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3 years ago

What is the perimeter of a rectangle with length x+4 and a width of 5x-7

Mathematics

1 answer:

AlladinOne [14]3 years ago

8 0

Answer:

12x-6

Step-by-step explanation:

perimeter= 2l+2w

=2(x+4)+2(5x-7)

=2x+8+10x-14

=12x-6

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Surface Area of the pyramid

hichkok12 [17]

Answer:

Step-by-step explanation:

the total surface area of such a pyramid is the sum of 5 areas :

1 bottom square (8×8)

4 side triangles

the area of a triangle is

baseline × height / 2

now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?

the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).

we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

slant height = sqrt(65) = 8.062257748... in

so, we get a areas

bottom square = 8×8 = 64 in²

a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =

= 32.24903099... in²

all 4 side triangles = 4×32.24903099... =

= 128.996124... in²

and we get as total surface area

64 + 128.996124... = 192.996124... in² ≈ 193.00 in²

8 0

2 years ago

When a man observed a sobriety checkpoint conducted by a police department, he saw 671671 drivers were screened and 77 were arr

kifflom [539]

Answer:

$P(\overline W)=0.98957$

Step-by-step explanation:

Number of drivers Screened = 671

Number Arrested for Driving While Intoxicating = 7

If the W denotes the event of screening a driver and getting someone who is intoxicated.

The Probability of W, $P(W)=\frac{7}{671}=0.01043$

The Probability $P(\overline W)$ is the probability of the event of screening a driver and getting someone who is not intoxicated. Simply put, it is the Probability of the Complement of W.