The required equation that represent or approximate the population is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
To represent the population, P, as a function of time in days, t, we need to find an exponential growth equation.
Since the population grows exponentially by a factor of 3 every week, we need to convert the weekly growth to daily growth.
Let's break down the problem step by step:
The population grows by a factor of 3 every week.There are 7 days in a week, so the daily growth factor can be calculated by taking the 7th root of 3. (Growth factor per day = [tex]3^{(1/7)[/tex])The initial population is 1,500.Now, we can represent the population, P, as a function of time, t, using the exponential growth equation:
[tex]\mathrm P(t) = \mathrm{Initial \ Population} \times \mathrm {Growth \ Factor}^t[/tex]
where:
Initial Population (Po) = 1,500 (given)
Growth Factor per day = [tex]3^{(1/7)[/tex]
So, the equation representing the population as a function of time in days is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
Hence the required equation that represent or approximate the population is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
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Simplify 10cm:2m
Ratio
Answer:
1cm:20cm
Step-by-step explanation:
10cm:2m
1m=100cm
10cm:200cm
÷10
1cm:20cm
you start driving east with 14 miles turn left and Drive North for another 10 miles at the end of driving what is your straight line distance from your starting point
Answer:
17.205 miles
Step-by-step explanation:
Since these directions form a 90-degree angle, we can use the Pythagorean Theorem.
14^2 + 10^2 = c^2
196 + 100 = c^2
296 = c^2
It doesn't have a perfect square root, you can either say that it is [tex]\sqrt{296}[/tex] or approximately 17.205 miles.
Please solve and hurry
Answer:
225°
Step-by-step explanation:
[tex] \frac{5\pi}{4} = \frac{5 \times 180 \degree}{4} = \frac{900 \degree}{4} = 225 \degree \\ [/tex]
Abel wants to go on a trip around the world so he determines a budget for a month long trip in 14 months. If Abel determines the following cost, how much would he need to save a month in order to afford the trip?
Travel: $1,383.12
Food: $613.05
Hotel: $2,369.72
Other: $816.82
BEEN ASKING FOR AN HOUR NOW!! the following two triangles are similar to each other. find the length of the missing side.
Answer: just multiply the same sides that same number and that add the answers all together
Step-by-step explanation:
A rice farmer employs 15 men to harvest his crop. The men take 12 days to do the job. If he had employed 9 men, how many days would it have taken them?
Answer:
15 men * 12 days = 180 man-days
180 man-days / 9 men = 20 days
From a project management stand point man-days doesn’t really equate to much so while you can evaluate schedule, you would typically desire to see more information than this.
Step-by-step explanation:
Which of the following is an example of a sample that would NOT be random? A. Going through the list and choosing the first 25 names on the list. B. Writing each student’s name on a card and then drawing out 25 names without looking. C. Choosing one student at random from the list and going through the list and choosing every fifth student until she has 25 names. D. Separating the students on the list into boys and girls and choosing a sample from each group that is proportional to the size of the group.
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The numerator of a fraction is 9 and the denominator is 6. All of the following numbers are equivalent except ____.
○ 2/3
○ 3/2
○ 1 ½
○ 18/12
Answer:
2/3
Step-by-step explanation:
Look at the figure. How can you prove the triangles are congruent?
Answer:
SSS - The two triangles share all 3 sides, proving they are congruent.
Step-by-step explanation:
Two sides of each triangle are marked in the diagram as equal. The third side, [tex]\overline{BD}[/tex] is shared between both sides, meaning that both triangles share all three sides. This is known as SSS (side-side-side) and is a proof of congruence.
Step-by-step explanation:
In triangle ABD In triangle CBD
AB. = BC. [Given]
AD. = CD. [Given]
BD. = BD. [Common side]
Therefore,
According to SSS Congruence condition
Triangle ABD is congruent to Triangle CBD
What is the area of a circle with a radius of 4 ft?
(Use 3.14 for Pi.)
Step-by-step explanation:
A = Pi x r^2
r=4_____________
Answer:
50.26548
50.27 Rounded to the hundredths place .
what is the solution to the system?
y = 5x
y = 2x - 9
Pls help it’s for a grade in math pls help
Answer:
25,200
Step-by-step explanation:
First, find what 1% equals. Divide the total amount of people by 100. 105,000 divided by 100 = 1050. Multiply this by 24, because:
If 1% = 1050
To get 24% you need to multiply 1% by 24. Whatever you do to o ne side you have to do to the other.
1050 * 24 = 25,200
Therefore, the answer is 25,200 people
The factory receives an order for more than 1,100 boxes. Machine B has already packed 55 boxes. Write and solve an inequality to find the amount of time it will take Machine B to pack the additional boxes that are needed for the order, assuming none of the boxes are defective.
Answer:
no lo sé pero te ayudaría si lo supieraA candy store sells chocolate for $7.01 per pound. The piece you want to but weights .18 pound. How much will it cost?
it will cost abut $1.26! the exact answer being 1.2618, you can find this by multiplying 7.01 and 0.18, you round it up to something that can be an actual price! hope this helps! <3
Two functions are shown below.
f(x) = 1/3 (3)^x
g(x) - 2x + 4
What is the largest integer value of x such that f(x) < g(x)?
Answer: 3
Step-by-step explanation:
Given
[tex]f(x)=\dfrac{1}{3}3^x[/tex]
[tex]g(x)=2x+4[/tex]
For [tex]f(x)<g(x)[/tex] to be true, the domain is given by observing the graph of two i.e. [tex]x\in (-1.981,3.117)[/tex]. In this range [tex]g(x)[/tex] is greater than [tex]f(x)[/tex].
From the above domain largest integer that can satisfy the condition is 3.
(no links) Please Help!
9514 1404 393
Answer:
D, B
Step-by-step explanation:
Price per pound is found by dividing dollars by pounds.
Store A: $9/(3 lb) = $3.00 /lb
Store B: $9.75/(3 lb) = $3.25 /lb
Store C: $12.40/(4 lb) = $3.10 /lb
Store D: $14.50/(5 lb) = $2.90 /lb
Part A: The lowest price per pound is $2.90 per pound at store D.
Part B: The highest price per pound is $3.25 per pound at store B.
Need help like Right now
Find the area of the parallelogram shown.
The first step in solving a problem is to write a let statement
Answer:
whats this? can you provide more context?
Step-by-step explanation:
Let u=ln(x) and v=ln(y). Write the expression below in terms of u and v
=======================================================
Work Shown:
We'll apply these log rules
[tex]\text{Log Rule 1: } \ \ \ \ln\left(\frac{x}{y}\right) = \ln(x) - \ln(y)\\\\[/tex]
[tex]\text{Log Rule 2: } \ \ \ \ln\left(x^y\right) = y\ln(x)\\\\[/tex]
These log rules can be used for logs of any base, and not just natural logs.
[tex]z = \ln\left(\frac{\sqrt{x}}{y}\right)\\\\z = \ln\left(\sqrt{x}\right)-\ln\left(y\right) \text{ ... Use log rule 1}\\\\z = \ln\left(x^{1/2}\right)-\ln\left(y\right)\\\\z = \frac{1}{2}\ln\left(x\right)-\ln\left(y\right) \text{ ... Use log rule 2}\\\\z = \frac{1}{2}u-v\\\\[/tex]
Therefore,
[tex]\ln\left(\frac{\sqrt{x}}{y}\right) = \frac{1}{2}u-v\\\\[/tex]
when [tex]u = \ln(x) \ \text{ and } \ v = \ln(y)\\\\[/tex]
Convert to the given unit. 65 m = cm
Answer:
65m = 6500 Cm.
Step-by-step explanation:
Please help quickly as possible thank you! :)
Answer:
ertgyhj
Step-by-step explanation:
Answer:
B. 80 students
Step-by-step explanation:
[tex]\frac{56}{y} :\frac{70}{100}[/tex]
y · 70 = 56 · 100
70y = 5600
70y ÷ 70 = 5600 ÷ 70
y = 80
Solve the following system of equations algebraically:
Y = x^2 + 8x – 9
Y = 2x + 7
Find the circumference of a circle with diameter 2 cm. Use 3.14 for
Answer:
6.28 cm
Step-by-step explanation:
Given,
Diameter = 2 cm
pi = 3.14
To find : Circumference ( circle ) = ?
Radius ( r )
= Diameter / 2
= 2 / 2
= 1 cm
Formula : -
Circumference ( circle ) = 2 pi r
2 pi 4
= 2 × 3.14 × 1
= 6.28 cm
Answer:
6.28
Step-by-step explanation:
radius= diameter/2
r=2/2=1
circumference formula=2[tex]\pi[/tex]r
[tex]\pi[/tex]=22/7 or 3.14
So,
2[tex]\pi[/tex]r= 2*3.14*1= 6.28
If the radius is 3.5in, then the diameter is
Answer:
the diameter is 7
HELPPPP MEEEEE ITS 5 GRADE MATH IK HELP ME IM FAILING RN :(((((
Answer:
i think c
Step-by-step explanation:
Answer:
Gross income for an individual—also known as gross pay when it's on a paycheck—is the individual's total pay from their employer before taxes or other deductions. This includes income from all sources and is not limited to income received in cash; it also includes property or services received.
Net income- In business and accounting, net income is an entity's income minus cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.
I think its B
Step-by-step explanation:
Animals in an experiment are to be kept under a strict diet. Each animal should receive 60 grams of protein and 9 grams of fat. The laboratory technician is able to purchase two food mixes: Mix A has 30% protein and 6% fat; mix B
has 50% protein and 5% fat. How many grams of each mix should be used to obtain the right diet for one animal?
One animal's diet should consist of grams of Mix A
Answer:
hey there buddy
Step-by-step explanation:
3+6+2=61
2+8+3=31
4+7+4=42
5+6+4=62
8+7+4=?????
Answer:
6mm AR, a 6 mm wildcat version which shares 6.5 Grendel's casing, but sends a (usually) lighter projectile up to 1,000 yards (900 m). 6.5×42mm, also known as 6.5 MPC (Multi Purpose Cartridge), based on a necked up .223 Remington case.
Step-by-step explanation:
Answer: 19
Step-by-step explanation:
8+7+4
8+7=15
15+4=19
HELP ASAP WILL GIVE BRAINS LIST
jack and clint are running backs on rival college football teams. the table below shows the number of yards they have ran in each of their first five games of a season. how many yards would clint need to run in his next game to average the same number of yards as jack?
Answer:
Clint would have to run 127 yards next game to average the same number of yards as Jack.
Step-by-step explanation:
First, we find the boys' averages by adding all their yards and then dividing by the number of games.
For Jack, we get 490 yards in total, which we divide by 5, the number of games. We get a 98 yard average.
For Clint, we get 461 yards in total, which we divide by 5, the number of games. We get a 92.2 yard average.
We know Clint wants to average 98 yards at the end of the next game. That would make 6 games total. We can multiply 98 x 6 to get the total number of yards for a 98 yard average in 6 games. We get 588 yards in total. Clint already ran 461 yards in total, so we can subtract that from 588. We have 127 yards left. We now know that Clint needs to run 127 yards in the next game for a 98 yard average.
The number of yards that client needs to run in his next game to average the same number of yards as jack will be 127.
What is mean?The mean is the average of a data set. Mean gives us an idea of that how small the amount of overall data have.
In other words, the mean is the foundation of the deviation of data from all data sets.
Mean = sum of data / Number of data
The average of Jack = (123 + 87 + 108 + 80 + 92)/5 = 98
The average of Clint = (88 + 101 + 96 + 92 + 84)/5 = 92.2
To make this average 98 let's say Clint's score in the next game is x.
Mean = (88 + 101 + 96 + 92 + 84 + x)/6 = 98
(92.2 x 5 + x) = 98 x 6
x = 127
Hence"Clint needed to add 127 to be mean as same as Jack".
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Which fraction is greater 2/5 or 4/10
They are equal. 2/5 is 4/10.