Find the volume of the right triangular prism.

A) 120 cubic centimeters

B) 90 cubic centimeters

C) 60 cubic centimeters

D) 150 cubic centimeters

         Rate of interest by which amount $181.25 becomes $1450 in 7 years by continuous compounding will be 29.71%.

         Final amount = [tex]Pe^{rt}[/tex]

         Here, P = Principal amount

                    r = Rate of interest

                    t = Duration of investment

Given in the question,

P = $181.25

t = 7 years

Final amount = $1450

Substitute these values in the expression,

[tex]1450=181.25e^{7r}[/tex]

[tex]e^{7r}=8[/tex]

[tex]\text{ln}(e)^{7r}=\text{ln}(8)[/tex]

[tex]7r=2.07944[/tex]

[tex]r=0.2971[/tex]

[tex]r=29.71\%[/tex]

       Therefore, rate of intereset for the investment is 29.71%.

Learn more about continuous compounding here,

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Answer:

11X+55

Step-by-step explanation:

Multiplicacion

You mean Sigma notation not stigma ^^

Answer:

Look the attachment

Answer:

400

Step-by-step explanation:

3600/9=400

36/9=4

add the zeros back in after

Answer:

400

Step-by-step explanation:

I hope this helps you

Answer:

C

Step-by-step explanation:

Answer:

n > 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Go to algebra calculator it will show the answer.

Answer:

(x-1) (x+8)

Step-by-step explanation:

If you factor this question out correctly, you would get the answer above.

Answer:

the answer should be D.$90

Step-by-step explanation:

54 x .6 = 90

Answer:

i think 10

Step-by-step explanation:

Answer:

whattt do I have to do translate what???

Answer:

The blue image is a translation to the red image

Step-by-step explanation:

Answer:

18a^3b^2/2ab

To simplify the given expression, we apply property of exponents

18/2 = 9

x^m / x^n= x^ (m-n) In division we subtract the exponents

So given expression becomes

9a^2b

The answer has only positive exponents

i think this is what you want?

The simplified exponential notation of the given expression is [tex]9a^2b[/tex].

The given expression is: [tex]\frac{18a^3b^2}{2ab}[/tex]

An expression in the form of [tex]a^pb^qc^r[/tex].. is called exponential expression.

We can write the above expression as:

[tex](\frac{18}{2} )(\frac{a^{3} }{a} )(\frac{b^{2} }{b} )[/tex]

We know that [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]

[tex]\frac{a^{3} }{a} =a^{3-1} =a^{2} \\\frac{b^{2} }{b}=b^{2-1} =b[/tex]

So, [tex](\frac{18}{2} )(\frac{a^{3} }{a} )(\frac{b^{2} }{b} )[/tex] =[tex]9a^2b[/tex]

Hence, the simplified exponential notation of the given expression is [tex]9a^2b[/tex].

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Answer:

1000

Step-by-step explanation:

2×500=1000

hope it helps

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:

18

Step-by-step explanation:

9/2 / 1/4

keep 9/2

Change the operation to multiplication

flip 1/4 into 4 or 4/1

multiply on top and bottom and get 36/2

which 36/2 is 18 and 18 is the answer

Brainliest?

Answer:

25%

Step-by-step explanation:

Multiply the two probabilities.

P(heads)*P(even) = 1/2*1/2 = 1/4

1/4 = 25%

Answer:

Find the perimeter and area of each individual cube then add them up,

Area=length times width

Perimeter=4 times side

Step-by-step explanation:

Answer:

0.5 or 0.45

Step-by-step explanation:

this needs to be 20 characters long

Answer:

ACB=44°

DCE=35°

BCD=101°

Step-by-step explanation:

ACB is a triangle and all triangles are 180 degrees

78+58=136

180-136=44

DCE is also a triangle

85+60=145

180-145=35

a straight line is 180 degrees, we already know what the other two is.

35+44=79

180-79=101

Answer:

-1/3x+2y=4

Step-by-step explanation:

Substitute the negative reciprocal.

-1/3x+2y=4

Answer:

x = 2, y = -4

Step-by-step explanation:

Answer:

Substitution method answer: x=2, y=-4 (2,-4)

Step-by-step explanation:

Hi there!

[tex]\large\boxed{42\pi \text{in or } 131.88 \text{in}}[/tex]

Use the equation C = dπ to calculate the circumference:

d = diameter

C = circumference

C = 42 · π  = 42π in, or 131.88 in (π ≈ 3.14)

Answer:

The answer would be

2. y= x + 6

Answer: The answer would be

2. y= x + 6

Step-by-step explanation:

Answer:

1. 30.48cm

2. 5.77yds

3. 540min

4. 1200cm

5. 8.45qt

6. 168hr

7. 4535.92grams

8. 15yd

9. 32.808ft

Step-by-step explanation:

hope this helps :)

Answer:65

Step-by-step explanation:

Answer:

55.25

Step-by-step explanation:

Answer:

It’s b

Step-by-step explanation:

You can plot the points on the graph to test them out . B was the only one that made a rectangle

Answer:

triangular prism

Answer:

it will be triangular prism