a certain bacteria population obeys the population growth law. it is observed that the doubling time for the population is 4 hours. the length of time it will take for the population to increase to 3-times its original population is
Answers
According to the population growth law, the size of a population grows exponentially over time, with a growth rate proportional to population size. If the population doubling time is t, then the population size P can be written as:
[tex]P = P_0 * 2^{t/t_d)}[/tex]
where P_0 is the initial population size, t is the time elapsed, and t_d is the doubling time.
To find the time it will take for the population to increase to 3 times its original population size, we can set [tex]P = 3P_0[/tex] and solve for t:
[tex]3P_0 = P_0 * 2^{t/t_d}[/tex]
Dividing both sides by [tex]P_0[/tex] gives:
[tex]3 = 2^{t/t_d}[/tex]
Taking the logarithm of both sides (using any base) gives:
[tex]log(3) = log(2^{t/t_d} )[/tex]
Using the logarithmic identity
[tex]log(a^b) = b*log(a),[/tex]
we can rewrite this as:
[tex]log(3) = (t/t_d)*log(2)[/tex]
Solving for t, we get:
[tex]t = t_d * (log(3)/log(2))[/tex]
Substituting [tex]t_d[/tex] = 6 hours (given in the problem), we get:
[tex]t = 6 * (log(3)/log(2)) hours[/tex]
Simplifying using the change of base formula
[tex](log(a)/log(b) = log_b(a))[/tex], we get:
[tex]t = 6 * log_2(3)[/tex] hours
Therefore, the answer is (f) None of the above.
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Correct question should be
Click on image for question
Related Questions
5x-5=3x+15
it’s confusing someone help
Answers
Answer:
x=10
Step-by-step explanation:
First, add 5 to both sides of the equation, getting rid of the -5 on the left side but still making them equal.
5x=3x+20
Then, do the same with 3x, Subtract from both sides.
2x=20
Lastly, Divide both sides by 2 and you'll get your answer
x=10
Answer:
[tex] \sf \: x = 10[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x - 5 = 3x + 15
Then the value of x will be,
→ 5x - 5 = 3x + 15
→ 5x - 3x = 15 + 5
→ 2x = 20
→ x = 20 ÷ 2
→ [ x = 10 ]
Hence, the value of x is 10.
You order a pizza with a 12” diameter. What is the area of the pizza?
What is the radius of a pizza that is 25% larger??
Pls help
Answers
Answer:
1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:
r = 12 / 2 = 6 inches
The area of the pizza is then:
A = πr^2 = π * 6^2 = 36π square inches
2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:
increase = 6 * 0.25 = 1.5 inches
The new radius will then be:
new_r = 6 + 1.5 = 7.5 inches.
Step-by-step explanation:
Answer:
113.1, 8
The equation to find the area of a circle is:
Area = π (d/2)^2Now we can input 12 into the equation:
Area = π (12/2)^2Area = 113.1To find the radius of a pizza that is %25 larger, we can use this equation:
Radius × 1.25 = new radiusWhy do we multiply by 1.25?Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.
Fitting the radius into the equation:
6 × 1.25 = 8Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.
Is either x=8 or x=10 solution 4x < 34
Answers
Answer:
x=8 is true for the this condition
Step-by-step explanation:
4x<34
if x=8
4*8<34
32<34
which is true
if x=10
40 is not greater than 34, so it not satisfied the condition
Sarah Meeham blends coffee for Tasti-Delight. She needs to prepare 120 pounds of blended coffee beans selling for $4. 17 per pound. She plans to do this by blending together a high-quality bean costing $5. 25 per pound and a cheaper bean at $2. 00 per pound. To the nearest pound, find how much high-quality coffee bean and how much cheaper coffee bean she should blend
Answers
Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.
In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.
Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:
x + y = 120
The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:
4.17(120) = 501.6
We can also find the cost of the high-quality and cheaper beans in terms of x and y:
5.25x is the cost of the high-quality beans
2.00y is the cost of the cheaper beans
The total cost of the two types of beans is the sum of their individual costs:
5.25x + 2.00y
Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:
5.25x + 2.00y = 501.6
Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:
x = 120 - y (from the first equation)
5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)
Simplifying and solving for y, we get:
630 - 5.25y + 2.00y = 501.6
3.25y = 128.4
y ≈ 39.5
Now we can use this value of y to find x:
x = 120 - y
x = 120 - 39.5
x ≈ 80.5
Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.
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solve for x
13x-64=-2x+86
Answers
Answer:
x=10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
a heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high. (a) how much work w is done in pulling the rope to the top of the building?
Answers
A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high, the work done in pulling the rope to the top of the building is 1785 ft-lb.
To calculate the work done in pulling the rope to the top of the building, we need to use the formula:
W = F x d
where W is the work done, F is the force applied, and d is the distance over which the force is applied.
In this problem, we can calculate the force required to pull the rope as the product of its weight per unit length (0.7 lb/ft) and the length of the rope (30 ft). Thus, the force required is:
F = 0.7 lb/ft x 30 ft = 21 lb
To calculate the distance over which the force is applied, we need to calculate the total length of the rope that needs to be lifted. This can be found using the Pythagorean theorem, as follows:
l = √(30^2 + 80^2) = 85 ft
So the distance over which the force is applied is 85 ft.
Now we can substitute the values for F and d into the formula for work to get:
W = F x d = 21 lb x 85 ft = 1785 ft-lb
This calculation shows how the formula for work can be used to calculate the energy required to lift an object against gravity over a given distance.
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fifth fifth generation equipment is state the advantage and disadvantage how such computers were designed
Answers
Answer:
Step-by-step explanation:
Advantages of Fifth Generatin of Computer:These computers are much faster than other generation computers. Development of true artificial intelligence.
Development of Natural language processing.
Advancement in Parallel Processing. Advancement in Superconductor technology. More user-friendly interfaces with multimedia features. Availability of very powerful and compact computers at cheaper rates.
Disadvantages of Fifth Generatin of Computer: They tend to be sophisticated and complex tools. ...
Example of Third Generation of Computer: Desktop.
the number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete
Answers
The number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete are not directly related. The time it takes for a person to complete a jigsaw puzzle depends on several factors, including the person's experience with puzzles, the level of difficulty of the puzzle, the size of the puzzle pieces, and the person's level of concentration.
For example, a 500-piece puzzle might take one person several hours to complete, while another person might be able to finish it in just a few hours. Similarly, a 1000-piece puzzle might take one person a full day to complete, while another person might be able to finish it in just a few hours.
In general, the larger the number of pieces in a puzzle, the more time it will take to complete. However, the actual time required can vary greatly depending on the individual and the specific puzzle.
Find the area of the composite figure:
11 m
4 m
6 m
ch
3
5m
5 m
Answers
Answer:
69 meters
Step-by-step explanation:
It takes Andre 4 min to swim 5 laps how many laps per min?
Answers
Answer:
1.25 laps per minute
Step-by-step explanation:
5 laps in 4 minutes so distance over time is equal to rate so
5/4=1.25
The volume of a cylinder is given by the formula V = ²h
where r represents the length of the radius of the base of
the cylinder and h represents the height of the cylinder.
A cylinder has a volume of 54 m³ and a radius of 3 m.
What is its height, h?
Answers
Answer: 0.95m or 3/π
Step-by-step explanation:
Volume of cylinder = 2π[tex]r^{2}[/tex]*h
54 = 2π*9*h
divide 2π*9 on both sides
54/2π*9 = h
54/18π = h
3/π = h
h = 0.95 m
Wendell purchased a hot dog and 3 orders of french fries for $6.00. If the hot dog cost $2.25, what was the cost of each order of french fries?
Answers
The cost of each order of french Fries is $1.75.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Wendell purchased a hot dog and 3 orders of French fries for $6.00.
If the hot dog cost $2.25.
Then the cost of Hot dog
= 6 - 2.25
= 3.75
and, the cost of each order of French Fries
= 3.75 / 3
= $1.25
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the workers in a company are in the ratio femalee:male 1:45
the company has 150 female workers
how many many worker are there altogether
PLSSS NOW 100 points.
Answers
Answer: 825 workers altogether
Step-by-step explanation:
well, if the ratio is 4.5 men to every woman, we just have to multiply 150 by 4.5, which means there will be 675 male workers and 150 female workers.
Situation
ion below. Then wr
1.
A rectangle is 4 times as long as it is wide. The
perimeter of a rectangle is 50 cm. What are the
dimensions of the rectangle?
Identify what you are looking
for and assign variables..
Write equations to model the
situation described in the
problem.
Answers
The dimensions will be as follows;
width is 5cm while the length is 20cm.
Let width = w
Let length = 4w (according to question)
Perimeter = 50cm
Perimeter formula for a rectangle = 2 (l +w)
Substituting in the variables (width and length)
2(w + 4w) = 50
2(5w) = 50
10w = 50
w = 5
Remember that length = 4w
length = 4w
length = 4(5)
length = 20cm
Therefore, the dimensions of the rectangle are 5cm by 20 cm.
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How do you factor with a leading coefficient greater than 1?
Answers
Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.
Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.
One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.
The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.
Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.
In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.
Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.
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The sales tax rate is 6%. If Sally buy sarowboat priced at $842,how much tax will she pay?
Answers
If the sales tax rate is 6% and if Sally buy rowboat priced at $842, the amount of tax she will pay, $50.52
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
To calculate the sales tax on the purchase of a sailboat priced at $842 with a sales tax rate of 6%, you can follow these steps:
1. Convert the sales tax rate from a percentage to a decimal by dividing by:
= 100: 6% ÷ 100
= 0.06.
2. Multiply the price of the sailboat by the sales tax rate to find the amount of tax:
= $842 × 0.06
= $50.52.
Therefore, Sally will pay $50.52 in sales tax for the purchase of the sailboat.
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The graph shows f(x)and its transformation g(x). Enter the equation for g(x) in the box. g(x) =
Answers
The function g(x) can be written as -
g(x) = f(x - 1)
What is graph translation?Graph translation is a process of moving the graph over the dimensional plane either vertically, horizontally or both.
A translation can take place either horizontally or vertically as -
Vertical translation → Upward (y + k) & Downward (y - k).Horizontal translation → Upward (x + k) & Downward (x - k).Given are the graphs of exponential functions f(x) and g(x).
We can write the exponential function g(x) as -
g(x) = f(x - 1)
Therefore, the exponential function g(x) can be written as -
g(x) = f(x - 1).
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Zendaya was comparing the price of grapefruit juice at two stores. The equation
y = 0.97x represents what Zendaya would pay in dollars and cents, y, for x bottles
of grapefruit juice at store A. Zendaya can buy 4 bottles of grapefruit juice at Store b
for a total cost of $6.80.
How much more is a bottle of grapefruit juice at Store B than
at Store A?
Answers
the hippo at the zoo weighs 1.5 tons.how many pounds does the hippo weigh
Answers
The required weight of a hippo in pounds is given as 3,000 pounds.
What is a unit of measurement?
Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.
Here,
One ton is equal to 2,000 pounds, so a hippo that weighs 1.5 tons would weigh,
1.5 tons × 2,000 pounds/ton = 3,000 pounds
Therefore, the hippo at the zoo weighs 3,000 pounds.
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If the diameter of the pie is ten inchefls, what is the approximate arc length of one slice of pie?
A. 1.67 inches
B. 13.08 inches
C. (c) 3.14 inches
D. D 5.24 inches
Answers
The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.
Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.
Diameter (D)=10.
So the radius will be D/2.
Radius (R)=10/2=5.
The pie's circumference is given by:
C=2πR
C=2π*5
C= 10π (in)
Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,
Length of Arc (L)= 10π/6
L = 5π/3
L= 5(3.14)/3
L=5.234=5.24
Therefore the approximate arc length of one slice of pie is 5.24 inches.
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Evelyn bought 8.4 gallons of gas for $23.94. Which equation can be used to determine the price of each gallon of gas?
8.4x = 23.94
StartFraction x over 8.4 EndFraction = 23.94
23.94 x = 8.4
StartFraction x over 23.94 EndFraction = 8.4
Answers
Answer:
Step-by-step explanation:
The required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.here,Let the cost of gas per gallon be x,Now according to the question,Cost of 8.4 gallons of fuel = 8.4xfrom the question,8.4x = 23.94Thus, the required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.
Find the polynomial function k(x) of lowest degree in standard form if it has roots:
x=1,3,2i
Answers
Answer:
So the polynomial function is
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
Step-by-step explanation:
A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),
From the above data we can get,
k(x) = (x - 1)(x - 3)(x - 2i)
After expanding the equation ,
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
So the polynomial function is
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
Add: 410 + 210 Write your answer in simplest terms
Answers
The addition of two numbers is 410+210 is 620.
From the given numbers,
First number is 410
Second number is 210.
One of the arithmetic operations is addition. The total of the numbers is provided. In other words, addition refers to the operation of adding the numbers together. "+" is the symbol used to denote addition. The outcome of the adding procedure is referred to as the sum. Addends are the numbers that are added together.
One of the four fundamental mathematical operations, addition indicates the sum of two or more numbers added together.The following are the rules of addition operation:
Positive Number + Positive Number = (Add) Positive NumberNegative Number + Negative Number = (Add) Negative NumberNegative Number + Positive Number = (Subtract) Take the sign of the number with the largest absolute valueNow,
⇒410+210=620
Therefore, the value is 620.
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The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.
1. What is the area of the base of the cylinder? Express your answer in terms of .
2. How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of .
3. Give a decimal approximation of your answer to the second question using 3.14 to approximate n.
Answers
Answer:
1) 16pi square cm
2) 112pi cubed cm
3) 351.68 cubed cm
Step-by-step explanation:
Question 1: The base of a cylinder is a circle. To find the area of a circle, we can use the formula A = pi(r^2). the radius is 4 centimeters. 4^2 = 16.
The answer to the question is 16pi square cm
Question 2: This question is asking for the volume of the cylinder. To find the volume of the cylinder, we must multiply the area of the base by its height. we know the area of the base is 16pi. 16pi x 7(the height) = 112 pi.
The answer to the question is 112 pi cubed cm
Question 3: If pi were to be 3.14, we just need to substitute pi in the equation for question two with 3.14:
16(3.14) x 7 = 351.68
The answer is 351.68 cubed cm
10. If the opposite angle of the parallelogram is 22 less, than thrice the other angle. Find the other angle (a) 24° (c) 22° (d) 32° (b) 34°
Answers
The measure of the other angle of the parallelogram is 22 degrees.
What is the other angle of the parallelogram?Opposite angles of a parallelogram are equal (or congruent).
Let the missing angle be represented by x.
First angle = xOpposite angle = 2x - 22Since the opposite angles of a parallelogram are equal (or congruent).
x = 2x - 22
Solve for x
2x - 22 = x
2x = 22 + x
2x - x = 22
x = 22°
Therefore, 22 degrees is the measure of the other angle.
Option C) 22° is the correct answer.
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Pls show your work thank you will mark the Brainliest
Answers
Since the initial value starts at 200,000 the y-axis has to start at 200,000. If the price rises 6% every year and the x-axis goes by 5 then at 5 years the graph should be at 1,000,000. The projection of graph A would be 1,000,000 at 5 years.
Which of the following shows measurements ordered from smallest to largest? answers: 60,000 mg, 1.5 kg, 3,000 g 3,000 g, 1.5 kg, 60,000 mg 1.5 kg, 3,000 g, 60,000 mg 60,000 mg, 3,000 g, 1.5 kg who ever help me get 100 brainy.
Answers
Answer:
60000 mg, 1.5 kg, 3000 g-----------------------
Given measurements:
60000 mg, 1.5 kg, 3000 gBring all to same unit, grams, then compare;
60000 mg = 60 g,1.5 kg = 1500 g,3000 gOrder them from smallest to largest:
60 g < 1500 g < 3000 g or 60000 mg < 1.5 kg < 3000 gAnswer:
The order of the measurements from smallest to largest is:
60,000 mg, 1.5 kg, 3,000 gStep-by-step explanation:
The three given measurements of mass are:
60,000 mg1.5 kg3,000 gDefinitions"g" means grams."mg" means milligrams. "Milli" means a thousandth.⇒ 1 mg = 0.001 g"kg" means kilograms. "Kilo" means one thousand.
⇒ 1 kg = 1000 g
Therefore, to be able to order the three given measurements from smallest to largest, first convert them to the same unit of mass (grams):
⇒ 3,000 g = 3,000 g
⇒ 60,000 mg = 60,000 × 0.001 = 60 g
⇒ 1.5 kg = 1.5 × 1000 = 1,500 g
Therefore, the order of the measurements in grams from smallest to largest is:
60 g < 1,500 g < 3,000 gSo, the order of the measurements in their original units from smallest to largest is:
60,000 mg, 1.5 kg, 3,000 gIf 4 is added to twice the number n, the result is the same as if n were increased by 7. What is the value of n?
Answers
Answer:
n = 3
Step-by-step explanation:
Starting equation:
2n + 4 = n + 7
Subtract by n on both sides:
n + 4 = 7
Subtract 4 on both sides
n = 3
Check to see if the answer works:
2(3) + 4 = 3 + 7
6 + 4 = 3 + 7
10 = 10
The solution works
n = 3
Helppp i need to find the transformations needed.
Answers
The transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
What is a transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
The given functions are f(x)=x³ and g(x)= -(x-4)³+1.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 4 Units
Vertical Shift: Up 1 Units
Reflection about the x-axis: None
Reflection about the y-axis: Reflected
Vertical Compression or Stretch: None
Therefore, the transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
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prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders. you can only use the definition of bk. per the definition, bk is formed by joining two bk−1 trees.
Answers
To prove that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, we will use mathematical induction.
Base case: For k = 1, removing the root of a 1st order binomial tree results in zero smaller binomial trees, which is true.
Inductive hypothesis: Assume that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, for some positive integer k.
Inductive step: We want to prove that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders.
By definition, a (k+1)-th order binomial tree, denoted by B(k+1), is formed by joining two k-th order binomial trees, denoted by Bk, with one of them as the leftmost child of the root of the other. Let us remove the root of B(k+1) to obtain a new binomial tree, denoted by B'.
Since B(k+1) is formed by joining two k-th order binomial trees, we can apply the inductive hypothesis to each of them to obtain that removing their roots results in k smaller binomial trees each. Let these smaller binomial trees be denoted by B1, B2, ..., Bk and C1, C2, ..., Ck,
respectively.
Now, consider B' and observe that it is a k-th order binomial tree, since it has k children, each of which is a smaller binomial tree. Moreover, B' is obtained from B(k+1) by removing the root, which is the parent of the two k-th order binomial trees Bk and Ck. Thus, we have decomposed B' into k smaller binomial trees, namely B1, B2, ..., Bk and C1, C2, ..., Ck.
Therefore, we have shown that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders, which completes the induction.
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