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6. Fill in the smallest digit to make the number divisible by:

Degger [83]

Answer:

(i) 71640, 321970

(ii) 1143, 47205, 2316

(iii) 1428, 9252, 7212

(iv) 24620, 9100, 6700

(v) 12320, 59016, 46424

Step-by-step explanation:

(i) In order for any number to be divisible by 5, its last digit must be either 0 or 5.

In this case, we should add a last digit, so we opt for 0 without any doubt since it gives a smaller number than 5 as the last digit: 71640 is smaller than 71645, the same way as 321970 is smaller than our second option, 321975.

(ii) If the sum of a number's digits gives a number divisible by 3, then the main number is also divisible by 3.

This means that we have to do some addition:

1_43: 1 + 4 + 3 = 8. Eight is not divisible by 3. But 9 is. So the smallest digit we can add for it to be divisible by three is 1: 1143.

47_05: 4 + 7 + 0 + 5 = 16. Since 16 is not, the next number that is divisible by 3 is 18, and therefore, the smallest digit we need here is 2: 47205.

_316: 3 + 1 + 6 = 10. Twelve is the next number divisible by 3, and that means 2 is the digit we choose: 2316.

(iii) Only numbers that are divisible by both 2 and 3 are also divisible by 6.

_428: In order for a number to be divisible by 2, its last digit must be 0 or divisible by 2. That is already the case here.

4 + 2 + 8 = 14 which is not divisible by 3. But 15 is. So the smallest digit we need is 1: 1428.

9_52: The number will be divisible by 2. And 9 + 5 + 2 = 16 which is not divisible by 3 but 18 is. This means the smallest digit we need is 2: 9252.

721_: Since the last digit can be any of these 0, 2, 4, 6, 8 for the number to be divisible by two, we will first see what digit we need for it to be divisible by 3.

7 + 2 + 1 = 10 which is not divisible by 3 but 12 is. We will then choose to add 2: 7212.

(iv) A number is divisible by 4 only if the number that is formed by its two last digits is also divisible by 4..

2462_: Since we need to add a last digit, this should be easy. The smallest two-digit-number that starts with 2 and is divisible by four is 20: 24620.

91__: Here we need to add both of the two last digits, and this should be the easiest example! All numbers that end in 00, meaning they have a round number of hundreds, are divisible by 4! Therefore our option is: 9100.

670_: In this case, we apply the same rule from the last example - and we choose 0: 6700.

(v) In order for a number to be divisible by 8, its last three digits need to be divisible by 8, or it can end in 000, since every number having a round number of thousands is also divisible by 8.

1232_: 320 is divisible by 8 since 8 × 40 gives 320. Therefore, our smallest digit here is 0: 12320.

59_16: If we add a 0 here, the last three digits form the number 016, which is divisible by 8. Our choice is again zero: 59016.

4642_: Unfortunately, 420 is not divisible by 8. The next number closest to 420 and which is divisible by 8 is 424. Its division by 8 gives 53. Therefore we should add 4: 46424.

7 0

3 years ago

Two numbers that add to -0.5 and multiply to 1

snow_lady [41]

X +(1/x) = -0.5 has no real solutions.

There are no real numbers that meet your requirements.

_____
The two complex numbers that meet your requirement are
-1/4 +i√(15/16), -1/4 -i√(15/16)

4 0

3 years ago

Diameter of a cylindrical tank is 9 feet and the height of a tank is 25 feet. Find the approximate volume of the cylindrical tan

Firlakuza [10]

The volume is
.. V = π*r^2*h
.. = π*(4.5 ft)^2*(25 ft)
.. ≈ 1590.43 ft^3

The closest choice is C 1589.63 ft^3.

_____
Apparently, someone used the 3-digit approximation 3.14 for π to compute a 6-digit result. That is why it is wrong in the last 3 digits.

7 0

3 years ago

4. What are the last TWO DIGITS of 2^2017

goldfiish [28.3K]

Compute 2²⁰¹⁷ modulo 100.

From the given table,

2²² ≡ 2⁴² ≡ 2⁶² ≡ 4 (mod 100)

and we have

2017 = 32 • 62 + 33

62 = 1 • 42 + 20

Then

2²⁰¹⁷ ≡ (2⁶²)³² • 2³³ (mod 100)

2²⁰¹⁷ ≡ 4³² • 2³³ (mod 100)

2²⁰¹⁷ ≡ (2²)³² • 2³³ (mod 100)

2²⁰¹⁷ ≡ 2⁶⁴ • 2³³ (mod 100)

2²⁰¹⁷ ≡ 2⁶² • 2²² • 2¹³ (mod 100)

2²⁰¹⁷ ≡ 4² • 2¹³ (mod 100)

2²⁰¹⁷ ≡ (2²)² • 2¹³ (mod 100)

2²⁰¹⁷ ≡ 2⁴ • 2¹³ (mod 100)

2²⁰¹⁷ ≡ 2¹⁷ (mod 100)

and from the table, we get

2²⁰¹⁷ ≡ 2¹⁷ ≡ 72 (mod 100)

8 0

3 years ago

Work out 2 1/7 + 1 1/4

adelina 88 [10]

Answer:

95/28

Step-by-step explanation:

7 0

3 years ago

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