the number of bacteria in a certain sample increases according to the following function, where is the initial number present, and is the number present at time (in hours). how many hours does it take for the size of the sample to double? do not round any intermediate computations, and round your answer to the nearest tenth.

The value of the function when x is -2 is -12. Therefore, the correct option is b.

Given the function f(x)=3.25x + c. Also, f(2)=1. Substitute the values in the given function to find the value of c. Therefore,

f(x)=3.25x + c

f(x=2) = 3.25(2) + c

1 = 3.25(2) + c

1 = 6.5 + c

1 - 6.5 = c

c = -5.5

Now, if the values f(-2) can be written as,

f(x)=3.25x + c

Substitute the values,

f(x=-2) = 3.25(-2) + (-5.5)

f(x=-2) = -6.5 - 5.5

f(x=-2) = -12

Hence, the correct option is b.

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The given question is incomplete, the complete question is below:

A function is defined as f(x)=3.25x+c. If f(2)=1, what is the value of f(-2)? (a)-32 (b) -12 (c) 12 (d) 32 (e) 52

For question 3, the unique solution is guaranteed if yo = 3. For question 5, the solution is lnx + In(y-x) = c. For the last question, the solution is y = x - 1 + ce^(-x).

For question 3, the initial value problem y' = √(x²-9), y(x) = yo has a unique solution guaranteed by Theorem 1.1 if yo = 3. The reason is that the square root expression inside the differential equation is only defined when x²-9 is non-negative. Since the square root of a negative number is undefined in the real number system, yo cannot be any value that results in x²-9 being negative. Therefore, yo = 3 is the only valid choice.

For question 5, the given differential equation (x-2y)dx + ydy = 0 can be solved by integrating. By integrating the left-hand side of the equation, we obtain the solution lnx + In(y-x) = c, where c is the constant of integration. This is the correct answer (b).

For the last question, the differential equation y' + y = x can be solved using the method of integrating factors. Multiplying both sides of the equation by e^x, we get e^x * y' + e^x * y = xe^x. The left-hand side can be rewritten as (e^x * y)' = xe^x. Integrating both sides with respect to x, we have e^x * y = ∫xe^xdx = x * e^x - e^x + c. Dividing both sides by e^x, we get y = x - 1 + ce^(-x). Therefore, the correct answer is (b), y = x - 1 + ce^(-x).

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we have

7y-1 =-2(4-2x)

convert to slope intercept form

y=mx+b

so

isolate the variable y

Adds 1 both sides

7y-1+1=-8+4x+1

simplify

7y=4x-7

divide by 7 both sides

7y/7=(4/7)x-7/7

Answer:

None

Step-by-step explanation:

9/13 = 0.6923076923076923 = 0.692

So they are both equally the same since they have the same value. On is not greater than the other

Hope this helped!

Have a supercalifragilisticexpialidocious day!

In total, Menaha traveled 97km 1000m (97.1km).

Distance is a numerical measurement of how far apart two objects, points, or places are in space. Distance can be measured in linear units such as meters, kilometers, feet, miles, etc. It can also be measured in angular units such as degrees or radians.

Distance can also refer to the space between two points in time, such as the time between two events. Distance can be used to measure physical distance, time, or even emotional distance.
To calculate this, the two distances must be added together.
The train distance is =86km 520m (86.52km)

and the car distance is =11km 480m (11.48km).
When added together, =86km 520m+11km 480m = 97.52km.
However, since the distances are measured in km and m,
it is necessary to convert the measurements into a single unit of measurement.
To do this, the measurements must be converted into metres.
The train distance is 86,520 metres

And the car distance is 11,480 metres.
When added together,

the total distance is 97,000 metres (97km).

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Answer:

$150

Step-by-step explanation:

we can make a ratio

20/100=30/x

cross multiple

20x=30(100)

20x=3,000

/20     /20

x=150 hopes this helps

Answer:

1. A

2. A

Step-by-step explanation:

Question 1

1 Factor out the common term 2.

2(x^2+6x+9)=0

2 Rewrite x^2+6x+9 in the form a^2+2ab+b^2a, where a=x and b=3.

2(x^2+2(x)(3)+3^2)=0

3 Use Square of Sum: (a+b)^2=a^2+2ab+b^2(a+b).

2(x+3)^2=0

4 Divide both sides by 2.

(x+3)^2=0

5 Take the square root of both sides.

x+3=0

6 Subtract 3 from both sides.

x=-3

Question 2

1 Move all terms to one side.

2r^2-5r-3=0

2 Split the second term in 2r^2-5r-3 into two terms.

2r^2+r-6r-3=0

3 Factor out common terms in the first two terms, then in the last two terms.

r(2r+1)-3(2r+1)=0

4 Factor out the common term 2r+1.

(2r+1)(r-3)=0

5 Solve for r.

r=-1/2,3

The player's average profit per game in the long run will be -$0.25.

To calculate the average profit per game, we need to determine the probabilities of each outcome and multiply them by the corresponding profit or loss.

When flipping a fair coin twice, there are four possible outcomes: no heads (Tails-Tails), one head (Tails-Heads or Heads-Tails), or two heads (Heads-Heads). Each outcome has a 1/4 probability of occurring because the coin is fair.

For no heads, the player loses $1 because they are charged to play the game. So the profit is -$1.

For one head, the player receives $1. Since there are two ways to get one head, the total profit for this outcome is 2 * $1 = $2.

For two heads, the player receives $5. So the profit for this outcome is $5.

Now, we calculate the average profit per game by multiplying each profit by its corresponding probability and summing them up:

(-$1 * 1/4) + ($2 * 1/4) + ($5 * 1/4) = -$0.25

Therefore, the average profit per game in the long run is -$0.25.

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Answer:

6, 8 and 10  and  -2, 0, 2

There are two roots x = -2 and 6,    

but the since I don't believe 0 is an even number the answer is 6, 8 and 10

I was incorrect according to G0ggle zero is an even number so another answer is  -2, 0, 2

Step-by-step explanation:

read the question and convert the English to mathematics

x, y and z    even consecutive number

y = x+2

z = y+2 = x+4

and

xyz = x³ + y² + 2z²                                   substitiute x terms  in for y and z

x(x+2)(x+4)  = x³ + (x+2)² + 2(x+4)²           solve for x by graphing on DEMOS

                                                                 x = -2, 6  solved algebraically below

x = -2   y=0   z=2

x = 6    y=8   z=10

Checked both answers

xyz = x³ + y² + 2z²

-2(0)2 = -8 + 0 + 8                  when x = -2

   0   =  0

and

6(8)(10)  =  6³ + 8² +2(10)²      when x = 6

   480   =  216+64+200

             =  480

x(x+2)(x+4)  = x³ + (x+2)² + 2(x+4)²                           solved algebraically

(x²+2x)(x+4)   = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32

x³ + 6x² + 8x = x³ + 3x² + 20x + 36

      3x² - 12x - 36 = 0         factor out the 3

      3[x² - 4x - 12] = 0

       3(x+2)(x-6) = 0     x = -2 and -12

Answer:

56

Step-by-step explanation:

to find the answer, divide 42 by 6/8

42 x 8/6 = 56

Answer:

The Great Western Trail = 4,455 miles

Step-by-step explanation:

The Iditarod Trail = 1,025 miles long

The Great Western Trail is 355 miles longer than 4 times the length of the Iditarod Trail.

The Great Western Trail = (4 × 1,025) miles + 355 miles

= 4,100 miles + 355 miles

= 4,455 miles

The Great Western Trail = 4,455 miles

Answer: here my answer IIn The picture .

Step-by-step explanation:

The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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To enumerate all the numbers between 60 and 70 that are divisible by both 4 and 5, we need to check each number in that range and see if it satisfies both conditions.

The answer to the question "Enumera toate numerele cuprinse intre 60 si 70 care pot fi impartite exact la 4 si la 5" is:
Numerele cuprinse intre 60 si 70 care pot fi impartite exact la 4 si la 5 sunt 60.

The explanations are given as follows:
Let's start with the number 60. We check if 60 is divisible by 4 by dividing it by 4 and seeing if the remainder is 0. In this case, 60 divided by 4 gives us a remainder of 0, so it is divisible by 4. Next, we check if 60 is divisible by 5 in the same way. Again, 60 divided by 5 gives us a remainder of 0, so it is divisible by 5 as well. Therefore, 60 satisfies both conditions and can be included in our list.
Moving on to the next number, 61, we repeat the same process. We divide 61 by 4 and 61 by 5 and check if the remainders are 0. If any remainder is not 0, then the number is not divisible by both 4 and 5. In this case, 61 is not divisible by either 4 or 5, so we exclude it from our list.
We continue this process for each number between 60 and 70. The numbers that satisfy both conditions, being divisible by 4 and 5, are included in our final list.
Based on this process, the number between 60 and 70 that can be divided exactly by both 4 and 5 is 60

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Answer:

\( \frac{p}{3} = 5\)

p = 15

\( \frac{15}{3} = 5\)

Answer:

4 mins

Step-by-step explanation:

Tank 1: 24

Tank 2: 8

Tanks 3: 12

So you add them all up to equal the "work". which is one. Looks like this:

*** x/24 + x/8 + x/12 = 1 ***

multiply all by 24

x+3x+2x=24

add like terms

6x=24

divided by 6

x=4

So x=4 minutes.

:)

*** You could check by putting 4 into x by the * (stared) problem

Answer:

x = 30

Step-by-step explanation:

2x - 6

-----------  =  9

    6

2x - 6

-----------  =  9(6)

    6(6)

2x - 6 = 54

     +6    +6

2x = 60

÷2    ÷2

x = 30

I hope this helps!

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

it is suggested that students allocate around 2-3 hours of study time per credit hour per week for a college-level course. However, the actual study time required may vary based on individual learning styles, prior knowledge, and the specific requirements set by professors or institutions.

Let's apply this general guideline to your scenario:

One three-credit class that is less demanding:

Assuming 2-3 hours of study per credit hour, for a three-credit class, you would ideally spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Two three-credit classes that are typically demanding:

Similarly, for each of the two three-credit classes, you would spend:

3 credits * 2-3 hours/credit = 6-9 hours per week.

Since you have two such classes, the total time would be:

2 * (6-9) hours = 12-18 hours per week.

One four-credit class that is very challenging:

Using the same guideline, for a four-credit class, you would ideally spend:

4 credits * 2-3 hours/credit = 8-12 hours per week.

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The graph of y = 3x + 1 lies in quadrants I and III. The graph of the equation y = 3x + 1 is a straight line with a positive slope.

To determine the quadrants in which the graph lies, we need to analyze the signs of the x and y coordinates in different regions of the coordinate plane.

Quadrant I: In this quadrant, both the x and y coordinates are positive. When we substitute positive values for x into the equation, we obtain positive values for y. Since the slope is positive, the line rises as we move from left to right. Therefore, the graph lies in quadrant I, where both x and y are positive.

Quadrant III: In this quadrant, the x coordinate is negative, while the y coordinate is positive. If we substitute negative values for x into the equation, we still obtain positive values for y. The positive slope ensures that the line rises from right to left. Hence, the graph also lies in quadrant III.

The graph does not pass through quadrants II and IV because the signs of the coordinates do not align with the equation. In quadrant II, the x coordinate is negative, but the y coordinate is negative as well. In quadrant IV, both the x and y coordinates are positive, which contradicts the equation. Therefore, the graph of y = 3x + 1 is confined to quadrants I and III.

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Answer:

0, 5%, 1/5, 5

5% is equal to 5÷100=0,05

1/5 is equal to 1÷5=0,2

The level of measurement that is appropriate for a classification where students are asked to rank their professors as good, average, or poor is the ordinal level of measurement.

Ordinal level of measurement is a statistical measurement level.

It involves dividing data into ordered categories.

For instance, when asked to rank teachers as good, average, or poor, the students' rating of the teachers falls under the ordinal level of measurement.

The fundamental characteristic of ordinal data is that it can be sorted in an increasing or decreasing order.

The numerical values of the categories are not comparable; instead, the categories are arranged in a specific order.

The ordinal level of measurement, for example, provides the order of the data but not the size of the intervals between the ordered values or categories.

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The equation of the line passing through the point (5,-3) and perpendicular to the line passing through the points (-1,1) and (-2,2) is y = x - 8.

To find the equation of the line passing through the point (5,-3) and perpendicular to the line passing through the points (-1,1) and (-2,2), we follow these steps:

Step 1: Find the slope of the line passing through (-1,1) and (-2,2).

Using the slope formula, we have:

m = (y2 - y1) / (x2 - x1),

where (x1, y1) = (-1, 1) and (x2, y2) = (-2, 2).

Plugging in the values, we get:

m = (2 - 1) / (-2 - (-1)) = -1.

Step 2: Find the slope of the line perpendicular to the line passing through (-1,1) and (-2,2).

Perpendicular lines have negative reciprocal slopes. Therefore, the slope of the line perpendicular to the line passing through (-1,1) and (-2,2) is the negative reciprocal of -1.

i.e. m' = -1/m' = -1/-1 = 1.

Step 3: Find the equation of the line passing through (5,-3) with slope 1.

We have the slope (m') of the line passing through (5,-3), and we also have a point (5,-3) on the line. We can use the point-slope form of the equation of a line to find the equation of the line passing through (5,-3) and perpendicular to the line passing through (-1,1) and (-2,2).

Point-slope form: y - y1 = m'(x - x1),

where (x1, y1) = (5,-3) and m' = 1.

Plugging in the values, we get:

y - (-3) = 1(x - 5),

y + 3 = x - 5,

y = x - 5 - 3,

y = x - 8.

Thus,y = x - 8 is the equation of the line travelling through the point (5,-3) and perpendicular to the line going through the points (-1,1) and (-2,2).

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Answer:

32 degrees

Step-by-step explanation:

If lines r and t are parallel then it would be 180-148

Answer:

x = 2.285 hours

y = 2.1425  feet

Step-by-step explanation:

Let us say that y represents the depth of the pool in feets and x represents the time in hours

The two set of equations are

y = 1/2x + 1

y= -1.25x + 5

Solving the above two equations we get

Subtracting eq (1) from eq (2), we get -

y-y = -1.25 x -0.5 x + 4

0 -1.75 x + 4

x = 4/1.75

x = 2.285 hours

y = 0.5 * 2.285 + 1

y = 2.1425  feet

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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a) The equation that fits the story is given as follows:

2x/5 = 28.

b) The length of the racetrack is given as follows: 70 meters.

c) Antonio had to go 42 meters farther to reach the finish line.

The length of the race track is obtained applying the proportions in the context of this problem.

His car stops 10m past the starting line. After he fixes a wheel, the car goes 2/5 the racetrack’s total distance and then stops for good. It is 38m from the starting line, hence the distance driven during this entire period is of:

38 - 10 - 28 m.

28 m is 2/5 of the track length, which is going to be called x, hence the equation is given as follows:

2x/5 = 28.

The track length is then obtained as follows:

2x = 5 x 28

x = 5 x 14

x = 70 meters.

Thus the remaining distance is of:

70 - 28 = 42 meters.

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Answer:

x = 26

y = 72°

Step-by-step explanation:

(4x - 16)° = (3x + 10)°

Subtract 3x to both sides

4x - 3x - 16 = 10

x - 16 = 10

Add 16 to both sides

x = 10 + 16

x = 26

(4x - 16)° + y° = 180°

4x - 16 + y = 180

4(26) - 16 + y = 180

104 - 16 + y = 180

88 + y = 180

Subtract 88 to both sides

y = 180 - 88

y = 72°

\(\rule[225]{225}{2}\)

Answer:

Below

Step-by-step explanation:

If you lose 5 %, you basically have 95 % remaining which is .95 in decimal

y = 1000 * (.95)^x       where x is the number of months  ( x = 9 in this case)

Answer:

\( t - 9 \)

Step-by-step explanation:

Given that t represents a number which is unknown to us, the difference of the number and 9 can be expressed algebraically as:

\( t - 9 \).

The difference of t and 9 = \( t - 9 \).