Determine whether the function given by the table is linear, exponential, or
neither. If the function is linear, find a linear function that models the data; if it is
exponential, find an exponential function that models the data.
Answers
The table represents the exponential function:
\(f(x) = 11^x\)
Which function is represented by the table?Here we have the table:
x y
-1 1/11
0 1
1 11
2 121
3 1331
Some things that are useful to identify this as an exponential equation are:
For any real number a different than zero:
\(a^{-1} = 1/a\\\\a^0 = 1\)
\(a^1 = a\)
With these three things, we conclude that we have an exponential equation, because when we evaluate in x = -1, we have a rational number.
When we evaluate in x = 0 we have 1.
Such that the function is:
\(f(x) = 11^x\)
Notice that:
\(f(-1) = 11^{-1} = 1/11\\\\f(0) = 11^0 = 1\\\\f(1) = 11^1 = 11\\\\f(2) = 11^2 = 11*11 = 121\)
And so on.
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Related Questions
A line passes through (2, 8) and (4, 12). Which equation best represents the line? (10 points)
y = 1 over 2 x + 6
y = 2x + 7
y = 2x + 4
y = 1 over 2 x + 10
Answers
Answer: y=2x+4
You first find slope which is y2-y1 divided by x2-x1 that gives you slope and then you put it into the formula y-y1=m(x-x1)
Which expressions describe the end behaviors of the function, f(x)= (3.25)^x+6, modeled by the graph? An exponential curve on a coordinate plane with horizontal x axis ranging from negative 10 to 10 in increments of 1. The vertical y axis ranges from negative 4 to 14 in increments of 1. The curve begins infinitely close to the line y equals 6 in the second quadrant. The curve increases through begin ordered pair 0 comma 7 end ordered pair. The curve passes through begin ordered pair 1 comma 9.25 end ordered pair and exits the first quadrant.
Answers
The expression that describe the end behavior of the expression f(x)= (3.25)^x + 6 is The curve begins infinitely close to the line y equals 6 in the second quadrant.
What is end behavior as used in math?The behavior of the graph of a function at its "ends" on the x-axis is referred to as the end behavior of a function, f.
For example, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞), the end behavior of a function explains the trend of the graph.
The graph of the function is attached and from the graph it shows that the graph continued to tend towards towards line y = 6
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what is −3x−6+(−1) ?
Answers
Answer:
-3x-7
Step-by-step explanation:
As a promotional feature, a store conducts a weekly raffle. During any week, 40% of the customers who turn in one or more tickets do not bother to turn in tickets the following week. On the other hand, 30% of the customers who do not turn in tickets will turn in one or more tickets the following week. Find and interpret the steady matrix for this situation.
Answers
Given statement solution is :- Interpreting the steady matrix:
The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.
The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.
The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.
To analyze the steady matrix for this situation, let's consider the two groups of customers: those who turn in tickets and those who do not turn in tickets.
Let's denote the proportion of customers who turn in tickets as X and the proportion of customers who do not turn in tickets as Y.
According to the given information:
40% of the customers who turn in tickets do not turn in tickets the following week. This means that 60% of the customers who turn in tickets will turn in tickets again the following week.
30% of the customers who do not turn in tickets will turn in tickets the following week. This means that 70% of the customers who do not turn in tickets will continue not turning in tickets the following week.
Based on these percentages, we can construct the steady matrix:
java
Copy code
| Customers turning in tickets (X) | Customers not turning in tickets (Y) |
----------|----------------------------------|--------------------------------------|
Next week 0.6 0.3
This week 0.4 0.7
Interpreting the steady matrix:
The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.
The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.
The value 0.4 in the bottom left cell represents the proportion of customers who do not turn in tickets this week but will turn in tickets next week.
The value 0.7 in the bottom right cell represents the proportion of customers who do not turn in tickets this week and will continue not turning in tickets next week.
These values describe the transition probabilities between the two customer groups. For example, if there are 100 customers in total, 60 of them will turn in tickets next week, and 40 of them will not. Similarly, 30 customers who turn in tickets this week will not do so next week, while 70 customers who do not turn in tickets this week will continue to not turn them in next week.
The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.
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step by step please
Answers
Solution:
We know that:
Given equation: 1/4(x - 2) = 3 - (x + 1/6)Simplify the distributive property.
1/4(x - 2) = 3 - (x + 1/6)=> x/4 - 2/4 = 3 - x - 1/6Further simplify both sides.
x/4 - 2/4 = 17/6 - xSubtract 17/6 both sides.
x/4 - 2/4 - 17/6 = 17/6 - 17/6 - x=> x/4 - 6/12 - 34/12 = -x=> x/4 - 40/12 = -xSubtract x/4 both sides.
x/4 - x/4 - 40/12 = -x - x/4=> -40/12 = -5x/4Use cross multiplication.
=> -160 = -60xDivide -60 both sides.
-160/-60 = -60x/-60=> x = 160/60 = 2 40/60 = 2 2/3find the value of x and the measure of angle axc
Answers
Answer:
x = 4
m<AXC = 150
Step-by-step explanation:
m<1 + m<2 = m<AXC
102 + 10x + 8 = 6(6x + 1)
10x + 110 = 36x + 6
26x = 104
x = 4
m<AXC = 6(6x + 1)
m<AXC = 6(24 + 1)
m<AXC = 150
Mina has 462 flowers if she wants to put nine flowers in each phase how many for vases will she have how many flowers will she have left over
Answers
Angles W and X are supplementary. If m∠W is 37°, what is m∠X?
Answers
Supplementary angles = 180
X = 180 - 37
X = 143
In a study of academic procrastination, the authors of a paper reported that for a sample of 451 undergraduate students at a midsize public university preparing for a final exam in an introductory psychology course, the mean time spent studying for the exam was 7.74 hours and the standard deviation of study times was 3.10 hours. For purposes of this exercise, assume that it is reasonable to regard this sample as representative of students taking introductory psychology at this university.
(a) Construct a 95% confidence interval to estimate μ, the mean time spent studying for the final exam for students taking introductory psychology at this university. (Round your answers to three decimal places.) TWO VALUES
(b) The paper also gave the following sample statistics for the percentage of study time that occurred in the 24 hours prior to the exam.
n = 451 x = 43.78 s = 21.96
Construct a 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam. (Round your answers to three decimal places.)
Answers
Answer:
a) The 95% confidence interval to estimate μ is (7.435, 8.045) hours.
b) The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).
Step-by-step explanation:
Question a:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = z\frac{\sigma}{\sqrt{n}}\)
In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.
\(M = 1.96\frac{3.3}{\sqrt{451}} = 0.305\)
The lower end of the interval is the sample mean subtracted by M. So it is 7.74 - 0.305 = 7.435 hours
The upper end of the interval is the sample mean added to M. So it is 7.74 + 0.305 = 8.045 hours.
The 95% confidence interval to estimate μ is (7.435, 8.045) hours.
Question b:
90% confidence interval means that \(Z = 1.645\)
The margin of error is:
\(M = 1.645\frac{21.96}{\sqrt{451}} = 1.701\)
43.78 - 1.701 = 41.079%
43.78 + 1.701 = 45.481%
The 90% confidence interval for the mean percentage of study time that occurs in the 24 hours prior to the exam is (41.079%, 45.481%).
Round to 2 decimal places 0.966
Answers
Answer:
Step-by-step explanation:
round to 2 places 0.966: 1.00
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 18, with an IQR of 16
Bus 47, with an IQR of 24
Bus 18, with a range of 16
Bus 47, with a range of 24
Answers
The bus that is the most consistent, given the data collected on travel times to school from two groups of students is C Bus 18, with a range of 10
How to find the consistent bus ?To determine which bus is the most consistent, we should use the interquartile range (IQR) as the measure of variability. The IQR measures the spread of the middle 50% of the data, which makes it less sensitive to outliers compared to the range.
Bus 47:
Median (Q2): 16
Q1: 10
Q3: 22
IQR = Q3 - Q1 = 22 - 10 = 12
Bus 18:
Median (Q2): 12
Q1: 8
Q3: 18
IQR = Q3 - Q1 = 18 - 8 = 10
Bus 18 has a smaller IQR than Bus 47 (10 vs. 12), which means the travel times for Bus 18 are more consistent.
Note: Figures might be different due to options being for different variant but Bus 18 is the most consistent.
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In the statement, a property of real numbers has been incorrectly applied.
Correct the right side of the statement.
3(x + 8) = 3x + 8
Answers
(-37)+(-2) please tell quickly
Answers
Answer:-39
Step-by-step explanation:
The first thing is to open the bracket.
By doing that, the question becomes -37-2.
note that plus×minus=minus.
Hence,-39 as the final answer
PLEASE PLEASE HURRY ITS AN EMERGENCY!!
Answers
Answer:
1 is 'given'
3 is 'vertical angle theorem'
dont know the other two sorry
Step-by-step explanation:
As of the moment I am writing this question, the population of the United States is 326,891,705 people. You are building an app that targets the US population and expect to get 1/10 of 1% of the population using your app in the first 4 months. The estimated data you need to store per user averages 10 GB. What is the minimum storage you must plan to have in place for app to serve the users in the first 4 months
Answers
Answer:
3.3 PB
Step-by-step explanation:
It is given tat the population of the U.S = 326,891,705 people.
Population expected to use the app in first 4 months = 1/10 of 1%
Storage capacity of an user is = 10 GB
Therefore,
\($\frac{1}{10} \text{ of}\ 1$\) % = 0.1%
= 0.001
The user content = 0.001 x 326,891,705
= 326891.705 users
10 GB storage per user.
Therefore,
Size = 326891.705 x 10
= 3268917.05 GB
= 3.26 PB
Hence size of the minimum storage would be 3.3 PB.
If we have a tv cabinet that is 64 inches long and 56 inches high, how large a tv could we put in the space (leave two inches on all sides for the edging of the tv)?
Answers
Answer:
60'' × 52'' or a 79.4'' TV
Step-by-step explanation:
Leaving a room of 2 inches on all sides means we subtract 4 inches from the height and length to find the maximum dimensions of the TV.
With this, we get 60'' × 52''. To find the diagonal length of the TV, use the Pythagorean Theorem which simply states the length of the diagonal is equal to the square root of the sum of the squared dimensions.
\(\sqrt{a^2+b^2} =c\)
\(\sqrt{60^2+52^2}=79.4\)
Therefore your TV can have a maximum size of 79.4 inches.
7. A floor is covered by 800 tiles measuring 10 squared cm. How many square tiles of side 8 cm would be needed to cover the same floor?
Answers
Answer:
1000 tiles
Step-by-step explanation:
Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.
Selling Price = $ 504 and Gain % = 12%
Answers
Answer:
Step-by-step explanation:
sp = 504
gain = 12%
in this case
sp =100%+12%=504
112%=504
1%=504/112 =4.5
100%=450
so cost =$450
Hope im correct, if i am im glad to be of service.
Rewrite the equation by completing the square. 4x^2-4x+1=0
Answers
Answer:
(x+(-x))²=0
Step-by-step explanation:
4 - a
-4 - b
1 - c
D = b²-4ac
D = (-4)² - 4×4×1
D = 16-16=0 => only one root
x= -b/2a
x= 4/2×4
x= 4/8 = 1/2 = 0.5
A third grade class has 16 girls and 15 boys a fourth grade class has 18 boys and 15 girls when picking for PE captains will make one selection from the fourth grade class and one selection from the third grade class before the other team pics assuming everyone has an equally like lee chance of being selected what is the probability that the first captain will choose two boys on the first pick
Answers
Answer:
\(\dfrac{90}{341}\)
Step-by-step explanation:
3rd grade:
Number of girls = 16
Number of boys = 15
Total number of students = 31
4th grade:
Number of girls = 15
Number of boys = 18
Total number of students = 33
Formula for probability of an event E can be observed as:
\(P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}\)
Probability of picking a boy from 3rd grade, \(P_{1} = \dfrac{15}{31} ..... (1)\)
Probability of picking a boy from 4th grade, \(P_{2} = \dfrac{18}{33} ..... (2)\)
These are two independent events of picking a boy from 3rd grade and 4th grade.
So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.
\(P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}\)
Answer:
a
Step-by-step explanation:
Katrina, Nelson, and Blake bike from the school to their homes. Katrina bikes 12 miles north from the school. • Nelson bikes 8 miles south from the school. • Blake bikes fewer miles than Katrina and more miles than Nelson. The location of the school is represented by 0. Which expression could represent the number of miles Blake bikes? A. 1141 B. 161 C. I-101 D. -16
Answers
The expression that could represent the number of miles that Blake bikes would be C. I-10|.
How to find the expression ?Given that Blake bikes fewer miles than Katrina (who bikes 12 miles) and more miles than Nelson (who bikes 8 miles), this means that Blake bikes a distance between 8 and 12 miles.
When the problem states that Blake bikes fewer miles than Katrina and more miles than Nelson, it's referring to the magnitude of the distance.
Given this information, |-10| would indeed be 10 (as the absolute value of -10 is 10), which falls between Nelson's 8 miles and Katrina's 12 miles.
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jalen drew a rectangle with a perimeter of 20 inches. the smaller side measured 3 inches. jalen said the longer side of the rectangle had to be 7 inches. is jalen correct?
Answers
Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(3 + 7)
20 = 2(10)
20 = 20 (True).
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Each square has a side length of 12 units. Compare the areas of the shaded regions in the 3 figures. Which figure has the largest shaded region? Explain or show your reasoning.
Answers
Answer:
The shaded region in all of the answers are equal.
Step-by-step explanation:
Since squares have equal sides, the area of each square is 12 squared or 144.
The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.
The area of the shaded region of A is 144-36pi.
In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.
The area of the shaded region of B is 144-36pi.
In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.
The area of the shaded region of C is 144-36pi.
What is the equation of the line that passes through the point (−0.5,8) and has a slope of −5?
Answers
Answer:
Slope=-1.8, X=-0.5, y=1.9
Equation is y^2-y^1=m(x^2-x^1).
Y-1.9=-1.8(X-(-0.5))
Y-1.9=-1.8x+0.90
Add 1.9 on both sides.
Y= -1.8x+1.
I hope this helps you.
Step-by-step explanation:
5th grade question PLEASE HELP!
Vedansh filled 10 lbs of candy equally into 6 bags to give to six of his friends. How
much candy does each friend get? Simplify your answer. I WILL MARK U BRAINLIEST!
Answers
Answer:
1.66666666666666666667
Step-by-step explanation:
if rounded by the nearest tenth it is 1.7
Hope this helps :)
Answer:
10/6 = 1 and 2/3
Step-by-step explanation:
10 pounds of candy, 6 bags.
that means 10 divided by 6, or 10/6
simplify that 10-6 = 4, 6 can only be subtracted once, so it is 1 and 4/6 or 2/3
2/3 is 0.666666... so add it together and you get 1.66666... or 1 and 2/3
I need this answer ASAP
Answers
Answer:
Option B
Step-by-step explanation:
20 cups of grape juice and 10 cups of apple juice
4*5=20
2*5=10
Can I plz have brainliest?
Answer: The answer is B or some people say its 2, and others #2: 20 cups of grade juice, and 10 cups of apple juice.
Step-by-step explanation: Ok so if there are 4 cups of grape juice and 2 cups of apple juice the we need to multiply both of them by 5 because it says what does she need to make 5 TIMES or x the recipe so 4x5=20 for grape juice and 2x5=10 for apple juice so The answer is B or some people say its 2, and others #2: 20 cups of grade juice, and 10 cups of apple juice.
plz mark me brainliest
How to mark brainliest on the bottom right of an answer is a crown if there is not refresh the page if there still is not the look if there are 2 answers if there are not then wait, to mark brainliest tap on the crown.
Hope this helps!
What is the measure of Angle P Q R?
Triangle P Q R. Angle R is 51 degrees. The lines of sides Q P and R P extend to form exterior angle at P of 74 degrees.
51 degrees
55 degrees
74 degrees
Answers
Answer:
74
Step-by-step explanation:
PQR is 74 degrees
Because PQR is a vertical angle with extended QP and RP side. And vertical angles are always equal
Find three consecutive integers such that the sum of the largest and 5 times the smallest is -244. Find the smallest integer.
Answers
Let the largest integer equal x, the 3rd number ( smallest-number) would be x - 2
The sum of the two would be:
X + 5(x-2) = -244
Simplify:
X + 5x -10
Combine like terms
6x -10 = -244
Add 10 to both sides:
6x = -234
Divide both sides by 6
X = -234/6
X = -39
The smallest number is x-2 = -39-2 = -41
The answer is -41
Twice the sum of consecutive numbers n and n + 1 is 510. What is the smaller number?
Answers
Answer:
The smaller number is 127
Step-by-step explanation:
Lets write the given problem in equation form
sum of consecutive numbers n and n + 1 = n + n + 1 = 2n + 1
now we find twice of the sum of consecutive numbers n and n + 1
2*(2n + 1) = 4n + 2
given that
twice the sum of consecutive numbers n and n + 1 is 510
thus,
4n + 2 = 510
=> 4n = 510 -2 = 508
=> n = 508/4 = 127
Thus, the numbers are n = 127
n+1 = 127 + 1 = 128
the smaller number is 127
evaluate f(-x)=x/x2+1
Answers
To evaluate f(-x) when f(x) = x/(x^2 + 1), we need to substitute -x for x in the function.
So f(-x) = (-x)/((-x)^2 + 1)
Simplifying the denominator we get:
f(-x) = (-x)/(x^2 + 1)
The function f(-x) is equivalent to the function f(x) with the x-value negated. The value of the function f(-x) is the same as the value of the function f(x) but with the x-value negated.
It's important to note that we can also express this as f(-x) = -f(x)
So the value of f(-x) is x/(x^2 + 1) with the x-value negated.