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Anit [1.1K]
2 years ago
9

Prove the divisibility of the following numbers:

Mathematics
1 answer:
fomenos2 years ago
5 0

Answer:


Step-by-step explanation:

prove : 25^9 + 5^7 ≡ 0 ( mod 30) or 5^18 + 5^7 ≡ 0 ( mod 30)

because : 25= 5²

calculate 5^p   for 1 ; 2;3 ; 4....

5^1  ≡ 5 ( mod 30)

5^2  ≡ 25 ( mod 30)

5^3  ≡ 5 ( mod 30)

5^4  ≡ 25 ( mod 30)

p = 2k+1   5^p ≡ 5 ( mod 30)

p = 2k    5^p ≡ 25 ( mod 30)

so : 5^18 ≡ 25 ( mod 30)  ......(*)

    5^7 ≡ 5 ( mod 30)...........(**)

add (*) and (**) :5^18 + 5^7 ≡ 0 ( mod 30) because : 30≡0 (mod30)

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Answer:

(0.55, 0.75)

Step-by-step explanation:

The range can be estimated to be 6 standard deviations wide.  Therefore, the standard deviation is:

σ = (0.72 - 0.42) / 6

σ = 0.05

The margin of error is ±2σ, so:

ME = ±0.10

Therefore, the interval estimate is:

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8 0
2 years ago
Find the area of the shaded region.
Papessa [141]

Answer:

21.46 cm²

Step-by-step explanation:

because the question want only for the SHADED REGION but NOT AREA OF THE SQUARE

(if we just multiply 10x10. you will get the area of a square which is hundered)

To find the shaded region:

1. area of a circle is πr² (we have 4 circle there)

2. Find the area of all circle

# how do we know the radius?

- half of 10 is 5

- 5 is the diameter of each circle

- the radius is half of 5 which is 2.5

- π(2.5)² = 25/4π (area of 1 circle)

3. since we have 4 circle then, 25/4π x 4 = 25π

4. the area of the square is 100cm²

5. we want the shaded region so we have to minus the area of the circle

6. 100 - 25π (use your calculator to find the answer)

answer should be 21.46 cm²

(hope this helps)

8 0
3 years ago
A cylinder has a volume of 140 x cubic meters and a height of 14 meters. What is the area of the base?
AleksandrR [38]

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Step-by-step explanation:

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3 years ago
Find the value of x. Then find the measure of each labeled angle
34kurt

Answer:

x = 109

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Bottom Right Angle = 71

Step-by-step explanation:

Notice the two right angles on the left and recognize that the figure is a a quadrilateral (4 sides). That means it adds up to a total of 360 degrees.

(x-38) + x + 90 + 90 = 360

2x + 142 = 360

2x = 218

x = 109

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2 years ago
What is y= 1/3 x - 9 written in standard form?
NISA [10]

Answer:

c

Step-by-step explanation:

8 0
3 years ago
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