After one hour, there would be 337,500 bacteria in the hamburger.
This problem involves exponential growth relation, which is as below:
[tex]P(t)=P_{o}*e^{rt}[/tex]
where, [tex]P_{o}[/tex] is the initial value (i.e. at t=0), P(t) is the value at time 't' and r is the growth rate.
Usually, one perceives growth as linear, which might seem logical in unspecified cases. But, when specified exponential growth, the scenario changes. The difference between linear and exponential growth is like the difference between velocity and acceleration.
In case of above stated problem; [tex]P_{o}[/tex]=100,000 and P(20)=150,000
For calculating r, we substitute values:
[tex]150,000=100,000*e^{r*20}\\e^{20r}=1.5\\20r=ln(1.5)\\r=0.0202733[/tex]
Now we have our growth rate. Using the same formula for t=60, we have:
[tex]P(60)=100,000*e^{0.0202733*60}\\P(60)=100,000*3.375\\P(60)=337,500[/tex]
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The Quantity of an element is decaying over time such that the amount of material at
time is given by the funetion K (t) = 2000(0.9)^t+2. Write an equivalent
function of the form K (t) = ab^t
Answer:
Below
Step-by-step explanation:
= 2000 (.9)^2 (.9)^t
= 2000(.81)(.9)^t
= 1620 (.9)^t
Answer:
[tex]K(t)=1620(0.9)^{t}[/tex]
Step-by-step explanation:
Given function:
[tex]K(t)=2000(0.9)^{t+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies K(t)=2000(0.9)^{t}\cdot(0.9)^2[/tex]
Simplify:
[tex]\implies K(t)=2000(0.9)^{t}\cdot0.81[/tex]
[tex]\implies K(t)=0.81 \cdot 2000(0.9)^{t}[/tex]
[tex]\implies K(t)=1620(0.9)^{t}[/tex]
A snail moves 7/50 of a mile in 7/8 of an hour. If the snail continues at this pace, how far, in miles, does it move in one hour?
The number of miles it takes the snail to move for an hour is 25/4 miles
How to find the number of miles the snail moves?Number of miles the snail moves = 7/50 of a mileNumber of hours the snail moves = 7/8 of an hourhow far, in miles, does it move in one hour?
let number of miles = xEquate the ratio of number of miles to number of hours
7/50 : 7/8 = x : 1
7/50 ÷ 7/8 = x / 1
7/50 × 8/7 = x / 1
50/8 = x / 1
cross product50 × 1 = 8 × x
50 = 8x
divide both sides by 8
x = 50/8
x = 25/4 miles
In conclusion, the snail moves 25/4 miles when traveling for an hour.
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a committee of three is chosen from a group of 13 people. how many different committees are possible if the following conditions apply?
There are total 246 ways to select a committee of 3 from a gorup of 13.
What is Combination?
A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations.
Solution:
Given that,
Total Number of Applicants = 13
Total Seats Available for the Committee = 3
Since, the order of selection is not relevant in the given question we will use combination.
13C3 = 13! / (10! * 3!)
13C3 = 13*12*11*10!/(10! * 6)
13C3 = 286
This means there are total 246 ways to select a committee from a gorup of 13.
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A teacher buys 100 pencils to keep in her classroom at the beginning of the school year. She allows the students to borrow pencils, but they are not always returned. On average, she loses about 8 pencils a month. Which equation represents the number of pencils she has left y after a number of x months?.
A teacher buys pencils= 100
the equation is y=8x/100.
total number of pencils = 100
average number of pencil lost in months = 8
number of pencil lost in one month = 8/100
pencil left = y
months = x
so the equation would be:
y = 8x/100.
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In Jayce's favorite video game, he collects stars to earn points. Today, he collected 80 silver stars and earned 160 points. He also collected 30 gold stars and earned 150 points. How many more points per star does Jayce earn from gold stars?
As a decimal or whole number
By taking some simple quotients, we will see that a gold star gives 3 points more than a silver star.
How many points the gold stars give?First, we know that 80 silver stars are equivalent to 160 points, to get the number of points that each star gives, we need to take the quotient between the number of points and the number of stars.
160/80 = 2
Each silver star gives 2 points.
We also know that 30 gold starts give 150 points, then:
150/30 = 5
Each gold star gives 5 points.
The difference is:
5 - 2 = 3
A gold star gives 3 points more than a silver star.
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(2x + 6)
The perimeter (adding up all the sides) of a rectangular
piece of land is 228 feet. The length of the land can be
shown by x and its width can be shown by (2x + 6).
Solve for x, and then plug it back in to find the Length
and the Width of the land.
The value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.
According to the question,
We have the following information:
The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land can be shown by x and its width can be shown by (2x + 6).
We know that the perimeter of rectangle is given by the following formula:
2(length+width)
2(x+2x+6) = 228
2(3x+6) = 228
Dividing by 2 on both the sides:
3x+6 = 228/2
3x+6 = 114
Subtracting 6 from both the sides:
3x = 114-6
3x = 108
x = 108/3
x = 36 feet
Now, the length of the rectangle = 36 feet
Width = 2x+6
Width = 2*36+6
Width = 72+6
Width = 78 feet
Hence, the value of x is 36 feet and the length of the rectangle is 36 feet and the width is 78 feet.
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The markup on a restaurant is 250%. A meal costs 7.30 to produce, How much will the customer be charged before tax and tip?
The amount that the customer be charged before tax and tip is $25.55
Given,
The markup on a restaurant = 250%
The cost of a meal to produce = $7.30
We have to find the amount will the customer be charged before tax and tip;
The markup price = 250/100 × 7.30 = 5/2 × 7.30 = 2.5 × 7.30 = 18.25
The Markup price on a restaurant is $18.25
Now,
The amount that the customer be charged before tax and tip = The cost of a meal to produce + The markup price
= 7.30 + 18.25
= 25.55
That is,
The amount that the customer be charged before tax and tip is $25.55
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when a survey questionnaire in english is translated into korean for use in south korea and then translated back into english to check its accuracy, it is described as:
When an English-language survey questionnaire is converted into a Korean version for usage in south Korea and then translated back into English to ensure accuracy.
Given statement;
When a survey questionnaire in English is translated into Korean for use in south Korea and then translated back into English to check its accuracy.
It can be described as back translation,
Back Translation:
Back translation, also known as reverse translation, is the process of literally translating text back into the source language from the target language. Translations from English to Swedish not affect would also include a reverse translation into English so that the meaning of the translated option could be clearly understood. Back translations have no effect on the translator's translation memory or other tools, such as glossaries.
It is described as a back translation.
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The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry.
In words, describe the graph of the proportional relationship.
A line from (0, 0) going through (20.70, 23) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (23, 20.70) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Cost (in dollars) and the y-axis is labeled Weight (in pounds)
The graph of the proportional relationship is
(c) A line from (0, 0) going through (38, 34.20) where the x-axis is labeled Weight (in pounds) and the y-axis is labeled Cost (in dollars)
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Given:
It costs $20.70 for 23 pounds of laundry and $34.20 for 38 pounds of laundry.
which shows that
(x, y) = (20.70, 23) and (34.20, 38)
Where
x = Weight and y = Cost
So, The graph is a proportional graph which means that line passes through the origin
So, we have
(x, y) = (0, 0), (20.70, 23) and (34.20, 38)
Hence, the graph of the proportional relationship is (c)
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A car with an initial velocity of 25 miles per hour begins to accelerate at a constant rate. The table shows the elapsed time after the car begins to accelerate and the velocity of the car at a particular time.
Which linear function best models the car's velocity, V(t), in terms of the elapsed time (t) after the car begins to accelerate?
Responses
Answer:
i need help please by german
Jane solved an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Jane’s mistake and what is the solution to the equation?
-3(4x - 5) = 6(x + 3) + 10
-12x + 15 = 6x + 18 + 10
-12x + 15 = 6x + 18
15 = -6x + 18
-3 = -6x
= x
the expression 18+1.5x is 8 less than 36.5. What is the value of 4x
In the expression 1.5x + 18 = 36.5 - 8 x is 7, hence 4x is 28.
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, An expression 18 + 1.5x is 8 less than 36.5.
∴ 1.5x + 18 = 36.5 - 8.
1.5x = 36.5 - 8 - 18.
1.5x = 10.5.
x = 10.5/1.5.
x = 7.
Therefore 4x is equal to 4(7) = 28.
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If x= 4-5 and y = -4 - 7i, what is x + y?
The value of x + y is -12i.
What are complex numbers?
Real numbers and imaginary numbers combine to form complex numbers, which have two components. Complex numbers serve as the foundation for more complex math, including algebra. They have numerous practical applications, particularly in the fields of electronics and electromagnetism.
Here, we have
Given x = 4 - 5i and
y = -4 - 7i
Now we have to find the value of x+y.
We will add both complex numbers and we get
x + y = 4 - 5i + (-4 -7i)
x + y = - 12i
Hence, the value of x + y is 12i.
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Please help!!! 20 Points!! The total price of 6 pieces of drawing paper and 1 ballpoint pen at $0.70 is equal to the total price of a piece of drawing paper and a box of paints How much is the price of a piece of drawing paper?
Answer:
$4.21
Step-by-step explanation:
6*70+1=421
During a one-month promotional campaign, Fran's Flix gave either a free DVD rental or a 12-serving box of microwave popcorn to new members. It cost the store $1 for each free rental and $2 for
each box of popcorn. In all, 50 new members were signed up and the store's cost for the incentives was $80. How many of each incentive were given away?
30 boxes of popcorn and 20 free DVD rentals were given away.
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
let a variable represent the number of the highest-cost item (boxes of popcorn). If that is p, then the number of DVD rentals is (53-p) and the total cost is ...
2p +(50 -p) = 80
p = 80 -50 = 30 . . . . . . . boxes of popcorn
50-p= (50 -30) = 20 . . . DVD rentals
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Triangle xyz was translated up 2 and right 3 units, creating triangle cab. Which relationship between the parts of the two triangles must be true?.
The congruency relationship which hold true after transformation is
YZ ≅ AB
What is congruent ?
In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes.
Explanation:
A translation is known as a rigid transformation. This is because it preserves congruence. Since CAB is created from XYZ, this tells us that:
X corresponds to C; Y corresponds to A; Z corresponds to B; XY corresponds to CA; YZ corresponds to AB; and XZ corresponds to CB.
Since the triangles are congruent, the corresponding pieces are congruent as well.
Out of these corresponding congruent pieces of triangles, the only one in our options is YZ ≅ AB.
Hence the answer is YZ≅AB.
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Describe the transformation of the parent
function f(x) = x².
f(x) = (x − 1)² +3
The transformation from the parent function is a translation by 1 unit right and 3 units up
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = x²
f(x) = (x − 1)² + 3
First, we have the transformation to be:
From f(x) = x² to f(x) = (x − 1)²
This means the function is translated right by 1 unit
Next, we have:
From f(x) = (x − 1)² to f(x) = (x − 1)² + 3
This means the function is translated up by 3 units
Hence, the transformation is 1 unit right and 3 units up
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what is the distribution of the number of fair coin tosses before one observed 3 heads in a row? markov chain
The distribution of the number of fair coin tosses before one observed three heads in a row is 14.
We have a coin. We have to find the number of fair coin tosses before one observes three heads in a row. We need to use the Markov chain. The probability of getting a head when a coin is flipped is 1/2. Let the probability be represented by the variable "p". Let the number of heads we want in a row be "n".
p = 1/2
n = 3
Using the Markov chain, the formula for getting "n" numbers of the same event in a row with the probability "p" is given below.
A(n) = [1 - p^(n)]/[(1 - p)*p^(n)]
We need to find the value of A(3).
A(3) = [1 - (0.5)^(3)]/[(1 - 0.5)*(0.5)^(3)]
A(3) = [1 - 0.125]/[(0.5)*(0.125)]
A(3) = 0.875/0.0625
A(3) = 14
Hence, the number of fair coin tosses before one observes three heads in a row is 14.
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Graph the polynomial function f(x) = x^3 + 3x^2 – 4x – 12 using its intercepts and end behavior
The graph of the polynomial f(x) is added as an attachment
How to plot the graph of the polynomial?From the question, the equation of the polynomial is given as
f(x) = x^3 + 3x^2 – 4x – 12
To start with, we need to represent the function of the polynomial properly
So, we have the following representation
f(x) = x³ + 3x² – 4x – 12
Solving further, we need to factorize the function
This gives
f(x) = x²(x + 3) - 4(x + 3)
Factor out x + 3
f(x) = (x² - 4)(x + 3)
Express as difference of two squares
f(x) = (x - 2)(x + 2)(x + 3)
When the above equation is solved, we have
x = 2, x = -2 or = -3
This means that the intercepts of the function are -3, -2 and 2
Next, we plot the polynomial function using the above intercepts and the end behavior
See attachment for the graph of the function
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HELP MEEEE PLEASE TYYY
Answer:
241.9026
Step-by-step explanation:
2*pi*r
Answer:
241.9 cm
Step-by-step explanation:
circumference= [tex]\pi[/tex]d
circumference= [tex]\pi[/tex](77)
circumference= 241.9 cm
What is the square of -37
Rounded to the whole number: 6
A parallelogram is shown.
7.5 cm
Area = 62 cm²
Work out the perimeter of this parallelogram.
Optional working
6.2 cm
Answer:
cm
The perimeter of the parallelogram is 35 cm.
What is the perimeter of a parallelogram?The length of the continuous line that a parallelogram's boundary forms are considered to be its perimeter. The same unit applies to it as it does to its sides. A closed shape made up of four line segments is referred to as a quadrilateral. If the opposing sides of a quadrilateral are parallel and the same length, the shape is referred to as a parallelogram.
Given, the area of the parallelogram = 62 cm²
We know the area of the parallelogram = base × height
62 = b × 6.2 cm
b = 62/6.2
b = 10 cm
So, the perimeter of the parallelogram is given by
P = 7.5 + 10 + 7.5 + 10 cm
P = 35 cm
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What is radius r length?.
A line segment that connects a circle, sphere, or other shape's center to its perimeter or border. Radius: 12 units
What is Pythagoras Theorem?According to the Pythagorean Theorem, a right triangle's hypotenuse (the side opposite the right angle) or, using conventional algebraic notation,[tex]a^{2} + b^{2} = c^{2}[/tex]
The Pythagorean theorem is well known for what reason?The Greeks established the existence of numbers that could not be expressed as rational numbers thanks to Pythagoras' theorem. For instance, if we assume that the two shorter sides of a right triangle are 1 and 1, we are left with a length hypotenuse that is not a rational number.
By Pythagoras theorem-
[tex]adjacent side^{2} + opposite side^{2} = hypotenuse^{2}[/tex]
35= opposite side
r= adjacent side
25+r= hypotenuse
[tex](25+r)^{2} = 35^{2} + r^{2}\\ 665 + r^{2} + 50r = 1225 + r^{2} \\50r = 600\\r=12 units[/tex]
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Need help for this question
Answer:
b) 6
Step-by-step explanation:
Given information,
→ P = (5x + 30)°
→ S = 80°
Forming the equation,
→ P + S = 140°
→ (5x + 30)° + 80° = 140°
Now the value of x will be,
→ (5x + 30)° + 80° = 140°
→ 5x + 110° = 140°
→ 5x = 140° - 110°
→ x = 30°/5
→ [ x = 6° ]
Hence, the value of x is 6.
Starter:
What is a factor?
What is a multiple?
Which is the odd number out of each list?
1. 16,32,40,52
2. 21,35, 62, 84
3. 24, 46, 84, 132
4. 18, 32, 48, 90
5. 16, 27, 54, 81
Main task:
Find the Highest Common Factor of these
numbers:
1. 18 and 30
2. 15 and 20
3. 16 and 24
4. 12 and 36
5. 20 and 30
6. 28 and 70
Find the Lowest Common Multiple of these
numbers
1. 6 and 7
2.4 and 6
3.5 and 8
4. 10 and 4
5. 16 and 5
6. 14 and 21
Factor:
A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.
Multiple:
multiple in math are the numbers you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.
How to find hcf of two or more numbers :
Steps 1:
Find all the factors of each given number.
Step 2:
Find common factors of the given number.
Step 3:
The greatest of all the factors obtained in Step 2, is the required highest common factor (H.C.F).
I'm only writing the answers below as I already told how to find it.
Highest common factor:
1. The factors of 18 are: 1, 2, 3, 6, 9, 18
The factors of 20 are: 1, 2, 4, 5, 10, 20
Then the greatest common factor is 2.
2. The factors of 15 are: 1, 3, 5, 15
The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20
The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20Then the greatest common factor is 5.
3. 8
4. 12
5. 10
6. 14
How to find lcm. of numbers :
Step 1: Find the prime factors of the given numbers by repeated division method.
Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.
Step 3: The product of these factors with the highest powers is the LCM of the given numbers.
I'm only writing the answers below as I already told how to find it.
Lowest common multiple :
1. 42
2. 12
3. 40
4. 20
5. 80
6. 42
hope it helps you..
Does anyone know the answer?
Answer:
a. -13
b. 14
c. -6
Step-by-step explanation:
a.
Substitute x = -3 into the equation.
f(-3) = 2(-3) - 7
= - 6 - 7
= -13
b.
Substitute f(x) = 21 into the equation.
2x - 7 = 21
2x = 28
x = 14
c.
Substitute x = 1/2 into the equation.
f(1/2) = 2(1/2) - 7
= 1 - 7
= -6
Explain how proving two triangles congruent can help prove parts of the triangle congruent.
Answer:
If two triangles are congruent, then by the definition of congruent triangles, 3 pairs of sides are congruent and 3 pairs of angles are congruent. In all, this is 6 statements of congruence.
There are ways of proving triangles congruent that require only 3 statements of congruence of corresponding parts, such as ASA, SAS, AAS, etc.
Sometimes in order to prove two segments or two angles congruent, since these segment and angles are parts of triangles, you prove the triangles congruent using some other statements of congruence, not involving these parts, and then you get 6 statements of congruence that includes the parts you wanted to prove congruent. That is where you use "corresponding parts of congruent triangles are congruent", or CPCTC for short.
inscribed in a circle is a quadrilateral having sides of lengths 25,~39,~5225, 39, 52, and 6060 taken consecutively. the diameter of this circle has length
The diameter of this circle has length of 65 when it is inscribed in a circle is a quadrilateral.
What is meant by diameter?The straight line that runs through the center of a round shape or object from one point on one edge to another: The diameter is twice as large as the radius. The pond is six feet across. Both definitions hold true for the diameter of a sphere.
We note that 25²+60²=65² and 39²+52²=65²
Let [tex]\bar{AB}[/tex]=25, [tex]\bar{BC}[/tex]=39, [tex]\bar{CD}[/tex]=52, [tex]\bar{DA}[/tex]=60
Let [tex]\bar{BD}[/tex]=x and ∠DAB=y
x²=25²+60²-3000cos(y)
x²=39²+52²-4056cos(180-y)
We obtain by performing some computation x²=4225-3000cos(y) and x²=4225-4056cos(y).
4056cos(y)=3000cos(180-y)
cos(180-y)=-cos(y)
So, by substituting we get 4056cos(y)= -3000cos(y)
cos(y)=0 or y=90.
∠BAD=90 and ∠BCD=90.
The diameter of a right triangle inscribed in a circle is the hypotenuse.
This means that the diameter is √4225=65
Therefore, the diameter of this circle has length of 65.
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Mark buy 2 pound of ham and 4 pound of turkey for 40$. Gigi buy 5 pound of ham and 4 pound of turkey for 51$
How much i a pound of ham?
Based on Mark's and Gigi's expenditure, a pound of ham costs $3.67.
Let us represent 1 pound of ham by x and 1 pound of turkey by y. Forming equation based on Mark's ham and turkey
2x + 4y = 40 : Equation 1
Forming equation based on Gigi's ham and turkey
5x + 4y = 51 : Equation 2
Subtracting Equation 1 from equation 2
5x + 4y = 51
(-) 2x (-) + 4y = (-) 40
The result we get on subtraction -
3x = 11
x = 11/3
Performing division on Right Hand Side of the equation
x = 3.67
Thus, one pound of ham cost $3.67.
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1. Find the average rate of change on the interval [-2, 2] for each of the functions below.
a. a(x) = 2x + 1
b. b(x) = x² + 2
d. Which function has the greatest average rate of change over the interval x = -2 to x = 2?
c. c(x) = 2x - 1
The greatest average rate is. x^2+1
What is ROC?
The rate of change is measured by a line's slope.Rate of Change: How quickly a variable changes over a predetermined amount of time. It is frequently used while discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.acc toour question-
(1+4x)/2 f(2) = 9/2; f(-1) = -3/2 AROC = (9/2 - -3/2)/3 = 12/2 over 3 = 6 /3 or is it 1+ 4x/2 = 1+2x ??? f(2) = 5; f(-1) = -1; AROC = (5 - -1)/3 = 6/3 = 2 <--- YES !!!B) f(2) = 2^2 - 2 = 4 - 2 = 2 f(-1) = (-1)^2 - (-1) = 1 - (-1) = 1+1 = 2 AROC = (2-2)/3 = 0/3 = 0 <--- NOC) f(2) = 2^2 = 4; f(-1) = (-1)^2 = 1; AROC = (4-1)/3 = 3/3 = 1 <--- NOd) f(2) = 2^2 + 2 = 4+2=6 f(-1) = (-1)^2 + (-1) = 1+(-1) = 0 (6-0)/3 = 6/3 = 2Learn more about roc click here:
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