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3 years ago

10

the equation y=15x+500 represents the amaunt y that lin earns by working for x hours plus a performance bonus. what is lin hourl

y rate

1 answer:

sp2606 [1]3 years ago

6 0

The hourly rate is the slope or $15 in this case.

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Convert the polar equation r = 2 secØ to a Cartesian equation.y = 2x = 2x^2 = 2

ss7ja [257]

Polar and cartesian equation<h2>Initial explanation</h2>

Let's analyze the relation between r and x and y:

We have that between the indicated value of r (of the polar coordinates) and x and y (of the cartesian coordinates) there is a relation because they form a triangle. If r changes, then the value of x and y will change.

<h2>STEP 1: given equation</h2>

Using the given equation

r = 2 secØ

we have that

$\begin{gathered} r=2secØ \\ \downarrow \\ \frac{r}{2}=secØ \end{gathered}$ <h2>STEP 2: secØ equation</h2>

Observing the image of the initial explanation we have a right triangle, we know that the equation of

secØ for any right triangle is given by:

$\sec Ø=\frac{\text{hypotenuse}}{\text{adjacent side}}$

In this case,

hypotenuse = r

adjacent side = x

then,

$\begin{gathered} \sec Ø=\frac{\text{hypotenuse}}{\text{adjacent side}}=\frac{r}{x} \\ \sec Ø=\frac{r}{x} \end{gathered}$ <h2>STEP 3: comparison between given equation and secØ equation</h2>

Then, we have that:

$\begin{gathered} \sec Ø=\frac{r}{x} \\ \sec Ø=\frac{r}{2} \end{gathered}$

This means that:

$\begin{gathered} \frac{r}{x}=\sec Ø=\frac{r}{2} \\ \downarrow \\ \frac{r}{x}=\frac{r}{2} \end{gathered}$

Then,

x = 2

The equation in cartesian coordinates is x=2.

Answer: x=2

6 0

1 year ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

OLEGan [10]

5x^2-3 is the anwser

4 0

3 years ago

Read 2 more answers

What is the measure of angle B in degrees

Hunter-Best [27]

Angle C and the 112 degree angle are supplementary, so angle C measures 180-112=68 degrees.

This means that by the exterior angle theorem, $m\angle B=51^{\circ}+68^{\circ}=\boxed{119^{\circ}}$

8 0

2 years ago

In a recent poll, 370 people were asked if they liked dogs, and 7% said they did. Find the margin of error of this poll, at the

Dennis_Churaev [7]

Answer:

$ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218$

Step-by-step explanation:

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".

$p$ represent the real population proportion of interest

$\hat p=0.07$ represent the estimated proportion for the sample

n=370 is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

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 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

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 replacing into formula (a) the values provided we got:

$ME=1.64\sqrt{\frac{0.07(1-0.07)}{370}}=0.0218$

The margin of error on this case would be ME=0.0218

5 0

4 years ago

Help pls??Thank you!!

Igoryamba

The answer would be 4700

6 0

3 years ago

Read 2 more answers