The temperature of a certain deserted, unheated house is in degrees Fahrenheit at time in hours. If the outside temperature is (about the average autumn temperature in the Boston area), and it takes 24 hours for the temperature of the house to drop from to use Newton's law of cooling to write down a differential equation for the temperature of the house.
Answers
Answer: Hello attached below is the well written complete question
answer:
T = 40 + 30e^-0.0288t
Step-by-step explanation:
To( outside temperature ) = 40°F
T = ?
k( thermal conductivity ) = constant
A( area of heat transfer) = constant
Hence Differential equation for the temperature of the house
T = 40 + 30e^-0.0288t
Attached below is the detailed solution of the problem
Related Questions
What is the distance between the points (2, 1) and (14, 6) on a coordinate
plane?
Answers
Answer:
it's 13 if you use the distance formula
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample
Answers
Answer:
19 beers must be sampled.
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 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
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.
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.
This means that [tex]\sigma = 0.26[/tex]
If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?
This is n for which M = 0.1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 1.645\frac{0.26}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 1.645*0.26[/tex]
[tex]\sqrt{n} = \frac{1.645*0.26}{0.1}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2[/tex]
[tex]n = 18.3[/tex]
Rounding up:
19 beers must be sampled.
X⁴-6x²-7-8x-x² what is the answers
Answers
Answer:
X⁴-7x²-8x-7
Step-by-step explanation:
A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of pounds. Assume that the population of weights is normally distributed. A pediatrician claims that the standard deviation of the weights of one-year-old girls is less than pounds. Do the data provide convincing evidence that the pediatrician's claim is true
Answers
Answer:
Paedtricians claim isn't true.
Step-by-step explanation:
The hypothesis :
H0 : σ = 7
H0 : σ > 7
The test statistic ; χ² :
χ² = [(n - 1) * s²] ÷ σ²
n = 25 ; s = 4.3, σ = 7
χ² = [(25 - 1) * 4.3²] ÷ 7²
χ² = [(24 * 4.3²] ÷ 49
χ² = 443.76 / 49
χ² = 9.056
At α = 0.01 ; critical value = 42.980
Since critical value > test statistic, we fail to reject the null, H0.
The following integral requires a preliminary step such as long division or a change of variables before using the method of partial fractions. Evaluate the following integral. x^4 + 7/x^3 + 2x dx Find the partial fraction decomposition of the integrand. x^4 + 7/x^3 + 2x dx
Answers
Division yields
[tex]\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}[/tex]
Now for partial fractions: you're looking for constants a, b, and c such that
[tex]\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}[/tex]
[tex]\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a[/tex]
which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then
[tex]\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}[/tex]
Now, in the integral we get
[tex]\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx[/tex]
The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get
[tex]\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}[/tex]
Find the value of x in each case
Answers
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
In one state lottery game, you must select four digits (digits may be repeated). If your number matches exactly the four digits selected by the lottery commission, you win.
1) How many different numbers may be chosen?
2) If you purchase one lottery ticket, what is your chance of winning?
3) There are ___ different numbers that can be chosen. (Type a whole number.)
4) There is a ___ chance of winning.*
*The answer choices for number 4 are:
1 in 10,000
1 in 6,561
1 in 100
1 in 1,000
1 in 9,999
Answers
Answer:
Part 1)
10,000 different numbers.
Part 2)
A) 1 in 10,000.
Step-by-step explanation:
Part 1)
Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:
[tex]T=\underbrace{10}_{\text{Choices For First Digit}}\times\underbrace{10}_{\text{Second Digit}}\times\underbrace{10}_{\text{Third Digit}}\times \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000[/tex]
Thus, 10,000 different numbers are possible.
Part 2)
Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.
This is equivalent to 0.0001 or a 0.01% chance of winning.
The data set shows the number of players on each softball team in a tournament:
9
12
8
7
7
21
11
9
8
7
10
7
10
11
Which of the following statements is true based on the data set?
There is one outlier that indicates an unusually large number of players on that team.
There are two outliers that indicate an unusually large number of players on those two teams.
There is one outlier that indicates an unusually small number of players on that team.
There are two outliers that indicate an unusually small number of players on those two teams.
Answers
Is this equation an identity? 6 + 5m = 4m
Answers
Answer:
Step-by-step explanation:
I don't think so. This equation has but one definite answer and the left and right sides don't produce the same result.
subtract 5m from both sides
6 = 4m - 5m
6 = - m Multiply both sides by - 1
-6 = m
An identity is something like 4x + 5x = 9x
It doesn't matter what x is. Any value of x will make the right side = to the left side. This becomes more important when you will study trigonometry.
Hi I need help with fraction
1
_ x 10
8.
Answers
Answer:
The answer is 1 1/4 or 5/4
Step-by-step explanation:
1/8 · 10 = 10/8
10/8 when simplified is 5/4
the Barnes family drove 140 miles the first day and 220 miles on the second day. If they drove about 60 miles per hour, approximately how many hours did they drive?
Answers
60x6=360
therefore your answer is 6 hours
Geometry Oddsseseyware
Answers
You may recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length.
Suppose that the length of a rectangle is 3 times the width. If the area is 300 square feet, then what is the width of the rectangle, in feet?
Do not type the units in your answer.
Answers
Answer:
The width is 10 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by the formula:
[tex]\displaystyle A=L\cdot W[/tex]
Where L is the length and W is the width.
We are given that the length of the rectangle is three times the width. In other words:
[tex]L=3W[/tex]
The total area is 300 square feet. And we want to determine the width of the rectangle.
So, substitute 300 for A and 3W for L:
[tex](300)=(3W)\cdot W[/tex]
Multiply:
[tex]300=3W^2[/tex]
Divide both sides by three:
[tex]W^2=100[/tex]
And take the principal square root of both sides. So:
[tex]W=10[/tex]
Thus, the width of the rectangle is 10 feet.
Can someone please help me, with part B
Answers
Step-by-step explanation:
let y = x+5/4
Interchanging x and y , we get ;
x = y+5/4
or, 4x = y+5
or, 4x-5 = y
or, g(x) -1 = 4x-5
Answer:
In verse of B.g(x)=[tex]\frac{x+5}{4}[/tex] is:
4x-5
Answer:
Solution given:
B.g(x)=[tex]\frac{x+5}{4}[/tex]
let
g(x)=y
y=[tex]\frac{x+5}{4}[/tex]
Interchanging role of x and y
we get:
x=[tex]\frac{y+5}{4}[/tex]
doing crisscrossed multiplication
4x=y+5
y=4x-5
So
g-¹(x)=4x-5
The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle. Suppose that we inspect 100 Volkswagen vehicles at random. (a) What is the approximate probability of finding at least 157 defects
Answers
Answer:
0.0207 = 2.07% approximate probability of finding at least 157 defects
Step-by-step explanation:
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\lambda[/tex] is the mean in the given interval.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
n instances of a Poisson distribution can be approximated to a normal distribution, with [tex]\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}[/tex]
The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.
This means that [tex]\lambda = 1.33[/tex]
Suppose that we inspect 100 Volkswagen vehicles at random.
This means that [tex]n = 100[/tex]
Mean and standard deviation:
[tex]\mu = n\lambda = 100*1.33 = 133[/tex]
[tex]\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53[/tex]
What is the approximate probability of finding at least 157 defects?
Using continuity correction(Poisson is a discrete distribution, normal continuous), this is [tex]P(X \geq 157 - 0.5) = P(X \geq 156.5)[/tex], which is 1 subtracted by the p-value of Z when X = 156.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{156.5 - 133}{11.53}[/tex]
[tex]Z = 2.04[/tex]
[tex]Z = 2.04[/tex] has a p-value of 0.9793.
1 - 0.9793 = 0.0207
0.0207 = 2.07% approximate probability of finding at least 157 defects
What is the slope of a line perpendicular to the line whose equation is 2x+4y=-642x+4y=−64. Fully simplify your answer.
Answers
9514 1404 393
Answer:
2
Step-by-step explanation:
Solving the given equation for y, you have ...
2x +4y = -64
4y = -2x -64
y = -1/2x -16
The coefficient of x is the slope of the given line: -1/2. The slope of the perpendicular line is the opposite reciprocal of this:
-1/(-1/2) = 2
The slope of the perpendicular line is 2.
I need help with this question.
Answers
Answer:
Step-by-step explanation:
f(x-2) means that x is happening sooner or a shift to the left and
+4 means that the whole function moves up 4.
The 1st choice looks good
How many people have at least 1?
Answers
Answer:
15
Step-by-step explanation:
3+7+5
PLEASE BRAINLIESTTTTTTTTT
A professor creates a histogram of test scores for 26 students in a statistics course. What is the probability of a student having scored between 65 and 100
Answers
Complete Question
Complete is Attached Below
Answer:
Option D
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=26[/tex]
Student scoring [tex]65-100 n'=12[/tex]
Generally the equation for probability of a student having score between 65 and 100 is mathematically given by
[tex]P(65-100)=\frac{12}{26}[/tex]
[tex]P(65-100)=12/26[/tex]
[tex]P(65-100)=0.462[/tex]
Option D
What is the mean?
9.12.34.6.8.9.
Answers
Answer:
13
Step-by-step explanation:
The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.
Answer:
The mean (average) of these numbers is equal to 13.
Step-by-step explanation:
Another word for the "mean" of numbers is the "average" of numbers. You can find the average by adding all the numbers together and then dividing the sum you got by the number of values you added together, so in our case, there are 6 values given, therefore we will find the sum of all these numbers and then divide it by 6...
[tex]\frac{9 + 12 + 34 + 6 + 8 + 9}{6} = \frac{78}{6} = 13[/tex]
Therefore, the mean (average) of this number is equal to 13.
What's the lateral area of the following cone?
11 cm
10 cm
511.23 cm
55 cm?
110.02 cm?
189.75 cm?
Answers
Answer:189.75
Step-by-step explanation:
The lateral area of the cone for the height of 11 cm and diameter 10 cm is given by option D. 189.75 cm²
To calculate the lateral area of a cone, find the curved surface area.
The lateral area of a cone can be calculated using the formula:
Lateral Area = π × r × l
where:
π is the mathematical constant pi (approximately 3.14159)
r is the radius of the base of the cone
l is the slant height of the cone
Height (h) = 11 cm
Diameter (d) = 10 cm
First, we need to find the radius (r) and the slant height (l).
The radius (r) is half of the diameter:
r
= d / 2
= 10 cm / 2
= 5 cm
The slant height (l) can be found using the Pythagorean theorem:
l² = r² + h²
l² = 5² + 11²
l² = 25 + 121
l² = 146
l = √146
≈ 12.083 cm
Now, calculate the lateral area:
Lateral Area = π × r × l
Lateral Area = 3.14159 × 5 cm × 12.083 cm
Lateral Area ≈ 189.75 cm²
Therefore, the lateral area of the cone is approximately 189.75 cm². The correct answer is C) 189.75 cm²
learn more about lateral area here
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-moves "The string of a kite is perfectly taut" and always makes an angle of 35 degrees above horizontal. (a) If the kite flyer has let out 500 feet of string, how high is the kite? (b) If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?
Answers
Answer:
a) [tex]h=286.8ft[/tex]
b) [tex]\frac{dh}{dt}=5.7ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Angle [tex]\theta=35[/tex]
a)
Slant height [tex]h_s=500ft[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=h_ssin\theta[/tex]
[tex]h=500sin35[/tex]
[tex]h=286.8ft[/tex]
b)
Rate of release
[tex]\frac{dl}{dt}=10ft/sec[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=lsin35[/tex]
Differentiate
[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]
[tex]\frac{dh}{dt}=10sin35[/tex]
[tex]\frac{dh}{dt}=5.7ft/s[/tex]
oludonts c) 2x + y = 2
2x + 2y = 0
Answers
Answer:
[tex]x = 2[/tex]
[tex]y = -2[/tex]
Step-by-step explanation:
Given
[tex]2x + y = 2[/tex]
[tex]2x + 2y = 0[/tex]
Required
Solfe for x and y
Subtract both equations
[tex]2x- 2x + y - 2y = 2 -0[/tex]
[tex]-y = 2[/tex]
Divide by -1
[tex]y = -2[/tex]
Substitute [tex]y = -2[/tex] in [tex]2x + 2y = 0[/tex]
[tex]2x+2 *-2 = 0[/tex]
[tex]2x-4 = 0[/tex]
[tex]x - 2 = 0[/tex]
Collect like terms
[tex]x = 2[/tex]
what term can you add to
[tex] \frac{5}{6} x - 4[/tex]
to make it equivalent to
[tex] \frac{1}{2} x - 4[/tex]
Answers
9514 1404 393
Answer:
-1/3x
Step-by-step explanation:
We want to find the term 'a' such that ...
(5/6x -4) + a = (1/2x -4)
Add 4-1/2x to both sides.
(5/6 -1/2)x -4 +4 +a = 0
(5/6 -3/6)x + a = 0 . . . . . . express the fractions using a common denominator
1/3x + a = 0 . . . . . . . . . . simplify the difference
a = -1/3x . . . . . . . . . . .subtract 1/3x
The term you can add to make the desired equivalent is -1/3x.
Multiple choice plss help
Answers
Answer:
D
Step-by-step explanation:
The correct answer Is D
A teacher teaches two classes with 8 students each. Each student has a 95% chance of passing their class independent of the other students. Find the probability that, in exactly one of the two classes, all 8 students pass.
Answers
Answer:
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Probability that all students pass in a class:
Class of 8 students, which means that [tex]n = 8[/tex]
Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]
This probability is P(X = 8). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]
Find the probability that, in exactly one of the two classes, all 8 students pass.
Two classes means that [tex]n = 2[/tex]
0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].
This probability is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]
0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.
Cole biked at 5 mph for 1 hours. Which of the following choices show how far he biked?
A=5.5 miles
B=6.5 miles
C=7.5 miles
D=10 miles
Answers
Answer:
Most Likely A, 5.5 Miles
Step-by-step explanation:
However the question doesn't make sense as the logical answer is simply 5 miles, but the safest choice is 5.5
Your sample is normally distributed with a mean age of 36. The standard deviation in this sample is 4 years. You would expect:
Answers
Kindly find complete question attached below
Answer:
Kindly check explanation
Step-by-step explanation:
Given a normal distribution with ;
Mean = 36
Standard deviation = 4
According to the empirical rule :
68% of the distribution is within 1 standard deviation of the mean ;
That is ; mean ± 1(standard deviation)
68% of subjects :
36 ± 1(4) :
36 - 4 or 36 + 4
Between 32 and 40
2.)
95% of the distribution is within 2 standard deviations of the mean ;
That is ; mean ± 2(standard deviation)
95% of subjects :
36 ± 2(4) :
36 - 8 or 36 + 8
Between 28 and 44
3.)
99% is about 3 standard deviations of the mean :
That is ; mean ± 3(standard deviation)
99% of subjects :
36 ± 3(4) :
36 - 12 or 36 + 12
Between 24 and 48
Use the relationship among the three angles of any triangle to solve. Two angles of a triangle have the same
measure and the third angle is 27° greater than the measure of the other two. Find the measure of each angle.
Please help :)
Answers
Answer:
51°,51°,78°
Step-by-step explanation:
The sum of angles in a triangle add up to 180°
There are 7 black balls and 8 red balls in an urn. If 5 balls are drawn without replacement, what is the probability that exactly 4 black balls are drawn
Answers
Answer:
(5/20)*(4/19)*(3/18)*(2/17) = 120/116280 = .001 = .1%
Step-by-step explanation:
