Consider the quadratic function f (x) = x2 - 5x + 6. What does b = ?

Mathematics

2 answers:

vaieri [72.5K]2 years ago

8 0

Answer:

b is the coefficient of the middle term. In this case, -5

Step-by-step explanation:

In a linear equation, the function is in the form of y=mx+b

In a linear equation <u>m</u> is the slope. <u>b</u> is a constant, and it is the y-intercept.

f(x) represents the "y" value obtained when a given number is plugged in to x.

In a quadratic equation, (and it would be helpful to insert a carat ^ [shift + 6] before the exponent so it is clear)

the form is $ax^{2} +bx +c$ a and b are the coefficients. if none, "1" is understood.

the exponent will determine the shape of the parabola.

The b will determine how far to the left or right the parent graph is transformed. ( divide by 2 and use the opposite sign)

but the c is a constant and still indicates the y-intercept.

Rashid [163]2 years ago

3 0

A quadratic function is represented as ax² + bx + c. In this case, if you look at the coefficient of x, you'll see that b = -5.

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One hundred divided by twice a number is ten

Ludmilka [50]

$\frac{100}{2x} = 10$

Are you trying to find x, or are you only suppose to translate it?

If you are trying to find x, you first multiply 2x on both sides

100 = 10(2x)

Divide 10 on both sides

10 = 2x

Divide 2 on both sides

5 = x

5 0

2 years ago

Construct a confidence interval that will capture the true population mean with 95% confidence. Population standard deviation is

kompoz [17]

A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459 , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$

as population variance is unknown so we used sample variance

$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$

Now

$\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$$

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$