Answer:
235 people
Step-by-step explanation:
Given:
P' = 15% = 0.15
1 - P' = 1 - 0.15 = 0.85
At 99% confidence leve, Z will be:
[tex] \alpha [/tex] = 1 - 99%
= 1 - 0.99 = 0.01
[tex] \alpha /2 = \frac{0.01}{2} = 0.005 [/tex]
[tex] Z\alpha/2 = 0.005 [/tex]
Z0.005 = 2.576
For the minimum number of 25-50 year old people who must be surveyed in order to estimate the proportion of non-grads to within 6%, we have:
Margin of error, E = 6% = 0.06
sample size = n = [tex] (\frac{Z\alpha /2}{E})^2 * P* (1 - P) [/tex]
[tex] = (\frac{2.576}{0.06}) ^2 * 0.15 * 0.85 [/tex]
= 235.02 ≈ 235
A number of 235 people between 25-30 years should be surveyed .
Answer:
n = 236
Step-by-step explanation:
Solution:-
- The proportion of people over the age of 50 who didn't graduate from high school are, p = 0.15 - ( 15 % )
- We are to evaluate the minimum sample size " n " from the age group of 25-50 year in order to estimate the proportion of non-grads within a standard error E = 6% of the true proportion p within 99% confidence.
- The minimum required sample size " n " for the standard error " E " for the original proportion p relation is given below:
[tex]n = \frac{(Z_\alpha_/_2)^2 * p* ( 1 - p )}{E^2}[/tex]
- The critical value of standard normal is a function of significance level ( α ), evaluated as follows:
significance level ( α ) = ( 1 - CI/100 )
= ( 1 - 99/100 )
= 0.01
- The Z-critical value is defined as such:
P ( Z < Z-critical ) = α / 2
P ( Z < Z-critical ) = 0.01 / 2 = 0.005
Z-critical = Z_α/2 = 2.58
- Therefore the required sample size " n " is computed as follows:
[tex]n = \frac{(2.58)^2 * 0.15* ( 1 - 0.15 )}{0.06^2}\\\\n = \frac{6.6564 * 0.1275}{0.0036}\\\\n = \frac{0.848691}{0.0036}\\\\n = 235.7475\\[/tex]
Answer: The minimum sample size would be next whole number integer, n = 236.
Please help
Find the volume of the sphere. Express your answer in terms of π.
13,500π in3
4,500π in3
67,500π in3
300π in3
Please consider the graph of the sphere.
We know that the volume of sphere is equal to [tex]\frac{4}{3}\pi r^3[/tex], where r represents radius of sphere.
We can see that diameter of sphere is 30 inches. We know that radius is half the diameter, so radius of the given sphere would be half of 30 inches that is [tex]\frac{30}{2}=15[/tex] inches.
[tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V=\frac{4}{3}\pi (15\text{ in})^3[/tex]
[tex]V=\frac{4}{3}\pi \times 3375\text{ in}^3[/tex]
[tex]V=4\times 1125\pi \text{ in}^3[/tex]
[tex]V=4500\pi \text{ in}^3[/tex]
Therefore, the volume of the given sphere is [tex]4500\pi\text{ in}^3[/tex] and option B is the correct choice.
According to a report from the United States Environmental Protection Agency, burning one gallon of gasoline typically emits about 8.9 kg of CO2. A fuel company wants to test a new type of gasoline designed to have lower CO2 emissions. Here are their hypotheses:
H0: μ = 8.9 kg
Ha: μ < 8.9 kg (where μ is the mean amount of CO2 emitted by burning one gallon of this new gasoline).
Which of the following would be a Type II error in this setting?
A. The mean amount of CO2 emitted by the new fuel is actually 89 kg but they conclude it is lower than 89 kg
B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg
C. The mean amount of CO2 emitted by the new fuel is actual 89 kg and they alto conclude it is lower than 89 kg and they conclude it is lower than 9 kg
D. The mean amount of CO2 emitted by the new fuels actually lower than 8.9
Answer:
B. The mean amount of [tex]CO_2[/tex] emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg
Step-by-step explanation:
A Type II error is the failure to reject a false null hypothesis.
Given the null and alternate hypothesis of a fuel company which wants to test a new type of gasoline designed to have lower [tex]CO_2[/tex] emissions.:
[tex]H_0: \mu = 8.9 kg\\H_a: \mu < 8.9 kg \\\text{ (where \mu is the mean amount of CO_2 emitted by burning one gallon of this new gasoline)}[/tex]
where [tex]\mu[/tex] is the mean amount of [tex]CO_2[/tex] emitted by burning one gallon of this new gasoline.
If the null hypothesis is false, then:
[tex]H_a: \mu < 8.9 kg[/tex]
A rejection of the alternate hypothesis above will be a Type II error.
Therefore:
The Type II error is: (B) The mean amount of [tex]CO_2[/tex] emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.
You can use the definition of type 2 error to find out which of the given option describes the type 2 error.
The Option which indicates Type II error is:
Option B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.
What is Type I and Type II error?Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.
The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false).The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.
What is the type II error in the given context?Since the null hypothesis here is [tex]H_0: \text{typically emitted } {\rm CO_2} = 8.9 \: \rm kg[/tex],
Thus the type II error would be when we fail to reject that CO2 emission is 8.9 kg (or say we accept that CO2 emission is 8.9 kg generally) but the actual amount was lower than 8.9 kg(the alternate hypothesis was true)
Thus,
The Option which indicates Type II error is:
Option B. The mean amount of CO2 emitted by the new fuel is actually lower than 89 kg but they fall to conclude it is lower than 89 kg.
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Solve the equation by completing the square.
X^2 + 4x =45
Answer:
The answer is x=5, −9
A national park keeps track of how many people per car enter the park.Today, 57 cars had 4 people, 61 cars had 2 people, 9 cars had 1 person, and 5 cars had 5 people. What is the average number of people per car
The average number of people per car visiting the national park is approximately 2.91.
Explanation:In order to find the average number of people per car, you would first multiply the number of cars by the number of people in each.
Therefore, 57 cars had 4 people (57*4=228), 61 cars had 2 people (61*2=122), 9 cars had 1 person (9*1=9), and 5 cars had 5 people (5*5=25). After this, add all the results (228+122+9+25 = 384).
The total number of cars is the sum of all cars, which is (57+61+9+5 = 132).
Now, to find the average number of people per car, you would divide the total number of people, which is 384 by the total number of cars, which is 132. Therefore, the average number of people per car is 384 / 132 = about 2.91 people per car.
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There is a 1% delinquency rate for consumers with FICO (Fair Isaac & Company) credit rating scores above 800. If the Jefferson Valley Bank provides large loans to 12 people with FICO scores above 800, what is the probability that at least one of them becomes delinquent? Based on that probability, should the bank plan on dealing with a delinquency?
Answer:
Yes
Step-by-step explanation:
What's 1 1/4 equal to?
Answer:
1.25
Step-by-step explanation:
can someone help me with this :(
Answer:
9
Step-by-step explanation:
6+x, when x = 3
6+(3)
6+3=9
Answer:
9
Step-by-step explanation:
6 + x, when x = 3
So, 6 + 3 = answer
So, 6 + 3 = 9
Stay Safe, Stay at Home!! Lots of Love <3 <3 =) :3
What is the radius and diameter of the following circle 7cm
Answer:
7
3.5
Step-by-step explanation:
Answer:
The radius of the circle is [tex]\(7 \, \text{cm}\)[/tex], and the diameter is [tex]\(14 \, \text{cm}\)[/tex].
Explanation:
The radius [tex](\(r\))[/tex] of a circle is half of its diameter ([tex]\(d\)[/tex]), and the diameter ([tex]\(d\)[/tex]) is twice the radius ([tex]\(r\)[/tex]). So, we can find the radius and diameter of the circle with a given radius of 7 cm.
Given:
Radius ([tex]\(r\)[/tex]) = 7 cm
To find the diameter ([tex]\(d\)[/tex]), we use the relationship:
[tex]\[d = 2r\][/tex]
Substituting the given value of the radius:
[tex]\[d = 2 \times 7\][/tex]
[tex]\[d = 14\][/tex]
So, the diameter of the circle is [tex]\(14 \, \text{cm}\)[/tex].
Therefore, the radius of the circle is [tex]\(7 \, \text{cm}\)[/tex], and the diameter is [tex]\(14 \, \text{cm}\).[/tex]
Question:
What is the diameter of a circle whose radius is 7 cm?
A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly.
If the student guesses on each question, what is the probability that the student will pass the quiz?
Answer:
The probability of the student will pass the quiz = .0546
Step-by-step explanation:
Given -
Total no of question = 10
If the student guesses on each question there are two outcomes true of false
the probability of guesses question correctly = [tex]\frac{1}{2}[/tex]
the probability of success is (p) = [tex]\frac{1}{2}[/tex]
the probability of guesses question incorrectly = [tex]\frac{1}{2}[/tex]
the probability of failure is (q) = 1- p = [tex]\frac{1}{2}[/tex]
If the student guesses on each question he must answered at least 8 question correctly
the probability of the student will pass the quiz = [tex]P(X\geq8 )[/tex]
= P(X = 8 ) + P(X = 9) + P(X = 10 )
= [tex]\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}[/tex]
= [tex]\frac{10!}{(2!)(8!)}(\frac{1}{2})^{8}(\frac{1}{2})^{10 - 8} +\frac{10!}{(1!)(9!)} (\frac{1}{2})^{9}(\frac{1}{2})^{10 - 9} + \frac{10!}{(0!)(10!)}(\frac{1}{2})^{10}(\frac{1}{2})^{10 - 10}[/tex]
= [tex]45\times\frac{1}{2^{10}} + 10\times\frac{1}{2^{10}} + 1\times\frac{1}{2^{10}}[/tex]
= [tex]\frac{56}{2^{10}}[/tex]
= .0546
Final answer:
The probability of a student passing the true or false quiz by guessing and getting at least 8 out of 10 questions correct is 7/128. This is calculated by finding the binomial probabilities for 8, 9, and 10 correct guesses and summing them.
Explanation:
To determine the probability that the student passes the quiz by guessing, we need to calculate the chances of them getting at least 8 out of 10 true or false questions correct. Since each question can only be true or false, there's a 1/2 chance of guessing each question correctly, and therefore, a 1/2 chance of guessing incorrectly.
The scenarios in which a student can pass are by getting 8, 9, or 10 questions correct. We will use the binomial probability formula, which is P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k), where 'n' is the number of trials (questions), 'k' is the number of successes (correct answers), and 'p' is the probability of success on an individual trial (1/2 for true/false questions).
The probability of getting exactly 8 questions right is (10 choose 8) * (1/2)^8 * (1/2)^(10-8).
The probability of getting exactly 9 questions right is (10 choose 9) * (1/2)^9 * (1/2)^(10-9).
The probability of getting all 10 questions right is (10 choose 10) * (1/2)^10 * (1/2)^(10-10).
We add these individual probabilities together to find the total probability of passing the quiz.
Using a calculator or the binomial coefficients, we find:
P(getting 8 right) = 45 * (1/2)^10,
P(getting 9 right) = 10 * (1/2)^10,
P(getting 10 right) = 1 * (1/2)^10.
Adding these together gives us the total probability:
P(8 or more correct) = [45 + 10 + 1] * (1/2)^10 = 56 * (1/2)^10
After simplifying, we find that the probability of passing the quiz with at least 8 correct answers is thus 56/1024, which can be reduced to 7/128.
A laptop computer is purchased for 2500 . After each year, the resale value decreases by 25% . What will the resale value be after 4 years?
Use the calculator provided and round your answer to the nearest dollar.
Answer: the resale value would be $791 after 4 years
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
y = b(1 - r)^x
Where
y represents the value of the laptop computer after x years.
x represents the number of years.
b represents the initial value of the laptop computer.
r represents rate of decay.
From the information given,
P = $2500
x = 4
r = 25% = 25/100 = 0.25
Therefore,
y = 2500(1 - 0.25)^4
y = 2500(0.75)^4
y = $791
Need help It is working with functions and I need assistance
Answer: its 4. Look at the graph, x is horizontal and y is vertical (first go sideways then go up.) if coordinates are x,y then first go sideways when looking for x. they give you x. 7. then we go up. the graph intersects 7 at 4, therefore the coords are 7, 4 and your y coordinate is 4.
Step-by-step explanation:
Rose and Jack plan to study together for the Math test. They decide to meet at the library between 8:00pm and 8:30pm. Assume that they each arrive (independently) at a random time (uniformly) in this interval. It is possible that someone has to wait up to 30 minutes for the other to arrive.
(a). What is the probability that someone (Rose or Jack, whichever arrives first) must wait more than 20 minutes until the other one arrives? What is the probability that Joe waits more than 20 minutes?
(b). What is the expected amount of time that somebody (the first person to arrive) waits? Formulate the problem and solve. Make sure you carefully define the random variables you use!
Answer:
(a) 1/3
(b) 1/15
Step-by-step explanation:
(a)Let X denote the waiting time in minutes. It is given that X follows a uniform distribution, and since the variable being measured is time, we assume it to be a continuous uniform distribution.
[tex] \[f_X(x) =\begin{cases} \frac{1}{30} & 0\leqx\leq 30\\ 0 & otherwise \end{cases}\][/tex]
Now
[tex] P(X>20) = \int_{20}^{30}f_X(x) = \frac{1}{30} \times 10 = \frac{1}{3}[/tex].
Jack or Rose arriving first is equally likely, therefore the probability of Jack waiting is just the half of the above obtained probability i.e [tex]\frac{1}{6}[/tex]
(b)Using the formula for the expectation of a uniform continuous distribution,
[tex] E(X) = \frac{30+0}{2} = 15[/tex]
^^^ what is the measure of angle C
Answer:
38
Step-by-step explanation:
An inscribed angle is an angle with its vertex "on" the circle, formed by two intersecting chords.
Inscribed Angle =1/2 Intercepted Arc
We know the intercepted are is 76 degrees
<c = 1/2 (76) = 38
The inscribed angle = 38
Answer:
38
Step-by-step explanation:
Its definetly under 90 degrees. And it is also under 76 degress, so thatmeans it is 38 degrees
Peter just buried a treasure chest on a remote island and is making a map so he can find it later. One of the key landmarks in the area is a small rectangular hut, 5m by 8m
Answer: 10 by 16
Step-by-step explanation:
The times between the arrivals of customers at a taxi stand are independent and have a distribution F with mean F. Assume an unlimited supply of cabs, such as might occur at an airport. Suppose that each customer pays a random fare with distribution G and mean G. Let W.t/ be the total fares paid up to time t. Find limt!1EW.t/=t.
Answer:
Check the explanation
Step-by-step explanation:
Let
\(W(t) = W_1 + W_2 + ... + W_n\)
where W_i denotes the individual fare of the customer.
All W_i are independent of each other.
By formula for random sums,
E(W(t)) = E(Wi) * E(n)
\(E(Wi) = \mu_G\)
Mean inter arrival time = \(\mu_F\)
Therefore, mean number of customers per unit time = \(1 / \mu_F\)
=> mean number of customers in t time = \(t / \mu_F\)
=> \(E(n) = t / \mu_F\)
Using the expression above choose the correct answer for the new balance in amount of interest earned in the following compound interest problem $950 at 7% for eight years compounded annually
Answer:
Given:
P=950
r=0.07
t=8
F=950(1.07)^8
= 1632.28 (total amount)
Interest = total amount - principal
=1632.28 - 950
=682.28
Step-by-step explanation:
The formula is:
Future value = accumulated amount, F = P(1+r)^t
P=principal
r=annual interest rate [compounded annually]
t=number of years of loan
Based on the number line which numbers are identified?
A. All numbers bigger than -3 and smaller than 3
B. All numbers between -3 and 3 including -3 and 3
C. All numbers bigger than 0
D. All numbers less than 3
Answer:
A is correct, "All numbers bigger than -3 and smaller than 3"
Step-by-step explanation:
The open circle means greater than, if it was filled in, it would be greater than or equal to. And the black line connecting each shows its more than -3 and less than 3. Hope this helps! Please rate brainliest if it does :)
Company claims that their tires outlast the tires ofCompany B by more than 10,000 miles. Data has been collected and summarized below: Test the claim at the .05 level assuming and equal Company An-16 -63,500 s- 4000 Company B n-12 K-49,500 s-6000
Answer:
The null hypothesis is rejected (P-value=0.0 28).
There is enough evidence to support the claim that that Company A tires outlast the tires of Company B by more than 10,000 miles.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that that Company A tires outlast the tires of Company B by more than 10,000 miles.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=10000\\\\H_a:\mu_1-\mu_2> 10000[/tex]
being μ1: average for Company A and μ2: average for Company B.
The significance level is 0.05.
The sample 1, of size n1=16 has a mean of 63,500 and a standard deviation of 4,000.
The sample 1, of size n1=12 has a mean of 49,500 and a standard deviation of 6,000.
The difference between sample means is Md=14,000.
[tex]M_d=M_1-M_2=63500-49500=14000[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{4000^2}{16}+\dfrac{6000^2}{12}}\\\\\\s_{M_d}=\sqrt{1000000+3000000}=\sqrt{4000000}=2000[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{14000-10000}{2000}=\dfrac{4000}{2000}=2[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=16+12-2=26[/tex]
This test is a right-tailed test, with 26 degrees of freedom and t=2, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2)=0.028[/tex]
As the P-value (0.028) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that that Company A tires outlast the tires of Company B by more than 10,000 miles.
In statistics, you can use a two-sample t-test to compare the lifespans of two types of tires. After setting up the null and alternative hypotheses, we use the alpha level, test statistic, and p-value to decide whether to reject the null hypothesis and accept the company's claim.
To clarify, testing this claim about tire lifespan falls under the category of hypothesis testing within statistics. In your case, you're comparing the lifespan of two types of tires which involves a two-sample t-test. Unfortunately, you've only provided raw data, but let's tackle this conceptually.
First, we set up the null and alternative hypotheses. The null hypothesis, usually denoted as H0, asserts that there's no difference between the means of the two populations. In this case, it says the lifespan of Company A's tires are the same as Company B's tires.
The alternative hypothesis, usually denoted as Ha, is the claim you're trying to test - in this case, that Company A's tires do last 10,000 miles longer than Company B's tires. In this hypothesis test, your alpha, which is the threshold of how much you're willing to be wrong, is 0.05.
After calculating the t-score and finding the p-value using statistical software or a t-distribution table, you compare the p-value to the alpha. If the p-value is less than the alpha, that means the result is statistically significant and thus you reject the null hypothesis.
Based on the decision and reason provided in your question, the conclusion would be that there is sufficient evidence at the 0.05 level to support the claim that Company A's tires outlast Company B's tires by more than 10,000 miles.
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Element X decays radioactively with a half life of 9 minutes. If there are 960 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?
y=a(.5)^t/h
Answer:
It will take 41.3 minutes for the element to decay to 40 grams
Step-by-step explanation:
The amount of element after t minute is given by the following equation:
[tex]x(t) = x(0)e^{-rt}[/tex]
In which x(0) is the initial amount and r is the rate that it decreases.
Element X decays radioactively with a half life of 9 minutes.
This means that [tex]x(9) = 0.5x(0)[/tex]. We use this to find r. So
[tex]x(t) = x(0)e^{-rt}[/tex]
[tex]0.5x(0) = x(0)e^{-9r}[/tex]
[tex]e^{-9r} = 0.5[/tex]
[tex]\ln{e^{-9r}} = \ln{0.5}[/tex]
[tex]-9r = \ln{0.5}[/tex]
[tex]9r = -\ln{0.5}[/tex]
[tex]r = -\frac{\ln{0.5}}{9}[/tex]
[tex]r = 0.077[/tex]
So
[tex]x(t) = x(0)e^{-0.077t}[/tex]
There are 960 grams of Element X
This means that [tex]x(0) = 960[/tex]
[tex]x(t) = 960e^{-0.077t}[/tex]
How long, to the nearest tenth of a minute, would it take the element to decay to 40 grams?
This is t when [tex]x(t) = 40[/tex]. So
[tex]x(t) = 960e^{-0.077t}[/tex]
[tex]40 = 960e^{-0.077t}[/tex]
[tex]e^{-0.077t} = \frac{40}{960}[/tex]
[tex]\ln{e^{-0.077t}} = \ln{\frac{40}{960}}[/tex]
[tex]-0.077t = \ln{\frac{40}{960}}[/tex]
[tex]0.077t = -\ln{\frac{40}{960}}[/tex]
[tex]t = -\frac{\ln{\frac{40}{960}}}{0.077}[/tex]
[tex]t = 41.3[/tex]
It will take 41.3 minutes for the element to decay to 40 grams
For the single roots -1 and 2,the graph ——— the x-axis at the intercepts
/crosses/
/does not intersect/
/touches/
—————————
For the double root 3 the graph ——— at the intercepts
/crosses/
/does not intersect/
/touches/
Answer:
crosses and touches is %100 RIGHT
Step-by-step explanation:
For the single roots -1 and 2,the graph crosses the x-axis at the intercepts
For the double root 3 the graph touches at the intercepts
What are intercepts?"These are the point at which the graph of the function intersects the x-axis or Y-axis"
What are roots of function?"These are the values for which the function equals zero."
For given question,
We have been given a function f(x) = (x + 1)(x - 2)(x - 3)²
To find the roots of function f(x)
⇒ f(x) = 0
⇒ (x + 1)(x - 2)(x - 3)² = 0
⇒ x + 1 = 0 or x - 2 = 0 or (x - 3)²=0
⇒ x = -1 or x = 2 or x = 3
This means x = -1, 2, 3 are the roots of the function f(x)
From the graph of the function we can observe that the for the single roots -1 and 2,the graph of the function f(x) crosses the x-axis at the intercepts x = -1 and x = 2 respectively.
And for the double root 3 the graph of the function f(x) touches at the intercept x = 3.
Therefore, For the single roots -1 and 2,the graph crosses the x-axis at the intercepts.
For the double root 3 the graph touches at the intercepts.
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What’s the area of the circle in terms of pi
Answer:
A = πr²
Step-by-step explanation:
(1 point) If f(t) is continuous for t≥0, the {\it Laplace transform} of f is the function F defined by F(s)=∫[infinity]0f(t)e−stdt and the domain of F is the set consisting of all number s for which the integral converges. (a) Find the Laplace transform of f(t)=1. (Make sure you can state the domain of F if we ask for it later!) F(s)=
Answer:
The Laplace transform of f(t) = 1 is given by
F(s) = (1/s) for all s>0
Step-by-step explanation:
Laplace transform of a function f(t) is given as
F(s) = ∫∞₀ f(t) e⁻ˢᵗ dt
Find the Laplace transform for when f(t) = 1
F(s) = ∫∞₀ 1.e⁻ˢᵗ dt
F(s) = ∫∞₀ e⁻ˢᵗ dt = (1/s) [-e⁻ˢᵗ]∞₀
= -(1/s) [1/eˢᵗ]∞₀
Note that e^(∞) = ∞
F(s) = -(1/s) [(1/∞) - (1/e⁰)]
Note that (1/∞) = 0
F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)
Hope this Helps!!!
In this exercise we have to use the knowledge of the Laplace transform to calculate the total value of the given function, thus we will find that:
[tex]F(s) = (1/s) \\for \ all\ s>0[/tex]
So we have that the Laplace transform can be recognized as:
[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt[/tex]
Find the Laplace transform for when f(t) = 1, we have that:
[tex]F(s) = \int\limits^\infty _0 { f(t) e^{-st} \, dt \\\\ F(s) = \int\limits^\infty _0 { 1 e^{-st} \, dt[/tex]
[tex]F(s) = \int\limits^\infty _0 { e^{-st} \, dt = (1/s) [-e^{-st}] \\[/tex]
[tex]F(s) = -(1/s) [(1/\infty ) - (1/e^0)] \\F(s) = -(1/s) [0 - 1] = -(1/s) (-1) = (1/s)[/tex]
See more about Laplace transform at brainly.com/question/2088771
Like charges repel and I like charges attract Coulomb’s law states that the force F of attraction or repulsion between two charges a1 and a2 is given by f=kq1q2/r^2
Step-by-step explanation:
For the charges that have same sign of charges will repel each other while for the charges that have different charges will attract each other. So, we can say that like charges repel and unlike charges attract each other.
The Coulomb's law of attraction of repulsion states that force between charges is directly proportion to the product of charges and inversely proportional to the square of distance between them. Mathematically, it is given by :
[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]
Hence, all the given statements are true.
7500 dollars is placed in an account with an annual interest rate of 7.75%. To the nearest year, how long will it take for the account value to reach 38200 dollars?
Answer:
It will take 55 years for the account value to reach 38200 dollars
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.
After t years, the total amount of money is:
[tex]T = E + P[/tex].
In this problem, we ahve that:
[tex]T = 38200, P = 7500, I = 0.075[/tex]
So
First we find how much we have to earn in interest.
[tex]38200 = E + 7500[/tex].
[tex]E = 38200 - 7500[/tex]
[tex]E = 30700[/tex]
How much time to earn this interest?
[tex]E = P*I*t[/tex]
[tex]30700 = 7500*0.075*t[/tex]
[tex]t = \frac{30700}{7500*0.075}[/tex]
[tex]t = 54.6[/tex]
Rounding up
It will take 55 years for the account value to reach 38200 dollars
Answer:
It will take approximately 53 years for the account value to reach 38200 dollars
Step-by-step explanation:
Given the following parameters:
Principal P = 7500
Interest Rate R = 7.75% = 0.0775
Let us find the simple interest for the first year
Simple Interest, I = PRT
with T = 1 year = 12 months
I = 7500 × 0.0775 × 1
= 581.25
The amount for the first year is the addition of the principal and simple interest.
Amount, A = 7500 + 581.25 = 8081.25.
Now, we want to find the time T when Amount A = 38200
Given A = P + I
And I = PRT
A = P + PRT
= P(1 + RT)
Let us make T the subject of the formula.
Dividing both sides by P
A/P = 1 + RT
A/P - 1 = RT
T = ((A/P) - 1)/R
T = ((38200/7500) - 1)/0.0775
= (307/75)/0.0775
= 52.8172043
≈ 53 years.
A butterfly population is decreasing at a rate of 0.82% per year. There are currently about 100,000 butterflies in the population. How many butterflies will there be in the population in 250 years?
Answer:
12,765
Step-by-step explanation:
The exponential formula for the population can be written as ...
population = (initial population)(1 -decay rate)^t
where t is in years, and the decay rate is the loss per year.
The given numbers make this ...
population = 100,000(0.9918^t)
In 250 years, the population will be about ...
population = 100,000(0.9918^250) ≈ 12,765.15
There will be about 12,765 butterflies in 250 years.
In 250 years, there will be approximately 12,765 butterflies in the population.
This figure is obtained by applying the exponential decay formula with a 0.82% decrease rate per year from an initial population of 100,000 butterflies.
To determine the butterfly population in 250 years given a yearly decrease rate of 0.82%, we utilize the exponential decay formula:
[tex]\[ P(t) = P_0 \times (1 - r)^t \][/tex]
where:
- (P(t)) represents the population after (t) years,
- (P_0) is the initial population, which is 100,000,
- (r) is the annual decrease rate in decimal form, which is 0.82% or 0.0082,
- (t) is the time in years, here 250 years.
By substituting the given values into the formula:
[tex]\[ P(250) = 100,000 \times (1 - 0.0082)^{250} \][/tex]
Upon calculation, the population after 250 years is found to be approximately 12,765, rounding to the nearest whole number for practical purposes. This result is based on the principle of exponential decay, reflecting how a consistent percentage decrease affects the population over a prolonged period.
A study was conducted on shoe sizes of students, reported in European sizes. For the women, the mean size was 38.73 with a standard deviation of 1.75. To convert
European shoe sizes to U.S. sizes for women, use the equation shown below.
USsize = EuroSize x 0.7987 - 22.2
a) What is the mean women's shoe size for these responses in U.S. units?
b) What is the standard deviation in U.S. units?
a) The mean women's shoe size in U.S. units is (8.73.
(Round to two decimal places as needed.)
s
.
b) The standard deviation in U.S. units is
(Round to two decimal places as needed.)
Answer:
The mean women's shoe size in U.S. units is 8.73.
The standard deviation in U.S. units is 1.40.
Step-by-step explanation:
For the women, the mean size was 38.73 with a standard deviation of 1.75. This size is expressed in European units.
If we want to convert to US units, we have to use the equation:
[tex]US\, size=EuroSize*0.7987-22.2[/tex]
If we use the properties of the expected value, then the mean expressed in US units is:
[tex]Property: E(y)=E(ax+b)=aE(x)+b\\\\\\E(y)=0.7987E(x)-22.2\\\\E(y)=0.7987*38.73-22.2\\\\E(y)=8.73[/tex]
To calculate the standard deviation, we use the properties of variance:
[tex]Property: V(y)=V(ax+b)=a^2V(x)\\\\\sigma_y=\sqrt{a^2V(x)}=a\sigma_x\\\\\sigma_y=0.7987*1.75=1.40[/tex]
Which investment has the highest liquidity and can be converted into cash easy
Answer: Stocks will have the highest liquidity and convertability to cash
What type of triangle is shown
Answer:
Where's the triangle?
Step-by-step explanation:
Suppose there are two full bowls of cookies. Bowl #1 has 12 chocolate chip and 24 plain cookies, while bowl #2 has 22 of each. Our friend Fred picks a bowl at random, and then picks a cookie at random. The cookie turns out to be a plain one. What is the probability that Fred picked Bowl #1? 56.8966
Answer:
0.5
Step-by-step explanation:
the volume of a cube when one side is 4
Answer:
64
Step-by-step explanation:
The answer is 64, because 4 to the 3rd power is 64. When finding the volume of a cube, find the length of one side to the 3rd.