The population of Orange County as represented by the function f(x)=87,000(0.9)^x. Where x is the number of years since 2010 The population of Greene Courcy was 78,000 in 2010. and has decreased exponentials y at a rate of 88 a each year.
How do the populations of these countess compare in 2016 ?
Drag a value or word to to cokes to correctly complete he statements:
Answers
The population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.
What is an exponential function?
The definition of an exponential function is given by the equation
y = aeᵇˣ, where a and b are constants.
The given function is f(x) = 87000(0.9)ˣ.
Given that x = 0 represents the year 2010.
Therefore, x= 5 represents the year 2015.
Substitute x = 5 into the given function:
f(5) = 87000(0.9)⁵
≈ 51373
Hence, the population of Orange country is about 51373 in 2015.
Now, the population of Greene country was 78000 in 2010 and has decreased exponentially at a rate of 8% each year.
The population of Greene city after 5 years is given by:
78000(1-8%)⁵
= 78000(1 - 0.08)⁵
= 78000(0.92)⁵
= 51408
Therefore, the population of Greene country in 2015 was 51408 which is greater than the population of Orange country in 2015.
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Related Questions
Help me please must use elimination
Answers
Answer:
(1,2)
(3, -1)
Step-by-step explanation:
2x + 5y = 12
4x -y = 2 Multiply this through by 5 and then add to the equation above
2ox - 5y = 10
2x + 5y = 12
22x = 22 Divide both sides by 22
x = 1
Substiture in 1 for x in either of the two original equations
2x +5y = 12
2(1) + 5y = 12
2 + 5y = 12 Subtract 2 from both sides
5y = 10 Divide both sides by 5
y = 2
(1,2)
2nd Problem
2x - 5y = 11 Multiply through by 2 4x - 10 y = 22
3x + 2y = 7 Multiply through by 5 15x + 10 y = 35
Add the two bold equation together
4x - 10y = 22
15x +10y = 35
19x = 57 Divide both sides by 19
x = 3
Substitute in 3 for x in one of the original equations to solve for y.
2x - 5y = 11
2(3) - 5y = 11
6 - 5y = 11 Subtract 6 from both sides
-5y = 5 Divide both sides by -5
y = -1
(3,-1)
help meeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Step-by-step explanation:
I just answered this with all explanations.
Marsha deposited $6,000 into a savings account 4 years ago. The simple interest rate is 4 %. How much money did earn in interest?
Answers
Answer:
960.00
Step-by-step explanation:
Interest = principle x rate x time
interest = 6000 x .04 x 4
960.00
Answer:
I = $ 960.00
Step-by-step explanation:
I = Prt
Since we are figuring out how much money was earned in interest, we will need to convert our R (which is the interest rate) into decimals, which will be, r = R/100 = 4%/100 = 0.04 per year.
Step 1. Divide R by 100, in this case, R is 4, so it will be 0.04.
Step 2. Times 6000 (the money that was deposited) by 0.04, then times it with 4 (the years) and you will get 960.
I = 6000 × 0.04 × 4 = 960
I = $ 960.00
I hope this helps you!
Question:
The instructions next to the register state the following: For all purchases less than $400 ask, “Would you like to put this on your Barnes preferred customer card?” What is the most likely reason for these instructions?
A.To build brand recognition with your customers
B.To get customers to join the preferred customer program
C.To keep credit charges from the bank low
D.To receive more credit charges from the bank
Answers
Answer:The answer is B
Step-by-step explanation:
The reason that the answer is b is because he wants to keep the prices low from them getting charged by the bank
please help!! will give brainliest and extra credits
Answers
Answer: 5
Step-by-step explanation: To find the distance between 2 points, we should use this formula:
d=√((x_2-x_1)²+(y_2-y_1)²)
So, using that it would be written as:
[tex]\sqrt{9 + 16}[/tex] (after simplified)
Now, we need to find the square root of 25
The square root of 25= 5
So, that is how I got my answer.
6.3¹
Given conversion factor ¹2 m, what is the above line segment's unit of
measure in inches? Round your answer to the nearest tenth.
Answer here
Answers
The line segment's unit of measure is 75.6 inches.
What is the conversion factor?
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is required, it must be done using the correct conversion factor to get an identical value.
Here, we have
Given
12in/1ft
We have to convert this into inches.
So, we apply here conversion factor and we get
= 6.3ft × 12in ÷1ft
= 75.6 inches
Hence, the line segment's unit of measure is 75.6 inches.
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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 19 more than the secondLet and represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles
Provide your answer below:
X=
Y=
Z=
Answers
The value of x= 35.5, y= 43.75 and z= 62.75
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the three angles are x, y and z.
x+ y + z = 180............(E3)
The sum of the measures of the second and third angles is three times the measure of the first angle.
So, y+ z = 3x
3x- y- z= 0.............(E1)
and, third angle is 19 more than the second
z= y+ 19
y- z= -19..........(E2)
So, E1+E2, and E3-E2,
3x- 2z= -19
x+ 2z= 161
Now, adding above
4x = 142
x= 35.5
and, y + z = 106.5, y- z = -19
Again, adding
2y= 87.5
y= 43.75
and, z= 62.75
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What is the value of x?
(7x-3)°
(11y-+5)°
Answers
Answer:
The answer is 9
Step-by-step explanation:
The given triangle is equivalent triangle
We know that in equivalent triangle all angles are equal to 60°
So,
(7x - 3)° = 60°
7x - 3° = 60°
7x - 3° + 3° = 60° + 3°
7x = 63°
x = 63°/7°
x = 9°
Thus, The value of x is 9°
For Verification Only;
(7x - 3)° = 60°
[7(9) - 3]° = 60°
(63 - 3) = 60°
60° = 60°
Hence,
L.H.S = R.H.S
(a) Show that the following polynomials form a basis of P, (the cubic polynomials). Hint: Use the standard basis of P, to prove linear independence. Pe=1 pi=1-1 P₂ = 2-41+1² P. = 6-181 +91- (b) Call the above basis C. Find the coordinate vector (C-name) of polynomial p(/) - 7-81+31° with respect to the C basis.
Answers
To prove the given statement we can take into account the matrix produced by the tuples (1,2,0), (1,0,1) and (1,0,1). The three vectors are linearly independent if the matrix's where determinant is nonzero.
det ( -1 2 0
-1 0 1
1 0 1 ) = 4
Now that P2 has a dimension of 3, those three vectors serve as the foundation for P2 by definition.
Therefore, the polynomial forms the basis of P.
Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables. x2+x-12 is an illustration of a polynomial with a single variable. There are three terms in this example: x2, x, and -12.
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"Question 60
Find the probabilities below using a standard 52 card deck.
Answers
1. d. 8/52 (Ace ∪ 5)
2. h. 0 (Ace ∩ 5)
3. b. 20/52 (Even')
4. c. 36/52 (Even ∪ black)
5. a. 3/52 (Face ∩ Diamond)
What is probability?
Probability means the quality or state of being the outcome; the extent to which something is likely to happen or take place. Probability means the possibility of any outcome which can take place in any event.
Solution:
1. Probability of Ace ∪ 5 = (No. of Aces + no. of cards with face value 5)/52 = 8/52
2. Probability of Ace ∩ 5 = (Intersection of Ace and face value of card 5)/52 = 0
∵ Intersection of ace and 5 is 0 as there is no intersection in between the 2 subevents.
3. Probability of Even complement = No. of cards with odd values/52
{A,3,5,7,9,A,3,5,7,9,A,3,5,7,9,A,3,5,7,9}/52 =20/52
4. Probability of Even ∪ black = {(2,4,6,8, 10)×4 types of cards odd black spades + odd black clubs = 20+16/52
= 36/52
5. Probability of Face ∩ Diamond = No. of face cards in diamonds/52
= {Jack, Queen, King}/52
= 3/52
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Emily wanted to make cookies.One batch of cookies needed 2/3 cup of milk.How much milk would Emily need to bake three batches of cookies?
Answers
than you need to multiply the fraction by 3 or 3/1 multiply the numerator by the numerator and the denominator by the denominator
2/3 *3/1 = 6/3 or simplified to...
2 cups of milk
Drag each label or value to the correct location on the image. Each label or value can be used more than once, but not all labels or values will be used.
A physics student drops a ball from a height of 64 feet into a vacant parking lot. After one bounce, the height of the ball is 48 feet, and after two bounces, the height of the ball is 36 feet.
This situation can be modeled by the following exponential function.
f(x)=64(0.75)ˣ
Complete the sentences below.
initial height height bounces 36 f(x) x
The variable, represents the number of times the ball bounces.
The variable, after The parameter, 64 , represents the
of the ball.
The parameter, 0.75, represents the percentage of left from each previous bounce.
Answers
The completed sentences that describe the height reached by the ball specified by the function, f(x), that indicates the balls height, based on the number of bounces, x, f(x) = 64·(0.75)ˣ, which is similar to a geometric progression, is presented as follows;
The variable, x, represents the number of times the ball bounces.
The variable f(x) represents the height of the ball after x bounces.
The parameter, 64, represents the initial height of the ball.
The parameter, 0.75, represent the percentage of height left from each previous bounce.
What is a geometric progression?A geometric progression is a number sequence, arranged such that the ratio between a term and the previous term is a constant, known as the common ratio of the geometric progression.
The exponential function that models the specified situation of finding the height of the ball is presented as follows;
f(x) = 64·(0.75)ˣ
The initial height from which the student drops the ball = 64 feet
The height the ball reaches after one bounce = 48 feet
Height of the ball after 2 bounces = 36 feet
The exponential function, f(x) = 64·(0.75)ˣ, is similar to the equation for a geometric progression, aₙ = a₁·r⁽ⁿ⁻¹⁾
Where;
a₁ = The first term = The initial height
r = The common ratio = 48/64 = 36/48 = 0.75
n = The number of times the ball bounces, in addition to the time the ball is dropped from the initial height, therefore;
x = n - 1, therefore;
x = The number of times the ball bounces
n = x + 1
The terms that complete the sentences are therefore:
The variable that represents the number of time the ball bounces = x
The variable that indicates the height of the ball after x bounces = f(x)
The initial height of the ball = The parameter 64
The percentage of the height the ball bounces to after the previous bounce = 0.75
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andom variable (RV) X-bar is computed from a set of n independent, normal RVs X 1...X.n. The sampling distribution refers to? the distribution on X-bar. the distribution on the X_ RVS. the distribution on the means of the Xi_RVS. the frequency distribution obtained from a set of n experimental data values. none of these
Answers
The sampling distribution refers to the distribution of the sample mean (X-bar) computed from a set of n independent, normal random variables (X1,...,Xn).
The sampling distribution is a theoretical distribution that describes how the sample mean would vary if you were to take multiple samples from the population and compute the sample mean for each sample. It is based on the assumption that the X1,...,Xn are independently and normally distributed with a common mean and variance.
The sampling distribution is important because it allows us to make inferences about the population mean based on the sample mean. By understanding the properties of the sampling distribution, we can calculate confidence intervals and perform hypothesis tests to determine whether the sample mean is significantly different from the population mean.
In contrast, the distribution on the individual random variables (X1,...,Xn) is the distribution of the individual observations in the sample. The distribution on the means of the individual random variables (Xi) is the distribution of the mean of each individual random variable.
The frequency distribution obtained from a set of n experimental data values is the distribution of the observed data values in the sample.
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Use the distributive property to write an equivalent expression.
2(m + 2n)
Answers
The answer would be
= 2m + 4n
I added a photo you could use in the future
The following coordinates are each a result of a single transformation. What type of transformation occurred for each image?
A (4,5) --> A (-4,-5)
Answers
There is a Rotation of 180 degrees
What is Co-ordinate Geometry?
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
We are given that point A is (4, 5) this means that the point lies in the First Quarter of the Co-ordinate System
and the transformed point lies in the Third Quarter of the Co-ordinate System
So, it can be very well said that there is a Rotation of 180 degrees
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Solve this expression
(8c²) (9c)
Answers
First try was incorrect
Use the graph to answer the questions below.
What is the domain of this function?
Answers
The domain of the function are all real numbers between -1 and 0. {x∈R|-1≤x≤0}
What is a function ?
A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function.
See if any vertical lines that were drawn touch the curve more than once by carefully examining the graph. The graph does not represent a function if there is any such line. The graph does reflect a function if no vertical line can cross the curve more than once.
The domain of function are set of values of x for which the function covers.
For the given function, from the graph the function starts from x =-1 and ends at x = 0.
So, the domain of the function are all real numbers between -1 and 0.
{x∈R|-1≤x≤0}
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Find how long it takes $2500 to double if it is invested at 6% interest compounded semiannually. Use the formula A=P(1+r/n) to solve the compound interest problem.
It will take approximately years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
The total years taken to double the money according to Compounding will be 12.5 years.
What is compound interest?
Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.
Main body:
Given :
rate = 6%
amount = $2500
Total amount = $5000
Compounded semi -anually,
so formula becomes,
Total amount = amount (1+r/200)^2t
T = [tex]A (1+\frac{r/2}{100})^{2t}[/tex])
5000 = 2500 (1+3/100)^2t
2 = [tex](1+0.03)^{2t}[/tex]
2 = [tex]1.03^{2t}[/tex]
taking log on both sides
log 2 = 2t *log 1.03
0.3/0.012 = 2t
t = 12.5 years
Hence the time taken to double the money is 12.5 years.
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In the isosceles triangle, solve for side AB
Please help me
Answers
Answer:
5
Step-by-step explanation:
In an isosceles triangle two of the angles are equal and the corresponding sides are also equal
Here ∠A = ∠B
AC = BC
3x + 4 = 10
3x = 6
x = 2
Side AB = x + 3 = 2 + 3 = 5
****
Which graph represents the inequality 2.5 is greater than the product of −0.5 and a number?
number line with open circle on point 0.2 and arrow shaded to the left
number line with open circle on point negative 5 and arrow shaded to the left
number line with open circle on point negative 0.2 and arrow shaded to the right
number line with open circle on point negative 5 and arrow shaded to the right
Answers
number line with open circle on point negative 5 and arrow shaded to the right is the right description for the graph of the inequality.
what is inequality?inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
let the number be x
so that 2.5 > -0.5x
dividing through by -0.5 we revert the inequality sign
2.5/-0.5 < x
-5 < x
Taking x to the other side we revert the inequality sign back to greater than
x > -5
In conclusion, number line with open circle on point negative 5 and arrow shaded to the right is the description of the graph
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Answer: D
Step-by-step explanation: I have proof! i got it right on test and i have a picture.
Use the formula A=P(1+r/n)ⁿt to solve the compound interest problem
Find how long it takes a $ 1700 investment to earn $ 500 interest if it is invested at 2 % interest compounded quarterly.
$ 500 interest will be earned in approximately years. (Round to the nearest tenth.)
Answers
Answer:
1.2+2.56.7×3218°÷456.7820
I need help on a question.
the picture below should help
Answers
2(4x5) = 40
2(4x2.5) = 20
2(2.5x5) = 25
85cm^2
Consider the function f(x) = (x²-x)(x + 5).
1. What are the zeroes of f(x)?
2. Write f(x) in standard polynomial form.
Answers
Step-by-step explanation:
[tex]( {x}^{2} - x)(x + 5)[/tex]
[tex]x(x - 1)(x + 5)[/tex]
[tex]x = 0[/tex]
[tex]x - 1 = 0[/tex]
[tex]x = 1[/tex]
[tex]x + 5 = 0[/tex]
[tex]x = - 5[/tex]
So our zeroes are 0,1, and -5
2.
[tex] {x}^{3} + 4 {x}^{2} - 5x[/tex]
The expression 12x + 8 represents the preimeter of a square. Write 12x+ 8 as a product. Then tell what expressions represents one side of the square.
Answers
Answer:
(3+2)
Step-by-step explanation:
Perimeter of a square = 4L
L is the length of one side of the square
Given the expression 12 + 8 that represents the perimeter of a square, factoring out 4 from both terms;
12 + 8
= (4*3)+(4*2)
= 4(3+2)
Comparing with 4L
4L = 4(3+2)
Divide both sides by 4
4L/4 = 4(3+2)/4
L = (3+2)
Hence the expression that represents one side of the square is (3+2).
Hope this helps!!! :)
PLEASE HELP ASAP!!!! FULL ANSWERS ONLY!!!!
Blake wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Blake has 950 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write a function for the area A of the enclosure in terms of w . (HINT: First write one equation with w and l and one equation with w and l and A. Solve for l in the first equation and substitute for l in the other). A ( w ) = ____________
b) What width w would maximize the area? w = __________________ ft
c) What is the maximum area? A = ______________ square feet
Answers
Answer:
(a) A(w) = w(950-2w) = 950w-2w^2
(b) w = 237.5
(c) A = 112812.5
Step-by-step explanation:
First of all the maximum area is always a square. You can get the answer first to check your work later.
950/4 = 237.5
One side is not needed so add that length to the non-parallel side.
237.5+237.5=475 feet is the length and 237.5 feet is the width(s)
A=475*237.5
A=112812.5 square feet
Doing the algebra...
P=l+2w
950=l+2w
950-2w=l
A=lw
A=(950-2w)w
A=950w-2w^2
(Score for Question 1: ___ of 5 points)
Simplify . Show your work.
Answer:
(Score for Question 2: ___ of 5 points)
Solve for x. Show your work.
Answer:
(Score for Question 3: ___ of 5 points)
Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria, how many would be in the petri dish after 24 hours? Show your work.
Answers
The bacteria after 24 hours will be equal to 450000.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Gina was working in the laboratory on an experiment involving the population of bacteria. If her initial starting amount in a petri dish was 125 bacteria.
The number of bacteria will be calculated as,
N = 125×(60×60)
N = 125×3600
N = 450000
Therefore, the bacteria after 24 hours will be equal to 450000.
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given the following list of numbers: $\frac{3}{5}, \frac{5}{6}, \frac{2}{3}, \frac{9}{8}, \frac{7}{9}, \frac{3}{4}$ what is the smallest number subtracted from the biggest number? express your answer as a decimal.
Answers
The difference between the largest and the smallest fraction is 0.24.
What are fractions?A fraction is a component of a whole.
Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided.
In a simple fraction, both are integers.
In a complex fraction, a fraction can be found in either the numerator or the denominator.
A suitable fraction has a numerator that is less than its denominator.
So, first, we will figure out the smallest and the greatest fraction:
We have: 3/5, 5/6, 2/3, 9/8, 7/9 and 3/4
LCM of denominators: 2*2*2*3*3*5 = 360
216/360, 300/360, 240/360, 405/360 (Improper), 280/360, 270/360
Smallest: 216/360
Largest: 300/360
Subtract smallest from largest:
300/360 - 216/360
84/360
7/30
0.2333
Round off: 0.24
Therefore, the difference between the largest and the smallest fraction is 0.24.
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A table is on sale for $297, which is 34% less than the regular price. WhAt Is the regular price?
Answers
Answer:Above $297 we need to add 34%. Thus the result :
297 X 34/100 =100,98
Result = 297 + 100,98 = 397,98
Step-by-step explanation:Good luck
Helpp 8 grade hellppp
Answers
With the given coordinates (-3, 1) and (0, 4), the slope is 1.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)
Here,
1) (-3, 1) and (0, 4)
Δy=(4-1)=3 and Δx=(0(-3))=3
So, m= Δy/Δx =3/3 =1
2) (-6, 27) and (2, 3)
Δy=(3-27)=24 and Δx=(2-(-6))=8
So, m= Δy/Δx =24/8 =3
3) (5, 27) and (0, -8)
Δy=(-8-27)=-35 and Δx=(0-5)=-5
So, m= Δy/Δx =(-35)/(-5) =7
4) (1, 0) and (-7, -24)
Δy=(-24-0)=-24 and Δx=(-7-1)=-8
So, m= Δy/Δx =(-24)/(-8) =3
5) (-3, 20) and (-5, 32)
Δy=(32-20)=12 and Δx=(-5-(-3))=-2
So, m= Δy/Δx =12/(-2) =-6
6) (5, -4) and (0, -9)
Δy=(-9-(-4))=-5 and Δx=(0-5)=-5
So, m= Δy/Δx =(-5)/(-5) =1
7) (-8, -2) and (-1, -4.5)
Δy=(-4.5-(-2))=-2.5 and Δx=(-1-(-8))=7
So, m= Δy/Δx = -2.5/7
8) (-7, -2) and (6, 11)
Δy=(11-(-2))=13 and Δx=(6-(-7))=13
So, m= Δy/Δx =13/13 =1
9) (-2, -6.5) and (4, -8)
Δy=(-8-(-6.5))= -1.5 and Δx=(4-(-2))=6
So, m= Δy/Δx = -1.5/6 = -1/4
Therefore, slope of a line with the coordinates (-7, -2) and (6, 11) is 1.
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What is x if 9: 12 = 15:x?
Answers
Answer:
Hi, the answer to your question is ×=20
X = 20
when we solve the given equation,
9/12 = 15/x
hence,
X = 15*12/9
X = 20
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