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3 years ago

Find the domain of: y = 3x + 1

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

6 0

y = 3x + 1

It's a linear function. The domain of linear function is the set of all real numbers.

$D=\mathbb{R}=(-\infty,\ \infty)$

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Find the greatest possible value for a+b+c+d if b is a positive integer and a,b,c,d satisfy the system of equations

snow_lady [41]

Answer:

$a+b+c+d = -5\cdot b$

Step-by-step explanation:

The given system of equations is now reduced:

1) $a+b = c$ , $b+c = d$ , $c+d=a$ , $b > 0$ Given

2) $a = c+d$ By 1)

3) $(c+d)+b=c$ 2) in 1)

4) $d = b + c$ By 1)

5) $[c+(b+c)]+b = c$ 4) in 3)

6) $2\cdot b + 2\cdot c = c$ Algebra

7) $c = -2\cdot b$ Algebra

8) $d = -b$ 7) in 4)/Algebra

9) $a = -3\cdot b$ 7) and 8) in 2)/Algebra

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4 0

3 years ago

Read 2 more answers

At least 96.00% of the data in any data set lie within how many standard deviations of the mean? Explain how you arrived at yo

zheka24 [161]

The answer assumes that the question is about the normal distribution.

Answer:

96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

Step-by-step explanation:

The key to solving this question is having into account that exists the standard normal distribution that permits obtaining any probability from any normally distributed data, doing the following transformation:

$\\ z = \frac{x-\mu}{\sigma}$

That is, in this case, we subtract a given value x from the population mean and then divide the result by the population standard deviation. This is a z-score, and this value is associated with the probability for a standard normal distribution, with a population mean = 0 and population standard deviation = 1.

Fortunately, for the standard normal distribution, there is associated a ubiquitous standard normal table for possible values of z and the corresponding probability. Then, knowing that the data are normally distributed and having both distribution parameters, namely, the population mean and population standard deviation, we can consult any standard normal table to find the probabilities for any data distributed following the normal distribution.

However, even without previously know the values of the normal parameters, the standard normal distribution can tell us how many standard deviations from the mean are 96.00% of the data for every normally distributed population.

<h3>Solving the question</h3>

Having all this information at hand, we know that the z-score value tells us how many standard deviations from the mean are the data normally distributed. As a result, we can determine how many standard deviations below and above the population mean represent the 96.00% of the cases for this normal distribution consulting a cumulative standard normal table from the mean.

If we divide 96.00/2 = 48, that is, 0.48, we need to find the z-score for this probability consulting a cumulative standard normal table from the mean. The values for a z-score for that probability is z=2.05, approximately. So, since the normal distribution is also symmetrical, those values are above and below the mean, that is, z =2.05 (above) and z=-2.05(below).

Thus, 96% of the data in any data set normally distributed is 2.05 standard deviations above and below the mean.

5 0

3 years ago

What is the value of the expression 2x2+3xy-y2, when x=2 And y=-4

Otrada [13]

Plug in 2 for x, and -4 for y

2(2)² + 3(2)(-4) - (-4)²

2² = 4(2) = 8
3(2) = 6(-4) = -24
-4² = 16

8 - 24 - 16 = answer

Simplify.

answer = 8 - 40
answer = -32

-32 is your answer

hope this helps

7 0

2 years ago

Two triangles are similar. The dimensions of the first are 7, 8, and 10, while the dimensions of the second one are 3.5, 4, and

Irina-Kira [14]

The scale factor used is .5 because 7, 8, and 10 multiplied by .5 will equal 3.5, 4, and 5.

5 0

3 years ago

Read 2 more answers

Express (x+9)^2 as a trinomial in standard form.

Andreyy89

Answer:

x^2 + 18x + 81