The cost of a can of Coca Cola in 1960 was $0.10. The exponential function that models the cost of a Coca Cola by year is given below, where t is the number of years since 1960. C(t)=0.10e^0.0576t Find the expected cost of a can of Coca Cola in 1970, 2005, 2015 and 2040 (rounded to the nearest cent).
Answers
The expected cost of a can of Coca-Cola in 1970 is 0.22 (rounded to the nearest cent).
The expected cost of a can of Coca-Cola in 2005 is 2.09 (rounded to the nearest cent).
The expected cost of a can of Coca-Cola in 2015 is 7.49 (rounded to the nearest cent).
The expected cost of a can of Coca-Cola in 2040 is 76.92 (rounded to the nearest cent).
Using the exponential function \(C(t)=0.10e^0.0576t\), given below,
where t is the number of years since 1960, the expected cost of a can of Coca-Cola can be calculated for different years, as follows:
For 1970: \(t = 10 (1970 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(10) = 0.10e^0.576≈0.22\)
Therefore, the expected cost of a can of Coca-Cola in 1970 is 0.22
For 2005: \(t = 45 (2005 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(45) = 0.10e^2.592≈2.09\)
Therefore, the expected cost of a can of Coca-Cola in 2005 is 2.09
For 2015: \(t = 55 (2015 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(55) = 0.10e^3.168≈7.49\)
Therefore, the expected cost of a can of Coca-Cola in 2015 is 7.49
For 2040: \(t = 80 (2040 - 1960)C(t) = 0.10e^0.0576t = 0.10e^0.0576(80) = 0.10e^4.608≈76.92\)
Therefore, the expected cost of a can of Coca-Cola in 2040 is 76.92
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Related Questions
A 225-foot support wire is attached to the top of a monument at a stake on the ground 100 feet from the
base of the monument, as shown
Part A
What is the approximate height of the monument?
А
125 feet
B
202 feet
С
246 feet
D
325 feet
Answers
Answer:
325??
Step-by-step explanation:
325+100
Answer:
It's 202
Step-by-step explanation:
if a + 1 by a is equal to 3 find the value of bracket a minus 1 by a bracket square
Answers
a+1 = 3
To find:(a - 1)^2
\( {a}^{2} - 2.a.b + {b}^{2} \\ \\ a - 2a + 1 \\ \\ 1 + 1 = 2\)
So, the answer is 2Hope it help youA hummingbird's nest is 12 feet high in a tree and a flower is on the ground 16 feet away
from the base of the tree. How far will the hummingbird need to fly to get from its nest to the
flower?
Answers
Answer:
the bird will need to fly 4feet closer to the flower
Constant of Variation
Which is the correct graph of y = 1/x² ?
a.
b.
c.
d.
Please select the best answer from the choices provided
Answers
Answer:
A.
Step-by-step explanation:
I calculated it logically
Answer:
d.
Step-by-step explanation:
\(y = \frac{1}{ {x}^{2} } \\ horizontal \: asymptote : \\ {x}^{2} = 0 \\ x = 0\)
Which number expresses 6.72 as a fraction in simplest from?
Answers
Yavonne has $15.90 in her checking account. She needs to buy items that cost $3.18 each. How many of these items can she buy?
a
4
b
5
c
6
d
7
Answers
Answer:
5.
Step-by-step explanation:
15.90 / 3.18 =
What is the mean of the data set?
14, 19, 18, 12, 22, 15, 16, 16, 14, 14, 21, 20
15.75
16.00
16.75
19.50
Answers
Answer:
16.75
Step-by-step explanation:
The mean of a set of numbers is the sum divided by the number of terms.
Answer:
16.8125 or 16.8
Step-by-step explanation:
Complete the inequality statement. 4/13__ 6/13
Answers
Answer:
4/13 < 6/13
Step-by-step explanation:
= means equal
< means less than
> means greater than
Since 4/13 is less than 6/13 the correct answer is 4/13 < 6/13
Fill in the blank. ASAP . . . . .
Answers
The equation y = [x - 5] +2 is?
![The equation y = [x - 5] +2 is?](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/T65BJhjYu9ZSnEXxWS7Cxbuh5yDNW5GW.png)
Answers
Answer:
Groot
Step-by-step explanation:
Please help me with this for a large reward please someone
Answers
The lengths arranged from shortest to longest is \(2\frac{7}{8}\), \(3\frac{1}{4}\), \(3\frac{1}{2}\) , \(3\frac{5}{6}\), \(4\frac{2}{3}\) (option H).
What is the order of the lengths of the wood?The lengths of the woods are expressed as mixed numbers. Mixed numbers are non-integers that consists of a whole number and a proper fraction. For example, \(3\frac{1}{4}\) is a mixed number. 3 is the whole number and \(\frac{1}{4}\) is the proper fraction.
In order to arrange the lengths of the woods from shortest to the longest, convert the mixed numbers to decimals for easy comparison.
\(3\frac{1}{4}\) becomes 3.25
\(2\frac{7}{8}\) becomes 2.875
\(3\frac{5}{6}\) becomes 3.833
\(4\frac{2}{3}\) becomes 4.667
\(3\frac{1}{2}\) becomes 3.5
The lengths arranged from shortest to longest is \(2\frac{7}{8}\), \(3\frac{1}{4}\), \(3\frac{1}{2}\) , \(3\frac{5}{6}\), \(4\frac{2}{3}\)
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6/7 divided by 12/14 please show the work
Answers
Answer:
1
Step-by-step explanation:
When dividing one fraction by another, the best way to solve it is to multiply by the reciprocal. The reciprocal just flipping the fraction over. So you would leave the 6/7 and the multiply by 14/12( because you are multiplying by the reciprocal). When you do that, you then can just multiply the top and the bottom to form one fraction. The numerator is 6*14 = 84, and the denominator is 7*14 = 84. So you are left with 84/84 which anything over itself is equal to one.
Hope this helps!
Matrix M has x-rows and (11-x) columns. Matrix N has y-rows and (y+5) columns. If MN and NM both are defined, find the values of x and y
Answers
Answer:
\(x=8, y=3\)
Step-by-step explanation:
Recall that if a matrix multiplication of two matrices is defined, then the number of columns of the first matrix is equivalent to the number of rows of the second matrix.
Since matrix M has (11-x) columns and matrix N has y rows, and MN is defined, so it follows:
\(y=11-x----(1)\)
Since matrix N has (y+5) columns and matrix M has x rows, and NM is defined, so it follows:
\(y+5=x----(2)\)
Substitute (1) into (2):
\(11-x+5=x\\2x=16\\\therefore x=8--(3)\)
Substitute (3) into (1):
\(y=11-8=3\)
I NEED HELP ASAP PLS
Answers
For the given circle the value of cotθ is -√30/√19.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The terminal side of an angle θ.
The standard position intersects the unit circle at (√30/7, -√19/7).
We need to find the value of cotθ.
Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)
cotθ=x/y
=-√30/7/√19/7
=-√30/7×7/√19
=-√30/√19
Hence, the value of cotθ is -√30/√19 for the given circle.
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Graph the line with slope -6 and y-intercept 3.
Answers
Answer:
See Attachment.
Genera Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define variables
Slope m = -6
y-intercept b = 3
Step 2: Write linear equation
Substitute into general form.
Slope-Intercept Form: y = -6x + 3
Step 3: Graph
Answer:
*See Below*
Step-by-step explanation:
It was hard to find this answer. Sorry if the graph glitches.
Find 4 + 20, if ü -< -3, -7> and =< 4, -2 >
<-4,-32 >
<7,-3>
<-8, -30
< 5, -11 >
2 0 0 0
Answers
Given statement solution is :- The Vector Calculations and Addition results are as follows:
ü -< -3, -7 > = < -3, -7 >
=< 4, -2 > - < -4, -32 > = < 0, -34 >
< 7, -3 > - < -8, -30 > = < 15, 27 >
< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >
And 4 + 20 = 24.
To find the sum of 4 + 20, we simply add the two numbers together:
4 + 20 = 24
As for the given vectors, let's perform the requested calculations:
ü -< -3, -7 > = < -3, -7 >
=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >
< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >
< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >
Therefore, the Vector Calculations and Addition results are as follows:
ü -< -3, -7 > = < -3, -7 >
=< 4, -2 > - < -4, -32 > = < 0, -34 >
< 7, -3 > - < -8, -30 > = < 15, 27 >
< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >
And 4 + 20 = 24.
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Greatest common factor
3m-12n
Answers
Answer:
3
Step-by-step explanation:
To find the Greatest common factor (GCF) of 3m-12n we find the highest letters and/or numbers that is a factor of both :
3m-12n
Both have a common factor of 3 :
\(\frac{3m-12n}{3} = m-4n\)
m-4n cannot be simplified anymore so the gcf of 3m-12n is 3.
Hope this helped and have a good day
Please Help! Which is the set of whole numbers between ten and fifteen? Responses {12, 14} {12, 14} all real numbers all real numbers {11, 12, 13, 14} {11, 12, 13, 14} null set
Answers
{11, 12, 13, 14} is the set of whole numbers between ten and fifteen
This is further explained below.
Which is the set of whole numbers between ten and fifteen?Generally, An aliquot is the number zero, a positive natural number or a negative integer with a negative sign.
The additive inverses of the positive numbers that they relate to are represented by the negative numbers.
In conclusion, {11, 12, 13, 14} is the set of whole numbers between ten and fifteen
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A car shop has 12 mechanics, of whom 8 can work on transmissions and 7 can work on brakes. a) What is the minimum number who can do both? b) What is the maximum number who can do both? c) What is the minimum number who can do neither? d) What is the maximum number who can do neither?
Answers
Answer:both a and b are correct
Step-by-step explanation:
(Quadratic Regressions) Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profitearned at that price, y. Write a quadratic regression equation for this set of data,rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 22 dollars.
Answers
The general quadratic equation is:
y = ax² + bx + c
where a, b and c are constants.
Substituting with x = 18.5 and y = 11397, we get:
11397 = a*18.5² + b*18.5 + c
11397 = 342.25a + 18.5b + c (eq. 1)
Substituting with x = 25.5 and y = 16256, we get:
16256 = a*25.5² + b*25.5 + c
16256 = 650.25a + 25.5b + c (eq. 2)
Substituting with x = 35 and y = 16109, we get:
16109 = a*35² + b*35 + c
16109 = 1225a + 35b + c (eq. 3)
Equations 1, 2 and 3 make a system of 3 equations and 3 variables (a, b, and c).
Isolating c from equation 1 and replacing into equations 2 and 3, we get:
11397 = 342.25a + 18.5b + c
11397 - 342.25a - 18.5b = c
16256 = 650.25a + 25.5b + 11397 - 342.25a - 18.5b
16256 - 11397 = 650.25a - 342.25a - 18.5b + 25.5b
4859 = 308a + 7b (eq. 4)
16109 = 1225a + 35b + 11397 - 342.25a - 18.5b
16109 - 11397 = 1225a - 342.25a - 18.5b + 35b
4712 = 882.75a + 16.5b (eq. 5)
Isolating b from equation 4 and replacing into equation 5, we get:
\(\begin{gathered} 4859=308a+7b \\ 4859-308a=7b \\ \frac{4859-308a}{7}=b \end{gathered}\)\(\begin{gathered} 4712=882.75a+16.5(\frac{4859-308a}{7}) \\ 4712=882.75a+16.5\cdot\frac{4859}{7}-16.5\cdot\frac{308}{7}a \\ 4712=882.75a+11453.36-726a \\ 4712-11453.36=156.75a \\ -\frac{6741.36}{156.75}=a \\ -43=a \end{gathered}\)Then, the value of b is:
\(\begin{gathered} b=\frac{4859-308\cdot(-43)}{7} \\ b=\frac{4859+13244}{7} \\ b=\frac{18103}{7} \\ b=2586.14 \end{gathered}\)And the value of c is:
c = 11397 - 342.25*(-43) - 18.5*2586.14
c = 11397 + 14716.75 - 47843.59
c = -21729.84
Therefore, the quadratic regression is:
y = -43x² + 2586.14x - 21729.84
If the price is $22, then x = 22, and the value of y (profit) is:
y = -43*22² + 2586.14*22 - 21729.84
y = -20812 + 56895.08 - 21729.84
y = 14353.24
4252.50=(18000)(r)(54)
Answers
Step-by-step explanation:
do you want to find r?
so do 4252.50/ (18000*54)
Please help me
liza uses a total of 20 cups of batter to make x cupcake and a cake .he uses 2/3 cup of batter for each cupcake 4 cups of batter for the cake.
How many cupcakes x , can liza make she uses the batter.
Answers
Answer:
I think it is 24 cupcakes
Which ones are functions, not a function, not enough information?
Answers
Answer:
The first two are functions, the last one is not
Step-by-step explanation:
Subtract the sum of 4 3/4 and 5 2/3 from 12 1/2.
Answers
Hope this helps
Determine if the rates are equivalent. Explain your reasoning.5 cans of soup for $3.75; 8 cans of soup for $6.00
Answers
Answer:
They are equivalent
Step-by-step explanation:
Since 3.75 divided by 5 is .75 that means that 6 divided by 8 would have to also be .75 which, if you divide it, it is.
Answer:
The rates are equivalent
Step-by-step explanation:
To find the unit cost you divide the price by the number of units
3.75÷5=0.75
6.00÷8=0.75
To determine whether or not the rates are equivalent, compare the unit costs
0.75=0.75
Therefore, the rates are equivalent
Hope this was helpful :)
А 10 0 B В 1) Which one of these shapes is not like the others?
Answers
In order to compare the figures and find the one that is not like the others, let's compare the proportion of their width and height:
\(\begin{gathered} A\colon \\ \frac{\text{width}}{\text{height}}=\frac{5}{4} \\ \\ B\colon \\ \frac{\text{width}}{\text{height}}=\frac{10}{8}=\frac{5}{4} \\ \\ C\colon \\ \frac{\text{width}}{\text{height}}=\frac{10}{6}=\frac{5}{3} \end{gathered}\)We can see that figure C has a different proportion, therefore figure C is the one that is not like the others.
A storage box in the garage is 3 feet tall, 4 feet long and has a volume of 9 cubic feet. How many square feet is the area of the base of the box?
Answers
Answer:
3 ft^2
Step-by-step explanation:
first find the width of the storage box using the given volume
V = L * W * H
9 = 4 * W * 3
9 = 12 * W
9/12 = W
W = 3/4 or .75
then with that to find the are of the base multiply the length and the width
a = l * w
a = 4 * 3/4
a = 3
Please help me graph this inequality
Answers
Answer:
rearrange to get x < -4
Step-by-step explanation:
A storage bin in the corner of Joe's room has the dimensions shown below. What is the volume of the bin?
Answers
Find the distance between the two points in simplest radical form
(6,-4) and (1,-6)
Answers
Answer
\(\sqrt29\)
Step-by-step explanation:
1. Write the distance formula:
\(\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)
2. Substitute
Substitue (6, -4) and (1, -6) into
\(\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}\)
\(\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}\)
3. Calculate
\(\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}\)
\(\sqrt(-5) ^{2} + (-2)^{2}\)
\(\sqrt5 ^{2} + 2^{2}\)
\(\sqrt25 + 4\)
\(\sqrt29\)