The amount of money Sarah earns per week is modeled by the function W below where h

Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. of the 80 male students who wer

Aloiza [94]

Total number of students surveyed = 200
Number of male students = 80
Number of female students = 200 - 80 = 120

Number of brown eyed male students = 60
Probability of a brown eyed male student = 60 / 80 = 0.75.

Since, <span>eye color and gender are independent, this means that eye color is not affected by the gender. Thus, we expect a similar probability of brown eye for female as we had for male.

Let the number expected of brown eyed females be x, then x / 120 = 0.75.

Thus, x = 120(0.75) = 90.

Therefore, the number female students surveyed expected to be brown eyed is 90.</span>

7 0

2 years ago

This is a question on my partial fractions homework, but no matter what I try I can't figure it out..

Ierofanga [76]

$\dfrac{x^2+x+1}{(x+1)^2(x+2)}=\dfrac{a_1x+a_0}{(x+1)^2}+\dfrac b{x+2}$
$\implies\dfrac{x^2+x+1}{(x+1)^2(x+2)}=\dfrac{(a_1x+a_0)(x+2)+b(x+1)^2}{(x+1)^2(x+2)}$
$\implies x^2+x+1=(a_1+b)x^2+(2a_1+a_0+2b)x+(2a_0+b)$
$\implies\begin{cases}a_1+b=1\\2a_1+a_0+2b=1\\2a_0+b=1\end{cases}\implies a_1=-2,a_0=-1,b=3$

So you have

$\displaystyle\int_0^2\frac{x^2+x+1}{(x+1)^2(x+2)}\,\mathrm dx=-2\int_0^2\frac x{(x+1)^2}\,\mathrm dx-\int_0^2\frac{\mathrm dx}{(x+1)^2}+3\int_0^2\frac{\mathrm dx}{x+2}$
$=\displaystyle-2\int_1^3\dfrac{x-1}{x^2}\,\mathrm dx-\int_0^2\frac{\mathrm dx}{(x+1)^2}+3\int_0^2\frac{\mathrm dx}{x+2}$

where in the first integral we substitute $x\mapsto x+1$ .

$=\displaystyle-2\int_1^3\left(\frac1x-\frac1{x^2}\right)\,\mathrm dx-\frac1{1+x}\bigg|_{x=0}^{x=2}+3\ln|x+2|\bigg|_{x=0}^{x=2}$
$=-2\left(\ln|x|+\dfrac1x\right)\bigg|_{x=1}^{x=3}-\dfrac23+3(\ln4-\ln2)$
$=-2\left(\ln3+\dfrac13-1\right)-\dfrac23+3\ln2$
$=\dfrac23+\ln\dfrac89$

4 0

3 years ago

The value of 4a( a - 3 ) is :

liubo4ka [24]

Answer:

Its -12 if a is meant to be multiplied

3 0

2 years ago

The light bulbs you use are on sale. But you only get the lower price if you buy 3 packages of bulbs. You want to know how much

weeeeeb [17]

Let’s let s = sale price per package
r = =regular price per package
c = cost savings.
Answer: c= 3r – 3s

8 0

2 years ago

Rewrite the equation in logarithmic form: 2³= 8

GrogVix [38]

Explanation: The base of the power in the original equation becomes the base of the log. So we have $^{log}2$ . Next, the exponent in the original equation goes on the other side of the equation and finally, the result in the original equation goes inside the log.

So we have $^{log} 2$ $8$ = $3$ which is 2³ = 8 written in logarithmic form.

6 0

2 years ago

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