Answer:
800,000
Step-by-step explanation:
To do this, simply divide the number by 10. 8000000/10 = 800,000.
Exponential Data
In this activity, you will graph and write exponential functions to model population data presented in tables. Then you’ll use your models to make predictions and draw a conclusion.
Question 1
A town’s population has been exponentially increasing for the past 10 years. The town council initially recorded the town’s population at 6,000 people and tracked it each year after that. The table represents their data.
Years Town Population
(in thousands)
0 6
1 6.9
2 9
3 10.5
4 13
5 14.2
6 18
7 20.8
8 26
9 31.3
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
Question
If the town continues to grow at the same rate, approximately what will be the population, to the nearest 100 people, 25 years after the town council started tracking the population data?
341,100 people
180,000 people
271,200 people
572,400 people
Question 2
Because of the growth in the town’s population, the agricultural department kept track of the town’s native bee population during the same time period. They feared with the increase of people in the town, the bee population would start to decrease, affecting the ecosystem. Their data is shown in the table.
Years Bee Population
(in thousands)
0 320
1 225
2 152.6
3 111.2
4 75
5 56.8
6 36.7
7 26.9
8 17.5
9 13.2
Use the graphing tool to plot the population data and determine the curve of best fit.
Part A
Question
What is the equation of the curve of best fit for the population data?
Enter the correct answer in the box by replacing a and b with the values from the graphing tool. Do not round the values of a and b.
Part B
After several years of recording the data, the agricultural committee requested help from the town council for a grant to boost the bee population. The council denied the request, saying it wouldn’t take any action until the population dropped below 5,000 bees.
In the 12th year after initially recording the bee population, the agricultural committee plans to speak with the board again. Will the committee have a good chance of convincing the board to help support bees this time around? Justify your conclusion using mathematical reasoning.
Answer:
1.The equation of best fit is ŷ = 2.69152X + 3.45818.
Step-by-step explanation:
if the earthquake has stronger magnitude what does it mean
Answer:
Step-by-step explanation:
The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.
5) Write the equation for the function that results from each transformation applied to the base function
y = 7²
a) reflect in the x-axis (vertical reflection)
c) stretch horizontally by a factor of 2.4
b) stretch vertically by a factor of 3
d) reflect in the y-axis and stretch vertically by bafo 7
The equation that results from each transformation is given as follows:
a) reflect in the x-axis (vertical reflection): y = -7^x.
b) stretch vertically by a factor of 3: 3(7)^x.
c) stretch horizontally by a factor of 2.4: y = (7)^(x/2.4).
d) reflect in the y-axis and stretch vertically by a factor of 7: y = 7^(1 - x).
How to obtain the functions?The parent function in the context of this problem is given as follows:
y = 7^x.
The reflection over the x-axis means that the sign of the entire function is exchanged, hence:
y = -7^x.
The vertical stretch by a factor of 3 means that the entire function is multiplied by 3, thus:
y = 3(7)^x.
The horizontal stretch by a factor of 2.4 means that x -> x/2.4, hence:
y = (7)^(x/2.4).
The reflection over the y-axis means that x -> -x, while the vertical stretch by a factor of 7 means that the function is multiplied by 7, hence the function for item d is given as follows:
y = 7(7)^(-x)
y = 7^(1 - x).
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Which of these is true about the result of 3 x 330?
A
It has only 2 multiples.
B
It has only 2 factors.
С
330 is its multiple.
D
11 is its factor.
990 has more than 2 multiples and also it has more than 2 factors and 11 is one of its factors.
What is a factor?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them. Factors can be found using either division or multiplication.
Given, A inequality that is 3*330 thus it can also be written as 990.
the factor of 990 is 3, 3, 2, 5, and 11.
Although there are more than two multiples and factors for 990, 330 is not one of them. As a result, only option D is correct (990/11 = 90).
Therefore, 990 has more than two multiples, and more than two components, and one of those factors are 11.
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for which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? responses
It is not appropriate to assume that the sampling distribution of the sample mean is approximately normal when the sample size is small and the population distribution is skewed to the right or to the left. So, the options C and D are not appropriate. A and B are appropriate as the sample size is large and the population is normally distributed. E is also appropriate as the sample size is large.
The central limit theorem states that if we have a large enough sample size (typically n >= 30) from any population with a well-defined mean and finite variance, then the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and variance equal to the population variance divided by the sample size.
However, if the population distribution is highly skewed, meaning it is not symmetric, then even a large sample size may not lead to a normal distribution of the sample mean.
In this case, it is not appropriate to assume that the sampling distribution of the sample mean is approximately normal. This is why options C and D are not appropriate as the sample size is large (10 and 75 respectively) but the population distribution is skewed to the right or to the left. On the other hand, options A and B are appropriate as the sample size is large and the population is normally distributed. Option E is also appropriate as the sample size is large, regardless of the shape of the population distribution.
The complete question is given below:
""
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal?
A) A random sample of 8 taken from a normally distributed population.
B) A random sample of 50 taken from a normally distributed population.
C) A random sample of 10 taken from a population distribution that is skewed to the right.
D) A random sample of 75 taken from a population distribution that is skewed to the left.
E) A random sample of 100 taken from a population that is uniform.
"
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Which parent functions have a range of (-infinity , infinity) select all that apply
A. a parent even-degree power function
B. a parent odd-degree power function
C. a parent even-degree root function
D. a parent odd-degree root function
E. a parent exponential function with a base greater than 1
F. a parent exponential function with a base between 0 and 1
G. a parent logarithmic function with a base greater than 1
H. a parent logarithmic function with a base between 0 and 1
Answer:b,d,g,h
Step-by-step explanation:
A function assigns the value of each element of one set to the other specific element of another set. The correct option is B, D, G, and H.
What are the domain and range of a function?A function assigns the value of each element of one set to the other specific element of another set.
The domain is the set of values for which the given function is defined.The range is the set of all values which the given function can output.From the given functions the function that has a range of (-∞, ∞) can be found by plotting the graph. Therefore, the parent function that has a range of (-∞, ∞) are:
B. a parent odd-degree power function
D. a parent odd-degree root function
G. a parent logarithmic function with a base greater than 1
H. a parent logarithmic function with a base between 0 and 1
Hence, the correct option is B, D, G, and H.
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You have a rectangular prism whose cross section is a square with side length
3 cm. You need to know its length, but you do not have a ruler. Luckily, you have a calibrated container of water nearby. The container has marks that measure cubic centimeters of liquid. It appears to have 70 cubic centimeters of water in it, but when you submerge the prism into the water, the water level rises to the 115-cubic-centimeter mark. Determine how long your prism is.
Answer:
side length = 5cm
Step-by-step explanation:
The volume of the prism is:
V = l × w × h
But we only know the width and height which are both 3cm. See image.
We put it in the calibrated container (container with markings on it) We find out the volume is 45. Because 115 - 70 is 45.
Divide to find the missing length. See image.
Vol
= 3 × 3 × sidelength
V = 9s
45 = 9s
5 = s
see image.
Need help please explain how you got the answer
Answer:
$600
Equation:
(Base) x (percent as a decimal) x (years) = interest
(B x .16 x 7.5 = 720)
Steps:
(Base) x (percent as a decimal) = (interest) / (years)
(B x .16 = 96)
Base = (interest / years) / (percent as a decimal)
(B = 600)
The average low temperatures in international falls minnesota are shown in the graph f(x) represents the function that contains these points find each of the following
The Relative Maximum will be (7, 50) and minimum is (12, 0).
We have the graph showing average low temperatures in international falls minnesota.
From the graph the maximum y coordinate is 50.
So, the Relative Maximum will be (7, 50).
and, the minimum y coordinate is 0.
So, the Relative minimum is (12, 0)
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if the function f(x) = x^2 + 2 has the domain {0,3,6,9}, what is the range?
We need to evalute the domain given in the function in order to obtain the range
we have the next function
\(f(x)=x^2+2\){0,3,6,9}
we will substitute each value
\(f(0)=0^2+2=2\)\(f(3)=3^2+2=9+2=11\)\(f(6)=6^2+2=36+2=38\)\(f(9)=9^2+2=81+2=83\)the range of the function for the domain given is {2,11,38,83}
As we can see the
The circle graphs shows the percentages of student participation in sports a certain school.
E
F
Other
11%
Track &
Field
14%
Baseball
15%
A
Football
22%
Basketball
17%
m EF =
Find m EF. Do not round.
Soccer
21%
C
B
From the given below solution the value of m EF is 25%.
What is circle graphs?A circle graph, also known as a pie chart, is a type of data visualization that displays data as a circular graph, divided into sectors that represent numerical proportions.
Each sector of the circle represents a percentage or proportion of the total data set, and the size of each sector is proportional to its corresponding value.
To find m EF, we need to add the percentages of participation in sports E and F:
m EF = percentage of participation in sports E + percentage of participation in sports F
m EF = 11% + 14%
m EF = 25%
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An appliance repairman charges $75 to come to your house and $35 per hour. During one week, he visited 9 homes and his total weekly income was $1305. How many hours did he spend working on appliances?
2tan(x/2)- csc x=0 interval [0,2pi)
Answer:
\(x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}\)
Step-by-step explanation:
Given trigonometric equation:
\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)
To solve the equation for x in the given interval [0, 2π), first rewrite the equation in terms of sin x and cos x using the following trigonometric identities:
\(\boxed{\begin{minipage}{4cm}\underline{Trigonometric identities}\\\\$\tan \left(\dfrac{\theta}{2}\right)=\dfrac{1-\cos \theta}{\sin \theta}$\\\\\\$\csc \theta = \dfrac{1}{\sin \theta}$\\ \end{minipage}}\)
Therefore:
\(2 \tan\left(\dfrac{x}{2}\right)- \csc x=0\)
\(\implies 2 \left(\dfrac{1-\cos x}{\sin x}\right)- \dfrac{1}{\sin x}=0\)
\(\implies \dfrac{2(1-\cos x)}{\sin x}- \dfrac{1}{\sin x}=0\)
\(\textsf{Apply the fraction rule:\;\;$\dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}$}\)
\(\dfrac{2(1-\cos x)-1}{\sin x}=0\)
Simplify the numerator:
\(\dfrac{1-2\cos x}{\sin x}=0\)
Multiply both sides of the equation by sin x:
\(1-2 \cos x=0\)
Add 2 cos x to both sides of the equation:
\(1=2\cos x\)
Divide both sides of the equation by 2:
\(\cos x=\dfrac{1}{2}\)
Now solve for x.
From inspection of the attached unit circle, we can see that the values of x for which cos x = 1/2 are π/3 and 5π/3. As the cosine function is a periodic function with a period of 2π:
\(x=\dfrac{\pi}{3} +2n\pi,\; x=\dfrac{5\pi}{3} +2n\pi \qquad \textsf{(where $n$ is an integer)}\)
Therefore, the values of x in the given interval [0, 2π), are:
\(\boxed{x= \dfrac{\pi}{3}, \;\;x=\dfrac{5 \pi}{3}}\)
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.
The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:
Define the formula p(x, y) as x = yo(x).
This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.
Define the set F as {(x, x) (x)}.
This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.
Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.
This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.
The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.
Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.
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Can someone help me with this pls
Answer:
Subtract the powers, 8-4.
When you simplify that equation itself, the answer is 10,000.
So when you do 10⁴, it's 10,000.
(3×10 – 4)(2×1010) whats the scientific notion
The result of the multiplication in scientific notation is given by:
\(6 \times 10^{6}\)
What is scientific notation?A number in scientific notation is given by:
\(a \times 10^b\)
With the base being \(a \in [1, 10)\).
When we multiply two numbers in scientific notation, we multiply the bases and add the exponents.
For this problem, the numbers are given by:
\(3 \times 10^{-4}, 2 \times 10^{10}\)
The result of the multiplication is given by:
\(3 \times 10^{-4} \times 2 \times 10^{10} = 6 \times 10^{-4 + 10} = 6 \times 10^{6}\)
The result of the multiplication in scientific notation is given by:
\(6 \times 10^{6}\)
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The volume of a rectangular prism is 2x2 + 9x2 - 8x-36 with height x + 2. Using synthetic division, what is the area of
the base?
O 2x3 + 13x2 +18%
O 2x2 + 5x2 - 18%
O 2x2 + 13x+18
O 2x2 + 5x-18
+
Answer:
2×2+5x-18 is the answer
Please hurry! Which set of numbers are rational numbers but not integers, whole numbers, or natural numbers?
Answer:
The last one
Step-by-step explanation:
its all fractions, fractions are rational numbers but not integers, whole, or naturals numbers
Mensah is 5 years old and Joyce is thrice as old as Mensah. In how many years will Joyce be twice as old as Mensah?
9514 1404 393
Answer:
5 years
Step-by-step explanation:
We want to find x such that ...
2(5 +x) = 15 +x . . . . . after x years, Joyce will be 2 times as old
10 +2x = 15 +x . . . . . eliminate parentheses
x = 5 . . . . . . . . . . . subtract x+10
Joyce will be twice as old as Mensah in 5 years.
Answer:
Joyce will be twice as old as Mensah in 5 years.
Step-by-step explanation:
Write the quadratic equation whose roots are 6 and 2, and whose leading coefficient is 2
Answer:
Step-by-step explanation:
y = 2(x-6)(x-2) = 2(x²-8x+12) = 2x² - 16x + 24
find the surface area of the prism
Answer: 132 cm cubed
Step-by-step explanation:
0.5*3*4*2=12
10*5=50
4*10=40
3*10=30
30+40+50+12=132 cm cubed
The graph of a linear relationship contains the points (1,10) and (3,16) write the equation of the line in slope
Answer:
Step-by-step explanation:
The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.
Answer y == 3
+7
Step-by-step explanation:
The graph of a linear relationship contains the points (1, 10) and (3, 16).
Write the equation of the line in slope-intercept fo
Step-by-step explanation:
the general slope-intercept form is
y = ax + b
a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.
b is the y-intercept - the y value when x = 0.
for the slope we see
x changes by +2 (from 1 to 3)
y changes by +6 (from 10 to 16)
so, the slope a is +6/+2 = 3
and the semi-ready equation is
y = 3x + b.
now we use one of the points in the equation to solve for b. I picked (1, 10) :
10 = 3×1 + b = 3 + b
b = 7
so, the full equation is
y = 3x + 7
Help plssssss I really need the answer asap! I’d really appreciate it
A car dealer will sell you the $16,850 car of your dreams for $3,290 down and payments of $333.97 per month for 48 months. What is the APR? (Round your answer to the nearest tenth of a percent.)
The APR of the given transaction to the nearest tent of a percent is; 4.8%
What is the APR?
We find how much you will pay for the car using the down and monthly payments:
3290 + 333.97(48) = $19608.56
Thus, the interest is:
I = (19608.56 - 16450) = $3158.56
Use the simple interest formula:
I = Prt
where;
I is the interest.
P is the principal.
r is the interest rate is the time in years.
Substitute I = $3158.56, P = $16450, and t = 4 years (48 months):
Thus;
3158.56 = (16450)r(4)
Expanding gives;
3158.56 = 65800r
r = 3158.56/65800
r ≈ 0.048 = 4.8%
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Another middle school conducted the same type of fundraiser as the
middle school in the Problems. The banner below shows the goals
for each grade.
Fundraising Goals
$300 for 8th grade
$120 for 5th grade
$180 for 6th grade
$240 for 7th grade
Write three statements that the principal could make when
comparing the goals each grade has set.
Answer
when comparing he might make the statement saying lets try to get to 5th grade goal so we can at least meet 1
Step-by-step explanation:
4. How many numbers of three different digits can be made by using the digits 1, 2, 3, 4,5,6? How many of them are even?
Answer:
Let the 3 digits are xyz.
For x we have 6 options, for y - 5, for z - 4 since all digits are different.
Number of options:
6*5*4 = 120Even numbers will have z = 2, 4 or 6, then
x - 5 options, y - 4 options
Number of options:
5*4*3 = 60Answer:
How many numbers of most three different digits can be formed from integers 1, 2, 3, 4, 5, and 6? Answer: 120 three-digit + 30 two-digit + 6 one-digit = 156 numbers be formed using 3 different digit at most.
Step-by-step explanation:
Hope This Helps & Have A Nice Day!
In a certain town there were 325 robberies last year .this year the number of robberies has gone down 23% how many robberies were there this year, to the nearest whole number
Answer:
325X23/100 = 74.75
325 - 74.75 = 250.25 ,,,,,Round to the nearest whole number is 250...
Step-by-step explanation:
Answer is 250
PLEASE HELP ASAP!!!!!! 1. The probability that birth in the United States is male during 2018 is 0.511. Suppose a random number generator from 1 to 1,000 is used as a statistical model to create simulated results for births in the United States during 2018. Suppose the numbers 1 to 511 represent a male birth in the United States during 2018 and 512 to 1,000 represent a female birth in the United States during 2018. Explain whether the following results are consistent with the model, and if not, explain the expected number of male births and the expected number of female births for 300 trials.
In 300 simulated trials, 171 of the births are female and 129 are male.
2.Mika is a local farmer who is interested in how often residents in her town go to a farmer's market each month. She surveys 124 families and finds that, on average, those families visit a farmers' market 4.2 times per month with a sample standard deviation of 1.3. If Mika wants to be 99% confident (z=2.58) using this sample, what should her margin of error be and what does it mean?
3. Lily is a traffic engineer who is investigating the number of vehicles that travel on a certain point of expressway each day. She places a traffic counter in one direction of the expressway for 14 days. The number of vehicles counted each day are provided in the accompanying table.
15,410 16,247 16,096 16,330 17,107 11,812 14,877
14,731 15,873 16,129 16,284 16,959 12,101 14,514
Lily says that she can model the data for the number of vehicles per day to a normal distribution because the distribution is symmetric. Explain whether Lily's statement is correct and if not, correct the statement she made.
Answer:
Step-by-step explanation:
too much
10th grade Geometry Question, I will give brainliest. NEED HELP ASAP!
Answer:
- 1 + 5 + 2 y is your answer I am the teacher
A triangular pyramid is formed from three right triangles as shown below.
Use the information given in the figure to find the length AC.
If applicable, round your answer to the nearest whole number.
The lengths on the figure are not drawn accurately.
A
41
B
85
Answer:
76 units
Step-by-step explanation:
You want the length of AC in the given triangular pyramid.
Pythagorean theoremThe Pythagorean theorem can be used to find the lengths of AD and CD.
AD² + 40² = 41²
AD² = 41² -40² = 81 . . . . . = 9²
and
CD² +40² = 85²
CD² = 85² -40² = 5625 . . . . . = 75²
It can also be used to find AC:
AD² + CD² = AC²
81 + 5625 = AC²
AC = √5706 = 3√634 ≈ 76
The length of side AC is about 76 units.
__
Additional comment
The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs of a right triangle.
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