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Using the combination formula, it is found that the probability that you, Charles, Margaret, and Sean are chosen is:

[tex]p = \frac{1}{495}[/tex].

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 4 people will be chosen from a set of 12, hence the number of ways to choose them is:

[tex]C_{12,4} = \frac{12!}{4!8!} = 495[/tex]

The desired combination is only one, hence the probability is:

[tex]p = \frac{1}{495}[/tex].

More can be learned about the combination formula at https://brainly.com/question/25821700

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Answer:

b.)  (6,7)

Step-by-step explanation:

the figure is translated 2 units to the left

Answer:

1 box of paper will cost $7.25.

Step-by-step explanation:

14.50 divided by 2 is 7.25, therefore one box of paper will be 7.25

Answer:

with what

Step-by-step explanation:

Answer:

a)4.15 years

b)22.18 years

c)188.53 years

d)3027.66 years

Step-by-step explanation:

Formula : [tex]P(X\leq t)=1-e^{\frac{-t}{\lambda}}[/tex]

So, [tex]P(X>t)=1-(1-e^{\frac{-t}{\lambda}})[/tex]

[tex]P(X>t)=e^{\frac{-t}{\lambda}}[/tex]

We are given that The half-life of such a persistent poison is that time beyond which the probability is .50 that a particular molecule will remain toxic i.e. P(X>t)=0.5

So, [tex]e^{\frac{-t}{\lambda}}=0.5[/tex]

Taking natural log both sides

[tex]ln(e^{\frac{-t}{\lambda}})=ln(0.5)\\\frac{-t}{\lambda}=ln(0.5)\\t=-\lambda ln(0.5)[/tex]

a)

[tex]\lambda =6[/tex]

t=-(6) ln(0.5)=4.15 years

b)

[tex]\lambda =32[/tex]

t=-(32) ln(0.5)=22.18 years

c)

[tex]\lambda =272[/tex]

t=-(272) ln(0.5)=188.53 years

d)

[tex]\lambda =4368[/tex]

t=-(4368) ln(0.5)=3027.66 years

Answer:

Step-by-step explanation:

3m + 7 = - 23

we pass the -7 to the right with a positive sign

3m = -23 - 7

we perform the sum of negative numbers

3m = -30

we pass the -3 to the right to divide

m = -30/3

we perform the division

m = -10

Answer:

The value is -6.

Step-by-step explanation:

First, you use subsitution.

4(3) - 3(6)

Then, you multiply.

12 - 18

Do the subtraction and you're left with -6 as your answer.

Answer:

Step-by-step explanation:

180-110+70

Answer:

um i dunna

Step-by-step explanation:

uuuuhhghhhh

Answer:

B

Step-by-step explanation:

the first fish tank has 100 gallons of water and 1 gallon is removed every hour which makes 100-h

the second tank has 40 gallons in it and 2 gallons are added every hour which makes 40+2h

after 20 hours the second tank will have more gallons than the first tank

this means that 40+2h would be greater than 100-h since it's also asking you "After how many hours will the first tank  have less water than the second?"

Answer:

6

Step-by-step explanation:

3,6,9.12

2,4,6,8,10,12

Answer:

D.83.8 ounces

Step-by-step explanation:

The z score for 65th percentile = 0.385

Mean weight of 83 ounces with a standard deviation of 2 ounces

The formula for calculating a z-score is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

x = ??

Hence:

0.385 = (x - 83)/2

Cross Multiply

0.385 × 2 = x - 83

0.77 = x - 83

x = 83 + 0.77

x = 83.77 ounces

Approximately = 83.8 ounces

Answer:

D.83.8 ounces

Step-by-step explanation:

The z score for 65th percentile = 0.385

Mean weight of 83 ounces with a standard deviation of 2 ounces

The formula for calculating a z-score is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

x = ??

Hence:

0.385 = (x - 83)/2

Cross Multiply

0.385 × 2 = x - 83

0.77 = x - 83

x = 83 + 0.77

x = 83.77 ounces

Approximately = 83.8 ounces

Answer:

estimate - 400

product - 385

Step-by-step explanation:

estimate - 77 rounds up to 80

80*5=400

product - 70*5=350

7*5=35

350+35=385

Answer:

The estimate is 390 while the real product is 385

Answer:

mDF = 18

Step-by-step explanation:

DE and EF must add up to DF.

Step 1: Set up equation

mDE + mEF = mDF

x + 7 + 7 = 4x + 2

Step 2: Solve for x

Step 3: Find mDF

mDF = 4x + 2

mDF = 4(4) + 2

mDF = 16 + 2

mDF = 18

Step-by-step explanation:

Using vertex form of a parabola:

y = a (x − h)² + k

where (h, k) is the vertex.

If we say the vertex is (0, 80), then:

y = a (x − 0)² + 80

y = ax² + 80

The roots of the parabola are (-60, 0) and (60, 0).  If we plug this in:

0 = a (60)² + 80

-80 = 3600a

a = -1/45

Noemi's team's answer is incorrect.

Answer:

It's 2000ft/h

Step-by-step explanation:

6000/3 = 1 hour rate

Answer:

-8

Step-by-step explanation:

First, write it out in standard form:

2 x (-4)

Then multiply!

Answer:

-8

Step-by-step explanation:

it is basically 2 x -4 and a negative times a positive is a negative which makes it -8

12 dolars / 20 dolars

the percentage is

(20-12) / 20

= 8/20

= 40 %

Answer:

The two in the middle are the negatives and the two that are on the sides are positive.

Answer:

12x+5y < 180

Step-by-step explanation:

12 (adults) + 5 (kids) < needs to be less than 180 dollars

Answer:

2nd Choice- $2.14 total

Step-by-step explanation:

The expression is just adding the factors, 1.19 and 0.95. Then the counting sets, a whole square shaded is 100 units, a bit more is shaded of the second square, which signifies the .19 cents. Then yellow shade shows the lip balm cost, which is 0.95.

Answer:

203 + 178 = 381

Step-by-step explanation:

Answer:

381

Step-by-step explanation:

i added

203

+178

381

NB: NOT HOW I WANTED IT TO TURN OUT

SORRY IF IT'S WRONG

Answer:

0?

Step-by-step explanation:

9515 1404 393

Answer:

Step-by-step explanation:

1. The system is represented by the matrix that has the coefficients in the left three columns and the constants in the rightmost column. Values and signs must match. Only Option 4 makes any sense in this context.

__

2. In the first equation, the y-term has a coefficient of 0. (There is no y-term.) The only matrix choice with a coefficient of 0 in the second column of the first row is Option 1.

__

3. Parallel lines do not intersect, so there can be no solution.

Answer:

$69.375

Step-by-step explanation:

To find the total cost: you will add the actual cost of the rug, $64 and the additional shipping and handling cost, $5.375.

[tex]64 + 5.375 = 69.375[/tex]

The total cost of the rug, including shipping and handling is $69.375

Answer:

$69.38

Step-by-step explanation:

64 plus 5 is 69. Add 375 for 69.375. Round the decimal up to get $69.38