Answer:
(x+5)^2
Step-by-step explanation:
(x+5)^2 Using the foil method 5+5=10 and 5x5=25
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:
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
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
Solution to the systems of equations,
g(x)=3x+2
f(x)=|x-1|+1
Hi there! :)
[tex]\large\boxed{\text{ x = 0, or (0, 2)}}[/tex]
The solution of g(x) = 3x + 2 and f(x) = |x - 1| + 1 is where the two lines intersect.
According to the graph, the functions intersect at the point (0, 2), or x = 0. This is the solution to the system of equations.
We could also prove this algebraically by setting the two equations equal to each other:
3x + 2 = | x - 1 | + 1
Assume the absolute value function is negative:
3x + 2 = -(x - 1) + 1
Simplify:
3x + 2 = -x + 2
Add x to both sides:
4x + 2 = 2
Subtract 2 from both sides:
4x = 0
x = 0. This is the solution to the system.
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)
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
Suppose a force of 100 newtons is used to push an object a distance of 5.0 meters in 15 seconds. Find the work done and the power for this situation.
work=force* distance
=100*5
=500 joules
=500/15
=33.33 Watts.
1/2 of _______ = 62
AnSwEr PlS
Answer:
124
Step-by-step explanation:
You can find this answer by simply multiplying 62 by 2. lol
$99.99, 19% discount
Answer:
$80.99
Step-by-step explanation:
Turn the percentage into a decimal.
19% -> 0.19
Multiply.
99.99 * 0.19 ≈ 19
Subtract.
99.99 - 19 = 80.99
Best of Luck!
at what points is the function y= cosx/4x continuous
Jeffrey needs $200 to buy a new iPod. Right now, he has $75. What percent of the $200 does he have?
PLEASE HELPPP
Answer:
40%
Step-by-step explanation:
Answer:
If you need help on further questions like this, divide what he has to what he needs or his goal
in order to get 37.5% you have to divide 75/ 200
You will get 0.357 and that is 37.5% this is ABOUT 40% but I reccomend putting 37.5% to be safe.
A meteorologist said that is was sunny for 70% of the
days the past 60 days.
On how many days was it NOT sunny?
If the perimeter of this trlangle is 15 centimeters, what is the value of n? 5n - 6 2n + 1 Express your answer as a decimal number. n =
Answer:
n =1.78
Step-by-step explanation:
2(5n-6)
2(n+1)
10n-12+4n+2=15
14n-10=15
subtract both sides by 10
14n=25
25/14
n=n =1.78571428571
plzzzzz help me brainlest
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 study suggested that childrenbetween the ages of 6 and 11 in the US have anaverage weightof 74 lbs. with a standard deviation of 2.7 lbs.If we assumethe weights are normally distributed, what proportion of childrenin this age range between 70 lbs. and 85 lbs.
Answer:
The proportion of children in this age range between 70 lbs and 85 lbs is of 0.9306.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A study suggested that children between the ages of 6 and 11 in the US have an average weightof 74 lbs, with a standard deviation of 2.7 lbs.
This means that [tex]\mu = 74, \sigma = 2.7[/tex]
What proportion of childrenin this age range between 70 lbs and 85 lbs.
This is the pvalue of Z when X = 85 subtracted by the pvalue of Z when X = 70. So
X = 85
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{85 - 74}{2.7}[/tex]
[tex]Z = 4.07[/tex]
[tex]Z = 4.07[/tex] has a pvalue of 1
X = 70
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{70 - 74}{2.7}[/tex]
[tex]Z = -1.48[/tex]
[tex]Z = -1.48[/tex] has a pvalue of 0.0694
1 - 0.0694 = 0.9306
The proportion of children in this age range between 70 lbs and 85 lbs is of 0.9306.
A number squared minus fifteen times the number is equal to 16. Write the equation and give the factors.
[tex]\huge{\mathfrak{\purple{Answer}}}[/tex]
Equation: x² - 15x = 16
Factors: x = -16 and x = 1
[tex]\huge{\mathfrak{\purple{Explanation}}}[/tex]
Given
A number squared minus fifteen times the number is equal to 16.
Equation: x² - 15x = 16
Factors:
x² - 15x - 16 = 0
So,
(x - 16) (x + 1)
=> x - 16 = 0, x + 1 = 0
= x = -16 and x = 1
#HopeItHelps
What is the area of a perimeter with 12 cm?
Answer:
shape name is it square or rectangle is needed to be told
Step-by-step explanation:
if it's square then area is 9cm^2
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 family-size pizza is $32 and costs 4 times as much as a small pizza. Steve buys two family-size pizzas and 4 small pizzas. How much does he spend in all?
A. $64
B. $86
C. $80
D. $96
What is the area of the shaded region?
Answer:
66ft^2
Step-by-step explanation:
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
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
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.
PLS HELP GIVING BRAINLESS TO CORRECT PERSON PLS HELP ASAP
Answer:
Correct Answer - It shows the unit rate of the graph in miles per hour.
Step-by-step explanation:
hope this helps
Enter an equation for the word sentence. Use the variable n.
The sum of a number and 4.4 is 8.1.
Answer:
[tex]n + 4.4 = 8.1[/tex]
Step-by-step explanation:
We know we have to write an algebraic equation for the sentence - so "translate" the phrases of the sentence step-by-step. Let the unknown number be represented by the variable n, as the question states.
Start with the phrase "the sum of a number and 4.4." A sum comes as a result of adding numbers together - therefore the first part of the equation must be [tex]n + 4.4[/tex].
Next, the sentence says "is 8.1." The "is" indicates that the expression we just wrote equals something, so that number must be 8.1. Therefore, the whole equation must be [tex]n + 4.4 = 8.1[/tex].
At a football game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 455 people attending the game supported the home team, what was the total number of people attending the game? Help me plz:))
Answer:
1300
Step-by-step explanation:
What is the value of (.5)^4
Answer:
0.0625 should be the answer of .5 to the fourth power.
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
Please help me with this. I give brainliest and give ratings. Don't answer just to take my points or your getting reported.
