The population of bacteria after h hours is 0.075.
Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providing no event occurs, the resulting daughter cells are genetically identical to the original cell. Hence, bacterial growth occurs. Both daughter cells from the division do not necessarily survive. However, if the surviving number exceeds unity on average, the bacterial population undergoes exponential growth.
The equation that models the population of bacteria h-hours after the original 275 bacteria were measured is given by:
P(h) = 275 × [tex](1 + 0.075)^h[/tex]
p(h)=0.075
where P(h) is the population of bacteria after h hours and 0.075 is the growth rate of 7.5% per hour.
Therefore, the population of bacteria after h hours is 0.075.
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Describe the transformations that maps figure RSTU onto figure R1 S1 T1 U1
Problems had to do with translation and units
Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.
what is transformation ?Deformations are four alternative approaches that can be utilized to change a point, line, or mathematical figure's orientation and/or shape. Both the Pre-Image, who describes the shape of the object there at initial state, and the Photograph, which describes the final state and location of the object following change, are words. Translations, reflection, and dilations are the three types of transformations that can be differentiated. A function can undergo two different types mathematical transformations: vertical (it affects the y-values) and sideways (affects the x-values). Its function's equation is provided below, and it comprises the share the information variables (a, b, h, and k). modifying the log. observation. even by square root, invert.
given
From the figure RSTU to R'S'T'U' R moved from P(5,2) to P(-3,0), translating 8 units to the left.
Hence, 5-(-3)= 8 = 2-0 = 0.
Down two units.
as well as reflection on the y axis.
Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.
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n a two-variable diagram, there is a straight line which is parallel to the vertical axis. the slope of this line is a. zero. b. infinite. c. indicative of a direct relationship between two variables. d. indicative of an inverse relationship between two variables.
The slope of a straight line that is parallel to the vertical axis is zero.
A slope of zero indicates that the line is flat and has no incline or decline. In a two-variable diagram, this means that there is no relationship between the two variables, as a change in one variable does not affect the value of the other. A line with a slope of zero is a horizontal line, and its equation is of the form y = b, where b is a constant value.
In contrast, a line with an infinite slope (or vertical line) would indicate a perfect correlation between the two variables, such that a change in one variable would result in an infinite change in the other. A line with a finite positive or negative slope would indicate a direct or inverse relationship between the two variables, respectively.
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Select all possible cross-sections of a sphere
Circle: a cross-section that goes through the center of the sphere and creates a circular shape.
Point: a cross-section that goes through the center of the sphere and creates a single point.
The population of India was 1,324,671,354 in 2016. Round the population to the nearest million people.
Answer:
1,325,000,000 people
Step-by-step explanation:
Million = 1,000,000
Number = 1,324,671,354
The 1st 4 is in the millionth place. 6 > 4 so round 4 up to 5.
Rounded = 1,325,000,000 people
Select the values that are solutions to the inequality x2 + 3x – 4 > 0. –6 –2 0 5
The values that are solutions to inequality are -6 and 5.
Options A and D are the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
x² + 3x - 4 > 0
Now,
Substituting x = -6, -2, 0, 5
(-6)² + 3(-6) - 4 > 0
36 - 18 - 4 > 0
36 - 22 > 0
14 > 0
True.
x² + 3x - 4 > 0
(-2)² + 3 x (-2) - 4 > 0
4 - 6 - 4 > 0
-6 > 0
This is not true.
x² + 3x - 4 > 0
0 + 3 x 0 - 4 > 0
0 + 0 - 4 > 0
-4 > 0
This is not true.
x² + 3x - 4 > 0
5² + 3 x 5 - 4 > 0
25 + 15 - 4 > 0
40 - 4 > 0
36 > 0
This is true.
Thus,
-6 and 5 are the solutions to inequality.
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Convert 1.05 • 10^-8 to standard form.
Answer:
0.0000000105
Step-by-step explanation:
Simply move the decimal 8 places to the left, since it is a negative exponent.
648 divided by 19 in long division
Books in the clearance section at Reading Central Bookmart cost $5.00 for paperbacks and $9.00 for hardbacks. Which inequality best describes the number of paperback books, p, and the number of hardback books, h, that can be purchased for $45.00 or less?
A.
5p + 9h < 45
B.
5p + 9h < 45
C.
9p + 5h > 45
D.
9p + 5h < 45
The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less
is 5p + 9h ≤ 45.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.
Also, we can only buy two types of books for $45 or less.
Therefore, The inequality representing the context is,
5p + 9h ≤ 45. (As the cost van be $45 or less not only less)
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Two model cars, A and B, are in a race.
They start together on the starting line.
Assume each car travels at a constant speed.
Car A takes 30 seconds to complete each lap of the track.
Car B takes a whole number of seconds to complete each lap of the track.
The two cars next cross the starting line together 150 seconds after the start of the race.
Find the four possible times that car B could take to complete one lap.
Step 1: Calculate the number of laps the cars have completed. To calculate the number of laps the cars have completed, divide the total time (150 seconds) by the time it takes car A to complete one lap (30 seconds), which gives us a total of 5 laps.
Step 2: Calculate the possible times for car B. To calculate the possible times for car B, we need to find out how many times car B must complete a lap in order to keep up with car A. Since car A takes 30 seconds to complete one lap and the cars have completed 5 laps in 150 seconds, car B must take the same amount of time as car A, i.e. 30 seconds, in order to keep up with car A. Therefore, the possible times for car B are 30, 60, 90, and 120 seconds.
Therefore, the four possible times that car B could take to complete one lap are 30, 60, 90, and 120 seconds.
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Explain the difference between the graphs of inverse variation functions When k > O and when k < 0.
Answer:
Step-by-step explanation:
Inverse variation functions have the form y = k / x, where k is a constant.
When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.
On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.
In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.
Two apple trees are going next to each other the oldest tree has a 36 ft Shadow the smaller Creek has a 12-in shadow and there is 8 ft tall how tall is the older tree
The old tree in 54 feet height.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that Two apple trees are going next to each other
the oldest tree has a 36 ft Shadow
the smaller Creek has a 12-in shadow and the tree is 8 ft tall.
We need to find the height of the older tree.
Let x be the height of older tree.
36/x=8/12
36×12=8x
432=8x
Divide both sides by 8
54=x
Hence, the old tree in 54 feet height.
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the letters in the word miami are rearranged at random so that every possible anagram is equally likely. what is the probability that it still spells miami?
The letters in the word MIAMI are rearranged at random so that every possible anagram is equally likely. The probability that it still spells MIAMI is 1/5.
Let us count the total number of ways MIAMI can be arranged regardless of condition.
There are 2 M’s 2 I’s 1 A in word.
Total ways of arrangement will be = 5!/2!2!
Total ways of arrangement will be = (5 × 4 × 3 × 2!)/2! × 2 × 1
Total ways of arrangement will be = 5 × 2 × 3
Total ways of arrangement will be = 30 ways
Now, ways in which all similar words are together, thus we have to consider 2M's as one unit, similarly 2 I's as a unit, so number of ways will be 3!.
Thus, the probability will be = 3!/30
The probability will be = (3 × 2 × 1)/30
The probability will be = 6/30
The probability will be = 1/5
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If one bestfriend went to the store with $5 and the other bestfriend went with $20 how many they had in total?
The amount of money they had in total is $25
How to calculate the amount of money that the best friends had in total?One bestfriend went to the store with $5
The other best friend went to the store with $20
The amount of money they had in total can be calculated as follows
= 20 + 5
= 25
Hence the amount of money the best friends had in total is $25
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Answer: 25$
Step-by-step explanation: 20 plus 5 equals 25.
answer question a and b please
The graph for the functions is attached.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
Given
A: graph of y = f(x)
since the graph is in form of a parabola so the function is a quadratic function,
f(x) = ax² + bx + c
the vertex of the graph is at (2, 0)
here in the given curve, the value of the y-axis is 0,
and y = f(x) - 3
in the equation y = f(x) - 3
the shape of the curve will be the same but only change in the vertex of the curve, the new vertex for the curve is (2, -3)
for x = 0 y = -3.
B: given y =g(x)
the graph shows the negative cubic function,
g(x) = -x³
and y = g(x + 4)
= -(x + 4)²
the graph will shift towards 4 units left.
Hence the graph is attached for both equations.
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Evaluate the expression when c=36 and d=24
The value of the expression after evaluating it according to the values of c and d is 42.
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Since, no expression is given, let us assume that the expression is
c + d / 4
Now we have to evaluate the value of the expression according to the values of c and d,
For that, we will simply put the given values in the expression and solved it accordingly,
Put c = 36 and d = 24 in the expression we assumed,
c + d / 4 = 36 + 24/4
= 36 + 6 = 42
Hence, the value of the expression after evaluating it according to the values of c and d is 42.
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Denise has $250 in her checking account. Each time she buys a bottle of water, she spends $2. If Denise buys
x bottles of water, how much money will remain in her account?(1 نقطة)
The remaining amount of money in Denise's account is $250 - (2x).
Therefore, if Denise buys x bottles of water, she will have $250 - (2x) remaining in her account.
Denise has $250 in her checking account.
Each time she buys a bottle of water, she spends $2.
If Denise buys x bottles of water, the total amount of money spent is 2x.
To calculate the remaining amount in Denise's account, we need to subtract the total amount of money spent (2x) from the original amount of money in her account (250).
Therefore, the formula to calculate the remaining amount is $250 - (2x).
Substituting the value of x in the formula, we get the remaining amount of money in Denise's account.
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For every bottle of water Denise buys her balance decreases by $2. So If Denise buys x bottles of water, her balance decreases by $2 * x.
Let's call the amount of money remaining in Denise's account after buying x bottles of water M.
The equation to find M is:
M = 250 - 2x
This equation says that the money remaining in Denise's account is equal to her initial $250 balance minus the amount she spent on buying x bottles of water, which is $2 per bottle.
In other words, for every bottle of water Denise buys, her balance decreases by $2. So, if she buys x bottles of water, her balance decreases by $2 * x.
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Solve for z zz. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. − 4 z + 31 ≥ 17 z + 23 −4z+31≥17z+23
[tex]-4z+31\geqslant 17z+23\implies 31\geqslant 13z+23\implies 8\geqslant 13z\implies \cfrac{8}{13}\geqslant z[/tex]
In the diagram below of triangle ABC, D is the midpoint of AC and E is the
midpoint of BC. If m/CB A = 16 + 6x, and m/CED = 48 - 2x, what is the
measure of ZC BA?
Answer: 40 degrees
Step-by-step explanation:
m/CBA = m/CED
16 + 6x = 48 - 2x; add 2x on both sides and subtract 16 on both
8x = 32; divide 8 on both sides to isolate the x
x = 4
m/CBA = 16+6(4) = 40
A string with a linear density of 2 kg/m and a tension of 100 N is fixed at both ends. Determine the frequency of the first harmonic of the string.
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be determined using the formula:
f = (1 / 2L) * √(T / μ)
where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density. Plugging in the given values:
f = (1 / 2 * L) * √(100 N / 2 kg/m)
= (1 / 2 * L) * √(50 N/m)
So, the frequency of the first harmonic depends on the length of the string, which is not specified in the problem.
Answer:
Step-by-step explanation:
The frequency of the first harmonic of a string fixed at both ends can be calculated using the formula:
f = (1 / 2L) * (T / μ)^(1/2)
where:
f = frequency
L = length of the string
T = tension
μ = linear density of the string
Plugging in the values:
f = (1 / 2 * L) * (100 N / 2 kg/m)^(1/2)
f = (1 / 2L) * (10 N/kg)^(1/2)
We don't have the length of the string, L, so we can't calculate the frequency.
In right triangle ABC, AC = 4 and BC = 5. A new triangle DEC is formed by connecting the midpoints of AC and BC. What is the area of triangle DEC
Answer:
5
Step-by-step explanation:
The midpoint of AC is (2,0), and the midpoint of BC is (0,2.5). The third vertex of triangle DEC is E, the midpoint of AB, which can be found using the midpoint formula:
E = ( (A_x + B_x) / 2, (A_y + B_y) / 2 )
= ( (0 + 2) / 2, (0 + 5) / 2 )
= (1, 2.5)
So the vertices of triangle DEC are (0, 2.5), (2, 0), and (1, 2.5). The area of triangle DEC is half the area of triangle ABC, which is (4 * 5) / 2 = 10. So the area of triangle DEC is 10 / 2 = 5.
8. Express the area of the figure as a monomial.
p2q4 and p2q4
The area of the figure as a monomial with the sides [tex]p^{2} q^{4}[/tex] and [tex]p^{2} q^{4}[/tex] is [tex]p^{4} q^{8}[/tex].
As per the given data we to express the area of the figure as a monomial.
Figure attached at the end of solution.
What is monomial?A polynomial with only one term is called a monomial. An algebraic expression known as a monomial has only one term but might have more than one variable and a higher degree.
As the sides are equal we use the area of the square formula.
Area of the square formula:
The formula for the area of a square is side × side
Simple multiplication is the answer to the equation.
Area of the given figure:
= [tex]p^{2} q^{4} \times p^{2} q^{4}[/tex]
= [tex]p^{4} q^{8}[/tex]
[tex]p^{4} q^{8}[/tex] is a monomial as it is expressed as a single term.
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Three pieces of software cost $20.75, $10.59, and $18.25. What is the total cost of the software.
Answer:
$49.59
Step-by-step explanation:
$20.75+$10.59+$18.25=$49.59
A car sales person makes $7.00 per hour plus $100.00 for every car sold. Which expression represents the amount in dollars the salesperson makes, before taxes, if x cars are sold in 40 hours?
The expression that represents the amount in dollars the salesperson makes, before taxes, would be equal to 7x + 100 = 40.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol that can also be used to indicate the logical syntax's order of operations and other features.
Given that car sales person makes $7.00 per hour plus $100.00 for every car sold.
Therefore, we have,
7x + 100 = 40
The expression that represents the amount in dollars the salesperson makes, 7x + 100 = 40.
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a man has two shirts and nine ties asuuming that they all match how many diferent shirtt and tie combination can he wear
The man can wear 27 different shirt and tie combinations.
Therefore the answer is 27.
The number of different shirt and tie combinations that a man can wear can be calculated by multiplying the number of choices for each item.
Number of choices for shirts = 3
Number of choices for ties = 9
Since the man has three different shirts and nine different ties, and each shirt can be paired with any one of the nine ties, the number of combinations is:
Combinations = 3 * 9 = 27
So the man can wear 27 different shirt and tie combinations.
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A recipe for biscuits calls for 1/4 teaspoon baking powder per 1 2/3 cups of flour. What is the unit rate for baking powder and flour?
The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.
The amount of baking powder per unit of flour is the unit rate for baking powder and flour. The amount of flour in this situation equals 1 2/3 cups. We must change the baking powder measurement to the same unit as the flour measurement in order to calculate the unit rate.
For every 1 2/3 cups of flour, 1/4 teaspoon of baking powder should be used as follows:
1/4 teaspoon / (1 2/3 cups)
By changing the numerator and denominator of the fraction on the right side to a standard unit, such as teaspoons, we may make it simpler. 1 2/3 cups equal 48 teaspoons, so:
1/4 teaspoon / (1 2/3 cups) = 1/4 teaspoon / (48 teaspoons)
The ratio of baking powder to teaspoons is as follows:
1/4 teaspoon / (48 teaspoons) = 1/192 teaspoon per teaspoon
So The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.
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Function Transformations
Given the point (-2,−1) is on the graph of f(x), find a point (written as an ordered
pair) that must be on each of the transformations of f(x) written below:
Ordered pair on the graph
y=f(x-4)-4
Ordered pair on the graph
y=f(x-4) +4
Ordered pair on the graph
y = f(x+4)-4
Ordered pair on the graph
y = f(x+4) +4
(-6,-5), (-2,3), (2,-5), (6,3) are the ordered pairs given on the graph.
What do you mean by transformation?In mathematics, a transformation is a process that changes the position, size, or orientation of a geometric shape or figure. The term is used in various branches of mathematics, including geometry, algebra, and calculus.
In geometry, transformations include translations, rotations, reflections, and dilations. A translation involves moving a shape a certain distance in a certain direction, while a rotation involves rotating a shape around a fixed point. A reflection involves flipping a shape over a line, and a dilation involves stretching or shrinking a shape by a given scale factor.
In algebra, transformations can involve changing the form of an equation, such as solving for a variable, transforming an equation into a different coordinate system, or solving a system of equations.
In calculus, transformations can involve changing the form of a function, such as finding its derivative or integral, or transforming a function from one coordinate system to another.
To find the ordered pairs that are on the transformations of the function, we can apply the transformations to the original point (-2, -1) to obtain the points on each transformation.
y = f(x-4) - 4: If we apply the x-4 transformation to the x-coordinate of the original point, we get -2-4 = -6. So, the point is (-6, f(-6) - 4).
y = f(x-4) + 4: The x-coordinate of the point is -6, so the point is (-6, f(-6) + 4).
y = f(x+4) - 4: If we apply the x+4 transformation to the x-coordinate of the original point, we get -2+4 = 2. So, the point is (2, f(2) - 4).
y = f(x+4) + 4: The x-coordinate of the point is 2, so the point is (2, f(2) + 4).
So, the ordered pairs that must be on each of the transformations of f(x) are:
y = f(x-4) - 4: (-6, f(-6) - 4)
y = f(x-4) + 4: (-6, f(-6) + 4)
y = f(x+4) - 4: (2, f(2) - 4)
y = f(x+4) + 4: (2, f(2) + 4)
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a rectangular table top is three times as it is wide. it's width is 2 meters. what is the area of the table top
12m² is the area of the table top in rectangle .
What is a rectangle, exactly?
The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. As a result, it is sometimes referred to as an equiangular quadrilateral.
The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.
area = length x width
We know that the width is 2 meters, and since the length is three times the width, the length would be 6 meters.
Therefore, the area of the table = 2 x 6 = 12 m2.
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Six ounces of orange juice contain 75 calories. About how many calories are in fourteen ounces of orange juice ? Part A. Write a proportion, make sure to include units. Let x= the unknown calories. Part B. Solve for X
Answer:
175 calories
Step-by-step explanation:
75 / 6 = 12.5
12.5 x 14 = 175
x = 12.5 x 14
Drag each expression to show whether the expression is equivalent to 24x−48 24 x - 48 , 36x+12 36 x + 12 , or neither.
the expression 24x - 48 is equivalent to 36x + 12
The label 24x - 48 applies to the expression because it is the same as itself. The value obtained by multiplying 24 by x and then taking 48 out is represented by this expression.
The label "36x + 12" applies to the expression because it is the same as itself. The value generated by multiplying 36 by x and then adding 12 is represented by this expression.
Since the formulations in both situations have distinct coefficients for x and various constant terms, they are not comparable to one another. Since both expressions are equal to one another, the term "neither" does not apply to them.
Therefore, the expression 24x - 48 is equivalent to 36x + 12
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what is 28 divided by the square root of 2
Answer:
14√2
Step-by-step explanation:
28/√2
Since you can't have a square root as the denominator of a fraction, we must multiply the denominator and the numerator to get rid of the square root.
Hence,
28 x √2 , √2 x √2
Your problem would now be:
28√2 / 2
Reduce the fraction by canceling out the common factor of 2
ANS = 14√2
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