A certain small town has a population of 5000 residents. You want to calculate a confidence interval for the average number of gallons of gas bought per month by the residents of this town. You want to be 95% confident that the true value of the population mean is within your interval, and you need to have a margin of error no higher than 10 gallons per month. Based on your previous research in simlar towns, you believe that the population standard deviation is 50 galons per month Give the appropriate statistical symbol or formula for each of the foliowing numbers in this 1, 5000= 2. 50 4 What is the value of a? 5, What is the value of α/2 ? 三6. What is the value of Zan? 1. What wil be the width of your confidence interval from the smaller number to the larger number? (Hint Think about how the MOE is related to the width of the confidence interval)
Answer:
1. 5000 = N
2. 50 = σ
3. 95% = confidence level (1-α)
4. α = 0.05
5. α/2=0.025=2.5%
6. z_(α/2)=-1.96
1. Width of confidence interval UL-LL=20
Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean (average number of gallons of gas bought per month by the residents of this town).
The margin of error has to be below 10 gallons/month.
The population standard deviation is considered 50 gallons/month.
1. 5000 = N.
This is the population size N for this study, as this is the total population of the town.
2. 50 = σ
This is the value of the population standard deviation σ, as it is estimated from other studies.
3. 95% = (1-α)
This is the confidence level of the interval, and is equal to 1 less the significance level α.
4. α = 0.05
This is calculated from the confidence level. As the confidence level is 95%, the level of significance is 5%.
[tex]1-\alpha=0.95\\\\\alpha=1-0.95\\\\\alpha=0.05[/tex]
5. α/2=0.05/2=0.025=2.5%
6. The value os z_α/2 is obtained from a standard normal distribution table, where:
[tex]P(z<z_{\alpha/2})=0.025\\\\z_{\alpha/2}=-1.96[/tex]
z_α/2=-1.96
1. As the margin of error is 10 (maximum value), the difference between upper and lower bound is:
[tex]UL-LL=2*MOE=2*10=20[/tex]
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.
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 = \(t / \mu_F\)
=> \(E(n) = t / \mu_F\)
FIND THE AREA OF THE SHADED REGION
Answer:
40 square inches
Step-by-step explanation:
The shaded area is the area of a triangle with base 10 in and height 8 in. It is given by the area formula ...
A = (1/2)bh = (1/2)(10 in)(8 in) = 40 in²
The shaded area is 40 square inches.
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.
Learn more about type I and type II error here:
https://brainly.com/question/26067196
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:
A software developer wants to know how many new computer games people buy each year. A sample of 1233 people was taken to study their purchasing habits. Construct the 99% confidence interval for the mean number of computer games purchased each year if the sample mean was found to be 7.4. Assume that the population standard deviation is 1.4. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean number of computer games purchased each year is between 7.3 and 7.5 games.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
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.
[tex]M = 2.575\frac{1.4}{\sqrt{1233}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7.4 - 0.1 = 7.3.
The upper end of the interval is the sample mean added to M. So it is 7.4 + 0.1 = 7.5
The 99% confidence interval for the mean number of computer games purchased each year is between 7.3 and 7.5 games.
Answer: = ( 7.3, 7.5)
Therefore at 99% confidence interval (a,b) = ( 7.3, 7.5)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 7.4
Standard deviation r = 1.4
Number of samples n = 1233
Confidence interval = 99%
z(at 99% confidence) = 2.58
Substituting the values we have;
7.4+/-2.58(1.4/√1233)
7.4+/-2.58(0.03987)
7.4+/-0.1028
7.4+/-0.1
= ( 7.3, 7.5)
Therefore at 99% confidence interval (a,b) = ( 7.3, 7.5)
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]
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:
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
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.
Learn more about Average calculation here:https://brainly.com/question/31930809
#SPJ3
Evaluate ∫SF⃗ ⋅dA⃗ , where F⃗ =(bx/a)i⃗ +(ay/b)j⃗ and S is the elliptic cylinder oriented away from the z-axis, and given by x2/a2+y2/b2=1, |z|≤c, where a, b, c are positive constants.
Answer:
Therefore surface integral is [tex]\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c[/tex].
Step-by-step explanation:
Given function is,
[tex]\vec{F}=\frac{bx}{a}\uvec{i}+\frac{ay}{b}\uvec{j}[/tex]
To find,
[tex]\int\int_{S}\vec{F}dS[/tex]
where S=A=surfece of elliptic cylinder we have to apply Divergence theorem so that,
[tex]\int\int_{S}\vec{F}dS[/tex]
[tex]=\int\int\int_V\nabla.\vec{F}dV[/tex]
[tex]=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV[/tex]
[tex]=\frac{a^2+b^2}{ab}\int\int\int_VdV[/tex]
[tex]=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}[/tex]
[tex]=\frac{a^2+b^2}{ab}\times \pi ab\times 2c=\pi (a^2+b^2)c[/tex]
If unit vector [tex]\cap{n}[/tex] directed in positive (outward) direction then z=c and,[tex]\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1}<\frac{bx}{a}, \frac{ay}{b}, 0> . <-z_x,z_y,1>dA[/tex]
[tex]=\int\int_{S_1}<\frac{bx}{a},\frac{ay}{b}, 0>.<0,0,1>dA=0[/tex]
If unit vector [tex]\cap{n}[/tex] directed in negative (inward) direction then z=-c and,[tex]\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}<\frac{bx}{a}, \frac{ay}{b}, 0>. -<-z_x,z_y,1>dA[/tex]
[tex]=\int\int_{S_2}<\frac{bx}{a},\frac{ay}{b}, 0>. -<0,0,1>dA=0[/tex]
Therefore surface integral without unit vector of the surface is,
[tex]\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c[/tex]
The value of ∫SF ⋅dA where F =(bx/a)i +(ay/b)j and S is the elliptic cylinder oriented away from the z-axis is 2πc(a² + b²).
How to solve the elliptic cylinder?From the information, F = (b/ax) + (a/by)j and S is the elliptic cylinder.
To evaluate ∫F.dA goes thus:
divF = (I'd/dx + jd/dx + kd/dx) × (b/ax)i + (a/by)j
= b/a + a/b
= (a² + b²)/ab
Using Gauss divergence theorem, this will be further solved below:
∫∫∫v(a² + b²/ab)dV
= (a² + b²/ab)∫∫∫vdV
= (a² + b²/ab) × Volume of cylinder
= (a² + b²/ab) × πab(2c)
= 2πc(a² + b²)
Learn more about cylinder on:
https://brainly.com/question/76386
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:
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.
For more such questions on hypotheses, click on:
https://brainly.com/question/34171008
#SPJ6
An article suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with μ = 0.50 and σ = 0.08. (Round your answers to four decimal places.) (a) What is the probability that the concentration exceeds 0.60?
Answer:
0.1056 = 10.56% probability that the concentration exceeds 0.60
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 0.5, \sigma = 0.08[/tex]
What is the probability that the concentration exceeds 0.60?
This is 1 subtracted by the pvalue of Z when X = 0.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.6 - 0.5}{0.08}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a pvalue of 0.8944
1 - 0.8944 = 0.1056
0.1056 = 10.56% probability that the concentration exceeds 0.60
Lue is rolling a random number cube.the cube has six sides and each one is labeled with a different number 1 through 6.what is the probability that he will roll a sum of 12 in two rolls
What type of triangle is shown
Answer:
Where's the triangle?
Step-by-step explanation:
^^^ 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
Solve the equation by completing the square.
X^2 + 4x =45
Answer:
The answer is x=5, −9
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.
(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
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
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 = $791
The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is = 24.9 + 0.301x, where x = price ($) and y = overall score.Brand Price ScoreBose 18 76Scullcandy 150 71Koss 95 62Phillips/O'Neill 70 57Denon 70 30JVC 35 34Round your answers to three decimal places.a. Compute SST, SSR, and SSE.
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
SST = 1800
SSR = 1512.376
SSE = 287.624
b
coefficient of determination is [tex]r^2 \approx 0.8402[/tex]
What this is telling us is that 84.02% variation in dependent variable y can be fully explained by variation in the independent variable x
c
The correlation coefficient is [tex]r = 0.917[/tex]
Step-by-step explanation:
The table shown the calculated mean is shown on the second uploaded image
Let first define some term
SST (sum of squares total) : This is the difference between the noted dependent variable and the mean of this noted dependent variable
SSR(sum of squared residuals) : this can defined as a predicted shift from the actual observed values of the data
SSE (sum of squared estimate of errors): this can be defined as the sum of the square difference between the observed value and its mean
From the table
[tex]SST = SS_{yy} = 1800[/tex]
[tex]SSR = \frac{SS^2_{xy}}{SS_{xx}} = \frac{4755^2}{14950} = 1512.376[/tex]
[tex]SSE =SST-SSR[/tex]
[tex]=1800 - 1512.376[/tex]
[tex]= 287.62[/tex]
The coefficient of determination is mathematically represented as
[tex]r^2 = \frac{SSR}{SST}[/tex]
[tex]= 1-\frac{SSE}{SST}[/tex]
[tex]r^2= 1-\frac{287.6237}{1800}[/tex]
[tex]r^2 \approx 0.8402[/tex]
The correlation coefficient is mathematically represented as
[tex]r = \pm\sqrt{r^2}[/tex]
Substituting values
[tex]r = \sqrt{0.84020}[/tex]
[tex]r = 0.917[/tex]
this value is + because the value of the coefficient of x in estimated regression equation([tex]24.9 + 0.301x,[/tex]) is positive
To compute SST, SSR, and SSE, we calculate the variability of the dependent variable around the mean, the variability explained by the regression model, and the variability not explained by the regression model.
Explanation:To compute SST, SSR, and SSE, we need to understand what each of them represents. SST (the total sum of squares) measures the total variability of the dependent variable (overall score) around the mean. SSR (the regression sum of squares) measures the amount of variability in the dependent variable that is explained by the regression model. Finally, SSE (the error sum of squares) measures the amount of variability in the dependent variable that is not explained by the regression model.
To compute these values:
Calculate the mean of the overall scores. In this case, the mean is (76 + 71 + 62 + 57 + 30 + 34) / 6 = 50.Calculate the total sum of squares (SST) by subtracting the overall score for each observation from the mean, squaring the differences, and summing them. In this case, SST = (76 - 50)^2 + (71 - 50)^2 + (62 - 50)^2 + (57 - 50)^2 + (30 - 50)^2 + (34 - 50)^2 = 5424.Calculate the regression sum of squares (SSR) by subtracting the predicted overall score for each observation from the mean, squaring the differences, and summing them. In this case, SSR = (24.9 + 0.301*18 - 50)^2 + (24.9 + 0.301*150 - 50)^2 + (24.9 + 0.301*95 - 50)^2 + (24.9 + 0.301*70 - 50)^2 + (24.9 + 0.301*70 - 50)^2 + (24.9 + 0.301*35 - 50)^2 = 10435.558.Calculate the error sum of squares (SSE) by subtracting the predicted overall score for each observation from the actual overall score, squaring the differences, and summing them. In this case, SSE = (76 - (24.9 + 0.301*18))^2 + (71 - (24.9 + 0.301*150))^2 + (62 - (24.9 + 0.301*95))^2 + (57 - (24.9 + 0.301*70))^2 + (30 - (24.9 + 0.301*70))^2 + (34 - (24.9 + 0.301*35))^2 = 171.442.Hence, SST = 5424, SSR = 10435.558, and SSE = 171.442.
Learn more about Calculating SST, SSR, and SSE here:https://brainly.com/question/35696157
#SPJ3
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.
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.
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
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]
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 :)
What's 1 1/4 equal to?
Answer:
1.25
Step-by-step explanation: