Answer:
[tex]r = \sqrt{ {( 4 - 3)}^{2} + {(( - 1) - ( - 4))}^{2} } [/tex]
[tex]r = \sqrt{ {1}^{2} + {3}^{2} } [/tex]
[tex] r = \sqrt{1 + 9} = \sqrt{10} [/tex]
So the equation for this circle is
[tex] {(x + 4)}^{2} + {(y - 3)}^{2} = 10 [/tex]
What it the mediam of 1 3 1 3 1 7 4 5 7
Answer: 1
Step-by-step explanation: It is the middle of the sequence, so you basically count until you find the middle
Trigonometric funcions
Which equation are true
Answer:
C and D
Step-by-step explanation:
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{4}{5}[/tex] ⇒ C
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{3}{5}[/tex] ⇒ D
Solve the equation
2x/3+1=7x/15+3
The answer is X = 10
⇒ Given [tex]\frac{2x}{3} + 1 = \frac{7x}{15} + 3[/tex]
⇒ [tex]\frac{2x+3}{3} = \frac{7x+45}{15}[/tex]
⇒ 15(2x + 3) = 3(7x + 45)
⇒ 30x + 45 = 21x + 135
⇒ 30x - 21x = 135 - 45
⇒ 9x = 90
⇒ x = [tex]\frac{90}{9}[/tex]
⇒ Therefore X = 10
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Use the table of random numbers to simulate the situation.
On an average, 35% of households will purchase a raffle ticket from a student. Estimate the probability that no more than 4 of the next 10 households that a student visits will purchase a raffle ticket.
The probability that no more than 4 of the next 10 households that a student visits will purchase a raffle ticket is 1%.
What is probability?Probability refers to the likelihood or chance of a particular event occurring, and it is usually expressed as a number between 0 and 1. An event with a probability of 0 is impossible, while an event with a probability of 1 is certain.
For example, if you toss a fair coin, the probability of getting heads is 0.5, and the probability of getting tails is also 0.5. If you roll a fair six-sided die, the probability of rolling a 6 is 1/6, and the probability of rolling any other number is also 1/6. Based on the information, the correct option is C.
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Sara owns a used furniture store. She bought a chest for 42$ and sold it for 73.50. What percent did she mark up the chest?
Answer:
75%
Step-by-step explanation:
We are given that Sara bought a chest for $42, and then sold it for $73.50.
Recall that when finding by how much something was marked up, you should use the following formula:
(new price-original price)/(original price)
Let's substitute the values, like so:
[tex]\frac{73.50-42}{42}=\\\\ \frac{31.50}{42}[/tex]
Now, set up a proportion to find what this fraction is as a percentage:
[tex]\frac{31.5}{42} =\frac{x}{100} =\\42x=3150=\\x=75[/tex]
So, the price was marked up by 75%.
a gambling game pays 4 to 1 and has one chance in five of winning. suppose someone plays the game 50 times, betting $2 each time, and keeps track of the number of wins. what should be the tickets in the box model?
The tickets in the box model should be:
- 1 ticket with a value of $6 (representing a win)
- 4 tickets with a value of -$2 (representing a loss).
In this gambling game, you have a 4 to 1 payout and a 1 in 5 chance of winning.
To create a box model for this scenario, follow these steps:
Identify the possible outcomes:
In this game, there are two possible outcomes:
winning (with a 1 in 5 chance) and losing (with a 4 in 5 chance).
Determine the payout for each outcome:
If a player wins, they receive a 4 to 1 payout on their $2 bet, so they win $8.
However, they also lose the original $2 bet, so the net gain is $6.
If a player loses, they lose their $2 bet.
Assign tickets to the box model based on the probability of each outcome:
Since there is a 1 in 5 chance of winning, there should be 1 ticket representing a win (net gain of $6) and 4 tickets representing a loss (net loss of $2).
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what is the confidence interval estimate of the population mean examination score if a sample of applications provided a sample mean (to the nearest whole number
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
The confidence interval estimate of the population means examination score can be calculated using the sample mean and the margin of error. The margin of error depends on the level of confidence and the sample size.
For example, if a sample of 100 applications provided a sample mean score of 80, and a 95% confidence level is used, the confidence interval estimate of the population mean examination score would be:
Margin of error = (critical value) x (standard error)
The critical value for a 95% confidence level with 99 degrees of freedom is 1.984. The standard error can be calculated using the formula:
Standard error = (standard deviation) / sqrt(sample size)
If the standard deviation of the examination scores is known, it can be used in the formula. If not, the sample standard deviation can be used as an estimate.
Assuming a sample standard deviation of 10, the standard error would be:
[tex]Standard\ error = \frac{10} { \sqrt{(100)}} = 1[/tex]
Therefore, the margin of error would be:
Margin of error = 1.984 x 1 = 1.984
The confidence interval estimate of the population means examination score would be:
80 ± 1.984, or between 78.016 and 81.984.
This means that we can be 95% confident that the true population means examination score falls within this range based on the sample data.
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The 95% confidence interval for the population mean examination score would be between 72.23 and 77.77, to the
nearest whole number.
To determine the confidence interval estimate of the population mean examination score based on a sample mean
provided to the nearest whole number, we need to know the sample size and the level of confidence.
Assuming a normal distribution and a level of confidence of 95%, we can use the following formula to calculate the
confidence interval estimate:
Confidence interval = sample mean +/- (critical value) x (standard error)
The critical value can be found using a t-distribution table or a calculator, based on the sample size and degrees of
freedom (n-1). For a sample size of 30 or more, we can use the z-score instead of the t-score.
The standard error is the standard deviation of the sample divided by the square root of the sample size.
For example, if a sample of 50 applications provided a sample mean of 75, and the standard deviation was 10, the
standard error would be 10/sqrt(50) = 1.41.
Assuming a level of confidence of 95%, the critical value for a sample size of 50 and degrees of freedom of 49 would be 1.96.
Therefore, the confidence interval estimate would be:
75 +/- 1.96 x 1.41 = 75 +/- 2.77
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For the following arithmetic sequences, find a and d and state the formula for the general term. Don't forget to simplify! a) - 10,- 4, 2, 8, 14, ... 2. b) 10, 8, 6, 4, ... c) 36, 31, 26, 21, ...
The formula for the general term of the arithmetic sequence is:
a) an = -10 + (n-1) * 6 and first-term = -10
b) an = -10 + (n-1) * 6 and first-term = 6
c) an = 36 + (n-1) * (-5) and first-term = 36
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers in which each term (after the first) is obtained by adding a fixed number called the common difference, d, to the preceding term. The first term of an arithmetic sequence is denoted by 'a'. The general formula for an arithmetic sequence is:
a, a + d, a + 2d, a + 3d, ...
where 'a' is the first term, 'd' is a common difference, and each term after the first is obtained by adding 'd' to the preceding term.
According to the given informationa) To find the common difference, we subtract any term from the term that comes after it. For example, we can subtract -10 from -4, or 2 from 8, and we get:
-4 - (-10) = 6
8 - 2 = 6
Since both of these subtractions give us the same result, we know that the common difference is d = 6. To find the first term, we can use any term and subtract the product of the common difference and its position in the sequence minus 1. For example, we can use the second term -4 and its position 2 to get:
a = -4 - (2-1) * 6 = -10
Therefore, the formula for the general term of the sequence is:
an = -10 + (n-1) * 6
b) The common difference between consecutive terms is -2 because each term is 2 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 8 and its position 2 to get:
a = 8 + (2-1) * (-2) = 6
Therefore, the formula for the general term of the sequence is:
an = 6 + (n-1) * (-2)
c) The common difference between consecutive terms is -5 because each term is 5 less than the term before it. To find the first term, we can use any term and add the product of the common difference and its position in the sequence minus 1. For example, we can use the second term 31 and its position 2 to get:
a = 31 + (2-1) * 5 = 36
Therefore, the formula for the general term of the sequence is:
an = 36 + (n-1) * (-5)
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Write an equation that represents a function that relates the value of Ethan’s car in dollars, g(t), and the time in years since he bought the car.
An equation that represents a function that relates the value of Ethan’s car in dollars, g(t), and the time in years since he bought the car.
[tex]g(t) = P * e^{(-rt)[/tex]
Assuming that Ethan's car depreciates in value over time, a commonly used function to model such depreciation is an exponential decay function of the form:
[tex]g(t) = P * e^{(-rt)[/tex]
where:
g(t) is the value of the car in dollars at time tP is the initial value (or purchase price) of the carr is the annual depreciation rate as a decimalt is the time in years since the car was purchasedTherefore, the equation that represents the function relating the value of Ethan's car in dollars, g(t), and the time in years since he bought the car is:[tex]g(t) = P * e^{(-rt)[/tex]
where P, r, and t are specific values based on the purchase price and depreciation rate of Ethan's car, as well as the time that has passed since he bought it.
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Anyone have the answers
Answer:
The answer is 7 pens
WILL MARK AS BRAINLEIST!!
Question in picture!!
The area of the region R is 4/3 square unit, while the value of c is 2 - √3.
Showing working for the area of region
To find the value of c for which the two subregions have the same area, we need to first find the points of intersection of the given curves.
Setting y = 2x - x^2 = 0, we get x = 0 and x = 2. So the curves intersect at the points (0,0) and (2,0).
Now, we can set up the integral to find the area of the region R:
A = ∫[0,2] (2x - x^2) dx
A = [x^2 - (x^3/3)]|[0,2]
A = (4/3) square units
Next, we need to find the value of c for which the two subregions of R have the same area. Let (a, 2a - a^2) be the point where the line y = cx intersects the curve y = 2x - x^2.
So we have:
2a - a^2 = ca
Rearranging, we get:
a^2 - 2a + c = 0
Using the quadratic formula, we get:
a = (2 ± √(4 - 4c))/2 = 1 ± √(1 - c)
Since a > 0, we must choose the positive root.
Now, we can set up the integrals to find the areas of the two subregions of R:
A1 = ∫[0,a] (2x - x^2 - cx) dx
A2 = ∫[a,2] (2x - x^2 - cx) dx
Setting A1 = A2, we get:
∫[0,a] (2x - x^2 - cx) dx = ∫[a,2] (2x - x^2 - cx) dx
Solving for c, we get:
c = (2a - a^2)/(2a - 2)
Substituting a = 1 + √(1 - c), we get:
c = 2 - √3
Therefore, the value of c for which the two subregions of R have the same area is 2 - √3.
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3. On Monday, James scored 9,755 points while playing a video game. On Tuesday, he scored 13,783 points while playing the same game. How many more points did he score on Tuesday than on Monday?
Answer:
4028
Step-by-step explanation:
Answer:
4028
Step-by-step explanation:
You need to subtract 9,755 from 13,783 on a calculator and you get your answer.hope it helps
Perform the operation. ( − 10x ^2 + 2 x− 10 ) − (-10x^2+3)
Answer:
2x-13
Step-by-step explanation:
First flip the operation to be (-10x^2+2x-10) + (10x^2-3).
Then you simplify it. The 10x^2 would get canceled out. You would then get 2x-13.
If A = 39°, B = 47°, and b = 27; Find a, and c.
The values of a and C using Law of sines is: a = 23.2 and C = 94°
How to use Law of sine?You can use the Law of Cosines, if only one of which is missing: three sides and one angle. Hence, if the known properties of the triangle is SSS(side-side-side) or SAS (side-angle-side), this law is applicable.
You can use the Law of Sines if you want to equate the ratio of the sine of an angle and its opposite side. This can be used if the known properties of the triangle is ASA(angle-side-angle) or SAS.
We are given the parameters as:
A = 39°, B = 47°, and b = 27
a/sin A = b/sin B
Thus:
a = (27 * sin 39)/sin 47
a = 23.2
Sum of angles in a triangle is 180 degrees. Thus:
C = 180 - (47 + 39)
C = 94°
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5. Select Yes or No to indicate whether each ordered pair is a point of intersection
between the line x - y = 6 and the circle y² - 26 = -x².
Ordered Pair
(1,-5)
(1,5)
(5,-1)
To determine if each ordered pair is a point of intersection between the line x - y = 6 and the circle y² - 26 = -x², we need to substitute the values of x and y in both equations and see if they are true for both.
Select Yes or No to indicate whether each ordered pair is a point of intersectionFor the ordered pair (1, -5):
x - y = 6 becomes 1 - (-5) = 6, which is true.
y² - 26 = -x² becomes (-5)² - 26 = -(1)², which is false.
Therefore, (1, -5) is not a point of intersection.
For the ordered pair (1, 5):
x - y = 6 becomes 1 - 5 = -4, which is false.
y² - 26 = -x² becomes (5)² - 26 = -(1)², which is true.
Therefore, (1, 5) is a point of intersection.
For the ordered pair (5, -1):
x - y = 6 becomes 5 - (-1) = 6, which is true.
y² - 26 = -x² becomes (-1)² - 26 = -(5)², which is false.
Therefore, (5, -1) is not a point of intersection.
So the answer is:
(1,-5) - No
(1,5) - Yes
(5,-1) - No
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#4 Please help!!!!!!!!!!
Answer:150°
Step-by-step explanation:
Find the probability of drawing the given cards from a standard deck of 52 cards with replacement. Leave answers as decimals rounded to 3 decimal places if the decimal does not end.
A face card, then a 2
The answer to this question is 0.077
I need help With surface area but I’m not in a room right now help
The prompt on measurement of rooms and surface area is given below. Note that the total surface area of the room is 752 ft².
What is the explanation for the above response? The room measured is the Sitting Roomdimensions of the room are length = 12 feet, width = 10 feet, and height = 8 feet.The area of the base of the room is the product of the length and width of the room. In this case, the area of the base of the room is 12 x 10 = 120 square feet.The perimeter of the base of the room is the sum of the lengths of all four sides of the base. In this case, the perimeter of the base of the room is 2(12 + 10) = 44 feet.To find the total surface area of the room, you need to calculate the area of each face of the rectangular prism and add them up.The area of the front and back faces is the product of the length and height of the room, which is 12 x 8 = 96 square feet.The area of the two side faces is the product of the width and height of the room, which is 10 x 8 = 80 square feet each, for a total of 160 square feet.The area of the top and bottom faces is the product of the length and width of the room, which is 12 x 10 = 120 square feet each, for a total of 240 square feet.Therefore, the total surface area of the room is 96 + 96 + 160 + 160 + 120 + 120 = 752 square feet.
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Nina uploaded a funny video on her website, which rapidly gains views over time.
The relationship between the elapsed time, ttt, in days, since Nina uploaded the video, and the total number of views, V(t)V(t)V, left parenthesis, t, right parenthesis, is modeled by the following function:
V(t)=500⋅(1. 8)t
Complete the following sentence about the daily percent change in the views of the video.
Every day,
\%%percent of views are
the total number of views of the video
Every day, the number of views of the video increases by 80% of the previous day's views.
Every day, the number of views of the video increases by a certain percentage. To find the daily percent change in the views, we can use the formula for percent change, which is given by:
percent change = ((new value - old value) / old value) * 100
In this case, the old value is the number of views at the start, which is 500, and the new value is the number of views after one day, which is given by:
V(1) = 500*(1.8)^1 = 900
Substituting these values into the formula, we get:
percent change = ((900 - 500) / 500) * 100 = 80%
In other words, for every day that passes, the number of views of the video is multiplied by a factor of 1.8.
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Problem
The table compares the heights (in centimeters) and the weights (in kilograms) of Karim's friends.
Can the weight of Karim's friends be represented as a function of their height?
Height (centimeters) Weight (kilograms)
163
163163
65
6565
167
167167
70
7070
154
154154
60
6060
172
172172
70
7070
167
167167
68
6868
159
159159
58
5858
160
160160
64
6464
166
166166
69
6969
Choose 1 answer:
Choose 1 answer:
(Choice A) Yes
A
Yes
(Choice B) No
B
No
Weight cannot be represented as a function of height.
Can the weight be represented as a function of their height?No, the weight of Karim's friends cannot be represented as a function of their height.
To represent weight as a function of height, there should be a consistent relationship between the height and weight values.
However, from the given data, we can see that for the same height, there are different weight values, and for the same weight, there are different height values.
This indicates that there is no one-to-one relationship between height and weight, and hence weight cannot be represented as a function of height.
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HELP!! View image! THANK U
The probability of selecting no Independents is $\frac{{7 \choose 2} + {8 \choose 2}}{{20 \choose 2}} = \frac{91}{190} \approx 0.4789$.
Of the 8 parent functions discussed. Select ALL of the parent functions
that have 180 degree rotational symmetry around the point (0,0)
We have identified three parent functions that exhibit 180-degree rotational symmetry around the point (0,0): the constant function f(x) = 0, the odd power functions f(x) = x²ⁿ⁺¹ for any integer n, and the tangent function f(x) = tan(x) on the interval (-π/2, π/2).
A function f(x) exhibits 180-degree rotational symmetry around the point (0,0) if and only if f(-x) = -f(x) for all x. To see why, consider rotating the graph of f(x) by 180 degrees around the origin.
Using this criterion, we can identify the parent functions that have 180-degree rotational symmetry around the point (0,0). These functions are:
The constant function f(x) = 0. This function is symmetric about the origin, and any rotation around the origin preserves this symmetry.
The odd power functions f(x) = x²ⁿ⁺¹ for any integer n. These functions are also symmetric about the origin, and any rotation around the origin preserves this symmetry. To see why, note that f(-x) = (-x)²ⁿ⁺¹ = -x²ⁿ⁺¹ = -f(x) for all x.
The tangent function f(x) = tan(x) on the interval (-π/2, π/2). This function has vertical asymptotes at x = π/2 and x = -π/2, but these do not affect its rotational symmetry around the origin.
To see why, note that f(-x) = tan(-x) = -tan(x) = -f(x) for all x in the interval (-π/2, π/2).
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In ABC, m A= 62° and mB=39⁰.
In XYZ, m Y=39° and m Z=79⁰.
Include in Your Answer:
What is mC?
What is mX?
• Is it possible for these two triangles to be similar? Why or
why not?
which data set is more centered around a high peak??
a. may
b. july
c. neither
d. both
The correct option a. may.The data shown in the may histogram is more centered around a high peak.
Explain about the histograms:A graph called a histogram is used to show the frequency distribution of a small number of data points for a single variable.
Histograms frequently divide data into different "bins" or "range groups" and count however many points are in each bin.The histogram illustration below shows test results for students. The scores of the student are divided into various ranges. Each bar's height indicates the number of students who received a score within that range.For the given two histograms,
May has the peak value for the frequency of day at 14.
July has the peak value for the frequency of day at 10.
Thus, The data shown in the may histogram is more centered around a high peak.
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Complete question-
which data set is more centered around a high peak??
a. may
b. july
c. neither
d. both
The diagram for the question is shown.
Evan takes 100 milligrams of medicine. The amount of medicine in his bloodstream decreases by 0.4 milligram each minute for a number of minutes, m, after that. He writes the expression 100 - 0.4m to find the amount of medicine in his bloodstream after m minutes. Which statement about his expression is true?
The statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
What is the equivalent expression?
Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.
The expression 100 - 0.4m represents the amount of medicine in Evan's bloodstream after m minutes, where the amount of medicine decreases by 0.4 milligrams each minute.
The coefficient of the variable m (-0.4) represents the rate of change of the amount of medicine in Evan's bloodstream per minute. It tells us that for every one minute that passes, the amount of medicine in his bloodstream decreases by 0.4 milligrams.
The constant term (100) represents the initial amount of medicine in Evan's bloodstream before the medicine starts to decrease.
Therefore, the statement that is true about Evan's expression is that it represents a linear function of the amount of medicine in his bloodstream, where the initial amount is 100 milligrams and the rate of change is -0.4 milligrams per minute.
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A label is placed around a soup can during manufacturing. If the label is represented by the rectangle in the figure, how many square inches is the label? Answer in terms of TT
60.8TT
92.8TT
32TT
29.6TT
60.8π square inches is the area of the label.
What is the Surface area?The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.
We wish to find the area of the rectangle A= L x W because we know the label is a rectangle that has been folded into a cylinder form.
W is known to be 7.6 inches.
We must determine the length that encircles the can's circumference.
Radius = 4 inches,
circumference = C = 2 πr.
(In terms of π, therefore don't multiply.) C = (2) π (4)
C = 8 pi millimeters
We now have L = 8π
And W is equal to 7.6.
A = L x W
A = 60.8π square inches.
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y
∝
√
x
If
y
=
60
when
x
=
36
find,
x
when
y
=
80
If y is proportional to the square root of x and y = 60 when x = 36, then the value of x when y = 80 is 64
We are given that y is proportional to the square root of x, or y ∝ √x.
Using the constant of proportionality k, we can write this relationship as:
y = k√x
To solve for k, we can use the values given in the problem
y = 60, x = 36
60 = k√36
60 = k × 6
k = 60 / 6
Divide the numbers
k = 10
Now that we know k, we can use the same equation to find x when y = 80
80 = 10√x
Squaring both sides, we get
6400 = 100x
x = 64
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The given question is incomplete, the complete question is:
y ∝ √x If y = 60 when x = 36, find x when y = 80.
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
(a) 1,0,1,1,0,0,1,1,1,0,0,0,1,.
(b) 1,2,2,3,4,4,5,6,6,7,8,8,.
(c) 1,0,2,0,4,0,8,0,16,0,.
(d) 3, 6, 12, 24, 48, 96, 192,.
(e) 15, 8, 1, -6, -13, -20, -27,.
(f) 3, 5, 8, 12, 17, 23, 30, 38, 47,
The next three terms of the sequence.
(a) The sequence alternates between a run of "1"s and a run of "0"s.
Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is
odd, and 0 if the number of "1"s in the first n-1 terms is even.
(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.
(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.
(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].
(e) The nth term is 15-7(n-1).
(f) The nth term is the sum of the first n positive integers minus 3, i.e.,
[tex]1+2+3+\cdots+n-3.[/tex]
To determine the next three terms of each sequence, we simply apply the rule or formula given above. For example, for sequence (a), the next three terms are 0, 1, 1, since the next term is 0 (since there are an even number of 1's so far), followed by two 1's (since there are now an odd number of 1's).
For sequence (b), the next three terms are 9, 10, 10, since the next term is 9 (since the next term in the pattern is odd), followed by two 10's (since the next two terms in the pattern are even). And so on for the other sequences.
(a) The sequence alternates between a run of "1"s and a run of "0"s.
Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is
odd, and 0 if the number of "1"s in the first n-1 terms is even.
(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.
(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.
(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].
(e) The nth term is 15-7(n-1).
(f) The nth term is the sum of the first n positive integers minus 3, i.e.,
[tex]1+2+3+\cdots+n-3.[/tex]
for such more questions on sequence
https://brainly.com/question/7882626
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cuantos números
primos son a la vez la suma y la diferencia
Answer: there is only one number
Answer:
Solo hay un número primo que se puede escribir como suma de dos números primos y también como diferencia de dos números primos.
Espero haber ayudado :D
Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 3.5 to create triangle A′B′C′. Determine the vertex of point C′.
C′(−10.5, 1)
C′(−10.5, 3.5)
C′(−3, 3.5)
C′(−10.5, −3.5)
Answer:
To dilate a triangle using a scale factor of 3.5, we multiply the distance between each vertex and the center of dilation (in this case, the origin) by 3.5.
Using this information, we can find the coordinates of each vertex of triangle A'B'C':
A' = (43.5, 33.5) = (14, 10.5)
B' = (33.5, -23.5) = (10.5, -7)
C' = (-33.5, 13.5) = (-10.5, 3.5)
Therefore, the vertex of point C' is (-10.5, 3.5).
So the correct answer is C′(−10.5, 3.5).