Answer:
Option B
Step-by-step explanation:
The data constitutes nominal scale of measurement when the observations can be classified into groups. For example, students are classified into groups on the basis of eye color. The numerical values can also be use in nominal scale for grouping. For example, the students can be categorize into 1,2 and 3 if they have brown, black and green eye color. But they have no numerical significance. Thus, data obtained from a nominal scale can be either numeric or non-numeric.
If v lies in the first quadrant and makes an angle π/3 with the positive x-axis and |v| = 4, find v in component form.
Answer:
v = <2, 2√3>
Step-by-step explanation:
Let v be the vector of form <x,y>
Since its determinant is |4|, then:
[tex]x^2 +y^2 =4^2=16[/tex]
If it makes a π/3 angle with the positive x-axis, then the tangent relationship yields:
[tex]tan(\pi/3) = 1.732=\frac{y}{x}\\3x^2=y^2[/tex]
Replacing in the first equation:
[tex]x^2 +3x^2 =16\\x=2\\y=\sqrt{16-4}\\ y=2\sqrt 3[/tex]
Therefore, v can be represented in component form as v = <2, 2√3>.
The vector [tex]v[/tex] that lies in the first quadrant, makes an angle of [tex]\frac{\pi}{3}[/tex] with the positive x-axis, and has a magnitude of [tex]4[/tex] is:
[tex]v = 2i + 2\sqrt{3}j[/tex]
To find the vector v in component form, we start by understanding the relationships between the angle, magnitude, and components of a vector in the Cartesian coordinate system.
Given Data:
Angle with positive x-axis, [tex]heta = \frac{\pi}{3}[/tex]Magnitude of vector, [tex]|v| = 4[/tex]Vector Components:
In the first quadrant, the components of vector [tex]v[/tex] can be calculated using the following formulas:
Calculating Components:
For the x-component:
[tex]v_x = 4 \cdot \cos\left(\frac{\pi}{3}\right)[/tex]
The cosine of [tex]\frac{\pi}{3}[/tex] is [tex]\frac{1}{2}[/tex], so:
[tex]v_x = 4 \cdot \frac{1}{2} = 2[/tex]
For the y-component:
[tex]v_y = 4 \cdot \sin\left(\frac{\pi}{3}\right)[/tex]
The sine of [tex]\frac{\pi}{3}[/tex] is [tex]\frac{\sqrt{3}}{2}[/tex], so:
[tex]v_y = 4 \cdot \frac{\sqrt{3}}{2} = 2\sqrt{3}[/tex]
Resulting Vector:
Thus, the vector [tex]v[/tex] in component form is:
[tex]v = v_x i + v_y j = 2i + 2\sqrt{3} j[/tex]
You’re trying to calculate the conversion rate on one of your forms. 600 people visited your landing page, but only 50 visitors submitted the form. What is the conversion rate of your form?
Answer: [tex]\dfrac{1}{12}[/tex] or 8.33%
Step-by-step explanation:
The conversion rate is given by :-
Conversion rate =(number of conversions ) ÷( total number of visitors)
As per given , we have
600 people visited your landing page, but only 50 visitors submitted the form..
i.e . Total number of visitors= 600
Number of conversions = 50
Then , the conversion rate would be:-
Conversion rate = (50) ÷ 600 [tex]=\dfrac{50}{600}=\dfrac{1}{12}[/tex]
Hence, the conversion rate of your form = [tex]\dfrac{1}{12}[/tex]
In percentage , the conversion rate= [tex]\dfrac{1}{12}\times100=8.33\%[/tex]
The conversion rate is calculated by dividing the number of form submissions by the total number of visitors to the page and multiplying by 100. In this case, the conversion rate is 8.33%.
Explanation:The conversion rate is central to tracking the effectiveness of your landing page. It's calculated by dividing the number of conversions (in this case, form submissions) by the total number of visitors to the page, then multiplying by 100 to get a percentage. In this case, the formula would look like this: (Number of forms submitted / Total visitors) x 100.
Plugging in your numbers, we get: (50 / 600) x 100 = 8.33%. So, the conversion rate of your form was 8.33%.
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The price of gas at the local gas station was $5.00 per gallon a month ago; today it is $5.50 per gallon. Suppose the price of gas goes down by the same percentage amount over the next month as it went up over the last month. What will the price of gas be then?
$4.95
Step-by-step explanation:
Initial price of gas was $5.00 a month ago
Today price of a gas is $5.50 per gallon
Increase in price= $5.50-$5.00=$0.50
%increase= 0.50/5.00 *100 =10%
Current price= $5.50
decrease current price by 10% is by multiplying the current price by 90%
90/100 * 5.50 = $4.95
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A measurement of fluoride ion in tooth paste from 5 replicate measurements delivers a mean of 0.14 % and a standard deviation of 0.05 %. What is the confidence interval at 95 % for which we assume that it contains the true value?
The confidence interval for the mean fluoride ion concentration in toothpaste at a 95% confidence level is [tex]$0.14 \pm 0.06\%$[/tex].
To calculate the confidence interval for the mean fluoride ion concentration in toothpaste, we use the formula:
[tex]\[ \text{Confidence interval} = \text{Mean} \pm \left( \text{Critical value} \times \frac{\text{Standard deviation}}{\sqrt{\text{Sample size}}} \right) \][/tex]
Given:
- Mean (sample mean) = 0.14%
- Standard deviation = 0.05%
- Sample size (replicate measurements) = 5
- Confidence level = 95%
We need to find the critical value corresponding to a 95% confidence level. Since the sample size is small (n < 30), we use a t-distribution and degrees of freedom [tex]\(df = n - 1 = 5 - 1 = 4\)[/tex].
From the t-distribution table or a statistical calculator, the critical value for a 95% confidence level with 4 degrees of freedom is approximately 2.776.
Now, we can calculate the confidence interval:
[tex]\[ \text{Confidence interval} = 0.14 \pm \left( 2.776 \times \frac{0.05}{\sqrt{5}} \right) \][/tex]
[tex]\[ \text{Confidence interval} = 0.14 \pm \left( 2.776 \times \frac{0.05}{\sqrt{5}} \right) \]\[ \text{Confidence interval} = 0.14 \pm 0.06 \][/tex]
So, the confidence interval is [tex]$0.14 \pm 0.06\%$[/tex].
Therefore, the correct option is [tex]$0.14( \pm 0.06) \%$[/tex].
Complete Question:
A measurement of fluoride ion in tooth paste from 5 replicate measurements delivers a mean of 0.14 % and a standard deviation of 0.05 %. What is the confidence interval at 95 % for which we assume that it contains the true value?
[tex]$0.14( \pm 0.06) \%$[/tex]
[tex]$0.14( \pm 6.2) \%$[/tex]
[tex]$0.14( \pm 0.07) \%$[/tex]
[tex]$0.14( \pm 0.69) \%$[/tex]
Find the
(a) mean,
(b) median,
(c) mode, and
(d) midrange for the given sample data.
An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1 equals smooth dash yellow1=smooth-yellow, 2 equals smooth dash green2=smooth-green, 3 equals wrinkled dash yellow3=wrinkled-yellow, and 4 equals wrinkled dash green4=wrinkled-green. Do the results make sense?
11 44 44 44 22 11 44 33 11 44 44 33 33 11
(a) The mean phenotype code is 2.82.8. (Round to the nearest tenth as needed.)
(b) The median phenotype code is 33. (Type an integer or a decimal.)
(c) Select the correct choice below and fill in any answer boxes within your choice.
A. The mode phenotype code is 44. (Use a comma to separate answers as needed.)
B. There is no mode.
(d) The midrange of the phenotype codes is 2.52.5. (Type an integer or a decimal.)
Do the measures of center make sense?
A. Only the mean, median, and mode make sense since the data is numerical.
B. Only the mean, median, and midrange make sense since the data is nominal.
C. Only the mode makes sense since the data is nominal.
D. All the measures of center make sense since the data is numerical.
Answer:
a) Mean = 2.8
b) Median = 3
c) Mode = 4
d) Mid range = 2.5
e) Option C) Only the mode makes sense since the data is nominal.
Step-by-step explanation:
We are given the following data set in the question:
1, 4, 4, 4, 2, 1, 4, 3, 1, 4, 4, 3, 3, 1
a) Mean
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{39}{14} = 2.78 \approx 2.8[/tex]
b) Median
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Sorted data:
1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4
[tex]\text{Median} = \dfrac{7^{th}+8^{th}}{2} = \dfrac{3+3}{2} = 3[/tex]
c) Mode
Mode is the observation with highest frequency. Since 4 appeared maximum time
Mode = 4
d) Mid range
It is the average of the smallest and largest observation of data.
[tex]\text{Mid Range} = \dfrac{1+4}{2} = 2.5[/tex]
e) Measure of center
Option C) Only the mode makes sense since the data is nominal.
Evaluate the function
k
(
x
)
=
−
x
2
+
6
k
(
x
)
=
-
x
2
+
6
at two different inputs and state the corresponding points.
Answer:Evaluate the function
k
(
x
)
=
−
x
2
+
6
k
(
x
)
=
-
x
2
+
6
at two different inputs and state the corresponding points.
Step-by-step explanation:
In a three-digit positive integer , if the hundreds digit cannot be 1 and the neighbor digits cannot be repetition, how many possibilities of these integers? A. 729 B. 504 C. 576 D. 448 E. 648
Answer:
Option (E) 648
Step-by-step explanation:
the 3 digit number can be represented by the blanks as " _ _ _ "
Now,
we have 10 choices ( i.e 0,1,2,3,4,5,6,7,8,9) available for each place in the blank if no condition is applied.
For the hundreds digit, using the conditions given in the question, we have 8 choices left
as 1 and 0 cannot be included in the hundreds place.
for the tens place
we will have 9 choices left out of 10 ( as 1 choice is less because we cannot have same number as on the hundred place )
similarly, for the ones place we have 9 choices left out of 10 ( as 1 choice is less because we cannot have same number as on the tens place )
Therefore,
Total possibilities = 8 × 9 × 9 = 648
Hence,
Option (E) 648
Find the equation of the line tangent to the graph at y=e^x at x =a
Answer:
find derivative of function
sub in x value of point to find gradient of tangent
put gradient into y=(gradient)x+c
Sub in point and solve for c
you have found the equation of the tangent.
Answer: Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line
Step-by-step explanation:
Let X1, X2, ... , Xn be a random sample from N(μ, σ2), where the mean θ = μ is such that −[infinity] < θ < [infinity] and σ2 is a known positive number. Show that the maximum likelihood estimator for θ is θ^ = X.
Answer:
[tex] l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)[/tex]
And then the maximum occurs when [tex] l'(\theta) = 0[/tex], and that is only satisfied if and only if:
[tex] \hat \theta = \bar X[/tex]
Step-by-step explanation:
For this case we have a random sample [tex] X_1 ,X_2,...,X_n[/tex] where [tex]X_i \sim N(\mu=\theta, \sigma)[/tex] where [tex]\sigma[/tex] is fixed. And we want to show that the maximum likehood estimator for [tex]\theta = \bar X[/tex].
The first step is obtain the probability distribution function for the random variable X. For this case each [tex]X_i , i=1,...n[/tex] have the following density function:
[tex] f(x_i | \theta,\sigma^2) = \frac{1}{\sqrt{2\pi}\sigma} exp^{-\frac{(x-\theta)^2}{2\sigma^2}} , -\infty \leq x \leq \infty[/tex]
The likehood function is given by:
[tex] L(\theta) = \prod_{i=1}^n f(x_i)[/tex]
Assuming independence between the random sample, and replacing the density function we have this:
[tex] L(\theta) = (\frac{1}{\sqrt{2\pi \sigma^2}})^n exp (-\frac{1}{2\sigma^2} \sum_{i=1}^n (X_i-\theta)^2)[/tex]
Taking the natural log on btoh sides we got:
[tex] l(\theta) = -\frac{n}{2} ln(\sqrt{2\pi\sigma^2}) - \frac{1}{2\sigma^2} \sum_{i=1}^n (X_i -\theta)^2[/tex]
Now if we take the derivate respect [tex]\theta[/tex] we will see this:
[tex] l'(\theta) = \frac{1}{\sigma^2} \sum_{i=1}^n (X_i -\theta)[/tex]
And then the maximum occurs when [tex] l'(\theta) = 0[/tex], and that is only satisfied if and only if:
[tex] \hat \theta = \bar X[/tex]
In the auditorium, there are 21 seats in the first row and 29 seats in the second row. Ths number of seats in a row continues to increase by 8 with each additional row.
Answer:
813 seats
Step-by-step explanation:
Given that,
In the auditorium, the number of seats in the 1st row = 21
In the auditorium, the number of seats in the 2nd row = 29
Therefore, the increasing number of seats in each of the row = 8.
According to the question,
The number of seats in a row continues to increase by 8 seats with each additional row. For example, 29, 37, 45 etc.
To find the number of seats in the 100th row, we have to use statistical formula.
As 21 is the total seats in the 1st row, and there is an increase of 8 seats, the formula should be = 21 + (n - 1) × 8
we have to deduct 1 so that we get 99th rows seat numbers as we have to add 21 with that to find the 100th number row.
As the question is to determine the number of seats in the 100th row, therefore, n = 100.
The number of seats in the 100th row = 21 + (100 - 1) × 8 = 21 + 99 × 8
= 21 + 792 = 813 seats.
An analyst for a large credit card company is going to conduct a survey of customers to examine their household characteristics. One of the variables the analyst will record is the amount of purchases on the card last month. The analyst knows that for all customers that have this card the average was $1622. In the sample of 500 customers the average amount of purchases last month was $1732. In this example the number 1732 is
Answer:
We can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.
Step-by-step explanation:
Previous concepts
A statistic or sample statistic "is any quantity computed from values in a sample", for example the sample mean, sample proportion and standard deviation
A parameter is "any numerical quantity that characterizes a given population or some aspect of it".
Solution to the problem
For this case the analyst knows that from previous records that the mean for all the customers (that represent the population of interest) is [tex] \mu = 1622[/tex]
He have a random sample of n =500 customers from the previous month and he knows that 1732 represent the sample mean for the selected customers calculated from the following formula:
[tex] \bar X = \frac{\sum_{i=1}^{500} X_i}{500}= 1732[/tex]
So on this case we can conclude that the value of 1732 is a statistic who represent the sample selected. And the value of 1622 represent the population mean from all the customers with the previous data.
Final answer:
The number 1732 represents the sample mean of monthly credit card purchases for a sample of 500 customers, distinct from the population mean of $1622.
Explanation:
The number 1732 in the scenario given refers to the sample mean, which is the average amount of money spent on purchases last month by the 500 customers in the sample. This contrasts with the population mean, which the analyst knows to be $1622 for all customers holding the credit card. The difference between the sample mean and the population mean can be a subject of further statistical analysis to understand customer behavior and spending patterns better.
Fill in the blanks using a variable or variables to rewrite the given statement. Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? a. Is there an integer n such that n has___________ b. Does there exist______such that if n is divided by 5 the remainder is 2 and if? Note: There are integers with this property. Can you think of one?
Answer:
Step-by-step explanation:
Yes, integers like 27,57,87,117,.... and so on gives a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6.
Yes, there is an integer that has a remainder of 2 when divided by 5 and a remainder of 3 when divided by 6. One example of such an integer is 23.
Explanation:Let's use variables to rewrite the given statement. We can represent the integer as 'n', and the two remainders as 'r1' and 'r2'.
The given statement is: Is there an integer that has a remainder of 2 when divided by 5 and a remainder of 3 when divided by 6?Rewriting it using variables, we have: Is there an integer 'n' such that 'n' has a remainder of 'r1' when divided by 5 and a remainder of 'r2' when divided by 6?Therefore, the rewritten statement is: Is there an integer 'n' such that 'n' has a remainder of 2 when divided by 5 and a remainder of 3 when divided by 6?
Yes, such integers exist. One example is 23. When 23 is divided by 5, the remainder is 3, and when it is divided by 6, the remainder is also 3.
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The initial value of a quantity Q (at year t = 0) is 112.8 and the quantity is decreasing by 23.4% per year. a) Write a formula for Q as a function of t. 2 Edit b) What is the value of Q when t-10? Round to three decimal places.
Answer:
a) [tex]Q(t) = 112.8*(0.766)^{t}[/tex]
b) When t = 10, Q = 7.845.
Step-by-step explanation:
The value of a quantity after t years is given by the following formula:
[tex]Q(t) = Q_{0}(1 + r)^{t}[/tex]
In which [tex]Q_{0}[/tex] is the initial quantity and r is the rate that it changes. If it increases, r is positive. If it decreases, r is negative.
a) Write a formula for Q as a function of t.
The initial value of a quantity Q (at year t = 0) is 112.8.
This means that [tex]Q_{0} = 112.8[/tex].
The quantity is decreasing by 23.4% per year.
This means that [tex]r = -0.234[/tex]
So
[tex]Q(t) = 112.8*(1 - 0.234)^{t}[/tex]
[tex]Q(t) = 112.8*(0.766)^{t}[/tex]
b) What is the value of Q when t = 10?
This is Q(10).
[tex]Q(t) = 112.8*(0.766)^{t}[/tex]
[tex]Q(t) = 112.8*(0.766)^{10} = 7.845[/tex]
When t = 10, Q = 7.845.
What are the factors of the function represented by this graph? the graph of a quadratic function y = (1/4)(x + 4)(x - 8) with a maximum value at the point (2,9) A. (x − 4) and (x − 8) B. (x − 4) and (x + 8) C. (x + 4) and (x − 8) D. (x + 4) and (x + 8)
Answer:
option C. (x + 4) and (x − 8)
Step-by-step explanation:
A factor is one of the linear expressions of a single-variable of the polynomial.
Given: y = (1/4)(x + 4)(x - 8)
When y = 0
∴ (1/4)(x + 4)(x - 8) = 0 ⇒ multiply both sides by 4
∴ (x + 4)(x - 8) = 0
So, the factors of the function are (x+4) and (x-8)
The answer is option C. (x + 4) and (x − 8)
A manufacturing company is shipping a certain number of orders that need to weigh between 187 and 188 pounds in order to ship. Use the dot plot data below to answer the following questions.
187, 187.1, 187.2, 187.3, 187.4, 187.5, 187.6, 187.7, 187.8 ,187.9 ,188
1. How many orders did the company ship between 196 and 197 pounds?
2. What was the most common order weight?
3. Was the average weight for this sample of orders closer to 196 pounds or 197 pounds?
The dot plot shows the distribution of order weights. There were no orders between 196 and 197 pounds. The most common order weight was 187.5 pounds, and the average weight was closer to 196 pounds.
Explanation:1. To find the number of orders between 196 and 197 pounds, we need to look at the dot plot. From the given data, there are no orders between 196 and 197 pounds.
2. The most common order weight from the dot plot is 187.5 pounds.
3. To determine if the average weight is closer to 196 or 197 pounds, we need to calculate the mean of the data. The mean weight is calculated as the sum of the weights divided by the total number of weights. In this case, the mean weight is closer to 196 pounds.
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Find the surface area
Answer:
Step-by-step explanation:
3. the diagram has 3 rectangles, 2 triangles
the surface area is the area of each shape
for the first rectangle = length x breadth = 8 x 6 = 48
for the second rectangle = length x breath = 6 x 6 = 36
for the third rectangle = length x breath = 6 x 6 = 36
for the triangles
(base x height )/2 = (8 x 4.5) /2 = 4 x 4.5 = 18
Surface Area = 48 + 18 + 36 + 36 = 138
4. there are 4 identical rectangles and a base rectangle
4 x (5 x3 ) + ( 5 x5) = 4 x 15 + 25 = 60 + 25 = 85 ft
5. there are 2 triangles of 6 x 8 and a rectangle of 10 x 8
surface area = 2 x( (base x height)/2) + 10x8
2 x ((6 x8) /2 ) + 80 = 2 x (48/2) + 80 = 48 + 80 = 128ft
Rationalize denominator when a monomial is in the denominator.Please show steps
Answer:
[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]
Step-by-step explanation:
step 1;-
Given [tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} }[/tex]
now you have rationalizing denominator (i.e monomial) with
[tex]\frac{\sqrt[3]{5 x^2} }{\sqrt[3]{12 y^2 z} } X \frac{\sqrt[3]{(12 y^2 z)^{2} } }{\sqrt[3]{(12 y^2 z)^2} }[/tex]
By using algebraic formula is
[tex]\sqrt{ab} = \sqrt{a} \sqrt{b}[/tex]......(a)now [tex]\frac{\sqrt[3]{5 x^2)(12 y^2 z)^2} }{\sqrt[3]{12 y^2 z)(12 y^2 z)^2} }[/tex][tex]\frac{\sqrt[3]{720 x^2 y^4 z^2} }{\sqrt[3]{(12 y^2 z)^{3} } }[/tex]....(1)again using Formula [tex]\sqrt[n]{a^{n} } =a[/tex]now simplification , we get denominator function
[tex]\frac{\sqrt[3]{720 x^2 y^4 z^2} }{12 y^2 z}[/tex]again you have to simplify numerator term
[tex]\frac{\sqrt[3]{2^3 y^3 90 (x^2 y z^2)} }{12 y^2 z}[/tex]now simplify
[tex]\frac{2 y\sqrt[3]{90 x^2 y z^2} }{12 y^2 z}[/tex]cancelling y and 2 values
we get Final answer
[tex]\frac{\sqrt[3]{90 x^2 y z^2} }{6 y z}[/tex]
g Determine if the statement is true or false. A linear system with three equations and five variables must be consistent. True False Justify your answer.
Final answer:
A linear system with three equations and five variables does not have to be consistent. The statement 'A linear system with three equations and five variables must be consistent' is false
Explanation:
A linear system with three equations and five variables does not have to be consistent. In fact, it is possible for the system to be inconsistent.
The statement that a linear system with three equations and five variables must be consistent is False. In linear algebra, the consistency of a system depends on whether there are any contradictions among the equations. For a system to be consistent, it must have at least one solution.
For example, consider the system of equations:
x + y + z = 5
2x + 3y + 4z = 10
5x + 2y + 3z = 8
Since there are more variables than equations, there will be infinitely many solutions if the system is consistent. But if the system is inconsistent, there will be no solution.
Therefore, the statement 'A linear system with three equations and five variables must be consistent' is false
The National Center for Education Statistics reported that 47% of college students work to pay for tuition and livingexpenses. Assume that a sample of 450 college students was used in the study.a. Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition andliving expenses.b. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition andliving expenses.c What happens to the margin of error as the confidence is increased from 95% to 99%?
Answer:
a) The 95% confidence interval for the population proportion of college students who work to pay for tuition andliving expenses is (0.4239, 0.5161).
b) The 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses is (0.4094, 0.5306).
c)The margin of error increases as the confidence level increases.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 450, p = 0.47[/tex]
a) Provide a 95% confidence interval for the population proportion of college students who work to pay for tuition andliving expenses.
95% confidence interval
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 1.96\sqrt{\frac{0.47*0.53}{450}} = 0.4239[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 1.96\sqrt{\frac{0.47*0.53}{450}}{119}} = 0.5161[/tex]
The 95% confidence interval for the population proportion of college students who work to pay for tuition andliving expenses is (0.4239, 0.5161).
b. Provide a 99% confidence interval for the population proportion of college students who work to pay for tuition andliving expenses.
95% confidence interval
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 - 2.575\sqrt{\frac{0.47*0.53}{450}} = 0.4094[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.47 + 2.575\sqrt{\frac{0.47*0.53}{450}}{119}} = 0.5306[/tex]
The 99% confidence interval for the population proportion of college students who work to pay for tuition and living expenses is (0.4094, 0.5306).
c What happens to the margin of error as the confidence is increased from 95% to 99%?
The margin of error is the subtraction of the upper end by the lower end of the interval, divided by 2. So
95% confidence interval
[tex]M = \frac{(0.5161 - 0.4239)}{2} = 0.0461[/tex]
99% confidence interval
[tex]M = \frac{(0.5306 - 0.4094)}{2} = 0.0606[/tex]
The margin of error increases as the confidence level increases.
What is the most plausible value for the correlation between spending on tobacco and spending on alcohol? 0.99 − 0.50 −0.50 0.80 0.08
Answer:
Option c) 0.80
Step-by-step explanation:
We have to approximate the most possible correlation between spending on tobacco and spending on alcohol.
Correlation is a technique that help us to find or define a relationship between two variables.A positive correlation means that an increase in one quantity leads to an increase in another quantity A negative correlation means with increase in one quantity the other quantity decreases. Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship. Values between 0 and -0.3 tells about a weak negative linear relationship, values between -0.3 and -0.7 shows a moderate negative correlation and a correlation value of of -0.7 and -1.0 states a strong negative linear relationship.a) 0.99
This shows almost a perfect straight line relationship between spending on tobacco and spending on alcohol. Thus, this cannot be the right correlation as the relationship between spending on tobacco and spending on alcohol is not so strong.
b)-0.50
This shows a negative relation between spending on tobacco and spending on alcohol which cannot be true as they share a positive relation.
c) 0.80
This correlation shows a strong positive correlation between spending on tobacco and spending on alcohol which is correct because the relationship between spending on tobacco and spending on alcohol is positive
d)0.08
This correlation shows a very weak positive correlation between spending on tobacco and spending on alcohol which cannot be true.
In a survey of 246 people, the following data were obtained relating gender to political orientation:
Republican (R) Democrat (D) Independent (I) Total
Male (M) 54 45 28 127
Femal (F) 44 55 20 119
Total 98 100 48 246
A person is randomly selected. What is the probability that the person is:
a) Male given that the person is a Democrat?
b) Republican given that the person is Male?
c) Female given that the person is an Independent?
Answer:
a) 45% probability that the person is a male, given that he is a democrat.
b) 42.52% probability that the person is a republican given that he is male.
c) 41.67% that an Independent person is a female.
Step-by-step explanation:
A probability is the number of desired people(outcomes) divided by the total number of people(outcomes).
Example.
In a sample of 50 people, 30 are Buffalo Bills fans. The probability that a randomly selected person is a Buffalo Bills is 30/50 = 0.6 = 60%.
So
a) Male given that the person is a Democrat?
There are 100 Democrats. Of them, 45 are male and 55 are female.
So there is a 45/100 = 0.45 = 45% probability that the person is a male, given that he is a democrat.
b) Republican given that the person is Male?
There are 127 males. Of those, 54 are Republican.
So there is a 54/127 = 0.4252 = 42.52% probability that the person is a republican given that he is male.
c) Female given that the person is an Independent?
There are 48 independent people. Of those, 20 are female.
So there is a 20/48 = 0.4167 = 41.67% that an Independent person is a female.
The probabilities that a randomly selected individual is: a) a male Democrat is 0.45, b) a male Republican is approximately 0.425, and c) a female Independent is approximately 0.417.
Explanation:The subject of your question is probability in mathematics. Given the data of a survey, where a person is randomly selected from a group of 246 people, we are asked to find the probability that the person is:
a Male given that the person is a Democrat a Republican given that the person is Male a Female given that the person is an Independent
For a), the total number of Democrats is 100, and out of these, 45 are males. So the probability is 45/100 = 0.45.
For b), the total number of males is 127, and out of these, 54 are Republicans. So the probability is 54/127 ≈ 0.425.
For c), the total number of Independents is 48, and out of these, 20 are females. So, the probability is 20/48 ≈ 0.417.
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Which of the following must be true?
Answer:
cos 38° = 17/c
Step-by-step explanation:
in the triangle shown
the sum of angles in a triangle is 180°
its a right angle triangle meaning one of the angles is 90°
the other part is 52°
the third part is described as x
90° + 52° + x = 180° ( sum of angles )
142° + x = 180°
x = 180 - 142 = 38°
cos 38° = adjacent/hypothenus = 17/c
cos 38° = 17/c
You determine there is a regression. Can you immediately claim that one certain way?
a. No, you must first decide if the relationship is positive or negative.
b. No, the correlation would need to be a perfect linear relationship to be sure.
c. Yes, a strong linear relationship implies causation between the two variables.
d. No, you should examine the situation to identify lurking variables that may be influencing both variables
Answer:
d. No, you should examine the situation to identify lurking variables that may be influencing both variables
Step-by-step explanation:
Hello!
Finding out that there is a regression between two variables is not enough to claim that there is a causation relationship between the two of them. First you have to test if other factors are affecting the response variable, if so, you have to control them or test how much effect they have. Once you controled all other lurking variables you need to design an experiment, where only the response and explanatory variables are left uncontroled, to learn if there is a regression and its strenght.
If after the experiment, you find that there is a significally strog relationship between the variables, then you can imply causation between the two of them.
I hope it helps!
a mechanical system is governed by the following differential equation what is the homogeneous solution
d^2y/dt^2 + 6 dy/dt + 9y = 4e^- t
The ODE has characteristic equation
[tex]r^2+6r+9=(r+3)^2=0[/tex]
with roots [tex]r=-3[/tex], and hence the characteristic solution
[tex]y_c=C_1e^{-3t}+C_2te^{-3t}[/tex]
For the particular solution, assume an ansatz of [tex]y_p=ae^{-t}[/tex], with derivatives
[tex]\dfrac{\mathrm dy_p}{\mathrm dt}=-ae^{-t}[/tex]
[tex]\dfrac{\mathrm d^2y_p}{\mathrm dt^2}=ae^{-t}[/tex]
Substituting these into the ODE gives
[tex]ae^{-t}-6ae^{-t}+9ae^{-t}=4ae^{-t}=4e^{-t}\implies a=1[/tex]
so that the particular solution is
[tex]\boxed{y(t)=C_1e^{-3t}+C_2te^{-3t}+e^{-t}}[/tex]
The number of students enrolled at a college is 15,000 and grows 4% each year. the percentage rate of change is 4%, so the growth factor b is
Answer:
The growth factor b is 1.04
Step-by-step explanation:
we know that
In this problem we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
y ---> is the number of students enrolled at a college
x ----> the number of years
a is the initial value or y-intercept
b is the growth factor
b=(1+r)
r is the rate of change
we have
[tex]a=15,000\ students[/tex]
[tex]r=4\%=4/100=0.04[/tex]
[tex]b=1+0.04=1.04[/tex]
therefore
The exponential function is equal to
[tex]y=15,000(1.04^x)[/tex]
How many different 7-letter permutations can be formed from 5 identical H's and two identical T's
Answer:
21
Step-by-step explanation:
7! / (5! x 2!) = 42/2 = 21
other explanation:
TTHHHHH THTHHHH THHTHHH THHHTHH THHHHTH THHHHHT ... 6
HTTHHHH HTHTHHH ........................................................................................... 5
HHTTHHH HHTHTHH ............................................................................................4
HHHTTHH HHHTHTH .............................................................................................3
HHHHTTH HHHHTHT .............................................................................................2
HHHHHTT ...................................................................................................................1
6+5+4+3+2+1 = 21
The number of different ways should be 21.
Calculation of no of different ways:Since there is 7-letter permutations can be formed from 5 identical H's and two identical T's
So,
[tex]= 7! \div (5! \times 2!) \\\\= 42 \div 2[/tex]
= 21
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In the envelope game, there are two players and two envelopes. One of the envelopes is marked ''player 1 " and the other is marked "player 2." At the beginning of the game, each envelope contains one dollar. Player 1 is given the choice between stopping the game and continuing. If he chooses to stop, then each player receives the money in his own envelope and the game ends. If player 1 chooses to continue, then a dollar is removed from his envelope and two dollars are added to player 2's envelope. Then player 2 must choose between stopping the game and continuing. If he stops, then the game ends and each player keeps the money in his own envelope. If player 2 elects to continue, then a dollar is removed from his envelope and two dollars are added to player 1 's envelope. Play continues like this, alternating between the players, until either one of them decides to stop or k rounds of play have elapsed. If neither player chooses to stop by the end of the kth round, then both players obtain zero. Assume players want to maximize the amount of money they earn.
(a) Draw this game's extensive-form tree for k = 5.
(b) Use backward induction to find the subgame perfect equilibrium.
(c) Describe the backward induction outcome of this game for any finite integer k.
Answer:
Step-by-step explanation:
a) The game tree for k = 5 has been drawn in the uploaded picture below where C stands for continuing and S stands for stopping:
b) Say we were to use backward induction we can clearly observe that stopping is optimal decision for each player in every round. Starting from last round, if player 1 stops he gets $3 otherwise zero if continues. Hence strategy S is optimal there.
Given this, player 2’s payoff to C is $3, while stopping yields $4, so second player will also chooses to stop. To which, player 1’s payoff in k = 3 from C is $1 and her payoff from S is $2, so she stops.
Given that, player 2 would stop in k = 2, which means that player 1 would stop also in k = 1.
The sub game perfect equilibrium is therefore the profile of strategies where both players always stop: (S, S, S) for player 1, and (S, S) for player 2.
c) Irrespective of whether both players would be better off if they could play the game for several rounds, neither can credibly commit to not stopping when given a chance, and so they both end up with small payoffs.
i hope this helps, cheers
Final answer:
The subgame perfect equilibrium of the envelope game for any finite integer k is that both players will choose to stop in the final round (k) and each player will keep their own money.
Explanation:
Extensive-form tree for k = 5:
Backward Induction:
To find the subgame perfect equilibrium, we start from the last round (round 5) and work our way backwards: 1. In round 5, both players have the choice to stop or continue. Since both players want to maximize their earnings, they will both choose to stop, resulting in each player keeping their own money. 2. In round 4, player 2 knows that player 1 will choose to stop in round 5. Therefore, player 2 will choose to stop in round 4, resulting in each player keeping their money. 3. In round 3, player 1 knows that player 2 will choose to stop in round 4. Therefore, player 1 will choose to stop in round 3, resulting in each player keeping their money. 4. In rounds 2 and 1, both players have the choice to stop or continue. Since both players want to maximize their earnings and they know that the other player will choose to stop in the previous rounds, they will both choose to stop, resulting in each player keeping their money.
Backward Induction Outcome for Any Finite Integer k:
Based on the backward induction analysis, the outcome of the game for any finite integer k is that both players will choose to stop in the final round (k) and each player will keep their own money. This outcome is the subgame perfect equilibrium of the game, as it represents the strategy that maximizes the earnings for both players.
The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions. The following costs are for a sample of six cars:
$800, $750, $900, $950, $1100, $1050.
1. What is the five-number summary of the total damage suffered for this sample of cars?
Answer: [tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]
Step-by-step explanation:
The five -number summary consists of five values :
Minimum value , First quartile [tex](Q_1)[/tex] , Median , Third Quartile [tex](Q_3)[/tex] , Maximum value.
Given : The Insurance Institute for Highway Safety publishes data on the total damage caused by compact automobiles in a series of controlled, low-speed collisions.
The following costs are for a sample of six cars:
$800, $750, $900, $950, $1100, $1050.
Arrange data in increasing order :
$750,$800, $900, $950, $1050, $1100
Minimum value = $750
Maximum value = $1100
Median = middle most term
Since , total observation is 6 (even) , so Median = Mean of two middle most values ($900 and $950).
i.e. Median[tex]=\dfrac{900+950}{2}=\$925[/tex]
First quartile [tex](Q_1)[/tex] = Median of lower half ($750,$800, $900)
= $800
, Third Quartile [tex](Q_3)[/tex] = Median of upper half ($950, $1050, $1100)
= $1050
Hence, the five-number summary of the total damage suffered for this sample of cars will be :
[tex]Min : $750\ ,\ Q_1= \$800\ ,\ Median : \$925\ ,\ Q_3=\$1050\ ,\ Max: \$1100[/tex]
The structure ABECD is loaded with P = 100 lbs and F = 125 lbs. Determine the internal loads (forces and moments) at section E, which is mid‐way between points B and C.
Answer:
P = 100 lbs in tension
F = 125 lbs in shear force downward direction
Moments are: 50 lb-ft and 125 lb-ft both in counter clockwise direction
Step-by-step explanation:
Forces
If we consider the entire structure as a system with two external forces P and F acting on it.
Translating these forces at point E,
Hence point E experiences the following forces:
P = 100 lbs in tension
F = 125 lbs in shear force
Moments
The bending moments are caused by the forces acting at respective offsets from point E
P = 100 lbs causes a bending moment of Mp = 100 lbs * (6/12) ft = 50 lb-ft
F = 125 lbs causes a bending moment of Mf = 125 lbs*(12/12)ft = 125 lb-ft
Moments are: 50 lb-ft and 125 lb-ft
The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate pa-rameterλfor C-14.
Answer:
λ = 1.3252 x 10⁻⁴
Step-by-step explanation:
Since we are already given the half-life, the decay expression can be simplified as:
[tex]N(t) = N_0*e^{-\lambda t}\\\frac{N(half-life)}{N_0}=0.5[/tex]
For a half-life of t =5230 years:
[tex]0.5 = e^{(-\lambda t)} \\ln(0.5) = -\lambda * 5230\\\lambda = 1.3252*10^{-4}[/tex]
The decay-rate parameter λ for C-14 is 1.3252 x 10⁻⁴