The population will reach 70 after approximately 18.02 years according to the logistic growth model equation. Therefore, the answer is 18.02 years.
To compute the equation, we can use the logistic growth model equation P(t) = L / (1 + C * e^(-k * t)), where P(t) represents the population at time t, L is the limiting population, C is the initial population constant, and k is the growth rate constant.
In this case, we are given P(1) = 260, which allows us to find the value of C.
Plugging in P(1) = 260 and simplifying the equation, we get 260 = L / (1 + C * e^(-k)), which can be rearranged to L = 260 + 260 * C * e^(-k).
To compute the time when the population will be 70, we substitute P(t) = 70 and solve for t.
We get 70 = L / (1 + C * e^(-k * t)), which can be rearranged to 1 + C * e^(-k * t) = L / 70.
Since we know the values of L, C, and k from the initial equation, we can substitute them into the rearranged equation and solve for t. The resulting value for t is approximately 18.02 years.
Therefore, the population will be 70 after approximately 18.02 years.
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Bernie helped design a magician costume for a school play. He used 5.75 feet of ribbon for the magician's wand. He used 11.75 feet of the same ribbon to decorate the magician's robe. If Bernie used $10.50 of ribbon in all, how much did the ribbon cost per foot?
The best solution gets brainlist
The ribbon cost $0.60 per foot.
Solution:\(\text{Total number of ribbon used} = (5.75 + 11.75) = 17.50 \ \text{feet}\)
\(\text{17.50 feet of ribbon cost} = \$10.50\)
\(\text{1 foot of ribbon cost = x}\)
Cross Multiply\(17.50 \times x = 1 \ foot \times \$10.50\)
\(x = 1 \ foot \times 10.50\div17.50\)
\(x = \$0.60\)
Therefore, The ribbon cost per foot $0.60 per foot.
Select the correct answer.
Which quadratic equation is part of the solution process for solving this rational equation using the least common denominator?
3:26-3+ 6 = 1
A. x2 + x + 10 = 0
B. 12 - 1 - 10 = 0
C. 12 + x - 2 = 0
D. 2 - x - 2 = 0
rational equation using is D
6. Given the graphs of a system of linear equations below, is there a solution to the system that we cannot see on this portion of the coordinate plane? That is, will the lines intersect somewhere on the plane not represented in the picture? Explain. 0 11 12. 10
The two lines will be parallel and won't overlap anywhere if they have separate intercepts but the same slope.
given
It appears from the graph that the two lines cross at the location (10, 0). But it's possible that the system has a solution that can't be seen from this part of the coordinate plane.
We would need further information about the slopes and intercepts of the two lines in order to establish whether there is a solution that we cannot see in this region of the coordinate plane.
We have already located the spot on the graph where the two lines will intersect if their slopes and intercepts are different.
The two lines will be parallel and won't overlap anywhere if they have separate intercepts but the same slope.
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consider the line 4x+5y=-2 what is the slope of a line perpendicular to this line? what is the slope of a line parallel to this one
Answer:
perpendicular is 5/4 (fraction)
parallel is -4/5 (fraction)
Step-by-step explanation:
f(n)=n^2+4n
g(n)=-n-5
Find f(n)+g(n)
Answer:
n^2+5n-5
Step-by-step explanation:
I think it is
n^2+4n+n-5
combine like terms
n^2+5n-5
Jeff lost 50 acres of wheat because of a late freeze. This was 25% of his total wheat crop. How many acres of wheat were planted? This is a type 2 percent problem: 25 percent of what number is 50?
Answer:
200
Step-by-step explanation:
I put the numbers in a cross multiply scenario:
So it looks like 25/100 and 50/?
So multiply 50 by 100.
Then divide that by 25!
Happy Halloween!
A computer monitor has a width of 14.60 inches and a height of 10.95 inches. What is the area of the monitor display in square meters? area How many significant figures should there be in the answer? 2 3 4 5
The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.
The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.
The conversion factor from inches to meters is 0.0254 meters per inch.
Width in meters = 14.60 inches * 0.0254 meters/inch
Height in meters = 10.95 inches * 0.0254 meters/inch
Area = Width in meters * Height in meters
We calculate the area:
Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters
Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters
Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters
Now, we determine the number of significant figures.
The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.
Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.
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x+y=-9
2x-y=6
slove by graphing
Answer:
x+y=9....(i)
2x-6=y....(ii)
then putting the value of y in (i) eqn
x+2x-6=9
3x=15
x=5
Now, putting the value of x in (ii) eqn
then 2*5- 6 =4
Step-by-step explanation:
SO the value of x is 5 and y is 4
HOPE IT HELPS YOU....❤
Find the area of the semicircle
Answer:
25.13 m
Step-by-step explanation:
pi r²÷2
pi 4²÷2=25.13
Every pint is 2 cups. This can be expressed using the equation y × 2 = Z, where y is equal to the number of pints and Z is equal to the total number of cups. Using the equation find the total cups in 7 pints._______ cups
for 7 pints
\(\begin{gathered} y\times2=Z \\ 7\times2=14 \end{gathered}\)answer 14 cups
what is the possible root combinations of a degree of 6?
Answer:
A polynomial can't have more roots than the degree. So, a sixth degree polynomial, has at most 6 distinct real roots. I may be wrong
Step-by-step explanation:
no step
Answer:
2sqrt9 would be the answer
Step-by-step explanation:
1. The square root of 9 is 3.
2. When you multiply 3 x 2 you get 6.
Please mark brainliest and have a great day!
The area of a rectangular yard is 5,063 square feet and its length is 61 feet. What is its width? Explain or show your reasoning.
Express the following quantities as ordinary decimal numbers: (use solution)
:: The estimated world population for the year 2000 was 6.130 x 10⁹.
Step-by-step explanation:
\(6.130 \times {10}^{9} = 9130000000\)
PLSSSSSS HURRRY (100 POINTS)
The right triangle is rotated one time to the right with respect to the left triangle. Then the pairs are:
e and g, f and h.
How to identify the correspondent angles?
Here we have two similar triangles, this means that one of the triangles can be a rotation + dilation of the other.
If you look at the dimensions of the second triangle and multiply these by 2, you see that the dimensions become:
2*2 = 4
2*3 = 6
2*4 = 8
Which are the same dimensions of the left triangle, but rotated one time to the right.
Now, knowing that, we caonclude that the corresponding angles are:
g and e.f and h.i and the missing angle.Then the correct option is the third one.
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) Tina planted 75 plants. N plants did not grow leaving her with 48 plants. Which equation expresses how many plants Tina lost?
Answer:
Step-by-step explanation: I think this is the answer
Tina planted 75 plants and only 48 grow
To know how much is lost we subtract 75 from 48 which gives us 27
75-48=27
a car leaves a stoplight and accelerates 15 seconds, and its speed reaches 60 km/hr. how fast did this car accelerate during this time?
Let A={(x-3)/(x-2)ЄR : X<0}
be a subset of real numbers.
i) Define A's supremum and infimum.
The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.
To define the supremum and infimum of the set A, we first need to determine the properties of the set.
The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.
To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.
Let's analyze the elements of A:
For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.
As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.
Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.
Again, analyzing the elements of A:
As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.
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Calculate the simple average and weighted average for the following data set.
Data set: 3.50 g
3.72 g
3.72 g
3.50 g
3.72 g
3.72 g
3.50 g
3.72 g
Simple Average: Weighted Average:
The simple average of the given data set is 3.72 g, and the weighted average cannot be determined without knowing the weights assigned to each data point.
To calculate the simple average, we sum up all the data points and divide the sum by the number of data points. In this case, the sum of the data points (3.50 g + 3.72 g + 3.72 g + 3.50 g + 3.72 g + 3.72 g + 3.50 g + 3.72 g) is 29.1 g. Dividing this sum by the number of data points (8), we get the simple average of 3.72 g.
The weighted average requires the weights assigned to each data point. Without knowing the weights, we cannot calculate the weighted average.
The weighted average takes into account the importance or significance of each data point by multiplying the data point by its corresponding weight, summing up the weighted data points, and dividing by the sum of the weights.
Since the question does not provide any information about the weights assigned to each data point, we cannot determine the weighted average in this case. So B is correct.
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Pensé un número, le saque la mitad y luego le reste 15,con lo que obtuve 125. ¿Cuál es el número que pensé?
A rental car company charges $0.50 per mile and a flat rate of $30.00 for any type of sedan
The linear relationship that represents a cost, C(m) of $130 is;
130 = 30.00 + $0.50m
How to find linear relationship?Linear equation is represented as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore,
c(m) = 0.5m + 30
where
C(m) represents the total cost for renting a sedan.
m represents the number of miles driven
Hence, the equation the linear relationship that represents a cost, C(m) of $130 is;
130 = 30.00 + $0.50m
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Based on the data provided, the probability that one student studied for exactly one hour is 0.22.
What is the probability in this case?When it comes to calculating the probability, we need to identify the frequency of a specific outcome (the probability a student studied for one hour) and compare it to the total outcome (total of students) as follows:
Total of students who studied for one hour: 8
Total of students: 1+8+2+5+9+7+3 = 35
Total of students who studied for one hour / total students
8/35 = 0.228 which can be rounded as 0.23 or 23% if expressed as a percentage.
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(-9)+5-6+9-(-9)+99-2+50
...........................................
Answer:
it just dots that all
Step-by-step explanation:
no step need
Carl has 9 1/2 cups of juice for a party. If each party goer gets exactly 3/5 cup of juice each, how many party goers will get their 3/5 cup of juice
Answer: 158
Step-by-step explanation:
Okay so the total is 9 5/10.
Each party goer needs 6/10
So 95/10 / 6/0=. 95/10x10/6
=950/6 = 158.
What are the answers to these questions
Answer:
135°
Step-by-step explanation:
You want QRT. So if you look at it you have a straight line, which equals 180°. you already have an angle at 45° so all you do is 180-45 and that equals 135°
Simon's salary has increased by 6% p.a. over the past three years. it is now $35730.40 p.a.
a) what did he earn per year three years ago
b) what is his gross monthly salary at the present rate
c) His deductions each month amount to 22.5% of his gross salary. what is his net pay per month?
Answer:
Step-by-step explanation:
The employee earns $10,100/month, with his employer paying 1.5 times the regular rate of pay for overtime hours. To date, he has earned $124,740 during the year. He has requested that his employer withhold 12% of gross pay, which is to be contributed to a 401(k) plan. Taxable income for federal income tax withholding = $
(a) Simon's salary three years ago is $33586.576.
(b) Gross monthly salary at the present is $2798.88.
(C) Net pay per month is $2169.09.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The Simon's salary at present = $35730.40 p.a.
Increased rate = 6% = 0.06
(a) Simon's salary three years ago:
⇒ \(\$35730.40(0.06)\)
⇒ \(\$2143.824\)
Original salary of Simon,
⇒ \(35730.40-2143.824\)
⇒ \(\$33586.576\)
(b) Gross monthly salary at the present:
⇒ \(\frac{33586.57}{12}\)
⇒ \(2798.88\)
(C) Net pay per month:
Deductions each month amount to 22.5% of his gross salary,
⇒ \(22.5\%=0.225\)
⇒ \(2798.88(0.225)\)
⇒ \(\$629.79\)
Thus net pay per month,
⇒ \(2798.88-629.79\)
⇒ \(\$2169.09\)
Hence we can conclude that
(a) Simon's salary three years ago is $33586.576.
(b) Gross monthly salary at the present is $2798.88.
(C) Net pay per month is $2169.09.
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Write an equation that describes the function.
Answer:
y = xplus1 sorry, new keyboard and it doesn't have a plus sign
PLS HELP ME ASAP!
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Maggie is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer. (5 points)
(10 points)
Account A: Decreasing at 8 % per year
Account B: Decreasing at 10.00 % per year
Account B shows the greater percentage change
What is Exponential Function?Exponential function, in mathematics, a relation of the form y = \(a^x\), with the independent variable x ranging over the entire real number line as the exponent of a positive number a.
Given:
f(x) = 9628(0.92)ˣ
A)The general formula for an exponential function is
y = a\(b^x\), where b = the base of the exponential function.
if b < 1, we have an exponential decay function.
So, ƒ(x) decreases as x increases.
Thus, Account A is decreasing each year.
B) Now, the formula for an exponential decay function as:
y = a(1 – b)ˣ, where
1 – b = the decay factor
If we compare the two formulas, we find
0.92 = 1 - b
b = 1 - 0.92 = 0.08
b = 8 %
The account is decreasing at an annual rate of 8 %.
The account is decreasing at an annual rate of 10.00 %.
Account B recorded a greater percentage change in the amount of money over the previous year.
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If the scale factor of volumes of 2 similar shapes is 15.625
what will be the scale factors of lengths?
Answer:
If the scale factor is one, it means that corresponding sides are equal in length. In this case the shapes would be congruent (ie identical) rather than similar. They have the same shape, the same angles and the same size.
Step-by-step explanation:
A machine fills 16 ounce coke bottles. It places coke in the bottles.
Not all bottles hold exactly 16 ounces. The volume of the coke is
normally distributed with a mean of 16.2 ounces and a standard
deviation of 0.3 ounces.
Make a curve to represent the distribution to help you answer the
following:
a. If you purchase a coke filled by the dispenser what is the
percentage it has less than 16.5 ounces?
b. If you purchase a coke filled by the dispenser what is the
percentage it has less than 15.9 ounces?
c. If you purchase a coke what is the percentage it has more than
15.3 ounces?
d. If you purchase a bag what is the percentage it has between 15.9
and 16.8 ounces?
Option B is best represents for the answer. A. 84.13%. B. 15.87%. 99.87%. D. 81.86%. To create the distribution curve, we can use the normal distribution formula: \(f(x) = (1/σ√(2π)) * e^(-0.5((x-μ)/σ)^2)\)
where:
f(x) = probability density function at value x
μ = mean = 16.2
σ = standard deviation = 0.3
Using this formula, we can calculate the probabilities for the given scenarios:
a. Probability of a coke having less than 16.5 ounces:
We need to find P(X < 16.5), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the value of 16.5:
z = (16.5 - 16.2) / 0.3 = 1
P(Z < 1) = 0.8413
Therefore, the probability of a coke having less than 16.5 ounces is 84.13%.
b. Probability of a coke having less than 15.9 ounces:
We need to find P(X < 15.9), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the value of 15.9:
z = (15.9 - 16.2) / 0.3 = -1
P(Z < -1) = 0.1587
Therefore, the probability of a coke having less than 15.9 ounces is 15.87%.
c. Probability of a coke having more than 15.3 ounces:
We need to find P(X > 15.3), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the value of 15.3:
z = (15.3 - 16.2) / 0.3 = -3
P(Z > -3) = 0.9987
Therefore, the probability of a coke having more than 15.3 ounces is 99.87%.
d. Probability of a bag having between 15.9 and 16.8 ounces:
We need to find P(15.9 < X < 16.8), where X is the volume of the coke in ounces.
Using the z-score formula, we can standardize the values of 15.9 and 16.8:
z1 = (15.9 - 16.2) / 0.3 = -1
z2 = (16.8 - 16.2) / 0.3 = 2
P(-1 < Z < 2) = 0.8186
Therefore, the probability of a coke having a volume between 15.9 and 16.8 ounces is 81.86%.
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