the population in Knox is 42000 and it is declining at a rate of 3.2% per year predict the population to the nearest whole number after 8 years
Answers
The predicted population of Knox, rounded to the nearest whole number, after 8 years is 32,599.
To predict the population of Knox after 8 years, we can use the given information that the population is currently 42,000 and it is declining at a rate of 3.2% per year.
To calculate the population after 8 years, we need to apply the rate of decline for each year. Let's break down the calculation step by step:
Calculate the population after the first year:
Population after 1 year = 42,000 - (3.2% of 42,000)
= 42,000 - (0.032 * 42,000)
= 42,000 - 1,344
= 40,656
Calculate the population after the second year:
Population after 2 years = 40,656 - (3.2% of 40,656)
= 40,656 - (0.032 * 40,656)
= 40,656 - 1,299.71
= 39,356.29
Continue this process for each year up to 8 years, applying the 3.2% rate of decline each time.
After performing these calculations for each year, we arrive at the population after 8 years:
Population after 8 years ≈ 32,599
Therefore, the predicted population of Knox, rounded to the nearest whole number, after 8 years is 32,599.
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Related Questions
Percentages are numerators of the fractions with denominator
Answers
9514 1404 393
Answer:
100
Step-by-step explanation:
The % symbol can be thought of as a shorthand way to write /100. That is, the symbol can be replaced by /100 wherever you see it, and vice versa:
23% = 23/100
23 is the numerator of the fraction with denominator 100.
Irina ran 1/2 in 3 1/2 minutes. At that rate, how long would it take her to run 2 miles?
Answers
Answer:
Step-by-step explanation:
14 mins
this is because if we divide 2 but 1/2 you would get 4
since she can run 1/2 a mile in 3 1/2 mins
we should multiply the 3 1/2 buy 4
this would lead to the answer 14
Which phrase represents this expression? (6242) x 3 O 3 times the difference of 42 and 62 O the difference of the product of 3 times 42 and 62 O the difference of 62 and the product of 3 times 42 O 3 times the difference of 62 and 42.
Answers
By using the concept of mathematical expression, it is obtained that
(62−42)×3 is represented by 3 times the difference between 62 and 42
First option is correct
What is mathematical expression?
A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.
Here the given mathematical expression is (62−42)×3
Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here
(62−42)×3 means whole of (62 - 42) is multiplied with 3
So, this is 3 times the difference between 62 and 42
First option is correct
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Correct Question
Which phrase represents this expression?
(62−42)×3
a) 3 times the difference of 62 and 42
b) 3 times the difference of 42 and 62
c) The difference of 62 and the product of 3 times 42
d) The difference of the product of 3 times 42 and 62
For a géometric sequence, if a1=9 and a5
=2304, what is the value of r?
Answers
The value of common ration r is 4.
Given that,
a₁ = 9
a₅ = 2304
We know that,
A geometric sequence is a sequence in which each term (except from the first term) is multiplied by a fixed amount to obtain the following term.
The following term in the geometric sequence must be obtained by multiplying it by a set term (referred to as the common ratio), and the previous term in the sequence can be obtained by dividing it by the same common ratio.
Since we know that nth term of GP is,
\(a_{n}\) = a₁ \(r^{n-1}\)
Therefore,
a₅ = a₁ \(r^{4}\) = 2304
⇒ 9 x \(r^{4}\) = 2304
⇒ \(r^{4}\) = 256
⇒ r = 4
Hence, r = 4
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Group the terms with variables on one side of the equal sign, and simplify.
5z + 3 = 36z
Answers
Answer:
z = 3/31
Step-by-step explanation:
5z + 3 = 36z
subtract 5z on both sides
3 = 31z
divide by 31 on both sides
z = 3/31
PLEASE HELP FAST. Maggie pays for a 6-month subscription to a video streaming channel. Because she purchased 6 months at once, she receives a $10 discount. Her final price after the discount is $43.94. What was the original price per month (H)?
Answers
Answer:
53.94$
Step-by-step explanation:
Answer:
53.94$
Step-by-step explanation:
Given that A, O & B lie on a straight line segment, evaluate COD.
C
D
(3x + 94)
(x + 18)
(2x 4)
A
B
The diagram is not drawn to scale.
CODE
Answers
A certain disease has an incidence rate of 0.3%. If the false negative rate is 6% and the false positive rate is 2%, compute the probability that a person who tests positive actually has the disease.
Answers
The probability that a person who tests positive actually has the disease is 0.006%
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Incidence rate = 0.3%False negative rate = 6%False positive rate = 2%The probability that a person who tests positive actually has the disease is represented as
Probability = Incidence rate * False positive rate
Substitute the known values in the above equation, so, we have the following representation
Probability = 0.3% * 2%
Evaluate the products
Probability = 0.006%
Hence, the probability is 0.006%
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I need help with this!! ASAP
Answers
Answer:
x = 16
Step-by-step explanation:
I'd explain but I should also be doing school so I can no longer help you in your journey of greatness my friend...
Goodbye!
factorise x^2-x-6 please help
Answers
Answer:
Ask: Which two numbers add up to -1 and multiply to -6
-3 and
2. Rewrite the expression using the above.
(x-3)(x+2)
Step-by-step explanation:
Answer:
x^2-3x+2x-6=0
x(x-3)+ 2(x-3)=0
(x+2)(x-3)=0
x=3,-2
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.1 in/s. At what rate is the volume of the cone changing when the radius is 120 in. and the height is 175 in.
Answers
Given:
\(\dfrac{dr}{dt}=1.4\text{ in/s}\)
\(\dfrac{dh}{dt}=-2.1\text{ in/s}\)
To find:
The rate of change in volume at \(r=120\text{ in. and }175\text{ in.}\)
Solution:
We know that, volume of a cone is
\(V=\dfrac{1}{3}\pi r^2h\)
Differentiate with respect to t.
\(\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]\)
Substitute the given values.
\(\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]\)
\(\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]\)
\(\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560\)
\(\dfrac{dV}{dt}=29920\)
Therefore, the volume of decreased by 29920 cubic inches per second.
Choose the function whose graph is given by:
Answers
The function whose graph is given is y = sin (x - 2).
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The graph of y = sin(x - 2) is a sinusoidal function that is shifted 2 units to the right from the standard sine function y = sin(x).
The sine function oscillates between -1 and 1 as x increases, and the value of x at which the function reaches its minimum or maximum value is a multiple of π.
When we subtract 2 from x in the equation y = sin(x - 2), the entire graph is shifted to the right by 2 units, which means that the minimum and maximum points occur at x-values that are 2 units greater than they would be for the standard sine function.
The graph of y = sin(x - a) is a sinusoidal function that is shifted a units to the right from the standard sine function.
So, in this case, the graph of y = sin(x-2) looks like the standard sine function shifted 2 units to the right.
The amplitude and period of the function remain the same as the standard sine function, but the phase shift changes.
Thus,
The function whose graph is given is y = sin (x - 2).
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Please answer this correctly without making mistakes
Answers
Answer:
$25-$9.9
Step-by-step explanation:
45/100
0.45*$25
$9.9
$25-$9.9
it cost 14.1
It is known that 5% of flashlight bulbs manufactured by a certain company are defective. a. Use the normal approximation to estimate the probability that, out of a random sample of 600 lightbulbs, at least 25 are defective. (5 points) b. Use the normal approximation to estimate the probability that, out of a random sample of 600 lightbulbs, fewer than 20 are defective. (5 points)
Answers
Using the normal approximation to the binomial, the probabilities are given by:
a) 0.8485 = 84.85%.
b) 0.0244 = 2.44%.
Normal Probability DistributionIn a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with \(\mu = np, \sigma = \sqrt{np(1-p)}\).In this problem, we have that:
There are 600 bulbs, hence n = 600.5% are defective, hence p = 0.05.The mean and the standard deviation of the approximation are given, respectively, by:
\(\mu = np = 600(0.05) = 30\)
\(\sigma = \sqrt{np(1-p)} = \sqrt{600(0.05)(0.95)} = 5.3385\)
Item a:
Using continuity correction, the probability is P(X > 24.5), which is one subtracted by the p-value of Z when X = 24.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{24.5 - 30}{5.3385}\)
\(Z = -1.03\)
\(Z = -1.03\) has a p-value of 0.1515.
1 - 0.1515 = 0.8485.
0.8485 = 84.85% probability.
Item b:
This probability is P(X < 19.5), which is the p-value of Z when X = 19.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{19.5 - 30}{5.3385}\)
\(Z = -1.97\)
\(Z = -1.97\) has a p-value of 0.0244.
The probability is of 0.0244 = 2.44%.
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3. [-/2 Points]
Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.)
4x² + 5x-6
x+2
DETAILS
20
lim
X--2
Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result.
g(x)
LARCALC12 1.3.044.
Need Help? Read It
Answers
The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2
To find the limit as x approaches -2, we substitute -2 into the function:
f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
= 4(4) - 10 + 12 + 2
= 16 - 10 + 12 + 2
= 20
Therefore, the limit of the function as x approaches -2 is 20.
To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.
However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.
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Twice a number added to another number is 15 the sum of the two numbers is 11 find the numbers.
Answers
Answer:
the numbers are 4 and 7
Step-by-step explanation:
"twice a number added to another number is 15" --- 4(2) + 7 = 15
"the sum of the two numbers is 11" --- 4 + 7 = 11
suppose that a population parameter is .7 and many samples were taken. if the size of each sample is 30 what is the standard error
Answers
The standard error is 0.0912.
The standard error (SE) is a measure of the precision of the sample mean estimate compared to the true population mean. To calculate the SE, we use the formula SE = standard deviation / square root of sample size.
In this scenario, the population parameter is 0.7, and the sample size is 30. If we assume that the sample mean is an unbiased estimator of the population mean, then the SE can be calculated using the above formula. However, we do not know the standard deviation of the population, so we use the sample standard deviation as an estimate.
Assuming the sample is large enough to assume normality, the formula becomes SE = \(\sqrt{(0.7*0.3)/30}\) = 0.0912. Therefore, the standard error for a sample size of 30 is 0.0912. This means that if we were to take multiple samples of size 30 from the same population, the standard deviation of the means of those samples would be around 0.0912 away from the population parameter of 0.7 on average.
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OZ
Find 4 consecutive odd integers such that the sum of the first and the last is the same as 9 less than the third
Answers
9514 1404 393
Answer:
-11, -9, -7, -5
Step-by-step explanation:
Let x represent the third of the odd integers. Then the first is (x -4) and the last is (x +2). We are told their sum is ...
(x -4) +(x +2) = x -9
2x -2 = x -9
x = -7 . . . . . . . . . . add 2-x
The integers are -11, -9, -7, -5.
In the similarly transformations of ABC
Answers
Your engineering position requires frequent travel to the west coast, typically through Chicago. In reviewing historical airline data, you have determined that over the last year flights into Chicago on Southwest have been normally distributed, arriving an average of 72.3 minutes late with a standard deviation of 9.8 minutes. Yesterday, a travel agent informed you that Southwest recently changed their scheduling into Chicago and has improved arrival times. To confirm this claim, you collect the arrival times for a random sample of 47 Southwest flights arriving into Chicago, and find a sample mean of 70.7 minutes and a sample standard deviation of 7.1 minutes. Has there been a change in the mean arrival times on Southwest
Answers
Answer:
The given data does not support the submission that there has been a change in the mean arrival times on Southwest
Step-by-step explanation:
The known mean late arrival time, μ = 72.3
The known standard deviation in late arrival time, σ = 9.8 minutes
The number of flights in the sample, n = 47
The sample mean late arrival time, \(\overline x\) = 70.7
The sample standard deviation late arrival time, s = 7.1
Using a significance level of 0.01
The null hypothesis is, H₀ ; μ = 70.7
The alternative hypothesis is, Hₐ ; μ ≠ 70.7
The test statistic is given as follows;
\(z=\dfrac{\bar{x}-\mu }{\dfrac{\sigma }{\sqrt{n}}}\)
\(z=\dfrac{70.7-72.3 }{\dfrac{9.8 }{\sqrt{47}}} \approx -1.119290547\)
∴ z ≈ -1.12
p-value = 2 × P(z < -1.12) = 2 × 0.13136 = 0.26272
Given that the p-value of 0.26272 is larger than the significance level, 0.05, we fail to reject the null hypothesis
Therefore, there is not enough statistical evidence to show that there has been a change in the mean arrival times on Southwest
Abcd is a cyclic quadrilateral. o is the center of the circle ∠bad = 40°,then angle BCD=?,m(arc BCD) =?,m( arc BAD)=?
Answers
Answer:
m∠BCD = 140°
m(arc BCD) = 80°
m(arc BAD) = 280°
Step-by-step explanation:
In the cyclic quadrilateral, every two opposite angles are supplementary.The measure of the subtended arc to an inscribed angle equals twice the measure of this angleLet us use these facts to solve the question
∵ ABCD is a cyclic quadrilateral in circle O
∵ ∠BAD and ∠BCD are opposite angles
→ By using the 1st fact above
∴ m∠BAD + m∠BCD = 180°
∵ m∠BAD = 40°
∴ 40° + m∠BCD = 180°
→ Subtract 40° from both sides
∴ 40° - 40° + m∠BCD = 180° - 40°
∴ m∠BCD = 140°
∵ Arc BCD subtended the inscribed ∠BAD
→ By using the 2nd fact above
∴ m(arc BCD) = 2(m∠BAD)
∵ m∠BAD = 40°
∴ m(arc BCD) = 2(40°)
∴ m(arc BCD) = 80°
∵ Arc BAD subtended the inscribed ∠BCD
→ By using the 2nd fact above
∴ m(arc BAD) = 2(m∠BCD)
∵ m∠BCD = 140°
∴ m(arc BAD) = 2(140°)
∴ m(arc BAD) = 280°.
In the expression 7g + 15, g is the
O coefficient
O variable
constant
operation
Answers
PLEASE HELP ME ITS DUE TODAY!!!
Answers
4. RSTU is a trapezoid because the opposite sides RS and UT are parallel.
5. RSTU is not an isosceles trapezoid because the diagonals are not congruent.
How to verify that RSTU is a trapezoid?In order to verify that RSTU is a trapezoid, we would have to determine slope of the pair of opposite sides and check whether at least one pair of opposite sides are parallel;
RU ║ ST
Slope of side RU = Slope of side ST
Slope of RU = (y₂ - y₁)/(x₂ - x₁)
Slope of RU = (1 + 3)/(5 + 3)
Slope of RU = 4/8
Slope of RU = 0.5.
Slope of RS = (y₂ - y₁)/(x₂ - x₁)
Slope of RS = (-9 + 3)/(-4 + 3)
Slope of RS = -6/-1
Slope of RS = 6.
Slope of ST = (y₂ - y₁)/(x₂ - x₁)
Slope of ST = (-2 - 1)/(10 - 5)
Slope of ST = -3/5
Slope of ST = -0.6.
Slope of UT = (y₂ - y₁)/(x₂ - x₁)
Slope of UT = (-2 + 9)/(10 + 4)
Slope of UT = 7/14
Slope of UT = 0.5.
Therefore, RSTU is a trapezoid because the opposite sides RS and UT are parallel.
Question 5.
In order to determine whether RSTU is an isosceles trapezoid, we would have to determine length of the diagonals by using the distance formula and check whether they are congruent;
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance RT = √[(-2 + 3)² + (10 + 3)²]
Distance RT = √170 units.
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Distance US = √[(5 + 4)² + (1 + 9)²]
Distance US = √181 units.
Therefore, RSTU is not an isosceles trapezoid because the diagonals RT and US are not congruent.
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Alejandro used a mathematical property to create two equivalent expressions.
6(x + 2) = 6x + 30
Which of the following is the missing term?
O 24
Х
O 5x
6
5
Answers
Sally owns a restaurant in Wooville. The city is trying to get a minor league team to move there in 2021, either to location A (near her restaurant) or location B. The team might stay in location C in another city. The probability of these events, and her estimated annual profit in 2021 are shown in the table below.
Answers
The standard deviation of the restaurant profits in 2021 is given by $71181.
Restaurant profit for outcome 'move to A' = $ 260000
Restaurant profit for outcome 'move to B' = $ 120000
Restaurant profit for outcome 'stay in C' = $ 100000
The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.
Standard deviation of the restaurant profits in 2021 is given by
= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)
= $ √(((100000)² + (40000)² + (60000)²)/3)
= $ √(15200000000/3)
= $ √5066666667
= $ 71181 (rounded to the nearest dollar)
Hence standard deviation of the restaurant profits in 2021 is given by $71181.
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The question is incomplete. The complete question will be -
Answer this please its about volumes on spheres
Answers
Volume is a three-dimensional scalar quantity. The volume of the largest sphere is 44602.24 yd³.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the sphere is given by the formula,
The volume of the sphere = (4/3)πR³
1. Volume = (4/3) × π × (4 in)³ = 268.08 in³
2. Volume = (4/3) × π × (12 ft)³ = 7238.23 ft³
3. Volume = (4/3) × π × (22 yd)³ = 44602.24 yd³
Hence, the volume of the largest sphere is 44602.24 yd³.
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● Blondies are squares with 3 inch sides. ● Brownies are squares with 6 inch sides. ● The tray that displays the blondies and brownies has an area of 648 square inches and is completely full. If she has 4 rows of blondies and 4 rows of brownies, what fraction of the area of the tray, in square inches, is blondies? Show your work.
Answers
The fraction of the area of the tray occupied by the blondies is 1/9.
To find the fraction of the area of the tray occupied by blondies, we need to determine the area occupied by the blondies and compare it to the total area of the tray.
Let's calculate the area of each individual blondie:
The blondies are squares with 3-inch sides, so the area of each blondie is 3 inches × 3 inches = 9 square inches.
Now, let's calculate the area occupied by the blondies in each row:
Since there are 4 rows of blondies and each row contains 4 blondies, the total number of blondies is 4 rows × 4 blondies per row = 16 blondies.
So, the total area occupied by the blondies is 16 blondies × 9 square inches per blondie = 144 square inches.
Next, let's determine the area occupied by the brownies:
The brownies are squares with 6-inch sides, so the area of each brownie is 6 inches × 6 inches = 36 square inches.
Since there are also 4 rows of brownies and each row contains 4 brownies, the total number of brownies is 4 rows × 4 brownies per row = 16 brownies.
Therefore, the total area occupied by the brownies is 16 brownies × 36 square inches per brownie = 576 square inches.
Now, let's calculate the total area of the tray:
Given that the tray is completely full and has an area of 648 square inches, we can subtract the area occupied by the brownies from the total area to find the remaining area occupied by the blondies:
Total area of the tray - Area occupied by the brownies = Area occupied by the blondies
648 square inches - 576 square inches = 72 square inches.
So, the fraction of the area of the tray occupied by the blondies is:
Area occupied by the blondies / Total area of the tray = 72 square inches / 648 square inches.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 72 in this case:
72 square inches / 648 square inches = 1/9.
Therefore, the blondies' percentage of the tray's surface area is 1/9.
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Tyler says there are indefinitely many additional numbers between 0 and 1 do you agree
Answers
Answer:
Yes
Step-by-step explanation:
There are infinite numbers between 0 and 1. Think of decimals. E.g.
1.1 , 1.2 , 1.3 , 1.31 , 1.32 , 1.30000000000000009
It goes on forever and never ends. So yes, Tyler is correct.
A walk alongside a railway track is represented on a map by an 86 mm straight line.
The walk is 17.2 km.
What is the scale of the map?
Answers
First we turn the 17.2 km into mm. To do that we turn it into 17,200 m then into 1,720,000 cm then into 17,200,000 mm. Then we just divide 17.2 million by 86 so 17,200,000÷86=200,000. so we know that the scale of the map is 1:200,000. Also pls mark as brainliest answer thx.
Select all of the complex numbers in the given table.
Answers
Answer:
the 2nd one
5th one
and 4th