Answers
Answer:
Initial temperature = 20° C
Temperature after 18 minutes = 4° C
Step-by-step explanation:
Function representing the relation in the temperature of the soda and time has been given as,
T(x) = [tex]-8+28e^{-0.045x}[/tex]
Here x = number of minutes since the can was placed in the cooler
For initial temperature of the soda,
x = 0,
T(0) = [tex]-8+28e^{(28\times 0)}[/tex]
= -8 + 28(1)
= 20° C
For the temperature after 18 minutes,
x = 18,
T(18) = [tex]-8+28.e^{-0.045\times 18}[/tex]
= [tex]-8+28.e^{(-0.81)}[/tex]
= [tex]-8+12.456[/tex]
= 4.456 C
≈ 4° C
Related Questions
2-[ 9 --[17:13]13
-2 07
08
13. What is B-CF?
-E-1
23 6.5
A.
- 11.4 44
-21 1.5
B.
12 -41]
26 8 -37
C.-7.4 51 56
25 -6 10
-19 6.5
D.
-6 -38]
Answers
An individual saves $5000 in a bank account at the beginning of each year for 10 years.
No further savings or withdrawals are made from the account. Determine the total amount saved if the annual interest rate is 8% compounded:
(a) annually;
(b) semi-annually.
Answers
Answer:
a) Amount saved if the interest is compounded annually is $5832
b) Amount saved if the interest is compounded semi-annually is $5849.5
Step-by-step explanation:
Principal Amount P = 5000
Time t = 10 years
Annual interest i = 8% = 0.08
We need to find amount saved if interest is compounded a) annually b) semi-annually
a) Amount saved if the interest is compounded annually
If interest compounded annually, n= 1
Using Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values:
[tex]A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{1})^{1*2}\\A=5000(1+0.08)^2\\A=5000(1.08)^2\\A=5000(1.1664)\\A=5832[/tex]
So, Amount saved if the interest is compounded annually is $5832
b) Amount saved if the interest is compounded semi-annually
If interest compounded semi-annually, n= 2
Using Formula: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values:
[tex]A=P(1+\frac{r}{n})^{nt} \\A=5000(1+\frac{0.08}{2})^{2*2}\\A=5000(1+0.04)^4\\A=5000(1.04)^4\\A=5000(1.1699)\\A=5849.5[/tex]
So, Amount saved if the interest is compounded semi-annually is $5849.5
(a). When compounded annually, the amount will be [tex]\$ 10,794.6[/tex]
(b). When compounded semi-annually, the amount will be [tex]\$ 10,955.6[/tex]
Compound interest:It is given that, an individual saves $5000 in a bank account at the beginning of each year for 10 years.
[tex]Principal(P)=5,000, t=10 years, rate(r)=8\%[/tex]
As we know that,
[tex]Amount=P(1+\frac{r}{100} )^{t} \\\\Amount=5,000(1+\frac{8}{100})^{10} \\\\Amount=5,000*(\frac{108}{100})^{10}\\\\Amount=\$ 10,794.6[/tex]
When interest is compounded semi-annually;
[tex]r=8/2=4\%, t=10*2=20[/tex]
[tex]Amount=5,000(1+\frac{4}{100})^{20} \\\\Amount=5,000*(\frac{104}{100})^{20}\\\\Amount=\$ 10,955.6[/tex]
Learn more about the compound interest here:
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A. ECONOMICS A sports team sells about
100 coupon books for $30 each during their annual
fundraiser. They estimate that for each $0.50
decrease in the price, they will sell about 10 more
coupon books. How much should they charge for
each book in order to maximize the income from
their sales?
A. $29.50
B. $20.00
C. $17.50
D. $15.00
Answers
Answer:C
Step-by-step explanation:
Is this paper 8 1/2 x 11 pls hurry pls pls pls I need help and can someone show me where 8 1/2 is on a ruler like this
Answers
Answer:
I believe that the paper should be around 8 1/2 x 11.
You can find 8 1/2 by going to the mark shown between 8 and 9 on the side with inches.
Please help with 5 :( I’ll mark u!
Answers
Answer:
m is slope, b is y=interecept and x and y is the coordinates
Step-by-step explanation:
b = y-intercept
x and y = coordinates of a point that lie on a line
Hope this helps! ✨❤️
PLZ HELP ME I WILL MARK BRAINLIEST!!!
Answers
Answer:
i just kno that D is 0
Step-by-step explanation:
-7 +7=0
The semiannual tuition payment at a major university is expected to be $30,000 for the 4 years beginning 18 years from now. What lump sum payment should the university accept now, in lieu of tuition payments beginning 18 years, 6 months from now? Assume that money is worth 6%, compounded semiannually, and that tuition is paid at the end of each half-year for 4 years. (Round your answer to the nearest cent.)
Answers
Answer:
$49,216.78
Step-by-step explanation:
A(n,k) = R[1-(1+i)^-n / i) (1+i)^-k
A = Present value of deferred annuity
R = Payment at the end of period
R = 30,000
i = 0.06 / 2
n = (4)*2 = 8
k = deferred period, (18)*(2) = 36
A(n,k) = 30,000*(1-(1+0.04)-^8 / 0.04)*(1+0.04)^-36
A(n,k) = 30,000*(1-(1.04)^-8 / 0.04)*(1.04)^-36
A(n,k) = 30,000*(1 - 0.730690205/0.04) * 0.24366872185
A(n,k) = 30,000*(0.269309795 / 0.04)*0.24366872185
A(n,k) = 30,000*6.732744875*0.24366872185
A(n,k) = 49216.78014700164
A(n,k) = $49,216.78
So the lump sum payment that the university accept now is $49,216.78
a solar panel is in the shape of a rhombus with sides 2.4f each and a height of 1.8ft. compute the area of the solar panel.
Answers
Answer:
4.32ft^2
Step-by-step explanation:
A of a rhombus = l x w
=2.4x1.8
=4.32
∴ the area of the solar panel is 4.32ft^2
Justin had 4 math worksheets for
homework this week. Each worksheet had
48 problems on it. If he only answered 5
questions incorrectly all week, how many
questions did Justin answer correctly?
Answers
Answer:187 questions answered correctly
Step-by-step explanation:
4*48=192
192-5=187
the line that passes through (−2,3) and (0,8)
Answers
Answer:
y=5/2x+8
Step-by-step explanation:
slope: (y2-y1)/(x2-x1); (8-3)/(0-(-2))= 5/2
y-intercept is 8
Sarah wants to buy a new pair of sandals. The sandals are $45 and she has a coupon for 30% off. What is the price of her sandles after the discount?
Answers
Answer:
$31.5
Step-by-step explanation:
-$45
-30 percent off of $45
30 times 45 divided by 100
1350/100
13.5
45-13.5
$31.5
You walk 1/5 miles to a clothing store. Than you walk another 1/4 miles to a shoe store. How many miles have you walked in all?
Answers
Answer: She has walked 9/20 miles in total
Step-by-step explanation:
1/5*4=4/20
1/4*5=5/20
4/20+5/20=9/20 miles
When high-density groups are separated by areas of low abundance, this distribution is termed: Group of answer choices random uniform logistic clumped
Answers
Complete question is;
When high-density groups are separated by areas of low abundance, this distribution is termed: Group of answer choices
A) random distribution pattern
B) uniform distribution pattern
C) logistic distribution pattern
D) clumped distribution pattern
Answer:
D: Clumped Distribution Pattern
Step-by-step explanation:
Looking at the options, the correct option is Clumped distribution pattern.
This is because in density and dispersion phenomenon, Clumped patterns will normally occur when resources get concentrated in small areas within a larger habitat or due to individuals that form social groups. However,on large spatial scales, majority of organisms will likely have clumped distributions mainly because their habitats are not distributed uniformly over wide areas.
Write an expression for the calculation 16 added to 10 and then divided by 2
Answers
Answer:
it is 16 + 10 ÷ 2
Step-by-step explanation:
Miguel divided 205 oranges evenly into 5 boxes. How many oranges were in each box?
Answers
Answer:
41
Step-by-step explanation:
205 divided by 5=41
Answer:
The Answer is 41 oranges in each box
Question down here
Look(+o+)
Answers
Answer:
3[tex]\frac{3}{4}[/tex] or number 3
Step-by-step explanation:
Answer : 3 3/4 cubic inches
If shoes were 15% off and you save nine dollars what was the original price
Answers
Divide amount saved by percentage:
9/0.15 = 60
The original price was $60
Answer:$60
Step-by-step explanation:
9/15=0.6
0.6=1%
0.6*10=$60
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=-16x^2+275x+127
Answers
Answer:
1308.6 feetStep-by-step explanation:
Given is the quadratic equation
y= -16x^2 + 275x + 127It has the maximum height at its vertex, x-coordinate of which is calculated by the formula:
x = -b/2ax = -275/2(-16) = 8.6 rounded to the nearest tenthsCalculating the highest point:
y = -16(8.6)^2 + 275(8.6) + 127 = 1308.6 feet rounded to the nearest tenthsthere are 12 flowers and Sasha garden and she picks 3 flowers for her father then she picks 2 flowers for her mother how many flowers are in the garden now
Answers
Answer:
7 FLowers
Step-by-step explanation:
If you take away 3 from 12, you end up with 9, then you take 2 more away, leaving you with 7 flowers.
A and B start toward each other at the same time from points 150 miles apart.
If A went at the rate of 20 miles an hour, at what rate must B travel if they
meet in 5 hours?
Answers
Answer:
B must travel at the rate of 10 miles per hour.
The speed at which B should travel is 10 mph
What is Speed?
Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the distance between A and B be D = 150 miles
Now , the equation will be
The speed of A = 20 mph
Let the speed of B be = B
The time required T = 5 hours
From the equation , Distance = Speed x Time
Substituting the values in the equation , we get
150 = ( A x T ) + ( B x T )
20 x 5 + ( B x 5 ) = 150
On simplifying the equation , we get
100 + 5B = 150
Subtracting 50 on both sides of the equation , we get
5B = 50
Divide by 5 on both sides of the equation , we get
B = 10 mph
Therefore , the value of B is 10 mph
Hence , the speed of B is 10 mph
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What is 19 less than a variable n
Answers
Answer:
-19+n
OR
n-19
Step-by-step explanation:
Which point is located at (Negative 0.5, 0.75)? On a coordinate plane, point B is 0.75 units to the right and 0.5 units down. Point G is 0.75 units to the right and 0.5 units up. Point M is 0.5 units to the left and 0.75 units down. Point Z is 0.5 units to the left and 0.75 units up. point B point G point M point Z hurry
Answers
Answer:
It’s b
Step-by-step explanation:
Which is point g
Answer:
Z
Step-by-step explanation:
What is the slope of the line that crosses points (6, 9) and (10, 11)
Answers
[tex]slope\; is\; unknown~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[/tex]
Answer:
2/4 or 1/2
Step-by-step explanation:
slope is rise/run, so count how many points are between your x-values and how many are between your y-values. there are 4 points between the x's and 2 between the y's.
y-axis is the rise because it goes up and down
x-axis is the run because it's horizontal
rise/run= 2/4= 1/2 because you always simplify.
James, Priya, and Siobhan work in a grocery store. James makes $9.00 per hour. Priya makes 40% more than James, and Siobhan makes 5% less than Priya. How much does Siobhan make per hour?
Siobhan makes $ per hour.
Answers
Answer:
$7.98 per hour
Step-by-step explanation:
Help me please hurry up
Answers
machine 2: Y=3/4x+0
2. i believe machine 2 is moving faster since it’s moving at a 0.75 and machine 1 is moving at 0.6 :)
Emma and her children went into a restaurant where they sell hotdogs for $4 each and drinks for $1.50 each. Emma has $30 to spend and must buy no less than 9 hotdogs and drinks altogether. If xx represents the number of hotdogs purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Answer:
6 hotdogs and 4 drinks
Step-by-step explanation:
4x + 1.50y = 30
For questions like this, you can do the equation that represents the price of the products first.
x + y [tex]\geq[/tex] 9
After that, you can write the equation that represents the quantities.
Now, you just have to graph it to find the solution. When you're graphing, make sure that y is alone on one side. Here's how you rearrange the equations:
The first equation:
4x + 1.50y =30
*Subtract 4x from both sides, which leads to:
1.50 y = -4x + 30
*Divide by 1.50 on both sides, which leads to:
y = -2.66x + 20
The second equation:
x + y [tex]\geq[/tex] 9
*Subtract x from both sides, which leads to:
y [tex]\geq[/tex] -1x + 9
Now, use any graphing calculator (I prefer Desmos) to graph these two equations. In fact, you can just graph it on paper, too.
Here is the graph: (it is attached as a file)
You can look for any points that are on the red line but are also shaded blue. Make sure you look only in Quadrant 1- don't go into the negatives! One good point to choose would be (6,4)- this means that you buy 6 hotdogs and 4 drinks.
Answer:
[tex]y\geq 9-x[/tex] shaded up
[tex]y\leq 20-\frac{8}{3} x\\[/tex] shaded down
4 hotdogs, 8 drinks
Step-by-step explanation:
Carlos can run 5 miles in 45 minutes, Kelly can run 10 miles in 80 minutes, and Mick can run 30 miles in 170 minutes
Answers
Answer:
Mick can run farther in less time if that's the question
Step-by-step explanation:
Mick's speed is faster.
What is speed?Speed is the ratio of distance and time.
It shows how fast an object is moving at a given time.
We have,
Carlos can run 5 miles in 45 minutes.
45 minutes = 45/60 = 0.75 hours
Speed.
= 5/0.75
= 6.66 miles per hour.
Kelly can run 10 miles in 80 minutes.
80 minutes = 1.33 hours
Speed.
= 10/1.33
= 7.5 miles per hour.
Mick can run 30 miles in 170 minutes
170 minutes = 2.8 hours
Speed.
= 30/2.8
= 10.7 miles per hour
Thus,
Mick's speed is faster.
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I need help like omg ....I’ve been asking for a tutor or if someone Is willing to help me I am not a bot ima real person .... i just need help with my math I swear !
Answers
Answer:
(0, -6) (-7, 9)
Step-by-step explanation:
I recommend watching a khan academy video, its how I learned, cause I don't really know how to explain it on here
3. Is the line through points P(0, -9) and Q(2, -8) perpendicular to the line through points R(1,4) and S(3, 3)?
Explain.
Answers
Answer:
no
Step-by-step explanation:
1. to make up the equations of lines PQ and RS:
(PQ) [tex]\frac{x-0}{2} =\frac{y+9}{1}; \ \frac{x}{2}=\frac{y+9}{1};[/tex]
(RS) [tex]\frac{x-1}{-2}=\frac{y-4}{1}; \ \frac{x-1}{-2}=\frac{y-4}{1};[/tex]
2. to write the pointed verctors of PQ and RS:
for PQ it is p=(2;1); for RS it is r=(-2;1).
3. according to the pointed vectors it is clear, the given lines are not perpendicular [2*(-2)+1*1≠0].
If your car gets 34 miles per gallon, how much does it cost to drive 370 miles when gasoline costs $3.30 per gallon?
The cost is $
nothing.
(Simplify your answer. Round to the nearest cent as needed.)
Answers
Answer:
15
Step-by-step explanation: