Answer:
Scale of the drawing would be 20/12 inch and 0.6 (6/12) inch
Step-by-step explanation:
For most of the residential buildings an scale of 1 inch = 12 feet can be used to draw the residential units.
In that case the scale of the drawing would be 20/12 inch and 0.6 (6/12) inch
Dave should label the dimensions in inches
I need help comment please
Answer:
41
Step-by-step explanation:
The angle were looking for is on the other side of the figure. It is also on the inside so we would divide 82 in half giving us 41.
We want to construct a box with a square base and we currently only have 10m2 of material to use in construction of the box. Assuming that all material is used in the construction process, determine the maximum volume that the box can have.
Answer:
The maximum volume of the box is:
[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]
Step-by-step explanation:
Given
[tex]Surface\ Area = 10m^2[/tex]
Required
The maximum volume of the box
Let
[tex]a \to base\ dimension[/tex]
[tex]b \to height[/tex]
The surface area of the box is:
[tex]Surface\ Area = 2(a*a + a*b + a*b)[/tex]
[tex]Surface\ Area = 2(a^2 + ab + ab)[/tex]
[tex]Surface\ Area = 2(a^2 + 2ab)[/tex]
So, we have:
[tex]2(a^2 + 2ab) = 10[/tex]
Divide both sides by 2
[tex]a^2 + 2ab = 5[/tex]
Make b the subject
[tex]2ab = 5 -a^2[/tex]
[tex]b = \frac{5 -a^2}{2a}[/tex]
The volume of the box is:
[tex]V = a*a*b[/tex]
[tex]V = a^2b[/tex]
Substitute: [tex]b = \frac{5 -a^2}{2a}[/tex]
[tex]V = a^2*\frac{5 - a^2}{2a}[/tex]
[tex]V = a*\frac{5 - a^2}{2}[/tex]
[tex]V = \frac{5a - a^3}{2}[/tex]
Spit
[tex]V = \frac{5a}{2} - \frac{a^3}{2}[/tex]
Differentiate V with respect to a
[tex]V' = \frac{5}{2} -3 * \frac{a^2}{2}[/tex]
[tex]V' = \frac{5}{2} -\frac{3a^2}{2}[/tex]
Set [tex]V' =0[/tex] to calculate a
[tex]0 = \frac{5}{2} -\frac{3a^2}{2}[/tex]
Collect like terms
[tex]\frac{3a^2}{2} = \frac{5}{2}[/tex]
Multiply both sides by 2
[tex]3a^2= 5[/tex]
Solve for a
[tex]a^2= \frac{5}{3}[/tex]
[tex]a= \sqrt{\frac{5}{3}}[/tex]
Recall that:
[tex]b = \frac{5 -a^2}{2a}[/tex]
[tex]b = \frac{5 -(\sqrt{\frac{5}{3}})^2}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{5 -\frac{5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{\frac{15 - 5}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{\frac{10}{3}}{2*\sqrt{\frac{5}{3}}}[/tex]
[tex]b = \frac{\frac{5}{3}}{\sqrt{\frac{5}{3}}}[/tex]
Apply law of indices
[tex]b = (\frac{5}{3})^{1 - \frac{1}{2}}[/tex]
[tex]b = (\frac{5}{3})^{\frac{1}{2}}[/tex]
[tex]b = \sqrt{\frac{5}{3}}[/tex]
So:
[tex]V = a^2b[/tex]
[tex]V =\sqrt{(\frac{5}{3})^2} * \sqrt{\frac{5}{3}}[/tex]
[tex]V =\frac{5}{3} * \sqrt{\frac{5}{3}}[/tex]
[tex]V =\frac{5}{3}\sqrt{\frac{5}{3}}[/tex]
The maximum volume of the box which has a 10 m² surface area is given below.
[tex]\rm V_{max} = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.
We want to construct a box with a square base and we currently only have 10 m² of material to use in the construction of the box.
The surface area = 10 m²
Let a be the base length and b be the height of the box.
Surface area = 2(a² + 2ab)
2(a² + 2ab) = 10
a² + 2ab = 5
Then the value of b will be
[tex]\rm b = \dfrac{5-a^2}{2a}[/tex]
The volume of the box is given as
V = a²b
Then we have
[tex]\rm V = \dfrac{5-a^2 }{2a}* a^2\\\\V = \dfrac{5a - a^3}{2}\\\\V = \dfrac{5a}{2} - \dfrac{a^3}{2}[/tex]
Differentiate the equation with respect to a, and put it equal to zero for the volume to be maximum.
[tex]\begin{aligned} \dfrac{dV}{da} &= \dfrac{d}{da} ( \dfrac{5a}{2} - \dfrac{a^3}{2} ) \\\\\dfrac{dV}{da} &= 0 \\\\\dfrac{5}{2} - \dfrac{3a^2 }{2} &= 0\\\\a &= \sqrt{\dfrac{5}{2}} \end{aligned}[/tex]
Then the value of b will be
[tex]b = \dfrac{5-\sqrt{\dfrac{5}{2}} }{2*\sqrt{\dfrac{5}{2}} }\\\\\\b = \sqrt{\dfrac{5}{2}}[/tex]
Then the volume will be
[tex]\rm V = (\sqrt{\dfrac{5}{2}} )^2*\sqrt{\dfrac{5}{2}} \\\\V = \dfrac{5}{3} *\sqrt{\dfrac{5}{2}}[/tex]
More about the differentiation link is given below.
https://brainly.com/question/24062595
how many terms are in the following expression 9c+2d-8
The nth term of a sequence is 5n.
Work out the 10th term of this sequence.
Answer:
The 10th term is 50
Step-by-step explanation:
5(10) = 50
I don’t know the answer help! ?
Answer:
m∠8=120°
Step-by-step explanation:
Given that lines L and M are parallel to each other, keep in mind that ∠1 and ∠8 are opposite exterior angles, so they will be congruent to each other. Therefore, m∠8=120°.
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct
This question is incomplete, the complete question is;
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple are written in increasing order but are not necessarily distinct.
In other words, how many 5-tuples of integers ( h, i , j , m ), are there with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1 ?
Answer:
the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Step-by-step explanation:
Given the data in the question;
Any quintuple ( h, i , j , m ), with n ≥ h ≥ i ≥ j ≥ k ≥ m ≥ 1
this can be represented as a string of ( n-1 ) vertical bars and 5 crosses.
So the positions of the crosses will indicate which 5 integers from 1 to n are indicated in the n-tuple'
Hence, the number of such quintuple is the same as the number of strings of ( n-1 ) vertical bars and 5 crosses such as;
[tex]\left[\begin{array}{ccccc}5&+&n&-&1\\&&5\\\end{array}\right] = \left[\begin{array}{ccc}n&+&4\\&5&\\\end{array}\right][/tex]
= [( n + 4 )! ] / [ 5!( n + 4 - 5 )! ]
= [( n + 4 )!] / [ 5!( n-1 )! ]
= [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
Therefore, the number of 5-tuples of integers from 1 through n that can be formed is [ n( n+1 ) ( n+2 ) ( n+3 ) ( n+4 ) ] / 120
A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $20.00 to prepare, and it costs $125.00 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs
Answer:
25
Step-by-step explanation:
From the given information;
Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.
= 1000x
Thus, the required number of hours it will take can be computed as:
[tex]\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}[/tex]
cost per hour = 125
If each plate costs $20 to make, then the total number of plate will equal to 40x
∴
The total cost can be computed as:
[tex]C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)[/tex]
[tex]C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)[/tex]
At C'(x) = 0
[tex]\dfrac{12500}{x^2} = 20[/tex]
[tex]\dfrac{12500}{20} = x^2[/tex]
[tex]x^2= 625[/tex]
[tex]x = \sqrt{625}[/tex]
x = 25
[tex]C'' (x) = -12500 \times \dfrac{-2}{x^3} +0[/tex]
[tex]C'' (x) = \dfrac{25000}{x^3}[/tex]
where; x = 25
[tex]C'' (x) = \dfrac{25000}{25^3}[/tex]
C''(x) = 1.6
Thus, at x = 25, C'' > 0
As such, to minimize the cost, the printer needs to make 25 metal plates.
Question attached please answer brainliest to best answer
Answer:
B
Step-by-step explanation:
Have a nice day :)
Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = -1.
Answer:
The equation of the parabola is y = x²/4
Step-by-step explanation:
The given focus of the parabola = (0, 1)
The directrix of the parabola is y = -1
A form of the equation of a parabola is presented as follows;
(x - h)² = 4·p·(y - k)
We note that the equation of the directrix is y = k - p
The focus = (h, k + p)
Therefore, by comparison, we have;
k + p = 1...(1)
k - p = -1...(2)
h = 0...(3)
Adding equation (1) to equation (2) gives;
On the left hand side of the addition, we have;
k + p + (k - p) = k + k + p - p = 2·k
On the right hand side of the addition, we have;
1 + -1 = 0
Equating both sides, gives;
2·k = 0
∴ k = 0/2 = 0
From equation (1)
k + p = 0 + 1 = 1
∴ p = 1
Plugging in the values of the variables, 'h', 'k', and 'p' into the equation of the parabola, (x - h)² = 4·p·(y - k), gives;
(x - 0)² = 4 × 1 × (y - 0)
∴ x² = 4·y
The general form of the equation of the parabola, y = a·x² + b·x + c, is therefore;
y = x²/4.
Simply the following ratio 1000:540:780
Please help, show work! Limits and functions! 85 points!
Answer:
Ok I might misunderstand this but this is what I got ( in order )
Match the vocabulary word to its correct definition
1. arithmetic sequence
an individual quantity or number in
a sequence
the fixed amount added on to get
2. common difference
to the next term in an arithmetic
sequence
a sequence in which a fixed
3. sequence
amount is added on to get the next term
a set of numbers that follow a
4 term
pattern, with a specific first number
Answer:
1. Term.
2. Common difference.
3. Arithmetic sequence.
4. Sequence.
Step-by-step explanation:
1. Term: an individual quantity or number in a sequence. For example, 1, 2, 3, 5, 6. The first term is 1 while 5 is the fourth term.
2. Common difference: the fixed amount added on to get to the next term in an arithmetic sequence. For example, 2, 4, 6, 8 have a common difference of 2 i.e (6 - 4 = 2).
3. Arithmetic sequence: a sequence in which a fixed amount such as two (2) is added on to get the next term. For example, 0, 2, 4, 6, 8, 10, 12.... is an arithmetic sequence.
4. Sequence: a set of numbers that follow a pattern, with a specific first number. For example, 1, 2, 3, 4, 5, 6 is a sequence.
help please! no links :)
Answer:
The answer is D-27.00 because you are rounding off to the nearest 100 I hope this helps you
Answer:
C. 26.75
Step-by-step explanation:
26.745 is rounded to 26.75
5/6+3/9 in the simplest form
HELP PLSS
Answer:
1 1/6
Step-by-step explanation:
5/6 + 3/9
Simplify 3/9 by dividing the top and bottom by 3
5/6 + 1/3
Get a common denominator of 6
5/6 + 1/3 *2/2
5/6 + 2/6
7/6
Rewriting
6/6 +1/6
1 1/6
which statement is true?
Answer:
A. The slope of Function A is greater than the slope of Function B.
Step-by-step explanation:
The slope of a function can be defined as rise/run. In Function A, the rise/run is 4. The slope in Function B is much easier to see: it is 2. Because 4 is greater than 2, Function A has a greater slope than Function B.
What is the difference between a bar chart and a histogram?
Answer:
In simple terms, a bar chart is used in summarizing categorical data, where a histogram uses a bar of different heights, it is similar to the bar chart in many terms but the histogram groups the numbers into the ranges while representing the data.
bar chart is a graph in the form of boxes of different heights, with each box representing a different value or category of data, and the heights representing frequencies.
but,
Histogram is graphical display of numerical data in the form of upright bars, with the area of each bar representing frequency.
The following set of data represents the ages of the women who won the Academy Award for Best Actress from 1980 - 2003:
31 74 33 49 38 61 21 41 26 80 42 29
33 35 45 49 39 34 26 25 33 35 35 28
Make frequency table using # of classes as per the following criteria:
i) if you are born in Jan, Feb, Mar: No of classes = 5
ii) if you are born in Apr, May, Jun: No of classes = 6
Answer:
Step-by-step explanation:
Given the data :
Using 6 classes :
Class interval ____ Frequency
21 - 30 _________ 6
31 - 40 _________ 10
41 - 50 _________ 5
51 - 60 _________ 0
61 - 70 _________ 1
71 - 80 _________ 2
The diameter of a circle is 15 in. Find its circumference in terms of \piπ
Answer:
15π in
Step-by-step explanation:
In order to solve this, we need to know that the circumference of a circle can be found by using the following formula...
Circumference = dπ (where d is the diameter of the circle)
Therefore the circumference equals...
Circumference = dπ = 15π in
[tex]\boxed{Given:}[/tex]
Diameter of the circle "[tex]d[/tex]" = 15 in.
[tex]\boxed{To\:find:}[/tex]
The circumference of the circle (in terms of π).
[tex]\boxed{Solution:}[/tex]
[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:15\:π\:in.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:πd }[/tex]
[tex] = \pi \times 15 \: in \\ \\ = 15 \: \pi \: in[/tex]
Therefore, the circumference of the circle is 15 π in.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
identify a transformation of a function f(x)=x^2 by observing the equation of the function g(x)=5(x)^2
Answer:
Thus the function g is the function f stretched vertically by a factor 5.
Step-by-step explanation:
Multiplication of a function by a constant:
When a function is multiplied by a constant a > 1, the function is stretched vertically by a factor of 5.
In this question:
f(x) = x^2
g(x) = 5x^2
Thus the function g is the function f stretched vertically by a factor 5.
A restaurant wants to study how well its salads sell. The circle graph shows the sales over the past few days. If 35 of the salads sold were Caesar salads, how many total salads did the restaurant sell?
Answer:
50
Step-by-step explanation:
From the circle graph :
Salad sold :
Caesar = 70%
Garden = 16%
Taco = 14%
If 35 of the salad sold were Caesar ;
Then ; this means
70% = 35
Total salad sold %= (70+16+14)% = 100%
Let total sales = x
70% = 35
100% = x
Cross multiply :
70% * x = 100% * 35
0.7x = 35
x = 35 / 0.7
x = 50
PLEASE HELP WITH THIS. WILL GIVE BRAINLEIST FOR AN ACTUAL ANSWER
Determine the distance from (-5,-6) to (3,1).
The rectangular ground floor of a building has a perimeter of 780 ft. The length is 200 ft more than the width. Find the length and the width.
The length is ___ and the width is ___
Answer:
perimeter of the rectangular ground floor
=2(length+width)
length=X+200
width=X
=2(X+200+X)
=4x+400
4x+400 =780
4x =780-400
4x =380
x =95
width=95 feet
length=95+200
=295 feet
a + b = 300 pls help i cant find out the answer
Answer:
a= 250
b= 50
250 + 50 = 300
Step-by-step explanation:
There's many solutions but this was the first one I could come up with.
Answer:
my opinion is seince a+b=300 then the sqaure of 300= 17.3?
Step-by-step explanation:
Question 7
Find the volume.
Answer:
A: 686π≈2,156
Step-by-step explanation:
First, you need to find the area of the circle then times that by 14.
π[tex]r^{2}[/tex] Formula for the area of a circle
π[tex]7^{2}[/tex] r stands for radius, so you divide the diameter by 2 and get 7.
π49 This is the area of the circle
π49×14 Now multiply by 14
=686π This is your answer.
=2155.13256 When you times it by pi this is what you get
=2156 This is your answer if you want it rounded up
Calculate the arithmetic mean 24, 36, 52, 48, 64, 40.
Answer:
Mean: 44
Step-by-step explanation:
1. 24 + 36 + 52 + 48 + 64 + 40 = 264
2. 264 divided by 6 = 44
(I divided it by 6 because there are 6 numbers (data points).)
HELP PLSS I WILL GIVE BRAINLYEST
I SUCK AT MATH
Answer:
W=11
Step-by-step explanation:
Just trust me with this one :3
what's the easiest way to answer how I know the answer pls?
What is the volume of a rectangular prism
8 inches long, 3 inches wide, and 5 inches high?
A
120 cubic inches
B
220 cubic inches
16 cubic inches
158 cubic inches
Answer:
A; 120 cubic inches
Step-by-step explanation:
Let us start with the formula of the volume of a rectangular prism,[tex]V=l*w*h[/tex], where l represents the length of the prism, w represents the width of the prism, and h represents the height of the prism. It is given to us that h =5 inches, w =3 inches, and l =8 inches. Let's plug the values in:
[tex]V= 8*3*5\\V=120[/tex]
A. The volume of the rectangular prism is 120 cubic inches.
I hope this helps! Let me know if you have any questions :)
Chris was given 1/3 of the 84 cookies in the cookie jar. He ate 3/4 of the cookies that he was given. How many cookies did Chris eat?
Answer:
21 cookies
Step-by-step explanation:
First we know that Chris was given a third of 84 cookies so we can start working on this problem by figuring out what a third of 84 is. We can do this by multiplying 84 by 1/3 or just dividing by 3, which gives us: 84/3 = 28
So now we know that Chris was given 28 cookies, we can figure out what 3/4 of that is to work out how many cookies he ate. 28 x (3/4) = 21 cookies.
Chris ate 21 cookies.
Hope this helped!
Answer:
21 cookies
Step-by-step explanation:
1/3 × 84 = 28
3/4 × 28 = 21
A bag with 12 marbles has 5 red marbles, 3 yellow marbles, and 4blue marbles. A marble is chosen from the bag at random. What is the probability that it is red? Write your answer as a fraction in simplest form.
Answer:
5/12 is already in simplest form
Step-by-step explanation:
12m = 5r + 3y + 4b
red is chosen = 5r / 12 = 5/12
Step-by-step explanation:
the answer is 5/12. It's quite simple
