17. lim (2ln(x) - In(5x² + 1)) x48
The value of the limit as x approaches 48 is -1.6100.
To evaluate the limit:
lim (2ln(x) - ln(5x² + 1)) as x approaches 48,
we can directly substitute the value of x into the expression:
lim (2ln(48) - ln(5(48)² + 1))
Simplifying further:
lim (2ln(48) - ln(5(2304) + 1))
lim (2ln(48) - ln(11520 + 1))
lim (2ln(48) - ln(11521))
We can find the numerical values of ln(48) and ln(11521) as:
ln(48) = 3.8712
ln(11521) = 9.3524
Substituting these values back into the expression:
lim (2ln(48) - ln(11521))
= 2(3.8712) - 9.3524
= 7.7424 - 9.3524
= -1.6100
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3. The Alvarez family bought a car for $2,000. They made a down
payment of $500. If they want to pay the balance in 5 equal
payments, how much will each of these payments be?
The first step is to subtract $500 from $2000 and then you end up with $1500 which you then divide by 5.
Each payment will have to be $300
F(x) = x-10 f(10)=
Can somebody help me
Point F is on line segment EG. Given FG = 3x - 5, EF = 2, and
EG = 5x – 8, determine the numerical length of FG.
Answer:
2.5
Step-by-step explanation:
EG = EF + FG;
5x-8 = 2 + 3x-5
2x = 5
x = 2.5
FG = 3x-5 = 2.5
Estimate the solution to the system of equations.
Hey there! I'm happy to help!
Since we are using graphs, we will do not need to algebraically solve this system of equations.
When you graph a system of equations, the solution is always the point at which the two lines intersect.
Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3
Have a wonderful day! :D
Help anyone.!!!!!!!!
Answer:
2/5 is the answer man ooooo
Answer:
\(\frac{1}{25}\)
Step-by-step explanation:
So when you have a negative exponent, it means reciprocal.
\(5^{-2}\) will now be \(\frac{1}{5^2}\)
Now find the squared 5. 5 * 5 is 25.
So, your answer is 1/25
Hope this helps !!
-Ketifa
A product engineer has developed the following equation for the cost of a system component: C= (10P^2), where Cis the cost in dollars and Pis the probability that the component will operate as expected. The system is composed of 3 identical components, all of which must operate for the system to operate. The engineer can spend $252 for the 3 components. What is the largest component probability that can be achieved? (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
The largest component probability that can be achieved for the system is approximately 0.9428.
The cost of a system component is given by the equation C = 10\(P^2\), where C is the cost in dollars and P is the probability that the component will operate as expected. In this case, there are three identical components in the system, and the engineer has a budget of $252 to spend on these components.
To find the largest component probability that can be achieved, we need to determine the maximum value of P while staying within the budget. We can set up the equation:
3C = 252
Substituting C with the given equation, we get:
3(10\(P^2\)) = 252
Simplifying the equation, we have:
30\(P^2\) = 252
Dividing both sides of the equation by 30:
\(P^2\) = 8.4
Taking the square root of both sides:
P ≈ \(\sqrt{8.4}\)
P ≈ 2.8978
Since we are dealing with probabilities, the component probability cannot be negative, so we consider only the positive value. Therefore, the largest component probability that can be achieved is approximately 0.9428, rounded to 4 decimal places.
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You invest $20,000 in the stock market. The stock market then plummets
over the next few weeks. Each day, your investment loses half of its value. How
much will you have invested after 14 days? Write the geometric sequence
formula and show all of your work.
After 14 days, you will have approximately $2.4414 invested in the stock market.
The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:
an = a1 x \(r^{(n-1)\)
Where:
an is the nth term,
a1 is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.
Substituting the given values into the formula, we have:
a14 = 20000 x\((1/2)^{(14-1)\)
a14 = 20000 x \((1/2)^{13\)
a14 = 20000 x (1/8192)
a14 ≈ 2.4414
Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.
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The amount you will have invested after 14 days is given as follows:
$2.44.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The explicit formula of the sequence is given as follows:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term of the sequence.
The parameters for this problem are given as follows:
\(a_1 = 20000, q = 0.5\)
Hence the amount after 14 days is given as follows:
\(a_{14} = 20000(0.5)^{13}\)
\(a_{14} = 2.44\)
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Choose the three rectangles that have a perimeter of 12 meters.
Answer:
I think the answers would be a d and b
Step-by-step explanation:
the perimeter formula for a rectangle is 2L + 2W
if we take the measurements for rectangle a and add 4 + 4, we get 8. then we can do 2 + 2 to get 4. lastly, we would add 8 + 4, which equals 12.
for rectangle d, we can do 3 + 3, which equals 6. because the measurements are the same on each side, we don't have to do another equation and we would just add 6 + 6 to get 12.
and for rectangle b, you can do 1 + 1 = 2 and 5 + 5 = 10, then add 10 and 2 together to get 12.
Discuss the population scenario of Dhaka City. How do you want to restructure the population of Dhaka City to mitigate the present traffic jam situation? \( (3+7) \)
To mitigate the present traffic jam situation in Dhaka City, it is important to consider restructuring the population distribution and implementing effective urban planning strategies.
Here are some possible approaches:
Decentralization: Encourage the development of satellite towns and economic centers outside the central areas of Dhaka City. This can help disperse the population and economic activities, reducing the strain on the city's infrastructure and transportation systems.Improved public transportation: Enhance the public transportation network by expanding the coverage, increasing the frequency of services, and improving the quality of transportation modes such as buses, metro rail, and waterways. This can encourage more people to rely on public transport, reducing the number of private vehicles on the roads.Mixed-use development: Promote mixed-use development in the city by integrating residential, commercial, and recreational areas. This can reduce the need for long commutes and decrease traffic congestion during peak hours.Traffic management and infrastructure improvement: Implement effective traffic management strategies, including the development of intelligent transportation systems, traffic signal synchronization, and efficient road network planning. Additionally, invest in improving road infrastructure, constructing new roads, flyovers, and pedestrian-friendly infrastructure to accommodate the growing population and enhance traffic flow.Encourage alternative modes of transport: Promote and incentivize the use of alternative modes of transport such as cycling, walking, and carpooling. Establish dedicated cycling lanes, pedestrian-friendly sidewalks, and carpooling initiatives to reduce the reliance on private vehicles.Urban planning and zoning regulations: Enforce strict urban planning and zoning regulations to control haphazard urban growth and prevent the concentration of population in specific areas. Encourage the development of mixed-income neighborhoods and provide affordable housing options in various parts of the city.Telecommuting and flexible working arrangements: Encourage businesses and organizations to adopt telecommuting and flexible working arrangements to reduce peak-hour traffic congestion. This can be achieved by promoting remote work options and implementing policies that support flexible working hours.In conclusion, mitigating the traffic jam situation in Dhaka City requires a comprehensive approach that includes restructuring the population distribution, improving public transportation, implementing effective traffic management strategies, and promoting alternative modes of transport. These measures, combined with urban planning initiatives and flexible working arrangements, can help alleviate congestion and create a more sustainable and livable city.
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how many meters are their in centimeter
Answer:
You mean how many centimerters are in a meter?
In that case 100.
Step-by-step explanation:
Lana cuts 2 pieces for every 7 inches from a dowel for a craft project, for a total of 7 pieces.
Answer:
24.5 inches need to be cut
Step-by-step explanation:
I got c which is 100 but I don’t know how jerry got A
Choice C is the correct answer because
\(\frac{(6+2)^3-12}{5}\\\\\frac{(8)^3-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100\\\\\)
So in short, \(\frac{(6+2)^3-12}{5}=100\\\\\)
------------------------------------------
The mistake Jerry likely made was that he only cubed the 2 and didn't realize the 6 was part of that cubing process. It seems he didn't add first and decided to cube before adding.
This is probably what steps Jerry did
\(\frac{6+2^3-12}{5}\\\\\frac{6+8-12}{5}\\\\\frac{14-12}{5}\\\\\frac{2}{5}\\\\\)
But as mentioned, those steps are incorrect because the 6 is part of the cubing operation. In other words, Jerry should have added the 6+2 first before cubing afterward (due to PEMDAS determining the order of operations).
Or you could think of it like this
\(\frac{(6+2)^3-12}{5}\\\\\frac{(6+2)(6+2)(6+2)-12}{5}\\\\\frac{(8)(8)(8)-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100\)
Solve for X. 4.5/x = 3/4
Answer:x = 6
Step-by-step explanation:
because each 1/4 is equal to 1.5 in this instance. Making 3 of these equal parts equal to 4.5, and all 4 of them equal to 6 (the denominator).
In the figure, RV, WS, and QT intersect at point P.
What is the value of x? Show your work.
Answer:
x = 12
Step-by-step explanation:
67+42+6x-1=180
108+6x=180
6x=72
x=12
Jake made cupcakes for his birthday. He made 13 chocolate and 9 vanilla. What percent of the cupcakes
were chocolate?
Answer:
59 1/11 %
Step-by-step explanation:
13 chocolate and 9 vanilla = 22 total cupcakes
Percent chocolate = 13 chocolate / 22 total
=13/22
=.59090909
=59 1/11 %
1 of 20 ans
A lion needs to eat at least 15 pounds of food each day. The zoo feeds the lion using canisters that each contain 3 pounds of food. The lion has already
consumed 9 pounds of food. How many more canisters I of food does the lion need to eat? Write your answer as an inequality
The solution is
Answer:
At least 2 canisters of food.
Step-by-step explanation:
We know that the lion has eaten 9 pounds out of the 15 so far. Therefore, the lion must eat 6 more pounds of food today. We know that 6/3=2. That means that the lion must eat at least two canisters of food today.
a random sample of 100 people was taken. there were sixty people in the sample who favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 50%. the p-value is
The p- value for the given sample and favored sample to determine the proportion is equal to 0.04135 which is statistically significantly , reject null hypothesis and accept alternative hypothesis.
As given in the question,
Sample size of people 'n' = 100
Number of favored candidates = 60
Success value 'p' = 60/100
= 0.60
1 - p = 1 - 0.60
= 0.40
Null hypothesis : H₀ > 50%
Alternative hypothesis : H₁ ≤ 50%
Test statistic :
Proportion of the population:
z = (p - \(\^{p}\) ) / √ p ( 1- p)/n
= ( 0.60 - 0.50)/ √ 0.60(0.40)/100
= 0.10/ √0.0024
= 0.10/0.049
= 2.04
p - value using table is equal to 0.04135
Significant level is 0.05
0.04135 < 0.05 .
Here conclusion is statistically significant, reject null hypothesis and accept alternative hypothesis.
Therefore, the p- value for the given sample and favored sample is equal to 0.04135 which is statistically significantly , reject null hypothesis and accept alternative hypothesis.
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How can you decompose the composite figure to determine its area?
Answer:
as a trapezoid, a rectangle, and two squares
i need help with this. its dividing polynomials
Answer:
I don't know how to solve it
Answer:
x^2 + 3x + 9 + 7/x-3
Please help me out it’s urgent
Answer:
I would say 109 it looks a bit bigger than a 90-degree angle.
Step-by-step explanation:
if we take the line which is 180 and subtract 127 we get 53 from it.
We use 360 as another number considering the other angle is bigger than 180 so we do 360-304=56
So adding both together we get that x should be 109
Hope this helped.
A brainliest is always appreciated.
Solve for x in the diagram below
The value of x will be 34°
Given that
(x+12)°+100°+x° are forming linear pair
Linear pair of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
As mentioned, adjacent angles are angles that are next to each other. If you are sitting next to someone in class or on the bus, you could say that you are adjacent to them. More specifically, adjacent angles share a vertex and have a common side.
(x+12)°+100°+x°= 180°
⇒ x+ 12+ 100+x = 180°
⇒ 2x+112 = 180°
⇒ 2x = 180- 112
⇒ 2x = 68
⇒ x= 68/2
⇒ x= 34
For verification we will put value of x
(34+12)°+100°+34°
⇒ 46°+100°+34°
⇒146°+34°
⇒ 180°
So here we can see that by putting value of x we are getting the sum of 180°
Therefore value of x is 34
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B? Submit your answer as a percentage and round to two decimal places (Ex. 0.00hi) ation of 22%. If the correlation befween A and B is 0.93, what lis the expected roturn for a portsolio comprised of 60 percent Asset A and 40 percent Asset
In this case, Asset A has a return of 16% and represents 60% of the portfolio, while Asset B has a return of 22% and represents 40% of the portfolio. The correlation between Asset A and B is given as 0.93.
To calculate the expected return of the portfolio, we use the following formula:
Expected Return = (Weight of Asset A * Return of Asset A) + (Weight of Asset B * Return of Asset B) + (2 * Weight of Asset A * Weight of Asset B * Correlation between A and B * Standard Deviation of Asset A * Standard Deviation of Asset B)The expected return for a portfolio composed of two assets, A and B, can be calculated using the weighted average of the individual asset returns, considering their respective weights in the portfolio.
By plug in the given values and performing the calculations, we can determine the expected return for the portfolio comprised of 60% Asset A and 40% Asset B.
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what equals 1/4 of 68
Step-by-step explanation:
1 ×68/4×1
=68/4
hope it helps
Simplify 10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity.
After simplification of equation √(x + 7) − 1 = x, the value of x = 2.
What is an equation?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.To find the value of x:
√(x + 7) − 1 = x√(x + 7) = x + 1x + 7 = (x + 1)²x + 7 = x² + 2x + 10 = x² + x − 60 = (x + 3) (x − 2)x = -3 or 2Check for extraneous solutions:
√(-3 + 7) − 1 = -3√4 − 1 = -32 − 1 = -31 = -3x ≠ -3So,
√(2 + 7) − 1 = 2√9 − 1 = 23 − 1 = 22 = 2x = 2Therefore, after simplification x = 2.
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The correct question is given below:
Simplify the square root of the quantity x plus 7 end quantity minus 1 equals x.
what was the most inaccurate version of pi? explain who, when and what the value was.
The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.
Describe about the history of pi?The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.
The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.
This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.
It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.
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Does anyone know what (-4.79) + (-0.4)
PLEASE HELP
Hello !
1. Introduction++ ⇒ +
-- ⇒ +
+- ⇒ -
-+ ⇒ -
2. Application(-4.79) + (-0.4)
= -4.79 - 0.4
= -5.19
3. ConclusionThe answer is -5.19.
A shoemaker sold a pair of for $245.99 if the buyer a $300.00 bill, how much will the buyer receive in change?
*two decimal places don't forget your $ sign. Example: $50.00 NOT 50*
Answer:
$54.01
Step-by-step explanation:
All you have to do is $300.00-$245.99 .
Class A has 30 pupils and class B has 30 pupils.
Both classes sit the same maths test.
The mean score for class A is 55.
The mean score for class B is 65.
What is the mean score in the maths test across both classes?
Answer:
30
Step-by-step explanation:
b/c mean is average by another word
55 + 65 = 120
120\2 = 60
How many pounds of a metal containing 20% nickel must be combined with 6 pounds of a metal containing 80% nickel to form an alloy containing 60% nickel
Let's denote the amount of the metal containing 20% nickel that needs to be combined as 'x' pounds.
The amount of nickel in the metal containing 20% nickel is 20% of 'x', which can be expressed as 0.2x pounds.
The amount of nickel in the metal containing 80% nickel is 80% of 6 pounds, which can be expressed as 0.8 * 6 = 4.8 pounds.
To form an alloy containing 60% nickel, the total amount of nickel in the alloy should be the sum of the nickel amounts in each metal. Therefore, we can set up the equation:
0.2x + 4.8 = 0.6(x + 6)
Simplifying and solving for 'x':
0.2x + 4.8 = 0.6x + 3.6
0.2x - 0.6x = 3.6 - 4.8
-0.4x = -1.2
x = -1.2 / -0.4
x = 3
Therefore, 3 pounds of the metal containing 20% nickel must be combined with 6 pounds of the metal containing 80% nickel to form an alloy containing 60% nickel.
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