Answer:
a. k = -0.01014 s⁻¹
b. [tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
c. [tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
d. y(t) = 130.485°F
Step-by-step explanation:
A hot metal bar is submerged in a large reservoir of water whose temperature is 60°F. The temperature of the bar 20 s after submersion is 120°F. After 1 min submerged, the temperature has cooled to 100°F.
(Let y be measured in degrees Fahrenheit, and t be measured in seconds.)
We are to determine :
a. Determine the cooling constant k. k = s−1
By applying the new law of cooling
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = k(T_1-T_2)[/tex]
[tex]\dfrac{dT}{dt} = k (T - 60)[/tex]
Taking the integral.
[tex]\int \dfrac{dT}{T-60} = \int kdt[/tex]
㏑ (T -60) = kt + C
T - 60 = [tex]e^{kt+C}[/tex]
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
After 20 seconds, the temperature of the bar submersion is 120°F
T(20) = 120
From equation (1) ,replace t = 20s and T = 120
[tex]120 = 60 + C_1 e^{20 \ k}[/tex]
[tex]120 - 60 = C_1 e^{20 \ k}[/tex]
[tex]60 = C_1 e^{20 \ k} --- (2)[/tex]
After 1 min i.e 60 sec , the temperature = 100
T(60) = 100
From equation (1) ; replace t = 60 s and T = 100
[tex]100 = 60 + c_1 e^{60 \ t}[/tex]
[tex]100 - 60 =c_1 e^{60 \ t}[/tex]
[tex]40 =c_1 e^{60 \ t} --- (3)[/tex]
Dividing equation (2) by (3) , we have:
[tex]\dfrac{60}{40} = \dfrac{C_1e^{20 \ k } }{C_1 e^{60 \ k}}[/tex]
[tex]\dfrac{3}{2} = e^{-40 \ k}[/tex]
[tex]-40 \ k = In (\dfrac{3}{2})[/tex]
- 40 k = 0.4054651
[tex]k = - \dfrac{0.4054651}{ 40}[/tex]
k = -0.01014 s⁻¹
b. What is the differential equation satisfied by the temperature y(t)?
Recall that :
[tex]\dfrac{dT}{dt} = k \Delta T[/tex]
[tex]\dfrac{dT}{dt} = \dfrac{- In (\dfrac{3}{2})}{40}(T-60)[/tex]
Since y is the temperature of the body , then :
[tex]\mathbf{\dfrac{dy}{dt} = - \dfrac{In(\dfrac{3}{2})}{40}(y-60)}[/tex]
(c) What is the formula for y(t)?
From equation (1) ;
where;
[tex]T = 60+ C_1 e^{kt} ---- (1)[/tex]
Let y be measured in degrees Fahrenheit
[tex]y(t) = 60 + C_1 e^{-\dfrac{In (\dfrac{3}{2})}{40}t}[/tex]
From equation (2)
[tex]C_1 = \dfrac{60}{e^{20 \times \dfrac{-In(\dfrac{3}{2})}{40}}}[/tex]
[tex]C_1 = \dfrac{60}{e^{-\dfrac{1}{2} {In(\dfrac{3}{2})}}}[/tex]
[tex]C_1 = \dfrac{60}{e^ {In(\dfrac{3}{2})^{-1/2}}}}[/tex]
[tex]C_1 = \dfrac{60}{\sqrt{\dfrac{2}{3}}}[/tex]
[tex]C_1 = \dfrac{60 \times \sqrt{3}}{\sqrt{2}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ t}{40}}}[/tex]
(d) Determine the temperature of the bar at the moment it is submerged.
At the moment it is submerged t = 0
[tex]\mathbf{y(0) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} \ e^{\dfrac{-In(\dfrac{3}{2})\ 0}{40}}}[/tex]
[tex]\mathbf{y(t) = 60+ \dfrac{60 \sqrt{3}}{\sqrt{2}} }[/tex]
y(t) = 60 + 70.485
y(t) = 130.485°F
Suppose that $2000 is invested at a rate of 2.6% , compounded semiannually. Assuming that no withdrawals are made, find the total amount after 10 years.
Answer:
$2,589.52
Step-by-step explanation:
[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]
We start with the compound interest formula above, where
A = future value
P = principal amount invested
r = annual rate of interest written as a decimal
n = number of times interest is compound per year
t = number of years
For this problem, we have
P = 2000
r = 0.026
n = 2
t = 10,
and we find A.
[tex] A = $2000(1 + \dfrac{0.026}{2})^{2 \times 10} [/tex]
[tex] A = $2589.52 [/tex]
Compound interest formula:
Total = principal x ( 1 + interest rate/compound) ^ (compounds x years)
Total = 2000 x 1+ 0.026/2^20
Total = $2,589.52
The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively.
Answer:
S = 250/tStep-by-step explanation:
If the rate of change of sales is inversely proportional to the time t, this is expressed mathematically as ΔS ∝ 1/Δt
ΔS = k/Δt where k is the constant of proportionality
If ΔS = S₂-S₁ and Δt = t₂-t₁
S₂-S₁ = k/ t₂-t₁
If the sales after 2 and 4 weeks are 162 units and 287 units respectively, then when S₁ = 162, t₁ = 2 and when S₂ = 287, t₂ = 4.
On substituting this values into the given functions, we will have;
287 - 162 = k/4-2
125 = k/2
cross multiplying
k = 125* 2
k = 250
Substituting k = 250 into the function ΔS = k/Δt
ΔS = 250/Δt
S = 250/t
Hence the value of S as function of t when the sales after 2 and 4 weeks are 162 units and 287 units, respectively is expressed as S = 250/t
Robert is putting new roofing shingles on his house. Each shingle is 1 2/3 feet long. The north part of the house has a roof line that is 60 feet across. How many shingles can be placed (side by side) on the north part of the house?
Answer: 36 shingles can be placed on the north part of the house.
Step-by-step explanation:
Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.
The north part of the house has a roof line that is 60 feet across.
Then, the number of shingles can be placed on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)
[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]
Hence, 36 shingles can be placed on the north part of the house.
The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of 7 cm/s. When the length is 12 cm and the width is 5 cm, how fast is the area of the rectangle increasing?
Answer:
129 [tex]cm^2/s[/tex]
Step-by-step explanation:
Increasing rate of length, [tex]\frac{dl}{dt}[/tex]= 9 cm/s
Increasing rate of width, [tex]\frac{dw}{dt}[/tex] = 7 cm/s
Length, l = 12 cm
Width, w = 5 cm
To find:
Rate of increase of area of rectangle at above given points.
Solution:
Formula for area of a rectangle is given as:
[tex]Area = Length \times Width[/tex]
OR
[tex]A = l \times w[/tex]
Differentiating w.r.to t:
[tex]\dfrac{d}{dt}A = \dfrac{d}{dt}(l \times w)\\\Rightarrow \dfrac{d}{dt}A = w \times \dfrac{d}{dt}l +l \times \dfrac{d}{dt}w[/tex]
Putting the values:
[tex]\Rightarrow \dfrac{dA}{dt} = 5 \times 9 + 12 \times 7\\\Rightarrow \dfrac{dA}{dt} = 45 + 84\\\Rightarrow \bold{\dfrac{dA}{dt} = 129\ cm^2/sec}[/tex]
In what order should you evaluate problems?
Answer:
(4) → (1) → (3) → (2)
Step-by-step explanation:
Order of operations in any question are decided by the rule,
P → Parentheses
E → Exponents
D → Division
M → Multiplication
A → Addition
S → Subtract
Following the same rule order of operations will be,
- Take care of anything inside the parentheses.
- Evaluate and raise the exponents
- Multiply or divide. Make sure to do whichever one comes first from left to right.
- Add or Subtract from left to right.
Options are arranged in the order of,
(4) → (1) → (3) → (2)
HELP ASAP
What is the area of the circle shown below?
Answer:
C
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
Here r = 18 cm , thus
A = π × 18² = 324π ≈ 1017.9 cm² → C
Answer:
C.) 1017.9 cm²
Step-by-step explanation:
For a given circle
radius (r) = 18 cm
Now,
Area of Circle
= πr²
= 3.14 × (18)² cm
= 3.14 × 324 cm
= 1017.9 cm²
A regression was run to determine if there is a relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y). The results were: y = a+bx b = -0.89 a = 23.65 r2 = 0.7038 If a person watches 14 hours of television a day, predict how many sit-ups he can do. What is the value of the correlation coefficient? Round to three decimal places.
Answer:
y = 11.19 ; 0.839
Step-by-step explanation:
Given the following :
relationship between hours of TV watched per day (x) and the number of sit-ups a person can do (y)
y = a + bx ; comparing with the linear regression model function
y = predicted variable
a = intercept
b = slope or gradient
x = independent variable
b = -0.89 a = 23.65 r2 = 0.7038
Therefore, if a person watches for 14 hours per day, that is x = 14, the number of sit-ups he can do will be :
y = 23.65 + (-0.89)(14)
y = 23.65 - 12.46
y = 11.19
About 11 sit-ups.
If the r^2 value = 0.7038
Then the Coefficient of regression = r
Will be the square root of r^2
r = sqrt(r^2)
r = sqrt(0.7038)
r =0.8389278 = 0.839
What is the best way you learn math?
Answer:
to provide interest in the subject
As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c
Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.
Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.
if you're next to your exams then just one thing, Start now!!
hope this helps!
What is credit?
an arrangement in which you receive money, goods, or services now in exchange for the promise of payment later
an arrangement in which you receive goods or services in exchange for other goods and services
an arrangement in which you receive money now and pay it bulk later with fees?
A function y = g(x) is graphed below. What is the solution to the equation g(x) = 3?
Answer:
See below.
Step-by-step explanation:
From the graph, we can see that g(x)=3 is true only when x is between 3 and 5. However, note that when x=3, the point is a closed circle. When x=5, the point is an open circle. Therefore, the solution is between 3 and 5, and it includes 3 but not 5.
In set-builder notation, this is:
[tex]\{x|x\in \mathbb{R}, 3\leq x<5\}[/tex]
In interval notation, this is:
[tex][3,5)[/tex]
Essentially, these answers are saying: The solution set for g(x)=3 is all numbers between 3 and 5 including 3 and not including 5.
Angles One angle is 4º more than three times another. Find
the measure of each angle if
a. they are complements of each other.
b. they are supplements of each other.
[tex] \Large{ \boxed{ \bf{ \color{purple}{Solution:}}}}[/tex]
Let the smaller angle be x
Then, Larger angle would be x + 4°
Case -1:❍ They are complementary angles.
This means, they add upto 90°So,
➙ x + x + 4° = 90°
➙ 2x + 4° = 90°
➙ 2x = 86°
➙ x = 86°/2 = 43°
Then, x + 4° = 47°
So, Our required answer:
Smaller angle = 43°Larger angle = 47°Case -2:❍ They are supplementary angles.
This means, they add upto 180°So,
➙ x + x + 4° = 180°
➙ 2x + 4° = 180°
➙ 2x = 176°
➙ x = 176°/2 = 88°
Then, x + 4° = 92°
So, Our required answer:
Smaller angle = 88°Larger angle = 92°✌️ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
Solve the inequality 7a + 13 < 48.
Hi there! :)
Answer:
[tex]\huge\boxed{a < 5}[/tex]
Given:
7a + 13 < 48
Isolate the variable "a" by subtracting 13 from both sides:
7a - 13 < 48 - 13
7a < 35
Divide both sides by 7:
7a/7 < 35/7
a < 5.
Answer:
a < 5
Step-by-step explanation:
7a + 13 < 48
Subtract 13 from each side
7a + 13-13 < 48-13
7a < 35
Divide each side by 7
7a/7 < 35/7
a < 5
AB||CD. Find the measure of
Answer:
135 degrees
Step-by-step explanation:
3x+15 = 5x - 5 because of the alternate interior angles theorem.
20 = 2x
x = 10
3(10) + 15 = 30+15 = 45
Remember that a line has a measure of 180 degrees. So we can just subtract the angle we found from 180 degrees to get BFG.
180-45 = 135.
Three-fourths (x minus 8) = 12
Answer:
x=24
Step-by-step explanation:
3/4(x-8)=12
3/4x-24/4=12
3/4x=18
18 dived by 3/4
x=24
your welcome :)
Sean earned 20 points. Charles earned p more points than Sean. Choose the expression that shows how many points Charles earned.
Answer:
the person above is correct if i did this correct
Step-by-step explanation:
The ball bearing have volumes of 1.6cm cube and 5.4cm cube . Find the ratio of their surface area.
Answer:
64 : 729
Step-by-step explanation:
Ratio of surface area
= (ratio of linear dimensions) ^2
= 1.6^2 : 5.4^2
= 256 : 2916
= 64 : 729
An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Hope this can help you.
1: 8 faces and 9 with the base 9 vertices and 16 edges
2: 3 faces and 5 with the bases 6 vertices and 9 edges
3: 3 faces and 4 with the base 4 vertices and 6 edges
Explain why within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1 g
Step-by-step explanation:
Here are some examples of ten integers (in this case prime numbers) chosen from 2 to 24;
2, 3, 5, 7, 9, 15, 17, 19, 21, 23
Lets take for example the integers 15 and 21, they have a common divisor 3 which is greater than 1. Which implies that the number 3 can divide through 15 and 21 without a remainder, that is, 21 ÷ 3 = 7, 15 ÷ 3 = 5. Also note that 3 is a divisor of 9.
Therefore, we could right say that within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1.
A. f(x) = -x^2 - x - 4
B. f(x) = -x^2 + 4
C. f(x) = x^2 + 3x + 4
D. f(x) = x^2 + 4
Answer:
B: -x^2 + 4
Step-by-step explanation:
If the equation was [tex]f(x)=x^2[/tex], then the vertex would be at 0, and the "U" would be facing straight up. Here, the "U" is upside down, so that means the "x^2" would have to be a negative number ([tex]-x^2[/tex]) to get the upside-down "U". Then, we could see that the vertex is at positive 4, so that means that the parabola moved up 4 units, so the equation should end in +4.
Our answer is:
B: -x^2 + 4
please this is easy show working out and please get correct
Answer:
$ 180,000
Step-by-step explanation:
All we are being asked to do in this question is take the simple interest, given a principle value of $100,000, with 8 percent interest each year over a course of 10 years. This is given the simple interest formula P( 1 + rt ).
Simple Interest : P( 1 + rt ),
P = $ 100,000 ; r = 8% ; t = 10 years,
100,000( 1 + 0.08( 10 ) ) = 100,000( 1 + 0.8 ) = 100,000( 1.8 ) = 180,000
Therefore you will have to pay back a total of $ 180,000
if the numbers x+3,2x+1and x-7are in AP then find x
Answer:
-3
Step-by-step explanation:
If these numbers are part of an arithmetic progression, their differences are the same:
(x -7) -(2x +1) = (2x +1) -(x +3)
-x -8 = x -2
-6 = 2x
-3 = x
___
The numbers in the sequence are 0, -5, -10.
Answer:
x = -3.
Step-by-step explanation:
As it is an Arithmetic Progression the differences between successive terms are common, so:
2x + 1 - (x + 3) = x - 7 - (2x + 1)
2x - x + 1 - 3 = x - 2x - 7 - 1
x - 2 = -x - 8
2x = -8 + 2 = -6
x = -3.
Salaries of 42 college graduates who took a statistics course in college have a mean, , of . Assuming a standard deviation, , of $, construct a % confidence interval for estimating the population mean .
Answer:
The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
Step-by-step explanation:
The complete question is:
Salaries of 42 college graduates who took a statistics course in college have a mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard deviation, σ of $10,016 construct a 99% confidence interval for estimating the population mean μ.
Solution:
The (1 - α)% confidence interval for estimating the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
The critical value of z for 99% confidence interval is:
[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]
Compute the 99% confidence interval for estimating the population mean μ as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]
Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).
where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50. (Round your answer to two decimal places.)
THIS IS THE COMPLETE QUESTION BELOW
The demand equation for a product is p=90000/400+3x where p is the price (in dollars) and x is the number of units (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50.
Answer
$168.27
Step by step Explanation
Given p=90000/400+3x
With the limits of 40 to 50
Then we need the integral in the form below to find the average price
1/(g-d)∫ⁿₐf(x)dx
Where n= 40 and a= 50, then if we substitute p and the limits then we integrate
1/(50-40)∫⁵⁰₄₀(90000/400+3x)
1/10∫⁵⁰₄₀(90000/400+3x)
If we perform some factorization we have
90000/(10)(3)∫3dx/(400+3x)
3000[ln400+3x]₄₀⁵⁰
Then let substitute the upper and lower limits we have
3000[ln400+3(50)]-ln[400+3(40]
30000[ln550-ln520]
3000[6.3099×6.254]
3000[0.056]
=168.27
the average price p on the interval 40 ≤ x ≤ 50 is
=$168.27
Pregnancy length in horses. Bigger mammals tend to carry their young longer before giving birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution, with mean 336 days and standard deviation 3 days. Use the 68–95–99.7 rule to answer the following questions.Required:What percent of horse pregnancies are longer than 339 days?
Answer:
16%
Step-by-step explanation:
The difference between the time of interest (339 days) and the mean (336 days) is 3 days, which is exactly 1 standard deviation.
The 68-95-99.7 rule tells you that 68% of pregnancies will be within 1 standard deviation. The remaining 32% will be evenly split between pregnancies that are longer than 339 days and ones that are shorter than 333 days. So, half of 32%, or 16%, will be longer than 339 days.
Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be reworked.Required:a. What is the (approximate) probability that X is at most 30?b. What is the (approximate) probability that X is less than 30?c. What is the (approximate) probability that X is between 15 and 25 (inclusive)?
Answer:
(a) The probability that X is at most 30 is 0.9726.
(b) The probability that X is less than 30 is 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.
Step-by-step explanation:
We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.
Let X = the number among these that are nonconforming and can be reworked
The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).
Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.
Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).
So, the new mean of X, [tex]\mu[/tex] = [tex]n \times p[/tex] = [tex]200 \times 0.11[/tex] = 22
and the new standard deviation of X, [tex]\sigma[/tex] = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{200 \times 0.11 \times (1-0.11)}[/tex]
= 4.42
So, X ~ Normal([tex]\mu =22, \sigma^{2} = 4.42^{2}[/tex])
(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}
P(X < 30.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{30.5-22}{4.42}[/tex] ) = P(Z < 1.92) = 0.9726
The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.
(b) The probability that X is less than 30 is given by = P(X [tex]\leq[/tex] 29.5) {using continuity correction}
P(X [tex]\leq[/tex] 29.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{29.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] 1.70) = 0.9554
The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.
(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = P(X < 25.5) - P(X [tex]\leq[/tex] 14.5) {using continuity correction}
P(X < 25.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{25.5-22}{4.42}[/tex] ) = P(Z < 0.79) = 0.7852
P(X [tex]\leq[/tex] 14.5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{14.5-22}{4.42}[/tex] ) = P(Z [tex]\leq[/tex] -1.70) = 1 - P(Z < 1.70)
= 1 - 0.9554 = 0.0446
The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.
Therefore, P(15 [tex]\leq[/tex] X [tex]\leq[/tex] 25) = 0.7852 - 0.0446 = 0.7406.
I NEED ALGEBRA HELP! Can you solve a system of equations using the substitution by solving one equation for x or y and then using the substitution method? x + 6y = 6 and 7x - 5y = -5
Answer:
let x be y
NOW,
X+6Y=6
Y+6Y=6
7Y=6
Y=0.87
In a genetics experiment on peas, one sample of offspring contained green peas and yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of that was expected? 350 127 3 4 The probability of getting a green pea is approximately . (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to ? Choose the correct answer below. 3 4 A. No, it is not reasonably close. B. Yes, it is reasonably close.
Answer:
The probability of getting an offspring pea that is green is is 0.733
YES, the probability is reasonably close to the expected value of 3/4 (0.750)
Step-by-step explanation:
The formula for calculating the probability of an event is;
P = Favorable Outcome / Sample space
Let A be an event of getting an offspring green peas, B be an event of getting an offspring yellow peas and N be the total number of peas.
number of green peas in an offspring are 350
number of yellow peas in an offspring are 127
total number of peas are 477
So in the genetic experiment, the number of times event A occurs is 350 and the number times event B occurs is 127
Now the probability of getting an offspring pea that is green is
P = number of green peas / total number of peas
p = n(A)/N
p = 350/477
p = 0.733
So YES, the probability is reasonably close to 3/4 ( 0.750 )
The probability of getting an offspring pea that is green is is 0.733.
YES, the probability is reasonably close to the expected value of 3/4 (0.750)
Hospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 18% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Required:a. Find the probability that both generators fail during a power outage.b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?c. Is that probability high enough for the hospital?
Answer:
a. 0.36
b. 0.1296
c. No.
Step-by-step explanation:
1. Note the probability of emergency backup generators to fail when they are needed = 18% or 0.18. Thus,
a. Probability of both emergency backup generators failing = P (G1 and G2 fails) where G represents the generators.
= P (G1 falls) x P ( G2 fails)
= 0.18 x 0.18
= 0.36
b. The probability of having a working generator in the event of a power outage = G1 fails x G2 works + G2 works x G2 fails
= 0.36 x 0.18 + 0.18 x 0.36
= 0.1296
c. Looking at the probability of any of the generators working, it is not meeting safety standards as lives could be lost if the backup generators needed to perform an emergency surgery operation fails.
nishan bought 7 marbles Rs.x per each. if he gave Rs.100 to the shop keeper. what is the balance he would receive?
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons. Assume that the population distribution is normal. (Use t Distribution Table.)
a-1. What is the value of the population mean?
16
Unknown
74
a-2. What is the best estimate of this value?
Estimate population mean
c. For a 90% confidence interval, what is the value of t? (Round your answer to 3 decimal places.)
Value of t
d. Develop the 90% confidence interval for the population mean. (Round your answers to 3 decimal places.)
Confidence interval for the population mean is and .
e. Would it be reasonable to conclude that the population mean is 68 gallons?
a) Yes
b) No
c) It is not possible to tell.
Correct question is;
The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 21 people reveals the mean yearly consumption to be 74 gallons with a standard deviation of 16 gallons.
a. What is the value of the population mean? What is the best estimate of this value?
b. Explain why we need to use the t distribution. What assumption do you need to make?
c. For a 90 percent confidence interval, what is the value of t?
d. Develop the 90 percent confidence interval for the population mean.
e. Would it be reasonable to conclude that the population mean is 68 gallons?
Answer:
A) Best estimate = 74 gallons
B) because the population standard deviation is unknown. The assumption we will make is that the population follows the normal distribution.
C) t = 1.725
D) 90% confidence interval for the population mean is (67.9772, 80.0228) gallons
E) Yes
Step-by-step explanation:
We are given;
Sample mean; x' = 74
Sample population; n = 21
Yearly Standard deviation; s = 16
A) We are not given the population mean.
So the closest estimate to the population mean would be the sample mean which is 74.
B) We are not given the population standard deviation and as such we can't use normal distribution. So what is used when population standard deviation is not known is called t - distribution table. The assumption we will make is that the population follows the normal distribution.
C) At confidence interval of 90% and DF = n - 1 = 21 - 1 = 20
From t-tables, the t = 1.725
D) Formula for the confidence interval is;
x' ± t(s/√n) = 74 ± 1.725(16/√21) = 74 ± 6.0228 = 67.9772 or 80.0228
Thus 90% confidence interval for the population mean is (67.9772, 80.0228) gallons
E) 68 gallons lies within the range of the confidence interval, thus we can say that "Yes, it is reasonable"
