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KiRa [710]
2 years ago
8

Two integers, a and b, have a product of 36. What is the least possible sum of a and b?

Mathematics
1 answer:
Minchanka [31]2 years ago
8 0
<h3>Answer:  12</h3>

==============================================================

Explanation:

The two integers multiply to 36, so,

ab = 36

which solves to

a = 36/b

Then we want to add the numbers such that we get the smallest possible result.

a+b = (36/b)+b

So we want (36/b)+b to be as small as possible.

Let's say we replace b with x and we consider this function

f(x) = (36/x) + x

The goal is to find when f(x) is smallest, ie, we want to minimize the function.

If we were to graph out the function, we get the curve shown below.

To make things easier, we'll only focus on positive values of x.

The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.

So the input x = 6 leads to the smallest output f(x) = 12.

This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.

In short, a = 6 and b = 6.

----------------------

As a check,

a*b = 6*6 = 36

a+b = 6+6 = 12

We can make a table of various values to help confirm that 12 is the smallest sum.

Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.

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algol [13]

Answer:

a. \ p=0.38\\\\b. \ \ H_o:p=0.38\\\ \ \ \ \\H_A:p\neq 0.38

Step-by-step explanation:

a. Let, p be the parameter being tested. From the sample, 38% would erase all of their personal information.

-we know that the value of probabilities are in the range [0,1]:

-Given that 38% is the true value of the claim can be symbolically expressed as p=0.5

b. The null hypothesis usually represents the true value parameter under study.

-As stated above, the true value of the parameter is 38%;

-Hence, the null hypothesis is H_o:p=0.38

#Alternative hypothesis is the control value, given the value of the parameter  p=0.38, the alternative hypothesis is that p has a different value other than 0.39:

H_A:p\neq 0.38

4 0
3 years ago
What is 519 divided by 11?
g100num [7]
The answer is 47.18181818
7 0
3 years ago
Cual de las siguientes expreciones permite a fatima obtener t que es la cantidad de palitos nesesaria para armar una figura n
Likurg_2 [28]

Answer:

T(n) = 4 + 12*n

Step-by-step explanation:

La pregunta completa se puede ver en la imagen de abajo.

En ella, podemos ver que:

La primera figura tiene: 16 palitos

la segunda figura, con n = 2, se añaden 3 palitos en cada extremo, por lo que tendremos 16 palitos + 4*3 palitos = (16 + 12) palitos

De manera similar, en la tercera figura se vuelven a añadir 3 palitos en cada extremo de la cruz, entonces esta figura tendrá:

(16 + 12) palitos + 4*3 palitos = (16 + 12 + 12) palitos.

Así, tenemos la relación:

T(1) = 16

T(2) = 16 + 12

T(3) = 16 + 12 + 12

Podemos asumir que la forma general será:

T(n) = 16 + 12*(n - 1)

podemos reescribir esto como:

T(n) = (12 + 4) + 12*(n - 1)

      = 4 + 12 + 12*(n - 1)

      = 4 + 12*n

La opción correcta es la primera.

4 0
3 years ago
Find the equivalent function to f(x) = 3(6)^2x
pogonyaev
This is the concept of algebra, the function given can be written as follows;
f(x)=3(6)^(2x)
f(x)=3(6^2)^x
when we expand the above we get:
f(x)=3(36)^x
the answer is f(x)=3(36)^x

3 0
3 years ago
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Jobisdone [24]

Answer: x = 1/5

//Hope it helps.

3 0
3 years ago
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