In mathematics, a set is a well-defined collection of distinct objects, called elements or members of the set. These objects can be anything: numbers, letters, people, or even other sets.
he concept of sets is fundamental in various branches of mathematics, including set theory, algebra, and statistics.There are different kinds of sets based on their properties:
Finite set: A set with a specific number of elements, which can be counted.Infinite set: A set with an endless number of elements.Empty set: A set with no elements. It is denoted by the symbol Ø or {}.
Singleton set: A set with only one element.Subset: A set whose elements are all contained within another set.Universal set: A set that includes all the possible elements of interest in a particular context.Operations on sets involve various ways of combining or manipulating sets:
Union: The union of two sets A and B is the set that contains all the elements from both sets. It is denoted by A ∪ B.Intersection: The intersection of two sets A and B is the set of elements that are common to both sets. It is denoted by A ∩ B.
Complement: The complement of a set A, denoted by A', is the set of all elements that are not in A but are in the universal set.Difference: The difference between two sets A and B is the set of elements that are in A but not in B. It is denoted by A - B.
Cartesian Product: The Cartesian product of two sets A and B is the set of all possible ordered pairs, where the first element is from set A and the second element is from set B. It is denoted by A × B.
For teaching the concept of the union of sets, you can use the following activity:
Activity: Venn Diagrams
Draw two overlapping circles on the board or use physical cut-out circles.Label one circle as Set A and the other as Set B.
Ask the students to suggest elements for each set and write them inside the circles.Discuss the elements that are common to both sets and write them in the overlapping region.Explain that the union of sets A and B represents all the elements in both sets.
Combine the elements from sets A and B, including the elements in the overlapping region, and write them in a new circle labeled as A ∪ B.Emphasize that the union includes all the distinct elements from both sets without repetition.
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Which of the rays or segments below is a chord of circle O?
A) ->
TC
B)—
SO
C)—>
TU
D)—
FC
The ray or segment that is a chord is (d) segment FC
How to determine the ray that is a chordFrom the question, we have the following parameters that can be used in our computation:
The circle
By definition, a chord is a straight line that joins points of the circle without passing through the center
The ray that has the above properties is ray FC
Hence, the segments that is a chord is (d) FC
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Find the co-vertices of the hyperbola defined by the equation.. 100pts
Answer:
(-13, -9) and (-5, -9)
Step-by-step explanation:
The given equation of the hyperbola is:
[tex]\dfrac{(y+9)^2}{25}-\dfrac{(x+9)^2}{16}=1[/tex]
As the y²-term of the given equation is positive, the transverse axis is vertical, and so the hyperbola is vertical (opens up and down).
The standard equation for a vertical hyperbola is:
[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h, k±a)co-vertices = (h±b, k)foci = (h, k±c) where c² = a² + b²Compare the given equation with the standard equation to find the values of h, k, a and b:
h = -9k = -9a² = 25 ⇒ a = 5b² = 16 ⇒ b = 4The formula for the co-vertices of a vertical hyperbola is (h±b, k).
Substitute the values of b, h and k into the formula:
[tex]\begin{aligned}\textsf{Co-vertices}&=(h\pm b,k)\\&=(-9\pm 4, -9)\\&=(-13,-9)\;\;\textsf{and}\;\;(-5, -9)\end{aligned}[/tex]
Therefore, the co-vertices of the given hyperbola are:
(-13, -9) and (-5, -9)The co-vertices of the hyperbola are (-4, -9) and (-14, -9).
What are the co-vertices of the hyperbola?To find the co-vertices of the hyperbola defined by the equation:
[(y + 9)² / 25] - [(x + 9)² / 16] = 1
We can compare the equation to the standard form of a hyperbola:
[(y - h)² / a²] - [(x - k)² / b²] = 1
In this case, we have h = -9 and k = -9.
The co-vertices of a hyperbola lie on the transverse axis, which is the line passing through the center of the hyperbola. The center of the hyperbola is given by (h, k), which in this case is (-9, -9).
For a hyperbola with the equation in this form, the co-vertices are located a units to the right and left of the center. In this case, since the equation is [(y + 9)² / 25] - [(x + 9)² / 16] = 1, we have a = 5.
Therefore, the co-vertices are located at (-9 ± a, -9), which gives us:
(-9 + 5, -9) = (-4, -9)
(-9 - 5, -9) = (-14, -9)
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what best describes the relationship between the computed mean of 52.4 and the actual mean of 52.7
The computed mean of 52.4 and the actual mean of 52.7 suggest a close relationship in terms of central tendency.
A computed mean is a statistical measure calculated by summing up a set of values and dividing by the number of observations. In this case, the computed mean of 52.4 implies that when the values are averaged, the result is 52.4.
The actual mean of 52.7 refers to the true average of the population or data set being analyzed. Since it is higher than the computed mean, it indicates that the sample used for computation might have slightly underestimated the true population mean.
However, the difference between the computed mean and the actual mean is relatively small, with only a 0.3 unit discrepancy.
Given the proximity of these two values, it suggests that the computed mean is a reasonably accurate estimate of the actual mean.
However, it's important to note that without additional information, such as the sample size or the variability of the data, it is difficult to draw definitive conclusions about the relationship between the computed mean and the actual mean.
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how can you write the expression with a rationalized denominator?
3 sqrt 2 / 3 sqrt 6
see photo attached for answers
The expression (3√2) / (3√6) with a rationalized denominator is 3√9 / 6. Option C is the correct answer.
To rationalize the denominator in the expression (3√2) / (3√6), we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √6 is -√6, so we multiply the expression by (-√6) / (-√6):
(3√2 / 3√6) * (-√6 / -√6)
This simplifies to:
-3√12 / (-3√36)
Further simplifying, we have:
-3√12 / (-3 * 6)
-3√12 / -18
Finally, we can cancel out the common factor of 3:
- 3√9 / - 6.
Simplifying further, we get:
3√9 / 6.
Option C is the correct answer.
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Francine currently has $55,000 in her 401k account at work, and plans to contribute $8,000 each year for the next 10 years. How much will she have in the account in 10 years, if the account averages a 4% annual return?
Answer:
Step-by-step explanation:
To calculate the future value of Francine's 401k account in 10 years, considering an annual contribution of $8,000 and an average annual return of 4%, we can use the formula for the future value of a series of regular payments, also known as an annuity.
The formula for the future value of an annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value
P is the payment amount
r is the interest rate per period
n is the number of periods
In this case:
P = $8,000 (annual contribution)
r = 4% or 0.04 (annual interest rate)
n = 10 (number of years)
Calculating the future value:
FV = $8,000 * [(1 + 0.04)^10 - 1] / 0.04
FV = $8,000 * (1.04^10 - 1) / 0.04
FV ≈ $8,000 * (1.480244 - 1) / 0.04
FV ≈ $8,000 * 0.480244 / 0.04
FV ≈ $8,000 * 12.0061
FV ≈ $96,048.80
Therefore, Francine will have approximately $96,048.80 in her 401k account in 10 years if the account averages a 4% annual return and she contributes $8,000 each year.
Complete the item by performing the proper operations of evaluation. (8y)2, (y=5)
Answer:
Step-by-step explanation:
To evaluate the expression (8y)², where y = 5, we substitute the value of y into the expression and perform the operations.
First, substitute y = 5:
(8y)² = (8 * 5)²
Next, perform the operation inside the parentheses:
(8 * 5)² = 40²
Now, calculate the square of 40:
40² = 1600
Therefore, when y = 5, (8y)² is equal to 1600.
ITV' is tangent to circle O at point H, and HIM
is a secant line. If mHM = 108°, find m/MHU.
Answer:
∠ MHU = 54°
Step-by-step explanation:
the angle MHU between the tangent and the secant is half the measure of the intercepted arc HM , then
∠ MHU = [tex]\frac{1}{2}[/tex] × 108° = 54°
What number completes the sequence below? Enter your answer in the input
box at the bottom.
8——-4
16——8
24——12
32——?
Answer:
16
Step-by-step explanation:
the numbers on the right of the arrow are half the value of the corresponding numbers on the left, then
32 → [tex]\frac{1}{2}[/tex] (32)
32 → 16
Write the equation of the trigonometric graph.
Answer:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
Step-by-step explanation:
The graph of the solid black line is the cosine parent function, y = cos(x).
The standard form of a cosine function is:
[tex]\boxed{y = A \cos(B(x + C)) + D}[/tex]
where:
A is the amplitude (height from the mid-line to the peak).2π/B is the period (horizontal distance between consecutive peaks).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift (the mid-line is y = D).From inspection of the graph, the x-values of the turning points (peaks and troughs) of the parent function and the new function are the same. Therefore, the period of both functions is the same, and there has been no horizontal shift. So, B = 1 and C = 0.
The mid-line of the new function is y = 3. Therefore, D = 3.
The y-value of the peaks is y = 5. The amplitude is the distance from the mid-line to the peak. Therefore, A = 2.
Substituting these values into the standard formula we get:
[tex]y = 2 \cos(1(x + 0)) + 3[/tex]
[tex]y=2 \cos (1(x))+3[/tex]
[tex]y= 2 \cos(x) + 3[/tex]
Therefore, the equation of the trigonometric graph is:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
Which of these relations are functions?
y = 5
x = -2
y=2x-5
2y=x-4
Answer:
True
EXPLANATIONDETAIL STEPS:
(A)Determine whether y = 5 is a function: Click for video explanations: True
(B)Determine whether x = -2 is a function: Click for video explanations: False
(7)Determine whether y = 2x-5 is a function: Click for video explanations: True
(D)Determine whether 2y = x-4 is a function: Click for video explanations: True
(A)Determine whether
=
is a function: Click for video explanations: True
(B)Determine whether
=
is a function: Click for video explanations: False
(7)Determine whether
=
is a function: Click for video explanations: True
(D)Determine whether
=
is a function: Click for video explanations: True
Angela lives in New York, which has a sales tax of 8.125%. She bought some word-processing software whose full price was $110, but she presented the retailer with a coupon for $30. What was the total amount that Angela paid?
Answer: 88.94
Step-by-step explanation:
First, l found what was 8.125 out of 110 which is 8.94
then added 8.125 and 8.94 which got 118.94
But Angela gave the retailer an $30 coupon so l subtracted 30 from 118.94 which got me 88.94
Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tacoma's population be in 2014?
people
Answer:424000
Step-by-step explanation:
First, you need to find out what is 8 percent of 200,000 which is 16000
So now we know that every year Tacoma's population grows by 16000
Now we calculate 16000 for 14 years which is 224000
Finally, we had the original population which was 200,000, and the people who moved to Tocoma in those 14 years which is 224000
Add it together and you get 424,000
Question 1-6
The diagram shows the shape and dimensions of a three-dimensional figure
What is the volume, in cubic units?
Enter your answer in the box. (Numbers Only)
cubic units
The volume of the right prism is equal to 312 cubic units.
How to determine the volume of a right prism
In this problem we find the representation of a right prism, whose volume must be found by means of the following formula:
V = A · h
Where:
A - Base areah - HeightAnd the area of the base can be found by following formula:
Triangle
A = 0.5 · w · l
Rectangle
A = w · l
Where:
w - Widthl - HeightThe volume of the solid is now computed:
V = (0.5 · 3 · 4 + 5 · 4) · 12
V = (6 + 20) · 12
V = 26 · 12
V = 312
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Let S be a set that contains atleast two different elements. Let R be the relation on P(S),
thesetofallsubsetsofS,definedby(X,Y)∈RifandonlyifX∩Y =φ.
(i) Determine whether R is reflexive, symmetric, antisymmetric, or transitive.
(ii) Why is it important that S has atleast 2 different elements?
(iii) Would any of the answers change in (i) if S was empty or had only one element?
(i) R is not reflexive, symmetric, vacuously antisymmetric, and not transitive.
(ii) It is important that S has at least two different elements because if S had only one element, then the power set P(S) would contain only two sets: the empty set and the set S itself.
(iii) If S was empty, there would be no elements in S, and hence the power set P(S) would only contain the empty set. The answers regarding reflexivity, symmetry, antisymmetry, and transitivity would all change, and the relation R would not possess any of these properties. If S had only one element, the power set P(S) would contain two sets: the empty set and the singleton set containing the one element of S. The relation R would be reflexive, symmetric, antisymmetric, and transitive, as it satisfies all these properties by definition.
(i)Let's analyze the properties of relation R on P(S):
Reflexive: A relation R is reflexive if for every element x in the set S, (x, x) belongs to R. In this case, since the intersection of any set with itself is never empty, the relation R is not reflexive.
Symmetric: A relation R is symmetric if for every pair (x, y) in R, (y, x) also belongs to R. In this case, since the intersection of two sets is commutative, if (X, Y) belongs to R, then (Y, X) also belongs to R. Thus, the relation R is symmetric.
Antisymmetric: A relation R is antisymmetric if for every distinct pair (x, y) in R, (y, x) does not belong to R. Since the relation R is defined by the condition X∩Y = φ, there are no distinct pairs (X, Y) that satisfy the condition. Therefore, the relation R is vacuously antisymmetric.
Transitive: A relation R is transitive if for every three sets X, Y, and Z such that (X, Y) belongs to R and (Y, Z) belongs to R, then (X, Z) also belongs to R. In this case, if X∩Y = φ and Y∩Z = φ, it does not imply that X∩Z = φ. Hence, the relation R is not transitive.
(ii) In this scenario, the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S, because the intersection of any two non-empty subsets would never be empty. Thus, the relation R would be trivial and uninteresting.
(iii) In this case, since there are no non-empty subsets in P(S), the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S.
In this case, the relation R would have only one possible pair (X, Y) with X and Y being the empty set, and their intersection would indeed be empty.
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GEOMETRY 50POINTS
What is the angle of elevation to the kite? TYSM
Answer:
10.4°
Step-by-step explanation:
the angle of elevation is the angle from the horizontal , upward from one point on the horizontal to another point, not on the horizontal
in this case the angle of elevation is represented by ∠ A
using the sine ratio in the right triangle
sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{36}{200}[/tex] , then
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{36}{200}[/tex] ) ≈ 10.4° ( to the nearest tenth )
the angle of elevation to the kite is approximately 10.4°
If a turtle travels 1/12 of a mile per hour how long will it take to get to a pond 5/6 of a mile away
Answer:
Step-by-step explanation:
To find the time it takes for the turtle to reach the pond, we can use the formula:
Time = Distance / Speed
Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:
Time = (5/6) / (1/12)
To simplify this, we can multiply the numerator by the reciprocal of the denominator:
Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10
Therefore, it will take the turtle 10 hours to reach the pond.
The base of a rectangular prism is a square whose sides each measure 9 inches. The height of the rectangular prism is 11 inches, find it’s volume?
Answer:
99
Step-by-step explanation:
since the height is 9 and the base is 11 we use the formula BH=V
substitute 9x11 and get 99
Input an ordered pair that satisfies the system of inequalities:
-
y < − x − 3
y> 2x - 4
To find an ordered pair that satisfies the given system of inequalities, we need to find a point that lies below the line y = -x - 3 and above the line y = 2x - 4.
One such point that satisfies both inequalities is (-1, 0).
Let's check if this point satisfies both inequalities:
For the first inequality, y < -x - 3:
0 < -(-1) - 3
0 < 1 - 3
0 < -2 (True)
For the second inequality, y > 2x - 4:
0 > 2(-1) - 4
0 > -2 - 4
0 > -6 (True)
Therefore, the ordered pair (-1, 0) satisfies the system of inequalities y < -x - 3 and y > 2x - 4.
Determine the perimeter of a soccer field with a length of 97 metres and a width of 69 metres
Answer: Therefore, the perimeter of the soccer field is 332 meters.
Step-by-step explanation:
To determine the perimeter of a soccer field with a length of 97 meters and a width of 69 meters, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (length + width)
Plugging in the values, we have:
Perimeter = 2 * (97 + 69)
Perimeter = 2 * 166
Perimeter = 332 meters
what is the value of f(x)=-1/3x-1/3 when x=-1/2
Answer:
f(-1/2) = -1/6
Step-by-step explanation:
To find the value of f(x) when x = -1/2, we substitute -1/2 for x in the expression for f(x) and simplify:
f(x) = (-1/3)x - 1/3
f(-1/2) = (-1/3)(-1/2) - 1/3
= 1/6 - 1/3
= -1/6
So, f(-1/2) = -1/6.
A coffee place is selling coffees for $2.50 each and cappuccinos for $3.75 each.
Today the coffee place sold a total of 70 drinks (coffees and cappuccinos) for a total of $222.50.
a) Write an equation that represents the information.
b) Solve the equation in (a) to find how many coffees and how many cappuccinos the coffee place sold today.
Answer:
Step-by-step explanation:
a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.
The equation that represents the given information is:
2.50x + 3.75y = 222.50
b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.
Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.
Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):
2.50(40) + 3.75y = 222.50
100 + 3.75y = 222.50
3.75y = 222.50 - 100
3.75y = 122.50
y = 122.50 / 3.75
y ≈ 32.67
In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.
We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.
Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.
QUESTION IN PICTURE
Please explain your answer in steps, thank you.
We can complete the blanks with the following ratios:
(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags
Since we do not need a flag at the starting line, then 32 flags will be required in total.
How to obtain the number of flagsTo solve the problem, we would first convert 400 yds to feet and miles.
To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.
To convert to miles, we would have 0.227 miles.
Now, we divide the entire race distance by the number of miles divisions.
This gives us:
7.5 mi /0.227 mi
= 33 flags
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One of the graphs represents the statement, "y is greater than two less than the product of x and three." Which graph is it?
Based on the analysis, the graph that represents the statement "y is greater than two less than the product of x and three" is Option C.
To determine which graph represents the statement "y is greater than two less than the product of x and three," we need to analyze the given options and match them with the statement.
The statement "y is greater than two less than the product of x and three" can be represented mathematically as:
y > 2 - 3x
Now let's examine the given graphs and compare them to the equation:
Option A: This graph shows a horizontal line at y = 2. It does not involve any product of x and three, so it does not match the given statement.
Option B: This graph shows a line with a positive slope passing through the point (0, 2). While it includes the product of x and three, it does not satisfy the condition of "y is greater than two less than the product of x and three." Therefore, it does not represent the given statement.
Option C: This graph shows a line with a positive slope passing through the point (0, 2) and includes the region above the line y = 3x - 2. This region satisfies the condition of "y is greater than two less than the product of x and three." Therefore, Option C represents the given statement.
Option D: This graph shows a horizontal line at y = -2. It does not match the given statement.
Option C is correct.
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Note: This is the final question on search engine
So i'm doing this Equation and it told me to use the values below, bit I'm so confused on how to do it can some of y'all help me out?
Part A: solve the equation---
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Part B: use the values
x= -0.5, 0, 1
Answer:
when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.
Step-by-step explanation:
Part A:
To solve the equation 5 + x - 12 = 2x - 7, follow these steps:
Combine like terms on each side of the equation:
-7 + 5 + x - 12 = 2x - 7
-14 + x = 2x - 7
Simplify the equation by moving all terms containing x to one side:
x - 2x = -7 + 14
-x = 7
To isolate x, multiply both sides of the equation by -1:
(-1)(-x) = (-1)(7)
x = -7
Therefore, the solution to the equation is x = -7.
Part B:
Now let's substitute the given values of x and evaluate the equation:
For x = -0.5:
5 + (-0.5) - 12 = 2(-0.5) - 7
4.5 = -1 - 7
4.5 = -8
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7
For x = 1:
5 + 1 - 12 = 2(1) - 7
-6 = -5
anna rolled a pair of number cubes what is the probability of getting even number on both sides PLSSS HELP ME
It is best to draw a table of outcomes and list all the possible outcomes when you roll a pair of numbered cubes. As follows:
1 2 3 4 5 6
1 ( 1 , 1 ) ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 )
2 ( 2 , 1 ) ( 2, 2 ) ( 2 , 3 ) ( 2 , 4 ) ( 2 , 5 ) ( 2 , 6 )
3 ( 3 , 1 ) ( 3 , 2 ) ( 3 , 3 ) ( 3 , 4 ) ( 3 , 5 ) ( 3 , 6 )
4 ( 4 , 1 ) ( 4 , 2 ) ( 4 , 3 ) ( 4 , 4 ) ( 4 , 5 ) ( 4 , 6 )
5 ( 5 , 1 ) ( 5 , 2 ) ( 5 , 3 ) ( 5 , 4 ) ( 5 , 5 ) ( 5 , 6 )
6 ( 6 , 1 ) ( 6 , 2 ) ( 6 , 3 ) ( 6 , 4 ) ( 6 , 5 ) ( 6 , 6 )
- Each cube has 6 faces, Hence, 6 numbers for each are expressed as row and column for first and second cube respectively.
- Now locate and highlight all the even pairs shown in bold.
- The total number of even pairs outcomes are = 9.
- The total possibilities are = 36.
- The probability of getting even pairs as favorable outcome can be expressed as:
P ( Even pairs ) = Favorable outcomes / Total outcomes
P ( Even pairs ) = 9 / 36
P ( Even pairs ) = 1 / 4.
- So the probability of getting an even pair when a pair of number cubes are rolled is 1/4
What is the third term of the sequence defined by the recursive rule f(1)=0.2,
f(n)=2fn(n-1)/5+1?
Answer:
f(3) = 1.432
Step-by-step explanation:
You want to know the third term of the sequence defined by ...
f(1) = 0.2f(n) = (2/5)f(n-1) +1SequenceThe terms of the sequence can be found one at a time by evaluating the recursive relation. The attached calculator output shows the first three terms are ...
f(1) = 0.2 . . . . . . . given
f(2) = 0.4(0.2) +1 = 1.08
f(3) = 0.4(1.08) +1 = 1.432
The third term of the sequence is 1.432.
__
Additional comment
The explicit form of the function is ...
f(n) = 5/3 -11/3(2/5)^n
Terms will asymptotically approach a value of 5/3.
<95141404393>
Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
for such more question on system of equations
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please answer ASAP I will brainlist
(a) The average cost in 2011 is $2247.64.
(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.
(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.6Inx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2011 - 2006) + 6
x = 5 + 6
x = 11 years.
Next, we would substitute 11 for x in the function:
g(11) = -1736.7 + 1661.6In(11)
g(11) = $2247.64
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
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The overnight temperature drops from 11°C to -2°C. B how many degrees has the temperature dropped?
Answer: I'm pretty sure it's 13.
Step-by-step explanation: Hope this helped!!
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
B
Step-by-step explanation:
SAS Similarity theorem: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
Side 28 is congruent to side 11.2, whereas side 20 is congruent to side 8 and both angles are congruent. Therefore both triangles are similar.