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kotykmax [81]
3 years ago
8

There are 3 consecutive integers. The third integer subtracted from the sum of the first two integers equals 9. What is the midd

le integer ?
Mathematics
1 answer:
Alexus [3.1K]3 years ago
3 0

Answer:

The middle integer is 11.

Step-by-step explanation:

Hi there!

Let <em>x</em> be the smallest of the three consecutive integers.

Let <em>x</em>+1 and <em>x</em>+2 be the next consecutive integers. This makes <em>x</em>+1 the middle integer.

We're given that the third integer subtracted from the sum of the first two integers equals 9. We can use this to construct an equation:

(x)+(x+1)-(x+2)=9

Combine like terms:

x+x+1-x-2=9\\x+x-x+1-2=9\\x-1=9\\x=10

Therefore, the smallest integer is 10.

Because the middle integer is <em>x</em>+1, the middle integer is 11.

I hope this helps!

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Step-by-step explanation:

We are given,

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Step-by-step explanation:            

We have been given some examples of functions and we are asked to classify which of the given functions are linear and exponential.

Since we know that values of a linear function changes at a constant rate, while rate of change of an exponential function is always proportional to the value of function.

Let us see our given function choices one by one.

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We can see from our function that rate of change for this function is constant as every year same number of cars cross the Golden Gate Bridge, therefore, our function represented by first option is a linear function.

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We can see from this function that rate of change is not constant as every next month the restaurant sells 2% more milkshakes than last month, therefore, the function represented in 2nd option is exponential function.

3. The number of visitors to the Eiffel Tower in Paris increases by 1.5% each year.  

We can see from this function that rate of change is not constant as every next year the number of visitors is 1.5% more than last year, therefore, the function represented in 3rd option is exponential function.

4. Each week you get $10 and add it to your savings account.

We can see from our function that rate of change for this function is constant as every next week same amount is added to savings account, therefore, our function represented by 4th option is a linear function.

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~~

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~~

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Assume that hybridization experiments are conducted with peas having the property that for​ offspring, there is a 0.75 probabili
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Answer:

(a) The mean and the standard deviation for the numbers of peas with green pods in the groups of 36 is 27 and 2.6 respectively.

(b) The significantly low values are those which are less than or equal to 21.8. And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is significantly​ low value.

Step-by-step explanation:

We are given that hybridization experiments are conducted with peas having the property that for​ offspring, there is a 0.75 probability that a pea has green pods.

Assume that the offspring peas are randomly selected in groups of 36.

The above situation can be represented as a binomial distribution;

where, n = sample of offspring peas = 36

            p = probability that a pea has green pods = 0.75

(a) The mean of the binomial distribution is given by the product of sample size (n) and the probability (p), that is;

                    Mean, \mu  =  n \times p

                                    =  36 \times 0.75 = 27 peas

So, the mean number of peas with green pods in the groups of 36 is 27.

Similarly, the standard deviation of the binomial distribution is given by the formula;

            Standard deviation, \sigma  =  \sqrt{n \times p \times (1-p)}

                                                  =  \sqrt{36 \times 0.75 \times (1-0.75)}

                                                  =  \sqrt{6.75}  =  2.6 peas

So, the standard deviation for the numbers of peas with green pods in the groups of 36 is 2.6.

             

(b) Now, the range rule of thumb states that the usual range of values lies within the 2 standard deviations of the mean, that means;

          \mu - 2 \sigma  =  27 - (2 \times 2.6)

                       =  27 - 5.2 = 21.8

          \mu + 2 \sigma  =  27 + (2 \times 2.6)

                       =  27 + 5.2 = 32.2

This means that the significantly low values are those which are less than or equal to 21.8.

And on the other hand, the significantly higher values are those which are greater than or equal to 32.2.

(c) The result of 15 peas with green pods is a result that is a significantly​ low value because the value of 15 is less than 21.8 which is represented as a significantly low value.

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