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3 years ago

Help #23 pleaseeeeeeeee

Mathematics

1 answer:

GuDViN [60]3 years ago

7 0

A bus holds 40 people and a van holds 10

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Use mathematical induction to prove that for each integer n > 4,5" > 2^2n+1 + 100.

Flura [38]

Answer:

The inequality that you have is $5^{n}>2^{2n+1}+100,\,n>4$ . You can use mathematical induction as follows:

Step-by-step explanation:

For $n=5$ we have:

$5^{5}=3125$

$2^{(2(5)+1)}+100=2148$

Hence, we have that $5^{5}>2^{(2(5)+1)}+100.$

Now suppose that the inequality holds for $n=k$ and let's proof that the same holds for $n=k+1$ . In fact,

$5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.$

Where the last inequality holds by the induction hypothesis.Then,

$5^{k+1}>(2^{2k+1}+100)\cdot (4+1)$

$5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100$

$5^{k+1}>2^{2k+3}+100\cdot 4$

$5^{k+1}>2^{2(k+1)+1}+100$

Then, the inequality is True whenever $n>4$ .

3 0

3 years ago

Justin and George bought some baked goods. Justin purchased 5 cookies for x dollars each and 4 doughnuts for y dollars each and

borishaifa [10]

The given statement 5x=4y=12 and x+6y=5 is true.

<u>Step-by-step explanation:</u>

The question comes from linear equations in two variables.

Here, two unknown variables represent a certain situation and their value can be obtained by solving both the given equations.

The cost of cookie is represented by the variable x and cost of doughnuts can be represented by the variable y.

The coefficient of each variable in the equation represent the quantity or the number of units of each baked good.

On comparing the given equations from the data provided in the question, the statement can be stated as true.

8 0

3 years ago

Read 2 more answers

uranmaximum [27]

Answer:

1. 1

2. 1

3. -1/125

4. 1/125

8 0

3 years ago

In my carpenter shop I make 3 legged stools and 4 legged chairs. I looked at my days output and counted 55 legs and 16 seats. Ho

Stells [14]

$x-number\ of\ stools\\y-number\ of\ chairs\\\\ \left \{ {{y+x=16} \atop {3x+4y=55}} \right. \\\\From\ first\ equation:\\\\y=16-x\\\\Substract\ to\ second\ equation:\\\\3x+4(16-x)=55\\3x+64-4x=55\\3x-4x=55-64\\-x=-9\\x=9\\\\y=16-9=7\\\\ \left \{ {{y=7} \atop {x=9}} \right.$

7 0

4 years ago

Please help me with this math problem, urgent please

cestrela7 [59]

Answer:

y = -3.5x + 15

Step-by-step explanation:

Your slope-intercept equation is always y = mx + b

Using this formula, we need to find slope first: m = (y2-y1) / (x2-x1)

Step 1: Find slope

m = (1-8) / (4-2)

m = -7/2

Step 2: Plug in into slope-intercept form

y = -3.5x + b

Step 3: Find <em>b </em>(Plug in a coordinate given)

1 = -3.5(4) + b

1 = -14 + b

b = 15

Step 4: Combine it all together

y = -3.5x + 15

And you have your final answer.

3 0

4 years ago