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iris [78.8K]
3 years ago
9

There are 4people in a room, and we are curious whether two of them have theirbirthday in the same month. We record the quadrupl

ethat describes the month ofbirthday for each person. E.g. (Oct, Jan, Jul, Apr) is one possible quadruple /outcome.(Since each month applies to a specific person, (Oct, Jan, Jul, Apr) is not the same as(Jan, Jul, Oct, Apr) and so order is important).
a. How many possible outcomes are there?
b. In how many of these outcomes, all four people have their birthday indifferent months?
c. In how many of these outcomes, at least two people have their birthday in the same month?
Mathematics
1 answer:
alukav5142 [94]3 years ago
7 0
Oh yes I think they have the right size but not sure how much I would do lol but they look nice lol but I’m gonna do that .. but yes yes lol yes yes that’s good for him and jhoels
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Need help on the level 10 question. Only comment if you know. Please step by step
skelet666 [1.2K]

2xy^2+xy^2+xy-2x

2x(y^2-1)+xy(y+1)

2x(y-1)(y+1)+xy(y+1)

(y+1)(2xy-2x+xy)

(y+1)(3xy-2x)

  • I divide 3xy^2 into 2xy^2+xy^2
4 0
3 years ago
John Doe, a super-genius student (known also under his nick-name Wile E. Coyote, super-genius) has just graduated from SPEA and
kirill [66]

Answer: See explanation

Step-by-step explanation:

a. Construct a decision tree for Wile

The solution to the question has been attached.

b. What is the expected value of the new car?

= [(0.2 × $10,000) + (0.8 × $18,000)] - $22,000

= $2000 + $14400 - $22000

= $16400 - $22000

= -$5600

c. What is the expected value of the used car?

= [(0.4 × $4000) + (0.6 ×$9000] - $12000

= $1600 + 5400 - $12000

= $7000 - $12000

= -$5000

d. What is the expected value of leasing the car?

= [(0.1 × -$2000) + (0.9 ×0)] - $8500

= -$200 - $8500

= -$8700

8 0
3 years ago
A culture of bacteria has an initial population of 9300 bacteria and doubles every 3
sp2606 [1]

Answer:

The approximate population of bacteria in the culture after 10 hours is 93,738.  

Step-by-step explanation:

<h3>General Concepts:</h3>
  • Exponential Functions.
  • Exponential Growth.
  • Doubling Time Model.
  • Logarithmic Form.

BPEMDAS Order of Operations:

  1. Brackets.
  2. Parenthesis.
  3. Exponents.
  4. Multiplication.
  5. Division.
  6. Addition.
  7. Subtraction.
<h2>Definitions:</h2>

We are given the following Exponential Growth Function (Doubling Time Model), \displaystyle\mathsf{P_{(t)}\:=\:P_0\cdot2^{(t/d)}} where:

  • \displaystyle\sf{P_t\:\:\rightarrow} The population of bacteria after “<em>t </em>” number of hours.
  • \displaystyle\sf{P_0 \:\:\rightarrow} The initial population of bacteria.
  • \displaystyle{t \:\:\rightarrow}  Time unit (in hours).
  • \displaystyle{\textit d \:\:\rightarrow}  Doubling time, which represents the amount of time it takes for the population of bacteria to grow exponentially to become twice its initial quantity.  
<h2>Solution:</h2>

<u>Step 1: Identify the given values.</u>

  • \displaystyle\sf{P_0\:=} 9,300.
  • <em>t</em> = 10 hours.
  • <em>d</em> = 3.  

<u>Step 2: Find value.</u>

1. Substitute the values into the given exponential function.

  \displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}

  \displaystyle\mathsf{\longrightarrow P_{(10)} = 9300\cdot2^{(10/3)}}

2. Evaluate using the BPEMDAS order of operations.

  \displaystyle\mathsf{P_{(10)} = 9300\cdot2^{(10/3)}\quad \Longrightarrow BPEMDAS:\:(Parenthesis\:\:and\:\:Division).}

  \displaystyle\sf P_{(10)} = 9300\cdot2^{(3.333333)}\quad\Longrightarrow BPEMDAS:\:(Exponent).}

  \displaystyle\sf P_{(10)} = 9300\cdot(10.079368399)\quad \Longrightarrow BPEMDAS:(Multiplication).}

 \boxed{\displaystyle\mathsf{P_{(10)} \approx 93,738.13\:\:\:or\:\:93,738}}

Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.  

<h2>Double-check:</h2>

We can solve for the amount of <u>time</u> <u>(</u><em>t</em> ) it takes for the population of bacteria to increase to 93,738.

1. Identify given:

  • \displaystyle\mathsf{P_{(t)} = 93,738 }.
  • \displaystyle\mathsf{P_0 = 9,300}.
  • <em>d </em>= 3.

2. Substitute the values into the given exponential function.

  \displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}

  \displaystyle\mathsf{\longrightarrow 93,378 = 9,300\cdot2^{(t/3)}}

3. Divide both sides by 9,300:

  \displaystyle\mathsf{\longrightarrow \frac{93,378}{9,300} = \frac{9,300\cdot2^{(t/3)}}{9,300}}

  \displaystyle\mathsf{\longrightarrow 10.07936840 = 2^{(t/3)}}

4. Transform the right-hand side of the equation into logarithmic form.

  \boxed{\displaystyle\mathsf{\underbrace{ x = a^y}_{Exponential\:Form} \longrightarrow \underbrace{y = log_a x}_{Logarithmic\:Form}}}    

  \displaystyle\mathsf{\longrightarrow 10.07936840 = \bigg[\:\frac{t}{3}\:\bigg]log(2)}  

5. Take the <em>log</em> of both sides of the equation (without rounding off any digits).  

  \displaystyle\mathsf{log(10.07936840) = \bigg[\:\frac{t}{3}\:\bigg]log(2)}

  \displaystyle\mathsf{\longrightarrow 1.003433319 = \bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996)}

6. Divide both sides by (0.301029996).

  \displaystyle\mathsf{\frac{1.003433319}{0.301029996} = \frac{\bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996) }{0.301029996}}

  \displaystyle\mathsf{\longrightarrow 3.3333333  = \frac{t}{3}}

7. Multiply both sides of the equation by 3 to isolate "<em>t</em>."

  \displaystyle\mathsf{(3)\cdot(3.3333333)  = \bigg[\:\frac{t}{3}\:\bigg]\cdot(3)}

  \boxed{\displaystyle\mathsf{t\approx10}}

Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.    

__________________________________

Learn more about Exponential Functions on:

brainly.com/question/18522519            

7 0
2 years ago
The difference of two numbers is 15.Five times the smaller is the same as 9 less than twice the larger.Find the numbers
Lana71 [14]

Answer:

small number = -3

large number = 12

Step-by-step explanation:

Suppose two numbers are x and y

smaller number = x

larger number = y

Given that,

The difference of two numbers is 15

<h2>Equation 1</h2><h3>y - x  = 15</h3>

Five times the smaller is the same as 9 less than twice the larger.

<h2>Equation 2</h2><h3>5x = 9 - 2y</h3>

Solve them

-x = 15 - y

x = y -15

put value of x in equation 2

5(y - 15) = 9 - 2y

-75 + 5y = 9 - 2y

-75 - 9 = -2y - 5y

-84 =  -7y

y = 84/7

y = 12

x = 12 - 15

x = -3  

8 0
3 years ago
What is the value of x, if the volume of the cone is 12mm?
Anna007 [38]

Answer:

<h2>V=1/3 pie r^2h (Formula)</h2><h2>12×22/7=1/3×22/7×3^2×h</h2><h2>Eliminate 22/7</h2><h2>12=(9×h)/3</h2><h2>Make "h" the subject of the equation </h2><h2>h=36/9</h2><h2>h=4m</h2>
3 0
3 years ago
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