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3 years ago

What is the domain of the function shown in the graph?

Mathematics

1 answer:

lara31 [8.8K]3 years ago

6 0

Answer:

the domain is the possible points on the x axis

Step-by-step explanation:

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What is the area of the trapezoid below?

Softa [21]

Answer:

Step-by-step explanation:

Hope this helps! have a great day!

3 0

3 years ago

If f(x) = 4x - 3, evaluate f(2).

hjlf

Answer: f(2) = 5

Explanation: If f(x) - 4x - 3, then f(2) = 4(2) - 3 which simplifies to 5.

8 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

2 years ago

The half-life of lead is 22 years. How long will it take for a sample of this substance t decay to 80% of its original amount?

Svetlanka [38]

Answer: 7 years

Step-by-step explanation:

$t_{\frac{1}{2} }$ = In2 / ∧

since the half life is given , we have :

22 = In 2/ ∧

∧ = In2/22

∧ = 0.032

Recall the formula for half life:

$\frac{N(t)}{N(0)}$ = $e^{-∧t}$

Therefore:

0.80 = $e^{-0.032t}$

Take the In of both sides

In 0.80 = - 0.032t

t = In 0.80 / - 0.032

t = 7 years

4 0

3 years ago

Question 2 of 20

Mademuasel [1]

2+v12 is the answer

3 0

3 years ago