A rancher has 360 yards of fencing with which to enclose two adjacent rectangular corrals, one for horses and one for cattle. A river forms one side of the corrals. If the width of each corral is x yards.
Required:
a. Express the total area of the two corrals as a function of x.
b. Find the domain of the function.
c. Determine the dimensions that yield the maximum area.
Answer:
a) A(x) = 360*x - 3*x²
b) The Domain of the function is ( 0 : ∞ )
c) x = 60 yards
y = 180 yards
c) A(max) = 10800 yd²
Step-by-step explanation:
Two rectangular corrals, with sides y and x ( y is the side parallel to the river) having a river as one side of the corrals means:
L length to be fenced
L = y + 3*x 360 = y + 3*x y = 360 - 3*x
The total areaof the two corrals as a function of x is
A(t) = x*y as y = 360 - 3*x by substitution we get
A(x) = x * ( 360 - 3*x)
A(x) = 360*x - 3*x²
Tacking derivatives on both sides of the equation we get:
A´(x) = 360 - 6*x A´(x) = 0 360 - 6*x = 0
x = 60 yards
and y = 360 - 3*x y = 360 - 180 y = 180 yards
A(max) = 60*180 = 10800 yd²
To find out if the value x = 60 is the x value for a maximum of A we go to the second derivative
A´´(x) = - 6 A´´(x) < 0 then there is a maximum value for function A in x = 60
The Domain of the function is ( 0 : ∞ )
I am interested in determining how long students take on average, to finish the first exam in my class. I specifically am interested in looking at students who take the class during the summer semester. I randomly pick 50 students from previous summer semesters and note how long the took on the first exam (TIME), which class they took with me - Stator Stat (CLASS), and whether they took the class online or in person (FORMAT).
Identity the following viables as either quantitative or qualitative
Class
Time
Answer:
jwruaijoii9auhyahd9i3u
w daF
wf
w
a
s
w sfjweiaeadfawjasawwg
Step-by-step explanation:
Quantitative data is supported by the empirical value in the form of counts or numbers, where each data set is attached with a particular numerical value. Qualitative data describes and can be expressed as the number of the subject.
For the class:
It is qualitative because the qualitative data is used to describes the qualifies or characteristics.In the given scenario the variable class differentiates students based on the information when the book stat I or Stat II.For the Time:
It is quantitative because the quantitative data is used to includes measurable quantity numbers.These numbers are used for the time of the quantitative variable.Learn more:
brainly.com/question/555216
If f(x) = - 2x +5 and g(x)=x2-1, then f(-3)+g(2) =
Answer:
[tex]{ \tt{f(x) = - 2x + 5}} \\ { \boxed{ \bf{f( - 3) = - 2( - 3) + 5 = 11}}} \\ \\ { \tt{g(x) = {x}^{2} - 1}} \\ { \boxed{ \bf{g(2) = {2}^{2} - 1 = 3}}} \\ f( - 3) + g(2) = 11 + 3 \\ = 14[/tex]
ASAP. There are three marbles in a bag. When is red and two are black. What is the probability of picking a black marble first, putting it back in the bag and then picking a black marble? Use the following probably need to find the answer.
Answer:
Number of black balls=2
Total number of balls=3
Probability =2/3
Complete the following statement mentally.
Answer:
The answer to your question is given below.
Step-by-step explanation:
Let the total number be U.
From the question given above, we were told that any number of B is 50% of the total number (i.e U).
Now, we shall determine the the total number (U) in terms of B.
50% of U = B
50/100 × U = B
50U / 100 = B
Cross multiply
50U = 100B
Divide both side by 50
U = 100B/50
U = 2B
Thus, the total number is 2B
Finally, we shall determine the answer to the question:
111 is 50% of ___
B = 111
Total number (U) = 2B
Total number (U) = 2 × 111
Total number (U) = 222
Therefore,
111 is 50% of 222
Anton needs to buy 3.5 meters of cloth for their project in TLE. If 1 meter of cloth costs P35.00, how much will he spend for 3.5 meters of cloth? a. What is asked in the problem? b. What are the given facts? c. What operation will be used? d. What is the nunber sentence? e. What is the answer?
Answer:
The correct answer is -
a. Amount Anton will spend for 3.5 m of cloth
b. 3.5 meters of cloth, 35.00 costs per meter.
c. Multiplication
d. 35.00 × 3.5/1 = N
e. P122.50 amount he will spend for 3.5 meters of cloth
Step-by-step explanation:
Solution:
A. in this question it is asked that how much it will cost Anton to buy the required cloth that is 3.5 meters cloth.
B. Given:
required cloth - 3.5 meters
price or cost of cloth per meter - 35 per meter
C. In this question multiplication will be used to get the answer so the operation would be - multiplication.
D. The number sentence is an equation to express inequality by using numbers and mathematical symbols, here the number sentence would be -
35.00 × 3.5/1 = N
E. The correct answer would be -
N = 35.00 × 3.5/1
= 122.5
Thus, the correct answer would be P 122.5.
For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation:
y = 3 x squared + 2 x minus 8
Answer:
Table A
Step-by-step explanation:
y = 3x^2 +2x -8
The quadratic is in the form
y = a x^2 +bx+c
a = 3 b = 2 c = -8
Since a > 0 it opens up
The y intercept is c so the y intercept is -8
PLEASE HELP!!!
Solve this system of equations for x and y. Use the addition method or the substitution method. Check your result:
2x + 4y = 10
x - 2y = 1
How will your solution to the previous problem change if we change it to this system of inequalities?:
2x + 4y ≤ 10
x - 2y > 1
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Answer:
(x, y) = (3, 1)
2y +1 < x ≤ 5 -2y where y < 1
Step-by-step explanation:
a) We can add twice the second equation to the first to eliminate y.
(2x +4y) +2(x -2y) = (10) +2(1)
4x = 12 . . . . . simplify
x = 3
3 -2y = 1 . . . . substitute for x in the second equation
2 = 2y . . . . . add 2y-1 to both sides
1 = y . . . . . . divide by 2
The solution is (x, y) = (3, 1).
__
b) The solution for a set of inequalities is generally the intersection of two half-planes. It is not just one point. The solution space is usually represented graphically, but we can write inequalities that express it.
The first inequality tells us that both x and y will be on or below the boundary line, which will have negative slope.
The second inequality tells us x will be above the boundary line with positive slope, and y will be below it. If we consider the boundary lines to cross in an X shape, the solution space will be in the bottom quadrant. This suggests the area can best be represented by expressing x as a range of values in terms of y.
Solving each inequality for x, we get ...
2x +4y ≤ 10 ⇒ x ≤ 5 -2y
x -2y > 1 ⇒ x > 2y +1
These give us the compound inequality ...
2y +1 < x ≤ 5 -2y
Of course, the relation between the limits must hold, so ...
2y +1 < 5 -2y
4y < 4 . . . . . . . add 2y-1
y < 1 . . . . . . divide by 4
The solution is 2y +1 < x ≤ 5 -2y where y < 1.
_____
The graph shows the region that is the solution to the system of inequalities. The vertex point (3, 1) is not part of that region. (It does not satisfy the left boundary condition.) However, that point is the solution to the set of equations. It is where the boundary lines meet.
__
Additional comment
Above, we noted that the inequalities have boundary lines that intersect to divide the Cartesian plane into 4 parts. We called the intersecting lines an X shape. In general, if the solution space is in the left- or right-portion of this shape, the compound inequality defining the solution will be one that bounds y. If it is in the top or bottom of this shape, then the compound inequality will be one that bounds x (as in this problem).
A different generality may apply if the boundary lines have slopes of the same sign.
Which is the graph of the parent function f(x) = x2?
Answer:
it should look like a U shape. Its called a parabola
(0,0) is the bottom center.
Step-by-step explanation:
What is the sum of the series 18 E n=4 (n+1) ^2? 1,239 2,415 2,440 2,469
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Answer:
(c) 2440
Step-by-step explanation:
The sum of the squares of numbers 1 .. n is ...
s(n) = n(n +1)(2n +1)/6
You want the sum of squares from 5 to 19. We can compute that from ...
s(19) -s(4) = (19(20)(39) -4(5)(9))/6 = (14820 -180)/6 = 2440
Answer:
C. 2440Step-by-step explanation:
hope it helps u too
Lance is selling T-shirts for $10 each and hats for $12.50 each. He wants to earn at least $400 per week to cover his expenses. Which graph best represents the number of T-shirts and hats Lance should sell to meet his goal?
Answer:
Step-by-step explanation:
Estimate the unit selling price of an item for which the following data is available. Labor 15 hours at $26/hr Overhead 150% of labor Material Costs $89 each Packing Costs 10% of labor Subcontract Cost $11 each Sales Commission 5% of selling price Profit 10% of selling price
Answer:
$1281.1
Explanation:
Unit selling price is total cost plus markup(percentage profit on total cost price)
Assuming overhead is already apportioned to each product at $585 each
Total cost:
Labor 15hrs at $26/hr=15×26=$390
Overhead 150% of labor=150%×390=$585
Material Costs= $89
Packing Costs= 10%×390= $39
Subcontract Cost= $11
Sales Commission= 5% of selling price=$55.7
Total cost = $1169.7
Profit =10% of selling price= $111.4
Selling price =total cost + profit
= $1281.1
I need help pleaseee
Answer:
7
Step-by-step explanation:
refer to solution in picture
The playground director has a total of
24 basketballs and footballs. He has
6 more footballs than basketballs, How
many of each does he have?
Answer:
9 basketballs
15 footballs
Step-by-step explanation:
The number of basketballs will be y.
The number of basketballs will be y + 6.
y + y + 6 = 24
2y + 6 = 24
2y + 6 - 6 = 24 - 6
2y = 18
2y ÷ 2 = 18 ÷ 2
y = 9
y + 6
9 + 6 = 15
MP of an article is $1400. Find the SP of that article in cents if the shopkeeper adds 13% VAT after allowing 45% discount. (100 cents =$1)
Answer:
87,010 cents is the SP.
Step-by-step explanation:
MP = $1400
VAT = 13%
Discount = 45%
so,
discount amount = 45% of MP
= 45% of $1400
= 45/100 * $1400
= 9/20 * $1400
= 9* $70
= $630
so,
MP - discount amount
= $1400 - $630
= $770(SP)
so,
VAT amount = 13% of SP
= 13% of $770
= 13/100 * $770
= $100.1
so,
SP + VAT
= $770 + $100.1
= $870.1
so,
$1 = 100 cents
$870.1 = 100*870.1
= 87,010 cents
Which function is graphed?
Answer:B
Step-by-step explanation:
This is the only possible answer trust me
Find the 22nd term of the arithmetic sequence whose common difference is d =3 and whose first term is a_1=-20
Find the length of X ( IN THE PICTURE)
Answer:
x=3
Step-by-step explanation:
The triangles are similar so we can use ratios to solve
x 4
----- = -----------
4.5 6
Using cross products
6x = 4.5 * 4
6x =18
Divide by 6
6x/6 = 18/6
x = 3
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE CYLINDER
Answer:
Find the volume of the cone, the answer i got was 37.68 but it asked to round so it should be 37.7
Hope this helps :)
Answer:
If we want to find volume of cone we must use this formule: πr²*high/3.
Step-by-step explanation:
let's solve step by step
firstly you know the radius is 3 and high is 4
if we accept π to 3. the answer is must be (3*3*4)/3 and finally the answer is 12 units³
The median of the values 3.4, 4.7, 1.9, 7.6, and 6.5
Answer:
4.7
Step-by-step explanation:
the median is the middle number in a set of numbers so first we need to put them in order
1.9 3.4 [4.7] 6.5 7.6
this one is easy since we have an odd number of digits
the answer is 4.7
no spam pls
for which x is f(x)=-3
1. -7
2.-4
3. 4
4. 5
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Answer:
(a) -7
Step-by-step explanation:
You are given f(x) = -3. Look for -3 in the f(x) column. (You will find it in the first row.)
You want the corresponding value of x. It will be in the first row of the x column. The value there is -7.
The value of x for f(x) = -3 is -7.
Suppose you are asked to take a sample of men and women in order to measure their emotional IQ. The emotional IQ scale that you administer has a minimum of 0 and a maximum of 100, with higher scores indicating higher emotional intelligence (the range of the scale is not pertinent to the question -- I simply provide it so that you have some context in which to provide your answer). You sample 25 men and 25 women. The mean for men is 70 with a standard deviation of 10 and the mean for women is 82 with a standard deviation of 15.
Required:
What is the 99% confidence interval for the scores of men and women?
Answer:
The 99% confidence interval for the scores of men is (64.406,75.594).
The 99% confidence interval for the scores of women is (73.609,90.391).
Step-by-step explanation:
We have the standard deviations for the sample, which means that the t-distribution will be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 25 - 1 = 24
99% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797.
For men:
Standard deviation of 10.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{10}{\sqrt{25}} = 5.594[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 70 - 5.594 = 64.406
The upper end of the interval is the sample mean added to M. So it is 70 + 5.594 = 75.594
The 99% confidence interval for the scores of men is (64.406,75.594).
For women:
Standard deviation of 15.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{15}{\sqrt{25}} = 8.391[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 82 - 8.391 = 73.609
The upper end of the interval is the sample mean added to M. So it is 82 + 8.391 = 90.391
The 99% confidence interval for the scores of women is (73.609,90.391).
Right angle Trigonometry, please help me solve and explain!
Answer:
5.01
Step-by-step explanation:
Reference angle (θ) = 24.3°
Length of side Opposite to reference angle = 2.06
Let the side length (Hypotenuse) we're looking for be represented as x
Apply SOH:
Sin θ = Opp/Hyp
Substitute the values into the equation
Sin 24.3° = 2.06/x
Multiply both sides by x
x × Sin 24.3° = 2.06/x × x
x × Sin 24.3° = 2.06
Divide both sides by Sin 24.3°
(x × Sin 24.3°)/Sin 24.3° = 2.06/Sin 24.3°
x = 5.01 (nearest hundredth)
if for a dog 1 year is 7 ears for them, how many hours in 24 hours is one day for dogs?
Answer:
168hrs in division terms of every 1 year x 7 etc...
It will always be 24hrs nothing changes set of units to same units.
However because the equivalent to a same length of life as human is 1/7 we can do the reciprocal = 7 and do 24 x 7 = 168 hrs, but as many younger and healthy dogs eat and sleep the same as humans then equivalent would be not a good way to compare a dogs life.
Longer life breeds like Labrador or mixed breed dogs if walked at least 4 times a day and away from other dogs and all day young kids can live older than 20 and have actually be more compared to 4-5 years and so the comparison would be like 96 hrs or 120 hrs, but hours stay 24 a day for all animals as units don't change same units. Day represents a day and a year represents sun rise to sun fall to sun rise again x 365.
what is the area of the figure below
Answer:
190 in²
Step-by-step explanation:
Cut the shape into simpler ones:
A=6 x 6= 36 in²
A=7x22= 154 in²
A=36 + 154= 190 in²
question- pls help me find the answer to this question
Answer:
(a) 6cm
Step-by-step explanation:
Hope you have good grades and study well...btw make me as brainliest ty sweetie!
Which angles are supplementary to 24? Select all that apply.
Answer:
<2, <3, <6, <7
Step-by-step explanation:
Supplementary to <4 means that, <4 and that angle equals 180. So we will move angle by angle.
<1 = Is not supplementary because both are virtually opposite angle and virtually opposite angles are equal.
<2 = Is supplementary angle because it is a vertical linear pair with <4.
<3 = Is supplementary angle because it is horizontal linear pair with <4
<5 = Is not supplementary angle because they are alternate interior angles and alternate angles are equal.
<6 = Is supplementary because angles on the same side and same interior/exterior are supplementary. (By interior/exterior, I meant that they have to be either interior or exterior. No both)You can also use the reason that 6 and 2 are corresponding angles, and corresponding angles are equal. So, if 2 is supplementary to 4, then 6 is also supplementary to 4. I think the latter is better than the first.
<7 = Is supplementary because it is vertically opposite to 6 and 6 is supplementary, so 7 is also supplementary.
<8 = Not supplementary. Because 4 and 8 are corresponding angles and corresponding angles are not equal. And also 8 is equal to 5. And 5 is not supplementary to 4. That means 8 is also not.
Ugh... I really hope u understand, and don't think that I am blabbering.
Thank You
Please mark me as the brainliest
A group of people were asked if they had run a red light in the last year. 315 responded "yes", and 190 responded "no".
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal accurate to at least 3 decimal places
Answer:
0.624
Step-by-step explanation:
Number who have run a red light = 315
Number who haven't run a red light = 190
From the data :
The total number of people sampled = total possible outcome = (315 + 190) = 505
Selecting a person at random, probability that the selected person has run a red light :
P = required outcome / Total possible outcomes
Required outcome = Number who have run a red light = 315
P(having run a red light) = 315 / 505 = 0.624
Find the measure of ∠BAC. Create another angle with the same measure. Measure the new angle to verify that it has the same angle measure. Take a screenshot of your work, and paste it below.
Answer:
The position and orientation of the new angle may vary, but it should have the same angle measure as ∠BAC
.Step-by-step explanation:
The measure of the angle is determined and the image is attached with the answer.
What is an Angle ?An angle is formed by two rays having a common end point.
The angle BAC is of certain measure.
To determine the value of the angle another angle is drawn in following steps
1. Draw a straight line XY
2. With an compass draw an arc of any length on BAC and on the new straight line XY keeping tip of the compass on the end points A and X.
3. Measure the point at which the arc cuts the angle BAC from the point at which it intersects AC and with the same measure , keeping the point of the compass on the point where the arc intersected XY ,cut an arc on the arc.
4. The intersecting point Z of the arc is joint to X
5.The angle ZXY is measured , and this is the value of the angle BAC.
The image is attached with the answer.
To know more about Angle
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Find the median and mean of the data set below: 6 , 37 , 2 , 38 , 1 , 3 , 46 6,37,2,38,1,3,46
Answer:
Mean: 19
Median: 6
Step-by-step explanation: