A Petri dish is filled with 250 bacterial cultures. The number of bacteria in the dish triples every hour.



a. Write a recursive and an explicit formula to represent the sequence that models the scenario.



Explicit formula:

Recursive formula:



b. Predict the number of bacterial cultures in the dish after 8 hours. Explain your reasoning.



c. Does this sequence represent a function? Explain your reasoning.

Answer:

5 1/2 cups

Step-by-step explanation:

I actually just did this question for someone else.

you have to do 11/2

to check your answer just use the inverse operation and flip it to make it 2x5.5=11

Answer:

0.00000343x

Step-by-step explanation:

here ya go

Answer:

\( \frac{3}{2} \)

Step-by-step explanation:

9/4 ÷ 3/2

9/4 × 2/3

= 18/12

÷ 6

=> 3/2

Hope it helps you

The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A

Wood 1:

Total = Length of each × Number of pieces

= 2 5/8 × 6

= 21/8 × 6

= 126 / 8

= 15 3/4 meters

Wood 2:

Total = Length of each × Number of pieces

= 1 1/5 × 3

= 6/5 × 3

= 18/5

= 3 3/5 meters

Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters

= 126/8 + 18/5

= (630+144) / 40

= 774/40

= 19 14/40

= 19 7/20 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A

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Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

x=–2

Step-by-step explanation:

x-8=-10

x=-10-8

x=–2

Answer:

-8= -10

, = -10+8

, = -2

\(t_{2(n+k)+1} \neq t_{2n+1}\), which contradicts the assumption that the sequence is periodic. Therefore, the sequence is not periodic.

A periodic sequence is a sequence of numbers that repeats itself after a certain fixed number of terms, called the period of the sequence. In other words, a periodic sequence is a sequence that has a repeating pattern.

Another example of a periodic sequence is the Fibonacci sequence modulo n, where n is a positive integer. This sequence is obtained by taking the Fibonacci sequence and computing each term modulo n. For example, the Fibonacci sequence modulo 5 is {0, 1, 1, 2, 3, 0, 3, 3, 1, 4, 0, 4, 4, 3, 2, 0, 2, 2, 4, 1, 0, 1, 1, 2, 3, ...}. This sequence has a period of 20, since it repeats itself every 20 terms.

Let's first find the first few terms of the sequence:

t₀ = 1

t₁ = 1 - t₀ = 1 - 1 = 0

t₂ = t₁ = 0

t₃ = 1 - t₂ = 1 - 0 = 1

t₄ = t₂ = 0

t₅ = 1 - t₄ = 1 - 0 = 1

t₆ = t₃ = 1

t₇ = 1 - t₆ = 0

t₈ = t₄ = 0

t₉ = 1 - t₈ = 1

t₁₀ = t₅ = 1

t₁₁ = 1 - t₁₀ = 0

t₁₂ = t₆ = 1

t₁₃ = 1 - t₁₂ = 0

t₁₄ = t₇ = 0

t₁₅ = 1 - t₁₄ = 1

t₁₆ = t₈ = 0

t₁₇ = 1 - t₁₆ = 1

t₁₈ = t₉ = 1

Looking at these terms, we can see that the sequence is not periodic because it does not repeat in a fixed cycle. However, we can also prove this more rigorously by contradiction.

Suppose the sequence is periodic with period length k, so that tₙ = \(t_{n+k}\) for all n. Then we must have:

\(t_{2n} = t_{n} = t_{n+k} =t_{2(n+k)} \\t_{2n+1} =1-t_{n} = 1-t_{n+k} = t_{2(n+k)+1}\)

Let m be the smallest odd integer such that \(t_{m}\) = 1. Then we can write m as m = 2n+1 for some n, and we have:

\(t_{2n+1} = 1-t_{n} =1\\t_{2(n+k)+1} = 1-t_{n+k}\)

But this means that \(t_{2(n+k)+1} \neq t_{2n+1}\), which contradicts the assumption that the sequence is periodic. Therefore, the sequence is not periodic.

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The length of y in the triangle is 18.55 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The side y of the triangle can be found using sine law.

Therefore,

a / sin A = b / sin B = c / sin C

Applying the sine law,

y / sin 106 = 15 / sin 51

cross multiply

y sin 51° = 15 sin 106°

divide both sides by sin 51°

y sin 51° / sin 51° = 15 sin 106° / sin 51°

y = 15 sin 106° / sin 51°

Therefore,

y = 15 × 0.96126169593 / 0.77714596145

y = 14.4189254391 / 0.77714596145

y = 18.5536589719

Hence,

y = 18.55 units

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Answer:

Positive 4

Step-by-step explanation:

4 squared is equal to 16 as 4 x 4 = 16. However, if it was -4 squared, it would equal -16.

Given:

Three numbers are 42, 90 and 144.

Required:

What is the highest common factor

Required:

We know the factors of 42

Answer:  42, 90 and 144.

Step-by-step explanation:

Figure O is reflected followed by a translation of 4 units in the left direction.

Given that:

Figure O and Figure P are shown on the graph.

The translation does not change the shape and size of the geometry. But changes the location.

Figure O is translated leftward by 4 units.

The reflection does not change the shape and size of the geometry. But flipped the image. A reflection is a transformation that maps every point P over a line such that the line segment PP' will intersect the line of reflection at a right angle.

The translated figure O is reflected across the x-axis.

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The surface area of the figure is approximately 997.5π cm².

We have,

The figure has two shapes:

Cone and a semicircle

Now,

The surface area of a cone:

= πr (r + l)

where r is the radius of the base and l is the slant height.

Given that

r = 15 cm and l = 19 cm, we can substitute these values into the formula:

= π(15)(15 + 19) = 885π cm² (rounded to the nearest whole number)

The surface area of a semicircle:

= (πr²) / 2

Given that r = 15 cm, we can substitute this value into the formula:

= (π(15)²) / 2

= 112.5π cm² (rounded to one decimal place)

The surface area of the figure:

To find the total surface area of the figure, we add the surface area of the cone and the surface area of the semicircle:

Now,

Total surface area

= 885π + 112.5π

= 997.5π cm² (rounded to one decimal place)

Therefore,

The surface area of the figure is approximately 997.5π cm².

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The calculated value of x at g(x) = 2 is x = 2.5

from the question, we have the following parameters that can be used in our computation:

f(x) = 3x - 1

Also, we have

g(x) = 2x - 3

When g(x) - 2, we have

2x - 3 = 2

So, we have

2x = 5

Divide by 2

x = 2.5

Hence, the value of x at g(x) = 2 is x = 2.5

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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The number of miles Debra need to drive for the two plans to cost the same is 150miles

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Initial fee of first plan=$47.96

Additional fee of first plan=$0.19 per mile

Initial fee of second plan=$53.96

Additional fee of second plan=$0.15 per mile

Now,

Let's call the number of miles Debra drives "m". Then the cost of the first plan would be:

47.96 + 0.19m

And the cost of the second plan would be:

53.96 + 0.15m

To find the number of miles at which the two plans cost the same, we can set these expressions equal to each other and solve for "m":

47.96 + 0.19m = 53.96 + 0.15m

0.04m = 6

m = 6 / 0.04

m = 150

Therefore, by  the unitary method answer will be 150 miles.

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Answer:

-65a -21 "that is the simplified version"

Answer:

-65a - 21

Step-by-step explanation:

7 ( -9a - 3 ) -2a

Distribute, multiply every term in the parenthesis by the term right outside of the parenthesis,

7 ( -9a - 3 ) - 2a

-63a - 21 - 2a

Simplify

-65a - 21

The given line AB is having endpoints A(-3,5) & B(1,-1).

To find the equation of line AB it can be written as\(y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\\)

Substituting the given points

\(y-(-1)=(x-1){(5-(-1))/(-3-1)}\\\)

y=-(3/2)x+1/2

For two perpendicular lines \(m_1*m_2=-1\)

Therefore, (-3/2)*\(m_2\)=-1

or \(m_2\) = 2/3

Also, the midpoint of AB will be \({1-(-3)}/2, {5-(-1)}/2\) = (2,3).

The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows

(y-3)=(2/3)(x-2)

3y-9=2x-4

3y=2x+5 is the required equation of the line.

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Answer:

x = 6/5

x = 1.2

x = 1 1/5

Step-by-step explanation:

The answers above are all the same, but in different forms.

The steps to getting x:

1. subtract 12 from the parenthesis which leaves us with 5x = 6

2. Then we want to divide 5 from x which gives up our answer 5x/5 = 6/5

Remember whatever you do on one side it has to be done on the other, hence the equal sign

The factor of \(6x^{2}y+8-30y-40\) is 2 ( \(3x^{2}y-15y-20\) ).

The factor is a number or quantity by which a given number, quantity, or expression is multiplied to produce another number, quantity, or expression. Factors are usually whole numbers, but they can also be expressions or fractions. Factors are used to simplify or solve equations and expressions. Factors can also be used to determine the greatest common factor (GCF) of two or more numbers or expressions.

The first step is to factor out the greatest common factor (GCF), which in this case is 2. The GCF of \(6x^{2}y+8-30y-40\) is 2. Once the GCF is factored out, the expression can be written as 2(\(3x^{2}y-15y-20\)). Finally, the remaining factors can be combined to get the final factor of 2(\(3x^{2}y-15y-20\)).

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Answer:

c.) 8/3

Step-by-step explanation:

the two sides must weigh the same, or 12 grams.

the weights labelled x combined with the 4 grams weight should equal 12 grams.

the equation solved for x would be:

3x + 4 = 12

3x = 8

x = 8/3

To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =\(A1 * (160/60)^(3-1)\)

Simplifying this equation, we have:

\(60 = A1 * (8/3)^260 = A1 * (64/9)\)

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =\((67.5/8) * (160/60)^(z-1)\)

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

5. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

Where r the statements?

Step-by-step explanation:

The equation X^2/2 - 8 = 2X - 2 has two solutions, X = 6 and X = -2. These are the values of X that satisfy the equation and make both equations Y = X^2/2 - 8 and Y = 2X - 2 intersect on the graph.

To find the solutions to the equation X^2/2 - 8 = 2X - 2, we need to set the two equations equal to each other and solve for X.

The equation is:

X^2/2 - 8 = 2X - 2

To simplify the equation, let's multiply both sides by 2 to eliminate the fraction:

X^2 - 16 = 4X - 4

Next, we rearrange the equation to have all terms on one side:

X^2 - 4X - 12 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring in this case:

(X - 6)(X + 2) = 0

Setting each factor equal to zero gives us two possible solutions:

X - 6 = 0 --> X = 6

X + 2 = 0 --> X = -2

So the solutions to the equation X^2/2 - 8 = 2X - 2 are X = 6 and X = -2.

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Answer:

See below

Step-by-step explanation:

Using the two pairs of (a, p) to determine the function:

The function would be:

Slope is:

p-intercept:

So the function is:

(a)

(b) Slope is negative, indicating the lower probability at greater age. P-intercept of 120.5 is of the non-real case as for zero age it gives more than 100% probability.

(c) The domain needs restriction in line with law, so minimum age and maximum to be determined in order not to have unrealistic outcome. It should be ok between 18 and 48.

(d) The values at given points:

Answer:

Step-by-step explanation:

You take items out of a square root if you have a pair of numbers or if you know the square root.  

\(\sqrt{48b^{7} }\)=\(\sqrt{4*4*3*bbbbbbb}\)

So I know the \(\sqrt{4}\)=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3

Now for the b's for every pair there are, you can take that out.  There are 3 pairs of b's so b³ is outside and one b is left inside.

Answer:

4b³\(\sqrt{3b}\)

The points representing the x-intercepts of the function g(x) graphed in this problem are given as follows:

(−5, 0) and (−4, 0).

On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

On the graph of the function, these values are the values of x for which the graph crosses the x-axis, hence the intercepts are given as follows:

Then the points are given as follows:

(−5, 0) and (−4, 0).

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