To grow 80000 bacteria, it will take 4.152 hours.
What is exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Given,
Initial number of bacteria = 4500
Number of bacteria get doubled each hour
Function for population growth of bacteria is given by
N = 4500(2ˣ)
x is time in hours
Future population is N = 80000
Then
80000 = 4500(2ˣ)
800 = 45 . 2ˣ
taking log on both sides
log 800 = log (45 . 2ˣ)
log(mn) = log m + log n and log mⁿ = nlogm
log800 = log45+ x log2
2.9030 = 1.653 + x . 0.3010
x = (2.9030 - 1.653)/0.3010
x = 4.152
Hence, it will take 4.152 hours to grow 80000 bacteria.
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10. Find the original price of an antique which was sold at £545 at a profit of 9%.
495.95
convert the percentage into a decimal
0.09
then do b=1-r
1 - 0.09 = 0.91
Now do 545 x 0.91
Answer: 495.95
Let's assume that the original price of the antique was x.
We know that the antique was sold at a profit of 9%, which means that the selling price is 109% of the original price:
[tex]Selling \: price = Original \: price + Profit[/tex]
[tex]£545 = x + 0.09x \\ £545 = 1.09x[/tex]
To find the original price, we can divide both sides of the equation by 1.09:[tex]x = \frac{545}{1.09} [/tex][tex]x = 500[/tex]
Therefore, the original price of the antique was £500.2. The area of a garden plot can be represented by
the expression 85.2z - 58.8. The garden will be
divided into six sections for planting six different
vegetables. The sections will be equal in area.
Write an expression that represents the area of
each section.
The expression that represents the area of each section is 14.2z - 9.8.
What is area ?
To find the area of each section, we need to divide the total area of the garden plot by the number of sections, which in this case is six.
The expression for the area of each section can be obtained by dividing the expression for the total area by 6:
(area of each section) = (total area of garden plot) / 6
(area of each section) = (85.2z - 58.8) / 6
Simplifying this expression, we can divide both terms by 6:
(area of each section) = 14.2z - 9.8
Therefore, the expression that represents the area of each section is 14.2z - 9.8.
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I need help with this question
The amount of Tylenol remaining after 8 hours is 47.1g
What is half life?half-life, in radioactivity, the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay (change spontaneously into other nuclear species by emitting particles and energy), or, equivalently, the time interval required for the number of disintegrations per second of a radioactive.
R = A(0.5)^t/3
R = 300(0.5)^8/3
R = 300( 0.157)
R = 47.1
therefore after 8 hours 47.1 g of Tylenol is is left
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Choose the correct sum of the polynomials (3x3 − 5x − 8) + (5x3 + 7x + 3).
8x3 + 2x + 5
2x3 − 12x − 11
2x3 + 12x − 5
8x3 + 2x − 5
Answer:
8x3 + 2x − 5
Step-by-step explanation:
WILL MARK BRAINLIEST! Which polygon appears to be regular?
O Figure A
O Figure B
O Figure C
O Figure D
Answer:
I'm 90% sure it's B.
Step-by-step explanation:
sorry if its not correct-
Answer: figure b
Step-by-step explanation:
this is because all of figure b's sides are congruent but the other figures sides are different lengths
Josh and Chris are training for baseball season. Josh did 36 pushups in 30 seconds. Chris did 56 pushups in 50 seconds
Who will do more pushups in 2 and a half minutes?
Josh will do more push ups than Charis in 2 1/2 minutes. This can be solved by using the concept of multiplication.
What is multiplication?Along with addition, subtraction, and division, multiplication is one of the four fundamental mathematical operations. Multiply in mathematics refers to the continual addition of sets of the same size. One of the fundamental mathematical processes is multiplication. The result of multiplying two or more integers together is known as the product. The first number used in a multiplication operation between two numbers is referred to as the multiplicand.
Given that,
Josh did 36 push ups in 30 seconds
Josh did push ups in 2 1/2 minutes:
= (36/30) × 150
= 180 push ups
Chris did 56 push ups in 50 seconds
Chris did push ups in 2 1/2 minutes:
= (56/50)× 150
= 168 push ups
Thus, Josh will do more push ups than Charis in 2 1/2 minutes.
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What is the rate of change?
Answer:
(-5,1) and (0,3)
in this first one the distance of x is -5 and y is 1, similarly in second x is in origin which means 0 and y is 3.....
Charles is flying a kite
that is on a string that
112 feet long. If the
angle of depression from
the kite to the ground is
27°, how high off of the
ground is the kite?
The height of the kite is 56 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
[tex]sin(30)=\frac{h}{112}[/tex]
h = 56 feet
Therefore, the height of the kite is 56 feet.
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Which phrase describes the algebraic expression Three-fourths x + 2?
The phrase to describes the algebraic expression Three-fourths x + 2 is three-fourths of a number plus two.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given in question;
The algebraic expression;
Three-fourths x + 2
Now,
The phrase that describes the algebraic expression Three-fourths x + 2;
three-fourths of a number plus two.
Therefore, the phrase of expression will be three-fourths of a number plus two.
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How much 5000000 won to usd?
Answer:
3,975.16 United States Dollar
Step-by-step explanation:
According to a Manila police, two people were killed when the 1,000 kg car illegally drag racing at a speed of 30 m/s had a head on collision with a 2,000 kg truck whose driver fell asleep as it traveled 20 m/s. Which vehicle has received the greater force?
Answer: To determine which vehicle received the greater force, we need to calculate the momentum change for each vehicle during the collision. The force experienced by a vehicle during a collision is equal to the rate of change of its momentum.
First, let's calculate the initial momentum for each vehicle:
The car has a mass of 1,000 kg and a velocity of 30 m/s, so its initial momentum is 1,000 kg * 30 m/s = 30,000 kg m/s.
The truck has a mass of 2,000 kg and a velocity of 20 m/s, so its initial momentum is 2,000 kg * 20 m/s = 40,000 kg m/s.
Next, let's calculate the final momentum for both vehicles after the collision:
The car and truck collide head-on, so their velocities will become zero after the collision. So the final momentum for both vehicles will be zero.
Finally, we can calculate the rate of change of momentum for each vehicle:
The rate of change of momentum for the car is equal to its final momentum minus its initial momentum, or 30,000 kg m/s - 0 kg m/s = 30,000 kg m/s.
The rate of change of momentum for the truck is equal to its final momentum minus its initial momentum, or 0 kg m/s - 40,000 kg m/s = -40,000 kg m/s.
Since the magnitude of the rate of change of momentum for the truck is greater than the magnitude of the rate of change of momentum for the car, the truck has received the greater force.
Step-by-step explanation:
I NEED HELP ASAP
Michael has $15 and wants to buy a combination of cupcakes and fudge to feed at least three siblings. A cupcake costs $2, and a piece of fudge costs $3.
This system of inequalities models the scenario:
2x + 3y ≤ 15
x + y ≥ 3
Part A: Describe the graph of the system of inequalities, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (5, 1) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
The description of the graph of the system of inequalities, including shading and the types of lines graphed, and the description of the solution set is given below:
How to make the graphx is the number of cupcakes.y is the number of fudge pieces.2x + y <= 8 is the inequality for the cost.
x + y >= 4 is the inequality for the number of cupcakes or pieces of fudge that she wants to buy.
using the desmos dot com calculator, you would graph the OPPOSITE of the inequalities.
the area on the graph that is NOT shaded is the feasible region
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s=n/2(a+l) make a the subject
Answer: a = (2S)/(n + l)
Step-by-step explanation:
a = (2S)/(n + l)
In this equation, 'a' is the subject, which means that it is the value being solved for. To solve for 'a', we can divide both sides by the denominator of the fraction on the right-hand side (n + l). This leaves us with the answer of a = (2S)/(n + l).
How do I divide 372 divided by 2
Answer:
186
Step-by-step explanation:
Division will yield 186 .
Given,
372 divided by 2.
Now,
For division firstly the common factors of 372 and 2,
372 = 2 * 2 *3 * 31
2 = 2 * 1
So common factor is 2,
Now divide 372 by 2
= 372/2
= 186
Thus the value of 372 divided by 2 is 186 .
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Determine the slope and the y-intercept of the equation. b=3.99a
The equation b = 3.99a has a slope of 3.99 and the y intercept is 0.
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
The standard form of a linear equation is:
y = mx + b
Where y, x are variables and b is the y intercept
Given an equation:
b = 3.99a
Comparing with the standard linear equation:
The slope is 3.99 and the y intercept is 0.
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Algebra 2 - F - Homework #7
Solve the following systems of equations. Graph the lines to check your
solutions. Make sure you show all the work:
1.{2x+y=2
{5x+3y − 9
2. {5x - 2y = -2
{3x + 4y − 30
3. {-x+2y =
{3x + y = 15
Please help
{2x + y = 2
{5x + 3y - 9
Solution: We can solve this system of equations either by substitution or elimination method. Here, let's use substitution method.
From equation 1, we have: y = -2x + 2
Substituting this in equation 2, we get: 5x + 3(-2x + 2) - 9 = 0
Expanding the right-hand side, we get: 5x - 6x + 6 - 9 = 0
Simplifying further, we get: -x + (-3) = 0
Adding x to both sides, we get: -3 = x
Substituting this value of x in y = -2x + 2, we get: y = -2(-3) + 2 = 6
So, the solution to the system of equations is (x, y) = (-3, 6)
{5x - 2y = -2
{3x + 4y - 30
Solution: We can solve this system of equations by either substitution or elimination method. Here, let's use elimination method.
We can multiply equation 1 by 3 and equation 2 by 2, to make the coefficients of y same in both equations. Doing this, we get:
15x - 6y = -6
6x + 8y - 60 = 0
Adding these two equations, we get: 21x + 2y - 60 = 0
Simplifying further, we get: 21x = 60 + 2y
Dividing both sides by 21, we get: x = (60 + 2y)/21
Substituting this in equation 1, we get: 5((60 + 2y)/21) - 2y = -2
Expanding the right-hand side, we get: 60/21 + 10/21 y - 2y = -2
Simplifying further, we get: 60/21 + (-12/21) y = -2
Adding 12/21 y to both sides, we get: 60/21 = (-2) + (12/21) y
Subtracting -2 from both sides, we get: 62/21 = (12/21) y
Dividing both sides by 12/21, we get: y = 62/12 = 5 1/6
Substituting this value of y in x = (60 + 2y)/21, we get: x = (60 + 2(5 1/6))/21 = (60 + 11 1/3)/21 = (71 1/3)/21 = 71/21 + 1/63
So, the solution to the system of equations is (x, y) = (71/21 + 1/63, 5 1/6)
Find the solution of the system of equations
8x+2y=38
2x-4y=-4
The solution of the system of equations is (4, 3)
How to solve the system of equations?Here we want to solve the system below:
8x+2y=38
2x-4y=-4
If we add 2 times the first equation and the second equation we will get:
2*(8x + 2y) + (2x - 4y) = 2*38 - 4
16x + 4y + 2x - 4y = 72
18x = 72
x = 72/18 = 4
And the vale of y is given by inputing x = 4 in one of the two equations.
2*4 - 4y = -4
8 - 4y = -4
-4y = -4 - 8
y = -12/-4 = 3
The solution is (4, 3)
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How do you calculate MLB magic number?
The magic number is calculated as G + 1 − [tex]W_{A}[/tex] − [tex]L_{B}[/tex], where G represents the season's overall number of games. The total victory for Team A is represented by the WA. LB is the total number of defeats Team B has suffered this year.
The "magic number" in baseball is used to estimate how likely a club is to advance to the postseason or win the division. Every year, in September, when teams get closer to clinching, it gains attention. The total number of victories and losses that must occur by a team's closest rival in order for that team to achieve a certain goal is known as its magic number. A team's magic number drops by one with each victory. The magic number additionally drops by one each time the team's closest rival for the division (or Wild Card) loses.
This is the precise formula: Games left in season: +1 (Losses by second place team - losses by first place team)
The magic number changes to reflect any further changes in the second-place team.
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Select the false statement involving p, and the arbitrary events A and B. a) P( A^c n B^c)=P(A^c) P(B^c) b). P( A n B)=P( A) + P( B) -P( A U B). c). P(A^) + P(A)=1.d). P(A n B^c)= P(A)-P(A n B).e). P(A^c n B)=P(B)-P(A n B). f). None of the above.
The false statement is (a) P( A^c n B^c)=P(A^c) P(B^c). The probability of the intersection of complements is generally not equal to the product of individual complements.
The misleading assertion including p, and the erratic occasions An and B is (a) P( A^c n B^c)=P(A^c) P(B^c).
This assertion is bogus in light of the fact that by and large, the likelihood of the convergence of the supplements of two occasions, A^c and B^c, isn't equivalent to the result of their singular supplements.
For instance, assume we flip a fair coin. Let A be the occasion of getting heads and B be the occasion of getting tails. Then, P(A) = P(B) = 1/2, so P(A^c) = P(B^c) = 1/2. In any case, A^c and B^c are a similar occasion (getting heads or tails, separately), so P(A^c n B^c) = P(A^c) = 1/2. Then again, P(A^c) P(B^c) = (1/2)(1/2) = 1/4, which isn't equivalent to P(A^c n B^c).
Consequently, proclamation (a) is misleading.
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Please help out on question 1
1. Cosx = 5/√(41)
2. An equation {tan(x) + cot(x)}/{tan(x)} =csc²(x)
What are the trigonometric identities?Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
1. tanx = -4/5
and tanx = perpendicular/adjacent leg
So, P = -4 and A = 5
So, H = √(-4)² + (5)²
H = √(41)
So, Cosx = 5/√(41)
2. A trigonometric identity,
{tan(x) + cot(x)}/{tan(x)}
Simplifying,
= {tan(x)/tan(x) + cot(x)/{1/tan(x)}
= 1 + cot²(x)
= csc²(x)
Therefore, Cosx = 5/√(41)
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The point of concurrency of the three angle bisectors of a triangle is _____
The point of concurrency of the three angle bisectors of a triangle is incenter
The three angle bisectors of a triangle are concurrent in a point equidistant from the sides of a triangle. The point of concurrency of the angle bisectors of a triangle is known as the incenter of a triangle.
The incenter is the point in the triangle's inscribed circle, which is the circle that is perpendicular to each of the triangle's three sides.The point where the triangle's angle bisectors cross is known as the incenter, which is equidistant from the triangle's three sides. It is a crucial location in triangle geometry, and numerous incenter properties are applied in various triangle-related constructions and proofs.
Therefore, the point at which the three angle bisectors of a triangle meet is called its Incentre.
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If there were 2,500 people in your city and we wanted to survey people about how they feel about building a prison near the schools what would be a representative sample to survey
The requried representative sample for the survey would consist of 385 people randomly selected from the city's population.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
To obtain a representative sample of the population, the sample should be randomly selected to ensure that each person in the city has an equal chance of being chosen. The size of the sample will depend on the level of precision required, the confidence level desired, and the margin of error that is acceptable. However, as a general rule, a sample size of at least 385 people would be required to obtain a margin of error of plus or minus 5% with a 95% confidence level.
Therefore, a representative sample to the survey would consist of 385 people randomly selected from the city's population.
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what is 250lb in kg ?
Using the formula to convert pounds to kilogram,
We know that :
1 lb/ Pound = 0.453592 kilogram
therefore,
250 lbs/ Pound = 113.398 kilogram.
Using the formula to convert pounds to kilograms, you find that 250 pounds equals 113.398 kilograms
To convert 250 pounds (pounds) to kilograms (kg), you must use the conversion factor 1 pound = 113.398 kilogram.
Therefore,
we multiply 250 pounds by 86.18 kg/lb to get the equivalent weight in kilograms:
250 pounds x 0.45359237 kg/lb = 113.398 kilogram
Therefore,
250 pounds is 113.4 kilogram.
To understand the conversion factor, you need to know that pounds and kilograms are units of mass, but are used in many parts of the world. In the United States and some other countries, the accepted unit of mass is the pound, while most other countries use the kilogram.
A conversion factor connects the number of pounds to the number of kilograms, so you can easily convert from one unit of measure to another. It is important to use the correct conversion factor for accurate conversion.
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What is the cost and area of the mat
The costs and areas of the mat are
Mat area = 2x + 2y + 4; Cost = 0.1x + 0.1y + 0.2Mat area = 4x + 4y + 16; Cost = 0.2x + 0.2y + 0.8How to determine the cost and area of the matRepresent the dimensions of the frame with
Length = x
Width = y
So, the frame area is
Area = xy
When the mat is 1 inch from the frame, we have
Whole Area = (x + 1 + 1) * (y + 1 + 1)
Whole Area = (x + 2) * (y + 2)
Expand
Whole Area = xy + 2x + 2y + 4
So, the mat area is
Mat area = xy + 2x + 2y + 4 - xy
Mat area = 2x + 2y + 4
The cost is
Cost = 0.05 * (2x + 2y + 4)
Cost = 0.1x + 0.1y + 0.2
When the mat is 2 inches from the frame, we have
Whole Area = (x + 4) * (y + 4)
Expand
Whole Area = xy + 4x + 4y + 16
So, the mat area is
Mat area = xy + 4x + 4y + 16 - xy
Mat area = 4x + 4y + 16
The cost is
Cost = 0.05 * (4x + 4y + 16)
Cost = 0.2x + 0.2y + 0.8
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Can anyone help in number 12 pls… I don’t have to draw anything just have to write down the equation of a and b
Answer:
y=3x-2
Step-by-step explanation:
At the beginning of a snowstorm, Abigail had 12 inches of snow on her lawn. The snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow was melting, how much snow would Abigail have on her lawn 5 hours after the snow began to fall? How much snow would Abigail have on her lawn after tt hours of snow falling?
The snow on the lawn after 5 hours is 14.50 inches.
The snow on the lawn after tt hours is 12 + 0.5tt inches
How much snow is on the lawn?The equation that represents the amount of snow after a number of hours is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of the equation is:
Total snow = snow on the lawn + (rate at which the snow falls x number of hours)
Snow after 5 hours = 12 + (0.5 x 5)
= 12 + 2.5 = 14.50 inches
Snow after tt hours = 12 + (0.5 x tt)
= 12 + 0.5tt inches
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The cost of an air conditioner is $110. The cost to run the air conditioner is $0.35 per
minute.
What is the range of the situation above?
Answer:
Step-by-step explanation:
How do I find the slope of the image below??!!
Answer:
Step-by-step explanation:
A flag is shown. Determine the area of the shaded part of the flag.
Answer:
84 square inches
Step-by-step explanation:
The shaded region comprises of two same trapeziums:
∴Area of shaded region = 2 × (Area of a trapezium)
= 2 × [tex]\frac{1}{2}[/tex] × (Sum of parallel sides) × (perpendicular height of trapezium)
= [tex]\frac{2}{2}[/tex] × (4 + 8) × (6)
= 84 square inches
suppose v varies directly as g , and = 70 when v=30. Find v when g=9
Answer:
v = 21
Step-by-step explanation:
Suppose v varies directly as g, meaning that there is a constant k such that v = kg. If v = 70 when g = 30, then we can use this information to find the value of k:70 = k * 30k = 70 / 30k = 7 / 3Now that we have the value of k, we can use it to find v when g = 9:v = kgv = (7 / 3) * 9v = 21So when g = 9, v = 21.In conclusion, by finding the value of the constant of proportionality k and using the formula v = kg, we determined that when g = 9, v = 21.