E. One sample z for one proportion. The philosophy major is interested in estimating the proportion of people who know what a philosophy major does, which is a proportion
This is because the philosophy major wants to estimate the proportion of people who know what a philosophy major does, and has a sample size of 100, which is large enough for a z-test.
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express as a trinomial (x−3)(2x−5)
The trinomial expression of (x−3)(2x−5) is 2[tex]x^{2}[/tex] − 11x + 15.
To express the product of two binomials (x−3) and (2x−5) as a trinomial, we can use the FOIL method or distributive property.
FOIL stands for First, Outer, Inner, Last. We multiply the First terms in each binomial, then the Outer terms, then the Inner terms, and finally the Last terms. We then add these four products together to get our trinomial.
Using the distributive property, we can multiply each term in the first binomial by each term in the second binomial. This gives us four terms, which we can then simplify by combining like terms to obtain the trinomial.
So, using either method, we get:
(x−3)(2x−5) = x(2x) + x(-5) - 3(2x) - 3(-5)
= 2[tex]x^{2}[/tex] -5x -6x + 15
= 2[tex]x^{2}[/tex] − 11x + 15
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K-7: Write a conversation with your friend in Telugu explaining the symmetry you observe in nature
A conversation with your friend explaining the symmetry you observe in nature is given below.
What is the conversation about?Me: Hey, have you ever noticed how symmetrical nature can be?
Friend: What do you mean?
Me: Well, think about things like snowflakes, leaves, and flowers. They all have a certain amount of symmetry to them.
Friend: Yeah, I guess I've noticed that before. But why is that?
Me: It's actually because of the way that nature grows and develops. The growth of these things is guided by physical laws and processes that tend to produce symmetrical shapes.
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If sin (alpha) = 24/25 where 0 < alpha < pi/2 and cos (beta) = 20/29 where 3 pi/2 < beta < 2 pi, find the exact values of the following. Sin (alpha + beta) cos (alpha - beta) tan (alpha - beta)
The exact values of sin(alpha + beta), cos(alpha - beta), and tan(alpha - beta) are 504/725, 567/725, and -12/5, respectively.
How to calculate the valuesin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta)
= (24/25)(20/29) + (7/25)(21/29)
= 504/725
cos(alpha - beta) = cos(alpha)cos(beta) + sin(alpha)sin(beta)
= (7/25)(20/29) + (24/25)(21/29)
= 567/725
tan(alpha - beta) = (sin(alpha)cos(beta) - cos(alpha)sin(beta))/(cos(alpha)cos(beta) + sin(alpha)sin(beta))
= (24/25)(20/29) - (7/25)(21/29))/((7/25)(20/29) + (24/25)(21/29))
= -12/5
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two students proposed two different designs for their system in their course project. the first student performed 5 experiments to determine the number of customers served within 5 minutes and the second student performed 7 experiments for the same measure. student number of customers served within 5 minutes 1 102 86 98 109 92 2 81 165 97 134 92 87 114 what would each student obtain as their 90% confidence interval for the mean number of customers served within 5 minutes using their respective designs.
Therefore, the 90% confidence interval for Student 1 is (89.61, 105.19). Therefore, the 90% confidence interval for Student 2 is (84.96, 131.24).
To calculate the 90% confidence interval for the mean number of customers served within 5 minutes for each student, we need to use the formula:
CI = X ± (tα/2 * s/√n)
where X is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value from the t-distribution with (n-1) degrees of freedom at the desired confidence level (in this case, 90%).
For Student 1:
X = (102 + 86 + 98 + 109 + 92)/5
= 97.4
s = √([(102-97.4)² + (86-97.4)² + (98-97.4)² + (109-97.4)² + (92-97.4)²]/(5-1))
= 7.94
n = 5
tα/2 = 1.895 (from t-distribution table with 4 degrees of freedom at 90% confidence level)
CI = 97.4 ± (1.895 * 7.94/√5)
= 97.4 ± 7.79
= (89.61, 105.19)
For Student 2:
X = (81 + 165 + 97 + 134 + 92 + 87 + 114)/7
= 108.1
s = √([(81-108.1)² + (165-108.1)² + (97-108.1)² + (134-108.1)² + (92-108.1)² + (87-108.1)² + (114-108.1)²]/(7-1))
= 30.18
n = 7
tα/2 = 1.895 (from t-distribution table with 6 degrees of freedom at 90% confidence level)
CI = 108.1 ± (1.895 * 30.18/√7)
= 108.1 ± 23.14
= (84.96, 131.24)
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The following linear regression model can be used to predict ticket sales at a popular water park.
Ticket sales per hour = -631.25 + 11.25(current temperature in degrees F).
In this context, does the intercept have a reasonable interpretation?
No, at 0°F the ticket sales would be -631.25 and it is not reasonable (or possible) to have negative ticket sales in a linear regression model for predicting ticket sales.
In the statistics, the concept of regression analysis is useful for creating a predictive model that predicts the value of a target or dependent variable using all the controlling independent or explanatory variables. Depending on the number of independent variables, regression can be called simple regression or multiple regression. We have a linear regression model that predicts ticket sales for popular water parks.
The regression line equion in this model is written as -631.25 + 11.25 (current temperature in degree F). Comparing above equation with y = a + bx, here, the interaction in the equation above means that hourly ticket sales will be -631.25 when the current temperature (in degrees Fahrenheit) is 0. This does not make sense because hourly ticket sales can be at least 0 but never a negative number. So, it is not reasonable interpretation.
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how many topologies can you find on a set of three elements. how many of those correspond to a topology induced by a metric?
there are only two possible topologies induced by a metric, and the remaining six topologies are not induced by a metric.
On a set of three elements, there are $2^{\binom{3}{2}} = 2^3 = 8$ possible topologies, since we need to consider all possible subsets of pairs of elements and each pair can be included or excluded from the topology.
To determine how many of these correspond to a topology induced by a metric, we need to verify the following axioms:
The distance between two points is non-negative.
The distance between a point and itself is zero.
The distance between two points is the same regardless of the order in which they are listed.
The triangle inequality holds.
For a set of three elements, there are only two possible metrics that satisfy these axioms: the discrete metric and the metric induced by the Euclidean distance on the real line.
The discrete metric gives rise to the discrete topology, where every subset is open, and the metric induced by the Euclidean distance gives rise to the topology with the following open sets: ${\emptyset, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}}$.
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which communication contrast is accurate? multiple choice only 10% of native-born americans speak a second language; 56% of european union citizens speak a second language. most native-born americans speak a second language, while few european union citizens speak a second language. less than 1% of native-born americans speak a second language; 76% of european union citizens speak a second language. at least half of native-born americans speak a second language, while about one-fourth of european union citizens speak a second language. almost all native-born americans speak a second language, while only a few european union citizens speak a second language.
the correct answer is: Only 10% of native-born Americans speak a second language; 56% of European Union citizens speak a second language.
The accurate communication contrast is:
Only 10% of native-born Americans speak a second language; 56% of European Union citizens speak a second language.
what is communication?
Communication refers to the exchange of information, ideas, thoughts, and messages between two or more individuals or groups. It involves the transmission and reception of messages through various channels, including verbal, nonverbal, and written modes. Effective communication requires the ability to express oneself clearly and listen actively to others, understand their perspectives, and respond appropriately.
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you roll a standard number cube. use the probability of rolling an even number to find the probability of rolling an odd number. enter your answer in simplified fraction form. the probability of rolling an odd number is
The probability of rolling an odd number on a standard number cube is 1/2.
The probability of rolling an even number on a standard number cube is 1/2 since there are three even numbers (2, 4, and 6) out of a total of six possible outcomes (1, 2, 3, 4, 5, and 6).
To find the probability of rolling an odd number, we can use the fact that the sum of the probabilities of all possible outcomes is 1. Therefore, the probability of rolling an odd number is:
1 - probability of rolling an even number
= 1 - 1/2
= 1/2
So, the probability of rolling an odd number on a standard number cube is 1/2.
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a pair of shoes on sale for $76.50 after a 15% discount was applied. What was the original price of the shoes?
The original price of the shoes would be = $102
How to calculate the original price of the pair of shoes?The sale price of the pair of shoes after discount = $76.50
The percentage discount of the shoes = 15% of original price
Therefore original price = X
But $76.50 = 75% of an unknown number.(that is 100-15 = 75%)
Let the unknown number = X
76.50 = 0.75x
X = 76.50/0.75
= $102
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Pls help I’m no good at maths
Answer:
30 meters
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
30 meters
Step-by-step explanation:
7. 2. 12 Is Question Help Let f(t) be a function on (0. 00). The Laplace transform of fis the function F defined by the integral F(s) (dt. Use this definition to determine the Laplace transform of the following function. F(t)= 23, 0
The Laplace transform of F(t) is F(s) = (-2/3s) [[tex]e^{-12s}[/tex] - 1 ]
To find the Laplace transform of the function F(t) = 2/3, 0<t<12, we can use the definition of Laplace transform
F(s) = L{F(t)} = ∫[0,∞) [tex]e^{-st}[/tex] F(t) dt
Since F(t) is a constant function on the interval (0,12), we have:
F(s) = ∫[0,12] [tex]e^{-st}[/tex] (2/3) dt
Using integration by substitution with u = -st, du = -s dt, and limits of integration u(0) = 0 and u(12) = -12s, we get:
F(s) = (2/3) ∫[0,-12s] [tex]e^{u}[/tex] (-1/s) du
= (-2/3s) [ [tex]e^{-12s}[/tex] - 1 ]
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A clerk entering salary data into a company spreadsheet accidentally put an extra ​"0​" in the​ boss's salary, listing it as ​$1,400,000 instead of ​$140,000. Explain how this error will affect these summary statistics for the company payroll. a) measures of center​ (median and​ mean)
​b) measures of spread​ (range, IQR, and standard​ deviation)
The error in the boss's salary will significantly affect the range and standard deviation, but will not affect the IQR.
a) Measures of center (median and mean):
The error in the boss's salary will significantly affect the measures of center, both the mean and the median.
The mean is the arithmetic average of all salaries in the company, while the median is the middle value when all salaries are arranged in increasing order.
Since the boss's salary is much higher than all other salaries, its inclusion will significantly increase the mean, but will not affect the median since it is still in the middle of the ordered list.
Therefore, the mean will be significantly larger than what it should be, while the median will remain unchanged.
b) Measures of spread (range, IQR, and standard deviation):
The error in the boss's salary will also affect the measures of spread. The range, which is the difference between the maximum and minimum salaries, will be larger since the maximum salary will be much larger than it should be.
The interquartile range (IQR), which is the difference between the 75th percentile and 25th percentile, will not be affected since the boss's salary is an extreme outlier and is not included in the middle 50% of the salaries.
The standard deviation, which measures the amount of variation around the mean, will also be affected.
Since the mean will be much larger than it should be, the standard deviation will be larger since it measures the deviation of each salary from the mean.
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