Answer:
x = 14 ft
y = 56 ft
A(max corral) = 784/3 = 261.33 ft²
Step-by-step explanation:
Let´s call y the side parallel to the barn, then only one y is going to be fenced.
If we are going to divide the area in three identical corrals we need 4 times x ( the other side perpendicular to the barn)
The perimeter of the rectangular area ( divide in three identical corrals)
112 = y + 4*x or y = 112 - 4*x
A (r) = x*y
Area as a function of x is
A(x) = x* ( 112 - 4*x) A(x) = 112*x - 4*x²
Tacking derivatives on both sides of the equation
A´(x) = 112 - 8*x A´(x) = 0 112 - 8*x = 0
x = 112/8
x = 14 ft
And y = 112 - 4*x y = 112 - 56
y = 56 ft
A(max) = 14 * 56 = 784 ft²
A(max corral) = 784/3 = 261.33 ft²
How do we know the area is maximum, tacking the second derivative
A´´(x) = - 8 A´´(x) < 0
Then the function A(x) has a maximum at the point x = 14
Answer:
14ft by 18 2/3 ft
Step-by-step explanation:
In a small metropolitan area, annual losses due to storm, fire, andtheft are assumed to be independent, exponentially distributed random variableswith respective means 1.0, 1.5, 2.4. Determine the probability that the maximumof these losses exceeds 3.
Answer:
[tex]0.4138[/tex]
Step-by-step explanation:
Given
[tex]x \to storm[/tex]
[tex]\mu_x = 1.0[/tex]
[tex]y \to fire[/tex]
[tex]\mu_y = 1.5[/tex]
[tex]z \to theft[/tex]
[tex]\mu_z = 2.4[/tex]
Let the event that the above three factors is greater than 3 be represented as:
[tex]P(A > 3)[/tex]
Using complement rule, we have:
[tex]P(A > 3) = 1 - P(A \le 3)[/tex]
This gives:
[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]
-----------------------------------------------------------------------------------------------------------
The exponential distribution formula of each is:
[tex]P(x \le k) = 1 - e^{-\frac{k}{\mu}}[/tex]
So, we have:
[tex]k = 3; \mu_x = 1[/tex]
[tex]P(x \le 3) = 1 - e^{-\frac{3}{1}} = 1 - e^{-3} = 0.9502[/tex]
[tex]k=3; \mu_y = 1.5[/tex]
[tex]P(y \le 3) = 1 - e^{-\frac{3}{1.5}} = 1 - e^{-2} = 0.8647[/tex]
[tex]k = 3; \mu_z = 2.4[/tex]
[tex]P(z \le 3) = 1 - e^{-\frac{3}{2.4}} = 1 - e^{-1.25} = 0.7135[/tex]
-----------------------------------------------------------------------------------------------------------
[tex]P(A > 3) = 1 - P(\{x \le 3\}\ n\ \{y \le 3\}\ n \{z \le 3\}\)[/tex]
[tex]P(A > 3) = 1 - (0.9502 * 0.8647 *0.7135)[/tex]
[tex]P(A > 3) = 1 - 0.5862[/tex]
[tex]P(A > 3) = 0.4138[/tex]
Diane looks around at an assembly. She notices her younger sister to her right and her older brother 6 feet ahead of her. If Diane's brother and sister are 10 feet apart, how far apart are Diane and her younger sister?
6 people share 12 muffins
What is the answer to this question?
8
[tex] \frac{50}{100} [/tex]
[tex]\sf\purple{0.5}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{50}{100} \\ = \frac{1}{2} \\ = 0.5[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Which choice below could represent the distance jake walked?
Answer:
50 yard South, 40 yard east 60 yard northwest
express 21/4 in the decimal form by long division method
Answer:
5.25
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
In a simple random sample of 1500 young Americans 1305 had earned a high school diploma.
a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?
b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma.
c. Report the 95% confidence interval for the percentage of all young Americans who earned a high school diploma.
d. Suppose that in the past, 80% of all young Americans earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young Americans who cam high school diplomas has increased? Explain.
Answer:
a) The standard error for this estimate of the percentage of all young Americans who earned a high school diploma is 0.87%.
b) The margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma is of 1.71%.
c) The 95% confidence interval for the percentage of all young Americans who earned a high school diploma is (85.29%, 88.71%).
d) The lower bound of the confidence interval is above 80%, which means that the confidence interval supports the claim that the percentage of young Americans who cam high school diplomas has increased.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Standard error:
The standard error is:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Margin of error:
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}} = zs[/tex]
The confidence interval is:
Sample proportion plus/minus margin of error. So
[tex](\pi - M, \pi + M)[/tex]
In a simple random sample of 1500 young Americans 1305 had earned a high school diploma.
This means that [tex]n = 1500, \pi = \frac{1305}{1500} = 0.87[/tex]
a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.87*0.13}{1500}} = 0.0087[/tex]
0.0087*100% = 0.87%.
The standard error for this estimate of the percentage of all young Americans who earned a high school diploma is 0.87%.
b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Then
[tex]M = zs = 1.96*0.0087 = 0.0171[/tex]
0.0171*100% = 1.71%
The margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma is of 1.71%.
c. Report the 95% confidence interval for the percentage of all young Americans who earned a high school diploma.
87% - 1.71% = 85.29%
87% + 1.71% = 88.71%.
The 95% confidence interval for the percentage of all young Americans who earned a high school diploma is (85.29%, 88.71%).
d. Suppose that in the past, 80% of all young Americans earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young Americans who cam high school diplomas has increased? Explain.
The lower bound of the confidence interval is above 80%, which means that the confidence interval supports the claim that the percentage of young Americans who cam high school diplomas has increased.
Use a calculator to find the lengths x and y of the legs of the right triangle shown
Answer:
y = 0.47
x = 0.91
Step-by-step explanation:
From the right angled triangle Given :
Applying trigonometry :
To Obtain y :
We use :
Tan θ = opposite / hypotenus
Tan 25 = y / 1
y = 1 * tan 25
y = 0.4663076 * 1
y = 0.47
For x :
We use :
Cosθ = adjacent / hypotenus
Cos 25 = x / 1
0.9063077 = x / 1
x = 0.9063077 * 1
x = 0.9063077
Hence, x = 0.91
3) Which inequality represents the graph?
-54
-36
-18
0
18
36
54
a) x<9
b) x>9
c) X29
d) XS9
Answer:
I need a picture to see what it represents.
Find the number if 2/5 of it is 22
Answer:
22×2/5=8.8
Step-by-step explanation:
Hope it helps you
Answer:
55
Step-by-step explanation:
2/5n = 22
multiply each side by 5/2 to get:
n = 110/2
n = 55
The graph shows two lines, A and B.
6
A
B В
5
4
3
1
0
1 2
3 4 5 6
Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer.
Part B: What is the solution to the equations of lines A and B? Explain your answer.
Answer:
A: 1 solution: the lines intersect at one point
B: (3,4), reference graph for solution
Step-by-step explanation:
A: solutions are equivalent to how many intersections two lines have, and we can see that these lines intersect once and won't intersect again
B: luckily the intersection point is super easy to plot, so we can just reference the graph for our solution!
Shelly receives a salary of $450 plus 20% commission on everything she sells. She sold $ 600 worth of office supplies. What was her total pay check
Answer:
$1140 or $540
Step-by-step explanation:
450*1.2=540
540+600=1140
A small airplane flies 1015 miles with an average speed of 290 miles per hour. 1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time; what was the average speed of the 747
Answer:
The average speed of the 747 was of 580 miles per hour.
Step-by-step explanation:
We use the following relation to solve this question:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
A small airplane flies 1015 miles with an average speed of 290 miles per hour.
We have to find the time:
[tex]v = \frac{d}{t}[/tex]
[tex]290 = \frac{1015}{t}[/tex]
[tex]290t = 1015[/tex]
[tex]t = \frac{1015}{290}[/tex]
[tex]t = 3.5[/tex]
1.75 hours after the plane leaves, a Boeing 747 leaves from the same point. Both planes arrive at the same time;
The time of the Boeing 747 is:
[tex]t = 3.5 - 1.75 = 1.75[/tex]
Distance of [tex]d = 1015[/tex], the velocity is:
[tex]v = \frac{d}{t} = \frac{1015}{1.75} = 580[/tex]
The average speed of the 747 was of 580 miles per hour.
The graph shows the relationship between tablespoons and teaspoons. Determine a rule that relates the number of tablespoons by writing the correct term or value from the tiles in each blank.
Answer:
Multiply
1/3
Step-by-step explanation:
You can divide by 3 or multiply by 1/3. Since it looks like 3 is grayed out, I guess you have to use the latter.
THIS IS WORTH 30 POINTS
1. Point B is located at (-4, -6). Where is the location of B’ after a reflection over the y-axis?
Answer:
your awnser would be [4, −6]
Step-by-step explanation:
hope this helps
Please help with this!!!
In need of a answer fast!
Answer:
You never attached anything so ill just say the answer is 4
Step-by-step explanation:
If you want a serious answer please edit your question so it is answerable.
:) Have a good day
A house has increased in value by 15% since it was purchased. If the current value is $391,000, what was the value when it was purchased?
help with this question
9514 1404 393
Answer:
A = 49π/36 or 59π/36
Step-by-step explanation:
The given angle is coterminal with the same angle modulo 2π.
(563/36)π = 14π +(59/36)π
so the coterminal angle is 59π/36 ≈ 1.6389π, a 4th-quadrant angle. The 3rd-quadrant angle with the same sine value is found by subtracting this angle from 3π:
A = 3π -(59π/36) = 49π/36
The two values of A that satisfy the equation are ...
A = 59π/36A = 49π/36_____
In degrees, the two angles are 245° and 295°.
What is the y-intercept of the Line y=3/4x + 2
Answer:
Step-by-step explanation:
What is -4.5 need help pls help fast I will give u a brilliant and thank
Answer:
its -4.5??? what is the question you're asking
In 2016, there were approximately 4.46 x 10 people in Asia. On average, a person takes 8.4 x 10 breaths per
year. Using this data, what was the number of breaths of all the people in Asia in 2016? Expressing your answer in
scientific notation in the form a x 10", what are the values of a and b?
What is the value of a?
What is the value of b?
Answer: 4
Step-by-step explanation:
I got this same question buddy im here to see the answer but there were not any
help will give brainliest
9514 1404 393
Answer:
198 $1.20Step-by-step explanation:
1. Let x represent the number of apples left. Then the number of mangosteens left is 1/6x. The starting number in each case is the number left plus the number sold. The starting numbers are equal, so we have ...
x + 201 = (1/6)x +366
5/6x = 165 . . . . . . . . . . subtract 1/6x+201
x = 198 . . . . . . . . multiply by 6/5
198 apples were left.
__
2. Let d represent the cost of a drink. The cost of a drink is 3/5 the cost of a snack, so the cost of a snack is 5/3 the cost of a drink. Then Alice's total expenditure was ...
15d +12(5/3d) = 42
35d = 42 . . . . . . . . . . . . . . collect terms
d = 42/35 = 6/5 = 1.20 . . . divide by 35
The cost of a drink was $1.20.
I need help please!!!
Answer:
Option D would be the correct answer!
Hope this helps!
father is 20 years older than son. if the sum of their ages is 40 years find their age
Answer:
20 is the father's 20 is the son
Step-by-step explanation:
20+20=40
40/2=20
40-20=20
another way:
20:n= 40
40-20=20
20:20=40
Answer:
Step-by-step explanation:
let the age of son be x
x+x+20=40
2x=40-20
x=20/2
x=10
since age of a father is 20 more than his son's so,
x+20=father's age
10+20
30
therefore fathers age is thirty years and son age is 10 years
PLEASE HELP ME !!! Can anyone help me find the function for this trig graph ?? i need a specific answer for the function , 50 pts and i will mark brainliest !!
Answer:
y = 5 sin (2x) + 4
Step-by-step explanation:
this is sines function,
the amplitude is [9 - (-1)]/2 = 10/2 = 5
the period is 2πx/π = 2x
the x-axis of actual function is at y = 4
so, the function is :
y = 5 sin (2x) + 4
Suppose that newborn harbor seal pups have a weight that is normally distributed, with a mean of 22.0 lbs and standard deviation of 1.1 lbs. Find the probability that a newborn pup has a weight above 24.0 lbs.
Answer:
0.0344 = 3.44% probability that a newborn pup has a weight above 24.0 lbs.
Step-by-step explanation:
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.
Mean of 22.0 lbs and standard deviation of 1.1 lbs.
This means that [tex]\mu = 22, \sigma = 1.1[/tex]
Find the probability that a newborn pup has a weight above 24.0 lbs.
This is 1 subtracted by the p-value of Z when X = 24. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 22}{1.1}[/tex]
[tex]Z = 1.82[/tex]
[tex]Z = 1.82[/tex] has a p-value of 0.9656.
1 - 0.9656 = 0.0344
0.0344 = 3.44% probability that a newborn pup has a weight above 24.0 lbs.
One hundred draws are made at random with replacement from box A, and 250 are made at random with replacement from box B. (a) 50 of the draws from box A are positive, compared to 131 from box B: 50.0% versus 52.4%. Is this difference real, or due to chance
Answer:
Therefore WE accept the Null hypothesis [tex]H_0[/tex] That 50.0% versus 52.4%.difference is real
Step-by-step explanation:
Sample size A [tex]n_a=100[/tex]
Sample size B [tex]n_b=250[/tex]
Positive draw from box A [tex]n_a=50[/tex]
Positive draw from box b [tex]n_b=131[/tex]
Generally the equation for Probability of Positive draw from Box A is mathematically given by
[tex]P_1=\frac{50}{100}[/tex]
[tex]P_1=50%[/tex]
Therefore
[tex]1-P_1=50\%[/tex]
Generally the equation for Probability of Positive draw from Box A is mathematically given by
[tex]P_1=\frac{131}{250}[/tex]
[tex]P_1=52.4%[/tex]
Therefore
[tex]1-P_1=47.6\%[/tex]
Generally the equation for Standard error S.E is mathematically given by
[tex]S.E=\sqrt{\frac{n_1(p_1)*(1-P_1)}{n_1^2}+\frac{n_2(P_2(1-p^2))}{n_2^2}}[/tex]
[tex]S.E=\sqrt{\frac{100(0.50)*(50)}{100^2}+\frac{(250)(0.524(47))}{250^2}}[/tex]
[tex]S.E=0.592[/tex]
[tex]S.E=59.2\%[/tex]
Therefore
[tex]Z=\frac{50-52.4}{59.2}[/tex]
Generally
[tex]P value P>0.05[/tex]
Therefore WE accept the Null hypothesis [tex]H_0[/tex] That 50.0% versus 52.4%.difference is real
Which town will eventually have more people?
The perimeter of the figure below is 64 m. Find the length of the missing side.
Simplify the ratio
6 doctors to 27 patients
Answer:
2 doctors to 9 patients
Step-by-step explanation:
Divide each by 3. They cant be simplified more.