
breadth=4
area2=l*b=9*4=36
total area=area1+area2=21+36=57
<u>T</u><u>he third figure </u>
It has a rectangle and triangle
r<u>ectangle</u>
length=20
breadth=6
area1=l*b=20*6=120
triangle
base=20-(8+6)=20-14=6
height=10-6=4
area2=1/2 bh=1/2*6*4=12
total area=area1+area2=120+12=132
Answer:
A.) The manager calculated mean and not standard deviation
B.) Standard deviation should be calculated with the use of formula.
Step-by-step explanation:
A.) The assumption that his customers do spend more than the national average is wrong because the standard deviation is not calculated and mean cannot be used as a substitute for standard deviation.
B.) Standard deviation tells us how value obtain from group measurement deviates from the average value or expected value of each item of observations.
When standard deviation is low, this show that the value is very close to the expected value or the average value.
If the national average value = $150 and average customer spends $160.
Deviation = 160 - 150 = 10
This is lower than $30
Or better still, the manager should make use of standard deviation formula. Which is the square root of variance.
Answer:
87 pages are filled with stamps.
Step-by-step explanation:
We need to know how many stamps are in the album. Since it can hold 500 but is missing 13%, we can say that it is 87% (100-13=87) complete.
500*0.87=435
The album has 435 stamps.
A page can hold 5 stamps. Thus, 435/5=87
12+49i
when you get i^2 it's the same as multiplying by -1 so
factoring it out will turn out like this
15i^2+40i+9i+27
instead of 15 i^2 multiply 15 x-1
-15+49i+27
12+49i