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Ray Of Light [21]
2 years ago
4

Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive

or nonconstructive :)
Mathematics
1 answer:
Vesnalui [34]2 years ago
5 0
Constructive. To prove that there is a positive integer that equals the sum of the positive integers not exceeding it. A plain and simple example is <span>
1.1 + 2 = 3</span>
<span>2.10 + 50 + 100 =160</span> <span>
3.6x + 8x + 2x = 16 x</span> <span>

Notice that the sum of the numbers is always greater than the addends. This only proves that any positive sum of any two positive addends will not compare and thus the addends not exceeding a greater value than the sum.   </span>  



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A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hot dogs and 13 dozen
Sergeu [11.5K]

Answer: Cost of each hot dog and bratwursts would be $1.1 and $1.35 each.

Step-by-step explanation:

Since we have given that

Cost of each dozen hot dogs be 'x'.

Cost of each dozen bratwursts be 'y'.

The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for $316.20.

So, the equation would be

8x+13y=\$316.20

.The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $375.00.

So, the equation would be

10x+15y=\$375.00\\\\2x+3y=\$75

So, the equations becomes

8x+13y=316.20--------------(2)\\\\(2x+3y=75)\times 4\\\\\implies 8x+12y=300------------(1)

So, by elimination method, we get that

8x+13y=316.20\\\\(-)8x+(-)12y=(-)300\\\\--------------\\y=\$16.20

Put the value of y in the eq(1), we get that

2x+3y=75\\\\2x+3(16.20)=75\\\\2x+48.6=75\\\\2x=75-48.60\\\\2x=26.4\\\\x=\dfrac{26.4}{2}\\\\x=\$13.2

Hence, the cost of hot dogs would be \dfrac{13.2}{12}=\$1.1

And the cost of bratwursts would be \dfrac{16.2}{12}=\$1.35

4 0
2 years ago
What is the total amount of sap trees produced that day? Please tell me ASAP(as soon as possible) because this lesson is due for
gogolik [260]

Answer: 5 gallons


Step-by-step explanation:

There are 3 x's on the graph for 1/4, so 1/4 times 3=3/4

There are 2 x's on the graph for 3/8, so 3/8 times 2=3/4

There are 4 x's on the graph for 5/8, so 5/8 times 4=5/2

There is only 1 x for 1, so it will remain 1.

So if you add these up,

3/4+3/4+5/2+1

6/4+10/4+1

16/4+1

4+1

There is 5 gallons of sap produced that day.

Hope this helped!


3 0
2 years ago
Read 2 more answers
Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random
lesya692 [45]
Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes P_B(A).

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
P(A|B)= \frac{P(A \cap B)}{P(B)}

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is \frac{1}{3}

Part A:
To find <span>the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}

</span><span>P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

</span><span>Thus P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}

Therefore, P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}


Part B:
</span>To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime<span>, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.
</span><span>
P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}

</span><span>P(D)= \frac{1}{3}</span><span>

Therefore, P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}</span>
3 0
2 years ago
The label on a ceiling lighting fixture warns you to use a lightbulb of 60 watts or less. The voltage to the lightbulb is 120 vo
patriot [66]

Answer:

0.5 A

Step-by-step explanation:

Hi,

I believe the question is incomplete. However, as per the information provided:

The simplest way to calculate the Current (unit is Amperage), is understanding the relationship between the three: Power, Voltage and Current.

<em>(Quick Tip: </em><em>W=AV</em><em>; where W -> Watts (Power), A -> Ampere (Current), V -> Volts (Voltage))</em>

Using the formula we calculate the Ampere:

W = A x V

60 = A x 120

60/120 = A (We divide the equation be 120)

0.5 = A  (Simply reduce the fraction 60/120  = 1/2 = 0.5)

Tip:

8 0
2 years ago
A population of 550 rabbits is increasing by 7.5% each year. in about how many years will the population be over 1000?
Furkat [3]

I believe this would take the form of an exponential equation:

A = Ao (1 + r)^t

where A is final population, Ao is initial population, r is rate of growth and t is time

 

A / Ao = (1 + r)^t

log A / Ao = t log (1 + r)

t = (log A / Ao) / log (1 + r)

t = [log (1000 / 550)] / log (1.075)

t = 8.27 years

 

SO the answer is B) about 9 years

5 0
2 years ago
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