HELP!!!!!!!!!!!!
A random number generator is used to create a real number between 0 and 1, equally likely to fall anywhere in this interval of values. (For the instance, 0.3794259832... is a possible outcome). a. Sketch a curve of the probability distribution of this random variable, which is the continuous version of the uniform distribution.
Answers
Answer:
The graph of the probability density function is attached.
Step-by-step explanation:
The probability function for this random number generator will be like the uniform distribution and defined for X ∈ [0, 1].
The probability density function can be written as:
[tex]f(x)={\begin{cases}{\dfrac {1}{1-0}}=1&\mathrm {for} \ 0\leq x\leq 1,\\[8pt]0&\mathrm {for} \ x<0\ \mathrm {or} \ x>1\end{cases}}[/tex]
The graph of the probability density function is attached.
Related Questions
3. Factor the expression.
d2 + 120 + 36
A (d + 6)2
B (d - 36)(0 - 1)
OC (d - 6)2
D (d + 6)(d - 6)
Answers
Answer:
The complete factored form of this equation is (d + 6)²
Step-by-step explanation:
The first step in factoring this equation is multiply the first term and the last term together. Out first term is d² and our last term is 36. Since d² does not have a coefficient, then we assume this number to be 1.
1 × 36 = 36
So, now we need to find two factors that multiply to 36 and add together to get 12. Two factors that best represents this is 6 and 6. So, we will plug these numbers into our equation. Replace 12d with 6d + 6d.
d² + 6d + 6d + 36
Group the first two terms together and the last two terms together.
(d² + 6d) + (6d + 36)
Now, find the greatest common factor of each parentheses and factor the terms.
d(d + 6) + 6(d + 6)
From looking at this, we can tell that this equation is a perfect squared equation. So, this means instead of writing both parentheses, we can just write one of the parentheses and square it.
So, the factored form of this equation is (d + 6)²
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim. (a) Which form of the hypotheses should be used to test the manager's claim? H0: - Select your answer - Ha: - Select your answer - The member of the hotel's accounting staff suspects that the total charges for guest bills have Select in recent months. To test the manager’s claim, the staff member will conduct Select test of the population Select . (b) What conclusion is appropriate when H0 cannot be rejected? When H0 cannot be rejected, there Select enough evidence to conclude that the total charges for guest bills have Select in recent months. (c) What conclusion is appropriate when H0 can be rejected? When H0 can be rejected, there Select enough evidence to conclude that the total charges for guest bills have Select in recent m
Answers
Answer:
a) Null hypothesis (H0): the mean guest bill for a weekend is $600.
Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.
b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600.
c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.
Step-by-step explanation:
a) The accountant, as he wants to see if there is evidence to support the claim that the mean guest bill has increased significanty, should write the hypothesis like that:
Null hypothesis (H0): the mean guest bill for a weekend is $600.
Alternative hypothesis (Ha): the mean guest bill for a weekend is significantly bigger than $600.
A sample of bills of the period in study needs to be taken in order to have a representation of the actual population of bills and then perform a t-test, as the sample mean and standard deviation will be used to perform the test.
b) When H0 can not be rejected, the conclusion is that there is no enough evidence to claim that the mean guest bill had increased from $600. If the P-value was low but not enough, they may take another sample to perform the test again or leave it like that.
c) When the H0 is rejected, they have enough evidence to claim that the mean guest bill is significantly bigger than $600.
T-Mobile sells 6 different models of cell phones and have found that they sell an equal number of each model. The probability distribution that would describe this random variable is called:
Answers
Answer:
Option A is correct.
A uniform distribution.
Step-by-step explanation:
Complete Question
T-Mobile sells 6 different models of cell phones and have found that they sell an equal number of each model. The probability distribution that would describe this random variable is called:
A) Uniform Distribution
B) Continuous Distribution
C) Poisson Distribution
D) Relative Frequency Distribution
Solution
A uniform distribution is one in which all the variables have the same probability of occurring.
It is also known as a rectangular distribution, as every portion of the sample space has an equal chance of occurring, with equal length on the probability curve, leading to a rectangular probability curve.
And for this question, 6 different models of phones sell an equal number, hence, the probability of selling each model is equal to one another, hence, this is evidently a uniform distribution.
Hope this Helps!!!
The tensile strength of a certain metal component is normally distributed with a mean of 10,000 kilograms per square centimeter and a standard deviation of 100 kilograms per square centimeter. Measurements are recorded to the nearest 50 kilograms per square centimeter.
Required:
a. What proportion of these components exceed 10,150 kilograms per square centimeter in tensile strength?
b. If specifications require that all components have tensile strength between 9800 and 10,200 kilograms per square centimeter inclusive, what proportion of pieces would we expect to scrap?
Answers
Answer:
a. 0.0668
b. 0.9545
Step-by-step explanation:
We have the following information:
mean (m) = 10000
standard deviation (sd) = 100
(a)
We must calculate the proportion of the components exceed 10150 kilograms per square centimeter in tensile strength as follows:
P (x> 10150) = P [(x - m) / sd> (10150 - 1000 /) 100]
P (x> 10150) = P (z> 1.5)
P (x> 10150) = 1 - P (z <1.5)
P (x> 10150) = 1 - 0.9332 (attached table)
P (x> 10150) = 0.0668
Therefore the proportion of the components exceed 10150 kilograms per square centimeter in tensile strength is 0.0668
(b)
We must calculate the proportion of all components has tensile strength between 9800 and 10200, as follows:
P (9800 <x <10200) = P [(9800 - 1000 /) 100 <(x - m) / sd <(10200 - 1000 /) 100]
P (9800 <x <10200) = P (-2 <z <2)
P (9800 <x <10200) = P (z <2) - P (z <-2)
P (9800 <x <10200) = 0.9773 - 0.0228 (attached table)
P (9800 <x <10200) = 0.9545
the proportion of pieces that would expect to scrap is 0.9545
What is the domain of the following set of ordered pairs (-2,-5),(-3,8),(12,6),(8,3),(4,0),(-5,7)
Answers
Answer:
domain = {-5, -3, -2, 4, 8, 12}
Step-by-step explanation:
The domain is the set containing the x-coordinates of all ordered pairs.
domain = {-2, -3, 12, 8, 4, -5}
If you'd like, you can put the numbers in ascending order:
domain = {-5, -3, -2, 4, 8, 12}
can someone help me again please im giving 20 points
Answers
Answer:
I answered this one for you already I think.
Consider random samples of size 900 from a population with proportion 0.75 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places. standard error
Answers
Answer:
[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]
And replacing we got:
[tex] SE=\sqrt{\frac{0.75*(1-0.75)}{900}}= 0.014[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n=900[/tex] represent the sample size selected
[tex]p = 0.75[/tex] represent the population proportion
We want to find the standard error and we can use the distribution for the sample proportion and for this case since the sample size is large enough and we satisfy np>10 and n(1-p) >10 we have:
[tex] \hat p \sim N (p,\sqrt{\frac{p(1-p)}{n}})[/tex]
And the standard error is given;
[tex] SE =\sqrt{\frac{p(1-p)}{n}}[/tex]
And replacing we got:
[tex] SE= \sqrt{\frac{0.75* (1-0.75)}{900}}= 0.014[/tex]
An Undergraduate Study Committee of 6 members at a major university is to be formed from a pool of faculty of 18 men and 6 women. If the committee members are chosen randomly, what is the probability that precisely half of the members will be women?
Answers
Answer:
5/33649= approx 0.00015
Step-by-step explanation:
Total number of outcomes are C24 6= 24!/(24-6)!/6!=19*20*21*22*23*24/(2*3*4*5*6)= 19*14*22*23
Half of the Committee =3 persons. That mens that number of the women in Commettee=3. 3 women from 6 can be elected C6 3 ways ( outputs)=
6!/3!/3!=4*5*6*/2/3=20
So the probability that 3 members of the commettee are women is
P(women=3)= 20/(19*14*22*23)=5/(77*19*23)=5/33649=approx 0.00015
The probability that precisely half of the members will be women is;
P(3 women) = 0.1213
This question will be solved by hypergeometric distribution which has the formula;
P(x) = [S_C_s × (N - S)_C_(n - s)]/(NC_n)
where;
S is success from population
s is success from sample
N is population size
n is sample size
We are give;
s = 3 women (which is precisely half of the members selected)
S = 6 women
N = 24 men and women
n = 6 people selected
Thus;
P(3 women) = (⁶C₃ * ⁽¹⁸⁾C₍₃₎)/(²⁴C₆)
P(3 women) = (20 * 816)/134596
P(3 women) = 0.1213
Read more at; https://brainly.com/question/5733654
Any help would be great
Answers
Answer:
2/5
Step-by-step explanation:
A school librarian purchases a novel for her library. The publisher claims that the book is written at a 5th grade reading level, but the librarian suspects that the reading level is higher than that. The librarian selects a random sample of 40 pages and uses a standard readability test to assess the reading level of each page. The mean reading level of these pages is 5.2 with a standard deviation of 0.8. Do these data give convincing evidence at the = 0.05 significance level that the average reading level of this novel is greater than 5?
Answers
Answer:
[tex]t=\frac{5.2-5}{\frac{0.8}{\sqrt{40}}}=1.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
Thep value for this case would be given by:
[tex]p_v =P(t_{(39)}>1.58)=0.061[/tex]
Since the p value is higher than the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that true mean is not significantly higher than 5.
Step-by-step explanation:
Information provided
[tex]\bar X=5.2[/tex] represent the sample mean
[tex]s=0.8[/tex] represent the sample standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is higher than 5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 5[/tex]
Alternative hypothesis:[tex]\mu > 5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{5.2-5}{\frac{0.8}{\sqrt{40}}}=1.58[/tex]
The degrees of freedom are given by:
[tex]df=n-1=40-1=39[/tex]
Thep value for this case would be given by:
[tex]p_v =P(t_{(39)}>1.58)=0.061[/tex]
Since the p value is higher than the significance level of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that true mean is not significantly higher than 5.
Alan has reached 25% of his weekly exercise time goal so far this week. If he has exercised for a total of 42 minutes this week, what is his weekly exercise time goal in minutes
Answers
Answer:
His weekly exercise time goal is 168 minutes.
Step-by-step explanation:
This question can be solved using a rule of three.
42 minutes is 25% = 0.25 of the total
x minutes is 100% = 1 of the total.
Then
42 minutes - 0.25
x minutes - 1
[tex]0.25x = 42[/tex]
[tex]x = \frac{42}{0.25}[/tex]
[tex]x = 168[/tex]
His weekly exercise time goal is 168 minutes.
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE = CE and BE = DE
B.
С
E
A
D
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Answers
Answer:
the gram
Step-by-step explanation:
casegunnell is my gram, follow if your a real g
Following are the calculation to the given points:
When the ABCD is parallelogram:
The properties of parallelogram:
[tex]\to \angle CBD = \angle ADB \\\\[/tex]
[tex]\to \angle BCA = \angle DAC \\\\[/tex]
When the Two-lines are parallel and alternate interior angles are equal:
[tex]\to \Delta BEC \cong \Delta AED \ \ \ \ \ \ \ \{ASA\} \\\\\to \overline {AE} \cong \overline{CE}\\\\ \to \overline{BE} \cong \overline{ED} \\\\[/tex]
When the properties of congruent triangle.
Learn more:
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Number of multiples of 7 between 200 and 1000
Answers
Answer:
114
Step-by-step explanation:
Answer:
144Step-by-step explanation:
A 12 ft ladder leans against the side of a house. The top of the ladder is 10ft off the ground. Find x, the angle of elevation of the ladder.
1. Remember to address each of the critical elements of the prompt:
Articulate your overall approach to solving this problem before tackling the details. In other words, think about what the question is actually asking, which pieces of information are relevant, and how you can use what you have learned to fill in the missing pieces.
2. Apply the mathematical process to solve the problem:
Interpret the word problem to identify any missing information.
Translate the word problem into an equation.
Appropriately use the order of operations and law of sines and cosines to determine the solution.
Check your work by ensuring that the known properties of triangles are met.
Answers
The image is missing, so i have attached it.
Answer:
x = 56.44°
Step-by-step explanation:
From the attached image, we can see that this is a right angle triangle which has opposite, adjacent and hypotenuse as sides. Since we want to find the angle x, thus, we can make use of trigonometric ratios.
From the attached image, the side opposite to angle x is 10ft and the hypotenuse is 12 ft.
From trigonometric ratios, we know that, sin x = opposite/hypotenuse
So, sin x = 10/12
x = sin^(-1) (10/12)
x = sin^(-1) 0.8333
x = 56.44°
The annual interest on a $14,000 investment exceeds the interest earned on a $7000 investment by $595 . The $14,000 is invested at a 0.5% higher rate of interest than the $7000 . What is the interest rate of each investment?
Answers
Answer:
x= 8.00 Interest rate on $14000
y= 7.50 Interest rate on $7000
Step-by-step explanation:
Let interest rate of $14000 be x%
and Interest rate for $7000 be y %
According to the first condition
14000 * x% - 7000 * y% = 595
multiply by 100
14000x-7000y = 59500
/700
20x-10y=85.................(1)
II condition
x%=y%+0.5%
x=y+0.5
x-y=0.5..................................(2)
solve (1) & (2)
20 x -10 y = 85 .............1
Total value
1 x -1 y = 0.50 .............2
Eliminate y
multiply (1)by 1
Multiply (2) by -10
20.00 x -10.00 y = 85.00
-10.00 x + 10.00 y = -5.00
Add the two equations
10.00 x = 80.00
/ 10.00
x = 8.00
plug value of x in (1)
20.00 x -10.00 y = 85.00
160.00 -10.00 y = 85.00
-10.00 y = 85.00 -160.00
-10.00 y = -75.00
y = 7.50
x= 8.00 Interest rate on $14000
y= 7.50 Interest rate on $7000
A car can travel 45 miles on 2 gallons of gasoline. How far can it travel on 5.6
gallons?
Answers
Answer:
It can travel 45 / 2 = 22.5 miles per gallon so the answer is 22.5 * 5.6 = 126 miles.
The equation of a circle is x2 + y2 = 56.25. Find the radius of the circle?
Answers
Answer:
r = 7.5
Step-by-step explanation:
Circle equation: [tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Since we are already give r², we simply just take the square root of 56.25, and we should get 7.5 as our final answer!
identify the property being demonstrated
if x/5 = 7, then x=35
a. division
b. multiplication
c. reflexive
d. symmetric
Answers
Answer:
[tex] \: \: \: \: \: \: \: \: \: \: \dfrac{x}{5} = 7 \\ \implies \: x = 7 \times 5 \\ \implies \: x = 35[/tex]
So,b. multiplication
Answer:
A. division
Step-by-step explanation:
[tex]x/5=7[/tex]
[tex]x[/tex] is being divided by an integer.
[tex]x=35[/tex]
[tex]35/5=7[/tex]
35 divided by 5 is equal to 7.
A laptop computer is purchased for $2300. Each year, its value is 75% of its value the year before. After how many years will the laptop computer be worth $700 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer.
Answers
Answer:
after the 1st year
Step-by-step explanation:
$2300 × 75% = $1725.00
$2300-$1725= $575
Determine whether the underlined value is a parameter or a statistic. In a national survey of high school students (grades 9 to 12), Modifying 25 % of the students who responded reported that someone had offered, sold, or given them an illegal drug on school property.
Answers
Answer:
I am assuming the underlined value is 25%. It is a parameter
Step-by-step explanation:
The value is is a parameter. This is because the parameter is a value that describes the population.
The survey carried out was a national survey of which there were 25% respondents who reported that someone had offered, sold, or given them an illegal drug on school property. It is not a statistics because a sample was not taken out of the population and a survey made on the sample.
The underlined 25% value is the value that summarizes the entire population of high school students
Please help Solving linear and quadratic equations
Answers
Answer: B.
x ≈2.5
Step-by-step explanation:
[tex]-\left(u\right)^{-1}-6=-u+10[/tex]
[tex]u=8-\sqrt{65},\:u=8+\sqrt{65}[/tex]
[tex]x=\frac{\ln \left(8+\sqrt{65}\right)}{\ln \left(3\right)}[/tex]
x=2.52...
Answer:
x=2.5
Step-by-step explanation:
Black walnut trees contain chemicals that inhibit the growth of other plants. In a simple experiment to test whether this is true, you grow several tomato plants in soil with and without decomposing leaves from a black walnut tree. You collect data on plant height as a measure of growth. In this experiment, __________ is the independent variable, __________ is the dependent variable, and __________ is the control.
Answers
Answer:
Height of tomato plant is the dependent variable
Presence of walnut leaves in the soil is the independent variable
Tomato plants grown without walnut leaves is the control
Step-by-step explanation:
An independent variable is the variable in an experiment that can be altered to test for a certain result. It is independent, or does not change with change in other factors in the experiment. In this case, the presence or absence, or quantity of walnut available in the soil is the independent variable in the experiment.
A dependent variable varies, and depends on the independent variable. It is what is measured in the experiment. In this case, the height of the tomato plants is the dependent variable that depends on the presence, absence or quantity of walnut in the soil.
A control in an experiment, is a replicate experiment, that is manipulated in order to be able to test a single variable at a time. Controls are variables are held constant so as to minimize their effect on the system under study. In this case, some of the tomato plants are planted without walnut in the soil, to test the effect of the absence of the walnut in the soil.
An equilateral triangle has an altitude of 4.8in. What are the length of the sides? Round to the nearest tenth.
Answers
Answer:
5.5 in
Step-by-step explanation:
The altitude is (√3)/2 times the length of a side, so the side length is the inverse of that times the length of the altitude:
side length = (2/√3)(4.8 in) ≈ 5.5 in
Find the Laplace transform F(s)=L{f(t)} of the function f(t)=sin2(wt), defined on the interval t≥0. F(s)=L{sin2(wt)}= help (formulas) Hint: Use a double-angle trigonometric identity. For what values of s does the Laplace transform exist? help (inequalities)
Answers
The Laplace transform of the function [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex] .
The Laplace transform exist when s > 0 .
Here, the given function is f(t) = sin²(wt) .
The Laplace transform of the the function f(t),
F(s) = f(t) = { [tex]{\frac{1}{2} \times 2sin^2(wt) }[/tex] }
F(s) = { [tex]\frac{1}{2} \times (1- cos2wt)[/tex] }
F(s) = { [tex]\frac{1}{2} - \frac{1}{2} \times cos(2wt)\\[/tex] }
F(s) = [tex]\frac{1}{2} (\frac{1}{s} - \frac{s}{s^2 + 4w^2} )[/tex]
Next,
The above Laplace transform exist if s > 0 .
Know more about Laplace transform,
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Consider three consecutive positive integers, such that the sum of the
squares of the two larger integers is 5 more than 40 times the smaller
one. Find the smaller integer.
Answers
Answer:
17
Step-by-step explanation:
Let x represent the smaller integer. Then we have ...
(x +1)² +(x +2)² = 40x +5
2x² +6x +5 = 40x +5
x² -17x = 0 . . . . . subtract (40x+5), divide by 2
x(x -17) = 0 . . . . . factor
The solution of interest is x = 17.
The smaller integer is 17.
The graph of the function f(x) =4 square root x is shown. what is the domain of the function?
Answers
Answer:
[0, positive infinity)
Step-by-step explanation:
The domain is all x values a graph inputs. In a square root function, you cannot have negative inputs as it will turn out imaginary numbers. Therefore, your domain is all values of x above and including 0.
Answer: d on Ed
Step-by-step explanation:
Just took the test
I need help for the solution
Answers
Answer:
[tex]\boxed{ \ dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t\ }[/tex]
Step-by-step explanation:
it is a long time I have not applied Ito's lemma
I would say the following
for [tex]f(x)=x^2[/tex]
f'(x)=2x
f''(x)=2
so using Ito's lemma we can write that
[tex]dY_t=2V_tdV_t+\phi^2dt[/tex]
[tex]dY_t=2(\theta+\psi V_t^2)dt+2\phi V_tdW_t+\phi^2dt[/tex]
[tex]dY_t=(2\theta+2\psi V_t^2+\phi^2)dt+2\phi V_tdW_t[/tex]
so it comes
[tex]dY_t=(2\theta+2\psi Y_t+\phi^2)dt+2\phi \sqrt{Y_t}dW_t[/tex]
A hotel manager believes that 27% of the hotel rooms are booked. If the manager is correct, what is the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6%
Answers
Answer:
The probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% is 0.9946.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The information provided here is:
p = 0.27
n = 423
As n = 423 > 30, the sampling distribution of sample proportion can be approximated by the Normal distribution.
The mean and standard deviation of the sampling distribution of sample proportion are:
[tex]\mu_{\hat p}=p=0.27\\\\\sigma_{\hat p}=\sqrt{\frac{\hat p(1-\hat p)}{n}}=\sqrt{\frac{0.27\times(1-0.27)}{423}}=0.0216[/tex]
Compute the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% as follows:
[tex]P(|\hat p-p|<0.06)=P(p-0.06<\hat p<p+0.06)[/tex]
[tex]=P(0.27-0.06<\hat p<0.27+0.06)\\\\=P(0.21<\hat p<0.33)\\\\=P(\frac{0.21-0.27}{0.0216}<\frac{\hat p-\mu_{\hat p}}{\sigma_{\hat p}}<\frac{0.33-0.27}{0.0216})\\\\=P(-2.78<Z<2.78)\\\\=P(Z<2.78)-P(Z<-2.78)\\\\=0.99728-0.00272\\\\=0.99456\\\\\approx 0.9946[/tex]
*Use a z-table.
Thus, the probability that the proportion of rooms booked in a sample of 423 rooms would differ from the population proportion by less than 6% is 0.9946.
The mean number of hours of part-time work per week for a sample of 317 teenagers is 29. If the margin of error for the population mean with a 95% confidence interval is 2.1, construct a 95% confidence interval for the mean number of hours of part-time work per week for all teenagers.
Answers
Answer:
The degrees of freedom are given by:
[tex]df=n-1=317-1=316[/tex]
And replaicing we got:
[tex]29-2.1=26.9[/tex]
[tex]29+2.1=31.1[/tex]
The 95% confidence interval would be between 26.9 and 31.1
Step-by-step explanation:
Information given
[tex]\bar X= 29[/tex] represent the sample mean
[tex]\mu[/tex] population mean
s represent the sample standard deviation
[tex] ME= 2.1[/tex] represent the margin of error
n represent the sample size
Solution
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
And this formula is equivalent to:
[tex] \bar X \pm ME[/te]x
The degrees of freedom are given by:
[tex]df=n-1=317-1=316[/tex]
And replaicing we got:
[tex]29-2.1=26.9[/tex]
[tex]29+2.1=31.1[/tex]
The 95% confidence interval would be between 26.9 and 31.1
two sides of a parallelogram meet at an angle of 50 degrees. If the length of one side is 3 meters and the length of the other side is 5 meters, find the length of the longest diagonal and the angles that it forms with each of the given sides.
Answers
Answer:
The longer diagonal has a length of 7.3 meters.
The angles are 31.65° and 18.35°
Step-by-step explanation:
If one angle of the parallelogram is 50°, another angle is also 50° and the other two angles are the supplement of this angle. so the other three angles are:
50°, 130° and 130°.
The longer diagonal will be the one opposite to the bigger angle (130°), and this diagonal divides the parallelogram in two triangles.
Using the law of cosines in one of these two triangles, we have:
[tex]diagonal^2 = a^2 + b^2 - 2ab*cos(130\°)[/tex]
[tex]diagonal^2 = 3^2 + 5^2 - 2*3*5*(-0.6428)[/tex]
[tex]diagonal^2 = 53.284[/tex]
[tex]diagonal = 7.3\ meters[/tex]
So the longer diagonal has a length of 7.3 meters.
To find the angles that this diagonal forms with the sides, we can use the law of sines:
[tex]a / sin(A) = b/sin(B)[/tex]
[tex]5 / sin(A) = diagonal / sin(130)[/tex]
[tex]sin(A) = 5 * sin(130) / 7.3[/tex]
[tex]sin(A) = 0.5247[/tex]
[tex]A = 31.65\°[/tex]
The other angle is B = 50 - 31.65 = 18.35°
Please check the image attached for better comprehension.