Is -1/16 a rational number?

A new law requires that 12% of an individual's income be invested in the stock market. Your accounts show that you need to put $

kozerog [31]

If you need to put $420 this year and the law requires 12% of the income to be invested in the stock market, then you earned:
$240/0.12 = $3500 this year

So, you earned a total of $3,500 this with 12% of it invested in the stock market which is 12% of your total earnings leaving you with just $3,080

4 0

4 years ago

Suppose that we wish to assess whether more than 60 percent of all U.S. households in a particular income class bought life insu

Yakvenalex [24]

Answer:

a) The probability is P=0.3982.

b) No. There is no enough evidence to say that the proportion of the population is not 0.6.

Step-by-step explanation:

a) In this question, we have a sample of the population, of size n=1000. To know what is the probability of observing a sample proportion that is at least 0.64 we have to know the parameters of the sampling distribution.

The parameters of the sampling distribution of the proportion will be:

$\mu=\pi=0.6\\\\ \sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.6(1-0.6)}{1000} }= 0.0155$

With these parameters, we can calculate the z-value for p=0.64 as:

$z=\frac{p-\pi}{\sigma}=\frac{0.64-0.6}{0.0155}= 0.258$

Then, we can calculate the probability of having a sample with p≥0.64:

$P(p\geq0.64)=P(z\geq0.258)=0.3982$

b) To know if the proportion of the population is greater than 0.6 the rigth thing to do is perform a hypothesis test, in which we test the following hypothesis:

$H_0: \pi\leq0.6\\\\H_1:\pi>0.6$

If the null hypothesis is rejected, we can conclude that there is evidence that the proportion of the population is greater than 0.6.

First, we assume a significance level of 0.05.

Second, we calculate the z value:

$z=\frac{p-\pi-0.5/N}{\sigma} =\frac{0.64-0.6-0.5/1000}{0.0155} =\frac{0.0395}{0.0155} =2.54$

The P-value for this z is P=0.4. The P-value is greater than the significance level, what means that there is no evidence to reject the null hypothesis.

In other words, a sample mean of 0.64 is a quite probable value even if the proportion of the population is 0.6.

6 0

3 years ago

What is 69 3/9 -10 2/5

alexandr1967 [171]

Answer:

59 1/15

Step-by-step explanation:

subtract the whole numbers leave those alone then subtract the fractions if you get a decimal then turn that decimal into a fraction. Hoped that helped plz make me brainiest answer i would really appreciate it.

3 0

3 years ago

irina1246 [14]

Two triangles with two sides and a non-included angle equal may or may not be congruent. If two angles on one triangle are equal, respectively, to two angles on another triangle, then the triangles are similar, but not necessarily congruent.

5 0

3 years ago

Read 2 more answers

Identify the quadratic function from the four functions

Alchen [17]

Quadratic Function is a function that takes the equation form of:

$\large \boxed{y = a {x}^{2} + bx + c}$

where a ≠ 0. However the form of Quadratic Function above can also be called "standard form" or general form because it is commonly used when defining the function. Quadratic Functions also have other two forms which are intercept form and vertex form.

Vertex Form

$\large \boxed{y = a {(x - h)}^{2} + k}$

Intercept Form

$\large \boxed{y = (ax - b)(bx - c)}$

The intercept form can be expressed as y = (x-a)(x-b) depending on the other perspective.

If you look at all four functions, you will notice that only two of functions have the second degree as highest degree while the third function has third degree as highest and fourth function has fourth degree. Recall the definition of Quadratic Function above that the highest degree of Quadratic Function can only be second degree (squared, x² as example). Therefore we can rule out the x³ and -2x⁴ away.

So our only quadratic functions are:

$\large{ \begin{cases}y = - {x}^{2} - 4 \\ y = {(x - 1)}^{2} - 7 \end{cases}}$

As for the f(x) = -x²-4. The equation is in standard form which is y = ax²+bx+c. The second equation is in vertex form which is y = a(x-h)²+k.

Answer

The only quadratic functions are f(x) = -x²-4 and f(x) = (x-1)²-7
-x²-4 is in standard form.
(x-1)²-7 is in vertex form.

Hope this helps and let me know if you have any doubts.

Also let me know if you want me to convert the function into other form. For ex. convert the vertex form to standard form.

Happy Learning and Good Luck with your assignment!

4 0

3 years ago