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3 years ago

Solve the following quadratic function by utilizing the square root method. y = 16 – x2

Mathematics

1 answer:

xxMikexx [17]3 years ago

3 0

Answer:

The solutions are x = -4 and x = 4.

Step-by-step explanation:

Solving a quadratic equation:

We have to find x for which $y = 0$ .

In this question:

$y = 16 - x^2$

$16 - x^2 = 0$

$x^2 = 16$

$x = \pm \sqrt{16}$

$x = \pm 4$

The solutions are x = -4 and x = 4.

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Find the variance of the following data. Round your answer to one decimal place. x 1 2 3 4 5 P(X=x) 0.3 0.2 0.2 0.1 0.2

Reptile [31]

The variance of a distribution is the square of the standard deviation

The variance of the data is 2.2

<h3>How to calculate the variance</h3>

Start by calculating the expected value using:

$E(x) = \sum x* P(x)$

So, we have:

$E(x) = 1 * 0.3 + 2* 0.2 +3 * 0.2 + 4 * 0.1 + 5 * 0.2$

This gives

$E(x) = 2.7$

Next, calculate E(x^2) using:

$E(x^2) = \sum x^2* P(x)$

So, we have:

$E(x^2) = 1^2 * 0.3 + 2^2* 0.2 +3^2 * 0.2 + 4^2 * 0.1 + 5^2 * 0.2$

$E(x^2) = 9.5$

The variance is then calculated as:

$Var(x) = E(x^2) - (E(x))^2$

So, we have:

$Var(x) = 9.5 - 2.7^2$

$Var(x) = 2.21$

Approximate

$Var(x) = 2.2$

Hence, the variance of the data is 2.2

Read more about variance at:

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4 0

1 year ago

3(4a+b) What matches this equation

vivado [14]

Answer:

12a + 3b.

Step-by-step explanation:

3(4a + b)

= 3 * 4a + 3 * b

= 12a + 3b.

Hope this helps!

8 0

2 years ago

Read 2 more answers

How many sixths are in 7 1/6

NNADVOKAT [17]

All we need to do is turn the mixed number into an improper fraction.

7 1/6 = 43/6

Therefore, there are 43 sixths in 7 1/6.

Best of Luck!

6 0

3 years ago

Read 2 more answers

Will give brainliest answer

olganol [36]

Answer:

Step-by-step explanation:

Area of a big right triangle = 1/2 * 4 * (2+2+6) = 1/2 * 4 *10 =20

Area of a left right triangle = 1/2* 2*2 = 2

Area of a right right triangle = 1/2 * 6*2 =6

Area of a square = 2*2 = 4

All together:

20+ 2+6+4 =32

3 0

3 years ago

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Complete the table shown to the right for the population growth model for a certain country.

marta [7]

The size of the population increases when the growth rate is positive and

decreases for a negative growth rate.

The completed table is presented as follows;

$\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&-2.255\%\end{array}\right]$

Reasons:

The table is presented as follows;

$\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&\end{array}\right]$

The population in growth rate is given by the following formula;

P = a·(1 + r)ˣ

Where;

a = The initial population in 2003 = 40.5 million

P = The population in 2029 = 20.9 million

x = The number of years = 2029 - 2003 = 26

Therefore;

20.9 = 40.5 × (1 + r)²⁹

$\left (1 + r\right)^{29} = \dfrac{20.9}{40.5}$

$r = \left(\dfrac{20.9}{40.5} \right)^{\dfrac{1}{29} } - 1 \approx -0.02255$

The population growth rate is r ≈ -0.02255 = -2.255 %

The completed table is therefore;

$\begin{array}{|c|c|c|}2003 \ Population (millions)&Projected \ 2029 \ Population \ (millions)&Growth \ rate \ K \\40.5&20.9&-2.255\%\end{array}\right]$

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6 0

2 years ago