After a special medicine is introduced into a petri dish full of bacteria, the number of bacteria remaining in the dish decreases rapidly.
The relationship between the elapsed time ttt, in seconds, and the number of bacteria, B_{\text{second}}(t)B
second
​
(t)B, start subscript, start text, s, e, c, o, n, d, end text, end subscript, left parenthesis, t, right parenthesis, in the petri dish is modeled by the following function:
Bsecond(t)=6000⋅(1516)t
Complete the following sentence about the rate of change in the number of bacteria in minutes.

Answer:

Step-by-step explanation:

if x were starting at 0, we would have

y = (x - 7)×7 = 7x - 49

but we start at x = 57. We need adjust for these extra 57 to get the above equation.

so, it

y = (x - 57 - 7)×7 = (x - 64)×7 = 7x - 448

so, for

y = (x - 64)×7

I choose x = 57

y = (57 - 64)×6 = -7×7 = -49

for

y = 7x - 448

I choose x = 58

y = 7×58 - 448 = 406 - 448 = -42

from this form we get the y-intercept (the y- value when x = 0) : -448

The function rules for each table are given as follows:

7. y = 5x - 2.

8. y = x³.

9. y = x³ + 1.

For item 7, when x increases by one, y is increased by 5, hence the function is a linear function with slope 5, as follows:

y = 5x + b

When x = 6, y = 28, hence the intercept b is given as follows:

28 = 5(6) + b

b = 28 - 30

b = -2.

Hence the function is:

y = 5x - 2.

For item 8, the each term is cubed, hence the function is given as follows:

y = x³.

For item 9, the function is one added to the function in the previous problem, hence:

y = x³ + 1.

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The additive inverse of 2 /- 7 is -2 /+ 7.

An additive inverse is a number that when added to the number in question, the sum is equal to zero. This can be expressed by the formula x + (-x) = 0, where x is the number in question. In this case, x is 2 /- 7. So, when 2 /- 7 is added to its additive inverse, -2 /+ 7, the sum is 0. This can be expressed mathematically as 2 /- 7 + (-2 /+ 7) = 0. Calculating this equation, we get 2 /- 7 + (-2 /+ 7) = -2 /+ 7 + (-2 /+ 7) = -4 /+ 14 = 0. Therefore, the additive inverse of 2 /- 7 is -2 /+ 7.

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Answer:

The cost at Pauline's print store can be described with the following equation, where y represents the cost in dollars of x copies:

y = 0.05x, because 1.25/25 = 2.75/55 = 90/4.50 = 0.05

Carla's Copy Shop charges a higher unit right

and it is $0.04 higher per copy

Step-by-step explanation:

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The two angle of the right triangle are found as 30 degrees and 60 degrees.

Less than 90 degrees is considered an acute angle. Right angles have a 90 degree angle. More than 90 degrees is found in obtuse angles.

By using angle sum property of right angle triangle:

x + 2x + 90 = 180

3x = 90

x = 30 (one angle)

2x = 60 (Other angle)

Thus, the two acute angle of the right triangle are found as 30 degrees and 60 degrees.

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The missing number of points scored in the last basketball game is 13.

What is the meaning of the data set?

A data set is a grouping of data. A data set refers to one or more database tables in the case of tabular data, where each column of a table represents a specific variable and each row corresponds to a specific record of the data set in question.

Given that,

the number of points scored in the last basketball game by each player on the Dragons basketball team are 7, 5,8,11,7,5,?.

Assume that the missing point is x.

The sum of points is 7+5+8+11+7+5+x = 43 + x.

The number of points is 7.

The mean is the sum of points/number of points

= (43+x)/7

Given that the mean of the data set is 8 points.

Therefore,

(43+x)/7 = 8

Multiply both sides by 7:

43+x = 8×7

43 + x = 56

x = 56 - 43

x = 13

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The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

The point, line, and plane are only a few of the many undefined terms in geometry. All other concepts in geometry may be defined from these three undefined terms.

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A parabola is the form of a quadratic function's graph because the vertex of a parabola is the location where the axis of symmetry of the curve crosses.

f(x) = ax^2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the form of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

Regarding a line known as the axis of symmetry, all parabolas are symmetric. The vertex of a parabola is the location where the axis of symmetry of the curve crosses.

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The solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

What is the graph of a function?

The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.

The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.

i) 2y - 4x < 8 can be solved by adding 4x to both sides and then dividing by 2, giving:

y < 2x + 4.

ii) -4y > -x + 12 can be solved by adding x to both sides and then dividing by -4, giving: y < x/4 - 3.

iii) | x + 3 | = y, you can split this into two cases:

i. x + 3 = y

ii. -(x + 3) = y

iv) |2x – 6| + 2 = y, you can split this into two cases:

i. 2x - 6 + 2 = y

ii. -(2x - 6) + 2 = y

We can use these equations to plot the graph on a coordinate plane.

Hence, the solution is the set of all points (x,y) that satisfy the inequalities:

y < 2x + 4,  y < x/4 - 3, x + 3 = y, and 2x - 6 + 2 = y.

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Step-by-step explanation:

he needs two pairs of jeans and 4 shirt for him to spend 4 days at the camp

Yes, 1 is a monomial, a unique type of polynomial.

You must first understand what a word is. A term is a real number multiplied by one or more variables, each of which has been raised to a power. Remember that a constant might appear in a phrase when a variable is multiplied by itself to the power of 0. (which is 1). A polynomial is just the sum of one or more terms that meet the criteria listed below:

1] There are no variables to split the words into.

The variables' exponents are whole numbers, e.g. 0, 1, 2, 3, etc.

Thus, 1 is just 1*(x0).

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The probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

The event of getting a "2" and the event of getting a "5" on the first roll of a die are mutually exclusive events because they cannot both occur in the same trial. The probability of either of these events occurring is P(A) = 0.16, and the probability of both events occurring at the same time is P(A ∩ B) = 0.00.

The event of getting a "2" on the first roll and the event of getting a "5" on the second roll of a die are independent events. This can be confirmed using the formula P(A ∩ B) = P(A)P(B). The probability of getting a "2" on the first roll is P(A) = 0.16 and the probability of getting a "5" on the second roll is P(B) = 0.16. Thus, the probability of both events occurring is P(A ∩ B) = P(A)P(B) = 0.16^2 = 0.0256.

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Therefore ,In light of this, the answer to the above equation issue is 

be 8.

An equation must always include two equal members and one or more unknown members (the unknown variables). When multiplied by itself, what number, for example, results in 16. To express this maths equation mathematically, use the equation or expression.

Here,

Replace -3 with the following in the above quadratic equation.

(-3)² - 5(-3) + c = 0

measuring c:

c = -24

a quadratic equation that looks like this

x² - 5x - 24 = 0

x's value can be determined using the quadratic formula as follows:

x = [-b ±√(b² - 4(a)(c))]

/2a

x = [-(-5) ± √((-5)² - 4(1)(-24))] /2(1)

x = 8, -3

Therefore ,In light of this, the answer to the above equation issue is 

be 8.

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Because he invented geometry, Euclid, a renowned mathematician, is frequently referred to as the father of geometry.

Constructions using a compass and a straightedge were a focus of classical geometry. Euclid, who brought mathematical rigour and the axiomatic technique still in use today, transformed geometry. Up until the middle of the 20th century, all educated people in the West were familiar with his book, The Elements, which is usually regarded as the most important textbook of all time.

Current geometric notions have undergone a high level of abstraction and complexity as well as calculus and abstract algebra techniques, resulting in several modern sections of the science that are hardly recognizably descended from early geometry.

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Answer:

Step-by-step explanation:

Craig's savings is c-48=16

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given:

Let craig's savings be c then we have c-48=16

                                                                  c=64

Hence, craig's savings is 64

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The equations equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

The correct answer is option B and C

2.3p – 10.1 = 6.5p – 4 – 0.01p

collect like terms

2.3p - 6.5p + 0.01p = -4 + 10.1

-4.19p = 6.1

p = 6.1/-4.19

p = -1.46

2.3p – 10.1 = 6.5p – 4 – 0.01p

= 2.3p – 10.1 = 6.49p – 4

Given options:

2.3p – 10.1 = 6.4p – 4

False

2.3p – 10.1 = 6.49p – 4

True

230p – 1010 = 650p – 400 – p

divide through by 100

= 2.3p – 10.1 = 6.5p – 4 – 0.01p

True

23p – 101 = 65p – 40 – p

False

2.3p – 14.1 = 6.4p – 4

False

Therefore, 2.3p – 10.1 = 6.49p – 4; 230p – 1010 = 650p – 400 – p are equivalent to 2.3p – 10.1 = 6.5p – 4 – 0.01p.

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Answer:

First you do what is in the parentheses.

2+4= 6

The equation is now:

6(6) -1 / 2 *3 + 1 =

Then you do the division:

-1 / 2 = -0.5

6(6) (-0.5) * 3 + 1 =

3 + 1 = 4

-0.5 * 4 = -2

The equation is now:

6 * 6 * -2

6 * 6 = 36

36 * -2 = -72

The area of a (equilateral) triangle with side 8cm is 16√3cm^2.

What is a triangle and its types?

A figure which has a three-sided closed figure is called a triangle.

Types

Equilateral Triangle

A triangle where all the sides are the same is called an equilateral triangle.

Isosceles Triangle

When two of the sides of a triangle are the same it’s called an isosceles triangle. It’s a hard one to spell, but an easy one to recognize!

Scalene Triangle

In our last triangle, none of the sides have the same length, so this is called a scalene triangle.

Acute Triangle

when the largest angle in the triangle  is less than 90, that is an acute triangle. Just remember that acute angles are less than 90 degrees.

Right Triangle

When the largest angle is exactly 90 degrees. You might remember that a 90-degree angle is a right angle, so this triangle is a right triangle.

Obtuse Triangle

When largest angle is more than 90 degrees, this is an obtuse angle, so we call this triangle an obtuse triangle.

Area of an equilateral triangle whose side is 8 cm is √3/4*a^2 where

a=8

= √3/4*8^2

= √3/4*64

= √3*16

Area=16√3

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Answer:

Its proportional

Step-by-step explanation:

Answer:

Proportional

Step-by-step explanation:

36/3 = 12

60/5 = 12

96/8 = 12

For the above set of similar triangles, the value of x is 23 units.

Similar triangles have the same proportionate side lengths and related angle measurements. Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion). Similar triangles will have the same form but may or may not have the same size. Similar triangles are triangles that have the same shape but differ in size. Similar items include all equilateral triangles and squares with any side length. In other words, if two triangles are identical, their corresponding angles and sides are congruent and in equal proportion.

Here,

Two triangles are comparable if their corresponding angles and sides have the same ratio (or proportion).

x-10/39=12/36

x-10=13

x=23

The value of x for given set of similar triangles is 23 units.

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The integral rate law for a first-order reaction has the following exponential form: [A] = [tex][A]_{0}e^{-kt}[/tex]

If there are constants c, M > 0, and T > 0 such that |f(t)| ≤ Mect for all t>T, then a function f is said to be of exponential order c.

It is helpful to keep in mind the exponential's definition and characteristics since they serve as the foundation for the solution of first-order linear differential equations.

The Concentration of the Reactant Decreases Exponentially with Time in First-Order Reactions. A plot of the natural logarithm of the concentration is a linear function of time according to this form.

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Answer:

<UVS and <WVX

Step-by-step explanation:

They are both supplementary to the same angle. (<SVW)

Otherwise, you could just see if they are across from each other.

Answer:

They might include variety of nuts, raisins, and healthy sweets

Step-by-step explanation:

a/a+b is the same as a/(a+b). This is because the division of two numbers is represented by the symbol '/', and when a and b are being divided, it is written as a/b.

In this case, a and b are being divided by a+b, so it is written as a/(a+b). This is known as a fraction, which represents a ratio of two numbers. This fraction represents the proportion of a to the total of a+b. The numerator (a) represents the part of the total that you are interested in, and the denominator (a+b) represents the entire quantity.

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We calculate the percentage of black paint in each mix by dividing the amount of black paint by the total amount of paint and multiplying by 100. Julian's mix has a black paint percentage of 52.94% while Harper's mix has a black paint percentage of 58.33%. Therefore, Harper's gray paint will be darker.

The first step to determine whose gray paint will be darker is to calculate the percentage of black paint each student has in their mix. To find this, one must know that the percentage is calculated by dividing the part (the quantity of black paint) by the whole (the total amount of paint) and then multiplying by 100.

Julian's percentage of black paint: (9 cups black / 17 total cups) * 100 = 52.94%

Harper's percentage of black paint: (7 cups black / 12 total cups) * 100 = 58.33%

Since the percentage of black paint correlates with the darkness of the gray paint, Harper's gray paint will be darker because it contains a higher percentage of black paint.

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