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3 years ago

If f(x) varies directly with x and f(x) = 4 when x = 12, then what is the value of f(x) when x = 60?

1 answer:

6 0

ANSWER

$f(60)=3\times60=180$

EXPLANATION
We were given that
$f(x)$
varies directly as
$x.$

We can write this mathematically as,

$f(x) \propto \: x.$

This implies that,

$f(x) = kx$
where k is the constant of variation.

$f(4)=4k$

This implies that,

$4k=12$

$k = 3$

The equation becomes

$f(x)=3x$

When $x=60$

$f(60)=3\times60=180$

You might be interested in

Graph y=x+1/x² and y=1/x for positive values of x.

AlekseyPX

Answer:

Graphic is showed in the figure below

Step-by-step explanation:

To graph the equations given, let's do a table for positive values of x, and, by replacing it in the equation, let's calculate the value of y. Knowing the coordinate points (x,y) we can build the graphic.

x y= x + 1/x² y = 1/x

1 2 1

2 2.25 0.2

3 3.11 0.33

4 4.06 0.25

When x->0 both equations -> ∞, because lim(1/x) x->0 = ∞

The graphic is showed below. In red there is y = 1 + 1/x² and in blue y = 1/x

6 0

2 years ago

Elena’s aunt bought her a $150 savings bond when she was born. When Elena is 20 years old, the bond will have earned interest an

Ghella [55]

Answer:

307.5$

Step-by-step explanation:

150$. 105% of it added.

Since 105% is 1.05, multiply the percentage by the cost to get the money added.

150*1.05=157.5

Then ADD it to the price/savings.

150+157.5=307.5$

8 0

3 years ago

Read 2 more answers

Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got: