![Given Lim F(x) = 6. What Is Lim [5f(x)]?x-1x-10506O 11O 30](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/rU75OPOabYrUQtUgPtKAm39fT2OVa8Ht.png)
Answers
The value for the limit function \(\lim_{x \to 1} [5f(x)]\) is obtained as Option D : 30.
What is limit?A limit in mathematics is a pοint at which a functiοn apprοaches the οutcοme fοr the specified input values. Calculus and mathematical analysis depend οn limits, which are alsο used tο determine integrals, derivatives, and cοntinuity.
Using the cοnstant multiple rule fοr limits, we have -
\(\lim_{x \to 1} [5f(x)] = 5 \times \lim_{x \to 1} [f(x)]\)
Since we know that \(\lim_{x \to 1} [f(x)]=6\), we can substitute that value and simplify.
The equation will be -
\(\lim_{x \to 1} [5f(x)] = 5 \times \lim_{x \to 1} [f(x)]\)
= 5 × 6 = 30
Therefore, \(\lim_{x \to 1} [5f(x)]=30\).
This means that as x apprοaches 1, the expressiοn 5f(x) apprοaches 30.
Intuitively, we can think οf this as scaling the functiοn f(x) by a factοr οf 5.
Since the limit οf f(x) as x apprοaches 1 is 6, we can expect the limit οf 5f(x) tο be 5 times larger, which is 30.
Therefοre, the value fοr the limit functiοn is 30.
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Answer:D
Step-by-step explanation:took on edge
Related Questions
x - 2y = 4
4x + 3y = 5
Answers
Answer:
1. x = 4 + 2y
2.\(x =\frac{5-3y}{4}\)
Step-by-step explanation:
1 add 2y to both sides
x = 4 2y + 2y = 4 + 2y
simplify
x = 4 _ 2y
2 subtract 3y from both sides
4x + 3y - 3y = 5 - 3y
simplify
4x = 5 - 3y
Divide both sides by 4
4x/4 = 5/4 - 3y/4
simplify
x = 5-3y/4
last one for finding lengths side, please answer correctly, thank you
Answers
∑ Hey, shanellmccullough ⊃
Answer:
(a) Width of the garden : 64 m
(b) Length of the window: 95 cm
Step-by-step explanation:
Given:
(a) The perimeter of a rectangular garden is 306 m. If the length of the garden is 89 m, what is its width?
(b) The area of a rectangular window is 5130 cm². If the width of the window is 54 cm, what is its length?
Solve:
(a) The perimeter of a rectangular garden is 306 m. If the length of the garden is 89 m, what is its width?
Formula for perimeter: P = (L + W) × 2
Which;
P = Perimeter
L = Length
W = Width
Which also could be written as:
L + L + W + W = P
Hence, since it given that;
306 = P and L = 89
Then
We know that ;
89L + 89L + W + W = 306
So we can add 89 + 89 or 89 × 2
which is 178
Now we know that;
178 + 2w = 306
Solving for 2w:
178 + 2w = 306
178-178 + 2w = 306 - 178
2w = 128
W = 64
Hence, width is 64.
Check Answer:
64 × 2 + 89 × 2 = 306
-------------------------------------------------------------------------------------------------------------
(b) The area of a rectangular window is 5130 cm². If the width of the window is 54 cm, what is its length?
Formula for area: A = Lw
Which;
A = Area
L = Length
W = Width
So, since we know the width we can just do 5130/54 to find Length
5130/54 = 95
Hence, the length of the window is 95 cm.
Check Answer :
A = Lw
A = 95 × 54
A = 5130 cm²
-------------------------------------------------------------------------------------------------------------
xcookiex12
8/18/2022
I NEED HELP PLEASE, THANKS! :) Heather invests $4,900 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year? (SHOW WORK)
Answers
Answer: $5,828.28
Step-by-step explanation:
Use the Compound Interest formula: \(A=P(1+\frac{r}{n})^{nt}\) where
A is the accrued amount (balance)P is the principal (initial amount invested)r is the interest rate (in decimal form)n is the number of times compounded each yeart is the time of the investment (in years)Given: P = 4,900
r = 3.5% (0.035)
n = 2
t = 5
\(A=4,900\bigg(1+\dfrac{0.035}{2}\bigg)^{2(5)}\\\\\\.\qquad = 4900(1.0175)^{10}\\\\\\.\qquad = \large\boxed{5,828.28}\\\)
hi im confused with this one question its about properties and exponents on math i really need help:(
Answers
(X+2)(x+y+1)
Can someone help me with this one
Answers
Answer:
x^2 +xy+3x+2y+2
Step-by-step explanation:
(x+2)(x+y+1)
Apply the distributive property by multiplying each term of x+2 by each term of x+y+1.
x^2+xy+x+2x+2y+2
Combine x and 2x to get 3x
x^2 +xy+3x+2y+2
Answer: x^2+xy+3x+2y+2
Step-by-step explanation:
Expand and simplify
Name two triangles that are congruent by ASA.Choose the correct answer below.AMNP = ATUVAMNP = AQRSAQRS = ATUV
Answers
Three triangles are given they are:
\(\Delta\text{PMN,}\Delta RQS,\Delta UTV\)The triangles that are congruent by ASA test are:
\(\Delta SQR\cong\Delta\text{VTU}\)Which can also be written as:
\(\Delta QRS\cong\Delta TUV\)So QRS is congruent to TUV.
A roll of wrapping paper is 40cm by 200cm. Find the area in cm^2 and also in m^2.
Answers
Given,
The length of the rolling paper is 200 cm.
The breadth of the rolling paper is 40 cm.
Required:
The area of the rolling paper.
The area of the rolling paper is,
\(\begin{gathered} Area\text{ = 40}\times200 \\ =8000\text{ cm}^2 \end{gathered}\)The area of the rolling paper in m^2 is,
\(\begin{gathered} Area=8000\text{ }\frac{m^2}{10000} \\ =0.8\text{ m}^2 \end{gathered}\)Hence, the area of the rolling paper is 0.8m^2.
X-2<3 I can’t do this I have adhd so it is really hard for me
Answers
Answer:
how much does it say that x equals?
what percent of 120 is 24
Answers
if you were to multiply 120 by .2, you find that it would be 24.
Answer:
The answer is 20%
Step-by-step explanation:
24/120 = 0.2= 20%
Hope that helps!
a batch of 200 iron rods consists of 50 oversized rods, 50 undersized rods and 100 rods of the desired length. if two rods are drawn at random without replacement, what is the probability of obtaining (a) two rods of the desired length, (b) exactly one of the desired length, (c) none of the desired length? show all steps and clearly write out your formulas and assumptions
Answers
(a) The probability of obtaining two rods of the desired length is (100/200) * (99/199) = 0.495.
This can be found by using the formula for independent events:
P(A and B) = P(A) * P(B)
Since the two draws are of rods without replacement,
the probability of the first-rod being of the desired length = 100/200 (there are 100 desired-length rods out of a total of 200).
The probability of the second-rod being of the desired length = 99/199 (since one of the desired length rods has already been drawn). Multiplying these two probabilities gives us the answer.
(b)The probability of obtaining exactly one rod of the desired length
=(100/200) * (100/199) + (100/200) * (100/199)
= 0.990.
This can be found by using the formula for the union of two events: P(A or B) = P(A) + P(B).
Since the two draws are rods without replacement, the first draw has a probability of 100/200 of being of the desired length (there are 100 desired-length rods out of a total of 200).
The probability of the second draw being of the desired length is 100/199 (since one of the desired length rods has already been drawn). Adding these two probabilities gives us the answer.
(c) The probability of obtaining none of the desired length is (50/200) * (50/199) = 0.015.
This can be found by using the formula for independent events
: P(A and B) = P(A) * P(B).
Since the two draws are of rods without replacement, the probability of the first-rod being of the undersized length is 50/200 (there are 50 undersized rods out of a total of 200).
The probability of the second-rod being of the undersized length is 50/199 (since one of the undersized rods has already been drawn). Multiplying these two probabilities gives us the answer.
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a field goal is 3 points and the field goal after a touchdown is only 1 point. in a not-so-recent post-season, adam vinatieri of the indianapolis colts made a total of 21 field goals and extra point kicks for 49 points. find the number of field goals and extra points he made.
Answers
Adam Vinatieri made 14 field goals and 7 extra points.
Given that,
a field goal is 3 points and the field goal after a touchdown is only 1 point.
Adam Vinatieri made 21 field goals and extra point kicks for 49 points.
Let x be the number of field goals and y be the extra point kicks.
So we get,
x + y = 21 -------------(1)
3x + y = 49 -----------(2)
Subtracting equation (1) from equation (2),
2x = 28
x = 14
putting the value of x in equation (1),
14 + y = 21
y = 7
Therefore Adam Vinatieri made 14 field goals and 7 extra points.
Field goal means a score of three points in football made by drop kicking or placekicking the ball over the crossbar from ordinary play. A field goal is a successful kick of the ball by a kicker through the goalpost. It is an offensive play that can score three points for a team.
Adam Vinatieri is an American former football placekicker who played in the National Football League.
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Which shape has Exactly Two lines of symmetry
Answers
Answer:
Rectangle
Step-by-step explanation:
A rectangle has exactly 2 lines of symmetry
Thank you
Show that log2 3 is an irrational number. Recall that an ir- rational number is a real number x that cannot be written as the ratio of two integers.
Answers
The number \(log_2^3\) is an irrational number.
For given question,
We need to prove \(log_2^3\) is an irrational number.
An irrational number is a real number x that cannot be written as the ratio of two integers.
Assume that \(log_2^3\) is rational.
⇒ \(log_2^3\) = a/b
where a and b are positive integers with no factor in common.
Then 3 = \(2^{(\frac{a}{b} )}\)
or
\(3^b=2^a\)
which is impossible since 3^(b) is odd and 2^(a) is even.
Hence \(log_2^3\) cannot be rational, that is it is irrational.
Therefore, \(log_2^3\) is an irrational number.
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teacher asked her students write down the number of hours studied rounded to the nearest half hour. she complies the results in develops the probability distribution below for randomly selected student. what is the mean of the probability distribution
Answers
Answer:
1.5
Step-by-step explanation:
The question is incomplete due to the probability distribution table, investigating you can find it so I will attach it.
Having the table, we need to find the mean of the probability distribution, which is defined as the sum of the product of probability and value of random distribution, that is:
M = Sum (xi) * P (xi)
We replace:
M = 0.5 * 0.07 + 1 * 0.2 + 1.5 * 0.46 + 2 * 0.2 + 2.5 * 0.07
M = 1.5
Therefore, the mean of the given table is 1.5
Heyo I need help on b
Chicken
Beef
Fish
Vegetarian
a) 32 people ate chicken.
How many people does
represent? I know its 8
b) Altogether, how many people
went to the restaurant?
Answers
Answer:
88
Step-by-step explanation:
We know that one figure represents 8 customers. There are a total of 4 + 2.5 + 1 + 3.5 = 11 figures so the answer is 11 * 8 = 88.
Perform the indicated operation:
(m^2 - 16n^2) ÷ (3m+12n)/mn
Please answer quick! Brainliest if correct!
Answers
The expression \(\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }\) is equal to \(\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}\).
How to simplify a composite algebraic expression
In this question we must use properties of real algebra to simplify a given expression as most as possible. We proceed to show each step with respective reason.
\(\frac{m^{2}-16\cdot n^{2}}{\frac{3\cdot m + 12\cdot n}{m\cdot n} }\) Given\(\frac{m\cdot n \cdot (m^{2}-16\cdot n^{2})}{3\cdot m + 12\cdot n}\) \(\frac{\frac{a}{b} }{\frac{c}{d} } = \frac{a\cdot d}{c\cdot b}\)\(\frac{m\cdot n \cdot (m-4\cdot n)\cdot (m+4\cdot n)}{3\cdot (m+4\cdot n)}\) Distributive property/\(a^{2}-b^{2} = (a +b)\cdot (a-b)\)\(\frac{m\cdot n \cdot (m-4\cdot n)}{3}\) Existence of the multiplicative inverse/Modulative property\(\frac{m^{2}\cdot n}{3} -\frac{4\cdot m\cdot n^{2}}{3}\) Distributive property/\(x^a\cdot x^{b} = x^{a+b}\)/ResultTo learn more on algebraic expressions, we kindly invite to check this verified question: https://brainly.com/question/953809
Answer:
mn(m-4n)/3
Step-by-step explanation:
sorry, I don’t have enough time to write the explanation!
PLEASE HELP If the lengths of two sides of a triangle are 2 and 6, then the length of the third side cannot be:
a)5
b)6
c)7
d)4
Answers
Answer:
I think is A
Step-by-step explanation:
But I'm not sure
4. In the diagram below TP and TR are tangents circle centered at O. IfPRT-65°, find ROP. O 65° R.
Answers
The measure of angle ROP is 25 degrees.
In the given diagram, TP and TR are tangents to a circle centered at O, and PRT is a triangle with angle PRT equal to 65 degrees. We need to find the measure of angle ROP in degrees.
Therefore, ∠PTO and ∠RTO are both 90 degrees.
We also know that the sum of the angles in a triangle is 180 degrees. Therefore, we can use this fact and the given angle PRT to find the measure of angle POR as follows:
∠PRT + ∠PTR + ∠PTR = 180 degrees
65 + 90 + 90 = 180 degrees
245 degrees = 180 degrees + ∠POR
∠POR = 65 degrees
Finally, we can find the measure of angle ROP by subtracting ∠POR from the given angle ∠TOR:
∠ROP = ∠TOR - ∠POR
∠ROP = 90 - 65
∠ROP = 25 degrees
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Solve the equation. 4−18=52
Answers
Answer:
-14
Step-by-step explanation:
Which of the following is a rational number?
√15
√16
√21
√22
Answers
Answer:
It would be the square root of 16
Step-by-step explanation:
Hope this helps... LOL
Answer:
B √16
Step-by-step explanation:
The first equation from the system of equations is
graphed. Graph the second equation to find the solution
of the system of equations.
y=-X,
y = 2x + 6
What is the point of intersection?
O (2,1)
O (-1,2)
O (0,6)
O (-2,2)
Answers
in how many ways can you create a two-element set where each element in the set is an positive integer less than 95?
Answers
In order to establish a two-element set with each element being a positive integer smaller than 95, there are thus 4371 possible combinations.
Combinations are defined by the following formula: C(n, r) = n! / (r! * (n-r)!)
Where n is the overall number of things and r denotes the number of items to be picked at random.
Without respect to order, we must select 2 elements from a possible total of 94. As a result, we can use the following formula to apply the rule: C(94, 2) = 94! / (2! * (94-2)!) = (94 * 93 * 92 *... * 3 * 2 * 1) / [(2 * 1) * (92 * 91 *... * 3 * 2 * 1)]
= (94 * 93) / (2 * 1) = 4371
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Please help me with this math problem!! I will give brainliest!! No links :)
Answers
Answer:
Hello, your
Step-by-step explanation:
For this particular problem (with units in mind), the formula for arc length is
Arc length
=
2
π
r
⋅
(
x
360
∘
)
,
Where
x
is the central angle measure and
r
is the radius of the circle.
You don't really have to work too hard to remember this formula. The arc length formula is easy to remember because it is just the circumference of the circle times the central angle over
360
∘
.
Anyway, let's continue with the problem. We are given that the central angle is
60
∘
, and that
r
, our radius, is
9
feet. So, let's plug that into our equation to find the arc length, in feet:
Arc length
=
2
π
r
⋅
(
x
360
∘
)
Arc length
=
2
π
(
9
)
⋅
(
60
∘
360
∘
)
Now, you might be tempted to plug this in your calculator, but let's simplify it a little bit more.
Arc length
=
2
π
(
9
)
⋅
(
60
∘
360
∘
)
Arc length
=
18
π
⋅
(
1
6
)
Arc length
=
3
π
feet
So, if you wanted an exact answer, it would be that the arc length is
3
π
feet
. If you wanted an approximate answer, then you can type
3
times
π
in your calculator to get a value of about
9.425
feet
as you alternative answer.
I hope that helps!
Trichloroethylene (TCE, C₂HC13) is a well-known pollutant in soils and groundwater in many places, including Mountain View, CA. One major concern is that TCE volatilizing into the air in houses from the surrounding soil can cause unhealthful indoor concentrations. This so-called "vapor intrusion" is a common problem in this region. One report states that shallow groundwater concentrations of TCE of 110 ppm have been measured. The healthful standard for airborne TCE is 25 ppm (long-term exposure), and 200 ppm (short-term exposure)
Let's consider a one-story bungalow with area Ah =10 m x 10 m (about 1000 sq ft) and a ceiling h = 4 m high, and the vapor comes in only through the floor. In order to maintain the house at acceptable levels of TCE, we will use a fan to ventilate the house.
(a) If the groundwater is in equilibrium with air in your house, does this air exceed either health standard? The dimensionless Henry's Law Constant for TCE at 20°C is HT=0.4.
(b) The flux of TCE through the floor of your house can be given by FT = k(c+ - CT) where k is a measured constant with value 106 m/s that depends on things like the type of walls in your house, the porosity of the soil, etc.; ct is the equilibrium air concentration of TCE (from part a); and CT is the concentration of TCE in the air in the house. The normal strategy for remediating vapor intrusion is to install fans in the house that ventilate the house with outside air with a throughput of Q, in units of m³/hour. Assume that the outside ambient air has a TCE concentration of ca ("a" is for ambient). Write a budget equation for TCE, i.e. dct/dt =< stuff >. You do NOT have to integrate this equation!
(c) Using the budget equation from (b), what is the equation for the characteristic time 7 for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation? Then substitute numbers to compute a value for T. Is a large or small value of 7 indicative of a significant TCE problem? (d) Assuming we want to keep CT below 20 ppm, compute the minimum value of Q. Compare your answer to Q = 40 cfm (cubic feet per minute), which is the residential requirement by law.
Answers
(a) Yes, the air in the house would exceed the long-term health standard if the groundwater is in equilibrium with the air in the house.
(b) The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT).
(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.
(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm.
(a) The Henry's Law constant for TCE is 0.4, which means that the concentration of TCE in air at equilibrium with water is 40% of the concentration in water. The groundwater concentration is 110 ppm, so the equilibrium air concentration would be 44 ppm. This exceeds the long-term health standard of 25 ppm.
(b) The flux of TCE through the floor is given by FT = k(c+ - CT), where k is a measured constant, c+ is the concentration of TCE in the groundwater, and CT is the concentration of TCE in the air in the house. The normal strategy for remediating vapor intrusion is to install fans in the house that ventilate the house with outside air. The outside ambient air has a concentration of ca. The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT), where dct/dt is the rate of change of the concentration of TCE in the house, k is the flux constant, c+ is the concentration of TCE in the groundwater, CT is the concentration of TCE in the air in the house, Q is the ventilation rate, and ca is the concentration of TCE in the outside air.
(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q, where Ah is the area of the house, k is the flux constant, and Q is the ventilation rate. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.
(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm. The difference is due to the fact that the groundwater concentration is much higher than the ambient air concentration.
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Among randomly selected drivers in the age bracket, were in a car crash in the last year. If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year? is it unlikely for a driver in that age bracket to be involved in a car crash during a year? is the resulting value high enough to be of concern to those in the age bracket? consider an event to be unlikely if its probability is less than or equal to 0. 5.
Answers
10 out of 400 means P(an accident/20-24)=10/400=1/40=0.025=2.5%
If less than 5% is unlikely, then 2.5% probability makes it unlikely a randomly selected driver in that age group would be in an accident.
No, it's not of concern if you only get concerned about likely events. But even an unlikely event is a worthy concern to the point of attempting to drive more safely, especially when insurance for the young is already very high, and would get even higher with an accident.
You might want to look at the car accidents. Were they minor fender benders or accidents with injuries and fatalities, or just car damage? The less damage or injuries, the less concern you probably would have.
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Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than
once.
y = -2x+3
4x + 2y = 6
y = -2x+3
4x+y=9
y = -2x+3
4x + 2y = 9
inconsistent
consistent
independent
dependent
Answers
The correct description will be;
⇒ y = - 2x + 3
4x + 2y = 6
These are independent.
⇒ y = -2x + 3
4x + y = 9
These are consistent.
⇒ y = -2x+3
4x + 2y = 9
These are inconsistent.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expressions are,
1. y = -2x+3
4x + 2y = 6
2. y = -2x+3
4x+y=9
3. y = -2x+3
4x + 2y = 9
Now,
From (1);
1. y = -2x+3
4x + 2y = 6
⇒ 2x + y = 3
4x + 2y = 6
⇒ 2x + y = 3
So We get;
⇒ 2/2 = 1/1 = 3/3
⇒ 1/1 = 1/1 = 1/1
These are independent.
From (2);
1. y = -2x+3
4x + y = 9
⇒ 2x + y = 3
4x + y = 9
So We get;
⇒ 2/4 ≠ 1/1
⇒ 1/2 ≠ 1/1
These are consistent.
From (3);
1. y = -2x+3
4x + 2y = 9
⇒ 2x + y = 3
4x + 2y = 9
So We get;
⇒ 2/4 = 1/2 = 3/9
⇒ 1/2 = 1/2 ≠ 1/3
These are inconsistent.
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100 POINTS!!!!!!!!!!! ( I NEED FAST ANSWERS ) The table below shows Karen's distance during the
marathon. Between which hours does Karen run the fastest?
Answers
Answer:
Between 6 and 9 hours.
Reason: the slope increases during 6-9 hour period.
Because the sloped increased
O No; there are y-values that have more than one x-value.
• No; the graph fails the vertical line test.
• Yes; the graph passes the vertical line test.
Yes; there are no y-values that have more than one x-value.
Answers
The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
How do functions work?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.
Please refer to the image instead of the graph, which is related to it.
The graphic displays a graph.
A parabola is seen on the graph.
The vertical line test determines if a graph can be a function, as is common knowledge.
The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
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Which of the following options have the same value as 70% of 80
Choose 3.
Answers
Answer:
56 is the answer so it's A, C and E.
Step-by-step explanation:
Graph the solution to this inequality on the number line.
−6x+8<−40
Answers
Answer:
x>8
Step-by-step explanation:
-6x+8<-40
-8. -8. (subtract f both sides)
-6x < -48
÷-6. ÷-6. (isolate variable)
x. > 8. ( when dividing and inequality by a neg number, flip the sign)