(1) D
[tex]L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt[/tex]
Integrate by parts, taking
[tex]u = t \implies \mathrm du=\mathrm dt[/tex]
[tex]\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}[/tex]
Then
[tex]L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]
[tex]L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]
[tex]L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}[/tex]
[tex]L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}[/tex]
(2) A
[tex]L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt[/tex]
[tex]L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}[/tex]
[tex]L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}[/tex]
1% defective parts. 100,00 parts made in total. The number of defects made should equal?
Answer:
1,000 defects
Step-by-step explanation:
Find how many defects that should be made by finding 1% of 100,000:
100,000(0.01)
= 1000
So, there should be 1,000 defects
Use the following data obtained from ages of the last six U. S. Presidents at the time of their inauguration to answer the following questions:
Ages of Last 6 Presidents at Inauguration
Ronald Reagan 69
George Bush 64
Bill Clinton 46
George W. Bush 54
Barack Obama 47
Donald Trump 70
a. Find the mean of the data set. (Round to one decimal place.)
b. Find the standard deviation of the data set. (Do not round until the final answer. Round final answer to 1 decimal place.)
c. What percentage of presidents' ages fall within one standard deviation of the mean
Answer:
a) The mean of the data set is 58.3.
b) The standard deviation of the data-set is of 10.8.
c) 50% of presidents' ages fall within one standard deviation of the mean
Step-by-step explanation:
Question a:
Sum of all values divided by the number of values.
[tex]M = \frac{69 + 64 + 46 + 54 + 47 + 70}{6} = 58.3[/tex]
The mean of the data set is 58.3.
Question b:
Square root of the sum of the difference squared between each value and the mean, divided by the number of values subtracted by 1. So
[tex]S = \sqrt{\frac{(69-58.3)^2 + (64-58.3)^2 + (46-58.3)^2 + (54-58.3)^2 + (47-58.3)^2 + (70-58.3)^2}{5}} = 10.8[/tex]
The standard deviation of the data-set is of 10.8.
Question c:
Between 58.3 - 10.8 = 47.5 and 58.3 + 10.8 = 69.1.
3 out of 6(Reagan, Bush and W. Bush), so:
3*100%/6 = 50%
50% of presidents' ages fall within one standard deviation of the mean
In the Spring of 2021 the statistics course did a survey of the average number of parking tickets students received by gender. Which has been shared below. Based on the data below which statement would be the best null hypothesis?
Gender # of hours
male 6
female 8
female 8
male 3
female 7
female 5
male 3
male 2
female 9
female 7
female 2
female 3
male 9
female 0
female 2
male 4
male 9
female 12
female 15
female 3
female 6
male 7
female 3
female 8
male 3
male 6
female 7
female 8
Answer:
There is no difference between the two groups.
Step-by-step explanation:
The test hypothesis (null and alternative) are usually employed in evaluating if there is a statistical significance in a claim about the mean, standard deviation or variance of a sample and it's population parameter.
When comparing two independent variables, The null hypothesis usually establish that there is no difference between the mean value of samples, while the alternative hypothesis is the opposite.
The data given shows values for two independent groups ; Male and Female.
The null hypothesis will be:
H0 : There is no difference between the two groups.
H0 : μ1 - μ2 = 0
A spring has natural length 20 cm. Compare the work W1 done in stretching the spring from 20 cm to 30 cm with the work W2 done in stretching it from 30 to 40 cm. (Use k for the spring constant) How are W2 and W1 related?
Answer:
W₂ is three times W₁ (W₂ = 3W₁)
Step-by-step explanation:
Applying,
W = ke²/2............. Equation 1
Where W = workdone in stretching the spring, k = spring constant, e = extension.
For W₁,
W₁ = ke₁²/2
Given: e₁ = 30-20 = 10 cm = 0.1 m
Substitute these value into equation 1
W₁ = k(0.1²)/2
W₁ = 0.005k Joules
For W₂,
W₂ = (ke/2)-W₁
Given: e = (40-20) = 20 cm = 0.1 m
Substitute these value into equation 1
W₂ = (k×0.2²/2)-0.005
W₂ = 0.015k Joules.
W₂/W₁ = 0.015k/0.005k
W₂/W₁ = 3
Therefore,
W₂ = 3W₁
Find the missing segment in the image below
Answer:
Step-by-step explanation:
You have collected data about the fasting blood glucose (FBG) level of participants in your study. You are delighted to find that the variable is normally distributed. If the mean FBG is 82 and the standard deviation is 2.8 in what range would you expect to find the FBG of 68% of your study participants
Answer:
Between 79.2 and 84.8.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 82, standard deviation of 2.8.
In what range would you expect to find the FBG of 68% of your study participants?
By the Empirical Rule, within 1 standard deviation of the mean, so:
82 - 2.8 = 79.2
82 + 2.8 = 84.8
Between 79.2 and 84.8.
(2√8)(√2) =
Select one:
a. 128
b. none of these
c. 6√10
d. 32
e. 8√16
Solve the system of equations.
4x + 3y + 5z = 6
6x + 8y + 6z = 4
4x + 2y + z = 8
(x = 1, y = -1,2 = 1)
b. (x = 3, y = -3,2 = 3)
a.
C. (x = 0, y = 0, 2 = 2)
d. (x - 2, y --2, z = 0)
CUSTOMERS AT A STORE
The bar graph above shows the number of customers who shopped at a store Monday through Thursday of
one week. If the number of customers on Friday was a one-fifth increase over the number of customers on
Thursday, how many customers shopped at the store on Friday?
O 480
O 500
O 525
O 600
Answer:
480
Step-by-step explanation:
We are looking for the total number of customers in the store on Friday using a chart and a fractional increase.
On Thursday there were 400 customers, so we need to find the amount of the increase.
1/5 of 400 =80
Increase Thursday's amount, 400, by the amount of the increase, 80, to find the number of customers on Friday.
400+80 = 480
Friday has 480
Answer:
480
Step-by-step explanation:
400 + 1/5(400) = 400 + 80 = 480
What is the largest product that can be made from whole numbers that add up to 100?
Answer:
Step 1: Find the largest product
50 + 50 = 100
50 * 50 = 2500
Answer: I believe that the largest product is 2500
the length of a rectangle is 4 meters longer than the width. if the area is 22 square meters , find the rectangle dimension
Let breadth be x
Length=x+4We know
[tex]\boxed{\sf Area_{(Rectangle)}=Length\times Breadth}[/tex]
[tex]\\ \sf\longmapsto x(x+4)=22[/tex]
[tex]\\ \sf\longmapsto x^2+4x=22[/tex]
[tex]\\ \sf\longmapsto x^2+4x-22=0[/tex]
By solving[tex]\\ \sf\longmapsto x=-2\pm\sqrt{26}[/tex]
It doesnot have any real roots
A sample of 42 observations is selected from one population with a population standard deviation of 3.3. The sample mean is 101.0. A sample of 53 observations is selected from a second population with a population standard deviation of 3.6. The sample mean is 99.0. Conduct the following test of hypothesis using the 0.04 significance level.
H0 : μ1 = μ2
H1 : μ1 ≠ μ2
a. State the decision rule.
b. Compute the value of the test statistic.
c. What is your decision regarding H0?
d. What is the p-value?
Answer:
a)
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b) [tex]z = 2.81[/tex]
c) Reject.
d) The p-value is 0.005.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and the subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Population 1:
Sample of 42, standard deviation of 3.3, mean of 101, so:
[tex]\mu_1 = 101[/tex]
[tex]s_1 = \frac{3.3}{\sqrt{42}} = 0.51[/tex]
Population 2:
Sample of 53, standard deviation of 3.6, mean of 99, so:
[tex]\mu_2 = 99[/tex]
[tex]s_2 = \frac{3.6}{\sqrt{53}} = 0.495[/tex]
H0 : μ1 = μ2
Can also be written as:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
H1 : μ1 ≠ μ2
Can also be written as:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error .
a. State the decision rule.
0.04 significance level.
Two-tailed test(test if the means are different), so between the 0 + (4/2) = 2nd and the 100 - (4/2) = 98th percentile of the z-distribution, and looking at the z-table, we get that:
[tex]|z| < 2.054[/tex]: Do not reject the null hypothesis.
[tex]|z| > 2.054[/tex]: Reject the null hypothesis.
b. Compute the value of the test statistic.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = \mu_1 - \mu_2 = 101 - 99 = 2[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.51^2 + 0.495^2} = 0.71[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{2 - 0}{0.71}[/tex]
[tex]z = 2.81[/tex]
c. What is your decision regarding H0?
[tex]|z| = 2.81 > 2.054[/tex], which means that the decision is to reject the null hypothesis.
d. What is the p-value?
Probability that the means differ by at least 2, either plus or minus, which is P(|z| > 2.81), which is 2 multiplied by the p-value of z = -2.81.
Looking at the z-table, z = -2.81 has a p-value of 0.0025.
2*0.0025 = 0.005
The p-value is 0.005.
Knowing that AQPT = AARZ, a congruent side pair is:
Answer:
A. QT ≅ AZ
Step-by-step explanation:
When writing a congruence statement of two triangles, the order of arrangement of the letters used in naming the triangles are carefully considered. Corresponding sides and angles of both triangles are arranged accordingly in the order they appear.
Given that ∆QPT ≅ ∆ARZ, we have the following sides that correspond and are congruent to each other:
QP ≅ AR
PT ≅ RZ
QT ≅ AZ
The only correct one given in the options given above is QT ≅ AZ
If anyone knows answer with steps that will be greatly appreciated :)
Answer:
The area formula is= 1/2(a+b)×height
1/2×20×6=60metres squared
Step-by-step explanation:
kindly correct me if am wrong
A company pays a bonus to four employees A, B, C, and D. A gets four times as much as B. B gets 50% of the amount paid to C. C and D get the same amount. If the total bonus is ¢1,800.00, set all necessary equations to ascertain the share of each employees.
Answer:
A = 800, B = 200, C = 400 Andy D = 400
Step-by-step explanation:
HELP PLS !!! Pls pls pls pls pls pls pls pls pls
Answer:
x=7
Step-by-step explanation:
6x+11=7x+4
Hoang spends $10 on movie tickets, $50 on rent, and $3 on snacks. How much money did Hoang spend on variable expenses?
Answer:
63
Step-by-step explanation:
50+10=60 60+3=63 dollars
he spends 63$ on variable expenses
What is the equation of a line that passes through the point (1,8) and is perpendicular to the line whose equation is y=x/2+3?
Answer:
m=1/2
y-8=1/2(x-1)
y-8=1/2x-1/2
multiply through by 2
2y-16=x-1
2y-16+1-x=0
2y-15-x=0
2y-x-15=0
what is the square root of 24
Answer:
the square root of 24 is 4.89897948557
Answer:
4.89
Step-by-step explanation:
2root 6........***
(WILL GIVE YOU 30 POINTS!!!)
The graph shows the functions f(x), p(x), and g(x):
Graph of function g of x is y is equal to 3 multiplied by 1.2 to the power of x. The straight line f of x joins ordered pairs minus 3, minus 3 and 4, 4 and is extended on both sides. The straight line p of x joins the ordered pairs minus 6, 1 and minus 3, minus 3 and is extended on both sides.
Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points)
Part B: Write any two solutions for f(x). (3 points)
Part C: What is the solution to the equation p(x) = g(x)? Justify your answer. (4 points)
Answer:
(a) No solution
(b)
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
(c) [tex](-6,1)[/tex]
Step-by-step explanation:
Given
See attachment for graph
Solving (a): Solution to p(x) and f(x)
Curve p(x) and line f(x) do not intersect.
So, there is no solution to the pair of p(x) and f(x)
Solving (b): Two solutions to f(x)
This means that we select any two point on straight line f(x)
From the line of f(x), we have:
[tex](x_1,y_1) =(-3,-3)\\(x_2,y_2) =(4,4)[/tex]
Solving (c): Solution to p(x) = g(x)
Here, we write out the point of intersection of p(x) and g(x)
From the graph, the point of intersection is: [tex](-6,1)[/tex]
K.Brew sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 18 sales receipts for mail-order sales results in a mean sale amount of $81.90 with a standard deviation of $22.25. A random sample of 8 sales receipts for internet sales results in a mean sale amount of $88.30 with a standard deviation of $23.25. Using this data, find the 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed. Construct the 98% confidence interval.
Answer:
kdjdeoksndoddmsnsksndjdjd
The baker bought the buttercream icing from Crave Cupcakes. Calculate how many containers of icing the baker needs to buy in order to ice a wedding cake. Each container of icing contains 16 ounces of icing. If it takes 56 ounces of icing to cover 678 square inches of cake, calculate the total cost for the icing before tax if each 16 ounce(2 cup) container of icing costs $10.
Answer:
$40.
Step-by-step explanation:
You need 4 16oz containers of icing to fully cover the cake. As each container costs $10, and you need 4 containers, the total cost of icing to cover the wedding cake, before tax, is $40.
A basketball player averages 22.5 points scored per game with a standard deviation of 6.2 points. In one game, the athlete scored 10 points. What is the z-score for the points scored in this game?
–2.02
–1.63
1.63
2.02
Answer:
Step-by-step explanation:
Z -2.02
x 10
µ 22.5
σ 6.2
g At a bank, there is a line of 3 people and only one cashier that serves one person at a time. The time that the cashier takes to serve each person has an exponential distribution with a mean of 5 minutes. Calculate the probability that the total time of serving the 3 people is less than 15 minutes. Assume that the serving times are independent.
Find the mean for the amounts: $17.482: $14.987: $13.587$14.500, $18.580. $14.993
Answer:
The mean of these numbers is 15.68816 with a repeating 6.
Step-by-step explanation:
Lainey is looking for a new apartment and her realtor keeps calling her with new listings . The calls only take a few minutes , but a few minutes here and there are really starting to add up . She's having trouble concentrating on her work . What should Lainey do ? a ) Tell her realtor she can only receive text messages b ) Limit the time spent on each call c ) Turn off her phone until she is on a break d ) Call her realtor back when customers won't see her on the phone
Answer:
c ) Turn off her phone until she is on a break
Find the missing length indicated
Answer:
x = 960
Step-by-step explanation:
x=√{576×(576+1024)}
or, x = √(576×1600)
or, x = √576×√1600
or, x = 24×40
or, x = 960
Answered by GAUTHMATH
Answer:
Step-by-step explanation:
What is the range & domain of the set
R: {(-6, 14), (10,19), (4, -9), (3, 2), (6, -13)}
Answer:
Domain { -6,3,4,6,10}
The range is the output values, listed from smallest to largest with no repeats
Range { -13,-9,2,14,19}
Step-by-step explanation:
The domain is the input values, listed from smallest to largest with no repeats
Domain { -6,3,4,6,10}
The range is the output values, listed from smallest to largest with no repeats
Range { -13,-9,2,14,19}
Answer:
Range: 14, 19, -9, 2, -13
Domain: -6, 10, 4, 3, 6
Step-by-step explanation:
I don't know but this is it I think .
Find the area of the triangle with the given
Answer:
616.2442
area to the nearest whole number=616
Step-by-step explanation:
using formula 1/2absinx
where a =44,b=29 ,x=105
1/2x44x29xsin105
44x29=1276
1276÷2=638
638 x sin 105
the sin of 105 is 0.9659
if u are using a four figure table where u can't find 105 under sin of angle
u simply subtract 105 from 180=75
638 x 0.9659 =616.2442
approx.616
What are the zeros of the polynomial function f(x)=x3-7x2+8x+16
Answer: x=4, -1
Step-by-step explanation:
Assuming you meant [tex]x^3-7x^2+8x+16[/tex], the zeros of the question are x = 4 and -1.
Step 1. Replace f(x) with y.
[tex]y = x^3-7x^2+8x+16[/tex]
Step 2. To find the roots of the equation, replace y with 0 and solve.
[tex]0 = x^3-7x^2+8x+16[/tex]
Step 3. Factor the left side of the equation.
[tex](x-4)^2 (x+1)=0[/tex]
Step 4. Set x-4 equal to 0 and solve for x.
[tex]x-4=0[/tex]
Step 5. Set [tex]x+1[/tex] equal to 0 and solve for x.
[tex]x=-1[/tex]
The solution is the result of [tex]x-4=0[/tex] and [tex]x+1=0[/tex].
[tex]x=4,-1[/tex]
