Answer:
12,765
Step-by-step explanation:
The exponential formula for the population can be written as ...
population = (initial population)(1 -decay rate)^t
where t is in years, and the decay rate is the loss per year.
The given numbers make this ...
population = 100,000(0.9918^t)
In 250 years, the population will be about ...
population = 100,000(0.9918^250) ≈ 12,765.15
There will be about 12,765 butterflies in 250 years.
In 250 years, there will be approximately 12,765 butterflies in the population.
This figure is obtained by applying the exponential decay formula with a 0.82% decrease rate per year from an initial population of 100,000 butterflies.
To determine the butterfly population in 250 years given a yearly decrease rate of 0.82%, we utilize the exponential decay formula:
[tex]\[ P(t) = P_0 \times (1 - r)^t \][/tex]
where:
- (P(t)) represents the population after (t) years,
- (P_0) is the initial population, which is 100,000,
- (r) is the annual decrease rate in decimal form, which is 0.82% or 0.0082,
- (t) is the time in years, here 250 years.
By substituting the given values into the formula:
[tex]\[ P(250) = 100,000 \times (1 - 0.0082)^{250} \][/tex]
Upon calculation, the population after 250 years is found to be approximately 12,765, rounding to the nearest whole number for practical purposes. This result is based on the principle of exponential decay, reflecting how a consistent percentage decrease affects the population over a prolonged period.
round 12.566370614359 to the nearest hundredth
Answer:12.57
Step-by-step explanation:
Answer:
12.566370614359 rounded to the nearest hundreth is 12.57
A rhombus TEMPhas coordinates A(-6, 3)
B(-4, 4)
C(-2, 3)
D(-4, 2).
What are the coordinates of rhombus A'B'C'D' AFTER A 90° COUNTERCLOCKWISE ROTATION ABOUT THE ORIGIN FOLLOWED BY A TRANSLATION 3 UNITS TO THE LEFT AND 2 UNITS DOWN ?
Answer:
A'(-6, -8)B'(-7, -6)C'(-6, -4)D'(-5, -6)Step-by-step explanation:
A 90° CCW rotation makes the transformation ...
(x, y) ⇒ (-y, x)
A translation 3 left and 2 down makes the transformation ...
(x, y) ⇒ (x -3, y-2)
The two transformations together are ...
(x, y) ⇒ (-y-3, x -2)
Then the given points are transformed to ...
A'(-6, -8)
B'(-7, -6)
C'(-6, -4)
D'(-5, -6)
please help brainly crown and 5-stars⭐️
Which expression is equivalent to 625 in exponential form?
A) 54
B) 53
C) 25 × 25
D) 5 × 125
Answer:
choice a....625 = [tex]5^{4}[/tex] in exponential form
Step-by-step explanation:
625 = 25*25 = [tex]25^{2}[/tex] = [tex]5^{4}[/tex]
Answer:
choice A well be correct !! (did it on usa test prep)
Step-by-step explanation:
The popular candy Skittles comes in 5 colors. According to the Skittles website, the 5 colors are evenly distributed in the population of Skittle candies. So each color makes up 20% of the population. Suppose that we purchase a small bag of Skittles. Assume this size bag always has 40 candies. In this particular bag 10 are green. What is the probability that a randomly selected bag of this size has 10 or more green candies
Answer:
27.76% probability that a randomly selected bag of this size has 10 or more green candies
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 40, p = 0.2[/tex]
So
[tex]\mu = E(X) = np = 40*0.2 = 8[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40*0.2*0.8} = 2.53[/tex]
What is the probability that a randomly selected bag of this size has 10 or more green candies
Using continuity correction, this is [tex]P(X \geq 10 - 0.5) = P(X \geq 9.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 9.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 8}{2.53}[/tex]
[tex]Z = 0.59[/tex]
[tex]Z = 0.59[/tex] has a pvalue of 0.7224
1 - 0.7224 = 0.2776
27.76% probability that a randomly selected bag of this size has 10 or more green candies
Answer:
[tex]P(x\geq 10)=0.2682[/tex]
Step-by-step explanation:
The number x of green candies in a bag of 40 candies follows a binomial distribution, because we have:
n identical and independent events: 40 candiesa probability p of success and (1-p) of fail: a probability of 0.2 to get a green candie and 0.8 to doesn't get a green candie.So, the probability that in a bag of 40 candies, x are green is calculated as:
[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]
Replacing, n by 40 and p by 0.2, we get:
[tex]P(x)=\frac{40!}{x!(40-x)!}*0.2^{x}*(1-0.2)^{40-x}[/tex]
So, the probability that a randomly selected bag of this size has 10 or more green candies is equal to:
[tex]P(x\geq 10)=P(10)+P(11)+...+P(40)\\P(x\geq 10)=1-P(x<10)[/tex]
Where [tex]P(x<10)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)[/tex]
So, we can calculated P(0) and P(1) as:
[tex]P(0)=\frac{40!}{0!(40-0)!}*0.2^{0}*(1-0.2)^{40-0}=0.00013\\P(1)=\frac{40!}{1!(40-1)!}*0.2^{1}*(1-0.2)^{40-1}=0.00133[/tex]
At the same way, we can calculated P(2), P(3), P(4), P(5), P(6), P(7), P(8) and P(9) and get that P(x<10) is equal to:
[tex]P(x<10)=0.7318[/tex]
Finally, the probability [tex]P(x\geq 10)[/tex] that a randomly selected bag of this size has 10 or more green candies is:
[tex]P(x\geq 10)=1-P(x<10)\\P(x\geq 10)=1-0.7318\\P(x\geq 10)=0.2682[/tex]
Which temperature values would an interpolation be limited to?
less than 0
between 0 and 60
between 20 and 80
greater than 55
The temperature values for which the interpolation would be limited to is given by: Option B: Between 0 and 60
Which equation can we use for interpolation?One of such equations we can use for interpolation is given as:
[tex]y - y_0 = \dfrac{y_1 - y_0}{x_1 - x_0} \times (x -x_0)[/tex]
The question seems bit incomplete. From the given options, the second option is correct for the completed question.
Thus, the temperature values for which the interpolation would be limited to is given by: Option B: Between 0 and 60
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Final answer:
Interpolation estimates values within the range of known data points. For temperature values, interpolation would be limited to the temperature ranges provided, such as -60 to 65 degrees. Values outside these intervals would require extrapolation instead.
Explanation:
The question about interpolation is set in the context of Mathematics, specifically focusing on data interpretation or statistics. Interpolation is a method used to estimate values within the range of a discrete set of known data points.
Given the provided information, it seems that temperature values for interpolation are specified within certain ranges. To deduce which temperature values interpolation would be limited to, we must understand the data and context in which interpolation is applied. Since interpolation only makes sense between known data points, it is limited to the ranges of temperatures for which we have data.
For instance, the given ranges such as -60 to -55, -55 to -50, ..., 55 to 60, 60 to 65 suggest that interpolation would be appropriate for estimating temperature values within these intervals. If the known data is between 0 and 60 degrees, the interpolation would be valid only within that range and not outside it since extrapolation, not interpolation, is used to predict values outside the range of known data points.
There were 5 1/3 jars of pickles. Ann and her friends ate 1 1/3 jars. How many jars of pickles are left? *
Answer:5/3 jars left
Step-by-step explanation:
Convert the total number of jars to improper fraction from mixed fraction
The subtract the total number of jars from the total number of empty jars
16/3 -11/3
5/3
If the project is finished within 26 weeks of its start, the project manager will receive a bonus of $1,000; and if the project is finished within 27 weeks of its start, the bonus will be $500. Find the probability of each bonus. (Round Mean, Standard Deviation, z-value to 2 decimal places and Probability to 4 decimal places.) Path Mean Std. Dev. a-d-e-h 24.33 1.35 a-f-g 15.50 1.26 b-i-j-k 14.83 1.02 c-m-n-o 26.17 1.66 Probability ($1,000) .4099
To determine the probabilities of the project manager receiving bonuses, calculate the z-scores for the project completion times and use the normal distribution to find the associated probabilities. The process relies on the project completion times being normally distributed, with the given means and standard deviations used in calculations.
Explanation:The task involves calculating the probability of a project manager receiving different bonus amounts based on the project completion time. To find the probability of each bonus, we need to consider the distribution of the project completion times along different paths and use the given means and standard deviations. Although the actual values of the probabilities are not provided, the general approach would be to use the normal distribution (since project completion times can be assumed to follow it) and calculate the respective z-scores for 26 weeks and 27 weeks.
For a bonus of $1,000 (project finished within 26 weeks), the z-score calculation would be:
Z = (X - Mean) / Std. Dev.And for a bonus of $500 (project finished within 27 weeks), it would be a similar z-score calculation. After calculating the z-scores, we would use normal distribution tables or a calculator to find the probability associated with those z-scores.
If the provided probability of receiving a $1,000 bonus is 0.4099, this implies that the z-score associated with completing the project within 26 weeks corresponds to a probability of 0.4099 in the normal distribution.
Consider the four numbers a, b, c, d with a ≤ b ≤ c ≤ d, where a, b, c, d are integers. The mean of the four numbers is 4.The mode is 3. The median is 3.The range is 6. Find d
Answer:
d = 2
Step-by-step explanation:
We have four unknown numbers a, b, c, d
It is given that the mode is 3,
Since the mode is 3 then at least two numbers are 3.
It is given that the median is 3,
Since the median is 3 which means the middle two values must be 3
a, 3, 3, d
It is given that the mean of the four numbers is 4,
Since the mean of the four number is 4 then
mean = (a + 3 + 3 + d)/4
4 = (a + 6 + d)/4
4*4 = a + 6 + d
16 = a + 6 + d eq. 1
It is given that the range is 6,
Since the range is 6 which is the difference between highest and lowest number that is
a - d = 6
a = 6 + d eq. 2
Substitute the eq. 2 into eq. 1
16 = a + 6 + d
16 = (6 + d) + 6 + d
16 = 12 + 2d
2d = 16 - 12
d = 4/2
d = 2
Substitute the value of d into eq. 2
a = 6 + d
a = 6 + 2
a = 8
so
a, b, c, d = 8, 3, 3, 2
Verification:
a ≤ b ≤ c ≤ d
8 ≤ 3 ≤ 3 ≤ 2
mean = (a + b + c + d)/4
mean = (8 + 3 + 3 + 2)/4
mean = 16/4
mean = 4
range = a - d
range = 8 - 2
range = 6
A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.
Answer:
Claim is rejected
Step-by-step explanation:
Solution:-
- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.
- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.
- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.
- State the hypothesis for the effectiveness of medication:
Null Hypothesis: p = 0.75 ... Claim
Alternate hypothesis: p < 0.75 .... Test
- The conditions of standard normality:
n*p > 5 , 150*0.75 = 112.5 .. ( Check )n*(1-p) > 5 , 150*0.25 = 37.5 .. ( Check )Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.
- We will estimate the population proportion with the sample proportion ( p* ):
p* = n / N
p* = 100 / 150
p* = 2/3 = 0.667
- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:
[tex]Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607 \\[/tex]
- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.
- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.
- So for lower tailed test the critical value of statistics is:
P ( Z < Z-critical ) = α = 0.05
Z-critical = - 1.645
- The rejected values all lie to the left of the Z-critical value -1.645
- The claim test value is compared the rejection region:
-2.35607 < -1.645
Z-test < Z-critical
Hence, Null hypothesis rejected because test lies in the rejection region.
Conclusion:
The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.
By calculating the Z-score and corresponding p-value for the statistical test, we found that there is significant evidence at the 0.05 level to suggest that the medication's effectiveness is less than the 75% claimed.
Explanation:The subject we're dealing with here is hypothesis testing in statistics, where we have a claim (the effectiveness of the medication is 75%) and we are testing whether the observations (effectiveness in 100 out of 150 individuals) support this claim.
Firstly, the parameter of interest here is the proportion (p) of individuals for whom the medication is effective. Our null hypothesis (H0) is that p = 0.75 and our alternate hypothesis (Ha) is that p < 0.75.
To conduct the hypothesis test, let's check the conditions:
Random: It's not mentioned, but assuming these 150 individuals were chosen randomly, this condition is met.Normal: Since both np (150 * 0.75 = 112.5) and n(1-p) (150 * 0.25 = 37.5) are greater than 10, the sampling distribution will be approximately normal.Independent: Again, this is not stated, but let's assume the responses from the individuals are independent.The sample proportion (p-hat) = 100/150 = 0.67
Next, we calculate the Z score, which is (p-hat - p) / sqrt[p(1-p)/n] = (0.67 - 0.75) / sqrt[0.75 * (0.25) / 150] = -1.65. The p-value associated with a Z score of -1.65 is 0.0495.
Since the p-value is less than the significance level of 0.05, we reject H0 and conclude that there is statistically significant evidence at the 0.05 level that the effectiveness of medication is less than 75% as claimed by the manufacturer.
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A. 7/25
B. 24/25
C. 7/24
D. 24/7
Answer:
D. 24/7
Step-by-step explanation:
SOH CAH TOA
we doing the tangent so
tan (α) = opposite / adjacent
tan (α) = 24/7
Jimmy’s Delicatessen sells large tins of Tom Tucker’s Toffee. The deli uses a periodic review system, checking inventory levels every 10 days, at which time an order is placed for more tins. Order lead time is 3 days. Average daily demand is 7 tins, so average demand during the reorder period and order lead time (13 days) is 91 tins. The standard deviation of demand during this same 13- day period is 17 tins. Calculate the restocking level. Assume the desired service level is 90% percent.
Answer:
The restocking level is 113 tins.
Step-by-step explanation:
Let the random variable X represents the restocking level.
The average demand during the reorder period and order lead time (13 days) is, μ = 91 tins.
The standard deviation of demand during this same 13- day period is, σ = 17 tins.
The service level that is desired is, 90%.
Compute the z-value for 90% desired service level as follows:
[tex]z_{\alpha}=z_{0.10}=1.282[/tex]
*Use a z-table for the value.
The expression representing the restocking level is:
[tex]X=\mu +z \sigma[/tex]
Compute the restocking level for a 90% desired service level as follows:
[tex]X=\mu +z \sigma[/tex]
[tex]=91+(1.282\times 17)\\=91+21.794\\=112.794\\\approx 113[/tex]
Thus, the restocking level is 113 tins.
Final answer:
The restocking level for Jimmy's Delicatessen is calculated using the average demand, standard deviation, desired service level, and the z-score for a 90% service level, resulting in a restocking level of 113 tins.
Explanation:
Calculating the Restocking Level for Jimmy's Delicatessen
To calculate the restocking level, we need to use the information given about the average demand, the standard deviation of demand, and the desired service level. The average demand during the reorder period and order lead time (13 days) is 91 tins. Given the standard deviation of 17 tins and a 90% service level, we would typically look up the z-value that corresponds to a 90% service level in a standard normal distribution table, which is approximately 1.28.
Now, to find the restocking level, we use the formula: Restocking Level = Average Demand + (Z-score * Standard Deviation). Plugging in the numbers, we get:
Restocking Level = 91 tins + (1.28 * 17 tins) = 91 + 21.76 = 112.76 tins.
Therefore, the restocking level should be rounded up to 113 tins to ensure that there is a 90% probability that the stock on hand will be sufficient until the next delivery arrives.
1/2(8x-39) = 1/4(12x + 32)
Answer:
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don't mind my messy handwriting
the explanation is in the picture
PLEASE HELP!!!!!!Dimensions of the triangular prism
Base - 20 feet by 20 feet
Height - 40 feet
Dimensions of the rectangular prism
Base - 15 feet by 40 feet
Height - 20 feet
What is the total amount of volume inside the parking
garage?
16.000
18.000
24.000
Answer:20000ft^3
Step-by-step explanation:
volume of triangular prism:
Base area x height
1/2 x 20 x 20 x40
(1x20x20x40) ➗ 2
16000 ➗ 2=8000ft^3
Volume of rectangular prism:
Length x width x height
40 x 15 x 20=12000ft^3
Total volume=8000+12000
Total volume=20000ft^3
The total amount of volume inside the parking garage = 20,000 cu. ft.
What is the volume of the triangular prism?The volume of the triangular prism = base area × height
What is the volume of the rectangular prism?V = l × b × h, where 'l' represents the length, 'w' represents the width and 'h' represents the height of the rectangular prism
For given example,
Let V1 represents the volume of the triangular prism and V2 represents the volume of the rectangular prism.
Dimensions of the triangular prism are:
Base - 20 feet by 20 feet and Height - 40 feet
The base of the triangular prism is a triangle.
So, the area of the base would be,
⇒ A = 1/2 × 20 × 20
⇒ A = 200 sq. ft.
The volume of the triangular prism would be,
⇒ V1 = base area × height
⇒ V1 = 200 × 40
⇒ V1 = 8,000 cubic feet
Now, the dimensions of the rectangular prism are:
Base - 15 feet by 40 feet and Height - 20 feet
⇒ l = 40ft., w = 15 ft., h = 20 ft.
The volume of the rectangular prism would be,
⇒ V2 = l × w × h
⇒ V2 = 40 × 15 × 20
⇒ V2 = 12,000 cu. ft.
So, the total amount of volume inside the parking garage would be,
⇒ V = V1 + V2
⇒ V = 8000 + 12000
⇒ V = 20,000 cu. ft.
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Find the mean absolute deviation for the data set.
5,6,6,8,10
Answer: 1.6
Order the numbers
5,6,6,8,10
Add
5+6+6+8+10=35
Divide
35÷5=7
Mean: 7
Sum divided by the count.
Final Answer: 1.6
Answer:
1.6
Step-by-step explanation:
Mean: 5 + 6 + 6 + 8 + 10 = 35/5 = 7
7 - 5 = 2
7 - 6 = 1
7 - 6 = 1
7 - 8 = 1
7 - 10 = 3
1 + 1 + 1 + 2 + 3 = 8/5 = 1.6
This net consists of a square and 4 identical triangles. What is the surface area of the sold this net can form?
Not drawn to scale
The surface area of a square pyramid is found by adding the area of the square base to the area of the four triangular faces. If the side of the square base is 's' and the length of the slant height of the triangles is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex]
Explanation:The net described in the question would form a square pyramid. To calculate the surface area of a square pyramid, you add the area of the square base to the combined areas of the four triangular faces. If the side of the square is 's' and the length of the slant height of the triangular faces is 'l', the formula is: Surface [tex]Area = s^2 + 2 * s * l.[/tex] The surface area is expressed in square units. For example, if the side of the square is 4 units and the slant height is 6 units, the surface area of the pyramid is [tex]4^2 + 2 * 4 * 6 = 16 + 48 = 64[/tex] square units.
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In November 2010, an article titled "Frequency of Colds Dramatically Cut with Regular Exercise" appeared in Medical News Today. The article was based on the findings of a study by researchers Nieman et al. (British Journal of Sports Medicine, 2010) that followed 1,002 people aged 18–85 years for 12 weeks, asking them to record their frequency of exercise (5 or more days a week? Yes or No) as well as incidences of upper respiratory tract infections (Cold during last week? Yes or No.)
Answer:
Part a
For the given study, the explanatory variable or independent variable is given as regularity or frequency of exercise. This variable is classify as categorical variable because variable is divided into two categories such as whether participant exercise 5 or more days a week or not.
Part b
For the given study, the response variable or dependent variable is given as frequency of colds. This variable is classified as quantitative variable because we measure the quantities or frequency of number of colds.
Part c
A confounding variable for this research study is given as incidence of upper respiratory tract infections that provides an alternative explanation for the lower frequency of colds among those who exercised 5 or more days per week, compared to those who were largely sedentary. This confounding variable is categorical in nature.
2. In a random sample of 100 people, the correlation between amount of daily exercise and weight was found to be –.21. What would be the likely effect on the absolute value of the correlation coefficient under the following circumstances? (Hint: would r be greater or smaller? Why?) a. The sample is restricted to people who weighed less than 180 pounds
Answer:
Correlation coefficient 'r' would be lower.
Step-by-step explanation:
Correlation is co movement relationship between two variables.
Correlation coefficient 'r' is positive, when variables move in same direction. 'r' is negative when variables move in opposite direction. So, 'r' lies between -1 (perfect negative correlation) & +1 (perfect positive correlation). High 'r' magnitude reflects strong correlation between the variables, Low 'r' reflects weak weak correlation between the variables.
Correlation studied between amount of daily exercise and weight : It is negative as exercise & weight are negatively correlated - more exercise, less weight & less exercise, more weight. 'r' is given = -0.21
If sample is restricted to people weighing less than 180 pounds : It would lead to fall in 'r'. Such because these low weight people are likely to have good natural metabolic rate, naturally slim body physique / figure. So, in their case, exercise & body weight are likely to be less (weakly) correlated than normal case.
PLEASE HELP!!!
Explain the difference between P(A|B) and P(A)and P(B) given that events A and B are independent events.
Answer:
for independent A and B, P(A|B) = P(A)
Step-by-step explanation:
The definition of conditional probability is ...
P(A|B) = P(A&B)/P(B)
When A and B are independent, ...
P(A&B) = P(A)·P(B)
so the conditional probability is ...
P(A|B) = (P(A)·P(B))/P(B) = P(A) . . . . . for independent A and B
In words, when A and B are independent, the probability of A given B is the same as the probability of A. That is, the probability of B has no effect on the probability of A.
Plz help me with my homework
Answer:
Option D, 72 cubic inches
Step-by-step explanation:
The formula for the volume of a rectangular prism is length*width*height, which in this case is 3*3*8=72 cubic inches, or option D. Hope this helps!
Answer: D) 72
Step-by-step explanation: To get the volume of the rectangular prism all you got do is multiply the width x length x height. Therefore:
3 x 3 x 8 = 72
The answer is D) 72
(Hope this helps)
A random sample of n = 16 professors from a university has been selected; salaries have been plotted on the following Q-Q plot. qqplot If we created a 95% confidence interval for salaries to be ($99,881, $171,172), how would we interpret that interval? Since n = 16 > 15, we can use the CLT to say we are 95% sure that all professors' salaries at this university are between $99,881 and $171,172. Since n = 16 > 15, we can use the CLT to say we are 95% sure the average of all professors' salaries at this university is between $99,881 and $171,172. We actually can't be 95% sure the average professor salary is in the interval, since the salaries are right-skewed and n = 16 < 30.
Answer:
The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance.
The conclusion we can make is that there is 95% of probability that the mean of the population (professor's average salary) is within $99,881 and $171,172.
Step-by-step explanation:
This is a case in which, from a sample os size n=16, a confidence interval is constructed.
The objective of the confidence interval is to give a range in which the real mean of the population is placed, with a degree of confidence given by the level of significance. In this case, the probability that the real mean is within the interval is 95%.
The table represents a linear function. Find the values of a, b, and c. Show your work.
x | y
a 7
3 8
5 9
7 b
c 11
Answer:
a = 1, b = 10, c = 9
Step-by-step explanation:
x is increasing by positive two from each number and y is increasing by 1 from each number.
mx+n=y
m*3+n=8
m*5+n=9
=>m*5+n-(m*3+n)=9-8
2m=1 => m=1/2
½ *3+ n =8
n=8-3/2
n=13/2
=> y=x/2 +13/2
y=(x+13)/2
7=(a+13)/2; a+13=14 => a=1
b=(7+13)/2; b=20/2; b=10
11=(c+13)/2, c+13=22 => c=9
Coach Riley needs eight new volleyballs. If the retail price for one ball is $20 at ALL SPORTS and the SPORT SHACK, which store should he buy from in order to pay the least amount? How much will he save?
Answer:
The way you worded this he should buy at either store because the price is 20 at both and he won't have any savings because they have the same price.
Step-by-step explanation:
Answer:
Well correct me if I am wrong but I think something is missing in this problem because I do not see another number to compare $20 to...
Researchers are studying two populations of wild horses living in the western regions of a country. In a random sample of 32 horses taken from the first population, the mean age of the sample was 21 years. In a random sample of 41 horses from the second population, the mean age of the sample was 19 years. Is the sampling distribution of the difference in sample mean ages approximately normal?
A Yes, because the two populations of wild horses can be modeled by a normal distribution.
B Yes, because the samples were selected at random.
C Yes, because the sample sizes are both greater than 30.
D No, because the populations are not normal.
E No, because the difference in sample mean ages was not 0.
Answer:
Correct option: (C) Yes, because the sample sizes are both greater than 30.
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample mean is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
For the first sample, the sample size of the sample selected is:
n₁ = 32 > 30
Ans for the second sample, the sample size of the sample selected is:
n₂ = 41 > 30
Both the samples selected are quite large.
So, the Central limit theorem can be used to approximate the distribution of of the two sample means.
Ans since the distribution of the two sample means follows a normal distribution, the difference of the two means will also follows normal distribution.
Thus, the correct option is (C).
C Yes, because the sample sizes are both greater than 30.
The following information should be considered;
Given that, [tex]n_1 = 32[/tex] and [tex]n_2 = 41[/tex]Here both sample size should be more than 30.By applying the central limit theorem, sampling distribution of difference should be normal. Therefore, the third option is correct.learn more; https://brainly.com/question/1368131?referrer=searchResults
NO CALCULATOR IS ALLOWED FOR THIS QUESTION.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.
Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
A particle moves along the l-axis so that its position at time t>0 is given by x(t)= (t^2 - 9)/(3t^2 + 8)
Show that the velocity of the particle at time t is given by v(t)=70t/(30t^2 + 8)^2
Answer:
We showed that if we have the position of the particle [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex] the velocity of the particle at time t is given by [tex]v(t)=\frac{70t}{\left(3t^2+8\right)^2}[/tex].
Step-by-step explanation:
Velocity is defined as the rate of change of position with respect to time.
[tex]v(x)=\frac{dx}{dt}[/tex]
To find velocity, we take the derivative of the position function [tex]x(t)= \frac{t^2 - 9}{3t^2 + 8}[/tex]
[tex]\mathrm{Apply\:the\:Quotient\:Rule}:\quad \left(\frac{f}{g}\right)'=\frac{f\:'\cdot g-g'\cdot f}{g^2}[/tex]
[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{\frac{d}{dt}\left(t^2-9\right)\left(3t^2+8\right)-\frac{d}{dt}\left(3t^2+8\right)\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]
Next, we find the values of [tex]\frac{d}{dt}\left(t^2-9\right)[/tex] and [tex]\frac{d}{dt}\left(3t^2+8\right)[/tex]
[tex]\frac{d}{dt}\left(t^2-9\right)=\frac{d}{dt}\left(t^2\right)-\frac{d}{dt}\left(9\right)=2t-0=2t[/tex]
[tex]\frac{d}{dt}\left(3t^2+8\right)=\frac{d}{dt}\left(3t^2\right)+\frac{d}{dt}\left(8\right)=6t+0=6t[/tex]
So,
[tex]\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{2t\left(3t^2+8\right)-6t\left(t^2-9\right)}{\left(3t^2+8\right)^2}[/tex]
Next, we expand [tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)[/tex]
[tex]2t\left(3t^2+8\right)-6t\left(t^2-9\right)=6t^3+16t-6t\left(t^2-9\right)=6t^3+16t-6t^3+54t=70t[/tex]
Therefore,
[tex]v(t)=\frac{d}{dt}\left(\frac{t^2-9}{3t^2+8}\right)=\frac{70t}{\left(3t^2+8\right)^2}[/tex]
This question lies in high school level Mathematics, more specifically in calculus. The process includes finding the derivative of a function x(t) to get v(t), which is the velocity of the particle. There appears to be an error in the provided equations in the question.
Explanation:The subject of this question falls under calculus, a branch of Mathematics, and the grade level would most likely be High School. The equation for the particle's position in terms of time x(t)=(t^2 - 9)/(3t^2 + 8) indicates the focus is on particle motion.
To find the velocity of a particle moving along a line at a given time, we find the derivative of the position function. This principle comes from the fact that velocity is the rate of change of position with respect to time. In this case, the derivative of the position function x(t) gives the velocity function v(t).
However, it seems there might be a mistake in the question because the derivative of x(t) is not v(t)=70t/(30t^2 + 8)^2. Please double-check the original problem to ensure the equations are correctly provided.
Learn more about Mathematics Derivatives here:https://brainly.com/question/15190681
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Find the circumference for the given situation below. Round your answer to the
nearest tenth. Use 3.14 for pi.
The world's tallest Ferris wheel is in Osaka, Japan, and stands 369 feet tall. Its wheel
has a diameter of 328 feet. Find circumference of the Ferris wheel.
Answer:
C = 1029.92 ft
Step-by-step explanation:
C = πd Use the equation for circumference
C = 3.14(328) Multiply
C = 1029.92 ft
If this answer is correct, please make me Brainliest!
Katelyn did a survey of 200 randomly selected gym members, and found that 72 of them are interested in yoga classes. The gym has 1,000 members. About how many gym members would be interested in yaga?
Answer:
360
Step-by-step explanation:
Divide by two on both numbers to get how many out of 100, or a percentage.
72 / 2 = 36
200 / 2 = 100
Multiply times ten to get 1000
100 x 10 = 1000
36 x 10 = 360
drag the correct step into order to evaluate 27- t x 3 for t = 6
Use PEMDAS and do the multiplication first.
Answer:
All steps below
Step-by-step explanation:
27 - t × 3
27 - 3t
t = 6
27 - 3(6)
27 - 18
9
a randon sample of 16 bookcases in one company have a mean height of 67.5 inches and a standard deviation of 2.1 inches. Construct a 99% confidence interval for the population standard deviation
Answer:
For 99% of confidence interval is 67.5±1.3524
Step-by-step explanation:
Given:
Mean height =67.5 inches
Standard deviation:2.1 inches
Z at 99%.
No of samples 16.
To find:
confidence interval
Solution:
We have formula for confidence interval,
=mean ±Z*{standard deviation/sqrt(no.of observation)}
Now
Z=99%
has standard value as ,
Z=2.576
Confidence interval= mean±Z{standard deviation/sqrt(No. of samples)}
=67.5±2.57{(2.1/sqrt(16)}
=67.5±2.576(2.1/4)
=67.5±1.3524
0.63 = how many hundredths
Answer:
There are 3 hundredths
Step-by-step explanation:
0.63
. tenths hundredths
There are 3 hundredths
At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the evening students is significantly different from 21. The average age of the students in the sample was 23 years. The population standard deviation is known to be 3.5 years. Determine whether or not the average age of the evening students is significantly different from 21. Use a 0.1 level of significance.
Answer:
[tex]z=\frac{23-21}{\frac{3.5}{\sqrt{49}}}=4[/tex]
[tex]p_v =2*P(z>4)=0.0000633[/tex]
When we compare the significance level [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.
Step-by-step explanation:
Data given and notation
[tex]\bar X=23[/tex] represent the sample mean
[tex]\sigma=3.5[/tex] represent the population standard deviation
[tex]n=49[/tex] sample size
[tex]\mu_o =21[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the average age of the evening students is significantly different from 21, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 21[/tex]
Alternative hypothesis:[tex]\mu \neq 21[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]z=\frac{23-21}{\frac{3.5}{\sqrt{49}}}=4[/tex]
P-value
Since is a two sided test the p value would be:
[tex]p_v =2*P(z>4)=0.0000633[/tex]
Conclusion
When we compare the significance level [tex]\alpha=0.1[/tex] we see that [tex]p_v<\alpha[/tex] so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.
Final answer:
To determine whether the average age of the evening students is significantly different from 21, we can conduct a hypothesis test using a z-test with a known population standard deviation.
Explanation:
To determine whether the average age of the evening students is significantly different from 21, we can conduct a hypothesis test.
First, we need to state our hypotheses:
Null hypothesis (H0): The average age of the evening students is equal to 21.
Alternative hypothesis (Ha): The average age of the evening students is not equal to 21.
Since the population standard deviation is known, we can use a z-test. We calculate the test statistic using the formula:
z = (sample mean - hypothesized mean) / (population standard deviation / sqrt(sample size))
Once we have the test statistic, we can compare it to the critical value at a significance level of 0.1. If the test statistic falls within the critical region, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
In this case, the test statistic is 2.8571, which falls outside the critical region. Therefore, we reject the null hypothesis and conclude that the average age of the evening students is significantly different from 21.