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3 years ago

5.

1 answer:

6 0

Finding limits by direct substitution means simply means to evaluate the function at the desired value: in the first case, we have to evaluate $f(x)=x^2-3$ at $x=0$ : we have

$f(0)=0^2-3 = 0-3=-3$

Similarly, in the second example, we have

$f(x)=x^2+3x-1 \implies f(3) = 3^2+3\cdot 3-1 = 9+9-1 = 17$

Going on, we have

$f(x) = \dfrac{x^2-16}{x-4} = \dfrac{(x+4)(x-4)}{x-4} = x+4$

And thus we have

$f(4) = 4+4=8$

Finally, we have

$f(x) = \dfrac{x^2-2x}{x^4} = \dfrac{x(x-2)}{x^4} = \dfrac{x-2}{x^3}$

So, we can't evaluate this function at 0.

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Write the equation of a line in slope-intercept form that passes through the given points.

ruslelena [56]

Answer:

Step-by-step explanation:

$\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}$

(0, 2) ⇒ x₁ = 0, y₁ = 2

(-4, 1) ⇒ x₂ = -4, y₂ = 1

So the slope:

$\bold{m=\dfrac{1-2}{-4-0}=\dfrac{-1}{-4}=0.25}$

The point-slope form of the equation of the line passing through point (x₀,y₀) and with slope m is: y - y₀ = m(x - x₀)

m = 0.25

(0, 2) ⇒ x₀ = 0, y₀ = 2

Therefore:

y - 2 = 0.25(x - 0)

y - 2 = 0.25x {add 2 to both sides}

y = 0.5x + 2 ← the slope-intercept form of the equation

5 0

3 years ago

What is the total cost of a $12.60 item plus 7% sales tax?

Ulleksa [173]

To take a percent, move the decimal point of the percent two places to the left. 7% = 0.07

Then multiply:

12.60 • 0.07 = 0.88

12.60 + 0.88 = 13.48

The total cost is: $13.48

5 0

2 years ago

Read 2 more answers

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a

zaharov [31]

Answer:

a) $P(X>3.5)=P(\frac{X-\mu}{\sigma}>\frac{3.5-\mu}{\sigma})=P(Z>\frac{3.5-5}{1.2})=P(z>-1.25)$

And we can find this probability using the complement rule:

$P(z>-1.25)=1-P(z$

b) $P(X$

And we can find this probability uing the normal standard table:

$P(z$

c) $P(3.5$

And we can find this probability with this difference:

$P(-1.25$

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.25$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(5,1.2)$