The question is incomplete. The complete question is :
The population of a certain town was 10,000 in 1990. The rate of change of a population, measured in hundreds of people per year, is modeled by P prime of t equals two-hundred times e to the 0.02t power, where t is measured in years since 1990. Discuss the meaning of the integral from zero to twenty of P prime of t, d t. Calculate the change in population between 1995 and 2000. Do we have enough information to calculate the population in 2020? If so, what is the population in 2020?
Solution :
According to the question,
The rate of change of population is given as :
[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex] in 1990.
Now integrating,
[tex]$\int_0^{20}\frac{dP(t)}{dt}dt=\int_0^{20}200e^{0.02t} \ dt$[/tex]
[tex]$=\frac{200}{0.02}\left[e^{0.02(20)}-1\right]$[/tex]
[tex]$=10,000[e^{0.4}-1]$[/tex]
[tex]$=10,000[0.49]$[/tex]
=4900
[tex]$\frac{dP(t)}{dt}=200e^{0.02t}$[/tex]
[tex]$\int1.dP(t)=200e^{0.02t}dt$[/tex]
[tex]$P=\frac{200}{0.02}e^{0.02t}$[/tex]
[tex]$P=10,000e^{0.02t}$[/tex]
[tex]$P=P_0e^{kt}$[/tex]
This is initial population.
k is change in population.
So in 1995,
[tex]$P=P_0e^{kt}$[/tex]
[tex]$=10,000e^{0.02(5)}$[/tex]
[tex]$=11051$[/tex]
In 2000,
[tex]$P=10,000e^{0.02(10)}$[/tex]
[tex]=12,214[/tex]
Therefore, the change in the population between 1995 and 2000 = 1,163.
If you were given a fractional strip, that did not have any subdivisions marked like this one pictured below, how would you determine the fractional amount of the bar that is shaded?
9514 1404 393
Answer:
it depends on the accuracy and resolution required of the answer
Step-by-step explanation:
The shaded portion appears to be about half the length of the unshaded portion, suggesting the shaded amount is 1/3.
__
Using a pair of dividers, one could determine the number of times the shaded portion fits into the whole bar. Depending on how much is left over, the process could repeat to determine the approximate size of the remaining fraction relative to the bar or to the shaded portion. (Alternatively, one could replicate the length of the bar to see what integer number of shaded lengths fit into what integer number of whole lengths.)
One could measure the shaded part and the whole bar with a ruler, then determine the relative size of the shaded part by dividing the first measurement by the second. The finer the divisions on the ruler, the better the approximation will be.
One number is 8 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 1090, find the numbers.
Answer:
Number one: x
Number two:8x
Number three: x+ 100
They added together equal to 1090:
x + 8x + x+ 100 = 1090
10x= 1090-100
10x=990
x=99
Number one: 99
Number two: 792
Number three: 199
Sum: 1090
khalil has a circular cake that he plans to share equally betweeb himself and 5 friends. if tge cake is 8 inched in a diameter, what will be the length of the arc of each slice of cake.
Answer:
4.2
Step-by-step explanation:
It would be 8/2 which gets 4 and put the .2 4.2
Length of the arc of each slice of cake is equals to 5.024inches.
What is length of the arc?
" Length of the arc is defined as the distance between any two points as a part of the circumference of the circle."
Formula used
Length of the arc = radius × central angle of the arc
l = r × θ
According to the question,
Number of friends = 5
Diameter of the cake = 8inches
Shape of the cake is circular.
Therefore angle formed = 360°
Angle for each piece of cake = [tex]\frac{360}{5}[/tex]
= 72°
Radius of the cake = [tex]\frac{diameter }{2}[/tex]
= [tex]\frac{8}{2}[/tex]
= 4 inches
Substitute the value in the formula to get the length of the arc we get,
L = 4 × 72 × [tex]\frac{\pi }{180}[/tex]
= 5.024inches
Hence, length of the arc of each slice of cake is equals to 5.024inches.
Learn more about length of the arc here
https://brainly.com/question/14675251
#SPJ2
Question 6 of 40
Which recursive formula can be used to represent the sequence
2, 6, 10, 14, 18, ... ?
& - 2
O A.
&, - 87-704
ay - 2
O B.
an - 2n-1-4
C. &-0
an - 2n-1 + 4
D.
ay - 2
an - 8-1 + 4
Gays
Step-by-step explanation:
I cannot really identify and read the provided answer options.
the solution to the sequence 2, 6, 10, 14, 18, ... is
an = 4×(n-1) + 2
recursive that is
a1 = 2
an = an-1 + 4
please pick the right option in your original problem definition that fits to this solution.
The recursive formula that represents the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant value to the previous term.
This fixed value is called the common difference, and it is the same for all terms in the sequence.
We have,
The given sequence has a common difference of 4 between its consecutive terms.
To represent this sequence using a recursive formula, we can start with the first term and use the common difference of 4 to find each subsequent term.
Let's assume that the first term of the sequence is a1. Then, we can represent the second term [tex]a_2[/tex] as:
[tex]a_2 = a_1 + 4[/tex]
Similarly, we can represent the third term (a3) as:
[tex]a_3 = a_2 + 4[/tex]
Substituting the value of a2 from the above equation, we get:
[tex]a_3 = (a_1 + 4) + 4 = a_1 + 8[/tex]
We can continue this pattern to find the recursive formula for the nth term of the sequence:
[tex]a_n = a_{n-1} + 4[/tex]
where [tex]a_1[/tex]= 2
Thus,
The recursive formula for the given sequence is:
[tex]a_n = a_{n-1} + 4[/tex]
Learn more about arithmetic sequence here:
https://brainly.com/question/10396151
#SPJ7
A sequence is defined by the recursive function f(n+1)=f(n)-2
If f(1)=10 what is f(3)?
Answer:
f(3) = 6
Step-by-step explanation:
Using the recursive rule and f(1) = 10 , then
f(2) = f(1) - 2 = 10 - 2 = 8
f(3) = f(2) - 2 = 8 - 2 = 6
Given :-
A sequence is defined by f(n + 1) = f(n) -2 .f(1) = 10To Find :-
The value of f(3) .Solution :-
As per Question ,
→ f(n + 1) = f(n) - 2
→ f(n + 1 ) - f(n ) = -2
Therefore , the second term of the sequence is ,
→ f(2) - f(1) = -2
→ f(2) - 10 = -2
→ f(2) = 10 -2
→ f(2) = 8
Similarly,
→ f(3) - f(2) = -2
→ f(3) = 8 -2
→ f(3) = 6
Hence the value of f(3) is 6 .PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of
research questions and types of data where one would expect the data to be skewed?
Answer:
Explained below
Step-by-step explanation:
A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.
B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.
Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.
Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.
C) Example of a research question is;
If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.
PYTHAGORAS
work out the side of b.
give your answers to one decimal place
Answer:
12 cm
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityTrigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a leg b is another leg c is the hypotenuseStep-by-step explanation:
Step 1: Define
Identify variables
a = 12 cm
c = 17 cm
Step 2: Solve for b
Substitute in variables [Pythagorean Theorem]: 12² + b² = 17²Evaluate exponents: 144 + b² = 289[Subtraction Property of Equality] Subtract 144 on both sides: b² = 145[Equality Property] Square root both sides: b = √145[√Radical] Evaluate: b = 12.0416Round: b ≈ 12.0Helena has an 80% chance and Rodriquez has a 50% chance of obtaining 'A' grades in their History examination. Find the probability that:
a both will obtain 'A' grades
b Rodriquez will get an 'A' and Helena will not
c.neither will obtain 'A' grades.
Answer:
a) 0.40
b) 0.10
c) 0.60
Step-by-step explanation:
Helena has 80% chance of getting A ,
[tex]P(A_H) = \frac{80}{100} = 0.80[/tex]
Rodriquez has 50% chance of getting A ,
[tex]P(A_R) = \frac{50}{100} = 0.50[/tex]
a)
[tex]P(A_H A_R) = P(A_H) \times P(A_R) = 0.80 \times 0.50 = 0.40[/tex]
b)
[tex]Probability \ Helena \ will \ not \ get \ A\ , \ P(A_H^{'} ) = 1 - P(A_H) = 1 - 0.80 = 0.20[/tex]
Probability Rodriquez will get A and Helena will not
[tex]P(A_RA_H^{'})[/tex] = 0.50 x 0.20 = 0.10
c) Probability neither will obtain A = 1 - Probability both will get A
= 1 - 0.40
= 0.60
Check my work
Concerns about climate change and CO2 reduction have initiated the
commercial production of blends of biodiesel (e.g., from renewable sources)
and petrodiesel (from fossil fuel). Random samples of 48 blended fuels are
tested in a lab to ascertain the bio/total carbon ratio.
(a) If the true mean is.9200 with a standard deviation of 0.0050, within what
interval will 99 percent of the sample means fall? (Round your answers to 4
decimal places.)
The interval is from
to
(
each runner in an 8 mile relay races runs 4/5 of a mile. How many runners are on the relay team?
Divide total distance of the race by the length each runner runs:
8 miles / 4/5
When dividing by a fraction flip the fraction over and multiply:
8 miles x 5/4 = (8x5)/4 = 40/4 = 10
There are 10 runners
Answer:
10 runners
Step-by-step explanation:
Is 8 Miles which equals to 40/5 miles. 40/5 miles divided by 4/5 = 10 so 10 runners.
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AD=40 and AC=48, what is the length of AB in simplest radical form?
Answer:
8[tex]\sqrt{30}[/tex]
Step-by-step explanation:
AB^2 = AD * AC
we got the answer
i need the answer fast please
Step-by-step explanation:
everything can be found in the picture
Factor the trinomial, or state that the trinomial is prime.
y2-9y+14
Please help
=====================================================
Explanation:
To factor this, we need to find two numbers that
A) multiply to 14 (last term)B) add to -9 (middle coefficient)Through trial and error, you would find that the two numbers are -2 and -7
-2*(-7) = 14
-2 + (-7) = -9
So that's why the given trinomial factors to (y-2)(y-7)
You can use the FOIL rule to go from (y-2)(y-7) back to y^2-9y+14 again.
A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 49 − x2. What is the largest possible area (in squared units) of the rectangle?
Let the base of the rectangle be of length 2x, so its vertices on the parabola are (−x, 49 − x²) and (x, 49 − x²).
The area A of the rectangle is given by A = 2x(49 − x²), which simplifies to A = 98x − 2x³.
What is Rectangle?A rectangle is a four-sided polygon with opposite sides being congruent and parallel to each other, and all interior angles measuring 90 degrees.
To find the maximum possible area, we need to find the value of x that maximizes A. To do this, we take the derivative of A with respect to x and set it equal to zero:
dA/dx = 98 - 6x² = 0
Solving for x, we get x = ±√(98/6) ≈ ±4.1
Since the rectangle is symmetric about the y-axis, we only need to consider positive values of x. Therefore, the length of the base of the rectangle is 2x ≈ 8.2.
The height of the rectangle is 49 − x² ≈ 47.9.
The maximum area of the rectangle is then A ≈ 392.18 square units.
Learn more about area of rectangle at:
https://brainly.com/question/20693059
#SPJ3
the sum of 3 times a number and 7 is 8 use the variable of w for the unknown number
Answer:
⅓
Step-by-step explanation:
I solved it in the picture above
Answer:
w = [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The equation representing the situation is
3w + 7 = 8 ( subtract 7 from both sides )
w = 1 ( divide both sides by 3 )
w = [tex]\frac{1}{3}[/tex]
GIVING OUT BRAINLIEST PLEASE HELP ME!!
Answer: B (0,0) r=4
Step-by-step explanation:
Ivan is saving money to buy a game. So far he has saved 8, which is one-fourth of the total cost of the game. How much does the game cost?
Answer:
[tex]\$32[/tex]
Step-by-step explanation:
Let the cost of the game be [tex]x[/tex]. Since one-fourth of the cost of the game is equal to 8 dollars, we have the following equation:
[tex]\frac{1}{4}x=8[/tex]
Multiply both sides by 4 to isolate and solve for [tex]x[/tex]:
[tex]x=8\cdot 4=\boxed{\$32}[/tex]
Solve each equation by graphing. Round to the nearest tenth.
X^2-6x= -8
A) 4, 2
B) −4, 2
C) −2, 4
D) −2, −4
Answer:
A
Step-by-step explanation:
That is the procedure above
the graph below shows how money has been budgeted for a certain company
The company has budgeted approximately 25% of its money on which of the following
Answer:
Shelter from a tornado should be sought:
in any of the above
in a room in the center of the first floor
in a basement
under a staircase in the center of the house
Shelter from a tornado should be sought:
in any of the above
in a room in the center of the first floor
in a basement
under a staircase in the center of the house
Borrows £10,000 over 5 years simple interest rate of 15%
Answer:
[tex]{ \tt{simple \: interest = p \times r \times t}} \\ = 10000 \times 15\% \times 5 \\ = £7500[/tex]
Algebra helppp 20 points
Answer:
D or A im leaning towards d but test your luck or not ur choice
Step-by-step explanation:
What is the explicit formula for this geometric sequence -4,-8,-16,-32
Answer:
an = - [2^(n+1)]
Step-by-step explanation:
-4,-8,-16,-32
a1 = -4
r = -8/-4 = 2
the formula :
an = -4. 2^(n-1) = - [2^(n+1)]
If f(x)=2x²-x find f(-3)
Answer:
21
Step-by-step explanation:
f(x) = 2x^2 - x
f(-3) = 2*(-3)^2 - (-3)
=2*9 +3
=18 +3
=21
Answer: 21
Step-by-step explanation: To find f(-3) or the value of the function when x = -3, we plug in a -3 for the x in our function and we have 2(-3)² - (-3).
Start by simplifying the exponent to get 9.
So we have 2(9) - (-3) or 18 + 3 which is 21.
PLEASE HELP ME WILL MARK BRAINLIEST
Answer:
C
Step-by-step explanation:
The sum of the measures of the three angles of a triangle is 180 degrees.
A
50 + 40 + 90 = 180 good
B
55 + 35 + 90 = 180 good
C
45 + 40 + 90 = 175 not good
Answer: C
Pat spent $25.89 for a new book bag, $3.15 for a notebook, and $4.59 for a new pack of pens. About how much did he spend?
$30
$33
$34
$32
Answer: $34
Hope this helps +
Which function has the domain x greater-than-or-equal-to negative 11?
Given:
Consider the below figure attached with this question.
To find:
The function that has the domain [tex]x\geq -11[/tex].
Solution:
We know that, a radical function is defined for only non negative radicand.
In option A, the function is defined if
[tex]x+11\geq 0[/tex]
[tex]x\geq -11[/tex]
The domain of this function is [tex]x\geq -11[/tex]. So, option A is correct.
In option B, the function is defined if
[tex]x-11\geq 0[/tex]
[tex]x\geq 11[/tex]
The domain of this function is [tex]x\geq 11[/tex]. So, option B is incorrect.
In option C and D, the function is defined if
[tex]x+5\geq 0[/tex]
[tex]x\geq -5[/tex]
The domains of these function are [tex]x\geq -5[/tex]. So, options C and D are incorrect.
Hence, option A is correct.
Answer:
A
Step-by-step explanation:
6a + 2b = 30
6a + 9b = 51
What are a and b
Answer:
a = 18
b = 3
hope it helps
have a nice day
Find the slope of the line containing the given pair of points. If the slope is undefined, state so.
(-1,-7) and (-6,1)
Answer:
m = [tex]-\frac{8}{5}[/tex]
Step-by-step explanation:
m = slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{1--7}{-6--1}[/tex]
m = [tex]\frac{8}{-5}[/tex]
m = [tex]-\frac{8}{5}[/tex]
Polygon ABCD is a rectangle. What is its area? Round your answer to the nearest tenth.
(2,5)
(-4,3)
(3, 2)
(-3,0)
Answer: The correct option is A.
Step-by-step explanation:
To calculate the distance between the points, we use the formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d= distance
[tex]x_2\text{ and }x_1[/tex] are the coordinates of the points on x-axis
[tex]y_2\text{ and }y_1[/tex] are the coordinates of the points on y-axis
For the given points:
A(-4,3), B(2,5), C(3,2) and D(-3,0)
Calculating the distance CD:[tex]x_2=3\\x_1=-3\\y_2=2\\y_1=0[/tex]
Putting values in above equation, we get:
[tex]CD=\sqrt{(3-(-3))^2+(2-0)^2}\\\\d=\sqrt{36+4}=6.32units[/tex]
Calculating the distance AD:[tex]x_2=-4\\x_1=-3\\y_2=3\\y_1=0[/tex]
Putting values in above equation, we get:
[tex]AD=\sqrt{(-4-(-3))^2+(-3-0)^2}\\\\d=\sqrt{1+9}=3.16units[/tex]
To calculate the area of a reactangle, we use the equation:
[tex]Area=l\times b[/tex] ....(1)
where,
l = length of the rectangle = CD = 6.32 units
b = breadth of the rectangle = AD = 3.16 units
Putting values in equation 1, we get:
[tex]Area=6.32\times 3.16\\\\Area=20.0 \text{ square units}[/tex]
Hence, the correct option is A.
Answer:
The answer is A.
Step-by-step explanation:
I got it correct.
How much would the combined production of pineapples increase for the two islands due to trade? How much would the combined production of pearls increase?
Step-by-step explanation:
find the coordinate of the foot of the perpendicular from(4,-2) to the line 2x-3y-4=0