y = 220/ ((10/3) * √22)
It is given that area is 200 square feet. Cost is 3 dollar per foot. Fourth side costs 12 dollars per foot.
This f(x,y) needs to represent the cost of the fence so we can look at each side's price. We can choose the fourth side to be along the x axis and be represented by 13x. The other sides therefore must be represented by 5y, 5y, and 5x.
So, our cost, f(x,y) = 13x + 5x + 5y + 5y = 18x + 10y
Our constraint is xy = 220 as defined by the area of a rectangle.
We can then take our constraint to be put in terms of exclusively x, giving us y = 220/x
Plugging this into our cost, the thing we are minimizing, we get f(x) = 18x + 2200/x
In order to find the minimum we use the first derivative test, taking f'(x) and finding the critical points.
f'(x) = 18 - 2200/x2
Setting this equation to be equal to 0 we find that x = ±√2200/18 . But the negative answer doesn't make sense because distance cannot be negative so we throw it out.
x = (10/3) * √22
We must verify that this is a minimum by confirming the following:
If x < (10/3) * √22, f'(x) < 0. So, f(x) is decreasing when x < (10/3) * √22.
If x > (10/3) * √22, f'(x) > 0. So, f(x) is increasing when x > (10/3) * √22.
Thus, we have guaranteed that (10/3) * √22 is the x dimension. Now we plug in this value in our original equation to find y and that is our y dimension. So, y = 220/ ((10/3) * √22)
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Find the perimeter and area of the following composite figure. GEOMETRY!! HELPPP PLS
Answer:
perimeter=80 area=252
Step-by-step explanation:
The perimeter is the total length of the boundary of the shape added together: 12+20+12+8+20+8=80
The area is the value of the space inside the shape: the rectangle would be 20*9=180 plus the two triangles: (8*9)/2 = 36 180+72=252
Answer:
p=80 a=252
Step-by-step explanation:
Add all side lengths to get the perimeter.
20+12+12+8+20+8=80
Perimeter is 80
Area of a trapezoid is average of parallel lines*height
((20+36)/2)*9=252
Area=252
Match the following items.
1.(4, 2)
2.(-4, -2)
3.(-5, 0)
4.(-1, 1)
5.(2, 5)
6.(2, -4)
7.(4, -2)
8.(0, -5)
A
C
E
F
H
B
D
G
Based on the points on the graph, the correct matches are:
A - (-4, -2).B - .(2, -4)C - (4, -2).D - (2, 5)E - (-1, 1)F - (-5, 0)G - (4, 2)H - (0, -5)How are points located on a graph?To find a point, you need to look at the x-axis first and then the y-axis.
Find where the point is located on the x-axis, and then look for where the point intersects with the y-axis point.
For instance, the point A is located at (-4, -2) so look at the -4 point on the x axis, then go down to the -2 point on the y-axis. You'll find point A.
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A researcher wishes to estimate the percentage of adults who support abolishing the penny what size sample should be obtained if he wishes the estimate to be within three percentage points with a 95% confidence if he:
A: uses a previous estimate of 26%?
B: he does not use any prior estimates?
Using the z-distribution, the sample sizes required are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Then, the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
Rounding up, a sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex], which is when the largest sample size is needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5(0.5)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
Rounding up, a sample of 1068 is needed.
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An engineering student is studying the effects of cryogenic treatments on a particular material. The treatment involves cooling the material with specific applications of liquid nitrogen.
The temperature of the material in degrees Celsius, y, can be modeled by the following graph, where x represents the time, in hours, since the treatment began.
The true statement about the graph from the attached image below is: The material's temperature reaches a minimum at 15 hours.
What is the parabolic graph of the quadratic equation?The parabolic graph is a curved U-shaped graph that is established from a quadratic equation.
The parabola of the graph can be downward creating a maximum or upward (minimum).
From the given image, the correct interpretation shows that as a result of cryogenic treatment, the material's temperature reaches a minimum at 15 hours.
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write the linear inequality shown in the graph the gray represents the shaded region
Using the angle addition postulate, m BAD+m DAC=?
0 BCA
0 BAE
0 90*
0 BAC
Answer:
0 BAC
Step-by-step explanation:
m BAD+m DAC=m BAC(180°)
The value of m(BAD) + m(DAC) is equal to the measure of angle BAC.
Let's use the angle addition postulate to find the value of m(BAD) + m(DAC):
The angle addition postulate states that if you have an angle formed by two rays, say ∠BAD, and another angle formed by two rays, say ∠DAC, then the sum of their measures is equal to the measure of the angle formed by the original rays extended to meet the rays of the second angle. In other words:
m(BAD) + m(DAC) = m(BAC)
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The line AB is shown on the grid.
a) Find the gradient of a line
perpendicular to AB.
b) Find the equation of the line
perpendicular to AB and passing
through the midpoint of AB.
X
a) The gradient of a line perpendicular to AB is -2.
b) equation of line is y=-2x+6
What is gradient?The gradient is the measure of the steepness of a straight line.
a)The gradient of line is
=(-2-2)/(7+1)
=-4/8
=-1/2
So, gradient of a line perpendicular to AB is -2
b)The coordinates of mid point (3, 0)
m = -2
So,
0= -6+ b
b= 6
So, equation of line is y=-2x+6
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4x^2-3x+4 What is the value of the expression below when x = 5?
NEED ANSWER PLEASE!
Answer:
89
Step-by-step explanation:
To find the value of the
Quadratic expressionwhen x = 5 we substitute x = 5 into the expression.
4x^2 - 3x + 4
putting x = 5
4(5)^2 - 3(5) + 4
4(25) - 15 + 4
100 - 11 = 89
What is the approximate circumference of the circle shown below?
A.20cm
B.31.4cm
C.62.8cm
D.40cm
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Formula for finding the circumference:}[/tex]
[tex]\mathbf{2\times\pi\times radius = circumference}[/tex]
[tex]\huge\textbf{So, your equation should look like this:}[/tex]
[tex]\mathbf{\boxed{\textbf{circumference}} \approx 2\times3.14\times10}[/tex]
[tex]\huge\textbf{Now, that we have that information}\\\\\huge\textbf{out of the way, we can answer the}\\\\\huge\textbf{question, shall we begin?}[/tex]
[tex]\mathbf{\boxed{\textbf{circumference}} \approx 2\times3.14\times10}[/tex]
[tex]\mathbf{\boxed{\text{\bf circumference}}\approx 6.28 \times 10}[/tex]
[tex]\mathbf{\boxed{\bf circumference} \approx 62.8}[/tex]
[tex]\huge\textbf{Answer:}[/tex]
[tex]\huge\boxed{\textsf{Option C. 62.8 cm}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
Answer is C 62.8cm
Step-by-step explanation:
I just took the quiz!
A train travels 75 miles in 46 minutes. what is the average speed of the train?
Given the distance travelled and the time elapsed, the average speed of the train is approximately 1.63 miles per minutes.
What is the average speed of the train?Given that;
Distance traveled d = 75milesTime elapsed t = 46 minAverage speed s = ?Average speed = distance traveled / elapsed time
Average speed = 75miles / 46min
Average speed = 1.63 miles per minutes
Given the distance travelled and the time elapsed, the average speed of the train is approximately 1.63 miles per minutes.
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A marble is selected from a bag containing eight marbles numbered 1 to 8. The number on the marble selected will be recorded as the outcome. Consider the following events. Event A : The marble selected has an even number. Event B : The marble selected has a number greater than 3. Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
Answer:
Event A: 1/2
Event B: 5/8
Can someone help me solve this alpine with an explanation thank u (will mark as brainlist if correct&explanation)
Answer:
(d). [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Answer: [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Sorry this took so long.. i needed to use paint
Alex reads about 200 words per minute. The book he needs to read is 320 pages long and has about 275 words per page. How many hours must he read if he has 7 days to read the entire book?
[ Please don't only do the answer, I have more questions like this and giving the steps would really help a lot !! Thank you! ]
Answer:
7.3333 hours
Step-by-step explanation:
if im wrong oh well lol 275x320=88000 divided by 200 =440 divided by 60=7.3333
Evaluate.
5a for a = 15
Answer: 75
Step-by-step explanation:
5a = 5(15) = 75
△JKL∼△PQR
Two similar triangles. JKL and PQR. The length of JL is 28. The length of LK is unknown. The length of JK is labeled x. Angle J is labeled 35 degrees. The length of PQ is 38. The length of PR is 42. Angle P is labeled 35 degrees.
What is the value of x?
Enter your answer in the box. Round to the nearest hundredth.
x =
Answer: 25.33
Step-by-step explanation:
Corresponding sides of similar triangles are proportional, so
[tex]\frac{x}{28}=\frac{38}{42}\\\\x={28} \left(\frac{38}{42} \right) \approx \boxed{25.33}[/tex]
the volume of a cylinder is 539 cm cube and the circumference of the base is 22 cm. find the height of the cylinder.
Answer:
13.994[tex]cm (5.sf)[/tex]
Step-by-step explanation:
We know that the base of the cylinder is a circular base.
So circumference of base = [tex]2\pi r[/tex]
Given [tex]2\pi r=22cm\\\\r=\frac{22}{2\pi } \\r=\frac{11}{\pi } cm\\[/tex]
Volume of a cylinder = [tex]\pi r^{2} h[/tex] = 539[tex]cm^{3}[/tex]
Substitute r into the formula for volume of cylinder.
[tex]\pi (\frac{11}{\pi } )^{2} h=539\\\pi (\frac{121}{\pi ^{2} } )h=539[/tex]
Now, we will cancel [tex]\pi[/tex] from the numerator and denominator.
[tex](\frac{121}{\pi } )h=539\\h = \frac{539}{\frac{121}{\pi } } \\h = 539 * \frac{\pi }{121} \\h = 13.994cm(5s.f)[/tex]
Answer:
Aproximated height is:
14 cm
Step-by-step explanation:
volume of a cylinder = л r² h
л = 3.1416 (aprox)
r = radius
h = height
r = circunference/2л
r = 22/(2*3.1416)
r = 3.5 (aprox)
then volume is:
539 = 3.1416 * 3.5² * h
539 = 3.1416 * 12.25 * h
539 = 38.5 * h
h = 539/38.5
h = 14 cm (aprox)
which coordinates represent a translation of B (1,2) 3 units to the left and 2 units up
Answer:
(-2,4)
Step-by-step explanation:
By going 3 back you go 0,-1,-2 then you are already up 2 so if you go up 2 more you are at (-2,4). Hope this helps!
A line passes through (5,-2) with a slope of 1/4. Write the equation in slope-intercept
form.
Answer: y = [tex]\frac{1}{4}[/tex]x - 3 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Slope-intercept form is in the form of y=mx + b where m is the slope and b is the y-intercept.
We are given the slope, so we will plug this in.
y = mx + b
y = ([tex]\frac{1}{4}[/tex])x + b
Now, we will solve for the y-intercept by plugging in the point they give us.
y = ([tex]\frac{1}{4}[/tex])x + b
(-2) = ([tex]\frac{1}{4}[/tex])(5) + b
-2 = 1.25 + b
-3 [tex]\frac{1}{4}[/tex] = b
Lastly, we will plug this variable into the equation we wrote above for our final answer.
y = [tex]\frac{1}{4}[/tex]x - 3 [tex]\frac{1}{4}[/tex]
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Find the tangent of angle Θ in the triangle below.
A. 7/7
B. 0
C. sqroot2
D. 1
E. 7/sqroot98
Answer:
The tangent of the angle is 1
Step-by-step explanation:
The solution is in the image
TConsider △RST and △RYX.
Triangle R S T is shown. Line X Y is drawn parallel to side S T within triangle R S T to form triangle R Y X.
If the triangles are similar, which must be true?
StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction
StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction
For similar triangles ΔRST and ΔRYX proportion RY/RS = RX/RT = XY/TS is true.
Given that, for ΔRST, line XY is drawn parallel to side ST within ΔRST to form ΔRYX.
Considering ΔRST and ΔRYX.
What is the relation between sides of similar triangles?The corresponding sides of similar triangles are proportional.
We get ∠RXY=∠RST (Corresponding angles, since XY║ST)
∠RYX=∠RTS (Corresponding angles, since XY║ST)
From AA similarity criteria ΔRST is similar to ΔRYX.
Now, RY/RS = RX/RT = XY/TS.
Therefore, for similar triangles ΔRST and ΔRYX proportion RY/RS = RX/RT = XY/TS is true.
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Solve 7x = 54.
Pls help
Answer:
x= 54/7
Step-by-step explanation:
x= 54/7
Answer:
x = 54/7
Step-by-step explanation:
7x = 54
Divide both sides by seven (7)
7x/7 = 54/7
7 cancel out 7
x = 54/7
I need help asappp please, I attached a image
Answer:
Just look at the other answer
Step-by-step explanation:
Translate The Following Into An Expression:
s% of 1/r
(1r is a fraction)
The equation s% of 1/r translates to the expression s/100r
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
s% of 1/r
= (s/100) * (1/r)
= s/100r
The equation s% of 1/r translates to the expression s/100r
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The question is in the photo
Answer:
Answer is in the photo
Step-by-step explanation:
The formula for multiplying two numbers with same base but different exponents is
a^m×a^n= a^(m+n)
Use the information in this table(in the attachment) to help you answer the questions. Remember, you have a budget of $20,000 for the car.
1. What add-on options do you want in your car?
2. Write an inequality to model purchasing a car from Dealership A with the desired add-on options and staying within your budget. Use x to represent the base price of the car. (Assume that only the base price of the car is taxed to simplify the problem.)
3. Solve for x. Explain in words what the solution to the inequality means.
4. Graph the possible base price values that are included in the solution. Please upload an image of your graph.
5. Complete 2–4 for Dealership B using the same add-on options.
Will you buy from Dealership A or from Dealership B? Why?
The best buy is from dealership A because the fees of dealership B is more expensive
The add-on optionsFor the purpose of this exercise, the add-on options to select are:
Air-conditioningSunroofGPSBluetoothPower door and windowDealership AThe total amount of the add-on options is:
Total = $1000 + $500 + $3500 + $500 + $750
Total = $6250
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 751.56 + 6250 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 751.56 + 6250 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 12998.44
Divide both sides by (1 + 6.75%)
x ≤ 12176.52
The solution means that the base price of the car cannot exceed $12176.52 for dealership A
The graph of the possible base price
See attachment
Dealership BThe total amount of the add-on options is:
Total = $500 + $750 + $2750 + $750 + $500
Total = $5250
The inequality
This is represented using:
Base price * (1 + Tax) + Fees + Add-on total ≤ 20000
So, we have:
(1 + 6.75%) * x + 1524.72 + 5250 ≤ 20000
Solve for x
We have:
(1 + 6.75%) * x + 1524.72 + 5250 ≤ 20000
Evaluate the like terms
(1 + 6.75%) * x ≤ 13225.28
Divide both sides by (1 + 6.75%)
x ≤ 12389.02
The solution means that the base price of the car cannot exceed $12389.02 for dealership B
The graph of the possible base price
See attachment
Where to buy fromBuy from dealership A because the fees of dealership B is more expensive
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The length of a rectangle is 5 inches more than the width. the perimeter is 30 inches. find the length and the width
Answer:
Length = 10 inches
Width = 5 inches
Step-by-step explanation:
p = 2w + 2l
l = w + 5
30 = (2w + 2(w + 5))
30 = 4w + 10
20 = 4w
w = 5
l = w + 5
= 5 + 5
= 10
Which table of values corresponds to the graph below?
On a coordinate plane, a line goes through points (0, negative 2) and (2, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, negative 1, 0, 2. Column 2 is labeled y with entries 0, 1, 2, 4.
A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 1, 2, 4. Column 2 is labeled y with entries negative 2, negative 1, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 1, 4. Column 2 is labeled y with entries 0, 2, negative 1, 2.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 1, 0, 2, 4. Column 2 is labeled y with entries 1, negative 2, 0, 2.
Answer: B i got it right
Step-by-step explanation:
Construct a perpendicular to t through A
A
The perpendicular line to line t is drawn below.
The two-line in which the angle between these two lines is 90° i.e. both are right angle to each other then two lines are perpendicular to each other.
Here the given point is point A.
and the line given is line t
we have to draw a line that should be perpendicular to line t.
Let that perpendicular line cut the line t at the point O.
OA ⊥ t
∠AOt= 90°
From above we can draw the line OA which is perpendicular to line t.
The picture is drawn below.
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Carson wants to use a sheet of fiberboard 29 inches long to create a skateboard ramp with a 19 degree angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary
Answer:
9.4 in
Step-by-step explanation:
sin A = O/H
sin 19° = x/29
x = 29sin19°
x = 9.441 in
x = 9.4 in
Ken has a total of 74 notes. They are either $2 or $5 notes. He has 16 more pieces of $5 notes than $2 notes. Find the total value of all his notes.
Answer:
$283
Step-by-step explanation:
Let,
x - for $2 notes
x + 16 - for $5 notes
EQUATION:
(x) + (x + 16) = 74
2x = 74 - 16
2x = 58
x = 29
SUBSTITUTE
x = 29 pieces of $2 notes
x + 16 = 29 + 16 = 45 pieces of $5 notes
TOTAL VALUE IS:
(29 x $2) + (45 x $5) = $283