Answer:
Step-by-step explanation:
l -> length
b -> width
h -> height
Find the area of four walls and ceiling. then subtract the area of four windows and a door form that area.
Area of four walls + ceiling = 2( lh + bh) +lb
= 2*(20*5 + 15*5) + 20*15
= 2( 100 + 75) + 300
= 2* 175 + 300
= 350 +300
= 650 sq m
Area of window = 2 *3 = 6 sq.m
Area of four windows = 4*6 = 24 sq.m
Area of door = 2 * 1 = 2 sq.m
Area of four walls excluding 4 windows and door = 650 - 24 - 2 = 624 sq.m
Cost of painting = 624 * 6.50
= $ 4056
Answer: 1950 dollars to paint the ceiling only (ignoring the walls)
The cost to paint the walls only is 2106 dollars.
The cost to paint the walls and ceiling is 4056 dollars.
==================================================
Explanation:
It seems a bit strange how your teacher mentions the windows and doors, but then asks about the ceiling only. Perhaps this is a red herring, but I'm not sure.
Anyway, to directly answer the question, we'll need to find the area of the ceiling first. The ceiling is a rectangle of dimensions 20 m by 15 m, so its area is 20*15 = 300 square meters.
Since paint costs 6.50 dollars per square meter, the total cost for the ceiling alone is 6.50*300 = 1950 dollars
If your teacher only cares about the ceiling, then you can stop here (and ignore the next section below).
---------------------------
If you wanted to find the cost to paint the walls, then we need to find the area of the walls.
For now, ignore the windows and door. Two opposite walls have area of 20*5 = 100 m^2 each. That accounts for 2*100 = 200 m^2 of wall area so far.
The other pair of opposite walls have area 15*5 = 75 m^2 each. That's another 2*75 = 150 m^2 of wall area.
In all, the total wall area without considering the windows or door is 200+150 = 350 m^2.
Now we consider the windows. Each window is 2 m by 3 m, yielding an area of 2*3 = 6 m^2. Four such windows have a total area of 4*6 = 24 m^2.
The door is 2 m by 1 m, so its area is 2*1 = 2 m^2
We'll subtract the wall area and the combined window+door areas to get
wallArea - windowArea - doorArea = 350-24-2 = 324
So after accounting for the windows and door, the amount of wall to paint is 324 m^2, which leads to a cost of 6.50*324 = 2106 dollars.
Therefore, painting the walls and ceiling gets us a total cost of 1950+2106 = 4056 dollars
This section is entirely optional if your teacher only cares about the ceiling.
The mathematical expressions of the thermal conditions at the boundaries are called the _____ conditions.
Answer:
Heat flux boundary condition.
Step-by-step explanation:
Heat flux is boundary condition in positive x-direction. The specified temperature is constant and steady heat conduction. Temperature of exposed surface can be measured directly with the thermal condition expression.
If there is an error in solving the equation below, then explain the error and in what step the error is in the equation. If no error, then just type “no error”
Answer:
To solve for x, you must multiply by the reciprocal.
In this case, multiply both sides by [tex]\frac{3}{2}[/tex] .
When doing this the result will be x = 3
Unit sales for new product ABC have varied in the first seven months of this year as follows: Month Jan Feb Mar Apr May Jun Jul Unit Sales 148 329 491 167 228 285 441 What is the (population) standard deviation of the data
Answer:
[tex]\sigma = 121.53[/tex]
Step-by-step explanation:
Required
The population standard deviation
First, calculate the population mean
[tex]\mu = \frac{\sum x}{n}[/tex]
This gives:
[tex]\mu = \frac{148+ 329+ 491 +167+ 228+285+ 441}{7}[/tex]
[tex]\mu = \frac{2089}{7}[/tex]
[tex]\mu = 298.43[/tex]
The population standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{(148 - 298.43)^2 + ..........+ (441- 298.43)^2}{7}}[/tex]
[tex]\sigma = \sqrt{\frac{103387.7143}{7}}[/tex]
[tex]\sigma = \sqrt{14769.6734714}[/tex]
[tex]\sigma = 121.53[/tex]
Help me please I need help 6
Answer:
69.6
Step-by-step explanation:
sin 55 = x / 85
0.8191520443 = x / 85
x = 69.6
The speed (S) an object falls varies directly with time. If the speed is 49.0m/s after 5 seconds, then what is the speed after 3 seconds
9514 1404 393
Answer:
29.4 m/s
Step-by-step explanation:
Speed is proportional to time, so we have ...
speed / time = s/3 = 49/5
s = 3/5(49) = 29.4
The speed of the object is 29.4 m/s after 3 seconds.
The formula for centripetal acceleration, a, is given by this formula, where v is the velocity of the object and r is the object’s distance from the center of the circular path:
A= V2/R
Solve the formula for r.
Answer:r=v^2/A
Step-by-step explanation: To solve for r means you have to isolate r on one side and put all the other terms on the other. To get r out from under the fraction, multiply both sides by r. This leaves:
A*r=v^2 so to isolate r, divide by A and get:
r=v^2/A.
check all that apply. sec theta is undefinded for theta = ____ . A. pi/2
B.0 C. pi D.3pi/2
Answer:
Step-by-step explanation:
secθ = 1/cosθ
cosθ = 0 for π/2, 3π/2
secθ is undefined for θ = π/2, 3π/2
.It is 12:00 and people are lining up for the matinee at the Bijou Cinema Six. In the first five minutes (12:05), 6 people get into line. At the end of the second five minutes (12:10), there are 11 people in line. At the end of the third five minutes (12:15) there are 16 people in line. If the people keep lining up at this rate, what time will it be when there are 81 people in line?
Answer:
65 minutes
Step-by-step explanation:
already 16 people in line
total is 81
81 - 16 equals 65
about 5 people every 5 minutes (basically 1 min per person)
so, answer probably 65
A survey found that the median number of calories consumed per day in a certain country was 3,304 and the mean was 3,204.9 calories. If a histogram were constructed for the data, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answer:
Skewed to the left
Step-by-step explanation:
Given
[tex]Median = 3304[/tex]
[tex]Mean = 3204.9[/tex]
Required
The type of distribution
From the given data, we have:
[tex]Median \ne Mean[/tex] --- Mean and Median are not equal
and
[tex]Median > Mean[/tex] --- Median is greater than mean
When the median is greater than the mean; the histogram is expected to be left skewed
someone please help. you have to find ge and I have no idea how to
Hello,
3x+9+8x-25=28
11x-16=28
x=44/11
x=4
So, GE=3x+9=3*11+9=42
How would 0.42 be shown as a percent?
A. 0.42%
B. 4%
C. 4.2%
D. 42%
Answer:
42%
Step-by-step explanation:
to find percentages, you move the decimal point twice to the right
I really don’t understand graphs
What is the factored form of x2 − 4x − 5?
(x + 5)(x − 1)
(x + 5)(x + 1)
(x − 5)(x − 1)
(x − 5)(x + 1)
Answer:
x2 - 4x - 5 factored form is (x - 5)(x + 1)
Answer:
(x − 5)(x + 1)
Step-by-step explanation:
The answer above is correct.
find (f o g)(x)
f(x) = 5x+1, g(x)= *square root of x*
Step-by-step explanation:
Hey there!
Here;
f(x) = 5x + 1
g(x) = (√x)
Now;
fog(X) = f(g(x))
= f(√x)
= 5√x + 1
Therefore, fog(X) = 5√x + 1.
Hope it helps!
Figure A
Figure B
Figure C
3 ft
3 ft
Sf
3 ft
3 ft
5 ft
5 ft
3 ft
3 ft
Sft
3 ft
3 ft
Х
?.
None of the figures
(a) Which figures are rectangles?
Mark all that apply.
Figure A Figure B Figure C
(b) Which figures are squares?
Mark all that apply.
Figure A Figure B Figure C
(c) Which figures are parallelograms?
Mark all that apply.
Figure A
Figure B
Figure C
None of the figures
None of the figures
Answer:
a) Figure B and Figure C
b) Figure C
c) Figure A, Figure B, and Figure C
Step-by-step explanation:
a) Rectangles are shapes that have four sides, and four right angels. Right angles are angles that are 90 degrees.
The only shapes with four sides AND four right angles are Figure C and Figure B.
b) Squares are shapes with four EQUAL sides and four right angles. The only shape with four equal sides and four right angles is Figure C.
c) Parallelograms are any shapes with four sides. All of these shapes have four sides.
Hope this helps!
will give brainyest (m^2/3 n^-1/3)^6
Step-by-step explanation:
here is the answer to your question
Find the inverse of the given function. (pictured below)
Answer:
4
3
0
Step-by-step explanation:
f(x) = y = -1/2 × sqrt(x+3)
2y = -sqrt(x+3)
4y² = x + 3
x = 4y² - 3
now renaming this, so that the normal symbols and names are used for this function definition, so that the input variable is called "x" :
f-1(x) = 4x² - 3
basically, just by itself, this function would be defined for all possible real values of x.
but because it is the inverse of the original function, which generates only values of y<=0, then for the inverse function that same range applies for its input variable x
x<=0
A rectangular auditorium seats 1144 people. The number of seats in each row exceeds the number of rows by 18. Find the number of seats in each row.
Answer:
44 seats in each row
Problem:
A rectangular auditorium seats 1144 people. The number of seats in each row exceeds the number of rows by 18. Find the number of seats in each row.
Step-by-step explanation:
Let n be the number of rows.
If the number of seats exceed the number of rows by 18, then the number ot seats can be represented by n+18.
So we have a n by n+18 rectangle whose number of seats in all is 1144.
So we need to solve n(n+18)=1144
Distribute: n^2+18n=1144
Subtract 1144 on both sides" n^2+18n-1144=0
What two numbers multiply to be -1144 but also add to be 18?
Hmmm.. let's break -1144 down a little into smaller factors.
-1144=2(-572)=4(-286)=8(-143)=-8(13)(11)=-26(44)
We found a pair of factors that will work? -26 and 44.
So the factorization of our quadratic equation is (n-26)(n+44)=0.
This implies either n-26=0 or n+44=0 .
n=26 by adding 26 on both sides for first equation.
n=-44 by subtracting 44 on both sides for second equation.
n=26 is the only one that works.
This means there are 26 rows and 26+18 seats in each row.
26 rows
44 seats in each row
That product does equal 1144 seats in all.
x²-7x+5 in the form (x-a)²-b
Answer:
( x - 3.5)² - 29/4
Step-by-step explanation:
Given :-
x² - 7x + 5Writing in ( x - a)² - b form ,
x² - 7x + 5 x² - 7 * 2/2 * x + 5 x² - (7/2) * 2 * x + 5 x² - (7/2)*2*x +(7/2)²-(7/2)²+5( x - 7/2)² + 5 - 49/4( x - 7/2)² + ( 20-49)/4( x - 3.5)² - 29/4Consider the functions z = 4 e^x ln y, x = ln (u cos v), and y = u sin v.
Express dz/du and dz/dv as functions of u and y both by using the Chain Rule and by expressing z directly in terms of u and v before differentiating.
Answer:
remember the chain rule:
h(x) = f(g(x))
h'(x) = f'(g(x))*g'(x)
or:
dh/dx = (df/dg)*(dg/dx)
we know that:
z = 4*e^x*ln(y)
where:
y = u*sin(v)
x = ln(u*cos(v))
We want to find:
dz/du
because y and x are functions of u, we can write this as:
dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/du) = 1/(u*cos(v))*cos(v) = 1/u
(dy/du) = sin(v)
Replacing all of these we get:
dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)
= 4*e^x*( ln(y)/u + sin(v)/y)
replacing x and y we get:
dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))
dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)
Now let's do the same for dz/dv
dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)
(dy/dv) = u*cos(v)
then:
dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]
replacing the values of x and y we get:
dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]
dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]
Which answers describe the shape below? Check all that apply.
A. Rectangle
B. Rhombus
C. Quadrilateral
D. Square
E. Parallelogram
F. Trapezoid
Answer:
E and C
Step-by-step explanation:
Identify the domain of the function shown in the graph.
Factorize : 4(x+y)^2 -9(x-y)^2
Answer:
Step-by-step explanation:
[tex]4(x+y)^{2} - 9(x-y)^{2}=4[x^{2}+2xy+y^{2}]-9[x^{2}-2xy+y^{2}]\\\\=4x^{2}+4*2xy + 4y^{2}-9x^{2}-2xy*(-9)+y^{2}*(-9)\\\\= 4x^{2}+8xy+4y^{2}-9x^{2}+18xy-9y^{2}\\\\= 4x^{2}-9x^{2} + 8xy + 18xy +4y^{2} - 9y^{2}\\\\= -5x^{2} + 26xy - 5y^{2}[/tex]
= -5x² + 25xy + xy - 5y²
= 5x(-x + 5y) - y(-x +5y)
= (-x + 5y)(5x - y)
Help meeee plzzzzzz!!!!
OPTION B is the correct answer.
Young invested GH150,000 and 2.5% per annum simple interest. how long will it take this amount to. yield an interest of GH11,250,00
Answer: 3 years
Step-by-step explanation:
Interest is calculated as:
= (P × R × T) / 100
where
P = principal = 150,000
R = rate = 2.5%.
I = interest = 11250
T = time = unknown.
I = (P × R × T) / 100
11250 = (150000 × 2.5 × T)/100
Cross multiply
1125000 = 375000T
T = 1125000/375000
T = 3
The time taken will be 3 years
how to solve for
LN and what are the variables
Answer:
v See below. v
Step-by-step explanation:
LM = MN
11x - 21 = 8x + 15
[tex]3x-21=15\\3x=36\\[/tex]
x = 12
LM = 11(12) - 21 = 132 - 21 = 111
MN = 8(12) + 15 = 96 + 15 = 111
LN = 111 + 111 = 222
The equation for the pH of a substance is pH = -log[H], where Ht iS the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration
of hydrogen ions between the two solutions?
Answer:
The difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.
Step-by-step explanation:
The pH is given by:
[tex] pH = -log[H^{+}] [/tex]
Where:
[tex] [H^{+}][/tex]: is the concentration of hydrogen ions.
For the basic solution (pH = 11.2), the concentration of H⁺ is given by:
[tex] [H^{+}]_{b} = 10^{-pH} = 10^{-11.2} = 6.31 \cdot 10^{-12} [/tex]
And, for the acidic solution (pH = 2.4) we have:
[tex] [H^{+}]_{a} = 10^{-pH} = 10^{-2.4} = 3.98 \cdot 10^{-3} [/tex]
Hence, the difference in the concentration of H⁺ between the two solutions is:
[tex] \Delta H^{+} = [H^{+}]_{a} - [H^{+}]_{b} = 3.98 \cdot 10^{-3} - 6.31\cdot 10^{-12} = 3.98 \cdot 10^{-3} [/tex]
Therefore, the difference in the H⁺ concentration between the two solutions is approximately equal to the H⁺ concentration of the acidic solution.
I hope it helps you!
Answer:
B. 4.0 x [tex]10^{-3}[/tex]
Step-by-step explanation:
EDG2021
HELP PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Answer:
12
Step-by-step explanation:
10 - 1/2 x = 12-4/3x
60 - 3x = 72-2x
-12 = - x
A flashlight is projecting a triangle onto a wall, as shown below.
A picture shows a flashlight projecting a triangle onto a wall. The original triangle and its projection are similar. The original triangle has 2 sides labeled 15 and one side labeled 20. The projected triangle has two sides labeled 30 and one side labeled n. The triangles have congruent angles.
The original triangle and its projection are similar. What is the missing length n on the projection?
Answer:
Hence the correct option is 3rd option. 40
Step-by-step explanation:
If two figures are similar, then the ratio of the corresponding sides is proportional.
[tex]\frac{15}{30} =\frac{20}{n} \\\\n=\frac{30 \times 20}{15} \\\\n= 40.[/tex]
Trigonometric ratio: find an angle measure
Answer:
[tex]T =56.3[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Measure of T
This is calculated as:
[tex]\cos T = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos T = \frac{5}{9}[/tex]
Take arccos
[tex]T = \cos^{-1}{(5/9)}[/tex]
[tex]T =56.3[/tex]