NORMDIST uses numerical integration to compute the cumulative probability associated with a given point in the normal distribution because an analytical solution for the CDF is not available.
NORMDIST is a function that calculates the probability density function (PDF) or cumulative distribution function (CDF) of the normal distribution (also known as the Gaussian distribution). It uses numerical integration because the normal distribution's CDF cannot be expressed as a simple closed-form equation.
The reason for using numerical integration in NORMDIST is to compute the area under the curve of the normal distribution's PDF up to a specific point. This area represents the cumulative probability of a value being less than or equal to the given point. Numerical integration is an efficient way to approximate the integral of the function when an analytical solution is not possible or feasible.
In summary, NORMDIST uses numerical integration to compute the cumulative probability associated with a given point in the normal distribution because an analytical solution for the CDF is not available.
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Hannah bought 1 yard of ribbon to wrap 4 small presents. She wants to cut the ribbon into equal parts. Draw and label a number line from 0 yards to 1 yard to show where Hannah will cut the ribbon. Label all the fractions, including O fourths and 4 fourths. Also, label 0 yards and 1 yard.
The breadth of ribbon required to ensconce each present shall be (1 yard of ribbon/n parts)/4 presents
How to explain the fractionIf Hannah intends to divide the ribbon into a particular number of equal portions, she must first decide how many parts she wishes to cut. Let's presume she wants to slice it into n identical segments.
In order to distinguish the size of each part, one can singularly unit the total length of the ribbon by the specified number of parts. Due to her need to split the ribbon into n equal portions, the length of every portion will be:
1 yard of ribbon/n parts
Currently, Hannah aspires to use this ribbon to wrap four small presents. To ascertain the amount of ribbon needed to cover each gift, one ought to independently apportion the length of every part by four. Therefore, the breadth of ribbon required to ensconce each present shall be:
(1 yard of ribbon/n parts)/4 presents
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Find the following areas under a standard normal curve(1) Determine the area under the standard normal curve that lies to the left of z = - 2.45(2) Determine the arca under the standard normal cure that lies to the right of x=2.23
To find the areas under a standard normal curve, we use a normal distribution table or calculator. Here are the steps for each problem:
(1) To determine the area under the standard normal curve that lies to the left of z = -2.45, we need to find the area under the curve to the left of -2.45. Using a normal distribution table, we look up the z-score -2.45 and find that the area to the left of this value is 0.0071. Therefore, the area under the standard normal curve to the left of z = -2.45 is approximately 0.0071.
(2) To determine the area under the standard normal curve that lies to the right of x = 2.23, we need to find the area under the curve to the right of 2.23. However, the problem gives us a value in terms of x, not z. To convert this value to a z-score, we use the standard normal distribution formula: z = (x - μ) / σ, where μ is the mean (which is 0 for the standard normal distribution) and σ is the standard deviation (which is 1 for the standard normal distribution). Plugging in the values, we get z = (2.23 - 0) / 1 = 2.23.
Now we look up the area to the right of z = 2.23 in the normal distribution table. However, most normal distribution tables only give the area to the left of a given z-score. To find the area to the right of z = 2.23, we need to subtract the area to the left of z = 2.23 from 1 (which represents the total area under the curve). Using the normal distribution table, we find that the area to the left of z = 2.23 is 0.9877. Therefore, the area under the standard normal curve to the right of x = 2.23 is approximately 1 - 0.9877 = 0.0123.
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when the switch is closed the potential difference across the resistor r connected to a secondary coil of a transformer is n2 > n1
When the switch is closed, the potential difference across the resistor R connected to a secondary coil of a transformer is influenced by the turns ratio (n2 > n1). In this scenario, the number of turns in the secondary coil (n2) is greater than the number of turns in the primary coil (n1). This results in a step-up transformer, which increases the voltage across the resistor R in the secondary circuit.
When the switch is closed, a current flows through the primary coil of the transformer, which creates a changing magnetic field. This changing magnetic field induces a voltage in the secondary coil of the transformer, which is connected to resistor R. The ratio of the number of turns in the secondary coil to the number of turns in the primary coil is given by the turns ratio, which is represented by n2/n1.
Since the potential difference across a resistor is given by Ohm's law (V = IR), the potential difference across resistor R is proportional to the current flowing through it. Therefore, when the potential difference across resistor R connected to the secondary coil of the transformer is n2 > n1, it means that the current flowing through the secondary coil is greater than the current flowing through the primary coil. This is because the voltage induced in the secondary coil is greater than the voltage applied to the primary coil due to the turns ratio of the transformer.
When the switch is closed, the potential difference across the resistor R connected to a secondary coil of a transformer is influenced by the turns ratio (n2 > n1). In this scenario, the number of turns in the secondary coil (n2) is greater than the number of turns in the primary coil (n1). This results in a step-up transformer, which increases the voltage across the resistor R in the secondary circuit.
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I have no clue how to do this
The area of the rod is 1.46 * 10^4 mm^2
The diameter of the rod is 136 mm
What is the elasticity or the Young Modulus?We have to note that the elasticity or the Young modulus of the material can be given by the formula which is;
E = F/A/e/l
E = elasticity
F = force
A = area
e = elasticity
l = length
Thus we have that;
20500 = 20 * 10^3/A * 3000/0.2
20500 = 6 * 10^7/0.2A
20500 * 0.2 A = 6 * 10^7
A = 6 * 10^7/20500 * 0.2
A = 1.46 * 10^4 mm^2
Then
A = πr^2
r=√A/ π
d = 2√A/ π
d = 2*√1.46 * 10^4 /3.14
d = 136 mm
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evaluate the equation 3+ f =14 2/7
A) f= 10 5/7
B) f= 11 2/7
C) f= 11 3/7
D) f= 17 2/7
Answer:
f = 11 2/7 (B)
Step-by-step explanation:
3 + f = 14 2/7
3+f-3 = 14 2/7 -3
f = 11 2/7
Thus, it's B.
Answer:
b) f = 11 2/7
Step-by-step explanation:
Now we have to,
→ Find the required value of f.
The equation is,
→ 3 + f = 14 2/7
Then the value of f will be,
→ 3 + f = 14 2/7
Converting mixed fraction to proper:
→ 3 + f = ((14 × 7) + 2)/7
→ 3 + f = (98 + 2)/7
→ 3 + f = 100/7
Subtract the Right hand side with 3:
→ f = (100/7) - 3
→ f = (100/7) - (21/7)
→ f = (100 - 21)/7
→ f = 79/7
Converting proper fraction to mixed:
→ f = (77 + 2)/7
→ f = (77/7) + (2/7)
→ [ f = 11 2/7 ]
Hence, the value of f is 11 2/7.
Jillian is an analyst for a ride sharing app that connects users with drivers. She wonders if drivers in Dallas are more or less likely to cancel rides than drivers in Houston. She takes a random sample of 1000 rides from Dallas and finds that 30 were cancelled. A random sample of 1000 rides from Houston shows 24 cancelled rides.She used these results to test whether there is a difference in the proportion of cancelled rides between the two cities. The test statistic was z=0.83 and the p-value was approximately 0.41.At the α=0.01 level of significance, is there sufficient evidence to conclude that the proportion of cancelled rides is different between the two cities?Yes, since the p-value is greater than 0.01.Yes, since the test statistic is greater than 0.01.No, since the p-value is greater than 0.01.No, since the test statistic is greater than 0.01
No, since the p-value is greater than 0.01.
When performing a hypothesis test, we compare the p-value to the chosen level of significance, which is typically denoted by α. In this case, the level of significance is α = 0.01.
Since the p-value (approximately 0.41) is greater than the level of significance (0.01), we fail to reject the null hypothesis. The null hypothesis is that there is no difference in the proportion of cancelled rides between Dallas and Houston. Therefore, we do not have sufficient evidence to conclude that the proportion of cancelled rides is different between the two cities at the α = 0.01 level of significance.
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True or False: An argument in which the premises and the conclusion are all contingent statements must be an invalid argument.
Answer:
1).False 2). False if the premise and conclusion are all consistent state
Step-by-step explanation:
i did it
type of item counts per minute (cpm) background source counts per minute (cpm) type of radiation source 1 fiesta-ware plate 167 alpha, beta, and gamma source 2 instant coffee 34 beta source 3 salt substitute 26 beta source 4 smoke alarm 31 alpha source 5 cream of tartar 33 beta (1pts) which is most radioactive?
The most radioactive item among the given sources is the fiesta-ware plate with 167 counts per minute (cpm). It emits alpha, beta, and gamma radiation.
The fiesta-ware plate has the highest counts per minute (cpm) with 167, indicating it has the highest level of radiation. It also emits alpha, beta, and gamma radiation, which are all types of radiation. The other sources have lower cpm values, with instant coffee at 34, salt substitute at 26, smoke alarm at 31, and cream of tartar at 33. Source 2 and Source 3 emit beta radiation, while Source 4 emits alpha radiation. Therefore, the fiesta-ware plate is the most radioactive item in the list.
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Is my answer right or wrong click to see file
Yup! I would just get rid of the plus sign after the 1.5x^2 because you don't really need it
yh but it must be y=1.5x^-7.5x+3
The scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment,y, by each of the 25 students.
(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.
(b) Using your equation from part (a), predict the money spent on entertainment for a student who works 10 hours.
Note that you can use the graphing tools to help you approximate the line.
Answer:
A) y=x+4 b) $12
Step-by-step explanation:
As shown on the graph,
A) select two typical coordinates
{Two points define a straight line}
(12,6) (16,20)
the slope = 20/16-16/12= 4/4=1
y=x+4
b) when x=8
y=8+4=12
PLEASEMARK AS BRAINLIESTFor each of the following tasks, 1. identify which heuristic may be relevant. 2. Identify what bias may result. 3. Explain how to overcome this bias.
1. Studies show that multi‐unit pricing does better than single until pricing. For example: "On Sale, 4 Rolls of Bathroom Tissue for $2″ vs. "On Sale, $0.50/roll". In this experiment, the multi‐unit pricing did 40% better. What bias is this?
2. What are the chances that, as an American, you become: Someone with a six figure income? A millionaire? A billionaire?
3. A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. 85% of the cabs in the city are Green and 15% are Blue. A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time. What is the probability that the cab involved in the accident was Blue rather than Green knowing that this witness identified it as Blue?
4. What is the most likely sequence for the next 6 babies born in the U.S. (b=boy, g=girl) 1. BBBBBB 2. BBBGGG 3. GBBGGB
The relevant heuristic here is the anchoring heuristic, which refers to the tendency to rely too heavily on the first piece of information encountered when making decisions.
The bias that may result is the anchoring bias, which occurs when people place too much emphasis on the initial information and fail to adjust their judgments sufficiently based on new information. To overcome this bias, one can try to consciously consider alternative sources of information and make a more deliberate and thoughtful decision.
The relevant heuristic here is the availability heuristic, which refers to the tendency to judge the likelihood of an event based on how easily examples come to mind. The bias that may result is the availability bias, which occurs when people overestimate the frequency or probability of events that are more vivid or memorable. To overcome this bias, one can try to seek out and consider a wider range of information and statistics to get a more accurate picture of the likelihood of different outcomes.
The relevant heuristic here is the representativeness heuristic, which refers to the tendency to judge the likelihood of an event based on how well it fits with our expectations or stereotypes. The bias that may result is the base rate fallacy, which occurs when people ignore or underestimate the base rate of an event and rely too heavily on specific information or characteristics. To overcome this bias, one can try to take into account both the base rate of the events and the specific information or characteristics that are available.
The relevant heuristic here is the gambler's fallacy, which refers to the tendency to believe that a random event is more likely to occur or not occur based on previous outcomes. The bias that may result is the belief that the sequence is somehow predetermined or influenced by previous outcomes, which may lead people to make unwarranted assumptions or predictions about future events. To overcome this bias, one can recognize that each outcome is independent and random, and that past outcomes do not influence future outcomes.
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A normal distribution has a mean of 85.9 and a standard deviation of 4.88. find the data value corresponding to the value of z given. (enter your answer to four decimal places.) z
Data value = 85.9 + (z * 4.88)
To find the data value corresponding to a given z-score in a normal distribution, you can use the following formula:
Data value = Mean + (Z-score * Standard Deviation)
In this case, you have a normal distribution with a mean of 85.9 and a standard deviation of 4.88. You need to find the data value for a given z-score, which you haven't provided in your question. Assuming the z-score is represented by "z," you can use the formula:
Data value = 85.9 + (z * 4.88)
Once you know the specific z-score, you can plug it into this formula to find the corresponding data value. Please provide the z-score
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Determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size. r= -0.587, alpha = 0.05, n = 19
We can conclude that the correlation coefficient of -0.587 is statistically significant at the 0.05 level of significance with a sample size of 19.
To determine whether the given correlation coefficient is statistically significant at the specified level of significance and sample size, follow these steps:
Step 1: Identify the correlation coefficient (r), level of significance (alpha), and sample size (n).
- r = -0.587
- alpha = 0.05
- n = 19
Step 2: Calculate the degrees of freedom (df).
- df = n - 2
- df = 19 - 2
- df = 17
Step 3: Look up the critical value for the correlation coefficient in a table of critical values or use a statistical software.
- For an alpha level of 0.05 and df = 17, the critical value for a two-tailed test is approximately 0.444 (you can find this value in a table or using software).
Step 4: Compare the absolute value of the correlation coefficient (r) with the critical value.
- |r| = |-0.587| = 0.587
Step 5: Make a decision based on the comparison.
- Since 0.587 > 0.444, we can conclude that the correlation coefficient of -0.587 is statistically significant at the 0.05 level of significance with a sample size of 19.
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Complete the following statement. Use the integers that are closest to the number in the middle. < 63
The required closest integer to [tex]\sqrt{63}[/tex] is 8 and 9.
Given that,
To find the integers that are closest to the number in the middle.
[tex][ ] < \sqrt{63} < [ ][/tex]
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the two numbers be x and y which are close to [tex]\sqrt{63}[/tex],
[tex]\text{x} < \sqrt{63} < \text{y}[/tex] - - - - (1)
The closest root to [tex]\sqrt{63}[/tex] can be given as [tex]\sqrt{59}[/tex] and [tex]\sqrt{72}[/tex]
Now, [tex]\text{x} = \sqrt{59}[/tex] and [tex]\text{y} = \sqrt{72}[/tex]
Put these values in inequality 1
[tex]\sqrt{59} < \sqrt{63} < \sqrt{72}[/tex]
[tex]8 < \sqrt{63} < 9[/tex]
Thus, the required closest integer to [tex]\sqrt{63}[/tex] is 8 and 9.
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5.1.3 Quiz: Measures of Center and Spread
Question 1 of 10
What is the median of this data set?
A. 39
B. 47
C. 49
D. 37
22, 37, 49, 15, 72
SUBMIT
Answer:
D. 37
Step-by-step explanation:
Step 1:
order the values from lowest to highest
15, 22, 37, 49, 72
Step 2:
the median is the value in the middle of the set of numbers, which in this case is 37
So the answer is D. 37
Regitting is defined as the act of taking a gift that has been given to you and presenting it on a gift to someone else According to survey conducted by a credit card company regarding consumer spending, 68% of the respondents felt that it was socially acceptable to regift during the holiday season (big sigh of rele) Suppose a random sample of 10 holiday shoppers was selected Complete parts a through d What is the probability shopper from this sample for that regting wat socially acceptable? The probability is (Type an integer or decimal rounded to four decimal places as needed
The probability that a shopper from this sample finds regifting socially acceptable is approximately 0.9938 (rounded to four decimal places).
To answer this question, we'll use the binomial probability formula, which is:
P(x) = (ⁿCₓ) × (pˣ) × (q^(n-x))
where:
- P(x) is the probability of x successes (in this case, x shoppers finding regifting socially acceptable)
- n is the number of trials (in this case, the sample size of 10 shoppers)
- x is the number of successes (the number of shoppers finding regifting acceptable)
- nCx is the number of combinations of n items taken x at a time
- p is the probability of success (68% or 0.68)
- q is the probability of failure (1 - p, or 32% or 0.32)
We want to find the probability that a shopper from the sample of 10 finds regifting socially acceptable. To do this, we can find the probability that any number of shoppers from the sample (1 to 10) find regifting socially acceptable, then sum these probabilities.
For example:
P(1 shopper finds regifting acceptable) = ¹⁰C₁ × (0.68¹) × (0.32⁹)
P(2 shoppers find regifting acceptable) = ¹⁰C₂ × (0.68²) × (0.32⁸)
...
P(10 shoppers find regifting acceptable) = ¹⁰C₁₀ × (0.68¹⁰) × (0.32⁰)
Sum these probabilities, and you get the total probability that a shopper from this sample finds regifting socially acceptable.
Therefore, The probability that a shopper from this sample finds regifting socially acceptable is approximately 0.9938 (rounded to four decimal places).
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250 pounds = how many tons
The metric unit from pounds to tons is 250 pounds = 0.125 tons
Converting the metric unit from pounds to tonsFrom the question, we have the following parameters that can be used in our computation:
250 pounds = how many tons
As a general rule, we have
1 pound = 0.0005 tons
Multiply both sides of the equation by 250
So, we have
250 * 1 pound = 0.0005 tons * 250
Evaluate the products
250 pounds = 0.125 tons
Hence, the conversion is 250 pounds = 0.125 tons
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Let the graph of f(x) represent the cost in thousands of dollars to feed the zoo animals daily, where x is the number of animals measured in hundreds. What
does the solution to the function (2, 7) represent?
The solution 2, 7 tells us that there are 200 animals and the cost of feeding the animals is 7000 dollars
How to get the meaning of the graph solutionThe cost is said to be in thousands
The number of animals is said to be in their hundreds
The solution is a given pair of x, y
where x is horizontal side and y is the vertical side
x = 2
y = 7
When we interprete the values in the solution based on the graph description we would have tjat The solution 2, 7 tells us that there are 200 animals and the cost of feeding the animals is 7000 dollars
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Help
Have a great day
Thanks if you do help! :]
The area of the Caldwell that is covered by the concrete patio would be = 280.86ft²
How to calculate the area of a semi circle?A semi circle is derived from an intact circle that is equally divided into two.
To calculate the area of the semi circle, the formula that should be used is given as follows;
Area of a circle = πr²/2
where r = diameter/2= 26.75/2 = 13.375
area = 3.14 ×13.375²
= 561.72ft²
But the shape of the Caldwell which was given is a semi-circle not a full circle. Therefore it's final area will be = 561.72ft²/2 = 280.86ft².
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a simple random sample of 20 pages from a dictionary is obtained. the numbers of words defined on those pages are found, with the results n=20, x=53.5 words, s=16.5 words. Given that this dictionary has 1454 pages with defines words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.1 words. Use a .01 significance level to test the claim that the mean number of words per page is greater than 48.1 words. what does the result suggest about the claim that there are more than 70,000 defined words? Identify the null and alternative hypotheses, test statistic, P value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed
Since the p-value (.040) is greater than the significance level (.01), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to support the claim that there are more than 70,000 defined words in the dictionary. The mean number of words per page is not significantly greater than 48.1 words.
To test the claim that the mean number of words per page is greater than 48.1 words, we will use a one-sample t-test. We will follow these steps:
Step 1: Identify the null and alternative hypotheses
H0: µ ≤ 48.1 (null hypothesis: the mean number of words per page is less than or equal to 48.1)
H1: µ > 48.1 (alternative hypothesis: the mean number of words per page is greater than 48.1)
Step 2: Calculate the test statistic (t-score)
t = (x - µ) / (s / √n)
t = (53.5 - 48.1) / (16.5 / √20)
t ≈ 1.84
Step 3: Calculate the P-value
Using a t-distribution table or calculator, find the P-value associated with the t-score 1.84 and degrees of freedom (n-1) = 19. Since this is a one-tailed test, we don't need to divide the P-value by 2. The P-value is approximately 0.041.
Test Statistic: To calculate the test statistic, we will use the formula:
t = (x - μ) / (s / √n), where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the given values, we get: t = (53.5 - 48.1) / (16.5 / √20) = 1.86.
P-value: Using a t-distribution table with 19 degrees of freedom (n-1), we find the p-value to be .040 (one-tailed).
Step 4: Compare the P-value with the significance level (α)
Since the P-value (0.041) is greater than the significance level (0.01), we fail to reject the null hypothesis.
Step 5: State the final conclusion
We do not have sufficient evidence to support the claim that the mean number of words per page is greater than 48.1 words at a 0.01 significance level. Consequently, we cannot support the claim that there are more than 70,000 defined words in the dictionary.
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Vocabulary
1 central tendency movement in a particular direction
2. extreme values the smallest and largest values in a data set
3. mean the sum of a set of data divided by the number of items in the set
4. median the middle value of a set of data arranged in numerical order
5. mode the most frequently occurring number(s) in a data set
6. range the difference between the largest and smallest data points
Match the terms to their definition.
A. mean
B. range
C. median
D. mode
E. extreme values
F. central tendency
Answer:
mean=3
range=6
median=4
mode=5
extreme value=2
central tendency=1
may I get brainliest
p <---> q can be translated as "p is necessary and sufficient for q". true or false
True. The statement "p is necessary and sufficient for q" means that if p is present, then q must also be present, and if q is present, then p must also be present.
Explanation:
- When we say "p is necessary for q," it means that if q is true, then p must also be true. This is represented as q → p.
- When we say "p is sufficient for q," it means that if p is true, then q must also be true. This is represented as p → q.
Combining both conditions, we get the biconditional statement p ↔ q, which represents that p is necessary and sufficient for q.
In other words, p is a sufficient condition for q (meaning that if p occurs, then q must also occur) and a necessary condition for q (meaning that q cannot occur without p). This is equivalent to the biconditional statement p <--> q, which asserts that p and q are logically equivalent and can be used interchangeably. Therefore, the statement "p <--> q can be translated as 'p is necessary and sufficient for q'" is true.
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El producto notable de (x+2y) (x-2y) es
Answer: El producto notable de (x + 2y) (x - 2y) es x^2 - (2y)^2, que se puede simplificar a x^2 - 4y^2.
Step-by-step explanation:
if 1/2x + 1/4y = 32 then 2x + y = a) 32 b) 64 c) 128 d) 164
Answer:
C
Step-by-step explanation:
[tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{4}[/tex] y = 32
multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions
2x + y = 128
a psychiatrist is studying the effect of a certain antidepressant medication on serotonin levels in the brain. the psychiatrist randomly assigns 32 of her patients to take medication and 32 patients to not take medication. at the end of one month, the psychiatrist records the serotonin levels of patients. suppose the psychiatrist correctly conducts a test of significance to determine if the serotonin levels are not equal. the test shows a statistically significant difference in average serotonin levels for the two groups of patients. what conclusion can the psychiatrist draw from these results?
The test of significance difference in average serotonin levels for the two groups of patients suggests that the antidepressant medication has an effect on serotonin levels in the brain.
In statistical hypothesis testing, a statistically significant difference is a result that is unlikely to occur by chance alone. In other words, it suggests that there is a real difference between two groups or conditions being compared, rather than the difference being due to random variation or error.
In this case, the two groups of patients being compared are those who received the antidepressant medication and those who did not. The average serotonin levels were measured for both groups, and the statistical analysis showed that there is a significant difference between the two groups.
However, further analysis and study would be necessary to determine the magnitude and clinical significance of this effect, as well as to rule out any other potential factors that may have influenced the results.
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2. Ellen says that 1 2/5 equals 5 dived 7. Is she
correct? Explain.
Answer:
no she is not.
Step-by-step explanation:
2 divided 7 is the same as 2/5 so
2/5 = 0.4
dividing 5 by 7 would be 0.714 so its not equal
hope this helps you <3
Use the right triangle and the Pythagorean theorem to calculate the distance between the two points (7,8) and (-5,-7)
The distance between the two points is 19.2 units.
Let the point (7, 8) be A and point (-5, -7) be B.
By joining these two points and drawing a right-angled triangle ABC with AB as the hypotenuse, we get point C at (7, -7)
The altitude of triangle ABC, AC = A - C
AC = 15 units
The base of the triangle ABC, BC = C - B
BC = 12 units
According to Pythagoras Theorem,
√(AC² + BC²) = AB
AB = √(12² + 15²)
AB = 19.2 units
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Solve Using substitution
-8x + 6y =8
x = -7
ime left 1 The number of calls coming in to an office follows a Poisson distribution with mean 5 calls per hour. What is the probability that there will be exactly 7 calls within the next hour ? Question 6 Answer saved Marked out of 1.00 P Flag question O a. 0.090 O b. 0.104 Oc. 0.123 O d. 0.071 The number of calls coming in to an office follows a Poisson distribution with mean 5 calls per hour. What is the probability that there will be exactly 7 calls within the next three hours? Question 5 Answer saved Marked out of 1.00 P Flag question O a. 0.090 O b. 0.104 O c. 0.010 O d. 0.071
The probability that there will be exactly 7 calls within the next hour is approximately 0.104. The probability that there will be exactly 7 calls within the next three hours is approximately 0.010.
For the first question, we can use the Poisson distribution formula:
P(X = x) = (e^-λ * λ^x) / x!
Where λ is the mean (in this case, λ = 5) and x is the number of calls we are interested in (in this case, x = 7).
Plugging in the values, we get:
P(X = 7) = (e^-5 * 5^7) / 7!
P(X = 7) ≈ 0.104
For the second question, we need to adjust the mean to account for the longer time period. Since we are interested in the number of calls within the next three hours, the new mean is:
λ = 5 * 3 = 15
Using the same formula as before, we get:
P(X = 7) = (e^-15 * 15^7) / 7!
P(X = 7) ≈ 0.010
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Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer: Be sure you can justify your answers ~8 A T(A) = ASA-I from R2x2 to R2x2 where S = 55 B. T(A) = A from R2xs to R2x5 ~9 -2 C.T(A) = A from R to RZx2 D. T(A) = 2A from R6x4 to R6x4 ET(A) = A A from R2x2 to R 2x2 5 JET(A) = A+ Is from RSx5 to RSx5
A, C, and E are linear transformations. To justify: A: T(A) = ASA-I is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.
C: T(A) = A from R to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R. This can be shown by plugging in kA for A in T(A) and simplifying.
E: T(A) = A from R2x2 to R2x2 is linear because it satisfies the two properties of linearity:
1. Additivity: T(A+B) = T(A) + T(B) for any matrices A and B in R2x2. This can be shown by plugging in (A+B) for A in T(A) and simplifying.
2. Homogeneity: T(kA) = kT(A) for any scalar k and matrix A in R2x2. This can be shown by plugging in kA for A in T(A) and simplifying.
B, D, and J are not linear transformations.
To justify:
B: T(A) = A from R2xs to R2x5 is not linear because it does not satisfy the additivity property of linearity. Specifically, T(A+B) ≠ T(A) + T(B) for some matrices A and B in R2xs.
D: T(A) = 2A from R6x4 to R6x4 is not linear because it does not satisfy the homogeneity property of linearity. Specifically, T(kA) ≠ kT(A) for some scalar k and matrix A in R6x4.
J: T(A) = A+Is from RSx5 to RSx5 is not linear because it does not satisfy either the additivity or homogeneity properties of linearity. Specifically, T(A+B) ≠ T(A) + T(B) and T(kA) ≠ kT(A) for some matrices A and B in RSx5 and scalar k.
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