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Nimfa-mama [501]
3 years ago
9

2.

Mathematics
1 answer:
Gekata [30.6K]3 years ago
7 0

Answer:

A. A(n) = 150 • (0.74)^n–1 ; 33.29 cm

Step-by-step explanation:

This is a geometric sequence.

a%5B1%5D=1.5m=150cm, r=0.74

The formula is

a%5Bn%5D=a%5B1%5Dr%5E%28n-1%29

Just substitute a1 = 150cm and r = 0.74

a%5Bn%5D=150%280.74%29%5E%28n-1%29

That's the rule.

For the second part, substitute n = 6

cm.

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Find 3 consecutive odd integers whose sum is 225, explain please
Gre4nikov [31]
Three consecutive integers whose sum is 225 are 74, 75, and 76.

Three consecutive odd integers add up to 225. This means the middle of the three numbers is one third of 225.

225/3=75

The middle number is 75. The other two numbers are 74 and 76.

Three consecutive integers whose sum is 225 are 74, 75, and 76.

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Y=(x+4)^2-25 , (4,-25)
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3 years ago
a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6?6x7x7=294 b) How many three-digit numbers
love history [14]

Answer:

a) 294

b) 180

c) 75

d) 168

e) 105

Step-by-step explanation:

Given the numbers 0, 1, 2, 3, 4, 5 and 6.

Part A)

How many 3 digit numbers can be formed ?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For unit's place, any of the numbers can be used i.e. 7 options.

For ten's place, any of the numbers can be used i.e. 7 options.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Total number of ways = 7 \times 7 \times 6 = <em>294 </em>

<em></em>

<em>Part B:</em>

How many 3 digit numbers can be formed if repetition not allowed?

Solution:

Here we have 3 spaces for the digits.

Unit's place, ten's place and hundred's place.

For hundred's place, 0 can not be used (because if 0 is used here, the number will become 2 digit) i.e. 6 options.

Now, one digit used, So For unit's place, any of the numbers can be used i.e. 6 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = 6 \times 6 \times 5 = <em>180</em>

<em></em>

<em>Part C)</em>

How many odd numbers if each digit used only once ?

Solution:

For a number to be odd, the last digit must be odd i.e. unit's place can have only one of the digits from 1, 3 and 5.

Number of options for unit's place = 3

Now, one digit used and 0 can not be at hundred's place So For hundred's place, any of the numbers can be used i.e. 5 options.

Now, 2 digits used, so For ten's place, any of the numbers can be used i.e. 5 options.

Total number of ways = 3 \times 5 \times 5 = <em>75</em>

<em></em>

<em>Part d)</em>

How many numbers greater than 330 ?

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 7

Number of options for unit's place = 7

Total number of ways = 3 \times 7 \times 7 = 147

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 7

Total number of ways = 1 \times 3 \times 7 = 21

Total number of required ways = 147 + 21 = <em>168</em>

<em></em>

<em>Part e)</em>

Case 1: 4, 5 or 6 at hundred's place

Number of options for hundred's place = 3

Number of options for ten's place = 6

Number of options for unit's place = 5

Total number of ways = 3 \times 6 \times 5 = 90

Case 2: 3 at hundred's place

Number of options for hundred's place = 1

Number of options for ten's place = 3 (4, 5, 6)

Number of options for unit's place = 5

Total number of ways = 1 \times 3 \times 5 = 15

Total number of required ways = 90 + 15 = <em>105</em>

7 0
3 years ago
Dominic works on the weekends and on vacations from school mowing lawns in his neighborhood. For every lawn he mows, he charges
Ivahew [28]

Answer:

20\ lawns = \$240

9 \ lawns = \$108

<em>See Attachment for Graph</em>

<em></em>

Step-by-step explanation:

Given

1\ lawn = \$12

Solving (a): Number of lawns in $240

1\ lawn = \$12

Multiply both sides by 20

20 * 1\ lawn = \$12 * 20

20\ lawns = \$240

Solving (b): Cost of mowing 9 lawns

1\ lawn = \$12

Multiply both sides by 9

9 * 1\ lawn = \$12 * 9

9 \ lawns = \$108

To create a graph, we need to generate a formula;

If

1\ lawn = \$12

2\ lawn = \$24

3\ lawns = \$36

x\ lawns = \$12x

So:

<em>The graph formula is</em>

y = 12x

<em>See Attachment for Graph</em>

5 0
3 years ago
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