Celia thinks that because the drop between the first two points is so large, the best model might actually have a y- intercept a little below 10. She uses (0, 9.4) to estimate a in her model. To estimate b, she finds the average of the ratios of successive data values. what is her model?use two digits for precision of all quantitites
Answers
The equation of Celia's exponential model is \(y = 9.4 * 0.75^x\)
How to estimate the model?The table that completes the question is added as an attachment
The y-intercept is given as:
(0,9.4)
The ratios of successive data values are calculated as:
\(r_1 = \frac{6.0}{10}= 0.6\)
\(r_2 = \frac{5.4}{6.0}= 0.9\)
\(r_3 = \frac{3.9}{5.4}= 0.72\)
\(r_4 = \frac{3.7}{3.9}= 0.95\)
\(r_5 = \frac{2.3}{3.7}= 0.62\)
\(r_6 = \frac{1.4}{2.3}= 0.61\)
\(r_7 = \frac{1.0}{1.4}= 0.71\)
\(r_8 = \frac{0.9}{1.0}= 0.9\)
\(r_9 = \frac{0.8}{0.9}= 0.89\)
\(r_{10} = \frac{0.5}{0.8}= 0.63\)
The average of the above values is
\(b = \frac{0.6 + 0.9 + 0.72 + 0.95 + 0.62 + 0.61 + 0.71 + 0.9 + 0.89 + 0.63}{10}\)
Evaluate
b = 0.75
An exponential function is represented as:
\(y = ab^x\)
Where
a = 9.4 as in the y-intercept (0,9.4)
b = 0.75
Substitute these values in \(y = ab^x\)
\(y = 9.4 * 0.75^x\)
Hence, the Celia's exponential model is \(y = 9.4 * 0.75^x\)
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Related Questions
propose new names for the numbers 11 12 13 14 15 16 17 18 19 so at the naming scheme is consistent with the number 20 and above?
Answers
Answer:
that is your answer 10.34
Find the standard form of the parabola
with vertex: (- 2,5) and directrix: x = 3.
Answers
Check the picture below, so the parabola looks more or less like so, the "p" distance is negative, because the horizontal parabola is opening to the left-hand-side, so
\(\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\)
\(\begin{cases} h=-2\\ k=5\\ p=-5 \end{cases}\implies 4(-5)( ~~ x-(-2) ~~ )=(y-5)^2 \implies -20(x+2)=(y-5)^2 \\\\\\ x+2=-\cfrac{1}{20}(y-5)^2\implies {\Large \begin{array}{llll} x=-\cfrac{1}{20}(y-5)^2-2 \end{array}}\)
Evaluating Linear Piecewise Functions
Consider the function:
f(x) =
7/2+ 2x, x≤-1
-5+3x/2, -1
1/4x, x≥3
< -5_-4_-3_-2_-1_0_1_2_3_4_5 >
What are these values?
f(-3) =[-19/2]ᵒʳ[-5/2]ᵒʳ[-3/4]ᵒʳ[5/2]
f(-1) =[-13/2]ᵒʳ[-3/2]ᵒʳ[-1/4]ᵒʳ[-3/2]
f(3) =[-7/4]ᵒʳ[-1/2]ᵒʳ[3/4]ᵒʳ[19/2]
PLEASE HELP ME ON A SERIOUS TIME CRUNCH!!
Answers
-3≤-1, so we must use the 7/2+2x function.
Insert x into the function that has a true domain statement:
f(-3)=7/2+2(-3)
Evaluate:
f(-3)=7/2-6
Obtain a common denominator to subtract fractions:
f(-3)=7/2-(6•2/1•2)
Remember, -6 is equivalent to -6/1, so we multiply the numerator and denominator by 2 to get a common denominator.
Simplify:
f(-3)=7/2-12/2
Subtract the numerators only; denominators stay as 2:
f(-3)=(7-12)/2
Answer: f(-3)=-5/2
—————————————————————
f(-1)
-1≤-1, so we must use the 7/2+2x function again. We must always check x in all domain piecewise cases.
Let’s evaluate f(-1):
f(-1)=7/2+2(-1)
f(-1)=7/2-2
Obtain a common denominator; -2=-2/1:
f(-1)=7/2-(2•2/1•2)
f(-1)=7/2-4/2
f(-1)=(7-4)/2
Answer: f(-1)=3/2
—————————————————————
f(3)
Let’s check all domain cases. We see the only true statement is: 3≥3, so we must use the 1/4x function.
f(3)=1/4(3)
Answer: f(3)=3/4
Hope this helps! Please give Brainliest
HELP what is the area of this figure BUT PLEASE GET IT RIGHT I HVE BEEN CRYING BECAUSE OF IXL what is the area of this figure
Answers
Answer:
Aww don't cry I'm here to help you :D
Step-by-step explanation:
First we will find the area of the triangle thing
area = bh / 2
= (5 cm)(13 cm) / 2
= 65 / 2
= 32.5 cm^2
Next find the area of the large blue section
area = lw
= (20)(9)
= 180 cm^2
Now the area of the smaller blue section
area = lw
= (7)(4)
= 28 cm^2
Finally add them all up to get the area
32.5 + 180 + 28 = 240.5 cm^2
Hope this helps! Best of luck <3
Two adults and one child go to a movie and pay $26. One adult and 3 children pay
$28. How much would it cost for one adult and one child to see the movie?
Answers
Answer:
adults pay $10
children pay $6
Step-by-step explanation:
x = adult
y = child
2x + y = 26
x + 3y = 28
you want to cancel out x or y
multiply -2 with (x + 3y = 28) which is -2x -6y = -56
2x + y = 26
-2x -6y = -56
-5y = -30
y = 6
put y back into an equation
2x + y = 26 is
2x + 6 = 26
x = 10
check the answer
Two adults and one child go to a movie and pay $26
20 + 6 = 26 : checks
One adult and 3 children pay $28
10 + 18 = 28 : checks
the sum of three consecutive integers is 78. what are the three Integers
Answers
Answer:
25, 26, and 27 are the three consecutive integers.
Step-by-step explanation:
Let the numbers be represented as x, x + 1 and x + 2.
We can write the equation:
\(x+(x+1)+ (x+2)=78\)
Opening the brackets and simplifying:
\(x+x+1+x+2=78\)
\(3x+3=78\)
Subtract 3 from both sides.
\(3x=75\)
Divide both sides by 3.
\(x=25\)
Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.
∴ 25, 26 and 27 are the three consecutive integers.
Answer:
25 , 26 and 27
Step-by-step explanation:
Copy the problems onto your paper, mark the given and prove the statements asked. Prove, triangle CAV is congruent to triangle CEV
Answers
Quadrilateral is a family of plane shapes that have four straight sides. Thus the sum of their internal angles is \(360^{o}\). Examples include rectangle, square, rhombus, trapezium, and kite.
A kite is a plane shape that has its adjacent sides to have equal measures.
The given diagram in the question is a kite that has its specific properties compared to other quadrilaterals.
Thus, the required proof is stated below:
Given: ΔCAV and ΔCEV
Prove that: ΔCAV ≅ ΔCEV
Then,
CE ≅ CA (length of side property of a kite)
EV ≅ AV (length of side property of a kite)
<ACV ≅ <ECV (bisected property of a given angle)
<AVC ≅ <EVC (bisected property of a given angle)
CV is a common side to ΔCAV and ΔCEV
Therefore it can be deduced that;
ΔCAV ≅ ΔCEV (Angle-Angle-Side congruent theorem)
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Last month you spent 40$ on clothing. This month you spend 160% of what you spent last month. Set up a percent equation to model this situation. How much did you spend this month.
Choose correct answer below
A. 160%=percent•40
B. part=160%•40
C. 40=160%•whole
Answers
Answer:
part = 160% *40
Step-by-step explanation: I say this because the question asks how much you spent this month. This month you 160% OF WHAT you spent last month so 160% * 40 = what you spent this month
Solve this correctly for brainliest !!!!!! 3(7) + 2 • |7 - 8| - 12
Answers
Answer:
3(7) + 2* |7 - 8| - 12 = 11
Step-by-step explanation:
3(7) + 2* |7 - 8| - 12
21 + 2* |-1| - 12
21 + 2* 1 - 12
21 + 2 - 12
23 - 12 = 11
Hope this helps! :)
The solid below is dilated by a scale factor of 4. Find the volume of the solid created
upon dilation. Answer in terms of TT.
Answer:
units³
3
Submit Answer
Answers
Step-by-step explanation:
the volume of a sphere is
4/3 × pi × r³
the original sphere had a radius of 3.
now, after a dilation of factor 4 the radius is 3×4 = 12.
the volume of that sphere is then
4/3 × pi × 12³ = 4/3 × pi × 1728 = 2304pi
PLEASE ANSWER!! Which unit of measure would be MOST appropriate to use when finding the weight of an Orange
Answers
Answer: ounces
Step-by-step explanation:
Top Kwartalan In Indonesian ☺
\( {5}^{5} = \)
![Top Kwartalan In Indonesian [tex] {5}^{5} = [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/AbLbuxj1DovQTLMwd6Tnfn1meaBfBxwu.jpeg)
Answers
Answer:
3125
Step-by-step explanation:
5*5*5*5*5
What expressions areequalivent to 6 x 4 1/2
Answers
Answer: 32 + 1 and 5 x 2
john can fix 3 chairs in 12 minutes joe can fix 5 chairs in 20 minutes how many chairs can they fix together in 60 minutes
Answers
Step-by-step explanation:
In one hour john can fix 15 chairs ( 3 x 5)
in one hour joe can fix 15 chairs (5 x 3)
total = 30 chairs in one hour
Answer: 15 chairs they fix together in 60 min.
Step-by-step explanation:
jhon efficiency =3/12=4
joe efficiency = 5/20 =4
both efficiency =8
there for 2/8*60
=15
is getting a pear of d rose 772 a bad choice because I'm white
Answers
Answer:
no, what you wear does not define you.
Step-by-step explanation:
At a dinner, the meal cost $22 and a sales tax of $2.09 was added to the bill. What is the tax rate for meals in this city?
Answers
Answer:
24.09 am I smart or what lol
Step-by-step explanation:
22 +2.09
Please help me please please help me will give brainly to whoever actually answers this question
Answers
9514 1404 393
Answer:
car value: $4,953.84population: 446maybe notStep-by-step explanation:
All of these exponential function problems use the same equation, but with different plug-in values. These can be easily accommodated by a spreadsheet or graphing calculator.
The general form of the value after t years is ...
(initial value)×(1 +annual growth rate)^(years)
The growth rate is positive for an increase, negative for a decrease.
a) Initial value: 22385; growth rate: -0.14; years: 10
value after 10 years: $22385×(1-0.14)^10 = $4953.84
__
b) initial value: 290; growth rate: 0.09; years: 5
population after 5 years: 290(1+.09)^5 = 446
__
c) initial value: $4000; growth rate: -0.10; years: 8
value after 8 years: $4000(1 -0.10)^8 = $1721.86
Selling the car for $1500 is selling it for less than its estimated value. That may not be a good decision.
_____
Additional comment
The property value of the car is not the only consideration when evaluating the sale. Other costs related to the car may come into play, and there may be tax implications.
Convert 0.4 to a percent
Answers
Answer:
0.4=40%
Step-by-step explanation:
hope this helps!!!
Assuming the scale drawing is 10 cm long and 5 cm wide, how long and how wide is the actual swimming pool?
Answers
Answer:
I AM NOT IN THIS GRADE
Step-by-step explanation:
THANK YOU FOR THE FREE POINTS
Select all the correct answers.
Which statements are true about function g?
Answers
Answer:
i need the question
Step-by-step explanation:
A flagpole casts a shadow that is 14 feet long. At the same time, a person standing nearby who is 5 feet 6 inches tall casts a shadow
that is 42 inches long. How tall is the flagpole?
Flagpole:
feet
Answers
Answer:
22 feet
Step-by-step explanation:
As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:
14 ft = 14 × 12 = 168 inches5 ft 6 in = 5 × 12 + 6 = 66 inchesTherefore:
Flaghole height = h inFlagpole shadow = 168 inPerson height = 66 inPerson shadow = 42 inDraw a diagram using the given information (see attachment).
From the diagram, we can see that the flagpole and the person are parallel. Therefore, the two triangles are similar.
In similar triangles, corresponding sides are always in the same ratio.
Therefore, set up a ratio of height to shadow length and solve for h:
\(\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow\)
\(\implies \sf h:168=66:42\)
\(\implies \sf \dfrac{h}{168}=\dfrac{66}{42}\)
\(\implies \sf h=\dfrac{66}{42} \cdot 168\)
\(\implies \sf h=\dfrac{11088}{42}\)
\(\implies \sf h=264\;inches\)
Convert the height into feet by dividing by 12:
\(\implies \sf h=\dfrac{264}{12}=22\;feet\)
Therefore, the height of the flagpole is 22 feet.
cual es la diferencia entre divisor y divisible
Answers
espero que esto ayude
The rabbit will never go over 75 pounds. If this rabbit is bom in July weighing 2 pounds, in which month will it weigh around 46 pounds?
Answers
What is the midpoint of the segment shown below? (1,2) (1, -5)
A. (1, - 3/2)
B. (2, - 3/2)
C. (1,-3)
D. (2, -3)
Answers
9514 1404 393
Answer:
A. (1, - 3/2)
Step-by-step explanation:
The coordinate of the midpoint is the average of the endpoint coordinates.
M = (A +B)/2
M = ((1, 2) +(1, -5))/2 = (1+1, 2-5)/2 = (2, -3)/2
M = (1, -3/2) . . . . . matches choice A
Answer:
A. (1, - 3/2)
Step-by-step explanation:
Find the area of the figures given
Answers
Answer:
A: 12.5
B: 36
C: 40
D: 88
Step-by-step explanation:
those are the answers
find the measure of m
Answers
Answer:
47*
Step-by-step explanation:
Each corner of the square is 90*
angle CBE + angle ABE = 90*
fill in the blanks
43 + x = 90
subtract 43 from both sides
x = 47*
simple equation:
6m=12
Answers
Step-by-step explanation:
Divide both sides of the equation by the same term6m/6 =12/6
Cancel terms that are in both the numerator and denominatorDivide the numbersm=2
Answer:
m=2
Step-by-step explanation:
Divide 6 on both sides
6m / 6 = 12/6
m= 12/6 = 2
So, m=2
Verification:
LHS = 6m m=2
6 * 2 = 12
RHS = 12
Both the LHS and RHS are same, so our answer is correct
The variables y and x have a proportional relationship, and y = 12 when x = 5.
What is the value of y when x = 8?
Answers
Y= 19.2
Answer:
y = 19.2
Step-by-step explanation:
We know there is relationship between y and x, so according to the formula \(y = kx\)
k = 12/5
we get one function y = 2.4x
when x = 8, input it into the function,
y = 2.4×8 = 19.2
Help me please in need of it
Answers
Answer:
-2
Step-by-step explanation:
Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).
Select the correct answer.
Which equation or inequality represents the statement?
3(14 + x) < 57
3(14) + x>57
3(14) + x = 57
3(14 + x) = 57
Answers
Answer:
3(14 + x) = 57
Step-by-step explanation:
I just answered the same question edmentum