If an exponential model was used to fit the data set below, which of the following would be the best prediction for the output of the model if the input was x=20?
Answers
Answer:
The equation is found to be: \(y = 50.6e^{0.16x}\)
y(20) = 1241.34
Step-by-step explanation:
The given data is:
x: 3 7 11 14 17
y: 83 142 301 450 722
Now, we find sum summation values, relevant to the formula of exponential regression model, using calculator:
∑ ln y = 27.77305, ∑x ln y = 308.1494, ∑x = 52, ∑ x² = 664
and, n = no. of data points = 5
Now, we use formulae of exponential regression model to find out values of constant:
b = (n∑x lny - ∑x ∑ln y)/[n∑x² - (∑x)²]
b = [(5)(308.1494) - (52)(27.77305)]/[(5)(664) - (52)²]
b = 0.16
Now, for a;
a = (∑ln y - b∑x)/n
Therefore,
a = [(27.77305) - (0.16)(52)]/5
a = 3.9
For, α:
α = e^a = e^3.9
α = 50.6
So, the final equation of exponential regression model is given as:
\(y = \alpha e^{bx}\\ y = 50.6e^{0.16x}\)
Now, we find value of y for x = 20:
y(20) = (50.6) e^(0.16*20)
y(20) = 1241.34
Related Questions
A mountain biker gets halfway up a hill and realizes he forgot his water, so he returns to his starting point.
Answers
Answer:
True
Explanation:
1/2 (up the hill) - 1/2 (down the hill) = 0
solve problems 12 and 14 with steps for both of them
Answers
Applying the necessary circle theorem, the measures of the missing angles are: 12. m<KJL = 115 degrees. 14. 76 degrees.
How to Apply Circle Theorems?12. The circle theorem to apply is the angle of intersecting chords theorem, which states that:
m<KJL = 1/2(measure of arc KL + measure of arc MT)
Plug in the values:
m<KJL = 1/2(160 + 70)
m<KJL = 115 degrees.
14. The circle theorem to apply is the tangent theorem:
this means that the tangents form right angles with the radii of the circle, therefore:
Measure of the indicated angle = 360 - 90 - 90 - 104 = 76 degrees.
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There is a straight road between town 4 and town B of length 130 km. Maxi travels from town 4 to town B. Pippa travels from town B to town A. Both travel at a constant speed of 40 km/h. Maxi leaves 30 minutes before Pippa. Work out how far from town A they will be when they pass each other
Answers
The distance from town A that they will be, when they will pass each other is 44 4/9 .
How can the distance be calculated?It should be noted that time traveled in each segment is constant, which implies that in this case the average speed can be regarded as the simple mean of speeds. An in the case whereby the distance traveled in each segment is constant, average speed can be described to be the reciprocal of simple mean .
This can be expressed mathematically as
Average speed = Reciprocal [ 1/40 & 1/50].
Average speed = Reciprocal of (1/40 + 1/50)/2
= Reciprocal of [(5+4)/400]
= 44 4/9 .
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I will give you brainliest answer if u help me with 4 problems
Answers
Find the height of the tower using the information given in the illustration.
Answers
using SOH CAH TOA
Tan 85.144 =h/130
h=tan 85.144*130
h=1530.19 fr
What is 2^4+2(10-4)-3?
Answers
Step-by-step explanation:
We have to solve :
\(2^4 + 2 (10 - 4) - 3 \)
BODMAS will be used here,
B = Bracket
O = off
D = Division
M = Multiplication
A = addition
S = Subtraction
First let's solve
\(2^4\)
\(2 \times 2 \times 2 \times 2\)
\(16\)
Now,
Bracket of ,
16 + 2 (6) - 3
16 + 12 - 3
28 - 3
25
16+2•6-3
16+12-3
25
Find the value of (f o g)' at the given value.
Answers
To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.
To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.
What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).
What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value
step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)
Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)
Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11
Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)
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a. If the dog house is 8 inches wide on the scale drawing, how wide is the
dog house in real life?
feet
Answers
Answer: If the dog can fit in there it’s not a problem u don’t need to know the inches that’s what she said
Step-by-step explanation:
4. Patti and her friends want to see one of
two movies. One movie starts in 1 day
2 hours 20 minutes. The other movie
starts in 1 day 4 hours 10 minutes. The
later movie starts at 5:00 P.M. At what
time does the earlier movie start?
Answers
Answer:
The earlier movie starts at 1610 (4:10 PM)
Step-by-step explanation:
The later movie starts at 1700 (5:00 PM), and is in 1 day, 4 hours and 10 minutes. That means the time is __:50. Additionally, it's in 4 hours. 1700 - 400 = 1300 (1:00 PM). Now we know the time is 1350 (1:50 PM) presently.
If it's currently 1:50 PM, and the earlier movie starts 2 hours from this time tomorrow, then it begins at 1350 + 200 = 1550 (3:50PM). Take into account that there's also another 20 minutes before the movie commences, it will be 1610 (4:10 PM).
Good luck!!
solve 276x28 using the standard algorithm
Answers
Answer:
7728
work is shown in the image I attached!!
Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - 4x = -2 has.
Answers
Answer:
We can use three solution and they are
(1)completing the square
(2)quadratic formula
(3) factorisation method
The quadratic equation 2x^2 - 4x = -2 has two values .
What is quadratic equation ?According to our definition, a quadratic equation is one with degree 2, implying that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: y = x^2 + 3x + 1.Kind of solutions -(1)completing the square
(2)quadratic formula
(3) factorization method
Given,
quadratic equation 2x^2 - 4x = -2
2x² - 4x + 2 =0
Now solve this equation by factor,
2x² - 4x + 2 = 0
2x² - ( 2+2)x +2 = 0
2x² - 2x -2x + 2 = 0
2x(x- 1 ) -2 ( x -1) = 0
(2x - 2) ( x- 1) =0
2x - 2 = 0 or x - 1 = 0
x = 1 or x = 1
So, this equation has 2 value of x.
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Please help and thank you
Answers
Daniella: Were you thinking of perpendicular lines?
Ori: It seems like you've got the basic idea, but your definition could be more precise.
Kaori: Yes! Well done. Here, have a cookie. You've earned it.
complete the steps to solve the equation
Answers
Answer:
attached below
Step-by-step explanation:
minus 2 from each side in order to isolate T with the coefficient. To get rid of the coefficient multiply to get 1 which is 5 in this case. Then the answer will be 75
find the domain and function of y=6+9x/6-|x-1|
Thank you so soooo much for the help!!
Answers
======================================================
Explanation:
Rule: We cannot divide by zero.
Because of that rule, we'll set the denominator equal to zero and solve for x. This way we can determine the x value(s) that are to be excluded from the domain.
6 - |x-1| = 0
|x-1| = 6
x-1 = 6 or x-1 = -6
x = 6+1 or x = -6+1
x = 7 or x = -5
Those x values are to be excluded from the domain, since they make the denominator zero.
Imagine a number line in which we poked open holes at -5 and 7
The portion to the left of -5 is x < -5The portion between -5 and 7 is -5 < x < 7The portion to the right of 7 is x > 7Combining everything gets us x < -5; -5 < x < 7; x > 7
Para la construcción de una cabaña en el campo don Samuel compró 7,943 clavos hasta el momento ha utilizado 473 ¿cuantos clavos le queda?
Answers
Restando la cantidad utilizada de el total, tiene-se que 7470 clavos le quedan.
----------------------
En total, para la construcción, Samuel compró 7,943 clavos.De toda esta cantidad, 473 fueron utilizadas.La cantidad de clavos que le quedan es la subtracción da cantidad total por la utilizada, o sea, 7943 restado de 473.\(7943 - 473 = 7470\)
Le quedan 7470 clavos.
Un problema similar es dado en https://brainly.com/question/24554492
PLS HELP ME ANSWER THIS QUESTION..
Answers
Answer:
b. 4
c. 90⁰
Step-by-step explanation:
a. is in the diagram
If a sample proportion is 0.65, which range of possible values best describes
an estimate for the population parameter?
O A. (0.5, 0.89)
• B. (0.5, 0.8)
• C. (0.65, 0.7)
• D. (0.6, 0.69)
Answers
The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8)
How to estimate proportion?The range of possible values that best describes an estimate for the population parameter is; (0.5, 0.8).
When we are talking about population parameters, we also have to look at the way of estimating the population, we have to add two extremes and divide by 2.
Thus, the correct one is;
(0.5 + 0.8)/2 = 0.65
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a carpet is laid on a rectangular floor which measures 4meters by 5meters. if the carpet covers 60% of the floor find the area of the carpet
Answers
Answer:
12 m²
Step-by-step explanation:
Area of the floor:
area = length * width
area = 4 m * 5 m
area = 20 m²
area of carpet = 60% of area of the floor
area of carpet = 0.6 * 20 m²
area of carpet = 12 m²
Keenan, Ariel, Denise, and Turner went to a baseball game on a bright sunny day, but they only
brought 1 pair of sunglasses! The friends agreed that each person would wear the sunglasses for
an equal amount of time during the 3-hour game.
How long did each person wear the sunglasses?
Answers
Answer:
there is one pair of sunglasses right, okay so there are 4 friends also
and if the game was 3 hours then.........
then 4 divided by 3 that would be uh,,,mm sorry i don't know im only in the 5th grade
Step-by-step explanation:
???
Five runners need to be arranged in 5 lanes for a race so that there is a runner in each lane
How many unique ways are there to arrange the numbers in the 5 lanes
Answers
Step-by-step explanation:
5 P 5 = 120 ways = 5!
Happy Card Co. designs personalized cards which cost $1.10 per card. The fixed cost to make the cards is $264 per day. If the company charges $5.10 per card, how many cards must be delivered daily to make a profit of $52? Show work below.
Answers
Step-by-step explanation:
x = number of cards
the production costs (PC) per day are
PC(x) = 264 + 1.1x
the sales (S) are
S(x) = 5.1x
the profit (P) per day is sales minus costs
P(x) = S(x) - PC(x) = 5.1x - (264 + 1.1x) =
= 5.1x - 264 - 1.1x = 4x - 264
we need to find the value of x, so that P(x) = 52.
52 = 4x - 264
316 = 4x
x = 316/4 = 79
79 cards must be delivered daily to make a profit of $52.
For the third week of April, Patricia Thomas worked 53 hours. Patricia earns $11.90 an hour. Her employer pays overtime for all hours worked in excess of 40
hours per week and pays 1.5 times the hourly rate for overtime hours.
Calculate the following for the third week of April (round your responses to the nearest cent if necessary):
1. Regular pay amount
2. Overtime pay
3. Gross pay
Answers
Given statement solution is :- For the third week of April, Patricia's:
Regular pay amount is $476.
Overtime pay is $231.45.
Gross pay is $707.45.
To calculate Patricia's pay for the third week of April, we'll need to determine her regular pay, overtime pay, and gross pay.
Regular Pay:
Patricia worked 53 hours, but only 40 hours are considered regular hours. Therefore, the regular pay is calculated as follows:
Regular Pay = Regular Hours x Hourly Rate
Regular Pay = 40 hours x $11.90/hour
Regular Pay = $476
Overtime Pay:
Since Patricia worked 53 hours in total and 40 of those are regular hours, the remaining 13 hours are considered overtime hours. Overtime pay is calculated by multiplying the overtime hours by 1.5 times the hourly rate.
Overtime Pay = Overtime Hours x (Hourly Rate x 1.5)
Overtime Pay = 13 hours x ($11.90/hour x 1.5)
Overtime Pay = 13 hours x $17.85/hour
Overtime Pay = $231.45
Gross Pay:
Gross Pay is the sum of Regular Pay and Overtime Pay.
Gross Pay = Regular Pay + Overtime Pay
Gross Pay = $476 + $231.45
Gross Pay = $707.45
Therefore, for the third week of April, Patricia's:
Regular pay amount is $476.
Overtime pay is $231.45.
Gross pay is $707.45.
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A wireless keyboard is 10/12 foot long. The area of the wireless keyboard is 5/24 square foot. What is the width of the wireless keyboard, in feet? Enter the answer as a fraction in lowest
Answers
Answer:
1/4 ft
Step-by-step explanation:
A = l x w
5/24 = 10/12 x w
Solve for w
5/24 divided by 10/12 = w
Take inverse of 10/12 and multiply
5/24 times 12/10
1/4
Easy question about P-value:
Answers
The conclusion that the herds are not statistically different is false.
The correct option is B.
What is the hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
Given:
You conducted a t-test to determine whether two herds of elk have statistically different migration dates.
The resulting p-value was .03.
Here, the p-value is less than 0.05.
That means,
the p-value is statistically significant.
And there is a 3% chance that the null hypothesis should be rejected.
Your conclusion is that the herds are not statistically different.
Therefore, your conclusion is incorrect.
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What is 5x6 + (5x5-5) to the 2nd power
Answers
Answer: 2500
Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500
A water cooler can hold 50 pt of water.
About how many liters of water it can hold?
1 L ≈ 1.06 qt
A: 23.6 L
B: 26.5 L
C: 94.3 L
D: 106.0 L
Answers
Answer:
B
Step-by-step explanation:
Thwre are two pts in one qt, so if it holds 50 pts, it holds 25 qts.
Use the provided conversion of 1.06 and multiply by 25 to find the number of lines.
25x1.06=26.5.
Side AC corresponds to side
Angle BAC corresponds to angle
Answers
Answer:
Side AC corresponds to side FD
Angle BAC corresponds to angle BFD
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is
shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²
= √1 + 4
= √5
-
What error, if any, did Heather make?
A. She substituted incorrectly into the distance formula.
B. She subtracted the coordinates instead of adding them.
C. She made a sign error when simplifying inside the radical.
OD. She made no errors.
Answers
The distance between points R and S is \(\sqrt{ (185)\). The correct answer is D. She made no errors.
Heather's work to find the distance between two points, R(-3,-4) and S(5,7), is shown:
RS = √(-4) (-3))² + (7 − 5)²
= √(-1)² + (2)²= √1 + 4
= √5
The error is with the order of subtraction in the formula for the distance between two points.
Heather did not make any errors in calculating the distance between two points. Therefore, the correct answer to the question above is (OD) She made no errors.
The formula for the distance between two points, A (x1, y1) and B (x2, y2), in the coordinate plane is given as;
dAB = \(\sqrt{ ((x^2 - x1)^2 + (y2 - y1)^2)\)
Comparing the given question with the formula above, we have;
A = R (-3, -4) and B = S (5, 7)The distance, AB = RS.
Therefore, we have;
RS = \(\sqrt{ ((5 - (-3))^2 + (7 - (-4))^2)\)
On solving the above equation;RS = \(\sqrt{ ((5 + 3)^2 + (7 + 4)^2)\)RS
= \(\sqrt{ (8^2 + 11^2)RS\)
= \(\sqrt{ (64 + 121)RS\)
= \(\sqrt{ (185)\)
Therefore, the distance between points R and S is \(\sqrt{ (185)\).
From the calculation, it is clear that Heather did not make any errors while calculating the distance between two points. The answer obtained by Heather is correct.
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How do you write equations in Point-slope form?
Answers
For a line with a slope a and a known point (h, k), the point-slope form is:
y = a*(x - h) + k
How to write an equation in point slope form?A general linear equation can be written in slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that a line passes through a point (h, k), then the point-slope form of that line is:
y = a*(x - h) + k
Notice that particularly, the y-intercept can be written as (0, b), then the slope-intercept form is also a point-slope:
y = a*(x - 0) + b
y = a*x + b
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kate pays $203 in advance on her account at the athletic club. Each time she uses the club, $9 is deducted from the account. Find the remaining in the account after 12 visits
Answers
Answer:
95
Step-by-step explanation:
The equation to solving this would be 203 - (9 multiply 12). If you multiply 9 and 12 you get 108. Minus 108 from 203 and you get 95.