Answers
The solution to the limits (a) and (b) are 24 and 4 respectively.
Understanding LimitsGiven
lim f(x)=8
lim g(x)=-2
lim h(x)=0
Using the properties of limits and basic arithmetic operations, we can find the limit of the following:
(a) \(\lim_{x \to \ 3} [2f(x) - 4g(x)]\)
We can apply the properties of limits to each term separately:
lim [2f(x)] - lim [4g(x)] as x approaches 3.
Using the given information:
2 * lim f(x) - 4 * lim g(x) as x approaches 3.
Substituting the known limits:
2 * 8 - 4 * (-2) = 16 + 8 = 24.
Therefore, lim [2f(x) - 4g(x)] as x approaches 3 is equal to 24.
(b) \(\lim_{n \to \ 3} [2g(x)^{2} ]\)
We can apply the property of limits to the entire expression:
[lim (2g(x))]² as x approaches 3.
Using the given information:
[lim g(x)]² as x approaches 3.
Substituting the known limit:
(-2)² = 4.
Therefore, lim [2g(x)]² as x approaches 3 is equal to 4.
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Related Questions
Two amounts of money are in the ratio 8:3 if the second amount is 4.05,what is the value if the first amount?
Answers
Answer: 10.75 currency units
Step-by-step explanation:
The amounts of money are in the ration 8:3 which means that for every 3 units of the second amount, there are 8 units of the first.
Use direct proportion to solve:
8 : 3
x ; 4.03
Cross multiply to get:
3x = 32.24
x = 32.24 / 3
x = 10.75 currency units
Find the length (distance) of a pen that starts at the 4.1 inch mark on a ruler and ends at 11 inches
Answers
Answer:
All we need to do is 11 - 4.1. we know to turn 4.1 into a 5, we need to add 0.9. With this knowledge, we can do the equation 6.9 + 4.1, which equals 11. So, the length of the pen is 6.9 inches.
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This scale drawing shows an enlargement in a figure. What is the value of x?
Enter your answer as a decimal in the box. (the first figure has 10,4 and the second has 14,x
Answers
To find the value of x in the given scale drawing,we divide both sides of the equation by 10, giving us x = 56/10 = 5.6.Therefore, the value of x in the scale drawing is 5.6.
We can set up a proportion using the corresponding sides of the two figures. In the original figure, we have a side length of 10 units, and in the enlarged figure, the corresponding side length is 14 units. Let x represent the missing side length in the enlarged figure.
Setting up the proportion, we have:
10/4 = 14/x
To solve for x, we can cross multiply:
10x = 4 * 14
10x = 56
Dividing both sides by 10:
x = 5.6
Therefore, the value of x in the scale drawing is 5.6.
In the given scale drawing, we have two figures, with the first figure having a side length of 10 units and the second figure having a corresponding side length of 14 units. We need to find the value of x, which represents the missing side length in the enlarged figure.
To do this, we set up a proportion using the corresponding sides of the two figures. The proportion is given by 10/4 = 14/x.
Cross multiplying, we get 10x = 4 * 14.
Simplifying the right side, we have 10x = 56.
To solve for x, we divide both sides of the equation by 10, giving us x = 56/10 = 5.6.
Therefore, the value of x in the scale drawing is 5.6.
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Jenny is organising a barbecue. There are 30 bread rolls in a pack.
There are 16 sausages in a pack.
She needs exactly the same number of sausages as bread rolls.
What is the smallest number of packets she could buy?
— Help asap would be appreciated with explanation of how to get the answer! —
— Thank you in advance ✨
Answers
Answer:
16 bread roll packs and 30 sausages
Step-by-step explanation:
multiply 30 by 16 =480
to get 480
you need 16 bread roll packs and
30 sausages pack
16/2=8
30/2=15
So the smallest number of packets would be 8 packets of sausages and 15 packets of bread to have an equal number of sausages to bread.
6. The coordinates of point A are given. The midpoint of AB is (3,-5). Find the coordinates of point B.
a. A(4,-8)
b. A(2.5, -6.5)
Answers
Midpoint = (x1 + x2)/2, (y1 + y2)/2
In this case, we are given that the midpoint of AB is (3,-5). We can substitute this into the midpoint formula to find the coordinates of point B.
Midpoint = (x1 + x2)/2, (y1 + y2)/2
= (3 - x1)/2, (-5 - y1)/2
We can then solve for x1 and y1, which are the coordinates of point A.
x1 = 23 - x2
y1 = 2(-5) - y2
Substituting the given coordinates of the midpoint into these equations, we get:
x1 = 6 - x2
y1 = -10 - y2
We are given that the coordinates of point A are (4,-8). Substituting these values into the equations above, we can solve for x2 and y2, which are the coordinates of point B:
x1 = 6 - x2
4 = 6 - x2
x2 = 2
y1 = -10 - y2
-8 = -10 - y2
y2 = -6
Therefore, the coordinates of point B are (2,-6). This means that the correct answer is option (a), A(4,-8).
Use the number line to find the measure of AC.
A) 2
B)4
C)6
D)8
Answers
Answer:
j
bdufiduyr8ududgcjzloyetipp9ye9q5ysp
What is the answer to this equation \(10\sqrt{x} 20\)
Answers
Use the properties of radicals
Simplify the roots
Calculate
And your solution will be 20 overall 5
Message me if you want me to write it all down!
Randy was playing "Double Heads," a game in which he would flip two coins at a time. He recorded the number of times he flipped two heads at the same time. He flipped the coins 50 times, and there were 20 times when both coins landed heads up, which he recorded as 20/50. How does 20/50 compare to 50%?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Total number of coin flips = 50
Number of times both coins landed head up = 20.
Hence probability of having two heads :
Probability = required outcome / Total possible outcomes
P(both heads up) = 20/50
Comparing 20/50 to 50%
We convert 20/50 to percentage :
(20/50) × 100%
0.4 × 100% = 40%
20/50 is equivalent to 40%
Hence, 40% is less than 50%
Please solve this and show the steps on how you got your answer
Answers
well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so
\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)
Answer:
y = 28
Step-by-step explanation:
The dashes on line segments AC and BC indicate that the line segments are equal in length.
Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.
The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.
Interior angles of a triangle sum to 180°.
Therefore:
⇒ ∠A + ∠B + ∠C = 180°
⇒ 34° + 34° + 4y° = 180°
⇒ 68° + 4y° = 180°
⇒ 4y° = 112°
⇒ y = 112° ÷ 4°
⇒ y = 28
In a systematic random sample of size n drawn from a population of size N, how many random numbers need to be generated to identify those subjects who are included in the sample
Answers
A systematic random sample is obtained by choosing a random starting point and then selecting every kth individual from a population to participate in the study. The number of random numbers that must be produced to recognize individuals who are part of the sample is determined by the following formula:n/k is the number of random numbers required to identify the sample population of size n drawn from a population of size N by systematic random sampling.
To provide an example, consider a population of size N= 1000 and a sample of size n= 50. Assume that we must use systematic random sampling with a k=20. The population should be numbered, and the first random number between 1 and 20 is selected. The kth person after the first random number is chosen. This process is repeated for the entire population, with every kth person included in the sample. The number of random numbers generated would be 1000/20= 50. Therefore, to obtain a sample of 50 individuals, we must generate 50 random numbers to recognize each individual who will be included in the sample.
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Mia is 7.01568 x 10^*6 minutes old. Convert her age to more appropriate units using years, months, and
days. Assume a year has 365 days and a month has 30 days.
Mia is
years=,
= months, and =
days old.
Answers
\(7.01568 * 10^6=7015680\) minutes
There are:
60 minutes in an hour
24 hours in a day (60 * 24 = 1440 minutes)
30 days in a mouth (1440 * 30 = 43,200 minutes)
360 days in a year (1440* 365 = 525,600 minutes)
To find out how many years old she is we must divide the number of minutes old she is by the number of minutes in a year.
7015680 / 525,600 = 13 years with a remainder of 182,880 minutes
To find out how many months old she is we must divide the remaining minutes by the number of minutes in a month.
182,880 / 43,200 = 4 months with a remainder of 10,080 minutes
To find out how many days old she is we must divide the remaining minutes by the number of minutes in a day.
10,080 / 1440 = 7 days
Answer: Mia is 13 years, 4 months and 7 days old
The table shows the number of points scored by a basketball team in their first seven games.
Answers
Answer:
15
Step-by-step explanation:
the range is the largest number take away the smallest number
56-41=15
9+1.34+1\2(3.50+1.74) pls help
Answers
Answer:
12.96
Step-by-step explanation:
Helpsies pleasies hbjhbjubuguihhkuh
Answers
not shy not me
Consider the following linear programming problem: Maximise profit = 2X₁ - X₂ + 2X3 Subject to: 2X₁ + X₂ + 0x3 ≤10 X₁ + 2X₂ - 2X3 ≤ 20 0X₁ + X₂ + 2X3 ≤ 5 X₁ ,X2, X3 > 0 Change the objective function and constraints to simplex format by including the necessary additional variables.
Solve the problem above using the simplex method.
Answers
The linear programming problem is to maximize the profit function, given constraints, using the simplex method.
To convert the problem into the simplex format, we introduce slack variables to transform the inequality constraints into equalities. Let S₁, S₂, and S₃ be the slack variables for the three constraints, respectively. The converted objective function becomes Z = 2X₁ - X₂ + 2X₃ + 0S₁ + 0S₂ + 0S₃. The constraints in the simplex format are:
2X₁ + X₂ + 0X₃ + S₁ = 10,
X₁ + 2X₂ - 2X₃ + S₂ = 20,
0X₁ + X₂ + 2X₃ + S₃ = 5.
Now we can construct the initial simplex tableau:
┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│ Basis │ X₁ │ X₂ │ X₃ │ S₁ │ S₂ │ S₃ │ RHS │
├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│ Z │ 2 │ -1 │ 2 │ 0 │ 0 │ 0 │ 0 │
│ S₁ │ 2 │ 1 │ 0 │ 1 │ 0 │ 0 │ 10 │
│ S₂ │ 1 │ 2 │ -2 │ 0 │ 1 │ 0 │ 20 │
│ S₃ │ 0 │ 1 │ 2 │ 0 │ 0 │ 1 │ 5 │
└─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
Using the simplex method, we perform iterations until we obtain the optimal solution. In each iteration, we select the most negative coefficient in the Z row as the pivot column and apply the minimum ratio test to determine the pivot row. The pivot element is chosen as the value where the pivot column and pivot row intersect. We then perform row operations to make the pivot element equal to 1 and all other elements in the pivot column equal to 0.
After performing the necessary iterations, we reach the optimal solution with a maximum profit of 55 units. The values for the decision variables are X₁ = 0, X₂ = 5, and X₃ = 10. The final simplex tableau is:
┌─────────┬───────┬───────┬───────┬───────┬───────┬───────┬───────┐
│ Basis │ X₁ │ X₂ │ X₃ │ S₁ │ S₂ │ S₃ │
RHS │
├─────────┼───────┼───────┼───────┼───────┼───────┼───────┼───────┤
│ Z │ 0 │ 0 │ 1 │ 0.5 │ -1 │ -0.5 │ 55 │
│ X₂ │ 0.5 │ 0 │ 0 │ 0.5 │ -0.5 │ 0 │ 5 │
│ S₂ │ 0.5 │ 1 │ 0 │ -0.5 │ 0.5 │ 0 │ 15 │
│ X₃ │ -0.5 │ 0 │ 1 │ 0.5 │ 0.5 │ -0.5 │ 0 │
└─────────┴───────┴───────┴───────┴───────┴───────┴───────┴───────┘
Therefore, the optimal solution to the linear programming problem is X₁ = 0, X₂ = 5, and X₃ = 10, with a maximum profit of 55 units.
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find the values X and Y if L ll M .
Answers
Let's solve for x first.
To find x, use the interior angles on same side of a transversal theorem.
The interior angles on sam side of a transversal are supplemantary angles, and supplementary angles sum up to 180 degrees.
Thus, we have:
(23x - 16) + (8x - 21) = 180
23x - 16 + 8x - 21 = 180
Combine like terms:
23x + 8x - 21 - 16 = 180
31x - 37 = 180
Add 37 to both sides:
31x - 37 + 37 = 180 + 37
31x = 217
Divide both sides by 31:
\(\begin{gathered} \frac{31x}{31}=\frac{217}{31} \\ \\ x\text{ = 7} \end{gathered}\)To find y, use the vertical angles theorem.
Vertical angles are congruent.
Thus we have:
7y - 23 = 23x - 16
Since x = 7, substitute x for 7 in the equation above to find y.
7y - 23 = 23(7) - 16
7y - 23 = 161 - 16
7y - 23 = 145
Add 23 to both sides:
7y - 23 + 23 = 145 + 23
7y = 168
Divide both sides by 7:
\(\begin{gathered} \frac{7y}{7}=\frac{168}{7} \\ \\ y\text{ = }24 \end{gathered}\)x = 7
y = 24
ANSWER:
x = 7
y = 24
WILL GIVE BRANLIEST! pls help thank u sm!! :-) u are all amazing
Answers
Answer:
B. 81
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
√x + 3 = 12
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 3 on both sides: √x = 9[Equality Property] Square both sides: x = 81Answer:
B
Step-by-step explanation:
Given
\(\sqrt{x}\) + 3 = 12 ( subtract 3 from both sides )
\(\sqrt{x}\) = 9 ( square both sides )
x = 9² = 81 → B
Combine like terms: 2r + r² – 4 + r
Show Work Pls
Answers
Answer:
r^2+3r-4
Step-by-step explanation:
combine like terms:
2r+r
vvvv
3r+r^2-4
rearrange terms:
r^2+3r-4
market researchers would like to know if consumers can tell the difference between a product made with low calorie oil and the same product made with regular oil. a large representative sample of 400 people are blindfolded and given both products to taste. overall, 230 people correctly identify which of the two products is low calorie and with is regular. what is the probability that this proportion or more would identify the two products correctly if they were guessing?
Answers
0.002
The probability that this proportion or more would identify the two products correctly if they were guessing is 0.002.There are two possible outcomes when one guesses: identifying the low-calorie oil or not. Thus, there is a probability of 0.5 of choosing the right oil by guessing. This problem requires calculating the probability of obtaining 230 or more individuals who guessed right out of 400, assuming that people guessed with no knowledge of which oil was low calorie or not. That is, it is the same as the probability of getting 230, 231, 232, ..., 399, or 400 people who guessed correctly. This can be calculated using binomial probabilities.Binomial probabilities are expressed as follows:P(X) = (nCx)(p^x)(q^(n-x))where X is the number of successful outcomes, n is the total number of trials, p is the probability of success, and q is the probability of failure. nCx, called the binomial coefficient, is the number of combinations of n things taken x at a time, which is calculated as follows:nCx = n! / [(n-x)!x!]where n! is the factorial of n, or n! = n(n-1)(n-2) ... 3.2.1.To calculate the probability that 230 or more people would guess correctly, the following formula can be used:P(X >= 230) = P(X = 230) + P(X = 231) + ... + P(X = 399) + P(X = 400) = [400C230(0.5^230)(0.5^170)] + [400C231(0.5^231)(0.5^169)] + ... + [400C399(0.5^399)(0.5^1)] + [400C400(0.5^400)(0.5^0)]P(X >= 230) = 0.002 approximately. Therefore, the probability that this proportion or more would identify the two products correctly if they were guessing is 0.002.
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Please help I need this answer asap
a
b
c
d
Answers
Answer:
Step-by-step explanation:
b
Q 11. Luis and Baca have been weightlifting with each other and want to see how long it will take them to be the same weight. Luis weighs 194 pounds and gains 0.6 pounds of muscle per week. Baca weighs 218 pounds and gains 0.2 pounds of muscle per week. Create an equation that Luis and Baca can use to determine how long it will take for them to be the same weight. In the text box, write about how you formed the equation used to determine when Luis and Baca would be the same weight. BI
Answers
Luis and Baca would be the same weight after 60 weeks of weightlifting.
What is a linear Equation?A linear equation is one in which the highest power of the variable is consistently 1. A one-degree equation is another name for it. A linear equation with one variable has the formula Ax + B = 0, which is its standard form. x is a variable, A is a coefficient, and B is constant in this situation.
To create an equation that Luis and Baca can use to determine how long it will take for them to be the same weight:
Let the time taken by Luis and Baca to be of the same weight be x weeks,
Given:
Initial weight of Luis = 194 pounds
Initial weight of Baca = 218 pounds
Then,
Weight gained by Luis in x weeks = 0.6x pounds
Weight gained by Baca in x weeks = 0.2x pounds
Total weight of Luis after x weeks = (194 + 0.6x ) pounds
Total weight of Baca after x weeks = (218 + 0.2x) pounds
For Luis and Baca to be of the same weight,
Total weight of Luis after x weeks = Total weight of Baca after x weeks
Therefore, we equate the total weight gained by Luis and Baca after x weeks to determine the value of x
⇒ 194 + 0.6x = 218 + 0.2x
⇒ 0.6x - 0.2x =218 - 194
⇒ 0.4x = 24
⇒ x = 60
Hence, Luis and Baca would be the same weight after 60 weeks of weightlifting.
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The heights of the bars of a histogram correspond to:
Answers
Answer:
Frequency values
Step-by-step explanation:
The heights of the bars of a histogram correspond to the frequency values of the given data.
I put $300 into a back account that gives me 2.5% simple interest. How much interest do i earn after 3 years
Answers
Answer:
$23.07
Step-by-step explanation:
Present Value(PV) = $300
Interest rate(r) = 2.5 % or 0.025
Year(d) = 3 years
Find Future Value first.
This is the formula:
FV = PV(1 +r)\(^{d}\)
Put the values to it.
FV = 300(1 + 0.025)\(^{3}\)
FV = 300(1.025\()^{3}\)
FV = 300(1.076890625)
FV = 323.0671875 or $323.07
The future value is $323.07. Now subtract it to the present value to get the interest.
323.07 - 300 = $23.07
The interest is $23.07
If you go up to your attic on a summer day, which best explains why you may feel very hot?
A Conduction caused hot air to rise to the top of your house.
B Convection caused hot air to rise to the top of your house.
C The attic is insulated from the cooler temperatures below.
D None of the above
Answers
Answer:
Step-by-step explanatB Convection caused hot air to rise to the top of your house is the best explanation for why you may feel very hot when you go up to your attic on a summer day.
Convection is the transfer of heat by the movement of a fluid, such as air. On a hot summer day, the air inside your attic can become very hot, and because hot air rises, it will accumulate at the top of your house. When you go up to your attic, you will feel the heat from this accumulated hot air.
Conduction, on the other hand, is the transfer of heat through a material, such as the roof or walls of your house. While some heat may be conducted through the roof, it is unlikely to be the primary cause of the heat in your attic.
Insulation (option C) can help to keep the heat from the attic from escaping into the cooler temperatures below, but it is not the primary cause of the heat in the attic.
ion:
In physics, kinetic energy is the energy of an object in motion. Kinetic energy, K, measured in joules (J), is
calculated using the formula K= 1/2mv^2, where m is mass of the object, measured in kilograms (Kg), and v is the velocity of the object, measured in meters per second (m/s).
Rearrange the formula to solve for mass (M).
Answers
Answer:
\(m = \frac{2k}{v^{2} } \)
Step-by-step explanation:
\(k = \frac{1}{2} mv ^{2} \)
\(v ^{2} m = 2k\)
\(m = \frac{2k}{v ^{2} } \)
1. An equilateral triangle was reflected
relatively to the line passing through its
side. What is the result?
A. The second triangle has become
bigger than the initial triangle.
B. It turned into a versatile triangle.
C. The second triangle has become
smaller than the initial triangle.
D. The second triangle is the same size
as the initial triangle.
Answers
The second triangle will have the same side lengths and angles as the initial triangle.
The correct option is D.
The reflection of an equilateral triangle relative to the line passing through its side results in a new equilateral triangle that is the same size as the initial triangle. Therefore, the correct answer is D: The second triangle is the same size as the initial triangle.
When a figure is reflected across a line, every point on the figure is flipped to the opposite side of the line, maintaining the same distances and angles. In the case of an equilateral triangle, each side is reflected to the opposite side of the line, resulting in a new equilateral triangle with the same side lengths and angles.
The property of an equilateral triangle is that all three sides are equal in length, and all three angles are equal to 60 degrees. The reflection does not alter these properties. Therefore, the second triangle will have the same side lengths and angles as the initial triangle.
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Can someone help me with these two questions plss
Answers
Answer:
c. 6
d. 3
Step-by-step explanation:
:-)
Lines 60-64 ("Being . . . teenagers") suggest that
excluding a book from a reading list might
(A) enhance the reputation of the book’s author
(B) encourage students to protest the decision
(C) influence course curricula nationwide
(D) appease conservative parents
(E) disappoint the book’s fans
Answers
Lines 60-64 ("Being . . . teenagers") suggest that excluding a book from a reading list might enhance the reputation of the book’s author.
Why is reading important for teens?Reading helps kids broaden their perspectives as they discover more about people and the world, in addition to assisting them in academic success. Additionally, reading can help teenagers recognize that problems are a part of everyone's lives and may even help them find solutions to their own issues. Additionally, reading can help teenagers recognize that problems are a part of everyone's lives and may even help them find solutions to their own issues. Last but not least, reading is fun. It can be really enjoyable for teenagers. Every stage of a child's life, from birth through adolescence, benefits from reading aloud. Teenagers can be drawn to books in significant ways thanks to displays. There are some fantastic display collections on Pinterest.
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how to read a ruler in inches
Answers
One inch is equal to 2.54 centimeters on the ruler, so, to read on the ruler, every 2.54 cm will be equal to one inch.
Normally a ruler scale if of length 15cm. we have certain marks on the ruler to read the rules of the scale/ruler.
Now, from the standard unit conversion methods, we know, one inch is equal to about 2.54 centimeters.
Now, what we to is, to read the ruler, we mark every 2.54cm on the ruler and that becomes equal to one inch. On a scale of 15cm there will be 6 inches on the ruler.
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Please help me I need to finish today!
Answers
Answer:
C
Step-by-step explanation:
For Youfang, the time spent running is equal to 15 times the week