The number of 5-digit numbers that can be formed if the last digit is odd and no

Mathematics

1 answer:

Softa [21]3 years ago

7 0

Answer:

13,440

Step-by-step explanation:

10 possible digits 0 - 9

5 possible numbers for position 5 (odd digits only)

8 possible numbers for position 1 (cannot be zero or the odd number selected for position 5)

8 possible numbers remain for position 2 (10 minus 2 already selected)

7 possible numbers remain for position 3 (10 minus 3 already selected)

6 possible numbers remain for position 4 (10 minus 4 already selected)

5•8•8•7•6 = 13,440

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PLEASE HELP ME WITH THIS THANKS

kotykmax [81]

Answer:

SA = 1244.64 square centimeters

Step-by-step explanation:

From the attached figure

The formula of the surface area of the prism is SA = 2B + PH, where

B is the area of its base
P is the perimeter of its base
H is the distance between its bases

The base of the prism is a regular hexagon with side 8 cm

If you join each vertex of the hexagon with its center you will form 6 congruent triangles with base 8 cm and height 6.93 cm

The area of the hexagon = 6 × area of a triangle

∵ The base of the triangle = 8 cm

∵ Its height = 6.93 cm

- The formula of the area of a triangle is A = $\frac{1}{2}$ × base × height

∴ Area of the triangle = $\frac{1}{2}$ × 8 × 6.93 = 27.72 cm²

- Lets find the area of the hexagon

∴ The area of the hexagon = 6 × 27 .72 = 166.32 cm²

∴ B = 166.32 cm²

The formula of the perimeter of the regular hexagon is P = 6 × s, where s is the length of its side

∵ The side of the hexagon is 8 cm

∴ P = 6 × 8

∴ P = 48 cm

∵ The distance between the two bases is 19 cm

∴ H = 19 cm

Substitute the values of B, P and H in the formula of the surface area above

∵ SA = 2(166.32) + (48)(19)

∴ SA = 332.64 + 912

∴ SA = 1244.64 square centimeters

7 0

3 years ago

The equation (x-3)^2+(y+7)^2=64 models the position and range of the source of a radio signal. Describe the position of the sour

12345 [234]

$\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad 
radius=\stackrel{}{ r}\\\\
-------------------------------\\\\
(x-3)^2+(y+7)^2=64\implies [x-\stackrel{h}{3}]^2+[y-(\stackrel{k}{-7})]^2=\stackrel{r}{8^2}
\\\\\\
center~(3,-7)\qquad radius=8$

so, the broadcast location and range is more or less like the picture below.