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Oksana_A [137]
3 years ago
9

Solve for x, given the equation Square root of x-5+7=11

Mathematics
1 answer:
denis-greek [22]3 years ago
6 0

\sqrt{x-5+7} = 11\\x-5+7 = 11^2\\x-5+7 = 121\\x + 2 = 121\\x = 119

Check the answer:

\sqrt{119-5+7} \\\sqrt{114+7} \\\sqrt{121} \\11

This answer is correct,

x = 119

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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:

<em>A</em> = a student attended public high school

<em>B</em> = a student attended private high school

<em>C</em> = a student was home schooled

<em>D</em> = 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
1. Lisa walked 48 blocks in 3 hours <br> _________blocks per hour
scoray [572]
To solve this, we divide 48 by 3.
48÷3=16
16 blocks per hour.
7 0
3 years ago
Read 2 more answers
I need help with Algebra 2. Thank you! :)
andre [41]

Answer:

B: 6.0

Step-by-step explanation:

-3t^2+9t+54 = 0

This is the equation that needs to be solved

Divide both sides by -3

t^2 - 3t - 18 = 0

The factors of 18 are: (1 18) (2 9) (3 6)

3 - 6 = -3 and 3 x -6 = -18

So: (t + 3) (t - 6) = 0

t = -3, 6

It can't be negative so the answer is 6

7 0
2 years ago
The wheels on Reggie’s bike each have a 20-in. diameter. His sister’s mountain bike has wheels that each have a 26-in. diameter.
ExtremeBDS [4]
The answwer is 30 inches
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3 years ago
Which number has the greatest value
aleksklad [387]

Answer:

See the explanation below

Step-by-step explanation:

Which number has the greatest value

From the given list of numbers

Option A has the greatest value

A 8.07 x 10^5

This is because it is raised to a positive number 5, and also the integer is the largest that is raised to a non-negative number/power

6 0
2 years ago
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