Answer:
C(min) = 8763.4 $
Step-by-step explanation:
Area = 24000 ft²
In a rectangle, A = x * y x is the base side and y the height side
Cost of low and upper side (x) is 20 $ per foot
Cost of east and west sides ( y) is 10 $per ft
total cost is:
C(r) = 2 * 20* x + 2* 10* y
from A = x * y y = A / x y = 24000 / x
And by substitution in C(r) we get:
C(x) = 2 * 20* x + 2* 10* 24000 / x
C(x) = 40 * x + 480000 / x
Tacking derivatives on both sides of the equation:
C´(x) = 40 - 480000 / x²
C´(x) = 0 40 - 480000/x² = 0
40* x² - 480000 = 0
x² = 480000 / 40
x² = 12000
x = √ 12000 = 109,54 ft
and y = 24000 / 109,54
y = 219,09 ft
Chequing for second derivative
C´´(x) = 480000 / x⁴ is always positive so we have a minimum of C at the value x = 109,54
Minimum cost C (min) = 40* 109,54 + 20 * 219,09
C(min) = 4381.6 + 4381.8
C(min) = 8763.4 $
Which fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)?
Answer:
Step-by-step explanation:
slope=y2-y1/x2-x1
here x1=2 , y1=-4 , x2=-6 , y2=1
=1-(-4)/2-(-6)
=1+4/2+6
=5/8
-5/8 fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
the slope formula for the line containing (2, -4) and (-6, 1) we calculate by plugging the values to the slope formula.
m=1-(-4)/-6-2
m=1+4/-8
m=-5/8
Hence, -5/8 fraction shows a correct way to set up the slope formula for the line containing (2, -4) and (-6, 1)
To learn more on slope of line click:
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A tiling company completes two jobs. The first job has $1200 in labor expenses for 40 hours worked, while the second job has $1560 in labor expenses for 52 hours worked. The relationship between the labor expenses and the hours worked is linear. Which equation can be used to calculate the y-intercept of the linear equation?
Answer: 1560 = 30(52) + b
Step-by-step explanation:
Based on the information given in the question, the straight line passes through two points which are (40, 1200) and (52, 1560). Then, the equation if the straight line will be:
y - 1560 = (1200 - 1560)/(40 - 52) (x - 52)
y - 1560 = (-360)/(-12) (x - 52)
y - 1560 = 30(x - 52)
Lets put the value of x to be 0.
y - 1560 = 30(x - 52)
y - 1560 = 30(0 - 52)
y - 1560 = -30(52)
Therefore, 1560 = 30(52) + b
Can somebody help me with this question
Answer:
[tex]\text{a) }1,080^{\circ}, \\\text{b) }360^{\circ}, \\\text{c) }135^{\circ}, \\\text{d) }45^{\circ}[/tex]
Step-by-step explanation:
a) The sum of the interior angles of a polygon with [tex]n[/tex] sides is equal to [tex](n-2)180[/tex]. Since an octagon has 8 sides, substitute in [tex]n=8[/tex]:
[tex](6-2)180=\boxed{1,080^{\circ}}[/tex]
b) The sum of the exterior angles for any polygon is equal to [tex]360^{\circ}[/tex].
c) By definition, all regular shapes have equal angles and sides. Since we've found the total sum of the interior angles of an octagon in part a, each interior angle of a regular octagon must be [tex]\frac{1080}{8}=\boxed{135^{\circ}}[/tex]
d) Similar to part c, all regular shapes must have equal angles and sides. From part b, we know the sum of the exterior angles of a octagon is [tex]360^{\circ}[/tex], thus we have [tex]\frac{360}{8}=\boxed{45^{\circ}}[/tex]
On their way up the hill, Jack and Jill were stopped by their parents. It seems the two of them were trying to skip out on some chores. They were told to mow the lawn, clean the kitchen, and sweep the leaves off the deck. If Jack can complete all the chores in 3 hours by himself and Jill takes only 2.25 hours to get all of it done on her own, how many minutes will it take for the two of them to get the work done together
Answer:
77.14 minutes.
Step-by-step explanation:
Jack's time = 3 hours
Jill's time = 2.25 hours = 2 1/4 = 9/4 hours
Combined time = x
Rates :
Jack = 1/3 ; jill = 1 / 2.25 = 1 / 9/4 = 4 /9
Combined rate = 1/x
Setting up the equation :
1/3 + 4/9 = 1/x
Lcm of 3 and 9 = 9
(3 + 4) / 9 = 1/x
7/9 = 1/x
Cross multiply :
7x = 9
x = 9/7 hours
x = (9/7)* 60
x = 77.14 minutes
Combined time = 77.14 minutes.
The probability that a battery will last 10 hours or more is 80%, but the probability that a battery will last 15 hours or more is only 15%. What is the probability that a battery will last 15 hours or more given that it has lasted 10 hours or more
Answer:
0.1875 = 18.75% probability that a battery will last 15 hours or more given that it has lasted 10 hours or more.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Lasting 10 hours or more.
Event B: Lasting 15 hours or more.
The probability that a battery will last 10 hours or more is 80%.
This means that [tex]P(A) = 0.8[/tex]
Probability of lasting 10 hours or more and 15 hours or more.
This is the probability of lasting 15 hours or more(if it has lasted 15 or more, it has lasted 10 or more).
The probability that a battery will last 15 hours or more is only 15%, which means that [tex]P(A \cap B) = 0.15[/tex]
What is the probability that a battery will last 15 hours or more given that it has lasted 10 hours or more?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.8} = 0.1875[/tex]
0.1875 = 18.75% probability that a battery will last 15 hours or more given that it has lasted 10 hours or more.
Antonio is planning a birthday party for his daughter. SkateWorld charges a flat fee of $50 plus $3 per child. Roller Land charges $5 per child. If Antonio's daughter wants to invite 21 friends from school and five friends from her basketball team, which rink should Antonio use and how much would he save by doing so?
Answer:
skateworld
Step-by-step explanation:
26x3+50=128 aka skate worlds price
26x5=130 aka roller land price
Antionio should use skateworld and he would save 2$
Answer: SkateWorld. He saves $2
Step-by-step explanation:
SkateWorld:
21 *3 =63
5*3=15
63+15=78
78+50= 128
Roller Land:
21*5= 105
5*5=25
105+25=130
130-128= 2
Which algebraic expression represents the phrase "seven more than half of a number"?
Answer:
Step-by-step explanation:
½X+7
The set of all numbers on a number line are called?
Answer:
This second number line is called an integer number line, since integers are the set of numbers including all whole numbers and their negative opposites. Two opposite numbers are the same distance from zero on the number line, but on opposite sides. For example, 3 and -3 are opposites.
Step-by-step explanation:
I hope it's help u
What is the exact value of tan 75 degrees
Answer: 56?
Step-by-step explanation:
Two numbers are in the ratio 5:6. If the smaller one is decreased by 5 and
the other is increased by 3, the new ratio is 2:3. Find the number.
Answer:
Smallest Number = 35
Other Number = 42
Step-by-step explanation:
Let the smaller number be x.
Let the other number be y.
Given:
x : y = 5 : 6
That is,
[tex]\frac{x}{y} = \frac{5}{6}[/tex]
[tex]=> 5y = 6x\\\\=>x = \frac{5y}{6}[/tex]
Next: Let the smaller number be reduced by 5, x - 5
Let the other number be increased by 3, y + 3
Given : (x - 5) : (y + 3) = 2 : 3
That is,
[tex]\frac{x-5}{y+3} = \frac{2}{3}\\[/tex]
[tex](x-5) \times 3 = (y+3)\times 2\\\\substitute \ x = \frac{5y}{6}\\\\3(\frac{5y}{6} -5) = 2y + 6\\\\\frac{5y}{2} - 15 = 2y + 6\\\\\frac{5y}{2} - 2y = 6 + 15\\\\\frac{5y-4y}{2} = 21\\\\y = 21 \times 2 = 42\\\\Substitute \ y \ in \ x = \frac{5y}{6} \\\\x = \frac{5 \times 42}{6} = 35[/tex]
any one got reddit
mine is u/RealAd8482
I use to have reddit sorry
Answer:
Yes
Step-by-step explanation:
Mines is u/Brown_Bear17
5 -3 over 2 x > 1 over 3
Answer:
It's true because 5-3/2 is grater than 1/3
Topic Test
Find the surface area of a rectangular prism.
a. 2468 sq. ft.
b. 6240 sq. ft.
c. 1234 sq. ft.
d. 1844 sq. ft.
Please select the best answer from choices provided
Answer:
A. 2468 sq. ft.
Step-by-step explanation:
I calculated it logically
The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 144 residents whose mean number of pounds of trash generated per person per week was 34.5 pounds and the standard deviation was 7.9 pounds. Round answers to 3 decimal places where possible. a. To compute the confidence interval use a
Answer:
32.966 ; 36.034)
Step-by-step explanation:
Given :
Sample size , n = 144
Mean, x = 34.5
Standard deviation = 7.9
The confidence interval :
Xbar ± Margin of error
Margin of Error = Zcritical * s/√n
Zcritical at 98% = 2.33
Margin of Error = 2.33 * 7.9/√144 = 1.534
Lower boundary = 34.5 - 1.534 = 32.966
Upper boundary = 34.5 + 1.534 = 36.034
(32.966 ; 36.034)
find the value of x.
Similar Triangles
You are visiting the Unisphere at Flushing Meadow Park in New York. To estimate the height of the stainless steel model of Earth, you place a mirror on the ground and stand where you can see the top of the model in the mirror. The Unisphere is 100 feet from the mirror and you are standing 4 feet from the mirror. If your height is 5.6 feet, what is the estimated height of the Unisphere? The diagram is not drawn to scale.
a. 140 feet
b. 22.4 feet
c. 2,240 feet
d. 71 feet
Please select the best answer from the choices provided
Answer:
A. 140 feet
Step-by-step explanation:
I calculated it logically
What is the name of this poligon?
A. Rhombus
B. trapezoid
C. rectangle
D. Square
Answer:
the correct answer is A. Rhombus
The answer is D (Square)
Because the sides of a square are equal.
Write the function
F(x)= 5x^2+10x+16 in standard form
Answer:
[tex]f(x) = 5x^2 + 10x + 16[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x^2 + 10x + 16[/tex]
Required
Write in standard form
The standard form of a quadratic function is:
[tex]f(x) = ax^2 + bx + c[/tex]
This implies that: [tex]f(x) = 5x^2 + 10x + 16[/tex] is already in standard form
The vertices of JKL are J(4,3), K(-3,4), L(-1,-1). Graph the image of JKL after a reflection in the line y=-x.
y=-x
J(-4,3)
K(3,-4)
L(1,1)
please help lolz ty besties
Volume of Prisms and Cylinders
a. 339.12 cu. in.
b. 113.04 cu. in
c. 226.08 cu. in.
d. 1356.48 cu. in
Please select the best answer from choices provided
Answer:
A. 339.12 cu. in.
Step-by-step explanation:
I calculated it logically
please help thx 7th grade
Answer:
All of them except a trapezoid
Step-by-step explanation:
The playground has two pairs of sides that are congruent to each other (70 = 70, 50 = 50), but a trapezoid only has ONE pair of sides that are congruent to each other; the other two are not the same. Therefore, this playground can be any shape besides a trapezoid.
If it takes 8 people to build a shed in 6 days, how long will it take 12 people?
Answer:
Step-by-step explanation:You can dowly/3fcEdSxnload the ans[tex]^{}[/tex]wer here. Link below!
bit.[tex]^{}[/tex]
Answer:
4 days
Step-by-step explanation:
(8×6)/12 = 48/12 = 4
Expand 20 - 3 (5w+2) - 4w
14 - 19w
26 - 11w
23 + 9w
Which one ?
what would be the value of y in the equation 2y + 7 = 7
y=0
Schools almost out, good luck!!
Simplify each expression using Order of Operations.
a. 2(3 + 4) + 3 to the 3rd power
b. 5 + (3 to the 2nd power - 2 to the 2nd power)
Answer:
a) 4,913
b) 10
Step-by-step explanation:
a) [2(3 + 4) + 3]³
= [2(7) + 3]³
= (14 + 3)³
= 17³
= 4913
b) 5 + (3² - 2²)
= 5 + (9 - 4)
= 5 + 5
= 10
Mr. Assan had 492 tickets left after the movie. He started with 2,009 tickets. How many tickets did Mr. Assan sell?
Answer:
1,517
Step-by-step explanation:
2,009 - 492 = 1,517
On the interval 0° < 0 < 380°, how many values of 0 satisfy the equation 2 cos0 + cos 0 - 1 = 0?
Answer:b
Step-by-step explanation:
pls help quicklyyy i will give 10 points pls
Answer:
[tex]0.156[/tex]
Step-by-step explanation:
[tex]15.6 \div 100[/tex]
[tex]0.156[/tex]
Hope it is helpful...hhhhhhhhelpp meeeeeee
Answer:
with what?
Step-by-step explanation: