Pls help
This is due in 7 minutes

Answer:

a) 1 = 100% probability that at least one sample will contain one or more bacterial colonies.

b) 1 sample should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony

Step-by-step explanation:

To solve this question, we need to understand the poisson and the binomial distributions.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Probability of a single sample having at least one bacterial colonies.

Poisson distribution with a mean of 3 per cubic centimeter (cm3), which means that [tex]\mu = 3[/tex]

This is:

[tex]P(X \geq 3) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0495[/tex]

[tex]P(X \geq 3) = 1 - P(X = 0) = 1 - 0.0495 = 0.9505[/tex]

(a) If eight 1 cm3 samples are independently selected from this water, find the probability that at least one sample will contain one or more bacterial colonies.

Multiples samples means that the binomial distribution is used.

0.9505 probability of a sample having at least one colony, which means that [tex]p = 0.9505[/tex]

8 samples means that [tex]n = 8[/tex]

The desired probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{8,0}.(0.9505)^{0}.(0.0495)^{8} \approx 0[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0 = 1[/tex]

1 = 100% probability that at least one sample will contain one or more bacterial colonies.

(b) How many 1 cm3 samples should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony

We have to find [tex]P(X \geq 1)[/tex] for samples of 1,2,3,..., until this probability is 0.95. So

n = 1

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{1,0}.(0.9505)^{0}.(0.0495)^{1} = 0.0495[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0495 = 0.9505[/tex]

0.9505 > 0.95

1 sample should be selected in order to have a probability of approximately 0.95 of seeing at least one bacterial colony

Answer:

Step-by-step explanation:

The correct answer is false.

Multiples 5 include: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, etc.

Bold numbers: even

Normal numbers: odd

Answer:

I belive it is 2.9716

Step-by-step explanation:

Answer:

360 - 169 equals 191

Step-by-step explanation:

191

Answer:

The answer is 6.451 or 6.5 rounded

Step-by-step explanation:

The way to solve this is to find all the degrees inside the triangle first

you have two given degrees which are 21 and 90 degrees

add those numbers up and subtract it from 180. That is the last corner degree

you then use that information to find all the side lengths using the given hypotenuse length.

Btw its geometry not really trig.

Answer: 6.45 units

Step-by-step explanation:

    To solve for x, we will set up an equation using the trigonometric functions. We are given an angle (21 degrees), the opposite side of that angle (x), and the hypotenuse (18). For this, we will use the sine function.

sin(21) = [tex]\frac{opposite}{hypotenuse }[/tex]

sin(21) = [tex]\frac{x}{18}[/tex]

18sin(21) = x

x = 18sin(21)

x = 6.4506230 ≈ 6.45 units

Answer:

The second one doesn't match.

Answer:

try

Step-by-step explanation:

try solving it on ur own or take a educated guess

Answer:     -100 and -63

Step-by-step explanation: Don't overthink it by trying to divide it.

Answer:

-81, - 82

Step-by-step explanation:

Let the two consecutive integers be x and (x + 1)

According to the given information:

x + (x + 1) = - 163

2x + 1 = - 163

2x =-163 - 1

2x = - 164

x = - 164/2

x = - 82

x + 1 = - 82 + 1 = - 81

Thus, the two consecutive integers are - 81, - 82

Answer:

[tex]-\frac{3}{4}[/tex]

Step-by-step explanation:

Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operation, and stands for:

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, subtract 3x from both sides of the equation:

3x (-3x) + 4y = (-3x) + 20

4y = -3x + 20

Next, divide 4 from both sides of the equation:

(4y)/4 = (-3x + 20)/4

y = (-3/4)x + 5

[tex]y = -\frac{3}{4}x + 5[/tex]

~

Note the equation.

y = mx + b

y = y

m = slope = [tex]-\frac{3}{4}[/tex]

x = x

b = y-intercept = 5

Answer:

252 menu

Step-by-step explanation:

Total number courses, n = 10

The largest number of menu the chef can plan using his 10 main courses.

There are various combinations of menu obtainable from the available courses :

Ranging from :

nC0 to nCn

The largest number of menu he can plan is the highest output obtainable between :

10C0 to 10C10

10C0 = 1

10C1 = 10

10C2 = 45

10C3 = 120

10C4 = 210

10C5 = 252

10C6 = 210

10C7 = 120

10C8 = 45

10C9 = 10

10C10 = 1

Hence, the largest number of menu he can plan using his 10 main courses is 252

Answer:

Q1

Q2

BC is given 23 mi

Maybe AB is needed

Q3

Q4

Let the angle is x

Q5

See attached

Added point D and segments AD and DC to help with calculation

Find the length of added red segments

Now we can find the value of BC

All calculations are rounded

Answer:

B) [tex]\frac{6}{12}[/tex]

Step-by-step explanation:

Note that you do not need to simplify. Simply multiply straight across:

[tex]\frac{3}{4} * \frac{2}{3} = \frac{3 * 2}{4 * 3} = \frac{6}{12}[/tex]

B) [tex]\frac{6}{12}[/tex] is your answer.

`

Answer:

C

Step-by-step explanation:

Answer:

0.4

Step-by-step explanation:

Answer: 8 dinos

Step-by-step explanation:

there are 4 boxes and 5 handfuls in each. divide 160 by 4 and divide that, 40, by 5 to get 8

Answer:

D

Step-by-step explanation:

dd

Answer:

30x+15

Step-by-step explanation:

Answer:

The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.

Step-by-step explanation:

Surface area of a snowball:

A snowball has a spheric format, which means that it's surface area is given by:

[tex]A = 4\pi r^2[/tex]

In which r is the radius, which is half the diameter. In function of the diameter, the area is given by:

[tex]A = 4\pi(\frac{d}{2})^2 = \pi d^2[/tex]

Solving the question:

To solve this question, we have to implicitly derivate the area in function of t. So

[tex]\frac{dA}{dt} = 2d\pi\frac{dd}{dt}[/tex]

Snowball melts so that its surface area decreases at a rate of 3 cm2/min

This means that [tex]\frac{dA}{dt} = -3[/tex]

Find the rate at which the diameter decreases when the diameter is 10 cm.

This is [tex]\frac{dd}{dt}[/tex] when [tex]d = 10[/tex]. So

[tex]\frac{dA}{dt} = 2d\pi\frac{dd}{dt}[/tex]

[tex]-3 = 20\pi\frac{dd}{dt}[/tex]

[tex]\frac{dd}{dt} = -\frac{3}{20\pi}[/tex]

[tex]\frac{dd}{dt} = -0.0477[/tex]

The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.

Answer:

Step-by-step explanation:

Volume formula:

Find r if V = 100 in³:

Answer:

$180

Step-by-step explanation:

$18 × 6

=$180

That's your answer

Answer:

part of it is cutted out show a better picture please ill answer it

Step-by-step explanation:

Answer:

31.5 or 31 1/2

Step-by-step explanation:

The formula for volume of a rectangular prism is lwh or length times width times height.

Multiply the numbers and you get 31.5 or 31 1/2

Hint: It is easier to multiply mixed numbers when converting them to decimals. When you are done just convert it back to a fraction if needed. :)

Answer:

$871.00

Step-by-step explanation:

Answer: 290

Step-by-step explanation:

11/22 is half so the percentage would be 50%.

As we know it's a half you would just have to half or divide 580 by 2.

580÷2=290

Hope this helps :)

Answer:

x=12

.......................

Answer:

1/13

Step-by-step explanation:

there are 10 people that use the gym and track and 10 is 1/13 of 130