24. [0/1 Points] DETAILS PREVIOUS ANSWERS WANEFMAC7 13.2.074. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find f(x) if f(2) = 0 and the tangent line at (x, f(x)) has slope x/(x^² + 3).
f(x) = 1/2en|x^2 + 3|-1/2en|7|
Answers
The function f(x) is: f(x) = \((1/2) ln|x^2 + 3| - (1/2) ln|7|\) given that f(2) = 0 and the tangent line at (x, f(x)) has a slope x/(x² + 3).
Let's find f(x) step-by-step:
1. We know that the slope of the tangent line is the derivative of the function, f'(x). So, we have f'(x) = x/(x² + 3).
2. To find f(x), we need to integrate f'(x) with respect to x.
3. Integrate x/(x² + 3) dx. Using substitution, let u = x² + 3, so du = 2x dx. Therefore, the integral becomes \((1/2)\int\ {(1/u)} \, du\).
4. Now, integrate \((1/2)\int\ {(1/u)} \, du\) = (1/2) ln|u| + C = (1/2) ln|x² + 3| + C.
5. We have f(x) = (1/2) ln|x² + 3| + C. To find the constant C, we'll use the given condition f(2) = 0.
6. Plug in x = 2: 0 = (1/2) ln|2² + 3| + C. Simplify and solve for C: C = - (1/2) ln|7|.
7. Now we have the function f(x) = \((1/2) ln|x^2 + 3| - (1/2) ln|7|\).
So, f(x) = \((1/2) ln|x^2 + 3| - (1/2) ln|7|\).
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Related Questions
It is advertised that the average braking distance for a small car traveling at 70 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 38 small cars at 70 miles per hour and records the braking distance. The sample average braking distance is computed as 112 feet. Assume that the population standard deviation is 25 feet. (You may find it useful to reference the appropriate table: z table or t table)a. State the null and the alternative hypotheses for the test. H0: μ = 120; HA: μ ≠ 120 H0: μ ≥ 120; HA: μ < 120 H0: μ ≤ 120; HA: μ > 120b. Calculate the value of the test statistic and the p-value. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)Find the p-value. 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 0.025 p-value < 0.05c. Use α = 0.01 to determine if the average breaking distance differs from 120 feet.
Answers
The alternative hypothesis is H0: μ = 120; HA: μ ≠ 120; test static is -1.9666; and p-value is between 0.025 and 0.05.
a. The null and alternative hypotheses for the test are:
H0: μ = 120; HA: μ ≠ 120
b. To calculate the value of the test statistic, use the following formula:
test statistic (z) = (sample average - population mean) / (population standard deviation / √sample size)
z = (112 - 120) / (25 / √38)
z = (-8) / (25 / 6.1644)
z = -8 / 4.0675
z = -1.9666 (rounded to 4 decimal places)
Now, find the p-value using the z-table:
Since the alternative hypothesis is a two-tailed test (μ ≠ 120), we need to find the two-tailed p-value.
From the z-table, the area to the left of -1.9666 is approximately 0.0247.
Since it's a two-tailed test, we multiply the area by 2.
p-value = 2 * 0.0247 = 0.0494 (rounded to 4 decimal places)
The p-value is between 0.025 and 0.05.
c. Since the p-value (0.0494) is greater than α = 0.01, we fail to reject the null hypothesis at the 0.01 significance level. Therefore, there is not enough evidence to conclude that the average braking distance differs from 120 feet.
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from a group of 10 people, a committee of 5 is to be formed. the committee consists of a chair, a secretary and 3 regular members. (a) how many dierent committees are possible?
Answers
The number of ways of selecting a committees of 5 members from a group of 10 people will be 252
Combination is a method to calculate different ways to select items from a set / group regardless of the order.
ⁿCₓ = n! / (n-x)! x!
Total number of people in group is 10
Number of people require to form committee is 5
By using Combination ,
¹⁰C₅ = 10! / (10 - 5 )! 5!
= 10×9×8×7×6×5! / 5! × 5!
Cancelling 5! from numerator and denominator
= 10×9×8×7×6 / 5!
expanding the factorial
= 10×9×8×7×6 / 5×4×3×2×1
= 252
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the gas tank in mr.makies car hold 15 1/5 gallongs of gas .how many gallongs are in the tank when its 1/4 full
Answers
Answer:
3.8 Gallongs
Step-by-step explanation:
15.2/4
a 20 ft ladder leans against building so that the angle between the ground and the ladder is 60 degrees. how far from the building is the base of the ladder?
Answers
Salut/Hello!
Answer: 20 ft
Step-by-step explanation:
We can imagine the ladder, wall and ground as a triangle.
(And because we don't know if our triangle has a 90 degrees angle it means it's an ordinary triangle.)
We know that a triangle that has an angle with 60 degrees means all of its angles have 60 degrees because 180 : 3 angles = 60 degrees which means the triangle is equilateral.
Definition of the equilateral triangle: The triangle that has the 3 side with the exact same length.
From the equilateral triangle we know all sides are equal. If the ladder is 20 ft that means the distance between the building and the base of the ladder (which is actually the base of our triangle) is 20 ft.
I hope it was useful! :]
the ratio of the measures of the three angles in a triangle is 14:5:11.Use the variable X as the uknown.Solve for X
Answers
The value of 'x' in the ratio 14 : 5 : 11 is 6.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the sum of all the interior angles in a triangle is 180°.
Given, The angles are in the ratio 14 : 5 : 11.
Let, 'x' be the ratio multiplier.
Therefore, 14x + 5x + 11x = 180.
30x = 180.
x = 180/30.
x = 6.
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a large retailer purchases 100,000 light bulbs per year. the bulb producer claims he has a defective rate of 0.01, but the retailer suspects it may be higher. 1050 bulbs are defective in the retailers lot. what is the p-value for the test of the claims?
Answers
The p-value for the test of the claims is roughly 0.004.
To test the claim of the bulb patron, we can use a thesis test with the following null and indispensable suppositions.
Null thesis: The imperfect rate of the bulbs is 0.01 or lower( i.e., p ≤0.01). Indispensable thesis: The imperfect rate of the bulbs is more advanced than 0.01 ( i.e., p>0.01).We can use the binomial distribution to calculate the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. This probability is the p-value of the test.
To calculate the p-value, we need to use the binomial distribution and find the probability of observing 1050 or further imperfect bulbs out of,000 if the imperfect rate is 0.01 or lower. Using a binomial calculator or statistical software, we can find that the probability of observing 1050 or further imperfect bulbs is roughly 0.004.
Since this p-value is lower than the significant position of 0.05, we can reject the null thesis and conclude that the imperfect rate of the bulbs is more advanced than 0.01.
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There was a sample of 500 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 3.8% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between y and t.
Answers
Answer:
y = 500 • (0.952)ⁿ
Step-by-step explanation:
y = 500 • (0.952)ⁿ
What is the answer to 5/8 ÷ 3/4 in fraction form
Answers
Answer:
5/6
Step-by-step explanation:
brainliest + ten points to first correct answer! word problem.
A high school soccer team has 18 players. There are 16 years, for juniors, four sophomores, and the rest are freshman. What is the ratio of seniors to freshman?
Answers
Incomplete question
How high is a weather balloon that is tied to the ground if it is secured by a 15m long rope and the angle between the rope and the ground is 35?
Answers
Joseph rented a surf board for $5.25 per hour plus a $16.75 fee. Write an expression that shows how much it will cost josheph to rent the surf board for x hours
Answers
Answer:
$22 dollars
Step-by-step explanation:
Add the two numbers. x means one for mathamatics.
PLEASE HELP ASAP WILL GIVE BRAINLIEST IF CORRECT
what is 15x + 21x/2??
Answers
Answer:
25.5x
Step-by-step explanation:
Simply convert the fraction into a decimal and add.
21/2x = 10.5x
10.5x + 15x = 25.5x
If you want to keep it in fraction form, 15 is 30/2, so,
30x/2 + 21x/2 = 51x/2
Answer:
51x/2
Step-by-step explanation:
Add it like a normal fraction equation
Have them both with the same denominator of 2
30/2 + 21/2
Add the numerators
51/2
Now put the x into the numerator since it started as in the numerator
Answer: 51x/2
Hope this helps!
there are multiple graph with degree sequence (4,4,4,4,4,4,2). explain why none of them are bipartite.
Answers
None of the graphs with the given degree sequence (4,4,4,4,4,4,2) can be bipartite.
To understand why none of the graphs with the given degree sequence (4,4,4,4,4,4,2) are bipartite, let's first define the key terms:
1. Degree: The degree of a vertex in a graph is the number of edges incident to it.
2. Sequence: A degree sequence is a list of the degrees of each vertex in a graph.
3. Bipartite: A graph is bipartite if its vertices can be partitioned into two disjoint sets such that no two vertices within the same set are adjacent.
Now, let's analyze the given degree sequence (4,4,4,4,4,4,2):
1. There are 7 vertices in the graph.
2. The sum of the degrees is 4+4+4+4+4+4+2 = 26, which is even (a necessary condition for a graph to be bipartite).
For a graph to be bipartite, it must satisfy the Handshaking Lemma. The Handshaking Lemma states that the sum of the degrees of all vertices in a set should be equal to the sum of the degrees of all vertices in the other set. In other words, the sum of the degrees of all vertices in one set is equal to the number of edges crossing between the two sets.
Let's assume we can divide the vertices into two disjoint sets, A and B. Since each vertex with degree 4 is adjacent to 4 vertices, it must be connected to vertices in the opposite set. However, we have six vertices with degree 4, so the total sum of degrees of vertices in set A would be 6 * 4 = 24, while the vertex with degree 2 in set B would only account for 2. This contradicts the Handshaking Lemma, as 24 ≠ 2.
Hence, none of the graphs with the given degree sequence (4,4,4,4,4,4,2) can be bipartite.
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In the fish tank 4 out of 5 fish are guppies. There are 25 fish in the tank. How many are guppies?
Answers
Answer:
20
Step-by-step explanation:
25/5=5
5*4=20
20/25=4/5
Answer=20
solve 3^x+1/3^x=82/9
Answers
Answer:
x= -2, 2
Step-by-step explanation:
Please assist me with this problem
Answers
Answer:
x = 192
Step-by-step explanation:
The three right triangles in the figure are all similar, so their sides are proportional.
ProportionThe length marked x is the long side of the smallest triangle, and the short side of the middle-size triangle. The long side of the middle-size triangle is ...
400 -144 = 256
We now have enough information to write the proportion ...
long side/short side = x/144 = 256/x
Multiplying by 144x gives ...
x² = (144)(256)
x = √(144×256) = 12×16 = 192
The length x is 192 units.
HELP ME PLS
1. Gio mows lawns for $25 each. He already has $250 in his bank account, but is trying to save $900. How many lawns will he need to mow to reach his goal?
2. Lani buys groceries at the store for $30.25. He spent $5.25 on apples, $3.25 on a box of crackers, and the rest on 3 pounds of lunch meat. How much did the lunch meat cost, in dollars per pound?
3. Sari is creating a dog run space in her backyard. She has 40 feet of fencing to go around the outside, and she wants to make it rectangular with a width of 8 feet. What will the length be, in feet?
4. Siara is baking biscuits for a bake sale. Each batch makes 75 biscuits, and her friend gives her another 60 biscuits. She ends up with 360 biscuits total for the bake sale. Use algebra to solve for how many batches she made.
5. Jose has a comic book collection that he keeps among 5 shelves with an equal number on each shelf. His father adds 20 comic books to the bottom shelf, so the shelf now has 125 books. How many total books are in his collection? Use algebra to solve the equation.
Answers
Answer:
Step-by-step explanation:
1. To reach his goal of $900, Gio will need to mow 900 - 250 = 650 dollars worth of lawns. Since each lawn mowing costs 25 dollars, he will need to mow 650 / 25 = 26 lawns.
2. The cost of the lunch meat was 30.25 - 5.25 - 3.25 = 22 dollars. Since there were 3 pounds of lunch meat, the cost per pound was 22 / 3 = 7.33 dollars.
3. Sari wants to create a rectangular dog run space with a width of 8 feet. Since the perimeter of the rectangle is 40 feet, the length of the rectangle must be 40 - 8 - 8 = 24 feet.
4. Let's call the number of batches Siara baked b. Siara's friend gave her 60 biscuits, so the total number of biscuits Siara baked is 360 - 60 = 300 biscuits. Since each batch makes 75 biscuits, Siara baked 300 / 75 = 4 batches.
5. Let's call the number of comic books on each shelf s. The total number of comic books in Jose's collection is 5 * s = 125 + 20 = 145 comic books. Therefore, s = 145 / 5 = 29 comic books. This means there are 29 comic books on each shelf, and Jose has a total of 29 * 5 = <<29*5=145>>145 comic books in his collection.
For each sequence, find the first 4 terms and the 10th term.
b) 5 - 2n
Answers
Answer:
first 4 terms: 3,1,-1,-3
10th: -35
Step-by-step explanation:
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Answer:
3, 1, - 1, - 3 and - 15
Step-by-step explanation:
To find the first 4 terms substitute n = 1, 2, 3, 4 into the rule, that is
a₁ = 5 - 2(1) = 5 - 2 = 3
a₂ = 5 - 2(2) = 5 - 4 = 1
a₃ = 5 - 2(3) = 5 - 6 = - 1
a₄ = 5 - 2(4) = 5 - 8 = - 3
The first 4 terms are 3, 1, - 1, - 3
For 10th term substitute n = 10 into the rule
a₁₀ = 5 - 2(10) = 5 - 20 = - 15
Can someone help me Simplify:
(-7) (-3)
????
Answers
21 is the value of expression .
What is a mathematical expression?
A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. This mathematical operation may be addition, subtraction, multiplication, or division.
An expression's basic components are as follows: Expression: (Math Operator, Number/Variable, Math Operator). Any mathematical statement made up of numbers, variables, and an action between them is called an expression or an algebraic expression.
= (-7) (-3)
= 21
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What has to be true if you want to convert one rate to another rate?
Answers
Answer:
i think it might be the "units of the first rate are both/all distinct from that of the converted rate, but it still represents the same measurement."
Step-by-step explanation:
$131,701. 32 is what percent of $790,207. 91?
Answers
To find the percentage, we can use the following formula:
Percentage = (Part / Whole) * 100
So, $131,701.32 is approximately 16.67% of $790,207.91.
In this case, the part is $131,701.32 and the whole is $790,207.91.
Percentage = ($131,701.32 / $790,207.91) * 100
Calculating the value:
Percentage ≈ 0.1667 * 100
Percentage ≈ 16.67%
Therefore, $131,701.32 is approximately 16.67% of $790,207.91.
Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:
Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%
So, $131,701.32 is approximately 16.67% of $790,207.91.
If you have any further questions, feel free to ask!
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Which of the following expressions are undefined? CHOOSE ALL THAT APPLY
A. 6/0
B. 5/0
C. 6/5-5
Answers
Answer:
6/0, 5/0, 6/5-5
Step-by-step explanation:
You cannot divide a number by 0:
6/0 is dividing by 05/0 is dividing by 06/5-5=6/0 which is dividing by 0Due rn !!
1.) 1 - c = ?
c=0.24
20 points !!
Answers
Answer:
0.76
Step-by-step explanation:
Since C= 0.24 input that into the equation
1 - 0.24 = 0.76
The mean age of all students at a certain college is 22 years and the standard deviation is 2 years. What is the probability that the mean age of a randomly selected sample of 100 students will be less than 21.8 years
Answers
The probability that the mean age of a randomly selected sample of 100 students will be less than 21.8 years is approximately 0.1587 or 15.87%
The Central Limit Theorem, which states that the sampling distribution of the sample means approaches a normal distribution as the sample size increases.
The population mean (μ) is 22 years and the population standard deviation (σ) is 2 years, we can calculate the standard error of the mean (SE) using the formula:
SE = σ / √n
where n is the sample size. In this case, n = 100.
SE = 2 / √100 = 2 / 10 = 0.2
Next, we need to calculate the z-score, which measures how many standard errors the sample mean is away from the population mean. The formula for the z-score is:
z = (X - μ) / SE
where X is the value we want to find the probability for, which is 21.8 years.
z = (21.8 - 22) / 0.2 = -0.2 / 0.2 = -1
Using a standard normal distribution table or a calculator, we can find the probability associated with the z-score of -1.
P(X < 21.8) = P(Z < -1)
From the standard normal distribution table, the probability associated with a z-score of -1 is approximately 0.1587.
Therefore, the probability that the mean age of a randomly selected sample of 100 students will be less than 21.8 years is approximately 0.1587 or 15.87%.
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Calculate Ocean Freight charges in Canadian dollar
We have a shipment of two different cargos:
2 skids of Apple, 100 cm x 100 cm x 150 cm, 400 kg each
3 boxes of Orange, 35" x 25" x 30", 100 kg each
Ocean freight rate to Mumbai: $250 USD / m3
1 USDD= 1.25 CND
1 m3=1000 kg
Answers
The ocean freight charges for the given shipment in Canadian dollars would be approximately 603.25 CAD.
To calculate the ocean freight charges in Canadian dollars for the given shipment, we need to follow these steps:
Step 1: Calculate the volume and weight of each cargo item:
For the skids of Apple:
Volume = 100 cm x 100 cm x 150 cm
= 1,500,000 cm³
= 1.5 m³
Weight = 400 kg each x 2
= 800 kg
For the boxes of Orange:
Volume = 35" x 25" x 30"
= 26,250 cubic inches
= 0.4292 m³
Weight = 100 kg each x 3
= 300 kg
Step 2: Calculate the total volume and weight of the shipment:
Total Volume = Volume of Apples + Volume of Oranges
= 1.5 m³ + 0.4292 m³
= 1.9292 m³
Total Weight = Weight of Apples + Weight of Oranges
= 800 kg + 300 kg
= 1,100 kg
Step 3: Convert the ocean freight rate to Canadian dollars:
Ocean freight rate to Mumbai = $250 USD / m³
Conversion rate: 1 USD = 1.25 CAD (Canadian dollars)
Freight rate in CAD = $250 USD/m³ x 1.25 CAD/USD
= 312.5 CAD/m³
Step 4: Calculate the freight charges for the shipment:
Freight charges = Total Volume x Freight rate in CAD
Freight charges = 1.9292 m³ x 312.5 CAD/m³
= 603.25 CAD
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Which expression is equivalent to 9 p minus 3 p 2? 8p 14p 6 p 2 9 p minus 1
Answers
The expression is 6 times 1 equals 6/6 + 2 = 8
Expression:
An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Let's say P is worth 1
9 times 1 equals 9
3 times 1 equals 3
9 - 3 = 6
6 + 2 = 8
So the expression equivalent to 9p minus 3p 2 is 8.
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what should a good residual plot look like if the regression line fits the data well?
Answers
A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.
This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where \(e = y - ŷ\), where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.
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what's 1.187939392 to the nearest tenth?
Answers
Answer:
1.2
Step-by-step explanation:
For this, everything after 8 doesn't matter.
Because 8 is bigger than 5, we will round the number to the left up.
It is because 8 is the hundreth.
=1.2
the distance from city a to city b is 256.8 miles. the distance from city a to city c is 739.4 miles how much farther is the trip to city c than the trip to city b
Answers
Taking a difference, we can see that the trip to city C is 482.6 mi longer.
How much farther is the trip to city c than the trip to city b?
Here we know that the distance from city a to city b is 256.8 miles, and the distance from city a to city c is 739.4 miles
To find how much farther is the trip to city c than the trip to city b, we just need to take the difference between the two distances above.
That means that we need to take the distance to city c and subtract the distance to city b.
We will get:
739.4 mi - 256.8 mi = 482.6 mi
The trip to city C is 482.6 mi more than the trip to city B.
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P(Z≤b)=0.0311 b ? a. −1.87 b. −1.86 c. −1.8 d. −1.865
Answers
The answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.
In this scenario, P(Z ≤ b) represents the cumulative probability of a standard normal distribution up to the value of b. To find the corresponding value of b, we need to find the z-score that corresponds to a cumulative probability of 0.0311.
By looking up the z-table or using a statistical calculator, we can find that the z-score corresponding to a cumulative probability of 0.0311 is approximately -1.865.
Therefore, the answer is option d. -1.865, as it is the value that satisfies P(Z ≤ b) = 0.0311. The other options (-1.87, -1.86, -1.8) do not correspond to the given cumulative probability.
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