Simplify (b^9)^3


(I use ^ to symbolize to the power of)

A) The equation for the growth of bacteria over time is : n(t) = 27(   [tex]e^{25t}[/tex])

B) The number of bacteria the would be in 5 minutes 1 hour is :

n(5mins) = 215.055 ,  n(1) = 1944132282109.422

C) The time it will take for the bacteria to reach a population of 10,000 is : t = 0.237 hours

Applying the mathematical growth and decay modelling

a. n(t) = [tex]n_{0}[/tex] [tex]e^{rt}[/tex]

[tex]n_{0}[/tex] = initial amount of bacterial

[tex]e^{rt}[/tex] = exponent

r = rate

t = time

n(t) = 27(   [tex]e^{25t}[/tex])

b. for 5 minutes

converting 5 minutes to hours; we divide by 60 minutes

[tex]\frac{5}{60}[/tex] = 0.083 hour

n(5 mins) = 27(   [tex]e^{25t}[/tex])

n(5 mins) = 27(   [tex]e^{25 * 0.083}[/tex])

n(5 mins) = 27(   [tex]e^{2.075}[/tex])

n(5mins) = 27(   7.965)

n(5mins) = 215.055

For 1 hour we have

n(1) = 27(   [tex]e^{25t}[/tex])

n(1) = 27(   [tex]e^{25 * 1}[/tex])

n(1) = 27(   [tex]e^{25}[/tex])

n(1) = 27 * (72004899337.386)

n(1) = 1944132282109.422

c. How long will it take for the bacteria to reach a population of 10,000?

10000 = 27(   [tex]e^{25t}[/tex])

[tex]\frac{10000}{27}[/tex] = (   [tex]e^{25t}[/tex])

370.370 = (   [tex]e^{25t}[/tex])

㏑ (370.370 ) = ㏑ (   [tex]e^{25t}[/tex])

5.915 = 25t

[tex]\frac{5.915}{25}[/tex] = t

t = 0.237 hours

In conclusion this type of question can be done by mathematical modelling

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Answer: False

Step-by-step explanation:

The lower case letter denotes a relation, not a function

Answer:

-1

Step-by-step explanation:

g(2) = (2) - 3(2) + 4(2) - 5

g(2) = 2 - 6 + 8 - 5

g(2) = 2 - 6 + 3

g(2) = 2 - 3

g(2) = -1

Answer:

for L 2, 2 and for LM it is -8,8

Step-by-step explanation:

easy

Answer:

8.5 × 10-2

Step-by-step explanation:

I believe this is it

The volume of the prism given its dimensions is equal to 160 cubic units.

The given prism is made up of two prisms. The volume of the prism is the volume of the two shapes.

Volume = 80

Volume = 80

Volume of the prism = 80 x 2 = 160 cubic units.

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Answer: No solution

Step-by-step explanation:

       These two equations have parallel slopes and therefore no solution.

-> See attached for graph. Since there is no point of intersection, there is no solution.

Answer:

30 quarts

Step-by-step explanation:

4 quarts = a gallon

4 quarts +2 quarts  = 6 quarts

5 containers*6 quarts(each)

5*6=30

Answer:

0.33=33%

0.07=70%

5.43=543%

1.5%=1/5

3%=3

38%=3/8

Step-by-step explanation:

hope this helps if not please let me know

Answer: 1/4

Step-by-step explanation:

ez

Answer:

Here,

Now,

Step-by-step explanation:

There two solutions. X can be zero cause anything divided by zero is undefined.

When dealing with positive numbers:

[tex]least \: to \: greatest \: for \: \: x \geqslant 1[/tex]

[tex] - \frac{1}{x} < \: \: 1 - x \: < \: \: x - 1 \: \: < x[/tex]

When dealing with negative numbers:

[tex]least \: to \: greatest \: for \: \: x < 0[/tex]

[tex] - x \: < x - 1 \: < - \frac{1}{x} \: < 1 - x[/tex]

Answer:

56

Step by step explanation:

[tex]62+x-x^2\\\\\text{When x = 3}\\\\62+3 -3^2 = 62+3-9 = 65-9 = 56[/tex]

Answer:

Odd: f(-x) = -f(x)

Step-by-step explanation:

Odd: f(-x) = -f(x)

f(-1) = 5

-(f(1)) = 5

Answer:

Give options :/

Step-by-step explanation:

Step-by-step explanation:

quotient is a result of the number

divided by a number

and if u want to divided with zero so division are not exis

can't divided by 0

The Quotients of the given expression (2m + 4) / 8 divided by (m + 2)/6 would be 3/2.

Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

(2m + 4) / 8 divided by (m + 2)/6

= (2m + 4) / 8 ÷ (m + 2)/6

= (2m + 4)/8 x (6 / (m + 2) )

= (m + 2)/4 x 6/(m + 2)

= 6/4

= 3/2

Thus, the quotients will be 3/2.

Learn more about Quotients;

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From the computation below, the area of the label is 707 Inches.

This calculation is carried out using the theorem of the area of curved shapes.

The formula for the Curved Surface Area of a Cylinder is given as:

                                               2 [tex]\pi[/tex] rh

                                              =  2 [tex]\pi[/tex] x 7.5 x 15.

This assumes that the label also ends at an equal distance from the top of the lid.  Hence 15in = 20 - (2.5 x2);

Recall that [tex]\pi[/tex] =  22/7, hence

= 2 x (22/7) x  7.5 x 15

= 707.142857143

Approximately, this equals; 707 Inches.

Hence, the area of the label = 707 inches.

Notice that the question is incomplete. From inference, however, the general calculation above contains the principles for calculating the area of a label.

Learn more about Surface Area of Curved Shapes at:
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Answer:

the total mass of the products is equal to the total mass of the reactants

Step-by-step explanation:

The sum of the relative formula masses of the reactants is equal to the sum of the relative formula masses of the products.

Answer:

the product

= (x+4)(x+5)

= x^2 + 5x + 4x +20

= x^2 + 9x + 20
hope this helps!!!

Answer:

Step-by-step explanation:

Applying Distributive Property :

Combining Like-Terms :

Answer:

530 m²

Step-by-step explanation:

First of all we need to label the missing sides ,please check the figure I provided for that :

x = 37 - (10+ 15) = 37 - 25 = 12

z = 10

y = 2 × 10 = 20

The shade does area = area of the whole rectangle − the white area

                                    = 37 × 20 − [ (15×20)÷2 + (10×12)÷2 ]

                                    =  740      − [    150        +      60       ]

                                    = 740.      −               210

                                    = 530

Answer:

0.0018

Step-by-step explanation:

Answer:

Slope of the line DV = -1

Step-by-step explanation:

Let point D (-5, 1) be [tex](x_{1}, y_{1})[/tex]

Let point V (-1, -3) be [tex](x_{2}, y_{2})[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Plug in the appropriate values,

[tex]m = \frac{-3-1}{-1-(-5)} = \frac{-4}{4} = -1[/tex]

slope equals -1

I'(-4, -3)     J'(-4, -2)

K'(-2, -2)     L'(0, -4)    

[tex]I(0,-3)\rightarrow I'(0-4,-3)\rightarrow I'(-4,-3)\\ J(0,-2)\rightarrow J'(0-4,-2)\rightarrow J'(-4,-2)\\ k(2,-2)\rightarrow k'(2-4,-2)\rightarrow k'(-2,-2)\\ L(4,-4)\rightarrow L'(4-4,-4)\rightarrow L'(0,-4)\\ \{Conversion\ principle\}[/tex]

I hope this helps you

:)

Model mural::

L*W = 0.3 sq. ft

--------------

Actual mural::

(5L)(5W) = 25*LW = 25*0.3 = 7.5 sq ft.

Answer:

39.37 in

Step-by-step explanation: