help pls asap ... Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept.
Answers
The approximate slope and y-intercept of the line of best fit is y = -0.17x + 33.3.
How to determine an equation of this line?In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]
Where:
m represent the slope.x and y represent the points.At data point (20, 20), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 20 = \frac{(10- 20)}{(80-20)}(x -20)[/tex]
y - 20 = -1/6(x - 20)
y = -x/6 + 20/6 + 20.
y = -x/6 + 200/6
y = -0.17x + 33.3
In this context, we can reasonably infer and logically deduce that a linear function that represent the line of best fit in slope-intercept form is y = -0.17x + 33.3.
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Related Questions
Cassius Corporation has provided the following contribution format income statement.Assume that the following information is within the relevant range.Sales (7,000 units)$210,000Variable expenses136,500Contribution margin73,500Fixed expenses67,200Net operating income$6,300The number of units that must be sold to achieve a target profit of $31,500 is closest to:A) 42,000 unitsB) 16,400 unitsC) 35,000 unitsD) 9,400 units
Answers
Cassius Corporation needs to sell to make a profit of $31,500 to sell the number of units that needs to be sold is 9,400 units. It can be found this out by using a formula that takes into account the company's sales revenue, variable expenses, fixed expenses, and contribution margin.Therefore Option D is correct.
The contribution margin is the amount of money left over from sales revenue after deducting variable expenses. In this case, we know that Cassius Corporation's contribution margin is $73,500.
To find out how many units the company needs to sell, we can use the following formula:
(Number of units * Contribution margin per unit) - Fixed expenses = Target profit
We know that the fixed expenses are $67,200 and the target profit is $31,500.
The contribution margin per unit by dividing the contribution margin by the number of units sold, which in this case is 7,000 units. This gives us a contribution margin per unit of $10.50.
Substituting these values into the formula, we get:
(Number of units * $10.50) - $67,200 = $31,500
Simplifying this expression:
(Number of units * $10.50) = $98,700
Number of units = $98,700 / $10.50
Number of units = 9,400 (rounded to the nearest whole unit)
The number of units that must be sold to achieve a target profit of $31,500 is closest to 9,400 units. Option (D) is correct.
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which of the contexts below could be modeled by a linear function? the amount of a certain medication in a person's bloodstream decreases by 1/3 every week. a town's population shrinks at a rate of 2.2% every year. a certain population of 4 aggressive zombies quintuples every hour. snow was falling at a rate of 2 inches per hour.
Answers
The context that could be modeled by a linear function is "snow was falling at a rate of 2 inches per hour."
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, a function takes an input and produces a corresponding output. It is often represented as a mathematical equation or a graph. Functions are used to model real-world phenomena and are an important tool in many areas of mathematics, science, and engineering.
Here,
A linear function describes a constant rate of change, and in this context, the rate of snowfall is constant at 2 inches per hour. The other contexts involve exponential or percentage change, which cannot be modeled by a linear function.
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What is 16/15 in simplest form
Answers
Values of 'x' satisfying: (x - 1)/(2 - x) >= 0
Answers
The values of x which satisfies the fractional inequality (x - 1) / (2 - x) ≥ 0 is x ≥ 1
What values of x satisfies the inequality?(x - 1) / (2 - x) ≥ 0
This is a fractional inequality whose numerator is (x - 1) and the denominator is (2 - x)
(x - 1) / (2 - x) ≥ 0
cross product
(x - 1) ≥ 0 × (2 - x)
(x - 1) ≥ 0
x - 1 ≥ 0
Add 1 to both sides
x ≥ 1
Therefore, x ≥ 1 satisfies the inequality.
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A sphere is to be designed with a radius of 72 in. Use differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5 in. 4 (Hint: The formula for the volume of a sphere is V(r) = ²³.) O 452.39 in ³ O 16,286.02 in ³ O 65,144.07 in ³ O 32,572.03 in ³
Answers
By using differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5. It will be 32,572.03 in³. Which is option (d).
How to measure the maximum error while measuring the volume of a sphere?The possible error in measuring the radius of the sphere is 0.5 in
The formula for the volume of a sphere is given by V(r) = 4/3πr³
The volume of the sphere when r=72 in is given by V(72) = 4/3π(72)³
When r= 72 + 0.5 in= 72.5 in, the volume of the sphere can be calculated using the formula:
V(72.5) = 4/3π(72.5)³
The difference between these two volumes, V(72) and V(72.5), gives us the maximum error while measuring the volume of a sphere. It can be calculated as follows:
V(72.5) - V(72) = 4/3π(72.5)³ - 4/3π(72)³= 4/3π [ (72.5)³ - (72)³ ]= 4/3π [ (72 + 0.5)³ - 72³ ]= (4/3)π [ 3(72²)(0.5) + 3(72)(0.5²) + 0.5³ ]≈ (4/3)π [ 777.5 ]= 3.28 × 10⁴ in³
Therefore, the maximum error while measuring the volume of a sphere with a radius of 72 in, where the possible error in measuring the radius is 0.5 in, is approximately 3.28 × 10⁴ in³ or 32,572.03 in³. Therefore coorect option is (D).
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Jack owns a company which sells handmade greetings cards.
Last year, the company sold 2340 cards and made a total profit of £3510.
This means the average profit per card was £1.50.
This year, Jack is aiming for the company to make 18% more total profit
than last year.
If the average profit per card is 22% lower than last year, how many cards
will Jack's company need to sell this year in order to make their target
profit?
Answers
The total profit this year can be calculated as:
Total profit = Average profit per card * Number of cards sold
From the given information, we know that:
Last year's profit = £3510
Last year's number of cards sold = 2340
Last year's average profit per card = £1.50
This year's profit target = 18% more than last year's profit = £3510 * 1.18 = £4135.80
This year's average profit per card = 22% lower than last year's average profit per card = £1.50 * 0.78 = £1.17
Using the above information, we can write the equation:
Total profit = Average profit per card * Number of cards sold
£4135.80 = £1.17x
Solving for x, we get:
x = 3540.68
Since we cannot sell a fraction of a card, we need to round up the number of cards to the nearest whole number. Therefore, Jack's company needs to sell at least 3541 cards this year to make their target profit.
Answer:
Jack's company needs to sell 3540 cards this year in order to make their target profit.
Step-by-step explanation:
Given the average profit per card last year was £1.50, and the average profit per card is 22% lower this year, this year's average profit per card will be:
[tex]\begin{aligned}\implies \sf Average\;profit\;per\;card&= \£1.50 - (22\% \;\text{of}\; \£1.50)\\&=\£1.50-0.22 \times \£1.50\\&=\£1.50-\£0.33\\&=\£1.17\end{aligned}[/tex]
Given the total profit Jack is aiming for this year is 18% more than last year's profit of £3510, this year's target profit is:
[tex]\begin{aligned}\implies \sf Target\;profit&=\£3510 + (18\%\;\text{of}\;\£3510)\\&=\£3510 + 0.18 \times \£3510\\&=\£3510 + \£631.80\\&=\£4141.80\end{aligned}[/tex]
To calculate how many cards Jack's company needs to sell to make this target profit, divide the total target profit by the average profit per card:
[tex]\begin{aligned}\implies \sf Number\;of\;cards&=\dfrac{4141.80}{1.17}\\\\&=3540\end{aligned}[/tex]
Therefore, Jack's company needs to sell 3540 cards this year in order to make their target profit.
The food service manager conducted a random survey of 200 students to determine their preference for new lunch menu items. There are 1,500 students in the school. Select all the manager’s predictions that are supported by the data
Answers
There are several predictions that the food service manager may make based on the data from the survey of 200 students regarding their preference for new lunch menu items. Let's examine some of these predictions and see if they are supported by the data.
The majority of students will like the new menu items.
The food service manager may predict that the majority of students in the school will like the new menu items, based on the positive responses from the 200 surveyed students. However, it's important to note that the sample size of 200 is relatively small compared to the total student population of 1,500. Therefore, it's possible that the preferences of the 200 surveyed students may not be representative of the preferences of the entire student population. To make a more accurate prediction, the manager may need to conduct a larger survey or pilot program to test the new menu items with a larger group of students.
Certain menu items will be more popular than others.
Based on the survey data, the food service manager may be able to identify which new menu items are more popular among the surveyed students. For example, if a majority of students indicate that they would like to see more vegetarian options, the manager may predict that introducing more vegetarian menu items will be popular among the broader student population. However, it's important to keep in mind that the preferences of the 200 surveyed students may not be representative of the preferences of the entire student population, so the manager may need to conduct additional research or testing to confirm these predictions.
The introduction of new menu items will increase overall satisfaction with the school lunch program.
If the survey data shows that a significant number of students are excited about the new menu items, the food service manager may predict that introducing these items will increase overall satisfaction with the school lunch program. However, it's important to note that satisfaction is a complex concept that can be influenced by many factors beyond just the menu items, such as the quality of service, cleanliness of the cafeteria, and overall atmosphere. Therefore, the manager may need to consider these other factors when predicting the impact of the new menu items on overall satisfaction with the lunch program.
In summary, while the data from the survey of 200 students can provide valuable insights into student preferences for new lunch menu items, it's important to interpret these results with caution and consider additional factors that may influence the broader student population. Conducting further research or testing can help to confirm these predictions and make more accurate decisions about the school lunch program.
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48 Points I, M, G, and N form a square on the Argand diagram. If points I, M, and G correspond to complex numbers 2+2i, 3−3i, −2−4i, respectively, then find the complex number that corresponds to point N. Find the length of the diagonal of the square IMGN.
Answers
Answer:
Since points I, M, G, and N form a square, we know that the diagonal IM is perpendicular to GN and has the same length as GN. Therefore, to find the complex number corresponding to point N, we can find the midpoint of the diagonal IM and then rotate it 90 degrees counterclockwise to get the corresponding point N.The midpoint of IM is (2+3)/2 + (2−3)/2 i = 5/2 − 1/2 i. To rotate this point counterclockwise by 90 degrees, we can swap the real and imaginary parts and negate the new real part. This gives us the complex number −1/2 + 5/2 i, which corresponds to point N.
To find the length of the diagonal IMGN, we can first find the length of the side of the square. The side length is the distance between I and M, which is |3−2i−2−2i| = |1−4i| = sqrt(1^2+4^2) = sqrt(17).
The diagonal IMGN is the hypotenuse of a right triangle with sides of length sqrt(17), so we can use the Pythagorean theorem to find its length:
|IMGN| = sqrt(2)*|IM| = sqrt(2)*sqrt(17) = sqrt(34).
Therefore, the complex number corresponding to point N is −1/2 + 5/2 i, and the length of the diagonal IMGN is sqrt(34).
Answer: Point N: -3+i
Diagonal length: sqrt52
Step-by-step explanation:
You can start by finding point N by graphing all the other solutions on an x-y graph, using a+bi. Where a=the x point, b= the y point. After looking at this you can deduct that point N has to be at -3+i. Because the x between I and M is 1, the distance between G and N has to be 1 too. Repeat with Y.
Next, you use Points N and M to find the distance. You use the same concept that a=x, and b=y and plug this into the distance formula. You would get sqrt(-3-3)^2+(1+3)^2. This evaluates to sqrt52.
Find the perimeter of a polygon with
Points A (4,2) B (-4,8) C (-7,4) and D (-1,-4)
Answers
The required perimeter is 25+√61 units.
How to find perimeter?We can find the distance between each pair of consecutive points and then add them up to get the perimeter of the polygon.
Using the distance formula, the distance between points A and B is:
[tex]$$AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-4 - 4)^2 + (8 - 2)^2} = \sqrt{100} = 10$$[/tex]
Similarly, the distances between the other pairs of points are:
[tex]$$BC = \sqrt{(x_C - x_B)^2 + (y_C - y_B)^2} = \sqrt{(-7 + 4)^2 + (4 - 8)^2} = 5$$[/tex]
[tex]$$CD = \sqrt{(x_D - x_C)^2 + (y_D - y_C)^2} = \sqrt{(-1 + 7)^2 + (-4 - 4)^2} = 10$$[/tex]
[tex]$$DA = \sqrt{(x_A - x_D)^2 + (y_A - y_D)^2} = \sqrt{(4 + 1)^2 + (2 + 4)^2} = \sqrt{61}$$[/tex]
Therefore, the perimeter of the polygon is:
[tex]$$AB + BC + CD + DA = 10 + 5 + 10 + \sqrt{61}$$[/tex]
= 25+√61
Thus, required perimeter is 25+√61.
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M/S Sing Trader purchased refrigerator for Rs.10,000 taxable amount. They sold it to
Amrutbhai for Rs. 12,000 taxable amount. The rate of GST is 28%, then find the CGST
and SGST to be paid by M/S Sing Trader
Answers
The CGST and SGST that M/S Sing Trader must pay as the GST rate is 28% is Rs. 280 CGST and Rs. 280 SGST.
Given that,
M/S Sing Trader spent Rs. 10,000 in taxable revenue for a refrigerator. For a taxable amount of Rs. 12,000, they sold it to Amrutbhai.
We have to find the CGST and SGST that M/S Sing Trader must pay as the GST rate is 28%.
We know that,
Input tax = 10000 × 28%
Output tax = 12000 × 28%
GST payable = 12000 × 28% - 10000 × 28%
GST payable = 28% (12000-10000)
GST payable = 28% (2000)
GST payable = [tex]\frac{28}{100}[/tex](2000)
GST payable = 28×20
GST payable = 560
CGST = SGST = [tex]\frac{GST}{2}[/tex] = [tex]\frac{560}{2}[/tex] = Rs. 280
Therefore, The CGST and SGST that M/S Sing Trader must pay as the GST rate is 28% is Rs. 280 CGST and Rs. 280 SGST.
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If the volume of a sphere is 4500cm squared what is the radius of the sphere
Answers
The radius of the sphere, considering it's volume, is given as follows:
r = 10.24 cm.
How to obtain the volume of a sphere?The formula for the volume of a sphere is given as follows:
V = (4/3) x π x r³
In which the parameters of the formula are given as follows:
V is the volume of the sphere. π is a mathematical constant approximately equal to 3.14.r is the radius of the sphere.The volume of the sphere in this problem is given as follows:
4500 cm³.
Solving the formula for the radius, the radius of the sphere has the measure given as follows:
4500 = (4/3) x π x r³
r = (4500/(4/3 x π))^(1/3)
r = 10.24 cm.
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if two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}? hint [see example 2.]
Answers
If two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}The probability of the event {(3, 3), (2, 3), (1, 3)}
If two indistinguishable dice are rolled, it is 3/36 or 1/12.
Explanation: Indistinguishable dice are dice that appear identical to one another but do not have unique markings. As a result, indistinguishable dice will have the same number of faces, but the values on each face will be identical.
The total number of possible outcomes is 6 * 6 = 36 because there are six possible outcomes for each roll of a single die.
The probability of rolling the numbers (3, 3), (2, 3), or (1, 3) can be determined as follows: 3/36 or 1/12
For each die, there are six possible outcomes, so there are 6*6, or 36 possible outcomes for two dice.
Because (3, 3), (2, 3), and (1, 3) are the only possible ways to obtain a 3 on one of the dice and a 3, 2, or 1 on the other, the probability is 3/36 or 1/12.
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Graph the line with slope -1/5 and y-intercept of -5
Answers
A graph of the line with slope -1/5 and y-intercept of -5 is shown in the image attached below.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial value.Based on the information, an equation that models the line is given by this mathematical expression;
y = mx + c
y = -x/5 - 5
In this exercise, we would use an online graphing calculator to plot the above equation as shown in the graph attached below.
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help!!!
......................................
Answers
The axis should be labeled x-axis and y-axis respectively.
A graph of triangle ABC with the points A (-3, 0), B (-2, 4), and C (1, -1) is shown below.
The coordinates of triangle A'B'C' are A' (0, 3), B' (4, 2), and C' (-1, -4).
The coordinates of triangle A"B"C" are A" (0, 0), B" (4, -1), and C" (-1, -4)).
What is the rotation of a point 90° clockwise?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a rotation of 90° clockwise about the center (origin), the coordinates of triangle A'B'C' are as follows;
(x, y) → (y, -x)
Coordinate A = (-3, 0) → Coordinate A' = (0, -(-3)) = (0, 3)
Coordinate B = (-2, 4) → Coordinate B' = (4, -(-2)) = (4, 2)
Coordinate C = (1, -1) → Coordinate C' = (-1, -(1)) = (-1, -1)
Next, we would translate A'B'C' 3 units down:
(x, y) → (x, y - 3)
Coordinate A' = (0, 3) = A" (0, 0)
Coordinate B' = (4, 2) = B" (4, -1)
Coordinate C' = C" (-1, -4).
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Pls answer this!!!!
with simple working out
<333
Answers
Answer:
Step-by-step explanation:
A is 40
B 3 on the the top after 9 is 27
term is 3
c is 4 on top after 32 is 128
term is 4
d after 300 is 3,000
term is 10
NEED ANSWER IN THE NEXT 45 MINS PLSSS HELP
4. A venue sold 800 tickets to an event. If it cost
$2,500 to put on the event and the venue
profited at least $12,500, find c, the cost per
ticket.
A. c≥ $18.75
B. c≤ $18.75
C. c≥ $12.50
D. c≤ $12.50
Answers
Answer: the answer is A
Step-by-step explanation:
$21,000 is invested for 3 years with an APR of 3% and daily compounding. What is the balance after 3 years?
Answers
The balance after 3 years with daily compounding at an APR of 3% is $23,284.94.
To calculate the balance after 3 years with daily compounding, we need to use the formula for compound interest,
A = P(1 + r/n)^(nt)
Where,
A = the balance after 3 years
P = the initial investment, which is $21,000 in this case
r = the annual percentage rate, which is 3%
n = the number of times the interest is compounded per year. In this case, since it's daily compounding, n = 365 (the number of days in a year).
t = the number of years, which is 3 years.
Substituting the given values in the formula, we get
A = 21000(1 + 0.03/365)^(365×3)
A = $23,284.94
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Let X be the average of a sample of 16 independent normal random variables with mean 0 and variance 1. Determine c such that
P (|X| < c) = .5
Answers
Answer: Let X¯¯¯¯
be the average of a sample of 16
independent normal random variables with mean 0
and variance 1
. Determine c such that P(|X¯¯¯¯|<c)=.5
I am having a lot of trouble with this question. I know it is related to chi-square but I don't know how to even start.
Step-by-step explanation:
Please help!!!!!!!
What is the axis of symmetry of the quadratic function below?
Answers
Answer:
x = -1
Step-by-step explanation:
The axis of symmetry is a line that divides the two sides of a parabola through the vertex.
The area of a rectangle is x2 – 6x +8. Find its possible length and breadth:
Answers
Answer:
Step-by-step explanation:
To find the possible length and breadth of the rectangle, we need to factor the given expression:
x^2 - 6x + 8 = (x - 4)(x - 2)
Therefore, the length and breadth of the rectangle can be any combination of (x-4) and (x-2).
For example, if we choose (x-4) as the length and (x-2) as the breadth, we have:
Length = x - 4
Breadth = x - 2
Conversely, if we choose (x-2) as the length and (x-4) as the breadth, we have:
Length = x - 2
Breadth = x - 4
So, the possible length and breadth of the rectangle are (x-4) and (x-2), and vice versa.
Answer:(x-4) and (x-2)
Step-by-step explanation:
Find the sum
2 1/6 + 1/2
Answers
Answer:
[tex]\frac{7}{4}[/tex]
Step-by-step explanation:
mixed fraction [tex]\frac{13}{6}[/tex]
sum =[tex]\frac{13}{6}[/tex] +[tex]\frac{1}{2}[/tex] ( LCM)= 12
[tex]\frac{13}{6}[/tex]×[tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex]×[tex]\frac{6}{6}[/tex]
[tex]\frac{26+2}{12}[/tex]
[tex]\frac{28}{12}[/tex] Simplify = [tex]\frac{7}{4}[/tex]
Determine whether the Mean Value theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = 9x3, [1, 2] Yes, the Mean Value Theorem can be applied. No, because f is not continuous on the closed interval [a, b]. No, because fis not differentiable in the open interval (a, b). None of the above. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that f'(c) = - w f(b) – f(a) 2. (Enter your answers as a comma-separated list. If the Mean Value Theorem cannot Ent b - a be applied, enter NA.) C=
Answers
Answer: Yes, the Mean Value Theorem can be applied to f(x) = 9x^3 on the closed interval [1, 2].
To find all values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a), we first find the derivative of f(x):
f'(x) = 27x^2
Then, we can use the Mean Value Theorem to find a value c in the open interval (1, 2) such that:
f'(c) = (f(2) - f(1))/(2 - 1)
27c^2 = 9(2^3 - 1^3)
27c^2 = 45
c^2 = 5/3
c = +/- sqrt(5/3)
Therefore, the values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a) are:
c = sqrt(5/3), -sqrt(5/3)
Note that these values are not in the closed interval [1, 2], as they are not between 1 and 2, but they are in the open interval (1, 2).
Step-by-step explanation:
You invest $20 000 in a building society account, which pays 4% interest each year. If the interest is added to the account at the end of each year. What is the value of the account after 2 years?
Answers
Answer:
21632
Step-by-step explanation:
20000×1.04=20800
20800×1.04=21632
porter
Con
multiple CIVILE
all day
1. Write a ratio in simplified form of the vertical length to the horizontal length for the red triangle. (1 point)
02:3
03:2
01:1
Onone of the above
Answers
2:3 is a simple ratio of the red triangle's vertical and horizontal lengths.
Explain about the ratio?In order to put numbers into the proper perspective and so simplify difficulties, ratios are widely used in daily life.
A ratio is a tool used only to compare the sizes of two or much more numbers in relation to one another in mathematics. By making amounts easier to understand, ratios enable us to measure but also express quantities.
When translating from one currency to another, ratios are used.
Ratios can be used, for instance, to transform pound to euros or dollars.A ratio is used to determine wager winnings.Ratios can be used to determine how many drink bottles you'll require to host a party.In a recipe, ratios can be employed to produce a particular dish.For the red triangle:
horizontal length = 3 units
vertical length = 2 units
vertical length / horizontal length = 2/3
Thus, 2:3 is a simple ratio of the red triangle's vertical and horizontal lengths.
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Which expression is equivalent to (4−2x)(4+2x)
Answers
The expression that is equivalent to (4 - 2x)(4 + 2x) is equal to 16 - 4x^2 approximately.
To simplify the expression (4 - 2x)(4 + 2x), we can use the FOIL method, which stands for First, Outer, Inner, Last. This method involves multiplying each term in the first factor by each term in the second factor and then combining like terms.
Using the FOIL method, we get:
(4 - 2x)(4 + 2x) = 4 × 4 + 4 × 2x - 2x × 4 - 2x × 2x
Simplifying the expression, we get:
16 + 8x - 8x - 4x^2
The two middle terms cancel each other out, leaving us with:
16 - 4x^2
We can also check our answer by factoring the simplified expression back to the original expression. If we factor 16 - 4x^2, we get:
16 - 4x^2 = 4(4 - x^2)
We can then use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b), to factor further:
4(4 - x^2) = 4(2 + x)(2 - x)
This gives us back the original expression, (4 - 2x)(4 + 2x), confirming that 16 - 4x^2 is equivalent to (4 - 2x)(4 + 2x).
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The value of 5^2000+5^1999/5^1999-5^1997
Answers
Answer:
Step-by-step explanation:
We can simplify the expression by factoring out a common factor of 5^1999 from the numerator:
5^2000 + 5^1999
= 5^1999(5 + 1)
= 5^1999(6)
And we can also factor out a common factor of 5^1997 from the denominator:
5^1999 - 5^1997
= 5^1997(5^2 - 1)
= 5^1997(24)
So the entire expression simplifies to:
(5^2000 + 5^1999) / (5^1999 - 5^1997)
= (5^1999 * 6) / (5^1997 * 24)
= (6/24) * 5^2
= 5/2
Therefore, the value of the expression is 5/2.
Describe the error in finding the distance between A(6, 2) and B(1,−4)
Answers
The error is the substitution of coordinates. Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space.
Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identifies a specific point's precise location on a grid. This grid is referred to as a coordinate plane.
The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by
[tex]AB = \sqrt{(x_{1} , x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
Observe that the x-coordinate of B is subtracted from the x-coordinate of A. This goes with the y-coordinates.
Therefore, the error is the substitution of coordinates.
The correct computation is
[tex]AB = \sqrt{(6-1)^{2} + [2 - (-4)]^{2} }[/tex]
[tex]= \sqrt{5^{2} + 6^{2} }[/tex]
[tex]= \sqrt{25 + 36} \\[/tex]
[tex]= \sqrt{61}[/tex]
≈ 7.81
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The complete question is as follows:
Describe and correct the error in finding the distance between A(6, 2) and B(1, -4). AB = √[(6 - 2)² + {2 - (-4)}²] = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.4.
Work out the recipricol of 0.5
Answers
Answer:
the answer is 2
Step-by-step explanation:
this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0
Suppose E and F are two events, with the following probability table F F’
E 0.1 0.3 E' 0.2 0.4 a) Compute P(EF). b) Are E and F independent? Explain. c) Are E and F mutually exclusive? Explain.
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a) With the following probability table F F, Let’s apply the formula for the intersection of events to solve the first part of the problem.
P(EF) = P(E) x P(F|E).We know that P(E) = 0.1 and that P(F|E) = 0.3. Therefore,P(EF) = P(E) x P(F|E) = 0.1 x 0.3 = 0.03.b) Two events E and F are independent if and only if their intersection is equal to the product of their individual probabilities.
P(EF) = P(E) x P(F) if and only if E and F are independent. We know that P(E) = 0.1 and that P(F) = 0.1 + 0.3 = 0.4. Therefore, P(EF) = 0.03, which is different from 0.1 x 0.4 = 0.04.
Since P(EF) is different from P(E) x P(F), it means that E and F are not independent.c) Two events E and F are mutually exclusive if and only if their intersection is the null set.P(EF) = ∅ if and only if E and F are mutually exclusive. We know that P(EF) = 0.03, which is not equal to the null set. Therefore, E and F are not mutually exclusive.
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Find the Laplace transform Y(s) of the solution of the given initial value problem. Then invert to find y(t) . Write uc for the Heaviside function that turns on at c , not uc(t) .y'' + 16y = e^(?2t)u2y(0) = 0 y'(0) = 0Y(s) =y(t) =
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The Laplace transform is a mathematical technique used to solve differential equations and analyze signals and systems in engineering, physics, and other fields. It is named after the French mathematician Pierre-Simon Laplace.
The Laplace transform of the given initial value problem is given by:
Y(s) = (2s^2 + 16) / (s^2(s^2+16))
Inverting the Laplace transform to find y(t) gives us:
y(t) = e^(-8t) * (1-cos(4t)) + 2sin(4t) + u2(t)
Where u2(t) is the Heaviside function that turns on at t = 2.
To find the Laplace transform of y(t), we first take the Laplace transform of both sides of the differential equation:
L(y''(t)) + 16L(y(t)) = L(e^(-2t)u_2(t))
Using the property L(y''(t)) = s^2Y(s) - sy(0) - y'(0) and noting that y(0) = 0 and y'(0) = 0, we can simplify to get:
s^2Y(s) + 16Y(s) = L(e^(-2t)u_2(t))
Using the property L(e^(-at)u_c(t)) = 1/(s + a) * e^(-cs), we can substitute to get:
s^2Y(s) + 16Y(s) = 1/(s + 2)^2
Now we can solve for Y(s):
Y(s) = 1/(s^2 + 16) * 1/(s + 2)^2
To find y(t), we need to take the inverse Laplace transform of Y(s). We can use partial fraction decomposition to simplify the expression:
Y(s) = A/(s^2 + 16) + B/(s + 2) + C/(s + 2)^2
Multiplying both sides by the denominator and solving for A, B, and C, we get:
A = 1/8
B = -1/4
C = 1/8
Substituting these values, we get:
Y(s) = 1/8 * 1/(s^2 + 16) - 1/4 * 1/(s + 2) + 1/8 * 1/(s + 2)^2
Taking the inverse Laplace transform of each term, we get:
y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t)
Therefore, the solution to the initial value problem y'' + 16y = e^(-2t)u_2(t), y(0) = 0, y'(0) = 0 is y(t) = (1/8)sin(4t) - (1/4)e^(-2t) + (1/4)te^(-2t).
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