The cost of the Coca-Cola can will be $1 in the year 2000.
Given that the cost of a can of Coca-Cola can in 1960 = $0.10
The function which models the cost of a Coca-Cola by year 't' is
c(t) = [tex]0.10e^{0.0576t}[/tex].
Here, 't' denotes the number of years since 1960.
c(t) is an exponential function.
We have to find the year in which the cost of a can will be $1.
So substitute c(t) = 1, we get,
1 = [tex]0.10e^{0.0576t}[/tex]
⇒ [tex]10 = e^{0.0576t}[/tex]
We have, [tex]ln(e^x) = x[/tex] .
Taking logarithm on both sides, we get,
log(10) = 0.0576t
⇒ [tex]t=\frac{ln(10)}{0.0576}[/tex] = 39.97 ≈ 40 years .
Thus the cost of a can of Coca-Cola will be $1 in the year, 1960 + 40 = 2000.
The question was incomplete. Find the complete question at:
The cost of a can of Coca-Cola in 1960 , was $0.10. The function that models the cost of a Coca-Cola by year is C(t)=0.10e^(0.0576t) , where t is the number of years since 1960 . In what year is it expected that a can of Coca-Cola will cost $1.00 ?
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Write 6.42 as a mixed number in simplest form.
6.42=
Answer:
6 [tex]\frac{21}{50}[/tex]
Can anyone pleases solve this?
By rationalization and algebra properties, the irrational expression 7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2) is equivalent to the integer 1.
How to simplify a subtraction of irrational fractions
In this question we find a composite irrational expression formed by a irrational fraction being subtracted by other two irrational fraction. Eliminating the irrational denominators by transforming it into rational numbers is an important step for this question, this can be done by means of rationalization, along with algebra properties.
The complete procedure of this exercise is shown below:
7√3 / (√10 + √3) - 2√5 / (√6 + √5) - 3√2 / (√15 + 3√2)
[7√3 · (√10 - √3)] / [(√10 + √3) · (√10 - √3)] - [2√5 · (√6 - √5)] / [(√6 + √5) · (√6 - √5)] - [3√2 · (√15 - 3√2)] / [(√15 + 3√2) · (√15 - 3√2)]
(7√30 - 21) / 7 - (2√30 - 10) - (3√30 - 18) / (- 3)
(7√30 - 21) / 7 + (10 - 2√30) + (3√30 - 18) / 3
(7√30 - 21 + 70 - 14√30) / 7 + (3√30 - 18) / 3
(49 - 7√30) / 7 + (3√30 - 18) / 3
(147 - 21√30 + 21√30 - 126) / 21
21 / 21
1
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Which numbers are a distance of 3 units from 12 on a number line?
Select each correct answer.
Answer:
9 and 15
Step-by-step explanation:
ans should be 9 and 15
i dun really understand what this qns wants u to find really bad qns to test
Can someone help me
Answer: well look you can fid live tutors
Step-by-step explanation:
n vcxvbnm
You are swimming each 25-yard length of a swimming pool 3 seconds
faster than your personal best. What integer represents your change in
time of your personal best after 200 yards?
24 seconds faster time of your personal best after 200 yards.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.Suppose the number of laps = m
According to the question, each lap of 25 yards is covered 3 seconds faster than the previous one, so the series become
x , x-3 , x-6 , x-9, ............................
25 * m = 200
m = 200/25
m = 8
As m is the number of laps, and each lap is 3 second faster.
So 8 laps will be 8*3 = 24 seconds faster.
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Damian is building a display case to hold
75 model cars. The case will have fewer
than 10 shelves, and each shelf will hold
no more than 15 cars. If Damian wants
each shelf to have the same number of
cars, how many shelves should he put in
the display case?
Find the distance between the two points on the graph.
Answer:
[tex]3 \sqrt{5} [/tex]
Step-by-step explanation:
See attached for details. Basically finding the distance between 2 points requires creating a right angle triangle. And we are looking for the hypotenuse.
The pythagorean theorem is used.
Solve the literal equation for x.
13. x + 5y = 2
14. 2x + 5 = 12y + 9
Answer:
x=2
Step-by-step explanation:
You would use substitution. In which x =-5y +2 and x = 6y+2. -5y + 2 = 6y + 2. So would solve for y value then plug it into the equation to solve x.
2. State what additional information is required in order to know that the triangles are congruent by the SSS Triangle Congruence Postulate
The additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
How to state the additional information required?The congruence postulate is given as:
SSS Triangle Congruence Postulate
The above means that the three sides of the triangles are congruent.
From the figure, the following side lengths are said to be congruent
UV and FV
TV and TV
For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent
This is represented as:
UT = T F
Hence, the additional information required to prove the SSS Triangle Congruence Postulate is UT = T F
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b.a slug takes 4.25 minutes to travel 11.2 centimeters. what is the speed of the slug in meters per second? predicted number of significant digits in answer: 2 or 3 answer value: actual number of significant digits:
Answer:
0.00375 meters per second,
Step-by-step explanation:
0.00375 meters per second, we know this is the answer because, 4.25*60=255 and 255/11.2=0.00375
russell runs 9/10 miles in 5 minutes. at this rate how many miles can he run in one mintue?
Answer:
1.8 miles
Step-by-step explanation:
Can someone please help I will be giving Brainliest to whoever can answer :)
Match the questions with the graphs that are labeled A-H. (keep in mind that some questions might have the same answer)
1. A = {(x, y): y > x^2}
2. B = {(x, y): y ≥ x^2+ 3}
3. C = {(x, y): y ≤ 3x^2 + 2}
4. D = {(x, y): y ≥ 2x^2- 5x + 1}
5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25}
6. x^2- 3x ≥ 0
7. x^2- 3x + 2 ≤ 0
8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1}
The questions are matched with the graphs that are labeled A-H. (
1. A = {(x, y): y > x^2} Matching answer D2. B = {(x, y): y ≥ x^2+ 3} Matching answer G3. C = {(x, y): y ≤ 3x^2 + 2} Matching answer C4. D = {(x, y): y ≥ 2x^2- 5x + 1} Matching answer A5. E = {(x, y): 16 ≤ x^2+ y^2 ≤ 25} Matching answer F6. x^2- 3x ≥ 0 Matching answer J (the curve should be solid line)7. x^2- 3x + 2 ≤ 0 Matching answer E8. {(x, y): y ≤ 1 - x^2} and {(x, y): y ≥ -1} Matching answer BHow to find the matching graphThe graph has some rules for matching them to the equation some of the rules are:
finding the rootsusing solid lineusing broken lineknowing about circlelearning about straight lineRead more on graphs here: https://brainly.com/question/19040584
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Can someone help me out
Answer:
I believe its graph 4 (not sure though, you can plug in some values to make sure)
Step-by-step explanation:
WILL GIVE YOU BRAINILEST or however you spell it
BIRDHOUSES Ebony can build 0.7 birdhouse in 1 day. How many birdhouses can she build in 10 weeks?
Step-by-step explanation:
0.7 birdhouses in 1 day.
how many in 10 weeks ?
for that we need to know how many days are in 10 weeks.
1 week = 7 days
assuming that she is working on the birdhouses also on weekends, that means 10 weeks = 10×7 = 70 days.
and that means she can build
0.7 × 70 = 49 birdhouses in 10 weeks.
now, if she works only Monday to Friday on the birdhouses, then that means
1 week = 5 days
and 10 weeks = 10×5 = 50 days.
and that means she can build
0.7 × 50 = 35 birdhouses in 10 weeks.
if there is really no other information about that, I would use the usual 7 days per week and the first solution (49).
please solve this question step by step
Answer:
Step-by-step explanation: The given question is wrong. To be a valid question, there must be "-9" in place of "-7" in the second given matrix.
laura runs a 100 m race in 20.0 s. what is her time in kiloseconds ? how long is the race in kilometers
Laura runs for 0.02 kiloseconds
The race is 0.1 kilometers
How to convert to kiloseconds and kilometers ?The first step is to convert 20 seconds to kiloseconds
= 20/1000
= 0.02 kiloseconds
The next step is to calculate the distance in kilometers
Convert 100 meters to kilometer
= 100/1000
= 0.1 km
Hence the race is 0.1 kilometers
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The square below represents one whole. What percent is represented by the shaded area?
Answer:
29%
Step-by-step explanation:
There are 100 boxes. 29 of them are shaded in, so we can divide that by 100.
29/100=0.29
0.29 is equal to 29%
Please help - thanks
Insert parentheses in the appropriate places:
8+ 3-2 ×9 =17
28 ÷ 4+3 × 4+3 =28
5× 3+2 ×6 ÷3 =50
6× 9-4 +3-3 ×4=30
5 ×3+2× 6÷3 =19
5× 3+2×6 ÷3 =25
Answer:
the answer is 27
Step-by-step explanation:
Please answer these two questions!
Answer:
The answer to your first question would be B. The answer to the second is C.
Step-by-step explanation:
Hope it helps! =D
Which algebraic expression is equivalent to the expression below?
4(4x + 5) + 4(11 - x)
A.
20x + 64
B.
12x + 24
C.
12x - 64
D.
12x + 64
Answer:
D. 12X + 64
Step-by-step explanation:
4(4x+5)+4(11-x)
4(4x+5)+4(11−x)
4(4x + 5) + 4(11 - x)
1 Expand by distributing terms.
16x+20+4(11-x)
16x+20+4(11−x)
2 Expand by distributing terms.
16x+20+44-4x
16x+20+44−4x
3 Collect like terms.
(16x-4x)+(20+44)
(16x−4x)+(20+44)
4 Simplify.
12x+64
12x+64
Answer:
D. 12x + 64
Step-by-step explanation:
expand the brackets by multiplying:
= 16x + 20 + 44 - 4x
= 12x + 64
brainliest pls :,)
Say you are given the graph of the line y = -x. Write the equation of the line that is perpendicular to the given line and goes through the point (-8, 2).
Linear equations are often organized in slope-intercept form: [tex]y=mx+b[/tex]
m = slopeb = y-interceptTo find a linear equation, we often first solve for the slope, and then solve for the y-intercept algebraically.
To find the slope of a perpendicular line, we must find the negative reciprocal of the slope of the reference line.
Solving the Question
We're given:
Reference line is [tex]y=-x[/tex]Perpendicular line passes through [tex](-8,2)[/tex]1) Find the slope of the reference line
We can rewrite the reference line to be clearer in slope-intercept form:
[tex]y=-1x+0[/tex]
This means that -1 is the slope.
2) Find the slope of the perpendicular line
The negative reciprocal of -1 is 1. Therefore, the slope of the perpendicular line is 1. Plug this into slope-intercept form:
[tex]y=x+b[/tex]
3) Solve for the y-intercept of the perpendicular line
[tex]y=x+b[/tex]
Plug in the given point (-8,2) and solve for b:
[tex]2=-8+b\\b=2+8\\b=10[/tex]
Therefore, the y-intercept of the perpendicular line is 10. Plug this back into our original equation:
[tex]y=x+10[/tex]
Answer[tex]y=x+10[/tex]
The figure shows two triangles on a coordinate grid:
What set of transformations is performed on triangle ABC to form triangle A′B′C′? (1 point)
a
A 180 degree counterclockwise rotation about the origin followed by a translation 5 units up
b
A 270 degree counterclockwise rotation about the origin followed by a translation 5 units up
c
A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin
d
A translation 5 units to the left followed by a 270 degree counterclockwise rotation about the origin
The set of transformations that is performed on triangle ABC to form triangle A′B′C′ is C. A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin.
What is a translation?A translation is a geometric transformation when each point in a figure, shape, or space is moved in a specific direction by the same amount. A translation can also be thought of as moving the coordinate system's origin or as adding a constant vector to each point.
In this case, it can be seen that the shape was rotated counterclockwise twice. That's 90° × 2 = 180°
Therefore, the transformation that is performed on triangle ABC to form triangle A′B′C′ is a translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin.
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. The oxygen saturation of a lake is found by dividing the
amount of dissolved oxygen the lake water currently has
per liter by the dissolved oxygen capacity per liter of the
water, and then converting that number into a percent.
If the lake currently has 6.4 milligrams of dissolved oxy-
gen per liter of water and the dissolved oxygen capacity
is 9.5 milligrams per liter, what is the oxygen saturation
level of the lake, to the nearest percent?
A. 64%
B. 67%
C. 70%
D. 89%
E. 95%
Answer:
70% i think
Step-by-step explanation:
please help question is in the image!
x1 = 4 x2 = -4
substitute the values into the given equations!!
(4 + (-4)) / 2 = (0 / 2) = 0
y1 = -5 y2 = 5
(-5 + 5) / 2 = (0 / 2) = 0
midpoint = (0, 0)
bold values - box answers :D
Write and solve a system of equations for each problem situation. Interpret the solution in terms of context.
Pedro has 97 athlete cards. In his collection, he has 39 more baseball player cards than football player cards. How many of each type of card does Pedro have?
Number of each type of cards after solving system of equations for given situation of Pedro cards are 29 and68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
As given,
Total number of cards=97
Let y=football cards
x=baseball cards
System of equations are
x + y=97 __(1)
x=y +39 __(2)
Substitute (2) in (1)
y+ 39 +y=97
⇒2y=58
⇒y=29
Substitute y=29 in (2),
x=29 +39
=68
Therefore, number of each type of cards after solving system of equations are football cards 29 and baseball cards 68.
Interpretation is Pedro collected 29 football cards and 68 baseball cards.
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a quarry needs to ship a marble block weighing 10000 pounds. if the cost of shipping is 110 per ton, how much will shipping cost?
The cost of shipping the marble block is 550.
The total weight of the marble block is 10,000 pounds.We need to convert the weight from pounds to tons.Unit conversion is the process of converting various units of measurement for the same amount, often using multiplicative conversion factors that modify the measured quantity value without affecting its effects.1 ton equals 2000 pounds.The total weight of the marble block in tons is 10000/2000.The total weight of the marble block is 5 tons.The cost of shipping is 110 per ton.The total cost of shipping the marble block = 5 * 110.The total cost of shipping the marble block is 550.To learn more about unit conversion, visit :
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Which algebraic expression represents each verbal expression?
a. the product of five and a number, decreased by eleven
b. the sum of a number and five less than eleven
c. five times a number fewer than eleven
d. the quantity of a number minus eleven, multiplied by five
Answer:
A) 5n − 11
B) 11 − (n + 5)
C) 11 − 5n
D) 5(n − 11)
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The required verbal algebraic expressions are given as ,
(a) 5x - 11 (b) (x + 5) - 11
(c) 5x - 11 (d) (x - 11)×5
What is an algebraic expression?The algebraic expression consists of constants and variables. eg x, y, z etc.
Here,
Let the number x,
a. The product of five and a number, decreased by eleven
⇒ 5x - 11
b. The sum of a number and five less than eleven
⇒ (x + 5) - 11
c. Five times a number fewer than eleven
⇒5x - 11
d. The quantity of a number minus eleven, multiplied by five
⇒(x - 11)×5
Thus, the required expression is shown above
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heidi was able to walk 2/3 of a mile in 12 minutes how far could heidi walk in 1 hour
Heidi is able to walk 10/3 miles in 1 hour (60 min).
What is described as unitary method?It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.
The value of many items is given in the unitary method, and we must either determine the worth of more or fewer items. To do so, we must first determine the value of one item by division and then determine the value of more as well as fewer items by multiplication.Now, for the given question;
It takes Heidi 12 minutes to walk 2/3 miles.
Applying the unitary method.
Then, for in 1 minutes Heidi will walk = 2/(3×12).
For walking in 1 hour or 60 min = (2×60)/(3×12).
Further simplifying;
In 1 hour = 10/3 miles.
Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.
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Is ✓225 + ✓196 a rational or irrational number?
Answer:
yes
Step-by-step explanation:
√225 + √196
15 + 14
29
29 can be written as 29/1 thus 29 is a rational number
What is the area, in square meters, of the shape below? Express your answer as a fraction in simplest form.
Area = 5/12 m².
For image see the attachment below-
Area of Triangle - A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC. Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.
The basic formula to find the area of a triangle is,
Area of triangle = 1/2 (b × h);
where b = base and
h = height of the triangle.
Now , we have been given that -
Base =5/3 m
Height = 1/2 m
Find out area of the triangle .
The area of a triangle = 1/2 x base x height
Put the values in formula
area of a triangle = 1/2 x 5/3 x 1/2
area of a triangle = (1x5x1)/ (2x3x2)
area of a triangle = 5/12 m².
Hence, the area in square meters of the given shape is 5/12 .
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