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ch4aika [34]
3 years ago
7

what is the greatest 5 digit number which when divided by 2, 3, 4, and 5 leaves a remainder of 1 in each case​

Mathematics
1 answer:
bogdanovich [222]3 years ago
6 0

Answer:99904.

Step-by-step explanation:

Find the LCM of

5

10 = 2x5

15 = 3x5

20 = 2x2x5

25 = 5x5

LCM = 2x2x3x5x5 = 300

Take the smallest 5-digit number: 10000 and divide it by 300 to get 33.33. Round it off to 34 and multiply it by 300 to get 10200. Finally add 4 to 10200 to get 10204 which is the smallest final 5-digit number.

Check: 10204/5 = 2040 as quotient and a remainder of 4. Correct.

10204/10 = 1020 as quotient and a remainder of 4. Correct.

10204/15 = 680 as quotient and a remainder of 4. Correct.

10204/20 = 510 as quotient and a remainder of 4. Correct.

10204/25 = 408 as quotient and a remainder of 4. Correct.

Answer: 10204.

To get the greatest 5-digit number take 99999 and divide it by 300 to get 333.33. Round it off to 333 and multiply it by 300 to get 99900. Finally add 4 to 99900 to get 99904 which is the final greatest 5-digit number.

Check: 99904/5 = 19980 as quotient and a remainder of 4. Correct.

99904/10 = 9990 as quotient and a remainder of 4. Correct.

99904/15 = 6660 as quotient and a remainder of 4. Correct.

99904/20 = 4995 as quotient and a remainder of 4. Correct.

99904/25 = 3996 as quotient and a remainder of 4. Correct.

Answer: 99904.

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~PLEASE HELP ASAP OFFERING 10 POINTS~
Marina CMI [18]
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3 years ago
Which graph represents the solution set of the equation 3y - x - 9 = 0?​
Arisa [49]

Answer:

Linear Graph

Step-by-step explanation:

7 0
3 years ago
4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t
Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

a_{n}=a_{1}r^{n-1}

a_{1} = the first term of the series

r = the geometric ratio

a_{1} would represent the height at which the ball is first dropped. Therefore:

a_{1} = k

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

r=\frac{3}{4}

Our general term would be:

a_{n}=a_{1}r^{n-1}

a_{n}=k(\frac{3}{4}) ^{n-1}

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

k represents the initial height:

k = 235\ ft

n represents the number of times the ball bounces:

n = 6

Plugging this back into our general term of the geometric series:

a_{n}=k(\frac{3}{4}) ^{n-1}

a_{n}=235(\frac{3}{4}) ^{6-1}

a_{n}=235(\frac{3}{4}) ^{5}

a_{n}=55.8\ ft

a_{n} represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. ​

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

S_{n}=\frac{a_{1}(1-r^{n})}{1-r}

We already know these variables:

a_{1}= k = 235\ ft

r=\frac{3}{4}

n = 12

Therefore:

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }

S_{n}=(4)(235)(1-\frac{3}{4} ^{12})

S_{n}=910.22\ ft

8 0
3 years ago
I cannot find the answer to this question please help
Troyanec [42]
The answer would be 689
8 0
3 years ago
Help ASAP with working if possible ​
NARA [144]

Answer:

1.  The volume of the cylinder is approximately 0.153 m³

2. 25 cm

3. 25.\overline 6 \ cm

4. 16 m

5. 1,785 m³

Step-by-step explanation:

The volume of a solid can be found by the product of the uniform cross-sectional area of the solid and the (continuous) length of the solid

1. The uniform cross-sectional area of the given cylinder = The area of the circle at the base or top

The dimension of the diameter of the circle at the top of the cylinder, d = 50 cm = 0.5 m

The area of the circular cross-section, A = π·d²/4

∴ A = π × 0.5²/4 = 0.0625·π

A = 0.0625·π m²

The height of the cylinder, h = The continuous length of the circular cross-section = 78 cm = 0.78 m

∴ The volume of the cylinder, V = A × h

∴ V = 0.0625·π × 0.78 = 0.04875·π ≈ 0.153

The volume of the cylinder, V ≈ 0.153 m³

2. The given volume of the trapezium, V = 8550 cm³

The length of the short and long parallel sides 'a', and 'b', are 17 cm and 21 cm respectively

The height of the trapezium from the diagram, h = 18 cm

The cross-sectional area of the trapezium, 'A', is found as follows;

A = (17 cm + 21 cm)/2 × 18 cm = 342 cm²

The volume of the trapezium, V = The cross-sectional, A × The (missing) length, 'l' of the trapezium

∴ l = V/A

By substitution, we have;

l = 8550 cm³/(342 cm²) = 25 cm

∴ The Missing Length, l = 25 cm

3. The given volume of the solid having a uniform cross-sectional area is, V = 385 cm³

The area of the (uniform) cross-section of the solid, A = 15 cm²

∴ The length of the solid, 'l', from V = A × l, is given as follows;

l = V/A

∴ l = 385 cm³/(15 cm²) = 25.\overline 6 cm

The length of the solid, l = 25.\overline 6 cm

4. From the diagram, we have;

The cross-sectional area of the solid, A = 216 m²

The length of the solid, l = 16 m

5. The cross-section of the solid can  can be assumed to be either;

1. A trapezium from which a rectangle has been removed of dimensions 8 m by 9 m.

2. A triangle located above a rectangle

For scenario one, we have;

The cross-sectional area, A = (12.5 + 9)/2 × 15 - 8 × 9 = 89.25

For scenario two, we find 'A' as follows;

A = 7 × 9 + 1/2 × 15 × 3.5 = 89.25

∴ The cross-sectional area of the solid, A = 89.25 m²

The length, 'l', of the solid, is given as l = 20 m

The volume of the solid, V = A × l

∴ V = 89.25 m² × 20 m = 1,785 m³

The volume of the solid, V = 1,785 m³.

3 0
3 years ago
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