Answer:
Therefore rate of payment = $ 3145.72
Therefore the rate of interest = =$1573.17
Step-by-step explanation:
Consider A represent the balance at time t.
A(0)=$ 7864.
r=13 % =0.13
Rate payment = $k
The balance rate increases by interest (product of interest rate and current balance) and payment rate.
[tex]\frac{dB}{dt} = rB-k[/tex]
[tex]\Rightarrow \frac{dB}{dt} - rB=-k[/tex].......(1)
To solve the equation ,we have to find out the integrating factor.
Here p(t)= the coefficient of B =-r
The integrating factor [tex]=e^{\int p(t) dt[/tex]
[tex]=e^{\int (-r)dt[/tex]
[tex]=e^{-rt}[/tex]
Multiplying the integrating factor the both sides of equation (1)
[tex]e^{-rt}\frac{dB}{dt} -e^{-rt}rB=-ke^{-rt}[/tex]
[tex]\Rightarrow e^{-rt}dB - e^{-rt}rBdt=-ke^{-rt}dt[/tex]
Integrating both sides
[tex]\Rightarrow \int e^{-rt}dB -\int e^{-rt}rBdt=\int-ke^{-rt}dt[/tex]
[tex]\Rightarrow e^{-rt}B=\frac{-ke^{-rt}}{-r} +C[/tex] [ where C arbitrary constant]
[tex]\Rightarrow B(t)=\frac{k}{r} +Ce^{rt}[/tex]
Initial condition B=7864 when t =0
[tex]\therefore 7864= \frac{k}{r} - Ce^0[/tex]
[tex]\Rightarrow C= \frac{k}{r} -7864[/tex]
Then the general solution is
[tex]B(t)=\frac{k}{r}-( \frac{k}{r}-7864)e^{rt}[/tex]
To determine the payment rate, we have to put the value of B(3), r and t in the general solution.
Here B(3)=0, r=0.13 and t=3
[tex]B(3)=0=\frac{k}{0.13}-( \frac{k}{0.13}-7864)e^{0.13\times 3}[/tex]
[tex]\Rightarrow- 0.48\frac{k}{0.13} +11614.98=0[/tex]
⇒k≈3145.72
Therefore rate of payment = $ 3145.72
Therefore the rate of interest = ${(3145.72×3)-7864}
=$1573.17
The payment rate that is required to pay off the loan in 3 years is approximately 2949.51 dollars/year. The interest paid during the 3-year period is about 984.53 dollars.
Explanation:To solve this problem, the formula for continuously compounded interest should be used which is A = P * e^(rt), where A is the value of the investment at a future time t, P is the principal amount, r is the annual interest rate, and t is the time the money is invested or borrowed for.
First, set up the equation: 7864 = k * (1/(0.13)) * (e^(0.13 * 3) - 1), then solve for k: k = 7864 * (0.13) / (e^(0.13 * 3) - 1) ≈ 2949.51 dollars/year.
Using the formula A = P * e^(rt), the total amount paid is A = 2949.51 * 3 = 8848.53 dollars. The interest paid during the 3-year period is calculated by subtracting the loan amount from the total amount paid, that is 8848.53 - 7864 = 984.53 dollars.
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In a data set with a minimum value of 54.5 and a maximum value of 98.6 with 300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.
Answer:
81.2 is the 62th percentile
Step-by-step explanation:
What is the interpretation for a percentile?
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
300 observations, there are 186 points less than 81.2. Find the percentile for 81.2.
So
[tex]p = \frac{186}{300} = 0.62[/tex]
81.2 is the 62th percentile
. Suppose that f is a continuous function and that −24 ≤ f 00(x) ≤ 3 for 0 ≤ x ≤ 1. If the Midpoint Rule of order n, namely Mn, is used to approximate R 1 0 f(x) dx, how large must n be to guarantee that the absolute error in using Mn ≈ R 1 0 f(x) dx is less than 1/100?
Answer:
Sew attachment for xomplete solution and answer
Step-by-step explanation:
Given that;
Suppose that f is a continuous function and that −24 ≤ f 00(x) ≤ 3 for 0 ≤ x ≤ 1. If the Midpoint Rule of order n, namely Mn, is used to approximate R 1 0 f(x) dx, how large must n be to guarantee that the absolute error in using Mn ≈ R 1 0 f(x) dx is less than 1/100
See attachment
A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. What is the standard error for the mean finish time of 30 randomly selected participants
Answer:
The standard error for the mean finish time of 30 randomly selected participants is 0.055 hours
Step-by-step explanation:
Standard error = sample standard deviation ÷ sqrt (sample size)
sample standard deviation = 0.30 hours
sample size = 30
standard error = 0.30 ÷ sqrt(30) = 0.30 ÷ 5.477 = 0.055 hours
As part of quality control, a pharmaceutical company tests a sample of manufacturer pills to see the amount of active drug they contain is consistent with the labelled amount. That is, they are interested in testing the following hypotheses:
H0:μ=100H0:μ=100 mg (the mean levels are as labelled)
H1:μ≠100H1:μ≠100 mg (the mean levels are not as labelled)
Assume that the population standard deviation of drug levels is 55 mg. For testing, they take a sample of 1010 pills randomly from the manufacturing lines and would like to use a significance level of α=0.05α=0.05.
They find that the sample mean is 104104 mg. Calculate the zz statistic.
−17.89−17.89
−8.00−8.00
−5.66−5.66
−2.53−2.53
−0.80−0.80
0.800.80
2.532.53
5.665.66
8.008.00
17.8917.89
Answer:
The z statistic is 0.23.
Step-by-step explanation:
Test statistic (z) = (sample mean - population mean) ÷ sd/√n
sample mean = 104 mg
population mean (mu) = 100 mg
sd = 55 mg
n = 10
z = (104 - 100) ÷ 55/√10 = 4 ÷ 17.393 = 0.23
Final answer:
The z-statistic for the given hypothesis test is calculated based on the sample mean, population standard deviation, and sample size.
Explanation:
The z-statistic for this hypothesis test can be calculated using the sample mean, population standard deviation, and sample size.
Given that the sample mean is 104 mg, population standard deviation is 55 mg, and sample size is 10 pills, the z-statistic is calculated as (104 - 100) / (55 / sqrt(10)), which equals 0.8.
Therefore, the correct z-statistic for this scenario is 0.80.
The paraboloid z = 8 − x − x2 − 2y2 intersects the plane x = 3 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (3, 2, −12). (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of t.)
When [tex]x=3[/tex], we get the parabola
[tex]z=-4-2y^2[/tex]
We can parameterize this parabola by
[tex]\vec r(t)=(3,t,-4-2t^2)[/tex]
Then the tangent vector to this parabola is
[tex]\vec T(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=(0,1,-4t)[/tex]
We get the point (3, 2, -12) when [tex]t=2[/tex], for which the tangent vector is
[tex]\vec T(2)=(0,1,-8)[/tex]
Then the line tangent to the parabola at [tex]t=2[/tex] passing through the point (3, 2, -12) has vector equation
[tex]\ell(t)=(3,2,-12)+t(0,1,-8)=(3,2+t,-12-8t)[/tex]
which in parametric form is
[tex]\begin{cases}x(t)=3\\y(t)=2+t\\z(t)=-12-8t\end{cases}[/tex]
for [tex]t\in\Bbb R[/tex].
The parametric equation of the tangent line is [tex]L(t)=(3,2+t,-12-8t)[/tex]
Parabola :The equation of Paraboloid is,
[tex]z =8-x-x^{2} -2y^{2}[/tex]
Equation of parabola when [tex]x = 3[/tex] is,
[tex]z=8-3-3^{2} -2y^{2} \\\\z=-4-2y^{2}[/tex]
The parametric equation of parabola will be,
[tex]r(t)=(3,t,-4-2t^{2} )[/tex]
Now, we have to find Tangent vector to this parabola is,
[tex]T(t)=\frac{dr(t)}{dt}=(0,1,-4t)[/tex]
We get, the point [tex](3, 2, -12)[/tex] when [tex]t=2[/tex]
The tangent vector will be,
[tex]T(2)=(0,1,-8)[/tex]
So that, the tangent line to this parabola at the point (3, 2, −12) will be,
[tex]L(t)=(3,2,-12)+t(0,1,-8)\\\\L(t)=(3,2+t,-12-8t)[/tex]
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Use the binomial theorem to find the coefficient of xayb in the expansion of (5x2 + 2y3)6, where a) a = 6, b = 9. b) a = 2, b = 15. c) a = 3, b = 12. d) a = 12, b = 0. e) a = 8, b = 9.
Answer:
Step-by-step explanation:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 6 15 20 15 6 1
we use these for the expansion of (5x² + 2y³)⁶
1(5x²)⁶(2y³)⁰ + 6(5x²)⁵(2y³)¹ + 15(5x²)⁴(2y³)² + 20(5x²)³(2y³)³+ 15(5x²)²(2y³)⁴+ 6(5x²)¹(2y³)⁵ + 1(5x²)⁰(2y³)⁶
78125ₓ¹²+187500ₓ¹⁰ y³ +37500ₓ⁸y⁶+20000ₓ⁶y⁹+6000x⁴y¹²+960x²y¹⁵+2y¹⁸
a.)a = 6, b = 9. the coefficient of xᵃyᵇ ( 20000ₓ⁶y⁹) = 20000
b) a = 2, b = 15. the coefficient of xᵃyᵇ ( 960x²y¹⁵) = 960
c) a = 3, b = 12. the coefficient of xᵃyᵇ is not present
d) a = 12, b = 0 the coefficient of xᵃyᵇ ( 78125ₓ¹²) = 78125
e) a = 8, b = 9. the coefficient of xᵃyᵇ is not present
The coefficients of xᵃyᵇ for respective given values of a and b have been provided below.
We are given the expression;
(5x² + 2y³)⁶
Using online binomial expansion calculator gives us;
15625x¹² + 37500x¹⁰y³ + 37500x⁸y⁶ + 20000x⁶y⁹ + 6000x⁴y¹² + 960x²y¹⁵ + 64y¹⁸
We want to find the coefficient of xᵃyᵇ in the binomial expansion;
1) When a = 6 and b = 9, the coefficient is 20000
2) When a = 2, b = 15; the coefficient is 960
3) When a = 3 and b = 12; there is no coefficient
4) When a = 12 and b = 0; the coefficient is 15625
5) When a = 8 and b = 9; there is no coefficient.
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Suppose that in a population of adults between the ages of 18 and 49, glucose follows a normal distribution with a mean of 93.5 and standard deviation of 19.8. What is the probability that glucose exceeds 120 in this population
Answer:
0.0904 or 9.04%
Step-by-step explanation:
Mean glucose (μ) = 93.5
Standard deviation (σ) = 19.8
In a normal distribution, the z-score for any glucose value, X, is given by:
[tex]Z= \frac{X-\mu}{\sigma}[/tex]
For X = 120, the z-score is:
[tex]Z= \frac{120-93.5}{19.8}\\ Z=1.3384[/tex]
A z-score of 1.3384 corresponds to the 90.96th percentile of a normal distribution. Therefore, the probability that glucose exceeds 120 in this population is:
[tex]P(X>120) = 1-0.9096=0.0904 = 9.04\%[/tex]
Answer:
Probability that glucose exceeds 120 in this population is 0.09012.
Step-by-step explanation:
We are given that in a population of adults between the ages of 18 and 49, glucose follows a normal distribution with a mean of 93.5 and standard deviation of 19.8, i.e.; [tex]\mu[/tex] = 93.5 and [tex]\sigma[/tex] = 19.8 .
Let X = amount of glucose i.e. X ~ N([tex]\mu = 93.5 , \sigma^{2} = 19.8^{2}[/tex])
Now, the Z score probability is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
So,Probability that glucose exceeds 120 in this population =P(X>120)
P(X > 120) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{120-93.5}{19.8}[/tex] ) = P(Z > 1.34) = 1 - P(Z <= 1.34)
= 1 - 0.90988 = 0.09012 .
The amount of cream sauce on the fettuccine at Al Fred-O's follows a Normal distribution, with a mean of 3.78 ounces and a standard deviation of 0.14 ounce. A random sample of 12 plates of fettuccine is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.81 ounces
Answer:
22.66% probability that the mean weight will exceed 3.81 ounces
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
Problems of normally distributed samples can be 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.
Central limit theorem:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 3.78, \sigma = 0.14, n = 12, s = \frac{0.14}{\sqrt{12}} = 0.04[/tex]
What is the probability that the mean weight will exceed 3.81 ounces
This probability is 1 subtracted by the pvalue of Z when X = 3.81. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.81 - 3.78}{0.04}[/tex]
[tex]Z = 0.75[/tex]
[tex]Z = 0.75[/tex] has a pvalue of 0.7734
1 - 0.7734 = 0.2266
22.66% probability that the mean weight will exceed 3.81 ounces
Answer:
Correct answer is 0.2290
Step-by-step explanation:
Show triangle XMZ is congruent to triangle YMZ. Support each part of your answer. Hint: mark the diagram.
Step-by-step explanation:
Let x be line xy.
y represents line zm.
z is line zx or line zy
The area of one of the smaller triangles is x/2* y.
same for the other triangle.
The perimeter for either one of the triangles is x/2+y+z.
- At a play, 211 quests are seated on the
main floor and 142 guests are seated in
the balcony. If tickets for the main floor
cost $7 and tickets for the balcony cost
$5, how much was earned in ticket sales?
Answer: $2187 was earned in ticket sales
Step-by-step explanation:
At the play, the total number of guests seated on the main floor is 211. If tickets for the main floor
cost $7, it means that the total cost of 211 ticket s is
211 × 7 = $1477
the total number of guests that were seated in the balcony is 142. If tickets for the main floor
cost $5, it means that the total cost of 142 tickets is
5 × 142 = $710
Therefore, the total amount of money earned in ticket sales is
1477 + 710 = $2187
The total amount earned in ticket sales is $2,187.
To determine the total amount earned in ticket sales at the play, we can use the following information:
- Number of guests on the main floor: 211
- Ticket price for the main floor: $7
- Number of guests in the balcony: 142
- Ticket price for the balcony: $5
We can calculate the earnings from each section separately and then sum them up.
Step-by-Step Calculation:
1. Calculate earnings from the main floor:
[tex]\[\text{Earnings from main floor} = \text{Number of main floor guests} \times \text{Ticket price for main floor}\][/tex]
[tex]\[\text{Earnings from main floor} = 211 \times 7 = 1477\][/tex]
2. Calculate earnings from the balcony:
[tex]\[\text{Earnings from balcony} = \text{Number of balcony guests} \times \text{Ticket price for balcony}\][/tex]
[tex]\[\text{Earnings from balcony} = 142 \times 5 = 710\][/tex]
3. Calculate total earnings:
[tex]\[\text{Total earnings} = \text{Earnings from main floor} + \text{Earnings from balcony}\][/tex]
[tex]\[\text{Total earnings} = 1477 + 710 = 2187\][/tex]
In a completely randomized experimental design involving five treatments, a total of 65 observations were recorded for each of the five treatments. The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) 9. Refer to Exhibit 1. The sum of squares within treatments (SSE) is a. 1,000 b. 600 c. 200 d. 1,600 10. Refer to Exhibit 1. The number of degrees of freedom corresponding to between treatments is
a. 60
b. 59
c. 5
d. 4
Answer:
5
Step-by-step explanation:
numerator degrees of freedom=[tex]Treatments-1[/tex]
[tex]N_d_f=5-1=4[/tex]
Total degrees of freedom=[tex]Treatments\times \ Observations Recorded-1[/tex]
[tex]T_d_f=5\times13-1=64[/tex]
Denominator Degrees of freedom=[tex]T_d_f-N_d_f=64-4=60[/tex]
Therefore, to calculate the degrees of freedom corressponding to treatments:
[tex]F=\frac{MSR}{MSE}\\MSR=200\div4=50\\MSE=(800-200)\div 60=10\\F=50\div10=5[/tex]
A telephone survey conducted by the Maritz Marketing Research company found that 43% of Americans expect to save more money next year than they saved last year. Forty-five percent of those surveyed plan to reduce debt next year. Of those who expect to save more money next year, 81% plan to reduce debt next year. An American is selected randomly. a. What is the probability that this person expects to save more money next year and plans to reduce debt next year? b. What is the probability that this person expects to save more money next year or plans to reduce debt next year? c. What is the probability that this person expects to save more money next year and does not plan to reduce debt next year? d. What is the probability that this person does not expect to save more money given that he/she does plan to reduce debt next year?
Answer:
A) P(A⋂B) = 0.35
B) P(A⋃B)= 0.53
C) P(A⋂B′) = 0.08
D) P(A|B) = 0.778
Step-by-step explanation:
We know the following from the question:
- Let Proportion of Americans who expect to save more money next year than they saved last year be
P(A) and its = 0.43
-Let proportion who plan to reduce debt next year be P(B) and it's =0.81
A) probability that this person expects to save more money next year and plans to reduce debt next year which is; P(A⋂B) = 0.43 x 0.81 = 0.348 approximately 0.35
B) probability that this person expects to save more money next year or plans to reduce debt next year which is;
P(A⋃B)= P(A) + P(B) − P(A⋂B)
So, P(A⋃B)= 0.43 + 0.45 − 0.35 = 0.53
C). Probability that this person expects to save more money next year and does not plan to reduce debt next year which is;
P(A⋂B′) = P(A) − P(A⋂B)
P(A⋂B′) =0.43 − 0.35 = 0.08
D) Probability that this person does not expect to save more money given that he/she does plan to reduce debt next year which is;
P(A|B) = [P(A⋂B)] / P(B)
So P(A|B) =0.35/0.45 = 0.778
The probabilities for the given scenarios are as follows: a. 34.93%, b. 53.07%, c. 8.07%, and d. 126.67%.
Explanation:a. To find the probability that a person expects to save more money next year and plans to reduce debt next year, we need to multiply the probabilities of both events occurring. The probability that a person expects to save more money next year is 43%, and of those who expect to save more money next year, 81% plan to reduce debt. Therefore, the probability is 0.43 imes 0.81 = 0.3493, or 34.93%.
b. To find the probability that a person expects to save more money next year or plans to reduce debt next year, we can add the probabilities of both events occurring and subtract the probability of both events occurring at the same time (found in part a). The probability of expecting to save more money next year is 43%, and the probability of planning to reduce debt next year is 45%. Therefore, the probability is 0.43 + 0.45 - 0.3493 = 0.5307, or 53.07%.
c. To find the probability that a person expects to save more money next year and does not plan to reduce debt next year, we subtract the probability from part a from the probability of expecting to save more money next year. The probability of expecting to save more money next year is 43%, and the probability of both expecting to save more money and planning to reduce debt is 34.93%. Therefore, the probability is 0.43 - 0.3493 = 0.0807, or 8.07%.
d. To find the probability that a person does not expect to save more money given that he/she does plan to reduce debt next year, we need to divide the probability of not expecting to save more money by the probability of planning to reduce debt next year. The probability of not expecting to save more money is 1 - 0.43 = 0.57, and the probability of planning to reduce debt next year is 45%. Therefore, the probability is 0.57 / 0.45 = 1.2667, or 126.67%.
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Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM.
Find the values of d and s_d. In general, what does μ_d represent?
Temperature (°F)at 8 AM 97.5 99.3 97.8 97.5 97.4
Temperature (°F)at 12 AM 98.0 99.6 98.1 97.1 97.7
Answer:
The value of [tex]\bar d[/tex] is -0.2.
The value of [tex]s_{\bar d}[/tex] is 0.3464.
[tex]\mu_{d}[/tex] = mean difference in body temperatures.
Step-by-step explanation:
The data for body temperatures from five different subjects measured at 8 AM and again at 12 AM are provided.
The formula of [tex]\bar d[/tex] and [tex]s_{\bar d}[/tex] are:
[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})[/tex]
[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}[/tex]
Consider the table below.
Compute the value of [tex]\bar d[/tex] as follows:
[tex]\bar d=\frac{1}{n}\sum (x_{1}-x_{2})=\frac{1}{5}\times-1=-0.2[/tex]
Thus, the value of [tex]\bar d[/tex] is -0.2.
Compute the value of [tex]s_{\bar d}[/tex] as follows:
[tex]s_{\bar d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}=\sqrt{\frac{0.48}{4}}=0.3464[/tex]
Thus, the value of [tex]s_{\bar d}[/tex] is 0.3464.
The variable [tex]\mu_{d}[/tex] represents the mean difference in body temperatures measured at 8 AM and again at 12 AM.
While driving in the car with this family Jeffery likes to look out the window to find Punch Buggies. On average Jeffery sees 3.85 Punch Buggies per hour. Assume seeing Punch Buggies follows a Poisson process. Find the probability Jeffery sees exactly 2 Punch Biggies in an hour. Round your answer to 4 decimal places.
Answer:
0.1577 or 15.77%
Step-by-step explanation:
The Poisson probability model follows the given relationship:
[tex]P(X=k) =\frac{\lambda^k*e^{-\lambda}}{k!}[/tex]
For a Poisson model with a parameter λ = 3.85 Punch Baggies/hour, the probability of X=2 successes (exactly 2 Punch Baggies in an hour) is given by:
[tex]P(X=2) =\frac{3.85^2*e^{-3.85}}{2!}\\P(X=2) =0.1577=15.77\%[/tex]
The probability is 0.1577 or 15.77%.
The rate at which a body cools also depends on its exposed surface area S. If S is a constant, then a modification of (2), given in Section 3.1, is dT dt = kS(T − Tm), where k < 0 and Tm is a constant. Suppose that two cups A and B are filled with coffee at the same time. Initially, the temperature of the coffee is 145° F. The exposed surface area of the coffee in cup B is twice the surface area of the coffee in cup A. After 30 min the temperature of the coffee in cup A is 95° F. If Tm = 65° F, then what is the temperature of the coffee in cup B after 30 min? (Round your answer to two decimal places.)
Answer:
76.25°
Step-by-step explanation:
The solution to the differential equation is an exponential curve with a horizontal asymptote at Tm. It passes through (0, 145) and (30, 95), so the equation can be written as ...
T = 80 +65((95-65)/(145-65))^(t/30)
T = 80 +65(3/8)^(t/30)
That is, the temperature difference is reduced to 3/8 of its original value in 30 minutes.
Since the coffee in cup B cools twice as fast, it will cool to the same temperature (95°) in 15 minutes. In the next 15 minutes, the temperature difference will be reduced to (3/8)^2 of the original 80°, so will be 11.25°. That is, the temperature of cup B will be ...
11.25° +65° = 76.25°
after 30 minutes.
The temperature of coffee in cup B after 30 minutes would be 45° F, as the rate of cooling is faster due to a larger exposed surface area.
Explanation:According to the given condition, the rate of cooling (dT/dt) is proportional to the exposed surface area (S). It suggests that, with the surface area doubled for cup B, the rate of cooling (change in temperature) would also be double. Therefore, in the first 30 minutes, the temperature of coffee would decrease twice as fast as it did in cup A. In cup A, the temperature decreases from 145° F to 95° F in 30 minutes hence a decrease of 50° F. If the temperature of cup B decreases twice as fast, it decreases 100° F in 30 minutes. So, the temperature of the coffee in cup B after 30 minutes would be 145° F - 100° F = 45° F.
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Because all airline passengers do not show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. a. What is the probability that every passenger who shows up can take the flight?b. What is the probability that the flight departs with empty seats?
Answer:
a) 0.9961
b) 0.9886
Step-by-step explanation:
We are given the following information:
We treat passenger not showing up as a success.
P(passenger not showing up) = 0.10
Then the number of passengers follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 125
a) probability that every passenger who shows up can take the flight
[tex]P(x \geq 5) = 1- P(x = 0) - P(x = 1)-P(x = 2) - P(x = 3) - P(x = 4) \\= 1-\binom{125}{0}(0.10)^0(1-0.10)^{125} -...-\binom{125}{4}(0.10)^4(1-0.10)^{121}\\=0.9961[/tex]
b) probability that the flight departs with empty seats
[tex]P(x > 5) =P(x\geq 5) - P(x = 5) \\= 0.9961 -\binom{125}{5}(0.10)^5(1-0.10)^{120}\\=0.9961-0.0075\\ = 0.9886[/tex]
Identify the rule of inference that is used to derive the conclusion "You do not eat tofu" from the statements "For all x, if x is healthy to eat, then x does not taste good," "Tofu is healthy to eat," and "You only eat what tastes good."
"You do not eat tofu" is derived using the Modus Tollens rule of inference.
The rule of inference that is used to derive the conclusion "You do not eat tofu" from the given statements is Modus Tollens.
Modus Tollens is a valid deductive argument form that follows this structure:
1. If P, then Q.
2. Not Q.
3. Therefore, not P.
The statements correspond to:
1. For all x, if x is healthy to eat, then x does not taste good.
2. Tofu is healthy to eat.
3. You only eat what tastes good.
Using these statements, we can infer:
1. If tofu is healthy to eat, then tofu does not taste good. (From statement 1)
2. Tofu does not taste good. (From statement 2 and the derived inference)
3. Therefore, you do not eat tofu. (Using Modus Tollens with statement 3 and the derived inference)
So, the conclusion "You do not eat tofu" is derived using the Modus Tollens rule of inference.
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Final answer:
The rule of inference used to derive the conclusion 'You do not eat tofu' is called Modus Tollens, which allows to deduce that if 'p implies q' is true and 'q' is false, then 'p' must also be false.
Explanation:
The student is asking about a logical inference rule used to derive a conclusion from a set of premises. Considering the provided statements, which can be summarized as:
For all x, if x is healthy to eat, then x does not taste good (All healthy foods taste bad).
Tofu is healthy to eat.
You only eat what tastes good.
We can see that the rule of inference used here is Modus Tollens. This rule of inference suggests that if we have a conditional statement (if p then q) and it is given that the consequent q is false (not q), then the antecedent p must also be false (not p).
To apply Modus Tollens:
Translate the given information into logical statements:
a) If something is healthy (p) then it does not taste good (q).
b) Tofu is healthy (p).
c) You do not eat what does not taste good (¬q).
Since tofu is healthy (p), it does not taste good as per the given rule (therefore, q is true). But the third statement says you do not eat what does not taste good, meaning (¬q). If (¬q) is valid, then by Modus Tollens, you do not eat tofu (¬p).
Thus, the usage of Modus Tollens allows us to infer that 'You do not eat tofu' from the given premises.
.Find the Z-sCore corresponding to the given value and use the z-SCore to determine whether the value is unusual. Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth if necessary. A test score of 50.0 on a test having a mean of 69 and a standard deviation of 10.
a. 1.9; not unusual
b. -19; unusual
c. -1.9; unusual
d. -1.9; not unusual
Answer:
d. -1.9; not unusual
Step-by-step explanation:
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]X = 50, \mu = 69, \sigma = 10[/tex].
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{50 - 69}{10}[/tex]
[tex]Z = -1.9[/tex]
A z-score of -1.9 is higher than -2 and lower than 2, so it is not unusual.
So the correct answer is:
d. -1.9; not unusual
Here, f(x) is measured in kilograms per 4,000 square meters, and x is measured in hundreds of aphids per bean stem. By computing the slopes of the respective tangent lines, estimate the rate of change of the crop yield with respect to the density of aphids when that density is 200 aphids per bean stem and when it is 800 aphids per bean stem. 200 aphids per bean stem 1 kg per 4,000 m2 per aphid per bean stem 800 aphids per bean stem 2 kg per 4,000 m2 per aphid per bean stem
Answer: The slope of the tangent line at density 200 is -1.67kg/bean stem
Step-by-step explanation: The attached graph file shows the relationship between the yield of a certain crop f(×) as a function of the density of aphid x.
The second attached file shows the solution.
An appliance store decreases the price of a 19-in. television set 29% to a sale price of $428.84. What was the original price?
ROUND TO THE NEAREST CENT
Answer: $553.20
Step by step explanation: Since they took the price down 29% multiply the price by 1.29 to add the 29 percent back to the total amount. 428.84 * 1.29 = 553.20
Disjoint, Independent, and Complement State whether the two events (A and B) described are disjoint, independent, and/or complements. (It is possible that the two events fall into more than one of the three categories, or none of them.) Australia plays Argentina for the championship in the Rugby World Cup. At the same time, Ukraine plays Russia for the World Team Chess Championship. Let A be the event that Argentina wins their rugby match and B be the event that Ukraine wins their chess match. Disjoint
Answer:
Independent Events
Step-by-step explanation:
Two events are mutually exclusive or disjoint if they cannot both occur at the same time.
Two events are independent if the probability of occurrence of one does not affect the probability of occurrence of the other.
The complement of any event B is the event [not B], i.e. the event that B does not occur.
Australia plays Argentina for the championship in the Rugby World Cup.
At the same time, Ukraine plays Russia for the World Team Chess Championship.
A = event that Argentina wins their rugby match.
B = the event that Ukraine wins their chess match.
The two events A and B are Independent as the outcome of one does not affect the outcome of the other
PLS HELP ASAP!!! WILL MARK BRAINLEST!!! Which statement best describes the relation (3, 4), (4, 3), (6, 3), (7, 8), (5, 4)? Question 2 options: The relation does not represent y as a function of x, because each value of x is associated with a single value of y. The relation does not represent y as a function of x, because each value of y is associated with two values of x. The relation represents y as a function of x, because one value of y is associated with two values of x. The relation represents y as a function of x, because each value of x is associated with a single value of y.
Answer:
The relation represents y as a function of x, because each value of x is associated with a single value of y.
In order to complete the service line information on claims when units of measure are involved insurance math is required. For example this is the HCPCS description for an injection of the drug Eloxatin: J9263 oxaliplatain, 0.5 mg if the physician provided 50 mg infusion of the drug instead of an injection the service line is j9263 x 100 to report a unit of 50(100x 0.5 mg=50). What is the unit reported for service line information if a 150 mg infusion is provided?
Answer:
The service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).
Step-by-step explanation:
The drug J9263 Eloxatin contains 0.5 mg oxaliplatain.
For a infusion of 50 mg the unit reported for service line information is:
- Service line: J9263 x 100
- Unit reported for service line information: 50 = 100 x 0.5 mg
Hence, for a infusion of 150 mg, the unit reported for service line information is:
- Unit reported: 150(300 x 0.5 mg = 150)
- Service line information: J9263 x 300
Therefore, if the physician provided 150 mg infusion of the drug instead of an injection the service line is J9263 x 300 to report a unit of 150(300x 0.5 mg = 150).
I hope it helps you!
The unit reported for service line information for 150 mg infusion based on the injection description is :
150(300x 0.5mg = 150) j9263 × 300Given the injection description :
0.5 mg if physician provided 50 mg of infusion Service line = j9263 × 100For 150 mg infusion :
(150 mg ÷ 50 mg) = 3Unit reported would be:
[50(100x 0.5mg = 150)] × 3 = 150(300x 0.5mg=150)3(j9263 × 100) = j9263 × 300Therefore, the service line information and the unit reported would be:
150(300x 0.5mg = 150)j9263 × 300Learn more : https://brainly.com/question/11277823
8. The distribution for the time it takes a student to complete the fall class registration has mean of 94 minutes and standard deviation of 10 minutes. For a random sample of 80 students, determine the mean and standard deviation (standard error) of the sample mean. What can you say about the sampling distribution of the sample mean and why
Answer:
Mean = 94
Standard deviation = 1.12
The sampling distribution of the sample mean is going to be normally distributed, beause the size of the samples are 80, which is larger than 30.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sample means with size n of at least 30 can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
In this problem, we have that:
[tex]\mu = 94, \sigma = 10[/tex]
By the Central Limit Theorem
The sampling distribution of the sample mean is going to be normally distributed, beause the size of the samples are 80, which is larger than 30.
Mean = 94
Standard deviation:
[tex]s = \frac{10}{\sqrt{80}} = 1.12[/tex]
The number of defective components produced by a certain process in one day has a Poisson
distribution with mean of 20. Each defective component has probability of 0.60 of being
repairable.
(a) Find the probability that exactly 15 defective components are produced.
(b) Given that exactly 15 defective components are produced, find the probability that
exactly 10 of them are repairable.
(c) Let N be the number of defective components produced, and let X be the number of
them that are repairable. Given the value of N, what is the distribution of X?
(d) Find the probability that exactly 15 defective components are produced, with exactly 10
of them being repairable.
To find the probability of different scenarios involving defective components produced by a certain process, we can use the Poisson and binomial distributions.
Explanation:(a) To find the probability that exactly 15 defective components are produced, we can use the formula for the Poisson distribution:
P(X=k) = (e^(-λ) * λ^k) / k!
Here, λ is the mean number of defective components produced in one day, which is 20. So, λ = 20. Substituting this value into the formula, we get:
P(X=15) = (e^(-20) * 20^15) / 15!
Calculating this expression will give us the probability.
(b) To find the probability that exactly 10 of the 15 defective components are repairable, we can use the binomial distribution since each defective component has a fixed probability of being repairable. Here, the number of trials is 15, and the probability of success (being repairable) is 0.60. Substituting these values into the binomial distribution formula, we can calculate the probability.
(c) Given the value of N, the number of defective components produced, X has a binomial distribution since X represents the number of repairable defective components. The probability of each component being repairable is constant, so it follows a binomial distribution.
(d) To find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, we can multiply the probabilities obtained from parts (a) and (b) together, since these events are independent. Multiplying the results will give us the desired probability.
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(a) The probability that exactly 15 defective components are produced is 0.0516
(b) Given that exactly 15 defective components are produced, the probability that exactly 10 of them are repairable is 0.1241.
(c) Given the value of N, X follows a binomial distribution
(d) The probability that exactly 15 defective components are produced, with exactly 10 of them being repairable is 0.0064.
(a) Probability of Exactly 15 Defective Components
A Poisson distribution with mean λ = 20 is used. The formula is:
[tex]P(X = k) = (e^{(-\lambda)} * \lambda^k) / k![/tex]
For k = 15 and λ = 20:
[tex]P(X = k) = (e^{(-20)} * 20^15) / 15! \approx 0.0516[/tex]
(b) Probability that Exactly 10 Out of 15 Defective Components are Repairable
This scenario uses a binomial distribution.
Given N = 15 defectives, the probability that exactly 10 are repairable (with p = 0.60) is:
[tex]P(X = 10 | N = 15) = C(15,10) * 0.6^{10} * 0.4^{5} \approx 0.1241[/tex]
(c) Distribution of X Given N
Given N = n
X (number of repairable components) follows a binomial distribution Bin(n, 0.60).
So, X | N = n follows Bin(n, 0.60).
(d) Probability of 15 Defective Components with Exactly 10 being Repairable
The joint probability is the product of the Poisson and binomial probabilities:
[tex]P(X = 15) * P(Y = 10 | X = 15)= 0.0516 * 0.1241 \approx 0.0064[/tex]
Events A1, A2 and A3 form a partiton of the sample space S with probabilities P(A1) = 0.3, P(A2) = 0.5, P(A3) = 0.2.
If E is an event in S with P(E|A1) = 0.1, P(E|A2) = 0.6, P(E|A3) = 0.8, compute
a. P(E) =
b. P(A1|E) =
c. P(A2|E) =
d. P(A3|E) =
a. By the law of total probability,
[tex]P(E)=P(A_1\cap E)+P(A_2\cap E)+P(A_3\cap E)[/tex]
and using the definition of conditional probability we can expand the probabilities of intersection as
[tex]P(E)=P(E\mid A_1)P(A_1)+P(E\mid A_2)P(A_2)+P(E\mid A_3)P(A_3)[/tex]
[tex]P(E)=0.1\cdot0.3+0.6\cdot0.5+0.8\cdot0.2=0.49[/tex]
b. Using Bayes' theorem (or just the definition of conditional probability), we have
[tex]P(A_1\mid E)=\dfrac{P(A_1\cap E)}{P(E)}=\dfrac{P(E\mid A_1)P(A_1)}{P(E)}[/tex]
[tex]P(A_1\mid E)=\dfrac{0.1\cdot0.3}{0.49}\approx0.0612[/tex]
c. Same reasoning as in (b):
[tex]P(A_2\mid E)=\dfrac{P(E\mid A_2)P(A_2)}{P(E)}\approx0.612[/tex]
d. Same as before:
[tex]P(A_3\mid E)=\dfrac{P(E\mid A_3)P(A_3)}{P(E)}\approx0.327[/tex]
(Notice how the probabilities conditioned on [tex]E[/tex] add up to 1)
Mary got 85% correct on her math test. Mary missed 6 questions. How many total questions were on her math final?
Answer: there were 40 questions on her math final.
Step-by-step explanation:
Let x represent the total number of questions in the math test.
Mary got 85% correct on her math test. This means that the number of questions that she got right is
85/100 × x = 0.85 × x = 0.85x
This also means that the number of questions that she missed would be
x - 0.85x = 0.15x
Therefore, if Mary missed 6 questions, it means that
0.15x = 6
Dividing both sides of the equation by 0.15, it becomes
0.15x/0.15 = 6/0.15
x = 40
3x^2+kx=-3 What is the value of K will result in exactly one solution to the equation?
Answer:
For k = 6 or k = -6, the equation will have exactly one solution.
Step-by-step explanation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
If [tex]\bigtriangleup = 0[/tex], the equation has only one solution.
In this problem, we have that:
[tex]3x^{2} + kx + 3 = 0[/tex]
So
[tex]a = 3, b = k, c = 3[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
[tex]\bigtriangleup = k^{2} - 4*3*3[/tex]
[tex]\bigtriangleup = k^{2} - 36[/tex]
We will only have one solution if [tex]\bigtriangleup = 0[/tex]. So
[tex]\bigtriangleup = 0[/tex]
[tex]k^{2} - 36 = 0[/tex]
[tex]k^{2} = 36[/tex]
[tex]k = \pm \sqrt{36}[/tex]
[tex]k = \pm 6[/tex]
For k = 6 or k = -6, the equation will have exactly one solution.
The company leased two manufacturing facilities. Lease A requires 20 annual lease payments of $200,000 beginning on January 1, 2019. Lease B also is for 20 years, beginning January 1, 2019. Terms of the lease require 17 annual lease payments of $220,000 beginning on January 1, 2022. Generally accepted accounting principles require both leases to be recorded as liabilities for the present value of the scheduled payments. Assume that a 10% interest rate properly reflects the time value of money for the lease obligations
Answer:
the present value of the lease obligation for lease A will be $1,702,712.74 while the present value of lease B will be $1,764,741.73
Step-by-step explanation:
the present value of annual lease payment will be determined by discounting the total amount to be received from lease payment over years.
for lease A , Pv = A [tex]\fracA{1 -(1+r)^{-n} }{r}[/tex]
= $200,000( 1 - (1+0.1)[tex]^{20}[/tex]) / 0.1 = $1,702,712.74
for lease B , Pv = $220,000( 1 - (1+0.1)[tex]^-{17}[/tex]) / 0.1 = $1,764,741.73
the amount to be dicloased in the balance sheet at 31 december, 2018
The present value of lease payments assesses the current value of future lease liabilities, using a specified interest rate. Calculations for Lease A and Lease B would involve discounting their respective future lease payments at the given 10% interest rate to understand the company's financial obligations.
Explanation:Present Value of Lease Payments
The present value of lease payments is a critical financial measure used by companies to assess the value of lease liabilities on their balance sheets. Generally, it accounts for all lease payments, discounted by a specific interest rate that reflects the time value of money. For Lease A, the company will make 20 annual payments of $200,000 each, starting on January 1, 2019. For Lease B, the company will make 17 annual payments of $220,000 each, starting on January 1, 2022. Using a discount rate of 10%, the present value of these lease payments can be calculated using the formula for the present value of an annuity.
For example, if a firm borrows $10,000 at an annual interest rate of 10%, it will owe $11,000 after one year because the original amount will accumulate interest. This illustrates the principle that a dollar today is worth more than a dollar in the future due to its potential to earn interest. Accordingly, the present value calculations for Lease A and Lease B will provide the amount the company should theoretically be willing to pay today to cover the lease payments over the course of the respective lease terms.
MULTIPLE LINEAR REGRESSION What is the model for the multiple linear regression when weight gain is a dependent variable and the explanatory variables are hemoglobin change, tap water consumption, and age. Be sure to define all symbols and model assumptions.
Multiple linear regression can be said to be a statistical technique that uses several explanatory variables to predict the outcome of a response variable.
The Formula for Multiple Linear Regression Is
yi= β0+β1xi1+β2xi2+...+βpxip+ϵ
where, for i=n observations
yi= Dependent variable
xi= Expanatory variable
β0= y - intercept (constant term)
βp= Slope coefficients for each explanatory variable
ϵ= The model’s error term (also known as the residuals)
From the question written above,
yi= weight gain which is dependent on the explanatory variables which are hemoglobin change, tap water consumption, and age. i.e. xi
Model assumptions
1. There is a linear relationship between the dependent variables and the independent variables.
2. The independent variables are not too highly correlated with each other.
3. yi observations are selected independently and randomly from the population.
4. Residuals should be normally distributed with a mean of 0 and variance σ.
(Investopedia, 2019)