Step-by-step explanation:
the surface area consists of 6 individual areas :
front and back (both are equal)
left and right (both are equal)
top and bottom
front and back are trapezoids.
the area of a trapezoid is
(base 1 + base 2)/2 × h
the bases are the 2 parallel sides.
in our case the area of one trapezoid is
(5 + 19)/2 × 12.1 = 145.2 ft²
front and back together then are 290.4 ft².
left and right are 8×14 rectangles:
8×14 = 112 ft²
together they are 224 ft².
the bottom is a 5×8 rectangle :
5×8 = 40 ft²
the top is a 19×8 rectangle :
19×8 = 152 ft²
so, the total surface area is
290.4 + 224 + 40 + 152 = 706.4 ft²
The problem can be solved step by step, if we know certain basic rules of summation. Following rules assume summation limits are identical.




Armed with the above rules, we can split up the summation into simple terms:





=> (a)
f(x)=28n-n^2=> f'(x)=28-2n
=> at f'(x)=0 => x=14
Since f''(x)=-2 <0 therefore f(14) is a maximum
(b)
f(x) is a maximum when n=14
(c)
the maximum value of f(x) is f(14)=196
Find the cost for one ticket for the science center.
36.75 ÷ 3 = 12.25
Multiply the product with 12 to get the cost of 12 tickets.
12.25 × 12 = 147
Find the cost of 1 zoo ticket.
51 ÷ 4 = 12.75
Find the cost of 12 tickets by multiplying the product and 12
12.75 × 12 = $153
12 Science Center Tickets cost $147
12 zoo tickets cost $153
The <u><em>Zoo</em></u> costs more than the Science Center.
To find out how much more the Zoo costed, subtract 147 from 153.
153 - 147 = 6
The zoo only costs <u><em>$6 </em></u>more for 12 students.
So, you're answers are Zoo and $6
Answer: first option.
Step-by-step explanation:
The formula you must use to calculate the volume of the figure shown is the following:

Where B is the area of the base and H is the height.
Assuming that the base of the pyramid is a square, you have that B is:

Substitute values into the formula, Then you obtain:

Answer:
k = 20
Step-by-step explanation:
Expressing 18, 36 and 54 as a product of their prime factors
18 = 2 × 3 × 3 = 2 × 3²
36 = 2 × 2 × 3 × 3 = 2² × 3²
54 = 2 × 3 × 3 × 3 = 2 × 3³
The common prime factors are 2 and 3²
HCF = 2 × 3² = 2 × 9 = 18
Thus
k - 2 = 18 ( add 2 to both sides )
k = 20