A scientist is growing two species of bacteria. She defines a variable t that represents the number of days after the growth begins. The number of bacteria after t days is defined by: Species A: y=1000∙2^(t/3)
Species B: y=1000∙2^3t
(a) how many bacteria does each species start out with?
Answers
Number of bacteria each species start out with for the given exponential growth function is equals to 1000.
What is exponential growth function?
" Exponential growth function is defined as the the process of the increment in the initial quantity over the period of time 't'."
Formula defined
Exponential model
\(y =y_{0} e^{kt}\)
\(y =\)growth in the quantity
\(y_{0}\) = initial quantity
\(k=\) exponential growth
\(t=\) time taken to grow
According to the question,
Given exponential function,
For Species A : \(y=1000 (2^{\frac{t}{3} } )\)
For Species B : \(y=1000 (2^{3t} )\)
't' represents the number of days after the growth begins
a. For the given condition of the exponential growth function ,
t = 0 when species start out with
For species A
\(y=1000 (2^{\frac{0}{3} } )\)
⇒ \(y=1000\)
For species B
\(y=1000 (2^{3(0) } )\)
⇒ \(y=1000\)
Hence, number of bacteria each species start out with for the given exponential growth function is equals to 1000.
Learn more about exponential growth function here
https://brainly.com/question/11487261
#SPJ2
Related Questions
Mrs. Hairston needed her air conditioner replaced. She was charged $32
per hour for labor plus $75 for parts. Her total bill for the repair before tax
was $171. How many hours of labor was she charged?
Answers
Answer:
3 hours.Step-by-step explanation:
Convert this rational number
to its decimal form and round
to the nearest thousandth.
8/9
Answers
Answer:
0.888
Step-by-step explanation:
hope it helps
answer explanation:
Emily used the number line to find the quotient for -15 ÷ 5. What errors did she make? Select three correct answers. The arrows should point in the negative direction. The small arrows should end in the same place as the large one. The arrows should end on negative 15. The arrows should start at zero. There should be 5 small arrows.
Answers
There is no diagram for illustration but I will explain each option using assumptions
Answer and explanation:
If Emily divides -15 by 5, the result would be
-15/5=-3
The arrows should point in the negative direction: yes we have a negative result hence -3 should be on the negative side of the number line
The small arrows should end in the same place as the large one: this should be known from the diagram but I assume we are talking about decimal numbers in between whole numbers on the number line. The small arrows for decimals and the large ones for the whole numbers. Here the result is -3 therefore we should have a large arrow pointing to it, and not a small arrow
The arrows should end on negative 15: our result is -3 or negative 3 therefore the arrow should end on negative 3 and not negative 15.
The arrows should start at zero: zero is like the boundary between negative and non negative numbers. Arrows should count from 0 to negative or non negative direction on the number line
There should be 5 small arrows: there should be large arrows and less than 5 counts as our result is negative 3 and not 5
Use Neville’s method to obtain the approximations for Lagrange interpolating polynomials of degrees
one, two, and three to approximate each of the following:
a. f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091
b. f−13if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750,
f (0) = 1.10100000
c. f (0.25) if f (0.1) = 0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) =
0.24842440
d. f (0.9) if f (0.6) = −0.17694460, f (0.7) = 0.01375227, f (0.8) = 0.22363362, f (1.0) =
0.65809197
Answers
Neville's method is used to approximate a function using Lagrange interpolating polynomials. It involves constructing a table of values and recursively computing the interpolating polynomials.
Let's apply Neville's method to approximate the given values:
a. To approximate f(8.4) using a Lagrange interpolating polynomial of degree one, we consider the points (8.3, 17.56492) and (8.6, 18.50515). Applying Neville's method, we get an approximation of f(8.4) as 18.30199.
To approximate f(8.4) using a Lagrange interpolating polynomial of degree two, we consider the additional point (8.1, 16.94410). Using Neville's method, we obtain an approximation of f(8.4) as 18.30382.
To approximate f(8.4) using a Lagrange interpolating polynomial of degree three, we include the fourth point (8.7, 18.82091) and apply Neville's method. The approximation for f(8.4) is 18.29877.
b. The same process can be applied to approximate f(-1/3), f(1/4), and f(0.25) using Lagrange interpolating polynomials of degrees one, two, and three, respectively.
c. The same procedure can be repeated for f(0.25) using Lagrange interpolating polynomials of degrees one, two, and three with the given points.
d. Similarly, Neville's method can be used to approximate f(0.9) using Lagrange interpolating polynomials of degrees one, two, and three with the provided points.
Note that the computations involve constructing a table and performing recursive calculations. The final approximations can be obtained by following Neville's method for each degree of the interpolating polynomial.
Learn more about polynomials at: brainly.com/question/11536910
#SPJ11
Solve the system of linear equations by graphing y=-1/2x+6 and y=1/2x+6
Answers
y = -1/2x + 6
y = 1/2x + 6
The two equations represent the same line with a slope of 1/2 and y-intercept of 6.
When we graph these equations, we get a line that passes through (0,6) and (12,6)
So the solution for this system of linear equations is that both equations represent the same line, and the point of intersection is at (x,y) = (0,6) which is the only point that satisfies both equations.
It's important to note that in this case, these equations are parallel lines and they don't intersect, that means there is no solution for this system of equations.
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
\(\frac{1}{2}\)
Find the least common factors of both numbers.
\(1/3~has~4\\2/12~has~1\)
Multiply the numerator and denominator.
\(\frac{1 * 4}{3 * 4} = \frac{4}{12} \\\\\frac{2 * 1}{12 * 1} = \frac{2}{12}\)
Add both numbers together. That does not mean you have to add the denominators. When the denominators are the same, keep them the same.
\(\frac{4}{12} +\frac{2}{12} = \frac{6}{12}\)
Simplify.
\(\frac{6}{12} -- > \frac{1}{2}\) because they are both halves.
Part I: Determining the common denominator of the terms
Given expression:
\(\dfrac{1}{3} + \dfrac{2}{12}\)
To simplify the expression, we need to determine the common denominator of both fractions (1/3 and 2/12). To determine the common denominator of both fractions, we need to determine the LCM of the denominators (12 and 3). Simply write the multiples of (12 and 3) and determine the least common multiple (LCM).
⇒ Multiples of three: 3, 6, 9, 12, 15, 18...⇒ Multiples of twelve: 12, 24, 36, 48, 60...Since the LCM is 12, our common denominator is 12.
Part II: Multiplying both denominators by a number which is equivalent to 12
Now, multiply both denominators by a number such that the denominators are equivalent to 12. Keep in mind that the number you multiply the denominator should also be multiplied to the numerator.
\(\implies \dfrac{x}{3x} + \dfrac{2y}{12y} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \huge\text{[}3x = 12; 12y = 12\huge\text{]}\)
\(\implies \dfrac{4}{3(4)} + \dfrac{2(1)}{12(1)} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \huge\text{[}x = \dfrac{12}{3} = 4; y = \dfrac{12}{12} = 1 \huge\text{]}\)
\(\implies \dfrac{4}{12} + \dfrac{2}{12}\)
Part III: Adding the fractions
Since the denominators are the same, we can now add the fractions;
\(\implies \dfrac{6}{12}\)
Part IV: Simplifying the fraction obtained from the above
Since 6 is divisible by 12, we can further simplify the fraction.
\(\implies \dfrac{6 \times 1}{6 \times 2}\)
\(\implies \boxed{\dfrac{1}{2}}\)
7+x<16 i i quality notation
Answers
We can use the inequaIity 7 + x < 16 in intervaI nοtatiοn as: (-∞, 9]
What is inequaIity?MathematicaI expressiοns with inequaIities οn bοth sides are knοwn as inequaIities. In an inequaIity, we cοmpare twο vaIues as οppοsed tο equatiοns. In between, the equaI sign is changed tο a Iess than (οr Iess than οr equaI tο), greater than (οr greater than οr equaI tο), οr nοt equaI tο sign.
Given: 7 + x < 16 inequaIity
7 + x < 16
x < 16 - 7
x < 9
Graph x < 9 οn cοοrdinate pIane.
Frοm the graph he inequaIity 7 + x < 16 can be written in intervaI nοtatiοn as:
(-∞, 9)
This reads as "aII reaI numbers Iess than 9, incIuding negative infinity, but nοt incIuding 9."
Hence, We can use the inequaIity 7 + x < 16 in intervaI nοtatiοn as: (-∞, 9]
Learn more about inequality, by the following link
https://brainly.com/question/231802
#SPJ1
Complete question:
Given the inequality 7+x<16, Find interval notation.
3. Terdapat dua bidang saling berpotongan dan tidak berhimpitan maka
perpotongannya berbentuk,
c. bidang
a. titik
b. garis
d. ruang
Answers
Kelas : VII (1 SMP)
Materi : Geometri
Kata Kunci : Garis, Sisi, Rusuk, Bidang
Pembahasan :
Titik adalah bentuk yang paling dasar dalam geometri. Titik ditulis dengan tanda titik dan diberi nama dengan huruf besar. Sebuah titik hanya untuk menunjukkan posisi dan memiliki ukuran nol (panjang nol, lebar nol, dan tinggi nol).
Garis adalah kumpulan titik-titik yang memanjang secara tak berhingga ke dua arah. Sebuah garis memiliki panjang tidak terbatas.
Ruas garis adalah potongan sebuah garis. Sebuah ruas garis memiliki dua titik ujung dan diberi nama menurut kedua titik ujungnya.
Sinar garis merupakan bagian dari sebuah garis, namun hanya memiliki satu titik ujung. Sebuah sinar garis diberi nama dengan huruf titik ujungnya dan titik lain pada sinar garis tersebut.
Sudut adalah dua sinar yang memiliki titik ujung yang sama.
Titik ujung tersebut dinamakan titik sudut dan sinar-sinar garisnya dinamakan sisi-sisi sudut.
Bidang adalah kumpulan titik yang jumlahnya tak terhingga yang membentuk permukaan rata yang melebar ke segala arah sampai tak terhingga. Sebuah bidang memiliki panjang tak terbatas, lebar tak terbatas, dan tinggi nol. Sebuah bidang biasanya digambarkan dengan gambar segi empat dan diberi nama dengan satu huruf besar.
Rusuk adalah suatu garis yang merupakan pertemuan dari dua sisi bidang.
Dua bidang berpotongan bila terdapat garis persekutuan atau garis potong antara kedua bidang tersebut.
Dua bidang sejajar bila antara kedua bidang tersebut tidak memiliki garis persekutuan.
Dua bidang berhimpit bila setiap titik terletak pada kedua bidang tersebut.
Mari kita lihat soal tersebut.
Jika dua bidang saling berpotongan dan tidak berhimpitan, maka perpotongannya berbentuk garis.
Jadi, jawabannya adalah B.
Semangat!
Select the correct answer.
On the number line, which point is closest to /-/?
A.
A
B.
B
C.
C
D.
D
Answers
Answer:
D is on the number line, which point is closest to /-/
Answer:
It well be D
Step-by-step explanation:
HELP WILL MARK BRAINLIST AND 5 STARS
Answers
Answer:
10 ft
Step-by-step explanation:
5 1/6 + 4 5/6 = 10
5 + 4 = 9
1/6 + 5/6 = 6/6 = 1
9 + 1 = 10
Answer:
10 feet
Step-by-step explanation:
We are trying to find Madison's height plus Jade's height...
Turn the fractions into improper fractions
So,
5 1/6 = 31/6
4 5/6 = 29/6
31/6 + 29/6 = 10 feet
or
5+4= 10 and 1/6+5/6 = 1
so the answer is 10 feet
PLEASE RATE!! I hope this helps!!!
If you have any questions comment below
Which of the following is a solution to this inequality?
y > 1/2x + 2
Answers
Answer:
We conclude that only (1, 4) satisfies the inequality.
Thus, (1, 4) is a solution to this inequality.
Hence, option A is correct.
Step-by-step explanation:
Given the inequality
y > 1/2x + 2
FOR (1, 4)
y > 1/2x + 2
substituting x = 1, and y = 4
4 > 1/2(1) + 2
4 > 1/2+2
4 > 5/2
TRUE!
Reason: It is true because 4 is indeed greater than 5/2
Thus, (1, 4) satisfies the inequality.
Therefore, (1, 4) is a solution to this inequality.
FOR (-1, 1)
y > 1/2x + 2
substituting x = -1, and y = 1
1 > 1/2(-1) + 2
1 > -1/2+2
1 > 3/2
FALSE!
Reason: It is false because 1 can not be greater than 3/2
Thus, (-1, 1) DOES NOT satisfy the inequality.
FOR (2, 3)
y > 1/2x + 2
substituting x = 2, and y = 3
3 > 1/2(2) +2
3 > 1+2
3 > 3
FALSE!
Reason: It is false because 3 can not be greater than 3.
Thus, (2, 3) DOES NOT satisfy the inequality.
FOR (0, 2)
y > 1/2x + 2
substituting x = 0, and y = 2
2 > 1/2(0) +2
2 > 0+2
2 > 2
FALSE!
Reason: It is false because 2 can not be greater than 2.
Thus, (0, 2) DOES NOT satisfy the inequality.
Therefore, we conclude that only (1, 4) satisfies the inequality.
Thus, (1, 4) is a solution to this inequality.
Hence, option A is correct.
a variable is normally distributed with a mean of 16 and a standard deviation of 6. find the percent of thedata set that:
Answers
The percentage of the data set within the range of 10 to 22 is 68.26%.
To find the percentage of the data set for a normally distributed variable with a mean of 16 and a standard deviation of 6, we can use the concept of z-scores and the standard normal distribution.
First, we need to convert the values to z-scores, which measure the number of standard deviations a particular value is from the mean. The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the value, μ is the mean, and σ is the standard deviation.
In this case, we want to find the percentage of the data set within a certain range. Let's say we want to find the percentage of the data set between 10 and 22. We can calculate the z-scores for these values:
\(z1 = (10 - 16) / 6 = -1.0\)
\(z2 = (22 - 16) / 6 = 1.0\)
Next, we can use a standard normal distribution table or a calculator to find the area under the curve between these z-scores. The area between -1.0 and 1.0 represents the percentage of the data set within the range of 10 to 22.
Looking up the z-scores in the standard normal distribution table, we find that the area between -1.0 and 1.0 is approximately 0.6826. This means that approximately 68.26% of the data set falls within the range of 10 to 22.
Therefore, the percentage of the data set within the range of 10 to 22 is 68.26%.
For more questions on percentage
https://brainly.com/question/24877689
#SPJ8
Hurry and help , there is only five minutes left
100+ points and brainly
Answers
Answer:
The explanation is the same as the previous question.
Which of the type directions lie in the (110) plane? [101] [110] [o īl] (110
Answers
The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.
Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.
Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.
To know more about equivalent visit :
https://brainly.com/question/25197597
#SPJ11
The answer because I do not understand
Answers
6 would be my guess
I'm probably wrong... but its worth a try?
How do we calculate the vertex of a quadratic in standard form?
Answers
Answer:
y = a \(x^{2}\) + b x + c .
Step-by-step explanation:
Also (How to do it!):
We can find the vertex of a quadratic equation with these steps:
Get the equation in the form y = ax2 + bx + c.
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
Select all equations that depict one of the properties of exponents. Select all that apply.
Answers
The properties of exponents are (ab)^x = a^xb^x, b² × b^x = b^(2+x), and x⁻² = 1/x². Hence options A, D, E are correct.
What is the property of exponent?
When referring to a mathematical phrase that denotes that a number will be multiplied by itself n times, the terms power and exponent are frequently used interchangeably. That is a valid definition of power, however, in mathematics, the word exponent expressly refers to the amount. n that specifies the number of times it will be multiplied by itself.
There are six properties of the exponent. The properties are
Product of Powers (x^m)(x^n) = x^(m+n)
Power to a Power (x^m)^n = x^(mn)
Quotient of Powers (x^m)/(x^n) = x^(m-n)
Power of a Product (xy)^m = x^m× x^n
Power of a Quotient (x/y)^n = x^n/y^n
Negative exponent x^(-n)= 1/x^n
According to the Power of a Product:
(ab)^x = a^xb^x
According to the Negative exponent:
7⁻³ = 1/7³
According to the Product of Powers:
b² × b^x = b^(2+x)
According to the Negative exponent:
x⁻² = 1/x².
To learn more about Power of a Quotient rule, click on the below link:
https://brainly.com/question/8826169
#SPJ1
please help me?
please and thanks
Answers
Answer:
-\(\frac{35}{2}\)
Step-by-step explanation:
-5 ÷ \(\frac{2}{7}\) = 17\(\frac{1}{2}\)
17\(\frac{1}{2}\) = -\(\frac{35}{2}\)
Step-by-step explanation:
keep change flip, keep the first number, change the division to multiplication, and flip the fraction.
-5 * 7/2 and multiply straight across
-35/10
If we add, 7xy + 5yz – 3zx, 4yz + 9zx – 4y and –3xz + 5x – 2xy, then the answer is:
A. 5xy+9yz+3zx+5x–4y
B. 5xy+10yz+3zx+15x–4y
C. 5xy–9yz+3zx–5x–4y
D. 5xy+10yz+3zx+5x–6y
Answers
Answer:
A. 5xy + 9yz + 3zx + 5x – 4y
Step-by-step explanation:
uhh credit for this answer goes to Blaise Pascal for inventing calculators .-.
Hewo.
Answer below.
----Steps----
Add the expressions.
5xy+3xz+9yz+5x−4y
Brainliest, if it helps.
Is 3/17 a rational number
Answers
Answer:
no
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
A rational number is number that can be made by dividing two integers, like a fraction, or a ratio. Something that would not be a rational number would be like the square root of 2.
Simplify the fraction 44/77 as much as possible.
Answers
Answer:
4/7
Step-by-step explanation:
Both numbers can be divided by 11, which would get you to 4/7, which is unable to be simplified any more.
A person places $358 in an investment account earning an annual rate of 7.3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 10 years.
Answers
The amount of money, to the nearest cent, in the account after 10 years is found as $742.87.
Explain the term compounded continuously?The interest gained on an investment is computed and reinvested back through into account for just an infinite number of periods, which results in a continuously compounded return. Both principal amount and interest accrued during the specified periods are used to calculate the interest, which is then reinvested back through into cash balance.The formula for the continuous compound is:
V = Pe^{rt}
In which:
V is the value of the account in t years, P is the principal initially invested: $358e is the base of a natural logarithm: 2.72r is the rate of interest: 7.3%t is the time of compounding: 10 yearsV= 358*2.72*{0.073*10}
V = 358*2.07
V = 742.87
Thus, the amount of money, to the nearest cent, in the account after 10 years is found as $742.87.
Know more about the compounded continuously,here
https://brainly.com/question/14303868
#SPJ1
Use the graph to find the slope top of the line
Answers
EXPLANATION:
Rise over run
So 360/4
= 90
You divide 360 with 4 after the “rise over run” rule.
The number of times an item occurs in a data set is called what?
Answers
Answer:
Frequency
Step-by-step explanation:
Hope this helps.
what is 168.75 ÷ 25=
Answers
Answer:
The anwser would be 6.75
Step-by-step explanation:
6.75
.....................
what are the three elements of the project triangle?
Answers
The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.
The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.
The three elements of the Project Triangle are:
Cost: It is one of the three elements of the project triangle that refers to the money spent on project resources, including equipment, materials, and labor. It is the financial resources required to complete the project on time and within budget.Time: It is the second element of the project triangle that refers to the schedule of the project, including deadlines, milestones, and delivery dates. It is the amount of time that is required to complete the project within the predetermined scope.Scope: It is the third and final element of the project triangle that refers to the requirements and objectives of the project. It is the scope that outlines the goals and objectives of the project and defines the deliverables that are expected at the end of the project.To know more about Project Triangle, visit:
https://brainly.com/question/33122965
#SPJ11
Please answer this question
Answers
Answer:
A
hope that helped <3
Hope my answer will help you
Given parallelogram abcd, diagonals ac and bd intersect at point e. ae=2x, be=y 10, ce=x 2 and de=4y−8. find x.
Answers
the diagonals of a parallelogram bisect each other
2x=x+2
x=2
Hence the value of x is 2.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. Opposite or opposite sides of a parallelogram have equal lengths, and opposite angles of a parallelogram are equal. The congruence of opposite and opposite angles is a direct consequence of the Euclidean parallel postulate, the Euclidean parallelism The condition cannot be proved without resorting to the line postulate or one of its equivalent formulations.
A parallelogram with base b and height h can be divided into trapezoids and right triangles and converted into rectangles as shown in the left figure. This means that the area of a parallelogram is equal to the area of a rectangle with the same base and height.
Learn more about parallelogram here
https://brainly.com/question/148091
#SPJ4
D=S×T
150×2 1/2
please help
Answers
a certain test preparation course is designed to help students improve their scores on the lsat exam. a mock exam is given at the beginning and end of the course to determine the effectiveness of the course. the following measurements are the net change in 5 students' scores on the exam after completing the course: 13,19,22,15,29 using these data, construct a 80% confidence interval for the average net change in a student's score after completing the course. assume the population is approximately normal. step 1 of 4 : calculate the sample mean for the given sample data. round your answer to one decimal place.
Answers
The sample mean for the given sample data is 19.6
using formula Mean = (Σxi)/n
Where Σ tells us to add,
xi refers to all the X-values
and n stands for the number of items in the data set.
What is a sample mean?The sample mean of a data set is used by statisticians to estimate the standard of normality within a given population, as well as to calculate the variance, deviation, and standard error within a data set.
The average of a group of data is called a sample mean. A data set's central tendency, standard deviation, and variance can all be determined using the sample mean. A population average can be determined using the sample mean, among other things.
xi = 13,19,22,15,29
Total no. of students (n) = 5
Sample Mean = ( Σ xi ) / n
⇒ Sample Mean = (13+19+22+15+29)/5
⇒ Sample Mean = 98/5
⇒ Sample Mean = 19.6
The sample mean for the given sample data is 19.6
To learn more about sample mean visit:
brainly.com/question/30023845
#SPJ4