Answers
Answer:
(2x -4)/(x -1)
Step-by-step explanation:
You want to simplify (2x² -2x -4)/(x² -1).
FactorsSimplifying a rational expression generally means cancelling common factors from the numerator and denominator. To do that, you must factor both the numerator and the denominator.
NumeratorThe numerator coefficients have a common factor of 2. Removing that can simplify the problem of factoring the numerator:
2x² -2x -4 = 2(x² -x -2)
To factor the quadratic, you look for factors of -2 that have a sum of -1. Those would be -2 and +1. The middle term is written as a sum using these values.
= 2(x² -2x +x -2)
This can now be factored by grouping terms in pairs, and factoring each pair.
= 2((x² -2x) +(x -2)) = 2(x(x -2) +1(x -2))
= 2(x +1)(x -2)
DenominatorThe denominator is the difference of squares, so is factored according to the pattern for that:
a² -b² = (a -b)(a +b)
x² -1 = (x -1)(x +1)
Simplified formNow you know enough to be able to simplify the expression. The common factors (x+1) cancel.
[tex]\dfrac{2x^2-2x-4}{x^2-1}=\dfrac{2(x+1)(x-2)}{(x+1)(x-1)}\\\\=\dfrac{2(x-2)}{x-1}=\boxed{\dfrac{2x-4}{x-1}}[/tex]
__
Additional comment
Even though the factor (x+1) has disappeared from the expression, the simplified form still carries the restriction that x ≠ -1. The graph of the original expression will have a "hole" at (-1, 3), where it is undefined. Otherwise, the graph looks like a graph of (2x-4)/(x-1).
Related Questions
what are the roots of 2x^2+10x+9=2x
Answers
The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots
Calculating the roots of the equationTo find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation
2x² + 10x + 9 - 2x = 0
Simplifying the left-hand side, we get:
2x² + 8x + 9 = 0
Now, we can use the quadratic formula to find the roots of the equation:
x = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = 8, and c = 9.
Substituting these values into the formula, we get:
x = (-8 ± √(8² - 4(2)(9))) / 2(2)
Simplifying the expression under the square root, we get:
x = (-8 ± √-8) / 4
The square root of -8 is not a real number
So, the equation has no real root
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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]
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 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) =
Answers
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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If Julie drives from York to corby via Derby. How many miles will she drive
Answers
Julie will have driven a total distance of 289 miles if she travels from York to Corby via Derby.
Starting from York, Julie needs to travel to Derby. The distance between York and Derby is given as 89 miles. So, we know that Julie will have driven 89 miles once she reaches Derby.
Next, Julie needs to travel from Derby to Corby, but the given information is a bit tricky here. The distance from Derby to Corby is not given directly. Instead, we are given two distances - Derby to Dory and Dory to Corby.
To find the distance from Derby to Corby, we need to add the distances between Derby and Dory, and Dory and Corby. From the question, we know that the distance between Derby and Dory is 127 miles and the distance between Dory and Corby is 73 miles. Adding these two distances gives us the total distance from Derby to Corby, which is 200 miles.
Finally, we can add up the distances traveled between each location to find the total distance traveled by Julie. Adding the distances of each leg of the journey, we get:
89 miles (York to Derby) + 200 miles (Derby to Corby via Dory) = 289 miles
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Complete Question:
If Julie drives from York to Corby via Dory how many miles will she have driven?
York 89
Derby 127 73
Corby
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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$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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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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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
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:
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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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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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
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.
Answers
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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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:
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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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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1)A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean length of the shafts. She randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. The lengths are known to follow a normal distribution whose standard deviation is 2 mm. Calculate a 95% confidence interval for the true mean length of the shafts. Input your answers for the margin of error, lower bound, and upper bound.
a)Determine Margin of Error for this 95% confidence interval.
b)Input the lower bound. (Round to three decimal places)
c)Input the upper bound. (Round to three decimal places)
2)To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error of ± 0.0001?
3)A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis for the standard treatment is two years. So the null hypothesis is that average survival time after diagnosis is the same for the new treatment and the standard treatment.
In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of 4.5 years. Even though the sample is small, the results are statistically significant at the 0.05 significance level. Consequently, she rejects the null hypothesis.
In a future study, it is determined that the new treatment does not increase the mean survival time in the population of all patients with this particular type of cancer. The researcher has
Committed a type I error.
Incorrectly used a 0.05 significance test when she should have computed the P-value.
Incorrectly used a 0.05 significance level when she should have used a 0.01 significance level.
Committed a type II error.
4)If the level of significance, α{"version":"1.1","math":"\alpha"}, is made very small, thereby making the probability of committing a Type 1 error very small, what happens to the probability of committing a Type 2 error?
By reducing the probability of committing a Type 1 error, we increase the probability of committing a Type 2 error.
There is no specific relationship between the two probabilities.
By reducing the probability of committing a Type 1 error, we also reduce the probability of committing a Type 2 error.
The relationship between the two probabilities depends on how the study is set up.
Answers
Therefore, with a 95% confidence interval, we can estimate the true mean length of the drive shafts to be between 992.16 mm and 1007.84 mm.
The true mean length of the drive shafts can be estimated using a 95% confidence interval. The margin of error is calculated as 2*1.96*2 = 7.84 mm. The lower bound of the confidence interval is 1000 - 7.84 = 992.16 mm and the upper bound is 1000 + 7.84 = 1007.84 mm.
This confidence interval states that there is a 95% probability that the true mean length of the drive shafts falls within the range of 992.16 mm to 1007.84 mm. The relationship between the two probabilities is that the probability of the true mean length falling within the confidence interval is 95%. If the sample size was increased, the margin of error would decrease, resulting in a tighter range and higher probability that the true mean would fall within the confidence interval.
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the cost for an upcoming field trip is 20 dollars the cost of the feild trip c is a function of the number of students x select all the possible outputs for the function defined by c(x)=20x
Answers
20 is the possible outputs for the function defined by c(x)=20x for all of the students that would pay for the field trip
How to solve for the functionThe function that is known to represent what would be the cost of the trip of these students is given as C(x)=20x.
The cost of the trip for one of the students is put at 20 dollars each.
We would have x as the total number of those that would be attending this trip. In order to get the output that would show us the cost of the trip.
We take X to be a whole number.
then x = 1
such that that c(1) = 20(1) = 20
Then the total is 20 per student
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the cost for an upcoming field trip is 20 dollars the cost of the feild trip c is a function of the number of students x select all the possible outputs for the function defined by c(x)=20x
A 20 B 30 c 50
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:
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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help!!!
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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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Graph the line with slope -1/5 and y-intercept of -5
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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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The following is a list of prices for zero-coupon bonds of various maturities. a. Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four years. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) YTM Maturity (Years) 1 Price of Bond $ 945.90 $ 911.47 % 2 % 3 $ 835.62 % % 4 $ 770.89 b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Maturity (years) 1 2 3 4 Price of Bond $ 945.90 911.47 835.62 770.89 Forward Rate Maturity (Years) 2 3 $ % Price of Bond 911.47 835.62 770.89 $ $ 4 % The following is a list of prices for zero-coupon bonds of various maturities. a. Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four years. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Answer is complete and correct. Maturity (Years) YTM 1 $ 5.72 % $ Price of Bond 945.90 911.47 835.62 770.89 2 3 4.74 6.17 >>> % % % 4 S 6.72 b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Maturity (years) 1 2. 3 4 Price of Bond $ 945.90 911.47 835.62 770.89 Answer is complete but not entirely correct. Price of Bond Forward Rate Maturity (Years) 2 $ 911.47 3.79 % 3.60 X % 3 $ 835.62 4 770.89 2.89 x %
Answers
For the fourth-year forward rate: The forward rate is equaI to [(770.89/835.62)(1/(4-3)] - 1 = 0.0289 or 2.89% .
What is equation ?An equation in mathematics is a cIaim that two mathematicaI expressions are equivaIent. The Ieft-hand side (LHS) and the right-hand side (RHS), which are separated by the equaI sign ("="), make up an equation. Equations are a common tooI for probIem-soIving and determining the vaIue of an unknowabIe variabIe since they are used to describe mathematicaI reIationships.
given
I For a bond having a one-year maturity:
[tex]YTM = [(1000/945.90)^{(1/1)}] - 1 = 0.0572 or 5.72%[/tex]
(ii) For a bond having a two-year maturity:
[tex]YTM = [(1000/911.47)^{(1/2)}] - 1 = 0.0474 or 4.74%[/tex]
(iii) For a bond having a three-year maturity:
[tex]YTM = [(1000/835.62)^{(1/3)}] - 1 = 0.0617 or 6.17%[/tex]
(iv) For a bond with a four-year maturity:
[tex]YTM = [(1000/770.89)^{(1/4)}] - 1 = 0.0672 or 6.72%[/tex]
We can use the foIIowing formuIa to determine the forward rates:
Forward rate is equaI to [((Bond Price 1/Bond Price 2)(1/(n2-n1))]]. - 1
where n₂-n₁ is the time period between the maturities, Price of Bond 1 is the price of the bond with maturity n₁, and Price of Bond 2 is the price of the bond with maturity n₂.
We may determine the forward rates using the bonds' current prices by foIIowing these steps:
I For the second-year forward rate:
((911.47/945.90)(1/(2-1))) is the forward rate. - 1 = 0.0379 or 3.79%
(ii) For the third-year forward rate:
The forward rate is equaI to [((835.62/911.47)(1/(3-2))] - 1 = 0.0360 or 3.60%
For the fourth-year forward rate: The forward rate is equaI to [(770.89/835.62)(1/(4-3)] - 1 = 0.0289 or 2.89% .
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Let A and B be arbitrary matrices for which the indicated product is defined. Determine whether the statement below is true or false. Justify the answer. The second row of AB is the second row of A multiplied on the right by B. Choose the correct answer below. OA. The statement is true. Let row (A) denote the ith row of matrix A. Then row (AB) = row (A)B. Letting i = 2 verifies this statement OB. The statement is false. The second row of AB is the second row of A multiplied on the left by B. OC. The statement is true. Every row and column of AB is the corresponding row and column of A multiplied on the right by B. OD. The statement is false. Let column (A) denote the ith column of matrix A. Then column (AB) =column (A)B. The same is not true for the rows of AB.
Answers
The second row of AB is indeed the second row of A multiplied on the right by B, which confirms that the statement is true.The correct answer is actually OA.
To justify that the statement is True we consider the following steps:
Let row(A) denote the [tex]i_{th}[/tex] row of matrix A. Let A and B be arbitrary matrices for which the indicated product is defined. Therefore, the second row of AB is the second row of A multiplied on the right by B.Then row(AB) = row(A)B. Letting i = 2 verifies this statement.Consider the (i,j) entry of the product AB. By the definition of matrix multiplication, this entry is given by the dot product of the [tex]i_{th}[/tex] row of A with the [tex]j_{th}[/tex] column of B. This means that the entire[tex]i_{th}[/tex]row of AB is obtained by multiplying the [tex]i_{th}[/tex]row of A on the right by B.Therefore, the second row of AB is indeed the second row of A multiplied on the right by B, which confirms that the statement is true.
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assuming the conditions for inference have been met, does the coffee shop owner have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5 percent level of significance? conduct the appropriate statistical test to support your conclusion.
Answers
The coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
What is proportion ?
A proportion refers to the number or fraction of individuals or items that exhibit a particular characteristic or have a certain attribute, relative to the total number or sample size being considered. It is often expressed as a ratio or percentage.
To test whether the distribution of sales is proportional to the number of facings, we can use the chi-squared goodness of fit test. The null hypothesis for this test is that the observed data follows a specific distribution (in this case, a proportional distribution), while the alternative hypothesis is that the observed data does not follow that distribution.
To conduct the test, we first need to calculate the expected frequency for each category assuming a proportional distribution. We can do this by multiplying the total number of sales (610) by the proportion of facings for each brand:
Starbucks: 610 x 0.3 = 183
Dunkin: 610 x 0.4 = 244
Peet's: 610 x 0.2 = 122
Other: 610 x 0.1 = 61
Next, we calculate the chi-squared statistic using the formula:
χ² = Σ((O - E)² / E)
where O is the observed frequency and E is the expected frequency. The degrees of freedom for this test are (k-1), where k is the number of categories. In this case, k = 4, so the degrees of freedom are 3.
Using the observed and expected frequencies from the table, we get:
χ² = ((130-183)²/183) + ((240-244)²/244) + ((85-122)²/122) + ((155-61)²/61) = 124.36
Looking up the critical value of chi-squared for 3 degrees of freedom and a significance level of 0.05, we get a value of 7.815. Since our calculated χ² value of 124.36 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that the observed distribution of sales is not proportional to the number of facings.
Therefore, the coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
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What is 16/15 in simplest form
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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:
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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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.