1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alex
3 years ago
8

HELP NOW!!!!

Mathematics
1 answer:
VMariaS [17]3 years ago
7 0

Using the concept of probability and the arrangements formula, there is a  

0.002 = 0.2% probability that the first 8 people in line are teachers.

----------------------------------

  • A probability is the <u>number of desired outcomes divided by the number of total outcomes.</u>
  • The order in which they are positioned is important, and all people will be positioned, and thus, the arrangements formula is used to find the number of outcomes.

The number of possible arrangements from a set of n elements is given by:

A_n = n!

----------------------------------

The desired outcomes are:

  • First 8 people are teachers, in <u>8! possible ways.</u>
  • Last 4 are students, in <u>4! possible ways.</u>

Thus, D = 8! \times 4!

----------------------------------

For the total outcomes, <u>number of arrangements of 12 people</u>, thus:

T = 12!

The probability is:

p = \frac{D}{T} = \frac{8! \times 4!}{12!} = 0.002

0.002 = 0.2% probability that the first 8 people in line are teachers.

A similar problem is given at brainly.com/question/24650047

You might be interested in
#10 i The table shows the admission costs (in dollars) and the average number of daily visitors at an amusement park each the pa
lions [1.4K]

The line of best fit is a straight line that can be used to predict the

average daily attendance for a given admission cost.

Correct responses:

  • The equation of best fit is; \underline{ \hat Y = 1,042 - 4.9 \cdot X_i}
  • The correlation coefficient is; r ≈<u> -0.969</u>

<h3>Methods by which the line of best fit is found</h3>

The given data is presented in the following tabular format;

\begin{tabular}{|c|c|c|c|c|c|c|c|c|}Cost, (dollars), x&20&21&22&24&25&27&28&30\\Daily attendance, y&940&935&940&925&920&905&910&890\end{array}\right]

The equation of the line of best fit is given by the regression line

equation as follows;

  • \hat Y = \mathbf{b_0 + b_1 \cdot X_i}

Where;

\hat Y = Predicted value of the<em> i</em>th observation

b₀ = Estimated regression equation intercept

b₁ = The estimate of the slope regression equation

X_i = The <em>i</em>th observed value

b_1 = \mathbf{\dfrac{\sum (X - \overline X) \cdot (Y - \overline Y) }{\sum \left(X - \overline X \right)^2}}

\overline X = 24.625

\overline Y = 960.625

\mathbf{\sum(X - \overline X) \cdot (Y - \overline Y)} = -433.125

\mathbf{\sum(X - \overline X)^2} = 87.875

Therefore;

b_1 = \mathbf{\dfrac{-433.125}{87.875}} \approx -4.9289

Therefore;

  • The slope given to the nearest tenth is b₁ ≈ -4.9

b_0 = \mathbf{\dfrac{\left(\sum Y \right) \cdot \left(\sum X^2 \right) - \left(\sum X \right) \cdot \left(\sum X \cdot Y\right)} {n \cdot \left(\sum X^2\right) - \left(\sum X \right)^2}}

By using MS Excel, we have;

n = 8

∑X = 197

∑Y = 7365

∑X² = 4939

∑Y² = 6782675

∑X·Y = 180930

(∑X)² = 38809

Therefore;

b_0 = \dfrac{7365 \times 4939-197 \times 180930}{8 \times 4939 - 38809} \approx \mathbf{1041.9986}

  • The y-intercept given to the nearest tenth is b₀ ≈ 1,042

The equation of the line of best fit is therefore;

  • \underline{\hat Y = 1042 - 4.9 \cdot X_i}

The correlation coefficient is given by the formula;

\displaystyle r = \mathbf{\dfrac{\sum \left(X_i - \overline X) \cdot \left(Y - \overline Y \right)}{ \sqrt{\sum \left(X_i - \overline X \right)^2 \cdot \sum \left(Y_i - \overline Y \right)^2} }}

Where;

\sqrt{\sum \left(X - \overline X \right)^2 \times \sum \left(Y - \overline Y \right)^2}  = \mathbf{446.8121}

\sum \left(X_i - \overline X \right) \times \left(Y - \overline Y\right) = \mathbf{-433.125}

Which gives;

r = \dfrac{-433.125}{446.8121}  \approx \mathbf{-0.969367213}

The correlation coefficient given to the nearest thousandth is therefore;

  • <u>Correlation coefficient, r ≈ -0.969</u>

Learn more about regression analysis here:

brainly.com/question/14279500

7 0
3 years ago
Heeeeeeeelp!!!!!!!!!!!
Natasha_Volkova [10]
A is the answer because if you calculate the answer correctly. that will be so.
8 0
3 years ago
A 1000 watt microwave does --------- joules of work in 5 seconds
ss7ja [257]

Answer:

5,000 Joules of work.

Step-by-step explanation:

3 0
3 years ago
Which of the following points are solutions to the system of inequalities shown below?
pychu [463]
This is easy, love. It's E 
3 0
3 years ago
Read 2 more answers
What is the value of x in the equation below?
Alexeev081 [22]
X equals 4

I just did it
8 0
3 years ago
Other questions:
  • How to simplify this algebraic fraction
    13·1 answer
  • What is the point slope equation of a line with slope -3 that contains the point (-8, -4)?
    5·1 answer
  • Which is a solution to the equation |10-5y|=20<br><br>y=2<br><br>y=4<br><br>y=6<br><br>y=10
    13·1 answer
  • A rectangle has perimeter 78 cm and length 32 cm. What is its width?​
    10·1 answer
  • Which set of side lengths form a right triangle?
    7·1 answer
  • Martinez purchased a pair of shoes on a web site. The original price of the shoes was $75. She used a coupon code to receive a 2
    5·2 answers
  • An important problem in industry is shipment damage. A windshield factory ships its product by truck and determines that it cann
    11·1 answer
  • If a = 3, what is the value of 2a2.<br><br>A. 6<br><br>B. 12<br>C. 18<br><br>D. 36<br>​
    6·2 answers
  • Use elimination and explain
    7·1 answer
  • 2. Choose all that apply: What are the coordinate point(s) that cross the x-axis
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!