Answer:
the distance between the ships is changing at 21.4 km/h
Step-by-step explanation:
Given;
distance between ship A and ship B = 150 km
speed of ship, A = 35 km/h
speed of ship B = 25 km/h
at 4 pm, the time difference = 4 hours
let the distance between A and B = C
The position of A after 4 hours = 35 km/h x 4 h = 140 km
The distance covered by A, a = 150 km - 140 km = 10 km
The distance covered by B, b = 25 km/h x 4 h = 100 km
The distance between A and B;
c² = a² + b²
c² = 10² + 100²
c² = 10100
c = √10100
c = 100.5 km
The change in the distance between A and B is calculated as;
[tex]c^2 = a^2 + b^2\\\\2c\frac{dc}{dt} = 2a\frac{da}{dt} + 2b\frac{db}{dt} \\\\c\frac{dc}{dt} = a\frac{da}{dt} + b\frac{db}{dt} \\\\100.5(\frac{dc}{dt}) = -10(35) + 100(25) \\\\(the \ negative \ sign \ indicates \ decrease \ in \ distance \ of \ A \ from \ B \ with \ time)\\\\100.5(\frac{dc}{dt})= 2150\\\\\frac{dc}{dt} = \frac{2150}{100.5} \\\\\frac{dc}{dt} = 21.39 \ km/h\\\\\frac{dc}{dt} \approx 21.4 \ km/h[/tex]
Therefore, the distance between the ships is changing at 21.4 km/h
The Laplace Transform of a function f(t), which is defined for all t > 0, is denoted by L{f(t)} and is defined by the improper integral L{f(t)}(s) = infinity 0 e-st.f(t)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of as a fixed constant)
1. Find L{t}. (hint: remember integration by parts)
A. 1
B. -1/s2
C. 0
D. 1/s2
E. -s2
F. None of these
2. Find L{1}.
a.1/s
b. 1
c. 0
d. -s
e. -1/s
f. none of these
(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]
Lines a and b are perpendicular. If the slope of line a is 3, what is the slope of
line b?
Answer:
-1/3
Step-by-step explanation:
Perpendicular lines have slopes that multiply to -1
a*b = -1
3 * b = -1
b = -1/3
The slope of line b is -1/3
The lines shown below are parallel. If the green line has a slope of 5, what is a
the slope of the red line?
Answer:
A. 5
Step-by-step explanation:
Parallel lines have the same slope.
Answer:
5
Step-by-step explanation:
m∠AFD=90° . m∠AFB=31°. Find m∠DFE.
A. 87
B. 29.5
C. 31
D. 28
Answer:
D. 28
Step-by-step explanation:
Given:
m∠AFD = 90°
m∠AFB = 31°
Required:
m∠DFE
Solution:
m<AFB = m<CFD (both angles are marked as congruent angles)
Since m<AFB = 31°, therefore,
m<CFD = 31°
m<AFB + m<CFD + m<BFC = m<AFD
Plug in the known values
31° + 31° + m<BFC = 90°
62° + m<BFC = 90°
Subtract 62° from each side
m<BFC = 90° - 62°
m<BFC = 28°
m<BFC = m<DFE = 28° (both angles are marked congruent to each other)
Therefore,
m<DFE = 28°
I need help guys thanks so much
Answer:
2
Step-by-step explanation:
8 ^ (5/3) ^ 1/5
We know a^b^c = a^(b*c)
8^ (5/3*1/5)
8^ 1/3
Rewriting 8 as 2^3
2^3 ^1/3
2 ^(3*1/3)
2^1
2
Answer:
2
Step-by-step explanation:
((2^3)^5/3)^1/5
= (2^5)^1/5
= 2
Answered by Gauthmath
I need some help please!!!
9514 1404 393
Answer:
13 < √181 < 14
Step-by-step explanation:
Apparently, you're supposed to know that ...
13² = 169
14² = 196
so √181 will lie between 13 and 14.
13 < √181 < 14
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
Answer:
i believe it'll cost 200 dollars
Solve for f(-7) plz thanks
Answer:
12
Step-by-step explanation:
If f(x) = 5 - x
Then f(-7) = 5 - (-7)
f(-7) = 5 + 7
f(-7) = 12
Mary takes out a loan for $6,000 at a simple interest rate of 12% to be paid back in 36 monthly instalments. What is the amount of her monthly payments?
Answer:
$199.29
Step-by-step explanation:
Total payments = $7,174.24
Total interest = $1,174.24
What is the area of the polygon given below?
Answer:
diện tích đa giác trong hình là :
186 cm2
Step-by-step explanation:
hãy tách hình đa giác trên thành 4 hình chữ nhật và tính diện tích từng hình chữ nhật
A family has a day of 7 activities planned: shopping, picnic, hiking, swimming, bike ride, video games, and movie. To make it more adventurous they decide to randomly pick the order of the activities out of a hat. Find the probability that bike ride and movie are chosen consecutively, in either order.
Answer:
[tex]Pr= \frac{1}{21}[/tex]
Step-by-step explanation:
Given
[tex]n(S) = 7[/tex] --- number of games
Required
Probability of bike and movie in consecutive order
This probability is represented as:
[tex]Pr = P(Bike\ and\ Movie) \ or\ P(Movie\ or\ Bike)[/tex]
So, we have:
[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]
The probability is an illustration of selection without replacement;
So, we have:
[tex]P(Bike\ and\ Movie) = P(Bike) * P(Movie)[/tex]
[tex]P(Bike\ and\ Movie) = \frac{n(Bike)}{n(S)} * \frac{n(Movie)}{n(S) - 1}[/tex] ---- without replacement
Bike and Movie appear in the game list 1 time.
So, the equation becomes
[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{7 - 1}[/tex]
[tex]P(Bike\ and\ Movie) = \frac{1}{7} * \frac{1}{6}[/tex]
[tex]P(Bike\ and\ Movie) = \frac{1}{42}[/tex]
Similarly,
[tex]P(Movie\ and\ Bike) = \frac{1}{42}[/tex]
So, we have:
[tex]Pr = P(Bike\ and\ Movie) \ +\ P(Movie\ or\ Bike)[/tex]
[tex]Pr= \frac{1}{42}+\frac{1}{42}[/tex]
Take LCM
[tex]Pr= \frac{1+1}{42}[/tex]
[tex]Pr= \frac{2}{42}[/tex]
[tex]Pr= \frac{1}{21}[/tex]
Please how do I solve this.
Answer:
Horizontal Shift: Right 1
Vertical Shift: Down 5
Reflection: None
Explanation: To find the transformation, compare the function to the parent function (being in this case g(x)=1/x) and check to see if there is a horizontal or vertical shift or a reflection.
So, the answer would be Right 1, and down 5
Hope this helps you out :)
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
In 2018, Mike Krzyewski and John Calipari topped the list of highest paid college basketball coaches (Sports Illustrated website). The following sample shows the head basketball coach's salary for a sample of 10 schools playing NCAA Division I basketball. Salary data are in millions of dollars.
University Coach's Salary University Coach's Salary
North Carolina State 2.2 Miami (FL) 1.5
Iona 0.5 Creighton 1.3
Texas A&M 2.4 Texas Tech 1.5
Oregon 2.7 South Dakota State 0.3
Iowa State 2.0 New Mexico State 0.3
a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division I basketball.
b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches.
c. What is the 95% confidence interval for the population variance?
d. What is the 95% confidence interval for the population standard deviation?
From the data given, we estimate the population mean and population standard deviation. Then, we use this estimate to find a 95% confidence interval for the population variance and the population standard deviation.
Sample:
Salaries in millions of dollars: 2.2, 1.5, 0.5, 1.3, 2.4, 1.5, 2.7, 0.3, 2.0, 0.3
Question a:
The mean is the sum of all values divided by the number of values. So
[tex]\overline{x} = \frac{2.2 + 1.5 + 0.5 + 1.3 + 2.4 + 1.5 + 2.7 + 0.3 + 2.0 + 0.3}{10} = 1.42[/tex]
The sample mean salary is of 1.42 million.
Question b:
The standard deviation is the square root of the difference squared between each value and the mean, divided by one less than the number of values.
So
[tex]s = \sqrt{\frac{(2.2-1.42)^2 + (1.5-1.42)^2 + (0.5-1.42)^2 + (1.3-1.42)^2 + (2.4-1.42)^2 + (1.5-1.42)^2 + (2.7-1.42)^2 + ...}{9}} = 0.8772[/tex]
Thus, the estimate for the population standard deviation is of 0.8772 million.
Question c:
The sample size is [tex]n = 10[/tex]
The significance level is [tex]\alpha = 1 - 0.05 = 0.95[/tex]
The estimate, which is the sample standard deviation, is of [tex]s = 0.8772[/tex].
Now, we have to find the critical values for the Pearson distribution. They are:
[tex]\chi^2_{\frac{\alpha}{2},n-1} = \chi^2_{0.025,9} = 19.0228[/tex]
[tex]\chi^2_{1-\frac{\alpha}{2},n-1} = \chi^2_{0.975,9} = 2.7004[/tex]
The confidence interval for the population variance is:
[tex]\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}[/tex]
[tex]\frac{9*0.8772^2}{19.0228} < \sigma^2 < \frac{9*0.8772^2}{2.7004}[/tex]
[tex]0.3641 < \sigma^2 < 2.5646[/tex]
Thus, the 95% confidence interval for the population variance is (0.3641, 2.5646)
Question d:
Standard deviation is the square root of variance, so:
[tex]\sqrt{0.3641} = 0.6034[/tex]
[tex]\sqrt{2.5646} = 1.6014[/tex]
The 95% confidence interval for the population standard deviation is (0.6034, 1.6014).
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A sample of 4 children was drawn from a population of rural Indian children aged 12 to 60 months. The sample mean of mid-upper arm circumference was 150 mm with a standard deviation of 6.73. What is a 95% confidence interval for the mean of mid-upper arm circumference based on your sample
Answer:
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 4 - 1 = 3
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm
The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
Question 4 of 16
If the probability of rain today is 35%, what is the probability that it will not rain
today?
A. 100%
B. 65%
C. 35%
D. 50%
Answer:
I think the answer is B. 65%
Can I get some help
Please!!
Answer:
option D is the answer
Step-by-step explanation:
using the HH,ll,ha and la,
where h is the hypotenuse and l is the leg
Max has 3 fiction books and 6 nonfiction books to donate to the community center. He wants to package them so that there is an equal number of fiction and nonfiction books in each group. He also wants to have as many packages as possible. How many books are in each group?
Answer:
Each group has 1 fiction book and 2 nonfiction book(s).
If you have a volume of 366,514 cm, how many ft does that make? Round to 1 decimal.
Answer:
12024.7
Step-by-step explanation:
Searched it up.
then rounded
Which points are also part of this set of equivalent ratios? Select all that apply.
a. (3, 2)
b. (4, 2)
c. (4, 8)
d. (8, 4)
e. (12, 6)
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Answered by GAUTHMATH
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Step-by-step explanation:
the person above me is correct
given the recursive formula below, what are the first four terms of the sequence
Answer:
c
Step-by-step explanation:
The first four terms are 17, 15, 13, and 11.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(n):
f(1) = 17
f(n) = f(n - 1) - 2 if n > 1
Now,
The first term is 17.
The second term.
f(2) = f(2 - 1) - 2
= f(1) - 2
= 17 - 2
= 15
The third term.
= f(3 - 1) - 2
= f(2) - 2
= 15 - 2
= 13
The fourth term.
f(4) = f(4 - 1) - 2
= f(3) - 2
= 13 - 2
= 11
Thus,
The terms are 17, 15, 13, 11
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Suppose that there are two internet service providers in Kabwe, Eyeconnect and Topconnect.
Currently, Eyeconnect has 180 000 customers and Topconnect has 120 000 customers.
Assume that, every year, 10% of the customer base of Eyeconnect switches to Topconnect
and 5% of the customer base of Topconnect switches to Eyeconnect. For the purposes of this
question, suppose no customer leaves a company without switching to the other one and no
company attracts customers that are not leaving the other (that is, the only changes in
customer base come from switching between the two companies).
a. Find the number of customers of Eyeconnect and Topconnect after one year.
b. Find the number of customers of Eyeconnect after many years.
Answer:
a. 168000 for Eyeconnect, 132000 for Topconnect
b. 100,000
Step-by-step explanation:
a.
Because the change in customers are only due to leaving companies, we can say that, after one year, Eyeconnect loses 10% of its customers to Topconnect and Topconnect loses 5% of its customers to Eyeconnect. This represents all changes in customers.
First, we can calculate how much Eyeconnect loses, which is 10% of 180,000 = 0.1 * 180,000 = 18,000 . They then have 180,000 - 18,000 = 162,000 employees
Next, Topconnect loses 120,000 * 5% = 120,000 * 0.05 = 6,000. They then have 120,000-6,000 = 114,000 employees
We can then add the customer amounts. Note that we are subtracting both sides before adding as both companies gain and lose customers simultaneously.
We can then add how much one company lost to the other company's customers.
Eyeconnect gains 6,000 customers, so they then have 162,000 + 6,000 = 168000 employees. Topconnect gains 18,000 customers so they then have 114,000 + 18,000 = 132,000 employees
b.
After many years, the number of customers Eyeconnect has will be less than the number of customers that Topconnect has. One way to find the end amount of customers that Eyeconnect has is to figure out when the customer bases even out, or when Eyeconnect loses the same amount of customers as Topconnect so the customer base stays the exact same. We know that no customers leave or join the companies except to leave/join the other, so the total amount of customers between the two companies stays the exact same. The amount of customers is 180,000 + 120,000 = 300,000. Therefore, at the end amount,
Eyeconnect customers (E) + Topconnect customers (T) =300,000
Furthermore, if the amount of customers that leave Eyeconnect is the same that leaves Topconnect, we can say
E * 0.1 = T * 0.05
divide both sides by 0.05 to isolate the T
E * 0.1 / 0.05 = T
2 * E = T
plug that into the first equation
E + 2 * E = 300,000
3 * E = 300,000
divide both sides by 3 to isolate E
E = 100,000 after many years
Please help please !!!
========================================================
Explanation:
You can use the AAS (angle angle side) theorem to prove that triangle ABD is congruent to triangle CBD.
From there, we can then say that AD and DC are the same length
AD = DC
3y+6 = 5y-18
3y-5y = -18-6
-2y = -24
y = (-24)/(-2)
y = 12
Ellicott City Manufacturers, Inc., has sales of $6,344,210, and a gross profit margin of 67.3 percent. What is the firm's cost of goods sold? Round your final answer to the nearest dollar.
Answer:
$3792116
Step-by-step explanation:
that's the answer above
Suppose you believe that the true average daily trade volume for General Electric stock is 49,829,719 shares and a standard deviation of 21,059,637 shares. Considering a 95% confidence level: What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares
Answer:
The minimum sample size is 1,704.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 21,059,637 shares
This means that [tex]\sigma = 21059637[/tex]
What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares?
This is n for which [tex]M = 1000000[/tex], so:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1000000 = 1.96\frac{21059637}{\sqrt{n}}[/tex]
[tex]1000000\sqrt{n} = 1.96*21059637[/tex]
[tex]\sqrt{n} = \frac{1.96*21059637}{1000000}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*21059637}{1000000})^2[/tex]
[tex]n = 1703.8[/tex]
Rounding up:
The minimum sample size is 1,704.
which ecpression is the simplest form of 3(3x-4)-5(x+3)
[tex]\boxed{ \sf{Answer}} [/tex]
[tex] \sf \: 3(3x - 4) - 5(x + 3) \\ \sf =( 3 \times 3x) - (3 \times 4) + ( - 5 \times x) +( - 5 \times 3 ) \\ \sf = 9x - 12 - 5x - 15 \\ \sf = 9x - 5x - 12 - 15 \\ = \underline{ \bf 4x - 27}[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
[tex]\\ \sf\longmapsto 3(3x-4)-5(x+3)[/tex]
[tex]\\ \sf\longmapsto 9x-12-5x-15[/tex]
[tex]\\ \sf\longmapsto 9x-5x-15-12[/tex]
[tex]\\ \sf\longmapsto (9-5)x-27[/tex]
[tex]\\ \sf\longmapsto 4x-27[/tex]
What is the distance between the following points?
WILL GIVE BRAINLIEST!!
Answer:
A. 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a coordinate planeCoordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Identify points from graph.
Point (8, 5)
Point (4, 2)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(8 - 4)^2 + (5 - 2)^2}[/tex][√Radical] (Parenthesis) Subtract: [tex]\displaystyle d = \sqrt{4^2 + 3^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{16 + 9}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{25}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 5[/tex]Probability of picking a blue marble and a yellow marble when 2 marbles are picked (without replacement) from a bag containing 4 blue and 4 yellow marbles
Answer:
9/49
Step-by-step explanation:
that is the procedure above
A triangle has base of 7 1/8 feet and height 6 1/4 feet. Find the area of a triangle as a mixed number.
Answer: The area is 22 17/64.
Step-by-step explanation:
base = 7 1/8 = 57/8
height = 6 1/4 = 25/4
area = 1/2*b*h
= 1/2*57/8*25/4
= 1425/64
= 22 17/64
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy when their third child is born, given that the first two children were both boys
The required probability of a couple having a baby boy when their third child is born is 1/2.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
Assuming boys and girls are equally likely.
The first two children were both boys
According to given question we have
The probability of having a baby girl is an independent probability.
The first two children were both boys
So, it is not related to the previous child.
So required probability = 1/2
Therefore, the required probability of a couple having a baby boy when their third child is born is 1/2.
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