a)The amount of untreated water inside the plant will be the difference between the difference f(t) - g(t), then, a(t) can be defined as follows:
[tex]a(t)=100+30cos(\frac{t}{6})-30e^{cos(\frac{t}{2})}[/tex]b) the derivative of a(t) is the following:
[tex]a^{\prime}(t)=-5sin(\frac{t}{6})+15sin(\frac{t}{2})e^{cos(\frac{t}{2})}[/tex]c) the critical values of a(t) over the interval [0, 24) are:
[tex]\begin{gathered} t=0 \\ t=6\pi \end{gathered}[/tex]Jamie paid the rent well past the due date for the months of April, May and June. As a result, he had been charged a total of $75 as a late fee. Howmuch did he pay as late fee per month?Use 'f to represent the late fee $$ per month.
Total fee = $75
Number of months = 3
Divide the total fee by the number of months
75/3 = $25 per month
y = 3× - 1y = -3× + 1
Given two equations,
[tex]\begin{gathered} y=3x-1 \\ y=-3x+1 \end{gathered}[/tex]Comapring both equations,
[tex]\begin{gathered} 3x-1=-3x+1 \\ 3x+3x=1+1 \\ 6x=2 \\ x=\frac{2}{6}=\frac{1}{3} \end{gathered}[/tex]Therefore, x = 1/3.
write the vertex form equation of the parabola with, vertex: (10,9), passes through: (12,-7)
Th equation of a parabola in its vertex form is;
y = a(x-h)² + k
(h,k) are the coordinates of the vertex and a is a constant
(h, k) = (10, 9)
substitute the above into the equation
y = a(x- 10)² + 9 -------------------(1)
Next is to find the value of a
substitute x=12 and y= -7 into equation (1)
-7 = a (12 - 10)² + 9
-7 - 9 = 4a
-16 = 4a
a = -4
The equation of the parabola will be formed by substituting a = -4 in equation (1)
y = -4(x - 10)² + 9
The volume of cylinder is 504 pi cm^(3) & height is 14cm Find the curved surface area 8 total surface area.
The Solution:
The correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Given that the volume of a cylinder with height 14cm is
[tex]504\pi cm^3[/tex]We are required to find the curved surface area and the total surface area of the cylinder.
Step 1:
We shall find the radius (r) of the cylinder by using the formula below:
[tex]V=\pi r^2h[/tex]In this case,
[tex]\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]504\pi=\pi r^2\times14[/tex]Finding the value of r by first dividing both sides, we get
[tex]\begin{gathered} \frac{504\pi}{14\pi}=r^2 \\ \\ r^2=36 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{r^2}\text{ =}\sqrt[]{36} \\ \\ r=6\operatorname{cm} \end{gathered}[/tex]Step 2:
We shall find the curved surface area by using the formula below:
[tex]\text{CSA}=2\pi rh[/tex]Where
[tex]\begin{gathered} \text{ CSA=curved surface area=?} \\ h=14\operatorname{cm} \\ r=6\operatorname{cm} \end{gathered}[/tex]Substituting these values in the formula above, we have
[tex]\text{CSA}=2\times6\times14\times\pi=168\pi=527.788\approx527.79cm^2[/tex]Step 3:
We shall find the total surface area by using the formula below:
[tex]\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh[/tex]Where
TSA= total surface area and all other parameters are as defined earlier on.
Substituting in the formula, we get
[tex]\text{TSA}=(2\pi\times6^2)+(2\pi\times6\times14)=72\pi+168\pi[/tex][tex]\text{TSA}=240\pi=753.982\approx753.98cm^2[/tex]Therefore, the correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
A __ is a polynomial with one term.
ANSWER
Monomial
EXPLANATION
A polynomial is a expression that contains variables, coefficients and sometimes constants.
These terms relate with one another by the use of mathematical signs like addition, subtraction, multiplication, etc
A polynomial with just one term is called monomial.
An example of a polynomial is:
[tex]x^2\text{ + x + 1}[/tex]An example of a monomial is:
[tex]\begin{gathered} x^2 \\ or\text{ } \\ \frac{x}{2} \end{gathered}[/tex]Answer:
monomial
Step-by-step explanation:
List the elements in the set
{x 1 x is a negative multiple of 5}
S={-5,-10,-15,-20,-25......}; these are few negative multiples of 5 as stated in the set builder form of set theory {x :x is a negative multiple of 5}.
What is set?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is the mathematical model for a collection of various things.
What is set builder form?Set builder notation is a type of mathematical notation used to describe sets by listing their components or highlighting the requirements that each member of the set must meet. We write sets in the form of in the set-builder notation.
{y | (properties of y)} OR {y : (properties of y)}
Here,
{x :x is a negative multiple of 5}
S={-5,-10,-15,-20,-25.....}
According to the set builder form of set theory, {x:x is a negative multiple of 5} S={-5,-10,-15,-20,-25...}; these are a few negative multiples of 5.
To know more about set,
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the probability he chooses orange fruit
Consider that the total number of fruits are 10. The probability to get some fruit is given by the quotient in between the number of suc a fruit and the total number of fruits.
Then, at the first time, the probability of getting a kiwi is:
p1 = 1/10 = 0.1 (becasue there is one kiwi)
After the kiwi is taken out, the number of fruits are 9. In this case, the probability of getting one orange is:
p2 = 3/9 = 0.33 (because there are three oranges)
THe probability of the two previous events, that is, to obtain one kwi and then one orange is the product of the probabilities p1 and p2:
P = p1*p2 = (0.1)(0.33) = 0.03
Hence, the probabilty is approximately 0.03
Compare f(0) and g(0)f(0) is <, =, or > to g(0)
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-82-123-164-20
Given :
The table for y and x is given as
Explanation :
The slope-intercept form is determined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]First find the slope of the equation using the coordinates from the table.
[tex]m=\frac{-12-(-8)}{2-1}=\frac{-12+8}{1}=-4[/tex]Now substitute the values in the slope-intercept form.
[tex]\begin{gathered} y-(-8)=-4(x-1) \\ y+8=-4(x-1) \\ y=-4x+4-8 \\ y=-4x-4 \end{gathered}[/tex]Answer:
Hence the equation of line is determined as
[tex]y=-4x-4[/tex]In a student council election there are 2 people running for treasure 3 people running for secretary 4 running for vice president and 2 people running for class president How many possible outcomes are there?
Given:
There are given that the 2 people running for treasure, 3 people running for secretary, 4 running for vice president, and 2 people running for class president.
Explanation:
According to the concept of outcomes:
The outcomes are defined for the possible results of an experiment.
Then,
In the given question, the outcomes are:
[tex]\text{Outcomes}=2+3+4+2=11[/tex]Final answer:
Hence, the total number of outcomes is 11.
How does the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3
The ways in which the graph of f(x) = (x + 7)^3 − 8 compare to the parent function g(x) = x^3 are as follows:
Shifted 7 units to the left.Shifted 8 units down. What is a translation?In Mathematics, the translation a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while translating a geometric figure down simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Geometry, g(x + 7) simply means shifting a graph 7 units to the left while subtracting 8 from the function simply means moving the graph down.
In this context, we can reasonably infer and logically deduce that the parent function g(x) was shifted 7 units to the left and 8 units down.
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Michael and Ashley each buy x pounds of turkey and y pounds of ham. Turkey costs $3 per pound at Store A and $4.50 per pound at Store B. Ham costs $4 per pound at Store A and $6 per pound at Store B. Michael spends $18 at Store A, and Ashley spends $27 at Store B. Could Michael and Ashley have bought the same amount of turkey and ham?
Step 1
Michael spends $18 at store A
He buys x pounds of turkey and y pounds of ham.
But turkey costs $3 in-store A and ham costs $4 in-store A
Therefore, we will have the following equation for Michael
[tex]3x+4y=18---(1)[/tex]Step 2
Ashley spends $27 in-store B
She buys x pounds of turkey and y pounds of ham.
But turkey costs $4.50 in-store B and ham costs $6 in-store B.
Therefore, we will have the following equation for Ashley
[tex]4.5x+6y=27----(2)[/tex]Step 3
Solve the equations graphically
If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations. Since the graphs are the same, then there are infinitely many solutions true for both equations.
For instance, the points if we test for the points on the graph, we will conclude if both Michael and Ashley bought the same amount of turkey and ham.
[tex]\begin{gathered} 3x+4y=18_{} \\ 4.5x+6y=27 \\ At\text{ x =2 and y=3} \\ we\text{ have,} \\ 3(2)+4(3)=18_{} \\ 6+12=18 \\ 18=18 \\ 4.5(2)+6(3)=27 \\ 9+18=27 \\ 27=27 \\ \text{At x=6, y=0} \\ we\text{ have} \end{gathered}[/tex][tex]\begin{gathered} 3(6)+4(0)=18 \\ 18=18 \\ 4.5(6)+6(0)=\text{ 27} \\ 27=27 \end{gathered}[/tex]Therefore yes, Michael and Ashley could have bought the same amount of turkey and ham.
Solve the system using any method. State your solution as an ordered pair. DO NOT include spaces in your answer.
Answer: (- 4, - 7)
Explanation:
The given equations are
y = 5x + 13
y = 2x + 1
We would equate both equations. We have
5x + 13 = 2x + 1
5x - 2x = 1 - 13
3x = - 12
x = - 12/3
x = - 4
Substituting x = - 4 into y = 2x + 1, we have
y = 2(- 4) + 1 = - 8 + 1
y = - 7
The solution is
(- 4, - 7)
The boats rate is ____ mph(Type an integer or decimal)
Let
x ----> rate of the boat in still water (mph)
y ---> rate of the current (mph)
Remember that
The speed is equal to dividing distance by the time
speed=d/t
d=speed*time
so
Upstream
speed=x-y
time=5 hours
100=(x-y)*5
x-y=20 --------> equation 1
Downstream
speed=x+y
time=4.5 h
100=(x+y)*4.5
x+y= 100/4.5 --------> equation 2
Adds equation 1 and equation 2
x-y=20
x+y= 100/4.5
-----------------
2x=20+(100/4.5)
2x=190/4.5
x=190/9
x=21.11 mph
therefore
The answer is 21.11 mphWhat do the following two equations represent?y-3=2(x - 3)y+5 = 2(x + 1) a. the same lineb. distinct parallel linesc. perpendicular linesd. intersecting, b it not perpendicular
Option A: The same line
Explanations:The slope-intercept form of the equation of a line can be written as:
y = mx + c
Where m is the slope
and c is the intercept
Let us express the two equations given in the slope-intercept form
For the first equation:
y - 3 = 2(x - 3)
y - 3 = 2x - 6
y = 2x - 6 + 3
y = 2x - 3
The slope, m = 2
The intercept, c = -3
For the second equation:
y + 5 = 2(x + 1)
y + 5 = 2x + 2
y = 2x + 2 - 5
y = 2x - 3
We can see that both equations simplify to y = 2x - 3, this means the both equations represent the same line
Tan (a) cos (a)= sin (a)Trig: use trigonometric identities to transform the left side of the equation into the right side
hello
the question here relates to trionometric identies and we can easily solve this once we know some of the identities
for example
[tex]undefined[/tex]What is the value of the expression 2c( a + b) when a = 2, b = 5, and c = 4
The given expression is
2c(a + b)
From the information given,
a = 2
b = 5
c = 4
By substituting these values into the expression, it becomes
2 * 4(2 + 5)
= 8(7)
= 56
The value of the expression is 56
i am stuck on this question. any help would be greatly appreciated
step 1
determine the slope of the given line
y=(3/5)x-17
The slope is m=3/5
Remember that
If two lines are parallel, then their slopes are equal
that means
The slope of the parallel line to the given line is m=3/5 too
step 2
Find out the equation of the line parallel to the given line
y=mx+b
we have
m=3/5
point (-5,15)
substitute and solve for b
15=(3/5)(-5)+b
15=-3+b
b=18
therefore
The equation of the line is
y=(3/5)x+18One cubic foot holds 7.48 gallons of water, and 1 gallon ofwater weighs 8.33 pounds. How much does 6 cubic feet ofwater weigh in pounds? In tons?
We know that
• 1 cubic foot holds 7.48 gallons of water.
,• 1 gallon of water weighs 8.33 pounds.
The given information is about ratios that we must use to find the answer. Remember that a ratio is a quotient between two magnitudes, that means each statement above represents a fraction which must multiply "6 cubic feet" in order to get the answer. As follows
[tex]6ft^3\cdot\frac{7.48gallons}{1ft^3}\cdot\frac{8.33lb}{1gallon}=\frac{6\cdot7.48\cdot8.33}{1}lb=373\text{.}85lb[/tex]Therefore, 6 cubic feet weighs 373.85 pounds.
On the other hand, 1 ton is equivalent to 2000 pounds. Knowing this, we calculate
[tex]373.85lb\cdot\frac{1ton}{2000lb}\approx0.19ton[/tex]Therefore, 6 cubic feet weighs about 0.19 tons.
60% discount on $500 sweater
The discount price of the sweater will be, the original price minus the percentage of discount of the original price.
First, express the percentage of discount as a decimal:
60% = 60/100 = 0.6
so:
[tex]\begin{gathered} 500-0.6\cdot500 \\ 500-300=200 \end{gathered}[/tex]The discount price of the sweater is $200
Given the venn diagram below, what is the correct notation?A. ⊘B. (M∩F)′C. (M∪F)′D. none of these
Given
SolutionThe complement of a set using Venn diagram is a subset of U. Let U be the universal set and let A be a set such that A ⊂ U. Then, the complement of A with respect to U is denoted by A' or AC or U – A or ~ A and is defined the set of all those elements of U which are not in AThe shaded region is
[tex](M\cup\text{ F \rparen'}[/tex]The final answerOption C
Test scores are normally distributed with a mean of 86 and a standard devotion of 2.2 what percent scored between 83.8 and 92.6? What percent scored below 83.8?
Z- Score formula is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z\text{ is the z-score (Standard score)} \\ X\text{ is the value to be standardized} \\ \mu\text{ is the mean} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]Here, the mean is 86, while the standard deviation is 2.2
Percent between 83.8 and 92.6 is;
[tex]P(\frac{83.8-86}{2.2}The percent between 83.8 and 92.6 = 0.83999[tex]P(Z<-1)=\text{ 0.15866}[/tex]Percent score below 83.8 is 0.15866
Which expression can be used to find the nth term in this sequence position: 1 2 3 4 5 nvalue of term: 2 5 10 17 26 ?
n²+1 where n is the position of the sequence
1) Considering the sequence (2,5,10,17,26,...) corresponding to 1,2,3,4,5,...
Let's figure out how that sequence grows:
5 -2 = 3
10 -5 = 5
17-10= 7
26-17= 9
And examining the differences from each difference we have:
5-3 =2
7-5 = 2
9-7 =2
2) So we can write the following table, where the first line is the sequence, then the positions, then the subtraction between them.
As it is a quadratic formula, we can write in the general form and then plug x=0
[tex]\begin{gathered} a_n=n^2 \\ 2\text{ 5 10 17 26} \\ 1\text{ 2 3 4 5 6 } \\ 1\text{ 4 9 25 36} \\ a_n=n^2+0n+1 \\ a_n=n^2+1 \end{gathered}[/tex]3) Hence, to find the 6th term, for instance, we plug n=6 so
6²+1 = 31. So the formula to find the nth term is n² +1
3) Finally, the sequence is given by n² +1 where n is the position of the term.
There is a total of $4,840 in an account after 2 years of earning compound interest at a rate of 10%. What was the original amount invested?
In order to find the original amount invested, we can use the following formula:
[tex]P=P_0(1+i)^t[/tex]Where P is the final amount, P0 is the original amount, i is the interest rate and t is the amount of time invested.
So, using P = 4840, i = 10% = 0.1 and t = 2, we have:
[tex]\begin{gathered} 4840=P_0(1+0.1)^2_{} \\ 4840=P_0\cdot1.1^2 \\ 4840=P_0\cdot1.21 \\ P_0=\frac{4840}{1.21} \\ P_0=4000 \end{gathered}[/tex]So the original amount invested is $4,000.
Find the missing number to make the fractions equivalent. 3/4 = 9/?
We have the following:
[tex]\frac{3}{4}=\frac{9}{x}[/tex]solving:
[tex]\begin{gathered} x=\frac{9\cdot4}{3} \\ x=12 \end{gathered}[/tex]Therefore, the answer is [B] 12
Find x rounded to the nearest whole degree. Be sure to round correctly!
answer: 36°
Multiply each term inside the parentheses by the factor outside the parentheses 2(x - 4) = 2 x + 2(-4) Multiply Simplify.2(×-4)=2x+2(-4)
We have the expression:
[tex]2(x-4)=2x+2(-4)[/tex]We solve as follows:
[tex]2x-8=2x-8[/tex]If we want to simplify further, we will get:
[tex]2x=2x\Rightarrow x=x\Rightarrow0=0[/tex]***
In order to simplify the expression:
[tex]2(x-4)=2x+2(-4)[/tex]We multiply 2 times x and add 2 times -4, that is:
[tex]2x+2(-4)=2x+2(-4)[/tex]Now, we multiply 2 times -4 in both sides, that is:
[tex]2x-8=2x-8[/tex]Match each expression on the left to its equivalent value on the right. Some answer options on the right will not be used.
Let us write out our expressions:
[tex]\begin{gathered} -29+(-7) \\ -34+(-94) \\ -8+(-14) \\ -12+(-48) \end{gathered}[/tex]The trick here is to get rid of the minus, then solve the sum as usual, and add a minus to the result. Let us do that for each of them:
-29+(-7)] Step one gives us:
[tex]29+7[/tex]Step two gives us:
[tex]36[/tex]Step three gives us:
[tex]-36[/tex]Then, -29+(-7) should be linked to -36.
-34+(-94)] Step one gives us:
[tex]34+94[/tex]Step two gives us:
[tex]128[/tex]Step three gives us:
[tex]-128[/tex]Thus, -34+(-94) should be linked to -128.
-8+(-14)] Step one gives us:
[tex]8+14[/tex]Step two gives us:
[tex]22[/tex]And step three gives us:
[tex]-22[/tex]This implies that -2+(-14) should be linked to -22.
-12+(-48)] Step one gives us:
[tex]12+48[/tex]Step two gives us:
[tex]60[/tex]And step three gives us:
[tex]-60[/tex]Then, -12+(-48) should be linked to -60.
What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why.
An example of situation involving quantitative comparison is:
The game-plan of an offensive coach for a NFL game.
What are quantitative variables?
Quantitative variables are variable that assume numbers as results, instead of labels such as yes/no or good/bad.
When an NFL offensive coordinator is game-planning, he has to consider numeric stats of the opponent defense, such as these ones:
Average passing yards allowed per play.Average rushing yards allowed per play.These stats are also compared to the NFL average to verify if the weak point of the opponent defense is the run or the pass, hence the game-plan is adjusted accordingly as follows:
Bad run defense: the coordinator should call more running plays.Bad pass defense: the coordinator should call more passing plays.A similar problem, also about quantitative variables, is given at https://brainly.com/question/15212082
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determine the lateral surface area of the cylinder
Question:
Solution:
Remember that the total area surface of the cylinders is given by the formula:
[tex]S\text{ = 2}\pi rh+2\pi r^2[/tex]where r is the radius of the cylinder and h is its height. Now, in this case, we have that r= 10 m and h = 5m, then replacing these values in the previous equation we obtain:
[tex]S\text{ = 2}\pi(10)(5)+2\pi(10^2)=942.48^{}[/tex]then, we can conclude that the correct answer is:
[tex]S\text{ =}942.48^{}[/tex]