Need help with this, the answer is 61 but I need the work for it.

The ordered pair does not lie on the graph of the exponential function

is (12, 0).

Option A is the answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To check whether an ordered pair lies on the graph of the exponential function f(x) = [tex]3(1/4)^x,[/tex]

We need to substitute the values of x and y into the function and see if the equation holds true.

A. (12, 0)

Substituting x = 12 and y = 0 into the function, we get:

[tex]f(12) = 3(1/4)^{12} = 0.000002861[/tex]

This does not equal y = 0, so (12, 0) does not lie on the graph of the function.

B. (-2, 48)

Substituting x = -2 and y = 48 into the function, we get:

[tex]f(-2) = 3(1/4)^{-2} = 48[/tex]

This does not equal y = 48, so (-2, 48) does lie on the graph of the function.

C. (2, 3/16)

Substituting x = 2 and y = 3/16 into the function, we get:

[tex]f(2) = 3(1/4)^2 = 3/16[/tex]

This equals y = 3/16, so (2, 3/16) does lie on the graph of the function.

D. (0, 3)

Substituting x = 0 and y = 3 into the function, we get:

[tex]f(0) = 3(1/4)^0 = 3[/tex]

This equals y = 3, so (0, 3) does lie on the graph of the function.

Therefore,

The ordered pair does not lie on the graph of the exponential function

is (12, 0).

Learn more about functions here:

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Answer: d

Step-by-step explanation:

You add all of his scores up and divide them by how many numbers there are which 3+1+ -3+ -2+ -4 equals -5 and you divide them by the five numbers which gives you one

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:

Volume formula:

Find r if V = 100 in³:

The answer is on the picture.

Answer:

try

Step-by-step explanation:

try solving it on ur own or take a educated guess

Answer:

360 - 169 equals 191

Step-by-step explanation:

191

9 centimetres is probably most accurate

Answer:

36cm

Step-by-step explanation:

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:

8 × [tex]x[/tex] = 12 x 18

8[tex]x[/tex] = 216

[tex]x[/tex] = 27cm

Step-by-step explanation:

I use that formula because they are similar triangles! :)

Hope this helps!

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:

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:

x=12

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

Answer:

i guess it is 54-11+7 , the second one

Answer:

The second one doesn't match.

Answer:

I believe the answer is 5.

Answer: x=-1

Step-by-step explanation:

Answer:

1/13

Step-by-step explanation:

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

Answer:

10 units^2

Step-by-step explanation:

Answer: 4 frames

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

When one component fails, so does the other one.

a + b = P

0.1 + 0.2 = 0.3

Your answer would be 0.3 or 30%.

Hope this helps. Have a nice day.

Answer:

the answer is place value

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: 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