The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number, the number of bacteria in the culture after 8 hours. The exponential function is b(t)=. After 8 hours, there are about bacteria in the culture

Answer: To find the equation of the tangent line to a function at a specific point, we can use the following steps:

Find the derivative of the function f(x) = 3x3 − x2 + 2

f'(x) = 9x^2 - 2x

Substitute the point a = 0 into the derivative to find the slope of the tangent line at that point

f'(0) = 9(0)^2 - 2(0) = 0

Use the point-slope form of a linear equation, y - y1 = m(x - x1) to find the equation of the tangent line, where m is the slope and (x1, y1) is the point at which the tangent line touches the function.

y - f(a) = m(x - a)

y - (3*0^3 - 0^2 + 2) = 0(x - 0)

y - 2 = 0

So the equation of the tangent line to the function f(x) = 3x3 − x2 + 2 at a = 0 is:

y = 2

Therefore, the correct answer is A. y = 2

Step-by-step explanation:

The solution of an expression 1/2 x 2 is 1.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

We have an expression 1/2 x 2.

We will apply the inverse property of multiplication.

= any number x its reciprocal

= 2 x 1/2

= 1

Therefore, 1 is the solution.

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The value of sin and cosine of angle x are √2 and √2/2

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

tan(x) = 2

Also, we have the interval to be

x = (0, ¤/2)

This means that the value of the angle x is from 0 to 90 degrees

Mathematically, we have

tan(x) = sin(x)/cos(x)

This means that

sin(x)/cos(x) = 1/2

So, we have

cos(x) = 2sin(x)

Let cos(x) = √2

This means that

sin(x) = √2/2

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[tex] \pmb{ \underline{\color{green} \huge{Αηςωεr : ∼}}}[/tex]

[tex] \large \frak{ \red{x } - 4 = 8}[/tex]

[tex] \: [/tex]

[tex] \large \frak{ \red{x } = 8 + 4}[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \large \frak{ \red{x } = \green{12}}}}[/tex]

[tex] \: [/tex]

hope it helps!

-5-4-3- is the solution for {n\n<3} and 2-1-0 is the correct set for this solution {n\n≥3).

A set is a well-defined collection of distinct objects, known as elements or members of the set. The objects can be anything, such as numbers, letters, words, animals, or even other sets. The defining feature of a set is that its elements are unique and distinct, meaning that no element can appear more than once in the set.

The solution set to 6 + 2n > 12 is n > 3. The correct representations of this solution are:

{n | n ≥ 3}

(3, ∞)

Option 1 {n | n < 3} is incorrect, as it represents the solution set of n being less than 3, which is the opposite of the solution set provided.

Option 2 -5-4-3- is Correct, as it is not in the correct format to represent a solution set.

Option 3 (3,0⁰0) is correct because it represents a point, not a set.

Option 4 and 5 -5-4-3-2-1 0 1 2 3 4 5 and 0 2 3 4 5 are also incorrect as they are not in the correct format to represent a solution set, and does not include the value 3.

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The graph of constant of proportionality is determined and attached with a green check on the mark box

The ratio between two quantities that are directly proportional is the constant of proportionality.

When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.

The equation shows that y = kx and the y intercept is zero, because of this the graph will start from the origin

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Grams are the ideal unit for calculating the quantity of spices in a batch of cookies (g).

A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:

The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.

You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, as an illustration. The unit of weight used here is the gram.

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Answer:

see attached

Step-by-step explanation:

Answer:

78.4 meters

Step-by-step explanation:

The distance between the given points is 8.1 units

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²)

From the given info, we have:

( 1 , 2 ) and (5, 9),

where x1 = 1, y1 = 2 and x2 = 5 and y2 = 9

d=√((x2 – x1)² + (y2 – y1)²)

d=√((5 – 1)² + (2 – 9)²)

d=√((4)² + (-7)²)

d = √65

d = 8.1 units

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Answer:

A=24+9t

B=40+5t

Step-by-step explanation:

see attached

Answer: Billy drives 171 miles in 3 hours, so he could drive 256.5 miles in 4.5 hours.

Step-by-step explanation:

Speed = Distance/Time

The number of miles driven varies directly with the number of hours in the car. Billy drives 171 miles in 3 hours. Then the number of miles he can drive in 4.5 hours will be. This meas that x will be the number of miles covered in 4.5 hours.

x / 4.5 = 171 / 3

x = 256.5 miles

I hope this helps!

Lengths of the legs of triangle are 6 cm and 8 cm by Pythagoras theorem of right triangle.

Let One short leg = x

then other = x+2

And hypotenuse is = 10 cm

so x²+(x+2)²=10²

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

From Pythagoras theorem : a^2 + b^2 = c^2

Where c is the hypotenuse and a,b are the other sides of a right angle triangle.

x²+ x²+4x+4=100

[(a + b)^2 = a^2 +2.a.b +b^2]

2 x²+4x-96=0

x²+2x-48=0

(x+8)(x-6)=0

x= -8 or 6

Neglecting - value x=6 as the length can not be negative.

So legs of triangle are 6 cm and 8 cm.

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The proof of ∠COP = ∠POD is below.

When viewed as a vector, a ray is a vector from a point to a point . In geometry, a ray is usually taken as a half-infinite line (also known as a half-line) with one of the two points and. taken to be at infinity.

Given is that AOB is a line. Ray OP is perpendicular to AB. OC is another ray between rays OA and OP. If ray OD is perpendicular to OC.

Refer to the figure attached.

In ΔOCP and ΔODP -

∠OPC = ∠OPD = 90°  {right angles}

OP = OP  {Common}

OC = OD

By SAS criteria, ΔOCP ≅ ΔODP.

So, we can write -

∠COP = ∠POD

Therefore, the proof of ∠COP = ∠POD is given above.

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The value to write in the blank so the equation would be true is -4. Option A. no values of x

It is important to note that an algebraic expression is an expression comprising of coefficients, terms, factors, constants and variables.

These algebraic expression also consist of mathematical operations, such as;

From the information given, we have the equation;

4x - 4 = 4x + _

To make the equation true, then, the values must be the same on both sides, the value to add is (-4) because expanding the bracket would give the same value. We have;

4x - 4 = 4x + (-4)

expand the bracket

4x - 4 = 4x - 4

0 = 0

Hence, the value is -4

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Answer:

Step-by-step explanation: Whats you answer? cant see it.

The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast is 4 / 5 hour.

The total fraction of an hour that Janine spends making the bed, getting dressed, and eating breakfast can be calculated by adding the fractions of time she spends on each activity:

1/10 hour + 1/5 hour + 1/2 hour

= (2 + 1 + 5) / 10 hour

= 8 / 10 hour

= 4 / 5 hour

The addition of two or more fractions with the same denominator is straightforward.

Simply add the numerators and keep the same denominator. For example:

(1/5) + (2/5) = (1 + 2) / 5 = 3/5

If the fractions have different denominators, you will need to find a common denominator before adding the numerators. The common denominator is the least common multiple of the denominators. Once you have found the common denominator, convert each fraction to an equivalent fraction with the common denominator and then add the numerators.

For example:

(1/5) + (2/3) = (3/15) + (10/15) = (3 + 10) / 15 = 13/15

So the addition of two or more fractions is performed by finding a common denominator, converting the fractions to equivalent fractions with the common denominator, and then adding the numerators.

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The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

To divide polynomials by a polynomial, we use the long division method.

When there is no common factor in both the numerator and the denominator, we can use the long division.

It may be used to find reminders and quotients while dividing.

Here we have

Divide 3x² + 6 by 3x – 3    

On dividing 3x² + 6 by 3x – 3 in long division method

we get the remainder as 9 and the quotient as (x - 1)

For more understanding understand the long division in the given picture.

Therefore,    

The quotient and remainder on dividing 3x² + 6 by 3x – 3 are (x - 1) and 9 respectively.

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Let x be the number of acres of Farm A planted with pine trees and birch trees, and let y be the number of acres of Farm B planted with pine trees and birch trees.

The system of equations would be as follows:

25x + 50y = 200 (the total number of pine trees planted)

75x + 75y = 450 (the total number of birch trees planted)

To solve this system of equations, we can use the method of substitution. Solving the first equation for x in terms of y:

x = (200 - 50y) / 25

We can substitute this expression for x into the second equation:

75((200 - 50y) / 25) + 75y = 450

Simplifying and solving for y:

(200 - 50y) + 75y = 450

25y = 250

y = 10

So 10 acres of Farm B are planted with pine and birch trees. To find the number of acres of Farm A that are planted with pine and birch trees, we can substitute this value of y back into the first equation:

25x + 50(10) = 200

25x = 50

x = 2

So 2 acres of Farm A are planted with pine and birch trees.

Therefore, the company will plant 25x = 50 pine trees and 75x = 225 birch trees on Farm A, and 50y = 500 pine trees and 75y = 750 birch trees on Farm B.

The summation notation of the sum is:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

The total amount is $84.

Summation notation, also known as sigma notation, is a mathematical notation used to represent the sum of a sequence of numbers. The notation typically uses the Greek letter sigma (∑) to represent the operation of summation.

Since each week Tom will raise $4 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job.

Let n represent the number of weeks

Thus, this can be written using summation notation as:

[tex]Sum = \[ \sum_{n=1}^{3} (4^{n})\][/tex]

Thus, the total amount = 4¹ + 4² + 4³ = $84

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Answer:

176/3

Step-by-step explanation:

58 2/3 = 58 + 2/3 = 58/1 + 2/3 = 174/3 + 2/3 = 176/3

The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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Answer: need photo

Step-by-step explanation:

Correlations are used both as a hypothesis test to check the relationship between two variables, and also as internal reliability check, again to check the relationship between two items is true.

To evaluate a hypothesis about a population, hypothesis testing uses sample data. A hypothesis test evaluates the result's unusualness, determining if there is a reasonable amount of random variation or whether the result is too extreme to be accounted for by chance.

Reliability can be measured by internal consistency. When a measurement is said to be reliable, it means that it will always produce the same result, given all other factors being equal.

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Answer:

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Lets use process of elimination.
A would result in biased results as Lin is on the basketball team herself and thus, her teammates would be inclined to vote for her.

B would result in biased results as well. It doesn't say every third person in the line but rather every third girl. The girls might be inclined to vote for a female candidate.

That leaves C as the only viable option.

The required number of baskets made in 90 minutes are 27 baskets.

It is given that Juwan makes 12 baskets in 40 minutes and continues to make the baskets for 90 minutes.

Number of baskets made in 90 minutes = ?

So, let us calculate the number of baskets made in 1 minute.

40 min - 12 baskets

1 min - 12/40 baskets

Now, we need to find out the number of baskets made in 90 minutes.

90 min - ?

1 × 90 min - 90 × 12/40 = 27 baskets

Thus, the required number of baskets made in 90 minutes are 27 baskets.

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The domain of the function shown in the graph above include the following: D. {x|x ≥ -4}.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using set builder notation, the domain of this function shown in the graph above can be written as follows;

Domain = {-4, ∞}

Domain = {x|x ≥ -4}

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Answer:

vanessa gest 80

Step-by-step explanation:

128/8 =16

5 * 16 =80

3*16. =48

Answer: £80

Step-by-step explanation:

Step 1:

Make a proportion:

5 - 8

x - 128

Step 2:

Cross multiply:

5*128=8x

640=8x

Step 3:

Divide by 8:

80=x or x=80