By substituting the correct coefficient, we can determine the original roots. In this case, the original roots are -2 and -15.
Let's start by considering the original quadratic equation with the unknown coefficient, which we will denote as p: x^2 + px + = 0. We know that the roots of this equation are -2 and -15.
To find the value of p, we can use the fact that the sum of the roots of a quadratic equation is equal to the negation of the coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the sum of the roots is -2 + (-15) = -17.
Since we were given that the coefficient of x was mistakenly taken as 17 instead of 13, we can deduce that the correct sum of the roots should be -13. Thus, we have -13 = -p/1, which gives us p = 13.
Now that we have the correct coefficient, we can substitute it back into the original equation: x^2 + 13x + = 0. By comparing this equation with the original one, we can see that the roots remain the same, which are -2 and -15. Therefore, the roots of the original quadratic equation are -2 and -15.
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Explain the process of solving a system of equations using substitution
One variable, from either of the equations, the subject of that equation and substitute it in the other equation.
We have,
To describe the process of solving a system of equations using substitution.
Now,
For any given system of linear equations, we use a method called substitution method for solving the equations.
We can make one variable, from either of the equations, the subject of equation and substitute it in the other equation.
This way, we get to find the value of the remaining variable and next we substitute this value in one of the equations to get the value of the variable left.
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a. Find the frequency if C (520) is raised by a fifth to G . ____________ cps.
b. Find the frequency if this G is lowered by a fourth to D. ____________ cps.
(Round to the nearest hundredth if necessary.)
The frequency of G when C (520 Hz) is raised by a fifth is 780 Hz.
The frequency of D when G is lowered by a fourth is 1040 Hz.
A. To find the frequency when C (520 Hz) is raised by a fifth to G, we can use the ratio of frequencies between the notes.
A fifth interval corresponds to a frequency ratio of 3:2.
So, we can calculate the frequency of G using the following equation:
Frequency of G = Frequency of C x (3/2)
Frequency of G = 520 Hz x (3/2) = 780 Hz
Therefore, the frequency of G when C (520 Hz) is raised by a fifth is 780 Hz.
B. To find the frequency when G is lowered by a fourth to D, we can use the ratio of frequencies between the notes.
A fourth interval corresponds to a frequency ratio of 4:3. So, we can calculate the frequency of D using the following equation:
Frequency of D = Frequency of G x (4/3)
Frequency of D = 780 Hz x (4/3) = 1040 Hz
Therefore, the frequency of D when G is lowered by a fourth is 1040 Hz.
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Noah and Gabriel have taken 6 quizzes in English class so far. There are no outliers in their quiz scores. Find the measure of variability for Noah’s scores. Noah’s scores: 84, 85, 85, 86, 90, 92 Mean: 87 Range: 92 – 84 = 8 Gabriel’s scores: 82, 85, 86, 86, 90, 94 Mean: 87. 17 Range: 94 – 82 = 12 MAD: 3. 22 What is Noah’s mean absolute deviation? StartFraction StartAbsoluteValue 87 minus 84 EndAbsoluteValue (2) StartFraction StartAbsoluteValue 87 minus 85 EndAbsoluteValue StartFraction StartAbsoluteValue 87 minus 86 EndAbsoluteValue StartFraction StartAbsoluteValue 87 minus 90 EndAbsoluteValue StartFraction StartAbsoluteValue 87 minus 92 EndAbsoluteValue over 6 EndFraction = StartFraction 3 4 1 3 5 over 6 EndFraction 1. 33 2 2. 67 3. 5.
Noah's mean absolute deviation is 2.67 when the mean score is 87.
Thus, option (3) is correct.
To calculate Noah's mean absolute deviation (MAD) based on his quiz scores, we need to find the average of the absolute differences between each score and the mean.
The formula to calculate mean absolute deviation (MAD) is
[tex]{\text} MAD[/tex] =
Given:
Noah's scores: 84, 85, 85, 86, 90, 92
Mean of Noah's scores: 87
Now, the absolute differences between each score and the mean, as
|87 - 84| = 3
|87 - 85| = 2
|87 - 85| = 2
|87 - 86| = 1
|87 - 90| = 3
|87 - 92| = 5
Now, the mean of these absolute differences are:
MAD = (3 + 2 + 2 + 1 + 3 + 5) / 6
= 16 / 6
= 2.67
Therefore, Noah's mean absolute deviation is 2.67.
Thus, option (3) is correct.
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The question attached here seems to be inappropriate form, the appropriate form is:
Noah and Gabriel have taken 6 quizzes in English class so far. There are no outliers in their quiz scores.
Find the measure of variability for Noah’s scores.
Noah’s scores: 84, 85, 85, 86, 90, 92
Mean: 87
Range: 92 – 84 = 8
Gabriel’s scores: 82, 85, 86, 86, 90, 94
Mean: 87. 17
Range: 94 – 82 = 12
MAD: 3. 22
What is Noah’s mean absolute deviation?
|87 -84| + {97 - 85| + |87-90| + |87-90| + |97-92| / 6
1. 1.33
2. 2
3. 2.67
4. 3.5
In "Saving Tobe", why does Serafin risk his life to help Tobe when he is in danger of drowning in the river?
Question 8 options:
His wife and children are watching, and he knows they expect him to act.
He is the first person to arrive at the river and feels responsible to act.
His brother drowned and he cannot bear to watch it happen to someone else.
He is the person who is most qualified to attempt to save Tobe
The correct option is : His brother drowned, and he cannot bear to watch it happen to someone else.
From the given options, the most appropriate answer to the question "In 'Saving Tobe', why does Serafin risk his life to help Tobe when he is in danger of drowning in the river?" would be:
His brother drowned, and he cannot bear to watch it happen to someone else.
This option suggests that Serafin has a personal connection and emotional trauma related to someone drowning, likely his own brother.
As a result, he empathizes with Tobe's predicament and takes it upon himself to prevent another tragic loss.
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The question attached here is in apprpriate form, the correct question is:
In "Saving Tobe", why does Serafin risk his life to help Tobe when he is in danger of drowning in the river?
The reason is:
His wife and children are watching, and he knows they expect him to act.He is the first person to arrive at the river and feels responsible to act.His brother drowned and he cannot bear to watch it happen to someone else.He is the person who is most qualified to attempt to save TobeWhat is double root at 3 and a single root at -7 factored
The factored form of a quadratic expression with a double root at 3 and a single root at -7 is (x - 3)^2(x + 7).
A quadratic expression in factored form has the general form (x - r1)(x - r2), where r1 and r2 are the roots of the expression. In this case, the roots are a double root at 3 and a single root at -7, which means that the expression can be factored as follows: (x - 3)(x - 3)(x + 7).
Simplifying, we can write this expression as (x - 3)^2(x + 7). The double root at 3 means that the quadratic equation has two identical roots, so (x - 3) appears twice in the factored form. The single root at -7 means that (x + 7) appears only once. The factored form can be useful for solving quadratic equations and for finding the roots of a quadratic expression.
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A game of "Doubles-Doubles" is played with two dice. Whenever a player rolls two dice and both die show the same number, the roll counts as a double. If a player rolls doubles, the player earns 3 points and gets another roll. If the player rolls doubles again, the player earns 9 more points. Whenever the player rolls the dice and does not roll a double, they lose points. How many points should the player lose for not rolling doubles in order to make this a fair game? Three-fifths StartFraction 27 Over 35 EndFraction Nine-tenths 1.
Given: A game of "Doubles-Doubles" is played with two dice.
Option (A) Three-fifths is correct.
Whenever a player rolls two dice and both die show the same number, the roll counts as a double.
If a player rolls, the player earns 3 points and gets another roll.
If the player rolls doubles again, the player earns 9 more points.
Whenever the player rolls the dice and does not roll a double, they lose points.
To make the game fair we need to find how many points the player should lose for not rolling doubles.
So, let the player lose p points for not rolling doubles.
Thus, the probability of getting doubles on a roll is
= 6/36
= 1/6
Therefore, the probability of not getting doubles on a roll is
= 1 - 1/6
= 5/6
Case1: Player gets doubles, the player earns 3 points and gets another roll.
Thus, the expected gain from this
= 1/6 × 3
= 1/2
Case2: Player gets doubles twice, the player earns 9 more points.
Thus, the expected gain from this
= 1/6 × 1/6 × 9
= 1/4
Case3: Player does not get doubles, he loses p points.
Thus, the expected gain from this
=5/6 (-p)
= - 5/6 p
Total expected gain = 1/2 + 1/4 - 5/6 p
Since the game is fair the expected gain from the game is zero.
Total expected gain = 0
1/2 +1/4 - 5/6 p = 0
- 5/6 p = - 1/4
p = 3/5
Thus, the player should lose 3/5 points for not rolling doubles to make the game fair.
Hence, option (A) Three-fifths is correct.
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X and Y are two different numbers selected from the first fifty counting numbers from 1 to 50 inclusive. What is the largest value that X Y/X-Y can have
The expression maximizes when we use X = 50 and Y = 49, the largest value that the expression can have is 2,450
How to find the largest possible value?Here we want to find the maximum value of the expression:
N = (X*Y)/(X - Y)
So we want to maximize the numerator and decrease the denominator.
This is ratter trivial, the maximum numerator is when we take the two largest numbers:
X = 50
Y = 49
Then the numerator is maximized:
X*Y = 50*49 = 2,450
And the denominator is minimized, because the difference between these two values is 1, so we have:
X - Y = 1
Then we have:
(X*Y)/(X - Y) = 2,450
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A parrallelogram with a base four times the height and an area less than 200 square feet
The height is less than 5√2 feet and the base is less than 20√2 feet.
A parallelogram is a two-dimensional shape with two pairs of parallel sides. It has four sides and four angles. It is similar to a rectangle, except that its opposite sides are parallel and not necessarily of equal length.
A parallelogram with a base four times the height has the formula A=bh, where b is the length of the base and h is the height. Therefore, if the base is four times the height, then we can write b=4h. We can substitute this value of b into the formula A=bh to obtain A=4h×h=4h². Thus, the area of the parallelogram is 4h².
Therefore, the height is less than 5√2 feet. We can find the corresponding value of the base by using the equation b=4h. Thus, the base is less than 4(5√2)=20√2 feet.Since we know the height and the base of the parallelogram, we can calculate its area. The formula for the area of a parallelogram is A=bh, so we can write:A=(20√2)(5√2)=200 square feet.Since the area of the parallelogram is less than 200 square feet, it must be less than this value.
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The perimeter of a form is 187. 2m. It its width is 39m, then find the ratio between its length an with
The ratio of the length to the width is 36.4 : 13.
To find the length of the form,
We have to subtract the twice the width from the perimeter.
Length = Perimeter - 2 x Width Length
= 187.2m - 2 x 39m Length
= 109.2m
The ratio of the length to the width of the form is therefore,
⇒ Length : Width = 109.2m : 39m
Simplifying this ratio by dividing both sides by 3, we get,
⇒ Length : Width = 36.4m : 13m
So the ratio of the length to the width is 36.4 : 13.
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You have a square piece of aluminum that is 12in x 12in. You apply a pressure of 5 psi to that plate, what is the TOTAL FORCE on the piece of aluminum.
To find the total force on the piece of aluminum, we need to calculate the pressure exerted on the surface and then multiply it by the area of the aluminum plate.
Given:
Pressure = 5 psi
Dimensions of the aluminum plate = 12in x 12in
First, let's convert the pressure from psi to pounds per square inch (psi to lb/in²). Since 1 psi is equivalent to 1 pound of force exerted per square inch, we can directly use the pressure value.
Pressure = 5 lb/in²
Next, we calculate the area of the aluminum plate. Since it is a square, the area is given by the formula:
Area = side^2
Area = (12in)^2 = 144 in²
Finally, we find the total force by multiplying the pressure by the area:
Total Force = Pressure × Area
Total Force = 5 lb/in² × 144 in²
Total Force = 720 lb
Therefore, the total force exerted on the piece of aluminum is 720 pounds.
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A rental car costs d dollars per day and $40 for insurance. If the total cost for a six day rental is $260, what is the daily rate? Write an equation and solve.
Answer: Let's denote the daily rate for the rental car as "d" (in dollars per day).
According to the given information, the rental car costs d dollars per day and an additional $40 for insurance.
For a six-day rental, the total cost is $260.
The equation to represent this situation is:
6d + 40 = 260
To solve for the daily rate (d), we can isolate the variable by subtracting 40 from both sides of the equation:
6d = 260 - 40
6d = 220
Finally, divide both sides of the equation by 6 to solve for d:
d = 220 / 6
d ≈ 36.67
Therefore, the daily rate for the rental car is approximately $36.67.
The price of an item is increased by 20% , if the new price is Rs36000 what is the price of item before increase? *
Let's denote the original price of the item as [tex]\(x\)[/tex]. According to the problem, the price is increased by 20% to reach a new price of Rs36000.
The increase in price can be calculated by multiplying the original price [tex]\(x\)[/tex] by the decimal equivalent of the percentage increase, which is [tex]\(1 + \frac{20}{100}\)[/tex] or [tex]\(1.2\)[/tex].
Thus, the new price can be expressed as:
[tex]\[1.2x = 36000\][/tex]
To find the original price, we need to isolate [tex]\(x\)[/tex] on one side of the equation. We can do this by dividing both sides of the equation by 1.2:
[tex]\[\frac{1.2x}{1.2} = \frac{36000}{1.2}\][/tex]
Simplifying the equation gives:
[tex]\[x = \frac{36000}{1.2}\][/tex]
Evaluating this expression:
[tex]\[x = 30000\][/tex]
Therefore, the price of the item before the increase was Rs30000.
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A regular octagon is mapped onto itself every time it is rotated.
A regular octagon is rotationally symmetric.
A regular octagon is a polygon with eight equal sides and eight equal angles. When a regular octagon is rotated by any multiple of 45 degrees (one-eighth of a full rotation), it appears exactly the same as its original orientation. This is because each vertex of the octagon is equidistant from the center of rotation, resulting in the same shape being mapped onto itself. The rotational symmetry of a regular octagon makes it a visually appealing and mathematically interesting geometric figure.
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How does a regular octagon behave when it is rotated and mapped onto itself repeatedly?
A football team carried out a report to see the impact of stretching on preventing injury. Of the 45 footballers in the squad 36 stretch regularly. Of those who stretch, 6 got injured last year. There was a total of 10 injured players last year. The results are presented in the frequency tree
Among the 45 footballers, stretching regularly is associated with a lower injury rate. Out of the 36 footballers who stretch, 6 got injured, while among the 9 footballers who do not stretch, 4 got injured.
The frequency tree represents the data from the report on the impact of stretching on preventing injury in a football team. The tree shows that out of the 45 footballers in the squad, 36 of them stretch regularly. Among the footballers who stretch, 6 got injured last year. The total number of injured players last year was 10.
From the given information, we can analyze the relationships between the different categories. Out of the 45 footballers, 36 stretch regularly, which means that 9 footballers do not stretch. Since the total number of injured players is 10 and 6 of them are from the stretching group, the remaining 4 injured players must come from the non-stretching group.
To summarize, the report suggests that among the 45 footballers, stretching regularly is associated with a lower injury rate. Out of the 36 footballers who stretch, 6 got injured, while among the 9 footballers who do not stretch, 4 got injured. These findings highlight the potential benefits of incorporating stretching exercises into the team's routine to help prevent injuries. However, it is important to consider other factors and conduct further analysis to establish a more comprehensive understanding of injury prevention in the football team.
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The selling price of a suit is $560
The discount on the suit is 12%
What is the new selling price
The new selling price of the suit after a 12% discount is $492.80 with initial selling price of a suit of $560.
A discount is a reduction or deduction in the price or cost of a product or service. It is a marketing strategy commonly used to incentivize customers to make a purchase or to promote sales.
We know that the selling price of a suit is $560. The discount on the suit is 12%.
We need to find the new selling price.
We can calculate the discount on the suit first.
Discount = (12/100) x 560
Discount = 0.12 x 560
Discount = $67.2
Now, we can find the new selling price of the suit.
New selling price = Selling price - Discount
New selling price = $560 - $67.2
New selling price = $492.8
Therefore, the new selling price of the suit is $492.8.
To calculate the new selling price after applying a discount, you need to subtract the discount amount from the original selling price.
Discount = 12% of the selling price
Discount amount = 12% × $560
= 0.12 × $560
= $67.20
New Selling Price = Selling Price - Discount Amount
New Selling Price = $560 - $67.20
= $492.80
Therefore, the new selling price of the suit after a 12% discount is $492.80.
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Amir is sorting his stamp collection. he made a chart of the fraction of stamps from each country in his collection. 7/12 of Amir's stamps are either from either Morocco or Spain.
Amir is sorting his stamp collection. He made a chart of the fraction of stamps from each country in his collection. 7/12 of Amir's stamps are either from either Morocco or Spain. The long answer to this question is given below:Answer:7/12 of Amir's stamps are either from Morocco or Spain.
5/12 of his stamps are from Spain and the remaining 2/12 of his stamps are from Morocco. The denominator of the given fraction is 12. Therefore, the numerator of the fraction represents the number of stamps from either Morocco or Spain. Let's consider the given fraction; 7/12The numerator of this fraction represents the number of stamps from either Morocco or Spain. Let S be the number of stamps from Spain.
Let M be the number of stamps from Morocco. Using the given information, we have: S + M = 7/12..... (1)Also, S/12 represents the fraction of stamps from Spain and 2/12 represents the fraction of stamps from Morocco. We can represent the number of stamps from Spain and Morocco in the following manner: S = 5/12 and M = 2/12Let's substitute these values in equation (1).We get:5/12 + 2/12 = 7/12Hence, 7/12 of Amir's stamps are either from either Morocco or Spain. Out of the 7/12 of the stamps, 5/12 are from Spain, and the remaining 2/12 are from Morocco.
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coordinate plane with triangles QRS and UTS with Q at negative 6 comma 2, R at negative 2 comma 6, S at negative 2 comma 2, T at negative 2 comma 0, and U at negative 4 comma 2
Which set of transformations would prove ΔQRS ~ ΔUTS?
Reflect ΔUTS over y = 2, and dilate ΔU′T′S′ by a scale factor of 2 from point S.
Reflect ΔUTS over y = 2, and translate ΔU′T′S′ by the rule (x − 2, y + 0).
Translate ΔUTS by the rule (x + 0, y + 6), and reflect ΔU′T′S′ over y = 6.
Translate ΔUTS by the rule (x − 2, y + 0), and reflect ΔU′T′S′ over y = 2.
The set of transformations that would prove ΔQRS ~ ΔUTS is to translate ΔUTS by the rule (x - 2, y + 0) and reflect ΔU'T'S' over y = 2.
To prove that ΔQRS ~ ΔUTS, we need to show that the two triangles are related through a combination of transformations.
The first transformation is a translation of ΔUTS by the rule (x - 2, y + 0). This means that every point in ΔUTS will be moved 2 units to the left and 0 units vertically. The translated triangle is denoted as ΔU'T'S'.
The second transformation is a reflection of ΔU'T'S' over the line y = 2. This reflection flips the triangle across the line, maintaining the same shape but reversing the orientation.
These two transformations combined, translation and reflection, establish a correspondence between the corresponding vertices of the two triangles. ΔU'T'S' is the transformed version of ΔUTS.
Since the two triangles undergo the same transformations, they have a proportional relationship and are therefore similar, which can be denoted as ΔQRS ~ ΔU'T'S'.
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An element with mass 780 grams decays by 16. 3% per minute. How much of the element is remaining after 16 minutes, to the nearest 10th of a gram?.
An element with a mass of 780 grams decays by 16.3% per minute. To find the amount of the element remaining after 16 minutes, we can use the following formula: `A = P(1 - r)ⁿ`, where `A` is the amount remaining, `P` is the initial amount, `r` is the rate of decay, and `n` is the number of minutes.
Using this formula, we can plug in the given values and solve for `A`:
```
P = 780 grams
r = 0.163 (since the element decays by 16.3% per minute)
n = 16 minutes
A = P(1 - r)ⁿ
A = 780(1 - 0.163)¹⁶
A ≈ 115.3 grams (rounded to the nearest 10th of a gram)
```
Therefore, after 16 minutes, approximately 115.3 grams of the element are remaining.
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The formula for simple interest is I=Prt, where I is the interest earned, P is the principal, r is the interest rate and tt is the number of years. Solve the formula for tt in terms of P, I and r
This equation allows you to calculate the number of years (t) based on the principal (P), interest earned (I), and interest rate (r) for simple interest calculations.
To solve the formula I = Prt for t in terms of P, I, and r, we can rearrange the equation to isolate t.
Starting with the original formula:
I = Prt
Dividing both sides by Pr:
I/Pr = (Prt)/Pr
Simplifying:
I/Pr = t
Therefore, t = I/Pr.
In terms of P, I, and r, the expression for t would be:
t = I / (P * r)
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Consider a battery whose voltage is a random variable with a variance of 1. Two independent measurements of the voltage are taken to estimate the voltage, the first with a variance of 1, and the second with a variance of 4. A) Write the weighted least squares voltage estimate in terms of the initial estimate 30 and the two measurements y1 and y2. B) If weighted least squares is used to estimate the voltage, what is the variance of voltage estimate after the first measurement
A) The weighted least squares voltage estimate is 0.1y1 + 0.9y2 + 30, (B) The variance of the voltage estimate after the first measurement is 0.5.
A) The weighted least squares voltage estimate is calculated by minimizing the sum of the squared errors between the measurements and the estimate. The weights are inversely proportional to the variances of the measurements.
In this case, the weights are 1/1 and 1/4. The weighted least squares voltage estimate is then: y_hat = (1/1)y1 + (1/4)y2 + 30
B) The variance of the voltage estimate is calculated by taking the weighted average of the variances of the measurements. In this case, the variances are 1 and 4.
The weights are 1/1 and 1/4. The variance of the voltage estimate is then: var(y_hat) = (1/1)var(y1) + (1/4)var(y2) = 0.5
It is important to note that the weighted least squares voltage estimate is not necessarily the same as the average of the two measurements. In this case, the weighted least squares voltage estimate is 30.5, while the average of the two measurements is 31.
The weighted least squares voltage estimate is a more accurate estimate of the voltage than the average of the two measurements because it takes into account the variances of the measurements.
The variance of a measurement is a measure of how spread out the data is. A measurement with a high variance is more likely to be different from the true value than a measurement with a low variance.
In this case, the first measurement has a low variance, while the second measurement has a high variance.
This means that the first measurement is more likely to be accurate than the second measurement. The weighted least squares voltage estimate takes this into account by giving more weight to the first measurement.
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En la siguiente tabla se muestra la cantidad de masa muscular que incrementaron en el último mes 4 amigos que van a entrenar a un gimnasio.
¿Para cuáles personas el incremento de masa muscular se representa por un número decimal periódico mixto?
A.
Daniel y Fabio.
B.
John y Fabio.
C.
Pedro y Daniel
D.
Pedro y John
De acuerdo con lo anterior podemos inferir que para los amigos Pedro y John, el incremento de masa muscular se representa por un número decimal periódico mixto.
¿Para cuáles personas el incremento de masa muscular se representa por un número decimal periódico mixto?El número decimal periódico mixto se refiere a un número decimal que tiene una parte entera, una parte decimal y una parte periódica, que se repite de forma continua.
Al observar los incrementos de masa muscular de los amigos, encontramos que Pedro tiene un incremento de masa muscular de 5/6 kg, lo cual se representa como 0.8(3) kg, donde el "3" se repite de forma continua.
Por otro lado, John tiene un incremento de masa muscular de 16/45 kg, que se representa como 0.3(5) kg, donde el "5" se repite de forma continua.
Entonces, la respuesta correcta es la opción D: Pedro y John.
Nota: Esta pregunta está incompleta. Aquí esta la información completa:
Imagen anexada.
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Ayana has saved $200 and spends $25 each week. Michelle just started saving $15 per week. In how many weeks will Ayana and Michelle have the same amount of money saved?
Answer:
After 5 weeks both will have the same amount.
Step-by-step explanation:
Framing algebraic expressions and solving:
Ayana:
Amount saved = $200
Each week, Ayana is spending $25. Let the number of weeks be 'x'.
Amount spent in 'x' week = 25*x = 25x
To find the remaining amount, subtract 25x from the total ($200).
Amount remaining after x weeks = 200 - 25x
Michelle:
Each week, Michelle is saving $15. Let the number of weeks be 'x'.
Amount saved in 'x' week = 15*x = 15x
Equate the two expressions, as the money after x weeks are same with both.
15x = 200 - 25x
15x + 25x = 200
40x = 200
x = 200 ÷ 40
x = 5 weeks
After 5 weeks both will have the same amount.
Cheer 61 took a $6000 distribution from her rough Ira 20% or $1200 is the distribution of earnings on her contribution the remaining $4800 is the distribution on her base char established the account more than 20 years ago where rough Ira's 1st became available how much of her distribution is taxableChar(61) took a $6000 distribution from her Roth Ira. Twenty percent, or1,200 is a distribution of earnings on her contributions. the remaining $4,800 is a distribution of her basis. char established the account more than 20 years ago, when Roth Iran's first became available. How much of her distribution is taxable?
To sum up, $1200 of Cheer 61's distribution is taxable while $4800 is not taxable.
Char's $1,200 distribution of earnings is taxable.
Char's $4,800 distribution of her base is not taxable, according to the details given in the question.
To explain further, an individual retirement account (IRA) is a kind of investment account that offers tax benefits for saving for retirement.
When a person contributes to a Roth IRA, the contribution is made with after-tax dollars and grows tax-free.
When the individual takes money out of the account, there are no tax consequences since they have already paid taxes on the contributions. However,
if the individual takes money out before they turn 59 1/2 or haven't held the account for at least five years, there could be tax consequences on the earnings portion of the distribution.
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What happens to the value of f(x) = log4x as x approaches [infinity]?.
As x approaches infinity, the value of the function f(x) = log4x approaches infinity as well. The logarithm function with a base greater than 1 increases without bound as its input increases, so the value of log4x becomes arbitrarily large as x becomes larger.
The logarithm function log4x represents the exponent to which the base 4 must be raised to obtain x. As x approaches infinity, the function evaluates the behavior of the logarithm for extremely large values.
In this case, as x becomes larger and larger, log4x increases without bound. This means that there is no finite limit or specific value that f(x) approaches as x approaches infinity. Instead, f(x) grows infinitely, indicating that the function's value becomes arbitrarily large as x becomes larger. Therefore, the value of f(x) = log4x approaches infinity as x approaches infinity.
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Part B
In the equation you wrote in part A, which is the independent value and which is the dependent value?
If the equation in part A is y = mx + b, then the independent variable would be x while the dependent variable would be y.
How to tell the dependent and independent variablesThe independent variable in an equation is that which is unaffected by another variable. It is the causative element that can be changed by the person solving the problem to get different forms of the y or dependent variable.
So, for the above equation, different values can be assigned to x to result in a change of y. If x is changed to 3, y becomes 6.
Complete Question:
Part B
In the equation, you wrote in part A, which is the independent value, and which is the dependent value? The equation is y = mx + b.
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How to do u substitution with indefinite integrals.
The corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.
To perform u-substitution with indefinite integrals, follow these steps:
Identify a suitable substitution: Look for a part of the integrand that resembles the derivative of a function. Choose a variable u to substitute for that part.
Calculate du: Take the derivative of u with respect to the original variable. This will help us express du in terms of the original variable.
Rewrite the integral: Substitute the chosen variable and du in the original integral, replacing the part to be substituted with u and the corresponding differential element du.
Integrate with respect to u: Treat the integral as a new integral with respect to u. Evaluate the integral using the rules of integration.
Replace u with the original variable: Rewrite the result of the integration in terms of the original variable.
Simplify and solve: If necessary, simplify the expression further or perform additional algebraic manipulations to obtain the final result.
Let's illustrate these steps with an example:
Consider the integral ∫(2x + 3)² dx.
Identify a suitable substitution: Let u = 2x + 3.
Calculate du: Take the derivative of u with respect to x: du/dx = 2. Rearrange the equation to solve for du: du = 2 dx.
Rewrite the integral: In terms of u and du, the integral becomes ∫u² (du/2).
Integrate with respect to u: Treat the integral as a new integral with respect to u: (1/2) ∫u² du = (1/2) * (u³/3) + C, where C is the constant of integration.
Replace u with the original variable: Substitute back u = 2x + 3 in the result: (1/2) * ((2x + 3)³/3) + C.
Simplify and solve: Further simplify the expression if necessary to obtain the final result.
In summary, to perform u-substitution with indefinite integrals, identify a suitable substitution, calculate the corresponding differential element, rewrite the integral in terms of the new variable, integrate with respect to the new variable, replace the new variable with the original variable, and simplify the expression to find the solution.
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Match each radical expression with the equivalent exponential expression. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. 3√4 3√ 2√3 2√5
Matching the radical expressions with their equivalent exponential expressions, we have 3√4 corresponding to 2^2/3, and 3√ to 2^1/3. Similarly, 2√3 can be matched with 3^1/2, and 2√5 with 5^1/2.
Radical expressions and exponential expressions are two different ways of representing the same mathematical concept. The radical symbol, denoted by √, represents the square root, cube root, or higher roots of a number. On the other hand, exponential expressions involve raising a base number to a given exponent.
In this case, the first radical expression is 3√4. The number inside the radical is 4, and the index outside the radical is 3, indicating the cube root. The equivalent exponential expression for this is 2^(2/3), where the base is 2 and the exponent is 2/3. This means taking the cube root of 4 is the same as raising 2 to the power of 2/3.
The second radical expression is 3√. Here, the number inside the radical is not specified, so we assume it to be 2 (as it is the most common convention). Therefore, the equivalent exponential expression is 2^(1/3), indicating the cube root of 2.
Moving on to the third radical expression, 2√3, the number inside the radical is 3, and the index outside the radical is 2, representing the square root. The corresponding exponential expression is 3^(1/2), which means taking the square root of 3.
Finally, the fourth radical expression is 2√5, where the number inside the radical is 5, and the index outside the radical is 2, representing the square root. The equivalent exponential expression is 5^(1/2), indicating the square root of 5.
In summary, the radical expressions 3√4, 3√, 2√3, and 2√5 can be matched with their equivalent exponential expressions: 2^(2/3), 2^(1/3), 3^(1/2), and 5^(1/2), respectively.
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Rapunzel cut off 2/3 of her hair. She donated 7/8 of what she cut off to a wig shop
What fraction of her hair did Repunzel donate?
Rapunzel cut off 2/3 of her hair. She donated 7/8 of what she cut off to a wig shop. The fraction of Rapunzel's hair that was donated to the wig shop is 7/8 x 2/3. This fraction simplifies to: 14/24. This is because to multiply fractions we simply multiply the numerators (top number) and denominators (bottom number) together to give the new fraction.
Rapunzel cut off 2/3 of her hair. She donated 7/8 of what she cut off to a wig shop. The fraction of Rapunzel's hair that was donated to the wig shop is 7/8 x 2/3. This fraction simplifies to: 14/24. This is because to multiply fractions we simply multiply the numerators (top number) and denominators (bottom number) together to give the new fraction. So, 7/8 x 2/3 can be expressed as (7 x 2)/(8 x 3) which is equal to 14/24. Therefore, Rapunzel donated 14/24 or 7/12 of her hair to the wig shop. Rapunzel cut off 2/3 of her hair.
This means she kept 1/3 of her hair. She then donated 7/8 of what she cut off to a wig shop. To calculate the fraction of her hair that she donated we need to find 7/8 of 2/3. Multiplying fractions requires multiplying the numerators (top numbers) and the denominators (bottom numbers) together. 7/8 x 2/3 = (7 x 2)/(8 x 3) = 14/24. Simplifying the fraction by dividing both numerator and denominator by 2 gives 7/12. So Rapunzel donated 7/12 of her hair to the wig shop.
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On a frictionless toy race track, a 0. 035 kg 0. 035 kg0, point, 035, space, start text, k, g, end text toy car moving right at 0. 30 m s 0. 30 s m 0, point, 30, space, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction collides with another 0. 040 kg 0. 040 kg0, point, 040, space, start text, k, g, end text toy car moving left at 0. 20 m s 0. 20 s m 0, point, 20, space, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction. After the collision, the 0. 035 kg 0. 035 kg0, point, 035, space, start text, k, g, end text car moves left at 0. 20 m s 0. 20 s m 0, point, 20, space, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction
The collision, the 0.035 kg car moves left at 0.20 m/s and the 0.040 kg car moves left at approximately 1.1125 m/s.
Based on the given information, we can analyze the collision using the principles of conservation of momentum and the law of motion.
First, let's calculate the initial momentum of each car before the collision:
Initial momentum of the first car (0.035 kg) moving right:
p1 = m1 * v1 = 0.035 kg * 0.30 m/s
Initial momentum of the second car (0.040 kg) moving left:
p2 = m2 * v2 = 0.040 kg * (-0.20 m/s) [negative because the car is moving in the opposite direction]
Next, let's consider the conservation of momentum during the collision. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision. Since the track is frictionless, no external forces act on the cars, so the total momentum should be conserved.
Therefore, we can write the equation:
p1 + p2 = p1' + p2'
After the collision, the 0.035 kg car moves left at 0.20 m/s. Let's denote the final velocity of the second car as v2':
Final momentum of the first car:
p1' = m1 * (-0.20 m/s) [negative because the car is moving left]
Final momentum of the second car:
p2' = m2 * v2' = 0.040 kg * 0.20 m/s
Now we can substitute the values into the momentum equation and solve for v2':
0.035 kg * 0.30 m/s + 0.040 kg * (-0.20 m/s) = 0.035 kg * (-0.20 m/s) + 0.040 kg * v2'
Simplifying the equation:
0.0105 kg m/s - 0.008 kg m/s = -0.007 kg m/s + 0.040 kg * v2'
Rearranging and solving for v2':
0.0025 kg m/s = 0.047 kg m/s + 0.040 kg * v2'
0.0025 kg m/s - 0.047 kg m/s = 0.040 kg * v2'
-0.0445 kg m/s = 0.040 kg * v2'
v2' = -0.0445 kg m/s / 0.040 kg
v2' = -1.1125 m/s
Therefore, after the collision, the 0.035 kg car moves left at 0.20 m/s and the 0.040 kg car moves left at approximately 1.1125 m/s.
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Which candidate in 1960
was seen by many to have
the perfect "American
Dream" family and lifestyle?
In the 1960 presidential election, the candidate who was seen by many to have the perfect "American Dream" family and lifestyle was John F. Kennedy.
John F. Kennedy, the Democratic nominee, presented an image of a youthful, charismatic leader with a charming family. He was married to Jacqueline Kennedy, known for her elegance and style, and they had two young children, Caroline and John Jr.
The Kennedys portrayed an idealized version of the American family, with their photogenic appearances and privileged upbringing. Their lifestyle, filled with glamour and sophistication, captured the imagination of the American public and symbolized the aspirations of the American Dream during that era.
Kennedy's charisma, family values, and relatable persona contributed to his popularity and the perception of his "perfect" American Dream family and lifestyle.
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