In a sports meet, Sonam’s team completes the run at 40 seconds during heat events. On championship day, his team completes the same run at 45 seconds. What is the percentage difference in the completion time from the best completion time?
A. 10.5%
B. 12.5 %
C. 15.5 %
D. 20.5 %
Answer:
20.5
Step-by-step explanation:
line a y=1/2x+2
line b y= -1/2 x +7
line c y=2x +4
line d y= 1/2x +5/4
which lines are perpendicular
Answer:
Line b and line c are perpendicular.
Step-by-step explanation:
Perpendicular lines have opposite reciprocal slopes, and -1/2 and 2 are opposite reciprocals.
A brine solution of salt flows at a constant rate of 4 L/min into a large tank that initially held 100 L of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 3 L/min. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach 0.1 kg/L?
Answer:
a. [tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex] b. 7.44 s
Step-by-step explanation:
a. If the concentration of salt in the brine entering the tank is 0.2 kg/L, determine the mass of salt in the tank after t min.
Let m(t) be the mass of salt in the tank at any time, t.
Now, since a brine solution flows in at a rate of 4 L/min and has a concentration of 0.2 kg/L, the mass flowing in per minute is m' = 4 L/min × 0.2 kg/L = 0.8 kg/min
Now, the concentration in the tank of volume 100 L at any time, t is m(t)/100 L. Since water flows out at a rate of 3 L/min, the mass flowing out per minute is
m(t)/100 × 3 L/min = 3m(t)/100 kg/min
Now the net rate of change of mass of salt in the tank per minute dm/dt = mass flowing in -mass flowing out
dm/dt = 0.8 kg/min - 3m(t)/100 kg/min
So, dm/dt = 0.8 - 0.03m(t)
The initial mass of salt entering m(0) = 0 kg
dm/dt = 0.8 - 0.03m(t)
separating the variables, we have
dm/[0.8 - 0.03m(t)] = dt
Integrating, we have
∫dm/[0.8 - 0.03m(t)] = ∫dt
-0.03/-0.03 × ∫dm/[0.8 - 0.03m(t)] = ∫dt
1/(-0.03)∫-0.03dm/[0.8 - 0.03m(t)] = ∫dt
-1/0.03㏑[0.8 - 0.03m(t)] = t + C
㏑[0.8 - 0.03m(t)] = -0.03t - 0.03C
㏑[0.8 - 0.03m(t)] = -0.03t + C' (C'= -0.03C)
taking exponents of both sides, we have
[tex]0.8 - 0.03m(t) = e^{-0.03t + C'} \\0.8 - 0.03m(t) = e^{-0.03t}e^{C'}\\0.8 - 0.03m(t) = Ae^{-0.03t} A = e^{C'}\\0.03m(t) = 0.8 - Ae^{-0.03t}\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\when t = 0 \\m(0) = 0\\m(0) = 26.67 - \frac{A}{0.03} e^{-0.03(0)}\\\\0 = 26.67 - \frac{A}{0.03} e^{0}\\26.67 = \frac{A}{0.03} \\\frac{A}{0.03} = 26.67\\\frac{A}{0.03} = 6.67\\A = 26.67 X 0.03\\A = 0.8\\m(t) = 26.67 - \frac{A}{0.03} e^{-0.03t}\\\\m(t) = 26.67 - \frac{0.8}{0.03} e^{-0.03t}\\[/tex]
So, the mass of the salt after t min is
[tex]m(t) = 26.67 - 26.67e^{-0.03t}[/tex]
b. When will the concentration of salt in the tank reach 0.1 kg/L?
When the concentration of the salt reaches 0.1 kg/L, m(t) = 0.1 kg/L
Solving the equation for t,
[tex]m(t) = 26.67 - 6.67e^{-0.03t}\\0.1 = 26.67 - 26.67e^{-0.03t}\\26.67e^{-0.03t} = 26.67 - 0.1\\26.67e^{-0.03t} = 26.57\\e^{-0.03t} = 26.56/26.67\\e^{-0.03t} = 0.9963\\[/tex]
taking natural logarithm of both sides, we have
-0.03t = ㏑0.9963
-0.03t = -0.0038
t = -0.0038/-0.03
t = 0.124 min
t = 0.124 × 60 s
t = 7.44 s
Pls help I’ll brainlest and add extra points for the right answer
Answer:
First blank: Divide
Second blank: Multiply
Third blank: 25
Step-by-step explanation:
For the first part, you would divide to get X as itself
For the second part, you would multiple to cancel out the fraction and be left with whole numbers, which is much easier to work with
1.3 x 25 = 32.5, so that would be that answer
3x + 2y = 22 −x + 4y = 2
Answer:x=11/2+y/2
Step-by-step explanation:
The solution of the given system of equation would be (6, 2)
What is a system of equations?Two or more equations to be solved together, i.e., the solution must satisfy all the equations in the system.
We have Given the equations, 3x + 2y = 22
-x + 4y = 2
Solving by elimination, Multiplying the second equation by 3,
3x+2y = 22
-3x + 12y = 6
Adding the equation, we get;
2y+12y = 22+6
24y = 28
y = 2
Putting y=2 we get;
3x+2*2=22
3x+4 = 22
3x = 18
x = 6
Hence, The solution is (6, 2)
For more references on system of equations, click;
brainly.com/question/24065247
#SPJ2
Suppose that a football coach gets a salary of one million dollars now, and a raise of 10% every year (so exponential growth model). Let s be the salary in millions of dollars, and t is time in years. (a) Write an initial value problem to represent the salary s. Label 0.2.14 (modified) (b) What is s(0) and s(1)
Answer:
a)
initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]
b)
S(0) = 1
Therefore; S(0) is 1 million dollar
S(1) = 1.105170918075647
Therefore; S(1) is 1.105170918075647 million dollar
Step-by-step explanation:
Given that;
Initial salary of football coach = 1 million dollar
raise of 10% every year (so exponential growth model) r = 10% = 0.10
a) initial value problem to represent the salary
lets S represent salary in millions dollars and t represent time in years.
S(t) = S₀[tex]e^{rt}[/tex]
so,
at S₀ = 1 million dollars } { r = 0.10 }
S(t) = 1.[tex]e^{0.10t}[/tex]
Therefore, initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]
b) What is s(0) and s(1)
at s(0)
S(t) = 1.[tex]e^{0.10t}[/tex]
we substitute
S(0) = 1.[tex]e^{0.10*0}[/tex]
S(0) = 1.[tex]e^{0}[/tex]
S(0) = 1
Therefore; S(0) is 1 million dollar
at s(1)
S(t) = 1.[tex]e^{0.10t}[/tex]
we substitute
S(1) = 1.[tex]e^{0.10*1}[/tex]
S(1) = 1.[tex]e^{0.10}[/tex]
S(1) = [tex]e^{0.10}[/tex]
S(1) = 1.105170918075647
Therefore; S(1) is 1.105170918075647 million dollar
Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax?
Answer:
7.48
Step-by-step explanation:
find what 6% of 7.95 is and then subtrct that from 7.95 which gives u ur answer
1/2 of _______ = 62
AnSwEr PlS
Answer:
124
Step-by-step explanation:
You can find this answer by simply multiplying 62 by 2. lol
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PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
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PLS SHOW THE WORK!!!!!!!!
Answer:
x=-4/11; y=-19/11
Step-by-step explanation:
Answer:
x = 4/11 ; y = 19/ 11
sorry i cant give you the explanation
i hope this will help u
pls add me as bainliest
Step-by-step explanation:
What dose that sing mean before the square root mean and also what is the answer
The thing before the square root means that the answer can be positive and negative.
(45 + 33) +7 = 45 + (33 + 7)
What property is that
Answer:
Associative
Step-by-step explanation:
I need help due in 10 minutes ah!
Answer:
30
Step-by-step explanation:
If CUB is 78 and that’s the full angle just to 48 minus 78 and you get your answer.
Given that, 1 Chinese yuan = £0.11, convert £460 into Chinese yuan. Give your answer to the nearest yuan.
will mark you as brainiest
Answer:
i so want to know this aswell
Step-by-step explanation:
Answer:
4182
Step-by-step explanation:
I gotten this question so I decided to find the answer but I still got it wrong and it said the answer was 4182
You want to buy a specific computer. A sales representative of the manufacturer claims that retail stores sell this computer at an average price of $1,249 with a very narrow standard deviation of $25. You find a website that has a price comparison for the same computer at a series of stores as follows:
$1,298; $1,229.96; $1,193.07; $1,279; $1,224.98; $1,229.97; $1,269.98; $1,248.
Can you argue that pricing has a larger standard deviation than claimed by the manufacturer?
Answer:
We fail to reject the null
Step-by-step explanation:
Given the data: 1298; 1229.96; 1193.07; 1279; 1224.98; 1229.97; 1269.98; 1248
Mean price, μ = 1249
Standard deviation, σ = 25
Variance, σ² =
Null hypothesis, H0 : σ² = 25²
Alternative hypothesis, H1 : σ² > 25
Using calculator, the sample standard deviation :
Sample standard deviation = s = 34.072
Sample size, n = 8
For chi² distribution :
X² = [(n - 1)s²] ÷ σ²
X² = [(8 - 1)*34.072^2] ÷ 25^2
X² = (7 * 1160.901184) / 625
X² = 13.002093
Using the Pvalue from Chisquare calculator, df = 8 - 1 = 7; α = 0.05
Pvalue =0.07206
0.07206 > 0.05
Since , Pvalue > α
We fail to reject the null; there is insufficient evidence to conclude that standard devuatue do selling a computer is greater than 25
ZA and ZB are vertical angles. If mZA= (5x – 4) and mZB = (2x – 1)º, then find the value of x. INI
Answer:
x = 1
Step-by-step explanation:
It is given that,
∠A and ∠B are vertical angles.
∠A = (5x – 4) and ∠B = (2x – 1)
We need to find the value of x.
We know that, the vertical angles are equal. So,
∠A=∠B
(5x – 4)=(2x – 1)
Taking like terms together,
5x-2x = 4-1
3x=3
x = 1
So, the value of x is equal to 1.
Two cities are approximately 350 miles apart on the surface of the earth. Assuming that the radius of the earth is 4,000 miles, find the radian measure of the central angle with its vertex at the center of the earth that has one city on one side and another one on the other side. a. 0.0775 radians b. 0.1025 radians c. 0.0875 radians d. 0.0825 radians e. 0.1075 radians ____ 6. Name the reference angle in both degrees and radians.
Answer:
[tex]\mathbf{\theta = 0.0875 \ radians}[/tex]
Step-by-step explanation:
Given that:
The distance between city A and city B = 350 miles; &
The radius of the earth = 4000 miles
We all know that:
l = rθ
[tex]\theta = \dfrac{l}{r}[/tex]
[tex]\theta = \dfrac{350}{4000}[/tex]
[tex]\mathbf{\theta = 0.0875 \ radians}[/tex]
From l = rθ; recall that l = a
so;
a = rθ
350 = 4000×θ
θ = 350/4000
θ = 35/400 degree
In radians;
θ = (35/400) × (π/180)
θ = (7π /800× 180) radians
A pair of fair dice is cast. Let Edenote the event that the number landing uppermost on the first die is a 1 and let Fdenote the event that the sum of the numbers falling uppermost is 5. Determine whether Eand Fare independent events.Show your calculationsby describing the sample space, theeventsE and F, and combinations of these events as needed.
Answer:
They are not independent
Step-by-step explanation:
Given
E = Occurrence of 1 on first die
F = Sum of the uppermost occurrence in both die is 5
Required
Are E and F independent
First, we need to list the sample space of a roll of a die
[tex]Event\ 1 = \{1,2,3,4,5,6\}[/tex]
Next, we list out the sample space of F
[tex]Event\ 2 = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,\[/tex]
[tex]6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]
In (1): the sample space of E is:
[tex]E = \{1\}[/tex]
So:
[tex]P(E) = \frac{n(E)}{n(Event\ 1)}[/tex]
[tex]P(E) = \frac{1}{6}[/tex]
In (2): the sample space of F is:
[tex]F = \{5,5,5,5\}[/tex]
So:
[tex]P(F) = \frac{n(F)}{n(Event\ 2)}[/tex]
[tex]P(F) =\frac{4}{36}[/tex]
[tex]P(F) =\frac{1}{9}[/tex]
For E and F to be independent:
[tex]P(E\ and\ F) = P(E) * P(F)[/tex]
Substitute values for P(E) and P(F)
This gives:
[tex]P(E\ and\ F) = \frac{1}{6} * \frac{1}{9}[/tex]
[tex]P(E\ and\ F) = \frac{1}{54}[/tex]
However, the actual value of P(E and F) is 0.
This is so because [tex]E = \{1\}[/tex] and [tex]F = \{5,5,5,5\}[/tex] have 0 common elements:
So:
[tex]P(E\ and\ F) = 0[/tex]
Compare [tex]P(E\ and\ F) = \frac{1}{54}[/tex] and [tex]P(E\ and\ F) = 0[/tex].
These values are not equal.
Hence: the two events are not independent
A computer is on sale for 25% off. If the sale price is $449, what was the original price?
Answer:
discount=25%
selling price=$449
original price=?
Step-by-step explanation:
we have
original price=selling price + discount% of original price
original price-discount% of original price=$449
original price (1-25/100)=$449
original price=$449/0.75=$598.66
Step 1 -3(3x+5)-6<6
Step 2. -3(3x+5)<12
Step 3. -9x-15<12
Step 4. -9<27
Step 5. x<-3
Between which two consecutive steps did mike make a mistake
(I understand where the mistake is but I don't know how it wants me to answer the question)
There are five marbles in
a bag. Three are green and
two are yellow You draw a
marble replace it, and then
crow another. What is the
product of choosing two
yelow marbles
Answer:
Step-by-step explanation:
2 to 5 or 2:5
or
2 to 3 or 2:3
A meteorologist said that is was sunny for 70% of the
days the past 60 days.
On how many days was it NOT sunny?
what is 3x4x19x39x4x9x11x10x20squared-10473408000 tee-hee
Answer:
A seizure and a half
Step-by-step explanation:
Answer:
495962981439552000
Jeremy's pizza was cut into 6 equal slices and he ate 4 pieces. Zachary's pizza was cut into 12 equal slices. How many pieces does Zachary need to eat so that he and Jeremy have eaten an equal amount? prove it with a picture
Answer:
8 pieces
Step-by-step explanation:
4/6 x 2 = 8/12
If Zachary wanted to eat the same amount. He would eat 8 pieces.
Zachary will have to eat 8 peices of pizza
Step-by-step explanation:
If you take Jeremys pizza and separate the 4 pieces he were to eat and the two he didn't and cut all of them in half then you would see there are 12 peices in all and that would make the 4 he were to eat 8 slices instead of just 4
plzzzzz help me brainlest
What integer does the arrow indicate?
+
-8
+ +
-6 -5
+
3
+
4
+
7
- 10 -9
-7
-4
-3
-2
-1
0
1
2
5
6
8
9
10
0-14
0-3
06
Answer:
-9
Step-by-step explanation:
Given
See attachment for number line
Required
What does the arrow integer
Represent the value of the arrow with x.
The arrow is on number -9.
This number is what the arrow represents.
Hence:
[tex]x = -9[/tex]
A coordinate plane.Three times a larger number is 30 more than 5 times a smaller number. The sum of the larger number and 5 times the smaller number is 50.Let x be the smaller number and y be the larger number.Create a system and graph it to find the solution.What are the two numbers?x =and y =
Answer:
6 and 20
Step-by-step explanation:
Pls help extra points and mark brainlist
Answer:
80 +30h
Step-by-step explanation:
Answer:
80 + 30h
Step-by-step explanation:
Distribute the 10 over the (8 + 3h). This means: multiply 10 by 8 and by 3h.
10 x 8 = 80
10 x 3h = 30h
10(8 + 3h) = 80 + 30h
Explain the attributes that make a rhombus different from a rectangle
Explain the attributes that make a square different from a rhombus
Answer:
Angles and sides are the main differences! In a rectangle, all angles will be 90 degrees. In a rhombus, opposite angles will always be congruent. And, all sides in a rhombus are congruent, while in a rectangle, opposite sides are congruent
Step-by-step explanation:
here
What is the value of (.5)^4
Answer:
0.0625 should be the answer of .5 to the fourth power.
Solve the given equation for x.
6 + x = C
Answer:
x=c-6
Step-by-step explanation:
6+x=c
-6 -6
x=c-6
