Find the missing value in the table.

PLEASE HELP 30 PTS!!! Select ALL the correct answers. Which expressions are equivalent to the following?

Oksanka [162]

Answer:

D: -5(-6x^2 + x + 2)

E: 5(2x + 1)(3x − 2)

Step-by-step explanation:

The first two answer choices have incorrect constants (25 and 3 vs -10). A factor of 5 is removed from the remaining answer choices, so let's remove a factor of 5 and see what we get:

30x^2 -5x -10 = 5(6x^2 -x -2)

An additional x cannot be factored from the expression, so choice C can be eliminated.

Multiplying each of these factors by -1 will make the product correspond to answer choice D.

Factoring will make it correspond to answer choice E, best verified by finding the x-term of the product of the binomial factors:

E: 2x(-2) +1(3x) = -x, as required

F: 2x(2) -1(3x) = x, wrong sign

The equivalent expressions are those of choices D and E.

7 0

3 years ago

Of the entering class at a college, % attended public high school, % attended private high school, and % were home schoole

Veronika [31]

Answer:

(a) The probability that the student made the Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

A = a student attended public high school

B = a student attended private high school

C = a student was home schooled

D = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

$P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})$

Compute the probability that the student made the Dean's list as follows:

$P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)$

$=(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655$

Thus, the probability that the student made the Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D)}$

$=\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411$

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

$P(C^{c}|D^{c})=1-P(C|D^{c})$

$=1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185$

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

3 0

3 years ago

How do you solve the problem 7.8%15

snow_tiger [21]

Answer:

I suppose that's 7.8% of 15.

Step-by-step explanation:

7.8/100=0.078‬

0.078‬*15=1.17

7 0

3 years ago

The Red Mills Children's Hospital has raised 70% of the money they need for medical supplies. If they need a total of $900, how

borishaifa [10]

Answer:

$630

Step-by-step explanation:

They raised 70% of $900.

70% of $900 = 70% × $900 = 0.7 × $900 = $630

3 0

2 years ago

What is the vaule of tan-240 degrees?

Tom [10]

The answer is 1.732

8 0

3 years ago