Answer:
The answer is "6.093 years".
Step-by-step explanation:
The rate of decline in sales in [tex]22\%[/tex] per year.
The starting sales is 100 units:
Using compounding formula:
[tex]\to 100 \times (1-\frac{22}{100})^t=22\% \ of \ 100\\\\\to 100 \times (\frac{100-22}{100})^t=\frac{22}{100} \times \ 100\\\\\to (\frac{78}{100})^t=\frac{22}{100}\\\\\to 0.78^t=0.22\\\\\text{taking \log on both the sides}\\\\[/tex]
taking log on both sides
[tex]\to \log_e \ 0.78^t= \log_e\ 0.22\\\\\to t \log_e \ 0.78= \log_e\ 0.22\\\\\to t = \frac{\log_e 0.22}{\log_e 0.78}\\\\[/tex]
[tex]= \frac{-0.6575}{-0.1079}\\\\= \frac{0.6575}{0.1079}\\\\=6.093[/tex]
The temperature of a cup of coffee varies according to Newton's Law of Cooling: -"dT/dt=k(T-A), where is the temperature of the coffee, A is the room temperature, and k is a positive
constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25*C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes,
74
67
60
42
Answer:
B) 67°C.
Step-by-step explanation:
Newton's Law of Cooling is given by:
[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]
Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.
And we want to find the temperature of the coffee after four minutes.
First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:
[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]
Take the integral of both sides:
[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]
Integrate:
[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]
Raise both sides to e:
[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]
The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:
[tex]\displaystyle T=Ce^{kt}+A[/tex]
We are given that A = 25. Hence:
[tex]\displaystyle T=Ce^{kt}+25[/tex]
Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:
[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]
Hence:
[tex]T=75e^{kt}+25[/tex]
We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.
So, T = 90 given that t = 1. Substitute:
[tex]90=75e^{k(1)}+25[/tex]
Solve for k:
[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]
Therefore:
[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]
Then after four minutes, the temperature of the coffee will be:
[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]
Hence, our answer is B.
PLS HELP ILL GIVE U BRAINLIEST HURRY!!!!!!!
Anna, Bob and Chris are altogether 31 years old. How old will all three be altogether in three years time? (A)32 (B)34 (C)35 (D)37 (E)40
Answer:
40
Step-by-step explanation:
A+B+C = 31
Add 3 years to each age
A+3 +B+3 + C+3 = 31 +3+3+3
They will be
A+3 +B+3 + C+3 = 40
Answer:
it will be 40
Step-by-step explanation:
If they are altogether 31 years old now in 3 years we just add 9 thus it is 40
which of the following must be true to prove Δ ABC≅Δ DEF by the AAS theorem?
A. C∠≅∠F
B. ∠B≅∠E
C. ∠E≅∠F
D.∠B≅∠C
Answer:
b must be because the therom is aas so
Answer:
B is answer
Step-by-step explanation:
just did it
Your plane leaves Boston (Eastern Standard Time) at 7:00am, bound for Los Angeles (Pacific Standard Time). The flight takes 5 hours. What is time when you arrive in Los Angeles
Answer:
The plane arrives Los Angeles at 9:00 am
Step-by-step explanation:
The Pacific Standard Time (PST) in Los Angeles is 3 hours earlier than the Eastern Standard Time (EST) in Boston
Therefore,
7:00 am at Boston = 4:00 am in Los Angeles
If the plane takes 5 hours
What is time when you arrive in Los Angeles
The plane arrives Los Angeles at 4:00 am + 5:00 hours
= 9:00 am
The plane arrives Los Angeles at 9:00 am
answer both of them please
Answer:
-5.5+2=x should be equal to 3.5 on the number line and as for the other question it is D) It is a decimal that terminates after three decimal places
Step-by-step explanation:
When graphing -5.5+2=x it equals to 3.5 on the Domain and the other question you just divide the numerator to its denominator equaling you with 0.875
Find X in this question
Answer:
Step-by-step explanation:
∠1 = 38 {Vertically opposite angles}
∠2 = 39 + 36 = 75
Exterior angle equals the sum of opposite interior angles.
x = ∠1 +∠2
= 38 + 75
x = 113
What percentage of 1hour is 6munites 20seconds
Answer:
10
Step-by-step explanation:
10 percentage for this question answer
Carmen likes to ski. The ski resort where she goes to ski got 3.2 feet of snow during a 5 day period. The average daily snowfall for a given number of days is the quotient of the total amount of snow and the number of days. Estimate the average daily snowfall.
Answer:
0.64 feet or 7.68 inches of snow on average over the 5 days.
Step-by-step explanation:
3.2/5
0.64ft
7.68in.
solve g(x)=(the square root of x+1)+3
Step-by-step explanation:
solve for what ?? do you mean graph the function??
Which of the equations below have the decimals aligned correctly? Check all that apply.
3.012
+ 4.21
6.71
+ 1.40
12.315
- 0.129
32.002
12.32
Answer:
B and C
Step-by-step explanation:
Decimals are well aligned when performing arithmetic operations if the equations are arranged in such a way that the decimal points are exactly vertically arranged, each following each other. This will ensure the right answer is gotten. Each place value is placed on the same vertical line on each other.
The equation in option B is correctly aligned. Because the decimal points are in the same vertical line and also the equation in option C.
7r-15/s when r= 3 and s = 5.
Answer:
21-3=18
Hope This Helps!!!
Answer:
18
Step-by-step explanation:
7(3)= 21
15/5=3
21-3=18
HELP CONGRUENCE BY SAS AND SSS WILL GIVE BRAINLIEST IF CORRECT
Answer:
1. Cong SSS 2.Cong SSS 3.Not Cong 4.Not Cong 5.Cong SAS 6.Cong SSS 7.Cong SAS 8.Cong SSS 9.Cong SSS 10.Cong SAS 11.d 12.a 13.a 14.b 15.a
Step-by-step explanation:
What is the solution for this equation:
Answer:
c) x=126
Step-by-step explanation:
tell me if I get it right
The graph of f(x) = −x2 − 2x + 8 is shown. Which of the following describes all solutions for f(x)?
a parabola passing through negative 4 comma zero, negative 1 comma 9, zero comma 8, and 2 comma zero
A. (x, −x2 − 2x + 8) for all real numbers
B. (−4, 0), (−1, 9), (0, 8), (2, 0)
C. (−4, 0), (2, 0)
D. (x, y) for all real numbers
Answer: C. (−4, 0), (2, 0)
Step-by-step explanation:
By solution, I believe it means the roots of the equation(aka zeros), meaning the points where the graph intersects the x-axis(aka x-intercepts). It intersects at two points: (−4, 0) and (2, 0)
Answer:
A) (x, −x2 − 2x + 8) for all real numbersStep-by-step explanation:
I got it right on my 8.06 exam! ✨ Keep believing, superstar!
and go see Sing 2 for me..its an awesome movie and it'll make u smile!
Amelia, Luis, Shauna, and Clarence used different approaches to solve the inequality
7.2b + 6.5 > 4.8b – 8.1.
Amelia started by subtracting 7.2b from both sides to get 6.5 > –2.4b – 8.1.
Luis started by subtracting 4.8b from both sides to get 2.4b + 6.5 < – 8.1.
Shauna started by subtracting 6.5 from both sides to get 7.2b > 4.8b – 14.6.
Clarence started by adding 8.1 to both sides to get 7.2b + 14.6 > 4.8b.
Which student’s first step was incorrect, and why?
Amelia’s, because the variable term must be isolated on the left side
Luis’s, because he flipped the inequality sign when he subtracted
Shauna’s, because she did not apply the subtraction property of equality properly
Clarence’s, because the terms he added together were not like terms
Answer:
Luis’s, because he flipped the inequality sign when he subtracted
Step-by-step explanation:
7.2b + 6.5 > 4.8b – 8.1.
Amelia started by subtracting 7.2b from both sides to get
6.5 > –2.4b – 8.1
Correct
Luis started by subtracting 4.8b from both sides to get
2.4b + 6.5 < – 8.1
Incorrect
Shauna started by subtracting 6.5 from both sides to get
7.2b > 4.8b – 14.6
Correct
Clarence started by adding 8.1 to both sides to get
7.2b + 14.6 > 4.8b
Correct
Luis’s is incorrect because he flipped the inequality sign when he subtracted
The Marked price of an article was fixed to Rs 1380 by increasing 15% on its actual price. Find the actual price.
Answer:
The actual price of the article was Rs. 1200.
Step-by-step explanation:
mp (marked price)
ap (actual price)
[tex]mp = 1380[/tex]
[tex]mp = ap + 15\%(ap)[/tex]
[tex]1 380 = ap + \frac{15}{100} ap[/tex]
[tex]1380 = \frac{100}{100} ap + \frac{15}{100} ap[/tex]
[tex]1380 = \frac{115}{100} ap[/tex]
[tex]1380 \div \frac{115}{100} = ap[/tex]
[tex]1380 \times \frac{100}{115} = ap[/tex]
[tex] \frac{138000}{115} = ap[/tex]
[tex]1200 = ap[/tex]
The actual price of the article is given by the equation A = $ 1,200
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the actual price of the article be A
Now , the equation will be
The marked price of the article be = $ 1380
The percentage of increase from the actual price = 15 %
So , the equation is
The actual price + percentage of increase from the actual price = 1380
Substituting the values in the equation , we get
A + ( 15/100 )A = 1380 be equation (1)
( 115/100 ) A = 1380
Multiply by 100 on both sides of the equation , we get
115A = 138000
Divide by 115 on both sides of the equation , we get
A = $ 1200
Therefore , the value of A is $ 1200
Hence , the actual price of the article is $ 1200
To learn more about equations click :
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A stereo was originally priced at 75.50. it was marked down 24%. a store had a big sale of 60% off the lowest marked price. what was the final price of the stereo
Answer:
We can calculate the price with both sales by multiplying the 75.5 units of money by both percentages (to multiply them, we divide them by 100 first):
75.5 * 0.24 * 0.6 [tex]\approx.[/tex] 10.8
What is the length of the unknown leg in the right triangle…?
As we know,
In a triangle, the sum of lengths of two side is greater than the third side.
[tex]20 + 25 > b[/tex]
[tex]b + 20 > 25[/tex]
[tex]25 + b > 20[/tex]
Answer = 15m
PLEASE ANSWER CORRECTLY FOR BRAINLIEST:
25.
26.
27.
29.
Answer:
x = 6
Step-by-step explanation:
5 (x - 3) + 2 = 5 (2x - 8) - 3
remove the parenteses
5x - 15 + 2 = 10x - 40 - 3
calculate5x - 13 = 10x - 43
move the terms5x - 10x = -43 + 13
collect like terms calculate-5x = -30
divide both sidesSolution
x = 6
Sam studied guinea pigs for his science fair project. He found that the amount of weight the guinea pigs gained varied directly with the number of calories they consumed.
The guinea pigs gained 1 ounce for every additional 218 calories in their diet. How many additional ounces would they gain if their diet was increased by 1,090 calories? Let W represent the weight in ounces, and let C represent the number of calories.
Answer: C= 1,090 and the W= 5.
What is the final step in solving the inequality –2(5 – 4x) < 6x – 4? x < –3 x > –3 x < 3 x > 3
Answer:
x > 3
Step-by-step explanation:
Given the inequality :
-2(5 – 4x) < 6x – 4
Expand the equation in bracket :
-10 + 8x < 6x - 4
Collect like terms
-10 + 4 < 6x - 8x
-6 < - 2x
Divude both sides by - 2
-6 / - 2 < - 2x / - 2
3 < x
x > 3
Which statement about y= 7x2 + 23x + 6 is true?
Answer:
Please include the statements too
URGENTTTTTTTT!! HELP QUICK PLZZZZZZZZz
Explanation:
The phrasing "given that he or she is a graduate" means we focus on the middle row only. We ignore everything else.
We see that A = 1879 graduates receive financial aid out of B = 2610 graduates total.
This means the probability we want is therefore A/B = 1879/2610 = 0.7199 approximately. This converts to 71.99% and that rounds to 72%
The parallel chord lie on opposite sides of the center of a circle of radius 13cm. Their lengths are 10cm and 24cm respectively. What is the between the chords
We are required to find the distance between both chords.
Answer:
17 cm
Step-by-step explanation:
The two chords are parallel to each other.
This means that a perpendicular line drawn from the centre of the circle will divide both of them into 2 equal sides.
This is depicted in the image attached.
From the Image,the diagonal drawn from one end of either chord through the centre will form the hypotenuse side of either chords.
Thus, using pythagoras theorem, we have for the chord that has a length of 10 cm. Perpendicular distance from centre of chord to centre of circle is;
d = √(13² - 5²)
d = √144
d = 12
Similarly, for chord with length = 24 cm, we have;
d' = √(13² - 12²)
d' = √25
d' = 5
Therefore, distance between chords = d + d' = 12 + 5 = 17 cm
What is the slope of the graph shown below
Answer:
B=-5
Step-by-step explanation:
Slope=rise/run
The line passes in
P1(-1,3)
and
P2(0,-2)
So slope=(3-(-2))/(-1-0)=5/-1=-5
When CP = Rs 1250 and SP = Rs 1500, find profit or loss percent ?
Answer:
profit=20%
Step-by-step explanation:
profit%=sp-cp/cp×100%
=1500-1250/1250×100
=250/1250×100
=20%
Nathan is 1.55 meters tall. At 1 p.m., he measures the length of a tree's shadow to be 38.15 meters. He stands 32.9 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .
Answer:
11.26 m
Step-by-step explanation:
The height of the tree is about 11.25 meters.
What are similar triangles?When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.
Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.
Let the height of the tree be x.
Note that the scenario makes two similar triangles.
Since the ratio of the side lengths of similar triangles is proportional, it follows:
(38.15 - 32.9)/1.55 = 38.15/x
5.25/1.55 = 38.15/x
3.39 = 38.15/x
x = 38.15/3.39
x = 11.25
Hence, the height of the tree is about 11.25 meters.
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Which graph represents the function of f(x) = 4x² - 4x -8/2x+2.
Answer:
I think that second option represents the function of f(x) = 4x² - 4x -8/2x+2.
Can someone explain how to do this please?
for the columns where is less than or equal zero, use the first line of the function to calculate the value of f(x)
[tex] { ( \frac{1}{3} ) }^{ - 2} - 1 = 9 - 1 = 8 \\ { ( \frac{1}{3} ) }^{ - 1} - 1 = 3 - 1 = 2 \\ { ( \frac{1}{3} ) }^{ 0} - 1 = 1 - 1 = 0[/tex]
for every x greater than zero, use the second line to determine the value
[tex] {3}^{1} - 2 = 3 - 2 = 1 \\ {3}^{2} - 2 = 9 - 2 = 7[/tex]
hope this helps and gives some insight what to do.
if there are open questions left, feel free to ask them in the comments
have a beautiful day
-Alex
