Answer:
Answer
Step-by-step explanation:
step by step Explantation
A tank contains 40 gallons of a solution composed of water and bleach. At the start there are 4 gallons of bleach in the tank. A second solution containing half water and half bleach is added tothe tank at the rate of 4 gallons per minute. The solution is kept throughly mixed and drains from the tank at the rate of 4 gallons per minute.
(a) How much blcach is in the tank after t minutes?
(b) Will there be at least 14 gallons of bleach in the tank after 10 minutes?
(c) How much bleach will there be in the tank after a very long time has passed?
Answer:
a) x* e∧ t/10 = 20 *e∧ t/10 + 2
b) x = 14,2 gall. In 10 min. we get 14,2 gallons of bleach in the tank
c) After a very long time we will find 20 gallons of bleach in the tank
Step-by-step explanation:
The variation of bleach in water in the tank is Δ(x)t:
Δ(x)t = [Amount of x added to the tank - Amount of x drain out of the tank]*Δt
Now the amount of x added to the tank is:
Rate of adding* the concentration
Rate of adding = 4 gallons per minute
Concentration half and half ( water + bleach) = 0,5
Rate of draining = 4 gallons per minute
Concentration of draining: Unknown but can be expressed as:
x(t)/40. According to this
Δ(x)t = [4 * 0,5 - 4 * x(t)/40]*Δt
Dividing by Δt on both sides of the equation and tacking limits we get
dx/ dt = 2 - x / 10
dx/dt + x/10 =2
Multyiplying by e∧ t/10 on both sides
e∧ t/10* [ dx/dt + x/10 ] = 2 *e∧ t/10
To solve it, integrating the first member is
x* e∧ t/10 = 20 *e∧ t/10 + C
for initial condition t = 0
4 = 20 + C
C = -16
a) x* e∧ t/10 = 20 *e∧ t/10 - 16
b) in 10 minutes
x* e∧ t/10 = 20 *e∧ t/10 - 16
x *e = 20*e - 16
x = 20 - 16/e
x = 20 - 16/2,718
x = 20 - 5,88
x = 14,2 gallons.
c) After a very long time we will find 20 gallons of bleach in the tank
One thousand six hundred fifty tickets
were sold at Friday night's football
game. Each adult ticket cost $3.50,
and each student ticket cost $2.00. The
total revenue for ticket sales was
$4,650. Write the pair of equations that
represent the number of a (adult)
tickets and s (student) tickets.
Answer:
a+s=1650, 3.5a+2s=4650
Step-by-step explanation:
a=adult, s=student
a+s=1650 equation 1
3.5a+2s=4650 equation 2
is this true or false
Answer:
False
Step-by-step explanation:
4x + 6 = 30
What is the solution to the equation?
A. X= 4
B. X= 9
C. X = 6
D. X = 24
Nee
Answer:
x<-4
Step-by-step explanation:
PLEASE HELP!!!
Find the area of the regular polygon with the given apothem a and side length s.
pentagon, a = 12.4 cm, s = 18 cm
The area is
cm2
Answer:
496 cm²
Step-by-step explanation:
Area of polygon :
A = 1/2(p * a)
P = perimeter
a = apothem
Perimeter = 5s (pentagon)
s = side length = 18
P = 5 * 18 = 80 cm
a = 12.4
A = 1/2(80 * 12.4)
A = 1/2(992)
A = 496 cm²
What is the lead coefficient of the polynomial below?
3x^2+ 8x + 5
Answer:
The lead coefficient is 8
Step-by-step explanation:
This is because it is the biggest number that is right before the x or that is the coefficient.
The leading coefficient of the polynomial is given by C = 3
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
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 polynomial equation be represented as A
Now , the value of A is
A = 3x² + 8x + 5
On simplifying the equation , we get
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the polynomial 3x² + 8x + 5 has a term with degree 2 (the x² term) and the coefficient of that term is 3
Hence , the lead coefficient of this polynomial is 3
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13. Your school is sponsoring a charity race. Which set of numbers best describes the number of people
who participate in the race?
a. Natural numbers
c. Rational numbers
b. Integers
d. Irrational numbers
Answer:c
Step-by-step explanation:
The set of numbers that best describes the number of people who participate in the race is given by: Option A: Natural numbers.
What are natural numbers, rational numbers, integers and irrational numbers?Natural numbers are: 1, 2, 3, .... Integer numbers are: ...., -2, -1, 0, 1, 2, ... (so it includes positive and negative natural number, and 0 )Rational numbers are numbers which can be written in the form of [tex]\dfrac{a}{b}[/tex]integers. Example: 1/2, 3.5 (which is writable as 7/5) etc.Irrational numbers are those real numbers which are not rational numbers. Example: [tex]\pi, \sqrt{2}[/tex] etc.Know that all natural numbers are integers, all integers are rational numbers. That means, natural numbers are not irrational.
The count of people participating in the race is going to be in integers, but only non-negative.
Actually the correct option would be 'whole numbers' (whole numbers are 0, 1, 2, ... so they include 0 in addition to natural numbers). It is because it may be that no one participates in the race.
But for the given condition, assuming that at least 1 person participates in the race, we deduce that the number of people participating in race is needed to be a natural number. (as people's count can't be negative, or in fractions, or irrational(which doesn't include integers at all) ).
Thus, the set of numbers that best describes the number of people who participate in the race is given by: Option A: Natural numbers.
Learn more about natural numbers here:
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The final three questions
5×45= 225
12×23= 276
276+225= 501
the answer is 501 ^^
Answer:
501
Step-by-step explanation:
my brain duh big brain me little brain you
Simplify the expression
-2(5z -7)
What is the midline of this function? y=
What is the amplitude of this function? Define a function, g, to represent the behavior of the graphed function. g(a)=
NO LINKS.
Answer:
Midline is at y = 0
Amplitude is; A = 1.5
g(a) = 1.5 sin 0.5x
Period = 4π
Max value; y = 1.5
Min value; y = -1.5
Step-by-step explanation:
From the graph, we know that amplitude is highest point of the graph which is 1.5.
Thus, A = 1.5
Now,period from the graph is distance between where the graph repeats which in this case is 2π + 2π = 4π
Now, equation of this curve is;
y = A sin(B(x + C)) + D
Where;
A is amplitude
B is 2π/period = 2π/4π = ½
C is phase shift
D is vertical shift
The function g(a) that will represent the behavior of the graphed function would be gotten by Plugging in the relevant values but in this case, there are no phase shifts or vertical shifts. Thus, C = D = 0
g(a) = 1.5 sin 0.5x
Midline is the point between the maximum and minimum values.
Max value is at y = 1.5
Min value is at y = -1.5
Midline of both from the graph is at x = -π/2 which is at y = 0
Y-intercept = -4
• Slope = -1
2
y
10
9
8
2
6
5
4
3
2
-10
-9
-8
-7
-6
-5
- 4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
2
-3
-4
-5
-6
-7
-8
-9
-10
Answer:
First point: -4 on y axis.
Second point: (2, -5)
Step-by-step explanation:
When graphing, we always set the equation as y=mx+b where m = slope and b = y intercept
y = mx + b
y = [tex]-\frac{1}{2}x-4[/tex]
Then we plot by starting with the y intercept going four units down, one unit below and two units to the right.
Jason has $6,700 in his bank account. He withdraws $1,900 from his bank account o pay for rent. Brett books a vacation 3-days later that costs $4,000. He withdraws $3,500 from his account and goes on a payment pay for the remainder
Answer:
thers no question
Step-by-step explanation:
Polygons Determine the measure of one through 12
Answer:
And there are twelve angles... So, the measure of the interior angle of a regular dodecagon is 150 degrees.
Step-by-step explanation:
To identify high-paying jobs for people that do not like stress, the following data were collected showing the average annual salary ($1000) and the stress tolerance for a variety of occupations (Business Insider, November 8, 2013). The stress tolerance for each job is rated on a scale from 0 to 100, where a lower rating indicates less stress.
Job Average Annual Salary ($1000s) Stress Tolerance
Art directors 81 69
Astronomers 96 62
Audiologists 70 67.5
Dental hygienists 70 71.3
Economists 70 63.3
Engineers 92 69.5
Law teachers 92 62.8
Optometrists 100 65.5
Political scientists 98 60.1
Urban and regional planners 102 69
Required:
Draw scatter diagram for these data with average annual salary as the independent variable.
Answer:
Y = -0.09594X + 74.35629
Step-by-step explanation:
Given the data :
Job average annual salary (X) :
81
96
70
70
70
92
92
100
98
102
Stress tolerance (Y) :
69
62
67.5
71.3
63.3
69.5
62.8
65.5
60.1
69
Using technology, the linear model Obtian by fitting the given data is :
Y = -0.09594X + 74.35629 ;
Where ;
Y = stress tolerance (dependent variable)
X= Average annual salary (Independent variable)
Slope = 0.09594
Intercept = 74.35629
What are 3 numbers that make this inequality True? 4x-9 > 27
Answer:
10, 11, 12
Step-by-step explanation:
simplify the inequlity:
=> 4x > 36
=> x > 9
x = 10, 11, 12...
la
You spend some time in the kitchen making sure the recipe is just right for
the cooking show. You spend 2 3/4 hours baking and half of an hour
cleaning up the kitchen. How much time were you in the kitchen?
Answer: 3¼ hours
Step-by-step explanation:
Number of hours used in baking = 2¾ hours
Number of hours used in cleaning up the kitchen = ½ hour
Therefore, the time used in the kitchen will be the addition of the time used in baking plus the time used in cleaning the kitchen which will be:
= 2¾ + ½
= 2 3/4 + 2/4
= 2 5/4
= 2 + 1¼
= 3¼ hours
Therefore, 3¼ hours was used in the kitchen.
ABCD is a parallelogram. Find x and the length of CD.
Answer:
3×+9=5x-5
-2×=-14
×=7...thenCD=3(7)+9=30
15. Solve for the specified variable:
-
х
+
7 8
- 10; for y.
Answer:
[tex]y=80-\frac{8x}{7}[/tex]
Step-by-step explanation:
15). Given equation is,
[tex]\frac{x}{7}+ \frac{y}{8}=10[/tex]
Multiply the equation by 8,
[tex]8(\frac{x}{7}+ \frac{y}{8})=10\times 8[/tex]
[tex]\frac{8x}{7}+y=80[/tex]
Subtract [tex]\frac{8x}{7}[/tex] from both the sides of the equation,
[tex]\frac{8x}{7}+y-\frac{8x}{7}=80-\frac{8x}{7}[/tex]
[tex]y=80-\frac{8x}{7}[/tex]
Therefore, value of the variable 'y' will be,
[tex]y=80-\frac{8x}{7}[/tex]
The table shows the record low temperatures In Juneau, Alaska for each of the 12 months of the year in degrees F.
Record Low Temp
Month
Year
(in °F)
January
-22
1972
February
-22
1968
March
-15
1972
April
6
1963
May
25
1972
June
31
1971
July
18
1895
August
27
1948
September
23
1972
October
11
1984
November
-5
2006
December
-21
1941
According to the data, what is the range of the record low temperatures in Juneau, Alaska?
O A. -22°
OB. 4.67°
D. 31°
E. 539
O c. 8.50
Answer:
i think -22
Step-by-step explanation:
Catherine sells bags of popcorn at the theatre. The bags come in three sizes.
small
60g
£1.49
medium
150g
£3.99
large
250g
£5.99
Catherine thinks the medium bag of popcorn is the best value for money.
Is the medium bag of popcorn the best value for money?
Use the space below to show clearly how you get your answer
Answer:
The answer is the most reasonable one which I think large is
Step-by-step explanation:
Because it's only 100 grams more and $2 bucks seems like a good deal
Solve the system of equations below by graphing. Y=-5x and y=x-6
9514 1404 393
Answer:
(x, y) = (1, -5)
Step-by-step explanation:
Using a graphing calculator to solve equations such as these is quick and easy. It is one of my favorite methods. The attached graph shows the solution is ...
(x, y) = (1, -5)
if 8.7%, of the 210,000,000 american are unemployed,how many Americans are unemployed?x
Answer:
it would be 45%
Step-by-step explanation:
Answer:
18,270,000 Americans
Step-by-step explanation:
8.7 x 210,000,000 = 1827000000
take 2 zeros out of 1827000000
18,270,000
Find the value of x. Round the lengths to the nearest tenth of a unit.
Please help!
Answer:
the other angle equal 52
we can use the specail trangle 3 4 5
300 400 500
the 38 degrees angle meet 300
and the 52 degrees angle meet 400
so the answer is 300 i dont know if you understand but i hope you are
pls ask in the comments and i will try to explain because my ebgilish the baddest
If f(x)=x^3−5x^2−2x+24 and (x+2) is a factor, what are the remaining factors?
Factor 1:
Factor 2:
Factor 3:
Answer:
(x+2), (x-4), (x-3)
Step-by-step explanation:
Use the rational root theorem to get started, then factor the remaining quadratic to find:
x^3 − 5x^2 − 2x + 24 = (x + 2)(x − 4)(x − 3)
Explanation:
Let f(x) =x^3 − 5x^2 − 2x + 24
By the rational root theorem, any rational zeros of f(x) must be expressible in the for p/q for integers p, q with p a divisor of the constant term 24 and q a divisor of the coefficient 1 of the leading term.
That means that the only possible rational zeros are the factors of 24, namely:
± 1, ± 2, ± 3, ± 4, ± 6, ± 12, ± 24
Try each in turn:
f(1) = 1 − 5 − 2 + 24 = 18
f(−1) = −1 − 5 + 2 + 24 = 20
f(2) = 8 − 20 − 4 + 24 = 8
f(−2) = −8 − 20 + 4 + 24 = 0
So x = −2 is a zero and (x + 2) is a factor.
x^3 − 5x^2 − 2x + 24 = (x + 2)(x^2 − 7x + 12)
We can factor
x^2 − 7x + 12 by noting that 4 × 3 = 12 and 4 + 3 = 7, so:
x^2 − 7x + 12 = (x − 4)(x − 3)
Putting it all together:
x^3 − 5x^2 − 2x + 24 = (x + 2)(x − 4)(x − 3)
help i dont understand this
Answer:
it's b 12 i think
Step-by-step explanation:
A study has been done to determine to see if the level of education determines how often people move between different states in America. If a person from the survey that attended college is randomly selected what is the probability that they also lived in 2 or more states during their life? P(2 state or more | College Degree)
This question is incomplete, the complete question is;
A study has been done to determine to see if the level of education determines how often people move between different states in America. If a person from the survey that attended college is randomly selected what is the probability that they also lived in 2 or more states during their life? P(2 state or more | College Degree)
Lived in just Lived in 2 or Total
1 state more states
No High School Diploma 6 2 8
High School Diploma 14 16 30
College Degree 2 18 20
Total 22 36 58
Options;
a) 0.111
b) 0.310
c) 0.500
d) 0.900
Answer:
The required probability is 0.9
Option d) 0.900 is the correct answer.
Step-by-step explanation:'
Given the data in the question;
Total number of people in the survey or sample size n = 58
Number of people with college degree who live in 2 or more state = 18
P(2 states or more and college degree) = Number of people with college degree who live in 2 or more state / Total number of people in the survey
P(2 states or more and college degree) = 18 / 58
Also, Total number of people with college degree = 2 + 18 = 20
so, P( College Degree ) = Total number of people with college degree / Total number of people in the survey
P( College Degree ) = 20 / 58
Therefore, P(2 state or more | College Degree) will be;
⇒ P(2 states or more and college degree) / P( College Degree )
⇒ ( 18 / 58 ) / ( 20 / 58 )
⇒ ( ( 18 / 58 )58 ) / 20
⇒ (( 18 × 58 ) / 58 ) / 20
⇒ 18 / 20
⇒ 0.9
Therefore, The required probability is 0.9
Option d) 0.900 is the correct answer.
Find an expression witch represents the difference when (10x-8y) is subtracted from (-4x-9y) in the simplest form
Answer:
ye
Step-by-step explanation:
What additional piece of information
would prove ALMK = ANMK by
Side-Angle-Side?
Answer:
MK bisects <LKN
Step-by-step explanation:
We can already say two sets of sides are equal; LK = NK because it is given and MK = MK because of reflexive property. In order to use Side-Angle-Side, we need to prove the angles between the sides are congruent. This means <LKM and <NKM. The only option that would help is with the is the lat option, MK bisects <LKN because, then we could say <LKM and NKM are congruent because MK would be an angle bisector. This is exactly what we want, so the answer is MK bisects <LKN.
The top rail of a boat is 4 ft out of the water. If the water rises 3 ft, how far out of
the water is the top rail of the boat?
Answer:
the correct answer is 1ft
Step-by-step explanation:
4ft-3ft
=1ft
Put these in order from least to greatest!: 6.879, 137/20, 6 10/11, 5.89
Thank you!!