Intro to Systems of Equations

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inher

lana66690 [7]

Answer:

a) $n=\frac{0.76(1-0.76)}{(\frac{0.01}{1.64})^2}=4905.83$

And rounded up we have that n=4906

b) For this case since we don't have prior info we need to use as estimatro for the proportion $\hat p =0.5$

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{1.64})^2}=6724$

And rounded up we have that n=6724

Step-by-step explanation:

We need to remember that the confidence interval for the true proportion is given by :

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

Part a

The estimated proportion for this case is $\hat p =0.76$

Our interval is at 90% of confidence, and the significance level is given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . The critical values for this case are:

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

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)

The margin of error desired is given $ME =\pm 0.01$ 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)

Replacing we got:

$n=\frac{0.76(1-0.76)}{(\frac{0.01}{1.64})^2}=4905.83$

And rounded up we have that n=4906

Part b

For this case since we don't have prior info we need to use as estimatro for the proportion $\hat p =0.5$

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{1.64})^2}=6724$

And rounded up we have that n=6724

3 0

2 years ago

Omg please answer i am so lost

Soloha48 [4]

A

Because X isn’t repeated in W but there are repeats in the others.

5 0

2 years ago

X=-1 a solution to 2(x-4)-5x =-5?

Afina-wow [57]

Answer:

X is equal to -1.

Step-by-step explanation:

bet

4 0

2 years ago

Read 2 more answers

4. Which ordered pair is a solution of 3y + 2 = 2x - 5?

Lyrx [107]

Answer:

we determine that none of the ordered pair is a solution of $3y\:+\:2\:=\:2x\:-\:5$ as none of the ordered pairs satisfy the equation.

Step-by-step explanation:

Considering the equation

$3y\:+\:2\:=\:2x\:-\:5$

Putting (-5,2) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(2\right)\:+\:2\:=\:2\left(-5\right)\:-\:5$

$8=-15$ ∵ L.H.S ≠ R.H.S

FALSE

Putting (0,-5) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(-5\right)\:+\:2\:=\:2\left(0\right)\:-\:5$

$-13=-5$ ∵ L.H.S ≠ R.H.S

FALSE

Putting (5,1) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(1\right)+\:2\:=\:2\left(5\right)-\:5$

$5\:=-5$ ∵ L.H.S ≠ R.H.S

FALSE

Putting (7,5) in the equation

$3y\:+\:2\:=\:2x\:-\:5$

$3\left(5\right)+\:2\:=\:2\left(7\right)-\:5\:\:$

$17=9$ ∵ L.H.S ≠ R.H.S

FALSE

From the above calculations, we determine that none of the ordered pair is a solution of $3y\:+\:2\:=\:2x\:-\:5$ as none of the ordered pairs satisfy the equation.

4 0

2 years ago

A conical perfume bottle has a radius of 3.4 centimeters and a height of 4.8 centimeters . Using 3.14 for pi, approximately how

Ghella [55]

Answer:

58.077 cubic cm

Step-by-step explanation:

Given that:

height : 4.8 cm
radius: 3.4 cm

As we know that, the volume of a conical perfume bottle is as following:

V = (1/3) * π * r² * h

So perfume can the bottle hold is:

V = (1/3) * 3.14 * 3.4² * 4.8 = 58.077 cubic cm

Hope it will find you well

5 0

3 years ago

Read 2 more answers