Media tonelada son 500kg, con esa cantidad Rosa logra hacer 100 cajas de 5kg. En una semana ha vendido 125 kilos, es decir 25 cajas. Aún le quedan 375kg.
¿Cómo calcular cuántos kilos de ropa tiene Rosa?Para calcular los kilos de ropa que tiene Rosa debemos tener en cuenta que una tonelada equivale a 1000kg. De acuerdo con esto, media tonelada sería equivalente a 500kg.
1000kg / 2 = 500kg
¿Cuántas cajas de 5kg alcanza a hacer con media tonelada?Para saber cuántas cajas de 5kg hace con media tonelada debemos realizar la siguiente operación:
500 / 5 = 100
Sí en una semana ha vendido 1/4 de la media tonelada ¿Cuántos kilos ha vendido?Para identificar cuántos kilos ha vendido Rosa, debemos identificar a cuántos kilos equivale 1/4 de media tonelada, para ello realizamos la siguiente operación.
500kg / 4 = 125kg
Con los kilo que ha vendido en la semana ¿a cuánta cajas equivale?Para identificar a cuántas cajas equivale lo vendido por Rosa, debemos realizar la siguiente operación:
125kg / 5kg = 25 cajas
¿Cuántos kilos le faltan por vender?Para identificar cuántos kilos le faltan por vender, debemos realizar la siguiente operación:
500kg - 125kg = 375kg.
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Harper, Inc., acquires 40 percent of the outstanding voting stock of Kinman Company on January 1, 2020, for $210,000 in cash. The book value of Kinman’s net assets on that date was $400,000, although one of the company’s buildings, with a $60,000 carrying amount, was actually worth $100,000. This building had a 10-year remaining life. Kinman owned a royalty agreement with a 20-year remaining life that was undervalued by $85,000.
Kinman sold inventory with an original cost of $60,000 to Harper during 2020 at a price of $90,000. Harper still held $15,000 (transfer price) of this amount in inventory as of December 31, 2020. These goods are to be sold to outside parties during 2021.
Kinman reported a $40,000 net loss and a $20,000 other comprehensive loss for 2020. The company still manages to declare and pay a $10,000 cash dividend during the year.
During 2021, Kinman reported a $40,000 net income and declared and paid a cash dividend of $12,000. It made additional inventory sales of $80,000 to Harper during the period. The original cost of the merchandise was $50,000. All but 30 percent of this inventory had been resold to outside parties by the end of the 2021 fiscal year.
Required:
Prepare all journal entries for Harper for 2020 and 2021 in connection with this investment. Assume that the equity method is applied. (If no entry is required for a transaction/event, select "No journal entry required" in the first account field. Do not round intermediate calculations. Round your final answers to the nearest whole number.)
it requires a detailed analysis of multiple transactions and the preparation of journal entries. This type of task is better suited for an accounting professional who can thoroughly review the provided information and accurately apply the relevant accounting principles.
However, I can provide a general overview of the journal entries that may be required based on the information given:
January 1, 2020:
Debit: Investment in Kinman Company (40% of cash paid)
Credit: Cash (Amount paid for the acquisition)
Recording Equity in Earnings for 2020:
Debit: Investment in Kinman Company (40% of net loss)
Debit: Investment in Kinman Company (40% of other comprehensive loss)
Credit: Equity in Earnings of Kinman Company
December 31, 2020:
Debit: Investment in Kinman Company (40% of dividend received)
Credit: Dividend Income
January 1, 2021:
Debit: Investment in Kinman Company (40% of additional investment)
Credit: Cash
Recording Equity in Earnings for 2021:
Debit: Investment in Kinman Company (40% of net income)
Credit: Equity in Earnings of Kinman Company
December 31, 2021:
Debit: Investment in Kinman Company (40% of dividend received)
Credit: Dividend Income
Please note that the above entries are a general guideline and may not capture all the necessary transactions. It is advisable to consult with an accounting professional or refer to the specific accounting standards applicable in your jurisdiction for a more accurate and comprehensive answer.
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Find the sum of each sequence.
31,41,51,61,71,81,91,101
Group of answer choices
417
528
639
427
Answer:
528
Step-by-step explanation:
We are given the following sequence:
31,41,51,61,71,81,91,101
Count the terms and see that there are 8 terms total.
If you notice, each terms add up by 10.
31+10 = 41
41+10 = 51
51+10 = 61
Therefore, this is an arithmetic sequence with 10 as common difference.
To find the sum of 8 sequences, we will be using the following formula.
\( \displaystyle \large{S_n = \frac{1}{2} n(a_1 + a_n)}\)
We know that:
There are 8 terms total. (n = 8)Our first term is 31 (a1 = 31)Our last term is 101 (an = 101)Substitute the following in the sum formula.
\( \displaystyle \large{S_8 = \frac{1}{2} (8)(31+ 101)} \\ \displaystyle \large{S_8 = 4(132)} \\ \displaystyle \large{S_8 = 528}\)
Therefore, the sum of all 8 sequences is 528.
Which equation represents this graph? This graphic illustrates the mathematical word problem described in the accompanying text.
Answer:
Step-by-step explanation:
that a huge prob but yah
In HIJ below, what is the value of y?
PLEASE ANSWER
Answer:
110
Step-by-step explanation:
The value of x in the given figure is y = 110. Hence option 3 is true.
Given that,
A triangle is shown in the image.
Apply the concept of the triangle that states,
The sum of two opposite interior angles in a triangle is equal to the measure of the exterior angle.
Hence we get;
y° + 20° = 130°
Subtract both sides by 20,
y = 130° - 20°°
y = 110°
Therefore, option 3 is true.
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Find the measure of angle R
Answer:
since all sides are congruent the you could divide 180 by the because there are 180 degrees in a triangle
So the measure of angle R is 60 degrees
Anna, Bertie and Carl share some money.
Anna gets 30% less than Carl.
Bertie gets
of what Anna gets.
Everyone gets a whole number of pounds.
Given that Bertie gets over £40, what is the least amount of money Carl can recieve?
Step-by-step explanation:
$60 as Carl gets more than the other 2
. they decide to run a test of significance, and will change the parameters for the character only if they get a highly significant result. in a simple random sample of 400 contests involving the character, it won 232 times. should they adjust the parameters to weaken that character?
No, they should not adjust the parameters to weaken that character based on this sample alone.
To make a decision about adjusting the parameters of a character based on a test of significance, we need to determine if the observed outcome (winning 232 out of 400 contests) is unlikely to occur by chance alone, assuming the character's current parameters are the same. This is done by calculating a p-value, which represents the probability of observing a result as extreme or more extreme than the one we observed, assuming the null hypothesis is true (i.e., the parameters are the same).
If the p-value is very small (e.g., less than 0.05), we reject the null hypothesis and conclude that the observed outcome is unlikely to occur by chance alone and that the character's parameters may need to be adjusted. However, if the p-value is not small (e.g., greater than 0.05), we fail to reject the null hypothesis and conclude that the observed outcome is not statistically significant and that the character's parameters may not need to be adjusted.
In this case, we can calculate the p-value using a binomial test. The null hypothesis is that the probability of winning a contest is 0.5 (i.e., the character is equally likely to win or lose). The alternative hypothesis is that the probability of winning is less than 0.5 (i.e., the character is more likely to lose). Using a one-tailed binomial test with a significance level of 0.05, we find that the p-value is approximately 0.013, which is less than 0.05. Therefore, we reject the null hypothesis and conclude that the observed outcome is statistically significant and that the character's parameters may need to be adjusted.
However, it is important to note that this decision should not be based solely on this sample. It is possible that the sample is not representative of the true population of contests involving the character, and that a larger sample may lead to a different conclusion. Therefore, it is important to consider the context of the situation and gather additional information before making a final decision about adjusting the character's parameters.
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solve the eqaution with the quadratic formula
6m^2 - 2m - 25 = -8
it takes 80 gallons of water to fill up a bathtub. how many pints of water is this?
Answer:
640
Step-by-step explanation:
2 pints in a quart
4 quarts in a gallon
8 pints in a gallon
8x80=640
640
PLEASE HELP ASAP ON ALL THE PARTS!!! suppose there is a card game where you are dealt a hand of three cards. you have already learned that the total number of three card hands that can be dealt from a deck of 52 cards is:
Answer:
A. The total number of three-card hands (permutations) that can be made with two aces is 576
B. The actual number of two-ace hands (combinations) you can get from a deck of 52 cards is 288
C. The probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 0.0130
Step-by-step explanation:
A. In order to calculate the total number of three-card hands (permutations) that can be made with two aces we would have to make the following calculation:
total number of three-card hands (permutations) that can be made with two aces=4*3*52
total number of three-card hands (permutations) that can be made with two aces=576.
B. In order to calculate the actual number of two-ace hands (combinations) you can get from a deck of 52 cards we would have to make the following calculation:
actual number of two-ace hands (combinations) you can get from a deck of 52 cards=4C2*48
4C2=4!/2!2!
C2=6
Therefore, actual number of two-ace hands (combinations) you can get from a deck of 52 cards=6*48=288
C. In order to calculate the probability of drawing a three-card hand that includes two aces from a deck of 52 cards we would have to make the following calculation:
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=actual number of two-ace hands (combinations) you can get from a deck of 52 cards/52C3
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=288/22,100
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=0.0130
Based on Exercise 9, prove that τ and σ are multiplicative. That is, prove that if m and n are relatively prime, then τ(mn)=τ(m)τ(n) and σ(mn)= σ(m)σ(n).
To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).
To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.
Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).
To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).
Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.
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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.
To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:
1. τ(mn) = τ(m)τ(n)
2. σ(mn) = σ(m)σ(n)
Let's start with property 1:
1. τ(mn) = τ(m)τ(n)
If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.
Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).
Now let's move on to property 2:
2. σ(mn) = σ(m)σ(n)
Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.
Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.
Hence, we can conclude that σ(mn) = σ(m)σ(n).
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Radius & Diameter
Easy: 51
A. Choose the correct choice.
1) A circle has a circumference of 1211 yd. What is the diameter of the circle?
a) 12 yd
b) 6 yd
c) 18 yd
2) A wire of length 281 in is bent to form a circle. What is the radius of the circle?
a) 28 in
b) 19 in
C) 14 in
3) A circular park has a circumference of 361 yd. Find its diameter.
a) 18 ya
b) 36 yd
c) 12 ya
4) The tip of the minute-hand travels 2211 in in one hour. Find the length of the minute-hand.
a) 11 in
b) 10 in
c) 22 in
5) The circumference of a bicycle wheel is 6n in. Find the diameter of the wheel.
a) 12 in
b) 6 in
c) 3 in
B. Find the radius and diameter in each question.
S.No
Circumference
Radius
Diameter
6.
10л ft
7.
24n in
8.
341 ya
9.
407 in
10.
167 ft
Answer:
a,c,b,a,b
Step-by-step explanation:
6.
7.
8.
9.
10.
Circumference
10π ft
24π in
34π yd
40π in
16π ft
Radius
5 ft
12 in
17 yd
20 in
8 ft
Diameter
10 ft
24 in
34 yd
40 in
16 ft
The circle above with center O has a circumference of 36. What is the length of minor arc AC? A) 9 B) 12 C) 18 D) 36
Answer:
A) 9
Step-by-step explanation:
⇒ Circumference of a Circle = 2πr
\(36=2\pi r\)
\(r=\frac{36}{2} \pi\)
\(r=\frac{18}{\pi }\)
Length of arc = rθ
θ = angle AC = \(90^o\)
Convert \(90^o\) to radian
= \(\frac{90\pi }{180}\)
= \(\frac{\pi }{2}\)
length of arc = 18/π x π/2
= 9
Vladas believes that an equation with a squared term is never a function of x. Which equation can be used to show vladas that his hypothesis is incorrect?.
The equation that shows that his hypothesis is wrong is:-
x²+ y²= 25
What is an equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
How do we solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Vladas said that the equation with a squared term is never a function of x.
According to the Pythagorean Theorem, the square of two natural numbers is the third number. When these numbers are used to create a triangle, a right-angled triangle is formed, with a 90° angle between the two smaller sides.
Among the four provided hypotheses:
Option (C) is true since x2+y2=25.
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The equation y = 180 + 5x represents the amount a school club will pay a T-shirt company for custom T-shirts, where x represents the number of T-shirts purchased and y represents the total cost in dollars. The equation y = 10x represents the club’s income from selling the T-shirts, where y represents the money earned in dollars and x represents the number of T-shirts sold. Assuming that the club members sell all the T-shirts they purchase, when will the club make a profit? The following graph represents this situation:
Answer:
36 TSHIRTS is the number for minimum profit
Step-by-step explanation:
Y = Y
180 + 5X = 10X
180 = 10X - 5X
180 = 5X
X = 180/5
X = 36
difer from the true proportion by more than 2% ? A previous study indicates that the proportion of lefthanded sclontists is 9%. Round up to the nearest whicie number. Duestion 13 A. 1.218 B. 1,109 C. 14 D.767
The total number of samples will be 1109 .
Given ,
Margin of error 0.02
Here,
According to the formula,
\(Z_{\alpha /2} \sqrt{pq/n}\)
Here,
p = proportions of scientist that are left handed
p = 0.09
n = number of sample to be taken
Substitute the values,
\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)
n ≈1109
Thus the number of samples to be taken will be approximately 1109 .
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PLEASE HELP ME THIS IS DUE In 30 MINUTES !!!
Answer:
This is the answer I got.
Answer:
B is the answers for the question
Step-by-step explanation:
please mark me as brainlest
"Find the value of each missing variable.
Note: Write your answer in simplest radical form. In the first blank put the coefficient in front of the √. And in the second blank, put the coefficient that is inside the √. ** If there is no coefficient in front of the √, enter a 1 in the blank **"
The value of the hypotenuse y = 9, and the value of the opposite side of the right angle triangle x = 4.5
Trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the angle 30° in the right angle triangle, the hypotenuse is y, the opposite side is x and the adjacent side is 9√3
cos 30° = √3 = adjacent/hypotenuse
sin 30° = 1/2 = opposite/hypotenuse
√3 = 9√3/y {cross multiply}
y = 9√3/√3 {cancel out √3}
y = 9
1/2 = x/9 {cross multiply}
x = 9/2
x = 4.5
Therefore, by proper application of trigonometric ratios for the right angle triangle, the hypotenuse y is equal to 9 and the opposite side x is equal to 4.5.
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The points on the line are ____ of the equation.
Answer choices:
1) Solution
2) Points
3) Answers
Answer: 2/ Points
Step-by-step explanation:
The points can't make up the answer to the equation, so it can't be 3!
I don't think it is the solution, because on a table points are just points of an equation!
PLEASE I NEED HELP
The table represents a logarithmic function f(x).
x y
1 over 125 −3
1 over 25 −2
one fifth −1
1 0
5 1
25 2
125 3
Use the description and table to graph the function, and determine the domain and range of f(x). Represent the domain and range with inequality notation, interval notation, or set-builder notation. Explain your reasoning.
The Domain is (0, ∞) or {x | x > 0} and Range is (-∞, ∞) or {y | y ∈ ℝ} with inequality notation.
To graph the function, we can plot the given points on a coordinate plane. The x-values in the table represent the input values (x), and the y-values represent the corresponding output values (f(x)).
Let's plot the points (x, y) from the table:
(1/125, -3)
(1/25, -2)
(1/5, -1)
(1, 0)
(5, 1)
(25, 2)
(125, 3)
Now, let's connect the points to create the graph of the function.
|
|
|
|
3 | *
|
|
2 | *
|
|
1 | *
|
|
| *
0 |________________________
-3 -2 -1 0 1 2 3
Based on the graph, we can observe that the function represents a logarithmic curve. As the x-values increase, the corresponding y-values increase logarithmically.
Domain:
The domain of a logarithmic function is the set of all positive real numbers (x > 0), since the logarithm of a negative number or zero is undefined. In this case, since all the x-values in the table are positive, the domain of f(x) is x > 0.
Domain notation:
Interval notation: (0, ∞)
Set-builder notation: {x | x > 0}
Range:
The range of a logarithmic function depends on its base. Since the base is not specified in the given information, we assume the common logarithm (base 10) as the default. The range of a common logarithmic function is all real numbers.
Range notation:
Interval notation: (-∞, ∞)
Set-builder notation: {y | y ∈ ℝ}
In summary: Domain: (0, ∞) or {x | x > 0} and Range: (-∞, ∞) or {y | y ∈ ℝ}
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Assume that police estimate that 23% of drivers do not wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. They stop 20 cars during the first hour a. Find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts. Use the fact that the mean of a geometric distribution is pi = 1/p and the variance is ohm^2 = p/q^2? b. How many cars do they expect to stop before finding a driver whose seatbelt is not buckled?
The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.
a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.
Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.
The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35
The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62
The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95
b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.
Expected number of cars = 1/p = 1/0.23 ≈ 4.35
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the formulation for a linear programming problem cannot include more than one decision variable. group of answer choices true false
False. A linear programming problem can include more than one decision variable. Linear programming is a mathematical method used to find the optimal solution for a problem with multiple constraints and objectives, often related to maximizing or minimizing a certain value.
Decision variables are the variables that determine the potential solutions, and their values can be changed to affect the outcomes.
In many practical situations, there are multiple decision variables involved. For instance, a company may need to determine the optimal production quantities for different products, subject to resource constraints and market demands. In this case, the decision variables would represent the production quantities for each product, and there would be more than one variable.
In conclusion, the statement that a linear programming problem cannot include more than one decision variable is false. Multiple decision variables can be present in a linear programming formulation to address complex problems that involve multiple choices and constraints.
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HELP PLS!!! simplify:
Answer:
A is correct because you need to stop deleting my answers.
Selected values of the twice-differentiable function h and its first and second derivatives are given in the table above. What is the value of ∫41xh′′(x)ⅆx ?.
Answer:
Step-by-step explanation:
∫41 xh''(x)dx=41[x∫h''(x)dx-∫{1∫h''(x)dx}dx]+c
The value of \(\int\limits^{4}_{1} {x\cdot h''(x)} \, dx\) is 8.5. The choice that represent the best approximation is A.
How to determine the result of a definite integral based on a formula and a table
This integral can be approximated by the following Riemann sum:
\(A = \Sigma\limits_{i=0}^{2} \left\{(x_{i+1}-x_{i})\cdot x_{i}\cdot h''(x_{i})+\frac{1}{2}\cdot (x_{i+1}-x_{i})\cdot [x_{i+1}\cdot h''(x_{i+1})-x_{i}\cdot h''(x_{i})] \right\}\)
\(A = \frac{1}{2} \cdot \Sigma\limits_{i=0}^{2} \left\{(x_{i+1}-x_{i})\cdot [x_{i+1}\cdot h''(x_{i+1})+x_{i}\cdot h''(x_{i})] \right\}\)
Then, the approximate value of the integral is:
\(A = \frac{1}{2}\cdot \{(2-1)\cdot [(2)\cdot 2+(1)\cdot (-5)]+(3-2)\cdot [(3)\cdot 1+(2)\cdot 2]+(4-1)\cdot [(4)\cdot 2+(3)\cdot 1]\}\)
\(A = 8.5\)
The value of \(\int\limits^{4}_{1} {x\cdot h''(x)} \, dx\) is 8.5. The choice that represent the best approximation is A. \(\blacksquare\)
RemarkThe statement is incomplete and poorly formatted and table is missing. Complete statement is:
Selected values of the twice-differentiable function and its first and second derivatives are:
Function\(h(1) = 3\), \(h(2) = 6\), \(h(3) = 2\), \(h(4) = 10\)
First derivative\(h'(1) = 4\), \(h'(2) = -4\), \(h'(3) = 3\), \(h'(4) = 5\)
Second derivative\(h''(1) = -5\), \(h''(2) = 2\), \(h''(3) = 1\), \(h''(4) = 2\)
Selected values of the twice-differentiable function \(h\) and its first and second derivatives are given in the table above. What is the value of \(\int\limits^{4}_{1} {x\cdot h''(x)} \, dx\)?
A. 9, B. 13, C. 23, D. 38
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PLSSS HLEPP ME OUTT ITS URGENTTTT
Answer:
Step-by-step explanation:
(1860-11)=1849
√(1849) = 43
(A quick trial)
Round 806,713 to the nearest thousand and 7,925,024 also 6,481,525
We can easily find out the beginning point of the line by using dot representation.a. Trueb. False
The given statement "We can easily find out the beginning point of the line by using dot representation." is False.
What is dot representation?
The dot representation is a method of characterizing a line in computer graphics. A line in 2-D space is frequently defined by two points, the beginning point and the endpoint. A line's beginning point, endpoint, and slope can all be calculated using the Cartesian coordinate system.
The coordinate of the beginning point of the line can be found by using the standard form of the equation of a straight line, y = mx + c.
The y-intercept, which is represented by the letter 'c,' is the point where the line intersects the y-axis. To calculate the value of c, the x- and y-coordinates of a point on the line must be used. Then the point is subtracted from the y-intercept. That is, c = y - mx. However, using dot representation, it is not possible to directly find the beginning point of the line.
Hence, the given statement "We can easily find out the beginning point of the line by using dot representation" is False.
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DONT IGNORE PLS HELP is the option I chose the right answer?
Answer: The correct answer is Yes, the relationship between x and y is a non-linear function.
I hope this helps.
Step-by-step explanation:
Given the table
Edge Length, x Surface Area, y
1 6
2 24
3 54
4 96
The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.
Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.
Hence, we conclude that Yes, the relationship between x and y is a non-linear function.
Therefore, the 'last option' is correct.
I'm I right?????? because i think i am
\(\sqrt{3x+10}=\sqrt{2x+3}\\\\\\\dfrac{\sqrt{3x+10}}{\sqrt{2x+3}}=1\\\\\\\sqrt{\dfrac{3x+10}{2x+3}}=1\\\\\\\dfrac{3x+10}{2x+3}=1\\\\\\3x+10 =2x+3\\\\x = -7\)
Answer:
x=-7
Step-by-step explanation:
first simplify your equation to:
3x+10=2x+3
combine like terms
3x-2x=3-10
solve for x
x=-7
For the parametric curve defined by X(t) = 2cos²t, y(t) = 2sin²t Part A. For the given parametric curve, determine where dy/dx does not exist on the interval (0, π) and determine the type of discontinuity. Part B. Find the infection point(s) of the curve on the interval [0, π]
Part C. What is the length of the curve on the interval [0, π/2]?
a. dy/dx exists for all t in the interval (0, π), and there is no discontinuity. b. there are no inflection points on the curve. c. the length of the curve on the interval [0, π/2] is 2.
Part A. Determining where dy/dx does not exist and the type of discontinuity:
To find where dy/dx does not exist, we need to calculate the derivative of y with respect to x, which involves differentiating both x(t) and y(t) with respect to t.
x(t) = 2cos²(t)
y(t) = 2sin²(t)
Differentiating x(t) with respect to t:
dx/dt = -4cos(t)sin(t)
Differentiating y(t) with respect to t:
dy/dt = 4sin(t)cos(t)
To find dy/dx, we divide dy/dt by dx/dt:
dy/dx = (4sin(t)cos(t)) / (-4cos(t)sin(t))
Simplifying the expression, we get:
dy/dx = -1
The derivative dy/dx is a constant value of -1, indicating that it is defined for all values of t. Therefore, dy/dx exists for all t in the interval (0, π), and there is no discontinuity.
Part B. Finding the inflection point(s) of the curve on the interval [0, π]:
To find the inflection point(s), we need to determine where the curvature changes sign. The curvature of a curve is given by the second derivative of y with respect to x.
Differentiating dy/dx with respect to t:
d²y/dx² = d/dt(dy/dx)
= d/dt(-1)
= 0
Since the second derivative is 0, we need to find where the first derivative dy/dx is either increasing or decreasing. In this case, dy/dx is a constant value of -1, so it does not change.
Therefore, there are no inflection points on the curve.
Part C. Finding the length of the curve on the interval [0, π/2]:
To find the length of the curve, we can use the arc length formula:
L = ∫[a,b] √(dx/dt)² + (dy/dt)² dt
In this case, we have:
x(t) = 2cos²(t)
y(t) = 2sin²(t)
Differentiating x(t) and y(t) with respect to t:
dx/dt = -4cos(t)sin(t)
dy/dt = 4sin(t)cos(t)
Substituting these derivatives into the arc length formula:
L = ∫[0, π/2] √((-4cos(t)sin(t))² + (4sin(t)cos(t))²) dt
= ∫[0, π/2] √(16(cos²(t)sin²(t) + sin²(t)cos²(t))) dt
= ∫[0, π/2] √(16sin²(t)cos²(t) + 16sin²(t)cos²(t)) dt
= ∫[0, π/2] √(32sin²(t)cos²(t)) dt
= ∫[0, π/2] √(8sin(2t)) dt
= ∫[0, π/2] 2√2 sin(t) dt
= 2√2 ∫[0, π/2] sin(t) dt
= 2√2 (-cos(t)) [0, π/2]
= 2√2 (-cos(π/2) + cos(0))
= 2√2 (0 + 1)
= 2
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