Answer:
The minimum cost is $17.30c
Step-by-step explanation:
Given
[tex]V = 288[/tex] --- Volume
[tex]C_1 = 0.06[/tex] --- cost of wall paint
[tex]C_2 = 0.16[/tex] ---cost of ceiling paint
Required
Minimum cost of paint
The volume is calculated as:
[tex]V =xyz[/tex]
Substitute 288 for V
[tex]288 =xyz[/tex]
Make z the subject
[tex]z = \frac{288}{xy}[/tex]
The surface area is calculated as:
[tex]Area = 2(yz + xz) + xy[/tex]
Because xy represent the dimension of the ceiling and the opposite of the ceiling (the floor) will not be painted. Hence, it does not require a coefficient of 2
The cost is:
[tex]C = 0.06 * 2(yz + xz) + 0.16 * xy[/tex]
Substitute [tex]z = \frac{288}{xy}[/tex]
[tex]C = 0.06 * 2(y*\frac{288}{xy} + x*\frac{288}{xy}) + 0.16 * xy[/tex]
[tex]C = 0.06 * 2(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = 0.12(\frac{288}{x} + \frac{288}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 * xy[/tex]
[tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
Differentiate w.r.t x and y
[tex]C_x = -\frac{34.56}{x^2} + 0.16y[/tex]
[tex]C_y = -\frac{34.56}{y^2} + 0.16x[/tex]
By comparison: [tex]x = y[/tex]
Set them equal to 0
[tex]C_y = -\frac{34.56}{y^2} + 0.16x=0[/tex]
[tex]-\frac{34.56}{y^2} + 0.16x=0\\[/tex]
Substitute x for y
[tex]-\frac{34.56}{x^2} + 0.16x=0[/tex]
[tex]0.16x=\frac{34.56}{x^2}[/tex]
Cross multiply
[tex]0.16x^3 = 34.56[/tex]
[tex]x^3 = \frac{34.56}{0.16}[/tex]
[tex]x^3 = 216[/tex]
Take the cube root of both sides
[tex]x = \sqrt[3]{216}[/tex]
[tex]x = 6[/tex]
[tex]x=y= 6[/tex]
Substitute 6 for x and for y in [tex]C = (\frac{34.56}{x} + \frac{34.56}{y}) + 0.16 xy[/tex]
[tex]C = (\frac{34.56}{6} + \frac{34.56}{6}) + 0.16 * 6* 6[/tex]
[tex]C = (\frac{2*34.56}{6}) + 5.76[/tex]
[tex]C = 11.52 + 5.76[/tex]
[tex]C = 17.28[/tex]
[tex]C = 17.3[/tex] --- approximated
the area of the square is 25 inches what is the measure on one side of the square??
Answer:
5
Step-by-step explanation:
area of a square= side x side
[tex]\sqrt{25}[/tex] = 5
xyz company's cost function for four months is c=500000+5q
find the break even dollar volume of sales if the selling price is 6 unit
The break even of a company is when cost equals selling function. The break even of xyz company is 500000 units.
Given that:
[tex]c=500000+5q[/tex] --- cost function
[tex]s = 6q[/tex] --- selling function
The break even is when the functions are equal
i.e.
[tex]s = q[/tex]
So, we have:
[tex]6q=500000+5q[/tex]
Collect like terms
[tex]6q - 5q=500000[/tex]
[tex]q=500000[/tex]
The break even is at 500000 units
Read more about break even at:
https://brainly.com/question/16889245
Find the circumference of a quarter of the circle (radius = 6)
Answer:
rajjsjdjdjxkkdkdkdkkdjxjjdjxjckfkjdjfuidid
What is the range of the following data set?
{2, 9,5, 4, 7, 8}
Answer:
7
Step-by-step explanation:
The range is the distance between the largest and smallest number. So 9-2=7
Hope this helped!
Answer: 9-2=7
Step-by-step explanation:Range is the highest value minus the lowest value in the data set.
Find the slope of the coordinates plane points
Answer:
-2
Step-by-step explanation:
When they give you 2 points use the formula so y2-y1/x2-x1
So -2-8/1 - -4
-10/1+4 so -10/5 = -2
Using the diagram below, calculate the value of x
Answer:
51°
Step-by-step explanation:
35°+(2x+16)°+(4x+3)°=360°
54°+6x=360°
6x=360°-54°
6x=306°
x=306°/6
x=51°
Somebody help me asap please giving brainliest
Please find the area
Answer:
b
Step-by-step explanation:
Area of parallelogram = Area of 2 small triangles
Therefore,
[tex]2( \frac{1}{2} \times 15.1 \times 7) = 105.7 {ft}^{2} [/tex]
Sarah is solving for X by the process of completing the square for the following problem..
2x^2+16x-12=0
She got to this point below - type the number that goes in the (?) spot
(x+?)^2=22
Answer:4
Step-by-step explanation: Since she did it by completing the square, then you must do the same thing to get the same form so you can see what that number is.
So first subtract the constant which is -12 so we need to add twelve to get the constant on the other side. So we now have 2x^2+16x=12
The constant of the x^2 must be 1 so we need to divide by 2 on every term to get x^2+8x=12
So to make it so to get a perfect factor we need to divide the x factor by 2 so we get 4.
So the answer is 4 cause it is a perfect factor so were going to get 4 on both factors.
Answer:
4
Step-by-step explanation:
x²+2(x)(?)+?²=22
multiply by 2 because the coefficient of the higher degree in the first equation is 2
2x²+2(2(x)(?))+2(?²)-2(22)=0
2x²+4x(?)+2?²-44=0
Comparison
4x(?)=16x
?=4
2?²-44=-12
So, 2?²=-12+44
2?²=32
?²=16
?=4
HELP MEEE!
Find the area and volume for both.
Answer:
Step-by-step explanation:
3.
area of one triangular face = ½×16×30 = 240 in²
area of base = 30×9 = 270 in²
area of diagonal face = 34×9 = 306 in²
area of vertical face = 16×9 = 144 in²
surface area = 2×240 + 270 + 306 + 144 = 1,200 in²
volume = 240×9 = 2,160 in³
:::::
4.
area of one triangular face = ½×10×10.5 = 52.5 ft²
area of base = 10.5×6 = 270 ft²
area of diagonal face = 14.5×6 = 87 ft²
area of vertical face = 10×6 = 60 ft²
surface area = 522 ft²
volume = 52.5×6 = 315 ft³
you have an ant farm with 34 ants. the population of your ants will double every 3 months. the table shows the population growth of the ants over 9 months. decide whether the table represents a linear function or a nonlinear function. after one year how many ants will there be on the farm?
A woman walks at a constant speed of 4.5 km per hr.How long will it take her to walk 10 km. using formula d=St how many hours and minutes
Answer:
1 hour and about 15 minutes.
Step-by-step explanation:
because in an hour she walks 4.5 km. and 4.5•2=9 so just another km will be 10 so estimatly it'll be 1 hour and 15 minutes
2 hours 13 minutes 20 seconds
Amath class has a total of 45 students. The number of males is 13 more than the number of females. How many males and
how many females are in the class
Number of males:
Number of females
Answer:
Males: 29
Females: 16
Step-by-step explanation:
2x+ 13 = 45
2x = 45 - 13
2x = 32
x = 16
16 + 13 = 29
29 +16 = 45
What is the slope of the line that passes through the points (-8,-1) and (-12,-2) ?
Answer:
1/3
Step-by-step explanation:
To find the slope subtract the second y-coordinate from the first y-coordinate and divide it by the result of the second x-coordinate from the first.
-2 - -1 = -1
-12 - -8= -3
-1/-3 = 1/3
Answer:
the answer is 4/1. Or just 4.
Step-by-step explanation:
-8-(-12) is -8+12=4. Then -1-(-2) is -1+2=1.
Only answer if you know!!!- Which phrase is represented by the expression - 8n? (1 point)
negative 8 more than a number
8 less than a number
negative 8 times a number
O a number divided by negative 8
Answer:
negative 8 times a number is the desired answer to this mathematical problem about algebra.
PLEASE PLEASE PLEASE HELP
Complete this table by entering the addictive inverse of each number.
Answer:
66. 4/8
Step-by-step explanation:
Answer:
-27 -> 27, - 8/3 -> 8/3
Step-by-step explanation:
-27 + 27 = 0
-3/8 + 3/8 = 0
Suppose in this semester, our Exam 1 average was about 86 with an SD of about 10. Suppose the correlation between our Exam 1 and Exam 2 scores will be similar to what it has been in the past, about 0.6, and finally, suppose our Exam 2 scores will be similar to previous semesters' Exam 2 scores with an average of 76 and a SD of 8.2. Use this information to answer the following questions:
1. What is the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores? Round to 3 decimal places.
2. What is the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 scores? Round to 3 decimal places.
Answer:
the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492
And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688
Step-by-step explanation:
Given the data in the question;
mean X" = 86
SD σx = 10
Y" = 76
SD σy = 8.2
r = 0.6
Here, Exam 2 is dependent and Exam 1 is independent.
The Regression equation is
y - Y" = r × σy/σx ( x - x" )
we substitute
y - 76 = 0.6 × 8.2/10 ( x - 86 )
y - 76 = 0.492( x - 86 )
y - 76 = 0.492x - 42.312
y = 0.492x - 42.312 + 76
y = 0.492x + 33.688
Hence, the slope of the regression equation for predicting our Exam 2 scores from Exam 1 scores is 0.492
And the y-intercept of the regression equation for predicting our Exam 2 scores from Exam 1 is 33.688
The rate of change of y is proportional to y. When t=0, y=4, and when t=2, y=8. What is the value of y when t=3?
Answer:
When t = 3, y = 12. y = 4t, for t>0
Step-by-step explanation:
8 = 4 x 2; y = 4 x 3 = 12.
Myopia in children. Myopia, also called short-sightedness, is a common visual impairment that is reaching alarming proportions worldwide. The condition typically develops in school-age children and adolescents. It has long been thought that the condition was associated with too much reading, but recent evidence suggests instead that a lack of exposure to natural outdoor light may play a role. To investigate this new theory, researchers compared rates of myopia among randomly selected young children (6 and 7 years old) of Chinese ethnicity living in either Sydney (Australia) or Singapore. The researchers found that 4 of the 124 children in the Australian sample had myopia, compared with 183 among the 628 children from Singapore
Required:
a. Display the findings in a two-way table. What percent of the children in the study had myopia?
b. What is that percent among the children living in Australia and among those living in Singapore?
Answer:
a. percentage of children with myopia = 24.87%
b. 3.23% of children living in Australia have myopia
29.14% 0f children living in Singapore have myopia
Step-by-step explanation:
a.
the table is an attachment
percentage of children with myopia in this study
number of children with myopia in Australia = 4
number of children with myopia in Singapore = 183
total children with myopia = 4 + 183 = 187
total number of Australian children = 124
total number of Singapore children = 628
total number of children = 124 + 628 = 752
percentage with myopia = 187/752 * 100 = 24.87%
2.
percentage of Australian children with myopia
total children from Australia = 124
those with myopia = 4
percentage = 4/124 * 100 = 3.23% of children living in Australia have myopia
percentage of Singapore children with myopia
total number of children = 628
those with myopia = 183
percentage = 183/628 * 100 = 29.14% 0f children living in Singapore have myopia
Use polar coordinates to find the volume of the given solid. Bounded by the paraboloid z = 6 + 2x2 + 2y2 and the plane z = 12 in the first octant
Answer:
[tex]\frac{9\pi }{4}[/tex]
Step-by-step explanation:
Paraboloid z = 6 + 2x^2 + 2y^2 ----- ( 1 )
plane z = 12
equation 1 becomes
12 = 6 + 2( x^2 + y^2 )
hence : ( x^2 + y^2 ) = 3
This shows that the solid lies under the parabolic and above the disk 0 : x^2 + y^2 ≤ 3
attached below is the remaining part of the solution
6
Solve the inequality. Graph the solution.
11.3 > b /4.3
The solution is
Step-by-step explanation:
Multiply to remove the fraction, then set equal to
0 and solve.
Inequality Form:
b<48.59
Interval Notation:
(−∞, 48.59)
The solution of the inequality 11.3 > b /4.3 is b< 48.59 along with the number line.
Given Inequality:
11.3 > b /4.3
To solve the inequality 11.3 > b / 4.3,
Multiply both sides of the inequality by 4.3 to eliminate the fraction:
11.3 * 4.3 > (b / 4.3) * 4.3
48.59 > b
The solution to the inequality is b < 48.59.
This means that any value of b that is less than 48.59 will satisfy the inequality.
To graph the solution, indicate that b is less than 48.59 by using an open circle at 48.59 and shading the line to the left of the open circle to represent all the values that satisfy the inequality.
Learn more about Inequality here:
https://brainly.com/question/20383699
#SPJ6
(-4.2)²×..........=-132.3
Answer:
-7.5
Step-by-step explanation:
-4.2×-4.2 = 17.64
-132.3/17.64= -7.5
A tabletop in the shape of a trapizoid has an area 8607 square centimeters. its longer base measures 123 centimeters, and the shorter base is 105 centimeters what is the height?
Answer:
286.94 cm
Step-by-step explanation:
Data:
Area = 8,607
b1 = 105
b2 = 123
Area = 1/2 * (b1 + b2) * h
h = 2 * Area/b1 + b2
h = 2 * 8,607/105 + 123
h = 286.94 cm
I'm not sure if it's right but that's what my calculator gave me.
Andre and Elena knew that after 28 days they would have 228 coins, but they wanted to find out how many coins that actually is. Andre wrote:
228=2⋅28=56
Elena said, “No, exponents mean repeated multiplication. It should be 28⋅28, which works out to be 784.” Do you agree with either of them? Explain your reasoning.
Answer:
no, exponents are how many times the base is used, it would be 2x2x2... so on until there are 28 2s
Step-by-step explanation:
Please solve! (best bet is to use paper)
use the distributive to simplify: 3{4x - 10}
2 1/5 + 1 2/3
explain please, I'm sorry if I'm asking a lot of questions!!
Answer:
2 1/5 = 11/5 x 3 = 33/ 15
1 2/3 = 5/3 x 5 = 25/ 15
= 33 + 25 = 58/ 15 = 3 13/ 15
:)
Answer: Fraction form: 3 13/15
plz mark me brainliest.
Step-by-step explanation: Fraction form: 3x5=15 so 2/3=10/15 and 1/5=3/15 so 13/15 and 2+1=3 so 3 13/15. plz mark me brainliest
How to mark brainliest:
Tap the crown, if there is no crown reload (there must be 2 answers)
3/4x 2 1/3 what is the answer to this question
Answer:
1.75
Step-by-step explanation:
nsjdjdjdjdjndnsjdjdjjddbjdjsjsj its 1.75
Answer:
7/4
Step-by-step explanation:
3/4 * 2 1/3 = 7/4
Hope this helps =]
Question 1 (1 point) What is the volume of the square-based pyramid shown below? 12 in. A. 96 cu in. B. 384 cu in. C. 256 cu in. D. 768 cu in.
Area of square pyramid:
⅓×[base area]×height
according to the question
⅓×[8×8]×12
simplify parentheses:
⅓×64×12
Simplify fraction
64×4
Simplify multiplication
256
256 did the test on k12 Answer:
c
Step-by-step explanation:
Baby Zoe drinks a lot of milk. How many gallons are in 20 pints of milk? (1 gallon=4 quarts, 1 quart= 2 pints)
Answer:
there are 2.5 gallons in 20 pints of milk, or she drinks 2.5 gallons of milk
Step-by-step explanation:
If she drinks 20 pints of milk, you have to convert by dividing.
1 qt= 2 pints
20/2=10
20 pints = 10 quarts
Then, 1 gal = 4 qts
10/4= 2.5
So, there are 2.5 gallons in 20 pints of milk, or she drinks 2.5 gallons of milk.
Hope this helps!!
-Ketifa
(Can I get brainliest?)
Answer:
ehoif :)
Step-by-step explanation: