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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(1 point) Suppose f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x,y) comes before (z, w) if x
Increasing lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).
Suppose that f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points.
Let's discuss what are critical points and how we can determine them,A critical point is a point on the graph where the derivative changes its sign.
In other words, the derivative either changes from negative to positive or from positive to negative. A critical point is also known as a stationary point or a turning point
To determine the critical points, we need to find the derivative of the given function and set it equal to zero.The given function is[tex]f(x,y) = xy(1 - 4x - 2y).[/tex]
Let's find the partial derivative of f with respect to [tex]x:f_x(x,y) = y(1 - 4x - 2y) - 4xy = (1-2y)(1-4x)y.[/tex] (1)
Now, find the partial derivative of f with respect to y:f_y(x,y) = x(1 - 4x - 2y) - 2xy = (1-2x)(1-2y)x. (2)
To find the critical points, we need to set both partial derivatives (1) and (2) equal to zero.
(1-2y)(1-4x) = 0 and (1-2x)(1-2y) = 0.
Solving both equations separately, we have the following critical points:(1/4, 1/2), (1/4, 0), (0, 1/2), and (0, 0).
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Fill in the blank A ____ is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution
answer options are
histogram
frequency polygon
scatterplot
normal quantile plot
Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.
What is a Normal Quantile Plot?
A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.
It plots sample data versus a theoretical normal distribution.
In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.
A normal quantile plot can be used to evaluate the following:
Whether or not a data set is normally distributedA data set's skewnessA data set's outliersA data set's center and spread whether or not a transformation is required to make a data set normally distributed.The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.
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I NEED HELP ON THIS ASAP!!
a) Graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380
b) The maximum profit of $5200 achieved.
Define the term selling profit?Selling profit is the profit that a business makes on the sale of its products or services. It is the difference between the selling price and the cost of product.
a) Let x be the number of boards of mahogany sold and y be the number of boards of black walnut sold. Then, the constraints of the problem can be represented by the following system of inequalities:
x ≥ 0 (non-negative constraint)
y ≥ 0 (non-negative constraint)
x ≤ 260 (maximum number of mahogany boards available)
y ≤ 320 (maximum number of black walnut boards available)
x + y ≤ 380 (maximum number of boards that can be sold)
To graph this system of inequalities, we can plot the lines x = 0, y = 0, x = 260, y = 320, and x + y = 380 on a coordinate plane and shade the feasible region that satisfies all of the constraints. The feasible region is the area that is bounded by these lines and includes the origin (0, 0).
b) The profit function P(x, y) can be defined as follows:
P(x, y) = 20x + 6y
To maximize the profit, we need to find the values of x and y that satisfy all of the constraints and maximize the profit function P(x, y).
One way to do this is to use the corner-point method. We can evaluate the profit function at each of the corners of the feasible region and find the corner that gives the maximum profit.
The corners of the feasible region are (0, 0), (0, 320), (260, 0), and (120, 260).
P(0, 0) = 0
P(0, 320) = 6(320) = 1920
P(260, 0) = 20(260) = 5200
P(120, 260) = 20(120) + 6(260) = 4720
Therefore, the maximum profit of $5200 can be achieved by selling 260 boards of mahogany and 0 boards of black walnut.
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Statistics question: (answer and explanation much appreciated)
a) The probability that the player is a non-pitcher not from the Dominican Republic is given as follows: 0.7578 = 75.78%.
b) The probability that a Dominican player is a pitcher is given as follows: 0.8595 = 85.95%.
c) The probability that a non-pitcher is not Dominican is given as follows: 0.4985 = 49.85%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
Of the Dominican players, the percentages are given as follows:
5.6% of 42%.x% of 58%.The total percentage of Dominican players is of 10.5%, hence the value of x is given as follows:
0.056 x 0.42 + 0.58x = 0.105
x = (0.105 - 0.056 x 0.42)/0.58
x = 0.1405.
Of the 58% of the batter, 14.05% are from the Dominican Republic, hence the probability of chosen a batter not from the Dominican Republic is of:
p = 1 - 0.1405/0.58
p = 0.7578 = 75.78%.
14.05% of the players from the Dominical Republic are batters, hence the probability of choosing a pitcher is given as follows:
1 - 0.1405 = 0.8595 = 85.95%.
Of the 58% of the batters, 14.05% are Dominican, hence the 85.95% are not Dominican, thus the probability of choosing a non-Dominican batter is given as follows:
0.58 x 0.8595 = 0.4985 = 49.85%.
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A function is shown.
f(x) = x² + 2x - 3
Use the Add Point tool to show the x-intercepts and maximum or minimum of the function.
the x-intercepts are (-3, 0) and (1, 0), and the minimum occurs at the vertex (-1, -4).
What is a function?
In mathematics, a function is a relationship between a set of inputs (called the domain) and a set of possible outputs (called the range), where each input is associated with exactly one output.
To find the x-intercepts, we set the function equal to zero and solve for x:
x² + 2x - 3 = 0
Using the quadratic formula, we get:
x = (-b ± sqrt(b² - 4ac)) / 2a
Where a = 1, b = 2, and c = -3.
Plugging in the values, we get:
x = (-2 ± sqrt(2² - 4(1)(-3))) / 2(1)
Simplifying, we get:
x = (-2 ± sqrt(16)) / 2
x = (-2 ± 4) / 2
x1 = -3, x2 = 1
Therefore, the x-intercepts are (-3, 0) and (1, 0).
To find the maximum or minimum, we can use the vertex form of the equation:
f(x) = a(x - h)² + k
where (h, k) is the vertex.
To get the vertex, we complete the square:
f(x) = x² + 2x - 3
f(x) = (x + 1)² - 4
The vertex is (-1, -4), which is a minimum since the coefficient of the squared term is positive.
Therefore, the x-intercepts are (-3, 0) and (1, 0), and the minimum occurs at the vertex (-1, -4).
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could someone help out?
Answer:
adjacent = cos(angle) x hypotenuse
Landon buys cookies and lemons at the store he pays a total of $29.12 He pays $2.66 for the cookies he by seven bags of lemons that each cost the same amount Which tape diagram could be used to represent the contacts if X represents how much each bag of lemons cost
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
what is unitary method ?A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.
given
The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.
The first segment on the left, which is $2.66, represents the price of the cookies.
The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
To find the perimeter, we need to add up the lengths of all the sides. In this case, we have four sides with lengths given by the expressions 2v-5, 4v+5, 2v-5, and 8v-7.
So the perimeter P is:
P = (2v-5) + (4v+5) + (2v-5) + (8v-7)
Simplifying and combining like terms, we get:
P = 16v - 12
Therefore, the perimeter is 16v - 12.
the radius of a circle is increasing at a rate of 4 cm/s. how fast is the area of the circle increasing after 10 seconds? g
Answer:
A = 1600π cm²
Step-by-step explanation:
Pre-SolvingWe are given that a circle's radius increases 4 cm every second.
We want to know how large the area of the circle is after 10 seconds.
SolvingWe first need to find how large the radius will be.
We know the proportion of the rate increase / time; for every 1 second, the rate increases by 4 cm.
We can write this as a proportion:
[tex]\frac{4 cm}{1 s} = \frac{x}{10s}[/tex]
We can cross multiply to get:
4 cm * 10 s = x * 1 s
Divide both sides by 1 s
(4 cm * 10 s) / (1 s) = 40cm = x
So, after 10 seconds, the radius will be 40cm.
We aren't done yet though, remember that the question wants us to find the area of the circle.
The area can be calculated using the equation A = πr², where r is the radius.
We can substitute 40 as r in the equation to get:
A = πr² = π * (40)² = 1600π cm²
every year educational services (ets) selects readers for the advanced placement exams. recently the ap* statistics exam has been graded in lincoln, nebraska. one objective of ets is to achieve equity in grading by inviting teachers to be readers from all parts of the nation. however budgets are a consideration also. the accountants at ets wonder if the flights from cities west of lincoln are the same as flight costs from cities east of lincoln. a random sample of the expense vouchers from last year was reviewed for the cost of airline tickets. costs (in dollars) are shown in the table. indicate what inference procedure you would use to see if there is a significant difference in the costs of airline flights between the west and east coasts to lincoln, nebraska, then decide if it is okay to actually perform that inference procedure. (check the appropriate assumptions and conditions and indicate whether you could or could not proceed. you do not have to do the actual test.)
To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.
Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.
Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.
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In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. What is the sampling distribution of their sample mean IQ? Must show work (explain) to justify choice.
- exactly normal, mean 112, standard deviation 20
- approximately normal, mean 112, standard deviation 0.1
- approximately normal, mean 112, standard deviation 1.414
- approximately normal, mean 112, standard deviation 20
The sampling distribution is approximately normal.
The sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414.What is the sampling distribution of their sample mean IQ?The standard deviation is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where σ is the population standard deviation and n is the sample size. So, we have:$${SD} = \frac{20}{\sqrt{200}} = \sqrt{\frac{20^2}{200}} = \sqrt{2} = 1.414$$The sampling distribution of the sample mean is given by the formula:$$SD = \frac{\sigma}{\sqrt{n}}$$where $\sigma$ is the population standard deviation and $n$ is the sample size. Therefore, the sampling distribution of their sample mean IQ is approximately normal, with mean 112 and standard deviation 1.414. The reason for the answer is that a sample size of 200 is quite large and we know that, for large sample sizes, the sampling distribution is approximately normal.
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Describe the center of the dot plot. What single dot would best represent the data?
The center, 6, is less frequent than the neighbor values, but the single dot that best represents the data still is 6.
What can we say about the center?Each point on the dot plot over each number represents the amount of times that we have that value in the data set.
Here the center is 6, and we can see that we have only one point in 6, while in the neighbors we can see more points, then we can see that the center is less populated than the neighbor values.
Now, what single dot would best represent the data?
To answer that we need to get the mean of the data set,
Counting the values in the graph, and dividing by the number of points, we have:
mean = (3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8+ 8+ 9)/12 = 6.16
Which we can round to 6.
So that is the single dot that best represents the data.
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3x+4y=34. In the equation, what is the y-value when x=10? x= 10 , y= ?
When x=10, the value of y in the equation 3x+4y=34 is y=1.
To find the value of y when x=10 in the equation 3x+4y=34, we can substitute x=10 into the equation and solve for y:
3x+4y=34
3(10) + 4y = 34
30 + 4y = 34
4y = 34 - 30
4y = 4
y = 1
An equation is a mathematical statement that shows the relationship between two or more variables using symbols and numbers. It is a statement that asserts the equality of two expressions. An equation typically consists of two sides, separated by an equals sign (=). Each side of the equation may contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Solving an equation involves manipulating the expressions on both sides of the equation to isolate the variable and find its value. Equations are used in various branches of mathematics, physics, engineering, economics, and other sciences to model and solve problems. For example, the equation "2x + 5 = 11" has two sides, left-hand side (2x + 5) and right-hand side (11), separated by an equals sign.
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If the radius of the circle is 8 cm, what would the area of the square that is around it be? Use 3.14 as π.
Answer: 201.06
Step-by-step explanation:
A=πr2=π·8^2≈201.06193
What is the number of normal subgroups of order 7 in a group of order 14?
In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,
we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.
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A triangle is shown on the coordinate plane below.
1 unit
H
y
(-1,9) of
-(-1, 2)
7
6
5
-3
3 d
(7,2)
-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7
-11
-2
What is the area of the triangle?
Il unit
X
You answer would be mate it would be x=66
the national center for heatlh has found that there is a 0.41% chance that an american citizen will die from falling. what is the probability that you will not die from a fall?
If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.
Answer: 99.59%.
What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?
Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.
what is Combination?In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.
The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:
[tex]nCk = n! / (k! *(n-k)!)[/tex]
where n! denotes the factorial of n, i.e., the product of all positive integers up to n.
by the question.
Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:
[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]
Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]
Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).
Since a_i >= 4 for i=1, we have:
[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]
Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:
[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]
This gives us:
[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]
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hi i want help with maths and the question i need help is
there are 32 students in a class and 20 of them owns at least one pet. what if the fraction of the class own pets? give answer in simplest form.
Get back to me quickly
Answer: 3/5
hope this helped you. Please brainliest! :D
Step-by-step explanation: If I am wrong tell me :D
Question is in photo answer a through d please
The products written in scientific notation are:
a) [tex]5.88*10^9[/tex]
b) [tex]15*10^{12}\\[/tex]
c) [tex]8.4*10^{-10}[/tex]
d) [tex]42*10^{-7}[/tex]
How to take the products?The first product we need to solve is:
[tex](4.2*10^6)*(1.4*10^3)[/tex]
We can reorder that product into the one below:
[tex](4.2*1.4)*(10^6*10^3)[/tex]
The exponents in the right side are added, so we get:
[tex](4.2*1.4)*(10^6*10^3) = 5.88*10^{3 + 6} = 5.88*10^9[/tex]
Now let's do the same in the others.
b)
[tex](5*10^5)*(3*10^7)\\= 5*3*10^{5 + 7}\\= 15*10^{12}\\[/tex]
Now we need to write the first number between 0 and 10, then we can rewrite this as:
[tex]1.5*10^{13}[/tex]
c) Again doing the same thing.
[tex](4*10^{-3})*(2.1*10^{-7}})\\= 4*2.1*10^{-3 - 7}\\= 8.4*10^{-10}[/tex]
d) Finally, this last product is:
[tex](6*10^{-2})*(7*10^{-5}})\\= 6*7*10^{-2 - 5}\\= 42*10^{-7}[/tex]
Again we need to have a number between 0 and 10, so we can rewrite this as:
[tex]4.2*10^{-8}[/tex]
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Greg sold small boxes of candy for $3 and
large boxes for $5. He sold a total of 21
boxes for $87. How many large boxes did he sell?
Answer:
12 large boxes, 9 small boxes
Step-by-step explanation:
Let s = number of small boxes
l = number of large boxes
We set up and solve this system of equations:
s + l = 21------->3s + 3l = 63
3s + 5l = 87------>3s + 5l = 87
----------------
2l = 24
l = 12, s = 9
please help with geometry
Step-by-step explanation:
Since it is equilateral the angle at the top is 60 °
for right triangles sin (angle ) = opposite leg / hypotenuse
sin (60) = sqrt 6/ x
x = sqrt 6 / sin (60) = sqrt 6 / sqrt(3)/2 =
2 sqrt 2 = 2.83
ADEF-AABC. What is the sequence of transformations that maps AABC to ADEF?
A reflection across the y-axis and a translation 4 units down
A rotation of 180* about the origin and a dilation with center (0,0) and scale factor 2
A reflection across the y-axis and a translation 2 units down.
A rotation of 90° about the origin and a translation 2 units down
The series of transformations consists of a translation down two units and a reflection across the y-axis. Thus, option C is correct.
What is transformation?The points A and C will be replaced with D and F, respectively, by a reflection across the y-axis, leaving B in the same location. As a result, the image of AABC is given, A'D'BCF.
The final image, denoted by the letters ADEF, is produced by translating all the points of the image A'D'BCF' down by two units.
ADEF and AABC are not in the same location, even if they are the same height and shape.
The first thing we notice is that ADEF and AABC are oriented the same way, so we don't need to rotate them. Instead, by utilising a reflection over the y-axis, we may swap out the places where A and B were for D and E, respectively.
A'B'C' is still not in the appropriate place even though it is 2 units to the left of ADEF. Hence, we must translate 2 units down in order to position A'B'C' where ADEF is.
Therefore, A reflection across the y-axis and a translation 2 units down.
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A random variable is normally distributed. It has a mean of 228 and a standard deviation of 16. If you take a sample of size 12, can you say what the shape of the sampling distribution for the sample mean is? Why?
A. If the sample size is 12, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.
B. If the sample size is 12, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.
C. If the sample size is 12, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30.
If a random variable is normally distributed, and has a mean of 228 and
a standard deviation of 16. If a sample of size 12 is taken, then the shape
of the sampling distribution for the sample mean is normally distributed
since the variable is normally distributed. Hence, option B is correct.
A normal distribution is a type of probability distribution in which the
value of the mean, standard deviation, and random variables are well
known. Sampling distribution refers to the probability distribution of the
statistics that have been derived from a sample taken from a population.
As per the Central Limit Theorem, if the sample size is large enough,
then the sampling distribution of the sample means will be normally
distributed, no matter how the population looks. If the random variable is
normally distributed, then the sampling distribution of the sample mean
will also be normally distributed, no matter what the size of the sample is.
Hence, option B is the correct answer as the sampling distribution of the
sample mean is normally distributed since the variable is normally distributed.
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could someone help out?
Answer:
r ≈ 44.25 cm
Step-by-step explanation:
You want the hypotenuse of a right triangle in which the side adjacent to the angle of 57° is 24.1 cm.
CosineThe cosine relation is ...
Cos = Adjacent/Hypotenuse
cos(57°) = (24.1 cm)/r
SolutionSolving for r gives ...
r = (24.1 cm)/cos(57°) ≈ 44.25 cm
The length r is about 44.25 cm.
__
Additional comment
The calculator shown in the attachment has its angle mode set to degrees.
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If the cost of 7m is Rs. 1470, find the cost of 5m cloth
By using unitary method, we found that the cost of 5m cloth is Rs. 1050.
According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,
Cost of 1m cloth = Total cost of 7m cloth/7
We know that the total cost of 7m cloth is Rs. 1470. Therefore,
Cost of 1m cloth = 1470/7
Cost of 1m cloth = Rs. 210
This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.
Cost of 5m cloth = Cost of 1m cloth x 5
Cost of 5m cloth = Rs. 210 x 5
Cost of 5m cloth = Rs. 1050
Therefore, the cost of 5m cloth is Rs. 1050.
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I WILL AWARD YOU THE BRAINLIEST!!!!!!!!!
whats 1+1-1
Answer:
1
Step-by-step explanation:
LOL
Answer:
1+1-1=1
Step-by-step explanation:
1+1=2
2-1=1
your answer is 1
PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).
How do the coordinates translate?In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.
Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.
A (-3, 0)
B (-1, 2)
C (2, 2)
D (3, -1)
E (1, -2)
The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:
A' = (-3 * 5, 0 * 5) = (-15, 0)
B' = (-1 * 5, 2 * 5) = (-5, 10)
C' = (2 * 5, 2 * 5) = (10, 10)
D' = (3 * 5, -1 * 5) = (15, -5)
E' = (1 * 5, -2 * 5) = (5, -10)
The coordinates of the dilated figure are:
A' (-15, 0)
B' (-5, 10)
C' (10, 10)
D' (15, -5)
E' (5, -10)
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how many four digit positive integers x are there with the property that x and 3x have only even digits?
16 four digit positive integers x are there with the property that x and 3x have only even digits.
There are 16 such four-digit positive integers x.
At first we have to find the four-digit positive integers x with the property that both x and 3x have only even digits, we need to consider the possible digits that x can have.
Since both x and 3x must have only even digits, the digits of x can only be 0, 2, 4, 6, or 8.
Let, the possible cases for the first digit of x:
If the first digit of x is 0:
In this case, x would be a three-digit number (e.g., 012, 024, 036, etc.). Now, if we multiply any three-digit number by 3, the resulting number will always have at least one odd digit.
we get, this case does not satisfy the condition.
If the first digit of x is 2 or 8:
In this case, the last digit of 3x will be 6 or 4, respectively. But since 6 is not an even digit and 4 is not a valid digit for x, this case is not possible either.
If the first digit of x is 4 or 6:
In this case, the last digit of 3x will be 2 or 8, respectively.
These are valid digits for x.
Now, we need to make sure that the second digit of x and 3x are also even.
The only even digits that can be used as the second digit are 0 and 8 (because 2 and 6 are already used as the first digit).
So, there are two possible cases for the first digit of x: 4 or 6.
Now, we have two choices for the second digit of x (0 or 8).
For each of these combinations, we have two choices for the third digit of x (0 or 8).
Finally, we have two choices for the fourth digit of x (0 or 8).
So, we get the total number of four-digit positive integers x with the property that both x and 3x have only even digits is:
Number of choices = 2 (choices for the first digit) * 2 (choices for the second digit) * 2 (choices for the third digit) * 2 (choices for the fourth digit) = 2⁴ = 16.
Therefore, there are 16 such four-digit positive integers x.
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The _____ in which ratio is expressed is important
In mathematics, a ratio is a comparison of two quantities or numbers expressed in terms of division. The order in which the quantities are expressed in a ratio is also important.
Ratios are used in various mathematical applications such as in finance, geometry, and physics. The units or quantities being compared in a ratio are crucial in determining the meaning and significance of the ratio.
For example, if the ratio is expressed as 2:1, it could mean that the first quantity is twice the size of the second quantity, or it could mean that the second quantity is half the size of the first quantity. Therefore, it is important to clearly define the units or quantities being compared to avoid any ambiguity or misunderstanding.
In the example above, if the ratio was expressed as 1:2 instead of 2:1, the meaning of the ratio would be reversed. Therefore, the order of the quantities in a ratio should be consistent with the context in which it is being used. In summary, the units and the order in which the quantities are expressed in a ratio are important in conveying accurate and meaningful information.
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Complete question:
In mathematics, the units or quantities being compared and the order in which they are expressed in a ratio are both important. The _____ in which ratio is expressed is important
