The true statement is that Jana has completed more than 75%
She has a little homework left to finishHow to find the statement that is trueTo determine the fraction of Jana's homework that she has completed, we need to add 1/4 and 2/3.
However, these fractions have different denominators, so we need to find a common denominator first.
A common denominator for 1/4 and 2/3 is 12.
To convert 1/4 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 3:
1/4 = (1 x 3)/(4 x 3) = 3/12
To convert 2/3 to an equivalent fraction with a denominator of 12, we need to multiply both the numerator and denominator by 4:
2/3 = (2 x 4)/(3 x 4) = 8/12
Now we can add the fractions:
1/4 + 2/3 = 3/12 + 8/12 = 11/12
Therefore, Jana has completed 11/12 of her homework.
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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 onetoone relationship between height and weight, and hence weight cannot be represented as a function of height.
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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 + (n1) * 6 and firstterm = 10
b) an = 10 + (n1) * 6 and firstterm = 6
c) an = 36 + (n1) * (5) and firstterm = 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  (21) * 6 = 10
Therefore, the formula for the general term of the sequence is:
an = 10 + (n1) * 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 + (21) * (2) = 6
Therefore, the formula for the general term of the sequence is:
an = 6 + (n1) * (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 + (21) * 5 = 36
Therefore, the formula for the general term of the sequence is:
an = 36 + (n1) * (5)
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This is precalc trig please help
The answer to the trigonometry question in the picture attached is:
= cos θ / [sin θ * (1  sin θ)] * (1 + sin θ)
Here is the step by step approach to solving the trigonometrySimplify 1csc θ as follows:
1  csc θ = (1  csc θ)(1 + csc θ) / (1 + csc θ)
= 1  csc^2 θ / (1 + csc θ)
= 1  1/sin^2 θ / (1 + 1/sin θ)
= 1  sin^2 θ / (sin θ + 1)
= (sin θ  sin^2 θ) / (sin θ + 1)
Simplify 1+csc θ as follows:
1 + csc θ = (1 + csc θ)(1  csc θ) / (1  csc θ)
= 1  csc^2 θ / (1  csc θ)
= 1  1/sin^2 θ / (1  1/sin θ)
= 1  sin^2 θ / (sin θ  1)
= (sin θ + sin^2 θ) / (sin θ  1)
Substitute the above simplifications in the expression cos θ/(1csc θ) * 1+csc θ/(1+ csc θ) to get:
cos θ / (sin θ  sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)
Simplify the expression by canceling out the sin^2 θ terms:
cos θ / (sin θ  sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)
= cos θ / (sin θ  sin^2 θ) * (1 + sin θ) / (sin θ + 1)
Simplify further by factoring out common terms in the numerator and denominator:
cos θ / (sin θ  sin^2 θ) * (1 + sin θ) / (sin θ + 1)
= cos θ * (1 + sin θ) / [(sin θ  sin^2 θ) * (sin θ + 1)]
Finally, simplify the expression by factoring out a sin θ term from the denominator:
cos θ * (1 + sin θ) / [(sin θ  sin^2 θ) * (sin θ + 1)]
= cos θ * (1 + sin θ) / [sin θ * (1  sin θ) * (sin θ + 1)]
= cos θ / [sin θ * (1  sin θ)] * (1 + sin θ)
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Isabella was asked to solve the following trigonometric equation for 0 < x < 2π.
sin(x) = cos(2x) = 0

Isabella worked the problem the following way:
Line 1: sin(x) (1  2 sin²(x)) =

Line 2: sin(x)  1+2 sin²(x) = 0
Line 3: 2 sin² (x) + sin(x) = 1
Line 4: sin(x) (2 sin(x) + 1) = 1
Line 5: sin(x) = 1,
Line 6: sin(x) = 1,
Line 7: x = 0, π
2 sin(x) + 1 = 1
sin(x) = 0
A. Isabella made a mistake in her work. In what line did the mistake occur? Justify your answer. (6
points)
B. What are the correct answers? Leave answers as exact values. WORK DOES NOT NEED TO BE
SHOWN. (6 points)
1. The equation she was supposed to solve was sin(x) = cos(2x), but she mistakenly added an extra "= 0" term.
2. The correct answers are x = π/6 and x = 5π/6.
How do we find the correct answers for the trigonometric equation?
To find the correct answers, we will solve the correct trigonometric equation sin(x) = cos(2x).
Since cos(2x) = 1  2sin²(x), the equation becomes:
sin(x) = 1  2sin²(x)
Now we can rewrite this equation as a quadratic equation in sin(x):
2sin²(x) + sin(x)  1 = 0
This equation can be solved using the quadratic formula:
sin(x) = [b ± sqrt(b²  4ac)] / 2a
where a = 2, b = 1, and c = 1:
sin(x) = [1 ± sqrt(1²  42(1))] / (2*2)
sin(x) = [1 ± sqrt(9)] / 4
sin(x) = (1 ± 3) / 4
There are two possible solutions for sin(x):
sin(x) = 1/2
sin(x) = 1
For sin(x) = 1/2, we have:
x = π/6, 5π/6
For sin(x) = 1, there is no solution in the interval 0 < x < 2π because the sine function does not reach 1 within this range.
So the correct answers are x = π/6 and x = 5π/6.
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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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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
Anyone have the answers
Answer:
The answer is 7 pens
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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you should help meeeee :)
When we compare this to the options provided, we can see that the equation is: a. y = x²/2+x+1. The answer is (a) y = x²/2+x+1.
What is equation of parabola?A parabola's equation can take many different forms, such as vertex form, standard form, or intercept form, depending on its particular shape and orientation.
The parabola's typical vertex form equation is y = a(x  h)² + k
We must locate the vertex form of the parabola in order to get its equation, which is:
y = a(x  h)² + k
Using to determine the vertex
h = b/2a
To begin, we can locate the vertex:
(1,0) (1,1.5) (3,0) (2, 3) (4,3) (3,6) (5,6)
In order to average the xvalues of the two sets of xintercepts, the vertex must be halfway between the parabola's xintercepts:
h = (1 + 3)/2 = 1
The vertex and another point can then be used to find the value of "a":
y = a(x  1)² + k
Using the point (4, 3):
3 = a(4  1)² + k
3 = 9a + k
Using the point (1, 1.5):
1.5 = a(1  1)² + k
1.5 = k
k = 1.5 is substituted into the second equation:
3 = 9a + 1.5
4.5 = 9a
a = 0.5
y = 0.5(x  1)² + 1.5
When we multiply the equation, we get:
y = 0.5x² + x + 1
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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 tdistribution table or a calculator, based on the sample size and degrees of
freedom (n1). For a sample size of 30 or more, we can use the zscore instead of the tscore.
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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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 sixsided 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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c. what is the probability that the duration of a rainfall event at this location is between 2 and 3 hours? d. what is the probability that a rainfall duration exceeds the mean value by more than 2 standard deviations?
The probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
a. The exponential distribution with a mean of 2.725 hours can be expressed as λ = 1/2.725. Using this parameter, we can calculate the probabilities as follows:
P(X ≥ 2) = [tex]e^{(λ2) }= e^{(1/2.7252)[/tex] ≈ 0.4800
P(X ≤ 3) = 1  [tex]e^{(λ3)} = 1  e^{(1/2.7253)[/tex] ≈ 0.6674
P(2 ≤ X ≤ 3) = [tex]e^{(λ2)}  e^{(λ3)} = e^{(1/2.7252)}  e^{(1/2.7253)}[/tex] ≈ 0.1474
b. The standard deviation of an exponential distribution is equal to the mean, so 2 standard deviations above the mean would be 2*2.725 = 5.45 hours. The probability that a rainfall event exceeds this duration can be calculated as follows:
P(X > 5.45) =[tex]e^{(λ5.45)} = e^{(1/2.7255.45)}[/tex] ≈ 0.0498
Therefore, the probability that a rainfall event exceeds the mean by more than 2 standard deviations is approximately 0.0498.
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Complete Question:
Suppose that rainfall duration follows an exponential distribution with mean value 2.725 hours.
a. What is the probability that the duration of a particular rainfall event is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (.4800, .6674, .1474)
b. What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations? (.0498)
Pieceswise defined functions
f(x) = {x, if x < 0
x^2, if x >= 0
This function is defined by two pieces: the formula x for x < 0, and the formula x^2 for x >= 0. The "jump" or change in formula occurs at x = 0.
A) From the given graph we see that, step function has 4 pieces. B) The step function is composed of 3 intervals: (0, 1), [1, 2), [2, 3), and [3, ∞). C) Point is not included in a function, it is indicated by an open circle.
What is a piecewise function?A function that is defined by various equations or formulae on various intervals or portions of its domain is known as a piecewise function. To put it another way, a piecewise function is a function made up of several functions that have been "stitched" together.
A piecewise function is defined on a particular interval or collection of intervals for each piece. A "jump" or change in the formula used to describe the function is commonly indicated by vertical lines that separate the intervals when different parts of the function are described.
A) From the given graph we see that, step function has 4 pieces.
B) The step function is composed of 3 intervals: (0, 1), [1, 2), [2, 3), and [3, ∞).
C) When a point is not included in a function, it is indicated by an open circle; when a point is included in a function, it is indicated by a closed circle.
D) Because each input (weight) translates into exactly one output (postage cost), this is a function. In other words, no two weights that are different from one another have the same shipping price.
E) Because each piece of this piecewise function can be represented by a linear equation of the form y = mx + b, where m and b are constants, the pieces of this piecewise function are linear.
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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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Trigonometric funcions
Which equation are true
Answer:
C and D
Stepbystep 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
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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All help is appreciated thank you.
Using the fact that the triangles are similar we can see that the value of x is 36
How to find the value of x?We can see that the triangles are similar due to the same interior angles, then ther is a scale factor k between them.
So we can write:
20*k = 48
k = 48/20 = 2.4
Then:
x = 15*2.4
x = 36
That is the value of x.
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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 180degree 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 180degree 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 180degree 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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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
1/2 x^4=8
Solve the equation
Answer:
x=2
Stepbystep explanation:
x^4=16
x=[tex]\sqrt[4]{16}[/tex]
x=[tex]2[/tex]
please help me with all the blank ones hurry i am running outta time
Answer:see below
Stepbystep explanation:
10.600
11.80000
12.17
13.48
14.4000
21. 1km=100m;0.5km=500m;0.1km=100m
22.50m=5000cm; 5m=500cm; 0.5m=50cm
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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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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Answer:
Stepbystep explanation:
5989.87
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.
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(sidesideside) or SAS (sideangleside), 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(anglesideangle) 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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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
Stepbystep explanation:
Answer:
4028
Stepbystep explanation:
You need to subtract 9,755 from 13,783 on a calculator and you get your answer.hope it helps
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 n1 terms is
odd, and 0 if the number of "1"s in the first n1 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^{(n1)/2}[/tex] times the parity (i.e., 0 or 1) of n.
(d) The nth term is [tex]3\cdot 2^{n1}[/tex].
(e) The nth term is 157(n1).
(f) The nth term is the sum of the first n positive integers minus 3, i.e.,
[tex]1+2+3+\cdots+n3.[/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 n1 terms is
odd, and 0 if the number of "1"s in the first n1 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^{(n1)/2}[/tex] times the parity (i.e., 0 or 1) of n.
(d) The nth term is [tex]3\cdot 2^{n1}[/tex].
(e) The nth term is 157(n1).
(f) The nth term is the sum of the first n positive integers minus 3, i.e.,
[tex]1+2+3+\cdots+n3.[/tex]
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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%
Stepbystep 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 priceoriginal price)/(original price)
Let's substitute the values, like so:
[tex]\frac{73.5042}{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%.
5. say we measure 20 coyotes. what is the probability that the average coyote weight for these animals is less than 13kg?
The probability that the average coyote weight for a sample of 20 coyotes is less than 13 kg is approximately 13.14%.
we need to know the mean and standard deviation of the coyote weight population. Let's assume that the population mean is μ = 13.5 kg and the population standard deviation is σ = 2 kg.
Since we are measuring a sample of 20 coyotes, we can use the central limit theorem to approximate the distribution of sample means. According to the central limit theorem, if the sample size is large enough (in general, if n > 30), then the distribution of sample means will be approximately normal, regardless of the distribution of the population.
The mean of the sample means will be equal to the population mean (μ) and the standard deviation of the sample means (also known as the standard error) will be equal to σ / √(n), where √(n) is the square root of sample size.
Using this information, we can calculate the zscore for a sample mean of 13 kg as follows;
z = (13  13.5) / (2 / √(20)) = 1.118
Next, we can use a standard normal distribution table (or a calculator or software that can calculate normal probabilities) to find the probability that a zscore is less than 1.118. The area to the left of this zscore is approximately 0.1314, or 13.14%.
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