The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.
So, if we want to find the approximate probability that a randomly selected x-value from the distribution is in a given interval, we need to determine how many standard deviations away from the mean the interval is and then use the empirical rule.
For example, let's say we want to find the approximate probability that a randomly selected x-value from the distribution is between 31 and 47.
First, we need to determine how many standard deviations away from the mean 31 and 47 are.
To do this, we can calculate the z-scores for each value using the formula:
z = (x - mean) / standard deviation
For x = 31:
z = (31 - 39) / 4 = -2
For x = 47:
z = (47 - 39) / 4 = 2
So, the interval from 31 to 47 is two standard deviations away from the mean.
Using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the approximate probability that a randomly selected x-value from the distribution is between 31 and 47 is approximately 95%.
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80% of blank equal 36
Which statement is true based on the image below? A rectangle with a long side of 3. An arrow points to a larger rectangle with a long side of 7.5 Question 6 options: A scale factor of 2.5 was applied to create the enlargement A scale factor of 2.5 was applied to create the reduction A scale factor of 25 was applied to create the reduction A scale factor of 0.25 was applied to create the enlargement
The statement true about the rectangle and scale factor is
A scale factor of 2.5 was applied to create the enlargement
Given data ,
A rectangle with a long side of 3 and an arrow points to a larger rectangle with a long side of 7.5
Now , the long side of the original rectangle is 3 units, and the long side of the enlarged rectangle is 7.5 units.
And , the ratio of the long sides is 7.5/3 = 2.5, which indicates that the rectangle was enlarged by a factor of 2.5.
Hence , the scale factor of dilation is d = 2.5
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rpapenfuse25
2 hours ago
Mathematics
High School
An ordinary (fair) die is a cube with the 1 numbers through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event 1: The sum is greater than 8 .
Event 2: The sum is divisible by 2 .
Write your answers as fraction
The probability of Event 1 is 5/36 and the probability of Event 2 is 1/2.
What is the probability of each of the given events?Comparing the results of the roll of two fair die yields the probability of each of the following events:
There are 6 × 6 = 36 outcomes that could occur.
Event 1: The total exceeds eight.
There are five outcomes where the total exceeds eight.
P(Event 1)=5/36
Event 2: The sum can be divided by two.
Where the total is divisible by 2, there are 18 possible results.
The likelihood of this occurrence is:
P(Event 2) =18/36
P(Event 2) equals 1/2
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a movie theater is offering a special summer pass. Passholders pay $8 per movie for the first 5 movies and watch additional movies for free, up to a maximum of 15 movies. The function C gives the total cost in dollars, for a passholder to watch n movies. If function C a piecewise fuction? Explain and describe the domain of c and range of c
Yes, the function C is a piecewise function.
The domain of C is the set of non-negative integers (0, 1, 2, 3, ...),
The range of C is the set of non-negative real numbers
(0, 8, 16, 24, ..., 40),
We have,
The function C is a piecewise function.
When a passholder watches between 1 and 5 movies, the cost is $8 per movie, so the total cost C is:
C(n) = 8n
When a passholder watches more than 5 movies, but not more than 15 movies, the cost is a fixed price of $40 for the first 5 movies plus additional movies watched for free.
Therefore, the total cost C is:
C(n) = 40, for 5 < n ≤ 15
When a passholder watches more than 15 movies, the cost is undefined since the maximum number of movies allowed is 15.
The domain of C is the set of non-negative integers (0, 1, 2, 3, ...), since you cannot watch a negative or fractional number of movies.
However, since the maximum number of movies allowed is 15, the domain is restricted to integers between 0 and 15, inclusive.
The range of C is the set of non-negative real numbers (0, 8, 16, 24, ..., 40), since the cost per movie is $8 and the cost for watching between 6 and 15 movies is a fixed price of $40.
The minimum cost is 0 (if no movies are watched) and the maximum cost is 40 (if 15 or more movies are watched).
Thus,
The domain of C is the set of non-negative integers (0, 1, 2, 3, ...),
The range of C is the set of non-negative real numbers
(0, 8, 16, 24, ..., 40),
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what is a paired t-test? question 4select one: a. given a single numeric variable, a test for that variable's population mean b. given a single categorical variable, a test for that variable's population mean c. given a two numeric variables, a test for the difference of those variable's population means d. given a two numeric variables measured on the same or very similar units, a test for the mean of the differences between those variables
d. A paired t-test is a statistical test used to determine if there is a significant difference between the means of two related or paired samples.
It is used when two numeric variables are measured on the same or very similar units and the goal is to test for the mean of the differences between those variables. For example, it could be used to test whether a new drug treatment is significantly more effective than a placebo treatment, by measuring the difference in response between the same individuals receiving the two treatments. The paired t-test is also sometimes called a dependent samples t-test or a matched pairs t-test.
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9) Norma and Lauretta went to a store to buy DVDs on sale for $5 each, tax included. Norma purchased two
and a half times as many DVDs as Lauretta purchased. Together they purchased 14 DVDs, Which system of
linear equations can be used to determine , the number of DVDs Norma purchased, and I, the number of DVDs
Lauretta purchased?
Answer: H
Step-by-step explanation:
The cost of $5 has not meaning for what we want. The are only trying to figure out the number each bought so that was thrown in to throw you off.
you know they bought 14 total DVDs
n+L=14 the number norma bought + number Lauretta bought is 14
Th next key sentence is Norma purchased two and a half times as Luaretta
In the sentence:
Norma is n
purchased is your = sign (usually in word problems "is" "costs" etc is =
Two and 1 half [tex]2\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex]
times is * (multiplied)
Lauretta is l
Substitute each symbol for each work
Norma(n) purchase(=) two and a half [tex]\frac{5}{2}[/tex] times* L
n= [tex]\frac{5}{2}[/tex]L
n+L=14 these are your 2 equations H
Solve the quadratic by factoring.
x^2 + 9x +25 = 5
Answer:
To solve the quadratic equation x^2 + 9x +25 = 5 by factoring, we first rearrange the equation to get:
x^2 + 9x +20 = 0
Next, we need to find two numbers that multiply by 20 and add to 9, the coefficient of x. The two numbers are 4 and 5.
So, we can factor the quadratic as:
(x + 4)(x + 5) = 0
Setting each factor to zero and solving for x, we get:
x + 4 = 0 or x + 5 = 0
Solving for x in each equation, we get:
x = -4 or x = -5
Therefore, the solutions to the quadratic equation x^2 + 9x +25 = 5 are x = -4 and x = -5.
set up and evaluate the optimization problems. (enter your answers as comma-separated lists.) find two positive integers such that their sum is 16, and the sum of their squares is minimized.
The two positive integers that satisfy the conditions and minimize the sum of their squares are 4 and 4.
We can use the method of Lagrange multipliers to solve this problem. Let x and y be the two positive integers we want to find, then we want to minimize the function [tex]f(x,y) = x^2 + y^2[/tex] subject to the constraint g(x,y) = x + y - 16 = 0.
The Lagrange function is L(x,y,λ) = f(x,y) - λg(x,y) =[tex]x^2 + y^2[/tex] - λ(x + y - 16).
Taking partial derivatives of L with respect to x, y, and λ, we get:
dL/dx = 2x - λ = 0
dL/dy = 2y - λ = 0
dL/dλ = x + y - 16 = 0
Solving for λ in the first two equations, we get λ = 2x = 2y. Substituting this into the third equation, we get 4x = 16, or x = 4. Then y = 4 as well, since λ = 2x = 2y.
Therefore, the two positive integers that satisfy the conditions and minimize the sum of their squares are 4 and 4.
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Hello! I'm really having trouble with this problem,if you can't see the image clearly here is the directions.
Determine if the two figures shown below are congruent,similar,or neither. Prove your answers using the transformations.
The transformations are Translation, Rotation,and Reflection.
Here's the words for the bottom part if you can't read it
Josiah believes the scale factor from ABC to FED is 1.5 since AB=2 and FE=3 (you can multiply by 1.5) why is he incorrect?
Please take your time with this, I know this is a lot.
The two given figures are neither similar nor congruent
How to determine if a figure is similar or congruent?Congruent figures are geometric figures that have the same shape and size. That is, if you can transform one figure into another figure by a sequence of translations , rotations , and/or reflections , then the two figures are congruent.
Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Therefore, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
Now, it is clear that both shapes are not congruent because the lengths are not congruent.
Similarly, the ratio of the two corresponding sides are not the same. Thus:
We can say neither of both are similar or congruent.
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Find the area of the figure.
Step-by-step explanation:
Answer:
306cm
Step-by-step explanation:
15x12=180 18+7=126
180+126=306
P.S i'm emo
P(A) x P(b) = P(a and b) in what type of data
Probabilistic data refers to data that involves uncertain or random events.
it is typically analyzed using probability theory or statistical methods. Examples of probabilistic data include the outcomes of a coin toss, the probability of a person having a certain genetic trait, or the likelihood of an event occurring given certain conditions. The formula P(A) x P(B) = P(A and B) is a probability formula that applies to probability theory and statistics, which deal with random events and their likelihoods. Therefore, it is related to probabilistic data
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true/false. in a sequential search algorithm, the boolean variable used as a flag is initialized to true.
Answer: False.
Explanation: In a sequential search algorithm, the boolean variable used as a flag is typically initialized to be false. This is because the flag is used to indicate whether a search item has been found or not. If the flag is set to false, it means the item has not been found yet.
False. In a sequential search algorithm, the boolean variable used as a flag is initialized to false. This flag is set to true if the search key is found in the sequence.
False. In a sequential search algorithm, the boolean variable used as a flag is usually initialized to false. The flag is set to true only when the desired element is found during the search process.
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25 POINTS IF U ANSWER THIS
The values of the variables x and y are 12 and 3 respectively, while the measure of angles m∠A and m∠B are 36° and 126° respectively
How to to evaluate for the values of variables and angles1). m∠A and m∠D are complementary angles so their sum is equal to 90°
3x + (4x + 6)° = 90°
7x = 90° - 6°
x = 84/7
x = 12
2). m∠A = 3(12) = 36°
3). m∠B and m∠C are on a straight line and their sum is equal to 180° {also called supplementary angles}.
18y + 42y = 180°
60y = 180°
y = 180°/60°
y = 3
4). m∠C = 42(3) = 126°
In conclusion, the values of the variables x and y are 12 and 3 respectively, while the measure of angles m∠A and m∠B are 36° and 126° respectively
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help please and thank youu
The statements that must be true based on the histogram are as follows:
A. The range of the data set is 50 min.
C. The most common amount of exercise is 0 to 9 min.
E. The distribution is skewed right.
How to determine the distributionYou can say that the distribution of a histogram is skewed right if the highest point in the distribution lies towards the left-hand side of the graph.
The graph above is an example of a distribution that is skewed right. Also, the range of the dataset is between 0 to 50 and the most common amount of exercise engaged in by the students is 0 to 9 min.
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teenagers who had no prior experience in tying knots were divided into groups to practice tying knots five days a week for five weeks. during the practice period, the blocked practice group practiced the butterfly knot each day of the week. the random practice group practiced the barrel hitch, butterfly knot, carrick bend, backup knot, and french whipping randomly in every practice session. the result of the retention and transfer tests proved that the performance of the random practice group was better than the blocked practice group. this scenario is an example of the
This statistics is an example of the "interference theory" in motor learning.
Interference theory suggests that when individuals learn multiple skills or movements in a random order, they perform better in retention and transfer tests compared to those who learn the same skills or movements in a blocked or constant order. The random practice group in this scenario was able to better transfer their knot-tying skills to new situations because they learned the knots in a more varied and unpredictable way, which helped them develop more adaptable and flexible motor patterns.
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find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros.
In a polynomial function of the lowest degree with rational coefficients that have the given numbers as some of its zeros, we can use the fact that if a number "a" is a zero of a polynomial function, then (x-a) is a factor of the function.
Therefore, we can start by multiplying together (x-a) for each given zero, and then simplify the resulting expression to get the polynomial function in standard form with rational coefficients.
For example, if the given zeros are 2, -1, and 1/2, we would start by multiplying (x-2)(x+1)(x-1/2), which gives:
(x-2)(x+1)(2x-1)
Expanding this expression, we get:
2x^3 - 3x^2 - 5x + 2
This is a polynomial function of degree 3 (highest exponent is 3) with rational coefficients (all coefficients are integers or fractions). Note that this is the lowest degree possible for a polynomial with these zeros, since there are three distinct zeros.
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a circle has a radius of 6cm. find the length of s of the arc intercepted by a central angle of 1.1 raidans.
The length of the arc intercepted by a central angle of 1.1 radians is 6.6 cm.
A central angle is an angle with its vertex at the center of a circle and its rays extending out to the edge of the circle, creating an intercepted arc.
The length of the arc intercepted by a central angle of 1.1 radians can be found by using the formula:
Length of arc = (central angle / 2π) × 2πr
where r is the radius of the circle.
Plugging in the given values, we get:
Length of arc = (1.1 / 2π) × 2π(6)
Length of arc = 1.1 × 6
Length of arc = 6.6 cm
Therefore, the length of the arc intercepted by a central angle of 1.1 radians is 6.6 cm.
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You may need to use the appropriate spend table or technology to the custom The following results are for independent random samples taken from the populations ASK YOUR TEACHER PRACTICE Sample Sample - 20 - 30 * - 223, -20.1 -24 5-40 (a) What is the point estimate of the difference between the two population means?
The point estimate of the difference between the two population means is -51.975.
The point estimate of the difference between the two population means can be calculated by finding the difference between the sample means. From the given samples, the sample mean for the first sample is (-20 + 30 + (-223))/3 = -71, and the sample mean for the second sample is (-20.1 -24 + 5 - 40)/4 = -19.025.
It is important to note that this is only an estimate and may not perfectly represent the true difference between the two population means.
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In the context of data patterns and variations in a time series, _____ are characterized by repeatable periods of ups and downs over short periods of time.
a.cyclical patterns
b.irregular variations
c.random variations
d.seasonal patterns
In the context of data patterns and variations in a time series, cyclical patterns are characterized by repeatable periods of ups and downs over short periods of time. The answer is: a. cyclical patterns.
Cyclical patterns refer to fluctuations that occur over an extended period of time, usually several years or more, and are often related to economic or business cycles. These patterns are not as predictable as seasonal patterns, as they may vary in amplitude and duration from cycle to cycle. Cyclical patterns can also be influenced by a variety of factors, including changes in consumer behavior, technological innovations, and geopolitical events.
Irregular variations, on the other hand, refer to unexpected, random fluctuations in the data that cannot be attributed to any known factors. Random variations are also unpredictable, but they are not necessarily cyclical in nature.
Seasonal patterns refer to regular, predictable fluctuations in the data that occur within a single year. These patterns are often related to seasonal changes in weather, holidays, or other seasonal factors that affect consumer behavior.
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seasonality is a regular, repeating pattern in the data that takes longer than 1 year to complete. group of answer choices true false
True. Seasonality refers to a regular, repeating pattern in the data that takes longer than one year to complete. It can occur in various forms such as monthly, quarterly, or even weekly patterns.
These patterns are usually associated with external factors such as weather, holidays, or other events that influence consumer behavior. By identifying seasonality in the data, businesses can use it to predict future trends and adjust their strategies accordingly. This information can be valuable in a range of industries such as retail, tourism, and agriculture.
Overall, understanding the repeating patterns in data is essential for making informed decisions and staying ahead of the competition.
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four less than the quotient of a number and two is no more than ten what is the number
{write and solve an inequality}
The inequality is represented as;
x/2 - 4 ≤ 10
x ≤ 28
What are inequalities?
Inequalities are described as the relation such that make an uneven comparison between two numbers, expressions or even variables.
The different signs of inequality are;
< represents less than> represents greater than ≥ represents greater than or equal to≤ represents less than or equal toFrom the information given, we have that;
four less than the quotient of a number and two is no more than ten what is the number
Let the number be x
This can then be represented as;
x/2 - 4 ≤ 10
x/2 ≤ 10 + 4
x/2 ≤ 14
x ≤ 28
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Lori has a coin and a number cube. The number cube is labeled one through six. She flips the coin once and rolls the number cube once. What is the probability that the coin lands heads up and the cube lands on a composite number?
The probability that the coin lands heads up and the cube lands on a composite number is 1/3 or approximately 0.333.
To find the probability that the coin lands heads up and the cube lands on a composite number, we need to first determine the number of outcomes in the sample space that satisfy these conditions, and then divide that by the total number of possible outcomes.
There are two possible outcomes for the coin flip: heads or tails. There are six possible outcomes for rolling the number cube: 1, 2, 3, 4, 5, or 6. To determine the number of outcomes in the sample space that satisfy the given conditions, we need to identify the composite numbers among the possible outcomes for rolling the number cube.
The composite numbers are 4, 6, and they occur two times each. Therefore, there are four outcomes that satisfy the given conditions: (heads, 4), (heads, 6), (tails, 4), and (tails, 6).
The total number of possible outcomes is the product of the number of outcomes for the coin flip and the number of outcomes for rolling the number cube, which is:
2 x 6 = 12
So the probability of the coin landing heads up and the cube landing on a composite number is:
4 / 12 = 1/3
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Find the length of the curve. r(t) = (5t, 3 cos t, 3 sin t), -4 lessthanorequalto t lessthanorequalto 4 Find the length of the curve. squareroot 2 ti + e^t j + e^-t k, 0 lessthanorequalto t lessthanorequalto 2 Reparametrize the curve with respect to arc length measured from the point where t 0 in the direction of increasing t. (Enter your answer in terms of s.) r(t) = 3ti + (6 - 4t)j + (8 + 2t)k r(t(s)) =
To find the length of the curve r(t) = (5t, 3 cos t, 3 sin t), -4 ≤ t ≤ 4, we can use the formula for arc length: L = ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt
Applying this formula to r(t),
we get: L = ∫_(-4)^(4) √(25 + 9sin^2t + 9cos^2t) dt Simplifying the expression under the square root, we get: L = ∫_(-4)^(4) √34 dt
Evaluating the integral, we get: L = 8√34
Therefore, the length of the curve is 8√34, To find the length of the curve √2ti + e^tj + e^-tk, 0 ≤ t ≤ 2, we can use the same formula: L = ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.
Applying this formula to the given curve, we get:
L = ∫_0^(2) √(2^2 + e^(2t) + e^(-2t)) dt, Simplifying the expression under the square root, we get: L = ∫_0^(2) √(e^(2t) + 2 + e^(-2t)) dt
Making a substitution u = e^t + e^(-t),
we get: L = 1/2 ∫_2^(e^2 + e^(-2)) √(u^2 - 4) du Making another substitution v = u/2, we get:
L = ∫_√2^(√(e^2 + e^(-2))/2) √(v^2 - 1) dv
Using a trigonometric substitution v = sec θ, we get:
L = ∫_(π/4)^(π/2) sec θ dθ
Evaluating the integral, we get:
L = ln(1 + √2) + ln(√(e^2 + e^(-2)) + 1)
Therefore, the length of the curve is ln(1 + √2) + ln(√(e^2 + e^(-2)) + 1).
To reparametrize the curve r(t) = 3ti + (6 - 4t)j + (8 + 2t)k with respect to arc length measured from the point where t = 0 in the direction of increasing t, we can use the formula for arc length:
s = ∫√(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2 dt.
We first find the arc length of the curve from t = 0 to some arbitrary value t: s = ∫_0^t √(9 + 16 + 4) dt
Simplifying, we get:
s = 3√29 t
Solving for t in terms of s, we get:
t = s/(3√29)
Substituting this expression into the given curve, we get:
r(s) = 3(s/(3√29))i + (6 - 4(s/(3√29)))j + (8 + 2(s/(3√29)))k
Simplifying,
we get: r(s) = si/√29 + (6 - 4s/(3√29))j + (8 + 2s/(3√29))k
Therefore, the reparametrized curve is r(s) = si/√29 + (6 - 4s/(3√29))j + (8 + 2s/(3√29))k.
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Based on past data, the Student Recreation Center knew that the proportion of students who prefer exercising outside over exercising in a gym was 0.822. To update their records, the SRC conducted a survey. Out of 84 students surveyed, 73 indicated that they preferred outdoor exercise over exercising in a gym. The 90% confidence interval is ( 0.8085 , 0.9296 ). Which of the following statements is the best conclusion?
Based on the survey results, it can be concluded with 90% confidence that the proportion of students who prefer exercising outside over-exercising in a gym is between 0.8085 and 0.9296. This interval does not include the previously known proportion of 0.822, which suggests that there may have been a change in student preferences over time.
However, it should be noted that the sample size of 84 is relatively small and there may be some degree of sampling error present. Overall, the SRC should continue to monitor student preferences for exercising and consider offering a variety of options to accommodate different preferences.
In the Student Recreation Center, it was found that 73 out of 84 students preferred exercising outside over exercising in a gym. This gives us a sample proportion of 73/84 = 0.869. This proportion's 90% confidence interval is (0.8085, 0.9296).
Since the past data proportion of 0.822 falls within the 90% confidence interval, we can conclude that there is no significant difference between the past data and the current survey results regarding students' preferences for outdoor exercise over gym exercise.
Based on past data, the Student Recreation Center knew that the proportion of students who prefer exercising outside over-exercising in a gym was 0.822. To update their records, the SRC conducted a survey. Out of 84 students surveyed, 73 indicated that they preferred outdoor exercise over-exercising in a gym. The 90% confidence interval is ( 0.8085, 0.9296 ).
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the sum of the two numbers is 16 and their difference is 27 what are these two numbers demonstrated with a system of equation
Answer:Let's call the two numbers we are trying to find "x" and "y".
We know that the sum of these two numbers is 16, so we can write the equation:
x + y = 16
We also know that the difference between these two numbers is 27, so we can write the equation:
x - y = 27
Now we have two equations and two unknowns. We can use substitution or elimination to solve for x and y.
Using the substitution method, we can solve for y in the first equation:
y = 16 - x
Now we can substitute this expression for y into the second equation:
x - (16 - x) = 27
Simplifying this equation, we get:
2x - 16 = 27
Adding 16 to both sides, we get:
2x = 43
Dividing both sides by 2, we get:
x = 21.5
Now we can substitute this value for x into either of the original equations to solve for y:
y = 16 - x = 16 - 21.5 = -5.5
So the two numbers are 21.5 and -5.5.
Step-by-step explanation:
Shelly invests $594 at 4.5% interest for 10 years. How much money will he have in the account? (round to nearest penny)
The amount of money he will have in the account is $922.46
How much money will he have in the accountFrom the question, we have the following parameters that can be used in our computation:
Principal, P = 594
Rate , r = 4.5%
TIme = 10 years
Teh amount of money is calcilated s
Amount = P * (1 + r)^t
substitute the known values in the above equation, so, we have the following representation
Amount = 594 * (1 + 4.5%)^10
Evaluate
Amount = 922.46
Hence, the amount is $922.46
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pls hurry i dont have much time 68 points
Answer: 9/4
Step-by-step explanation:
since each cube measure 1/2 of a centimeter on one side, the dimension is calculated first
length = 2 x 1/2 cm
width = 3 x 1/2 cm
height = 3 x 1/2 cm
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. A linear regression was performed on these data, and the result is the linear regression equation: Yi=-0.843+1.4100Xi Complete parts (a) through (d).a. Determine the coefficient of determination,r squared, and interpret its meaning.r squared= _______(Round to three decimal places as needed.)Interpret the meaning of r squared.The value of r squared indicates that ____% of the variation in _____ (online trailer reviews or box office gross) can be explained by the variation in______(online trailer reviews. or box office gross.) (Round to one decimal place as needed.)b. Determine the standard error of the estimate.Syx=_______ (Round to two decimal places as needed.)c. How useful do you think this regression model is for predicting opening weekend box office gross?A. It is not useful for predicting box office gross because the coefficient of determination is close to 0.B. It is not useful for predicting box office gross because the coefficient of determination is close to 1.C.It is very useful for predicting box office gross because the coefficient of determination is very close to 1.D.It is somewhat useful for predicting box office gross because the coefficient of determination is closer to 1 than it is to 0.d. Can you think of other variables that might explain the variation in opening weekend box office gross? Select all that apply.A.The amount spent on advertising might explain the variation in opening weekend box office gross, because viewers are probably more likely to watch a movie that has been advertised heavily.B.The timing of the release of the movie might explain the variation in opening weekend box office gross, because a movie released at the same time as multiple other major movies may get crowded out.C.The type of movie might explain the variation in opening weekend box office gross, since some genres are more heavily attended than others.
a. The coefficient of determination, r squared, is 0.669. Interpretation: The value of r squared indicates that 66.9% of the variation in box office gross can be explained by the variation in online trailer views.
b. The standard error of the estimate is 16.74.
c. The regression model is somewhat useful for predicting opening weekend box office gross because the coefficient of determination is closer to 1 than it is to 0.
d. Other variables that might explain the variation in opening weekend box office gross include: the amount spent on advertising, the timing of the release of the movie, and the type of movie.
a. To find the coefficient of determination (r^2), you will need to perform a linear regression analysis on the given data. Since we don't have the actual data values, we cannot calculate r^2 directly. However, once you calculate r^2 using the data, you can interpret its meaning as follows:
The value of r^2 indicates that ___% of the variation in box office gross can be explained by the variation in online trailer views. (Fill in the blank with the calculated r^2 value, rounded to one decimal place.)
b. Similarly, without the actual data values, we cannot calculate the standard error of the estimate (Syx). Once you have the data, you can calculate Syx using regression analysis.
c. The usefulness of the regression model depends on the calculated r^2 value. Choose the most appropriate answer based on the calculated r^2:
A. It is not useful for predicting box office gross because the coefficient of determination is close to 0.
B. It is not useful for predicting box office gross because the coefficient of determination is close to 1.
C. It is very useful for predicting box office gross because the coefficient of determination is very close to 1.
D. It is somewhat useful for predicting box office gross because the coefficient of determination is closer to 1 than it is to 0.
d. Other variables that might explain the variation in opening weekend box office gross are:
A. The amount spent on advertising might explain the variation in opening weekend box office gross because viewers are probably more likely to watch a movie that has been advertised heavily.
B. The timing of the release of the movie might explain the variation in opening weekend box office gross because a movie released at the same time as multiple other major movies may get crowded out.
C. The type of movie might explain the variation in opening weekend box office gross since some genres are more heavily attended than others.
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the mean per capita consumption of milk per year is 105 liters with a standard deviation of 26 liters. if a sample of 220 people is randomly selected, what is the probability that the sample mean would be less than 107.81 liters? round your answer to four decimal places.\
The probability is approximately 0.9429. Rounded to four decimal places, the probability is 0.9429. Therefore, the probability that the sample mean would be less than 107.81 liters is about 0.9429 or 94.29%.
To solve this problem, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
First, we need to calculate the standard error of the mean, which is the standard deviation of the sampling distribution of the mean:
standard error = standard deviation / square root of sample size
standard error = 26 / sqrt(220)
standard error ≈ 1.756
Next, we can standardize the sample mean using the formula for z-scores:
z = (sample mean - population mean) / standard error
z = (107.81 - 105) / 1.756
z ≈ 1.574
Finally, we can use a standard normal distribution table or calculator to find the probability of getting a z-score less than 1.574.
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According to data released by New Town Chamber of Commerce, the weekly wages of office workers have a mean of $723 and a standard deviation of $151. If 57 office workers are chosen at random New Town, what is the probability that the mean weekly wage of these workers will be greater than $750? (Write answer round to whole number like 6%)
The probability that the mean weekly wage of these 57 workers will be greater than $750 is approximately 9%.
To find the probability that the mean weekly wage of the 57 randomly chosen office workers will be greater than $750, we'll use the Central Limit Theorem and z-score formula.
1. Find the standard error (SE) by dividing the standard deviation ($151) by the square root of the sample size (57):
SE = $151 / √57 ≈ $20.03
2. Calculate the z-score:
z = (sample mean - population mean) / SE
z = ($750 - $723) / $20.03 ≈ 1.35
3. Look up the z-score in a standard normal distribution table or use a calculator to find the probability. For a z-score of 1.35, the area to the left is approximately 0.9115. Since we want the probability of the mean wage being greater than $750, we'll calculate the area to the right:
P(z > 1.35) = 1 - 0.9115 ≈ 0.0885
4. Convert the probability to a percentage and round to a whole number:
0.0885 × 100 ≈ 9%
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