To the nearest tenth, what is the population density of bacteria at the end of the third hour in petri dish A?

(a) The simplified expression is [tex]\[-0.49 \cdot |x|^{18.5} \cdot i\][/tex]. (b) The simplified expression remains [tex]\[15\sqrt{x} + 0.16c^{12}\][/tex].

Let's simplify the given expressions step-by-step.

a) Simplify [tex]\(\sqrt{x} \cdot 0.49x^{18}\) for \(x < 0\)[/tex]

Since [tex]\(x < 0\), \(x\)[/tex] is negative. This affects the interpretation of [tex]\(\sqrt{x}\)[/tex] in the real numbers because the square root of a negative number is not real. However, if we consider complex numbers, we need to include the imaginary unit [tex]\(i\).[/tex]

Given:

[tex]\[\sqrt{x} \cdot 0.49x^{18}\][/tex]

First, let's express [tex]\(\sqrt{x}\)[/tex] in terms of the imaginary unit:

[tex]\[\sqrt{x} = \sqrt{|x|} \cdot i\][/tex]

Next, rewrite \(x^{18}\):

[tex]\[x^{18} = (x^2)^9 \\= |x|^{18} \cdot (-1)^9 \\= -|x|^{18}\][/tex]

Thus, the expression becomes:

[tex]\[\sqrt{|x|} \cdot i \cdot 0.49 \cdot -|x|^{18}\][/tex]

Simplify the coefficients and combine terms:

[tex]\[0.49 \cdot -1 = -0.49\\\sqrt{|x|} \cdot |x|^{18} = |x|^{\frac{1}{2}} \cdot |x|^{18} = |x|^{18.5}\][/tex]

Therefore, the simplified expression is:

[tex]\[-0.49 \cdot |x|^{18.5} \cdot i\][/tex]

b) Simplify [tex]\(15\sqrt{x} + 0.16c^{12}\)[/tex]

Here, [tex]\(x\) and \(c\)[/tex] can be anything.

Given:

[tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]

There are no common factors to combine these terms, so the expression is already simplified. The terms involve different variables and exponents, and cannot be further simplified together.

So the simplified expression remains [tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]

a) The simplified expression is [tex]\[-0.49 \cdot |x|^{18.5} \cdot i\].[/tex]

b) The expression remains as usual given in the question:

[tex]\[15\sqrt{x} + 0.16c^{12}\][/tex]

Answer:

Each ticket cost $13

Step-by-step explanation:

Day 1-- 1 adult and 8 child ticket= Total of 9 tickets = $117

Day 2--6 adult and 8 child ticket= Total of 14 = $182

Brainliest please :)

Answer:

If you mean Area=2 and Area=36units times 2 and Area=64units times 2, then the answer is that A = 64units times 2 would be the largest square.

Step-by-step explanation:

The larger the area, the larger the square. The first square has an area of 2. The second square has an area of 72, and the third square has an area of 128, so the third square is the biggest.

Answer:

Credit Card

Step-by-step explanation:

This is most likely a credit card.

You only need to put a special code in when you're inputting a credit cards pin number.

it is c my dudes yes hes yes

Answer:

It would be 97.50 square deckles.

Step-by-step explanation:

Given:

On the distant plant, Mathology, a sports area covers 7400 yodels².

1 deckle = 75.9 yodels.

Now, to get the square deckles.

As given, 1 deckle = 75.9 yodels.

So, to get the square deckles by using conversion factor:

75.9 yodels = 1 deckle.

7400 yodels² = [tex]7400\div 75.9[/tex]

                       = [tex]97.50\ deckels ^2.[/tex]

Therefore, it would be 97.50 square deckles.

The area is approximately 1.286 deckles².

To convert the area from square yodels to square deckles, we need to use the given conversion factor: 1 deckle = 75.9 yodels.

First, we'll find out how many yodels one square deckle is by squaring the conversion factor.

1. Calculate the area of one square deckle in yodels: (75.9 yodels)² = 5752.81 yodels².

2. Convert the given area of the sports area from yodels² to deckles²: 7400 yodels² ÷ 5752.81 yodels²/deckle² ≈ 1.286 deckles².

Therefore, the sports area covering 7400 yodels² is approximately 1.286 square deckles.

Question:

If m (x) = StartFraction x + 5 Over x minus 1 EndFraction and n(x) = x – 3, which function has the same domain as (m circle n) (x)?

h (x) = StartFraction x + 5 Over 11 EndFraction

h (x) = StartFraction 11 Over x minus 1 EndFraction

h (x) = StartFraction 11 Over x minus 4 EndFraction

h (x) = StartFraction 11 Over x minus 3 EndFraction

Answer:

Option C: [tex]h(x)=\frac{11}{x-4}[/tex] has the same domain as [tex]$(m \circ n)(x)$[/tex]

Explanation:

It is given that [tex]m(x)=\frac{x+5}{x-1}[/tex] and [tex]n(x)=x-3[/tex]

Let us find the domain of [tex]$(m \circ n)(x)$[/tex]

[tex]$\begin{aligned}(m \circ n)(x) &=m(n(x))\\&=m(x-3) \\ &=\frac{(x-3)+5}{(x-3)-1} \\ &=\frac{x+2}{x-4} \end{aligned}$[/tex]

Now, let us equate the denominator equal to zero to determine the domain.

[tex]$x-4=0$[/tex]

     [tex]x=4[/tex]

Thus, the function becomes undefined at the point [tex]x=4[/tex]

Hence, the domain of [tex]$(m \circ n)(x)$[/tex] is [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]

Now, we shall find the function which has the same domain as [tex]$(m \circ n)(x)$[/tex]

Option A: [tex]h(x)=\frac{x+5}{11}[/tex]

The function h(x) has the domain of set of all real numbers [tex]$-\infty<x<\infty$[/tex]

Thus, the interval [tex](-\infty,\infty)[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]

Hence, Option A is not the correct answer.

Option B: [tex]h(x)=\frac{11}{x-1}[/tex]

Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=1[/tex]

Thus, the function h(x) has the domain of [tex]$(-\infty,-1) \cup(-1, \infty)$[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]

Hence, Option B is not the correct answer.

Option C: [tex]h(x)=\frac{11}{x-4}[/tex]

Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=4[/tex]

Thus, the function h(x) has the domain of [tex]$(-\infty, 4) \cup(4, \infty)$[/tex] is the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]

Hence, Option C is the correct answer.

Option D: [tex]h(x)=\frac{11}{x-3}[/tex]

Equating the denominator equal to zero, the function becomes undefined at the point [tex]x=3[/tex]

Thus, the function h(x) has the domain of [tex]$(-\infty,3) \cup(3, \infty)$[/tex] is not the same domain as [tex]$(-\infty, 4) \cup(4, \infty)$[/tex]

Hence, Option D is not the correct answer.

Answer:

It’s C

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The opposite of negative one half is the one half and the opposite of 5/2 is -5/2, or -2.5

Check the picture below.

Answer:

Step-by-step explanation:

Supplementary: ADC

Complementary: AC

Adjacent: ABC

Hope this helps.

Answer:

N

Step-by-step explanation:

Answer:

0.5 50/100 0.50

Step-by-step explanation:

Answer:

x = 70

Step-by-step explanation:

First to make the equation easy, divide 42 by 3 to get what 1/7 of Z equals.

42 / 3 = 14

Now to get 5/7 of Z, just multiply 14 by 5.

14 x 5 = 70

x = 70

Hope this helped.

Answer:

70

Step-by-step explanation:

convert the decimal & solve for Z.

(3/7)Z = 42

(0.4286)Z = 42

Z = 98

Now,

(5/7)Z = ?

putting the value of Z

(0.714) (98) = 70

Answer:

1

Step-by-step explanation:

You need to do the opposite of multiplying which is dividing so divide 6/3= 2 then you divide 2/2 which is 1

Answer:

All of the following fractions work: 1/2, 7/12, 8/12. There are endless possibilities.

Please mark as Brainliest! :)

Answer:

6/12 ; 7/12 ; 8/12

Step-by-step explanation:

³⁾3/4 = 9/12

5/12 < 6/12 < 7/12 < 8/12 < 9/12

Answer:

The scenario that represents a 85% of success on a test is C. 102 out of 120 points

Step-by-step explanation:

Let's analyze which of the scenarios given, represent a 85% of success on a test, this way:

Scenario A:

56 out of 70 points = 56/70 = 0.8

This scenario represents a 80% of success

Scenario B:

78 out of 90 points = 78/90 = 0.867

This scenario represents a 86.7% of success

Scenario C:

102 out of 120 points = 102/120 = 0.85

This scenario represents a 85% of success

The required values are WZ = 13.75 and YZ = 27.

A perpendicular bisector is defined as a line that divides an angle into two equal angles. Draw the given angle first, then cut it in half, and then draw the angle's bisector.

As per question 1,

We have been given that ZX is the perpendicular bisector of WY

YZ = 13.75

13.75 + 13.75 = 27.5

27.5 / 2 = 13.75

WZ = 13.75

As per question 2,

We have been given that ZX is the perpendicular bisector of WY

WZ = 4n - 13 and YZ = n + 17

To find YZ

According to the property of the perpendicular bisector,

WZ = YZ

4n - 13 = n + 17

4n - n = 17 + 13

3n = 30

n = 30/3

n = 10

Substitute the value of n = 10 in YZ = n + 17

So, YZ = 10 + 17 = 27

Thus, the required values are WZ = 13.75 and YZ = 27.

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Answer:

D

Step-by-step explanation:

Note the difference between consecutive terms is constant, that is

22 - 30 = - 8

14 - 22 = - 8

6 - 14 = - 8

To obtain a term in the sequence subtract 8 from the previous term, thus

6 - 8 = - 2

- 2 - 8 = - 10

- 10 - 8 = - 18

The next 3 terms in the sequence are - 2, - 10, - 18 → D

Distributive property: 5y-3y-6

Combine like terms: 2y-6

So there's your answer

To simplify the given expression, distribute the -3 to both terms inside the parentheses, then combine like terms.

To simplify the expression 5y - 3(y + 2), we need to follow the order of operations, which is parentheses first, then multiplication and division, and finally addition and subtraction.

First, distribute the -3 to both terms inside the parentheses:

5y - 3 * y - 3 * 2

Now, simplify each term:

5y - 3y - 6

Combine like terms:

2y - 6

This is the simplified form of the given expression.

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Answer:

225

Step-by-step explanation:

Total number of students =300

75% have had algebra

Number of students that have had algebra will be

= 75%/100% x 300

= 0.75 x 300

= 225

So, 225 of the 300 students have had algebra

Answer:225 students

There are 2 simple ways to get the answer.

Answer:

The length of the rectangle is 70 cm

The width of the rectangle is 32 cm

Step-by-step explanation:

Given:

perimeter of the rectangle  =   204 feet

Its length is six feet longer that twice its width

To Find:

The  dimensions of the rectangle = ?

Solution:

Let the width of the rectangle be x

Then its length  is six feet longer that twice its width.

That is length  = 6 + 2x

Now we know that the perimeter of the rectangle is

perimeter =  2(length + width)

204 = 2(6+2x+x)

204 = 2(6+3x)

204 = 12 +6x

204 - 12 = 6x

192 =  6x

x =[tex]\frac{192}{6}[/tex]

x = 32

Thus the width is 32 cm

Its length is  

=6 + 2x

=6 + 2(32)

=6 + 64

= 70 cm

The height of the liquid in the new cylinder is about 1.72 cm

Step-by-step explanation:

The formula of the volume of a cylinder is V = πr²h, where

∵ The volume of the liquid = 36 cm³

∵ The liquid is poured into another cylinder with radius 3 cm

∵ The radius of the base = 3 cm

- To find the height of the liquid in the new cylinder equate the rule

   of the volume by 36

∵ V = πr²h

∴ π(3)²h = 36

∴ 9πh = 36

- Divide both sides by 9π

∴ h = 1.273239545

The height of the liquid in the new cylinder is about 1.72 cm

Learn more:

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Answer: Yes it is

Step-by-step explanation: In mathematics, a function is a relation between sets that associates to every element of a first set exactly one element of the second set

Answer:  

yes

hope this helps

Answer:

6/10,9/15,12/20,15/25

Step-by-step explanation:

Step-by-step explanation:

5-in 5-in five interest answer

Answer:

If you can't afford a new laptop computer, then you haven't got 400$.

Step-by-step explanation:

The contrapositive is:

If A implies B then not B implies not A.

The probability of drawing two black balls from a bag containing 5 white and 5 black balls is 2/9 (approximately 0.22) if you do not replace balls after drawing them, and 1 if you replace any white balls that are drawn.

This question relates to the concept of probability in mathematics. The total number of balls in your bag is 10 (5 white balls and 5 black balls). If you want to draw two black balls, the probability will change based on the conditions of the question.

a) For the first draw, there are 5 black balls out of a total of 10 balls, so the probability is 5/10 or 0.5. If a black ball is drawn in the first draw, there are now 9 total balls and 4 of them are black, so the probability for the second black ball is 4/9. For both balls to be black, multiply the individual probabilities: (5/10) * (4/9) = 20/90 = 2/9 approximately equal to 0.22.

b) If you draw two balls and put back any white balls, then redraw until you have two balls, you are essentially ensuring that white balls are not counted. In this case, every draw will either be a black ball or a redraw with a white ball, so the probability is essentially 1 that you will eventually draw a black ball. Therefore, the probability of drawing two black balls using this method is (1/1) * (1/1) = 1.

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[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1[/tex]

Solution:

Given trignometric expression is:

[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x}[/tex]

We have to evaluate the above expression

Let us use the trignometric identities

[tex]sin^2x + cos^2x = 1[/tex]

Also, use another trignometric identitiy

[tex]1 + cot^2x = cosec^2x[/tex]

Therefore, upon rearranging we get,

[tex]cot^2 x -cosec^x = -1[/tex]

Apply these two identities in given expression

[tex]\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = \frac{1}{-1}\\\\\frac{cos^2x + sin^2x}{cot^2x - cosec^2x} = -1[/tex]

Thus value of given expression is -1

Answer:

- 13

Step-by-step explanation:

f(1) = 7

f(n) = f(n − 1) – 4

f(₂) = f(1) – 4 = 7 - 4 = 3

f(₃) = f(₂) – 4 = 3 - 4 = -1

f(₄) = f(3) – 4 = (-1) - 4 = - 5

f(₅) = f(₄) – 4 = (- 5) - 4 = - 9

f(₆) = f(₅) – 4 = (- 9) - 4 =  - 13

The value of f(6) is -13, calculated based on the provided recursive formula where each term is four less than the previous.

We are given that f(1) = 7, and the recursive equation for n is f(n) = f(n − 1) – 4. Since the equation shows that each next term is four less than the previous one, we can calculate the following iterations:

So, the value of f(6) is -13.

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Answer: Molly will have to save $10 each week for 9 weeks to get $189.

Step-by-step explanation:

Start at $99, count $10 every week until you get $189. Your answer is 9 weeks.

Answer:

936

Step-by-step explanation:

1 x 12 x 13 x 6= 936

Here is some evidence

Answer:36

Step-by-step explanation: L•w/2 = A for triangular