●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]\frac{1}{3} (x+1)+2x=2[/tex]
Step 1: Simplify both sides of the equation.
[tex]\frac{1}{3} (x+1)+2x=2[/tex]
[tex](\frac{1}{3}) (x) + (\frac{1}{3} ) (1) + 2x = 2[/tex] (Distribute)
[tex]\frac{1}{3} x + \frac{1}{3} + 2x = 2[/tex]
[tex]( \frac{1}{3} x + 2x ) + (\frac{1}{3}) = 2[/tex] (Combine Like Terms)
[tex]\frac {7}{3} x + \frac{1}{3} = 2\\\frac{7}{3} x + \frac{1}{3} = 2[/tex]
Step 2: Subtract 1/3 from both sides.
[tex]\frac{7}{3} x + \frac{1}{3} - \frac{1}{3} = 2 - \frac{1}{3} \\\\\frac{7}{3} x = \frac{5}{3}[/tex]
Step 3: Multiply both sides by 3/7.
[tex]( \frac{3}{7} ) * (\frac{7}{3}x) = ( \frac{3}{7}) * \frac{5}{3} \\\\x = \frac{5}{7}[/tex]
So the answer is : [tex]x = \frac{5}{7}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
During a camping trip, a group went one -third of the total distance by boat, 10km by foot and One – sixth of it by riding horses. Find the total distance of the trip.
The triangles are similar. Write a similarity statement for the triangles.
Answer:
Option (2)
Step-by-step explanation:
In the two triangles ΔWVZ and ΔYXZ,
If the sides WV and XY are parallel and the segments WY and VX are the transverse.
∠X ≅ ∠V [Alternate angles]
∠W ≅ ∠Y [Alternate angles]
Therefore, ΔWVZ ~ ΔYXZ [By AA postulate of the similarity]
Option (2) will be the answer.
The rate of earnings is 6% and the cash to be received in four years is $20,000. The present value amount, using the following partial table of present value of $1 at compound interest, is
Answer:
$15,842
Step-by-step explanation:
We use the Present value formula
Present Value = Future value/(1 + r)ⁿ
r = 6% = 0.06
n = 4 years
Future value = $20,000
Present value = 20,000/(1 + 0.06)⁴
= $15841.873265
≈ $15,842
what is the answer. plz heelp 5h+2(11-h)= -5
Answer:
h = -9
Step-by-step explanation:
5h+2(11-h)= -5
Distribute
5h +22 -2h = -5
Combine like terms
3h +22 = -5
Subtract 22 from each side
3h +22-22 = -5-22
3h = -27
Divide by 3
3h/3 = -27/3
h = -9
The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in meters) and t is the time (in seconds). What is the domain and range? Domain:
Answer:
Step-by-step explanation:
when h(t)=0
-4.9 t²+19.6t=0
4.9t(-t+4)=0
either t=0 or t=4
so domain is 0≤t≤4
for range
h(t)=-4.9t²+19.6t
=-4.9(t²-4t+4-4)
=-4.9(t-2)²+19.6
so range is 0≤h≤19.6
Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.
Range = 0<h<19.6, again, use less than or equal to signs.
What linear function defines the following Arithmetic Sequence?
-8, -4, 0, 4, 8, ...
A : an = -8 + 4(n - 1)
B : an= 8 + 4(n - 1)
C : an = -8 - 4(n - 1)
D : an = 8 - 4(n - 1)
The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, the sequence is -8, -4, 0, 4, 8, ...
a = -8
d = +4
The expression for the nth term will be written as,
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
To know more about arithmetic progression follow
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∫ ex (sec x + tan²x) dx = ? a) eˣsec²x b) eˣsecx c) eˣtan²x d) eˣtanx
None of these options seem to be correct. You can check each result by differentiation:
[tex](e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)[/tex]
[tex](e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)[/tex]
[tex](e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)[/tex]
[tex](e^x\tan x)'=e^x(\tan x+\sec^2x)[/tex]
But none of these are equivalent to [tex]e^x(\sec x+\tan^2x)[/tex]...
how do you slove 21 - 4d for d= 5
help!! I have problem to solve this question
Answer:
Step-by-step explanation:
[tex]\frac{x-1}{2} =t\\\frac{y-2}{3} =t\\\frac{z-3}{4} =t\\so~eq.~of~line~L_{1}~is\\\frac{x-1}{2} =\frac{y-2}{3} =\frac{z-3}{4} \\its~d.r's~are~2,3,4\\again~\frac{x-2}{1} =s\\\frac{y-4}{2} =s\\\frac{z+1}{-4} =s\\so~eq. ~of~line~L_{2}~is\\\frac{x-2}{1} =\frac{y-4}{2} =\frac{z+1}{-4} \\its~d.r's ~are~1,2,-4\\let ~the ~d.r's~of~line~perpendicular~to~both~L_{1}~and~L_{2}~be~a,b,c,~then~\\2a+3b+4c=0\\1a+2b-4c=0\\solving\\\frac{a}{3*-4-4*2} =\frac{b}{4*1-2*-4} =\frac{c}{2*2-3*1} \\[/tex]
[tex]\frac{a}{-20} =\frac{b}{-4} =\frac{c}{1} \\d.r's~of ~reqd~line~is~-20,-4,1~or~20,4,-1[/tex]
now you find the point of intersection.
then calculate the angle.
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Answer:
see below.
Step-by-step explanation:
1st row has four small boxes
2nd row has three big boxes
big box 1 has no items ragged in it.
big box 2 has small box 1 and also small box 1 dragged into it.
big box 3 has small box 3 and small box 4 dragged into it.
There are 50 mangoes 20 of which are unriped another basket contains 40 mangoes 15 unripe if we take 1 mangoes from each basket Find the probability of getting both are ripe Find the probability of getting both are unripe Find the probability of getting one ripe and one unripe Find the probability of at least one right Find the probability of at least one uripe
Answer:
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.375
Probability of one ripe and one unripe
=0.234375
Probability of at least one unripe
=0.625
Step-by-step explanation:
50 mangoes 20 of which are unriped in the first basket .
Riped = 50-20= 30
Probability of unripe = 20/50
Probability of unripe= 0.4
Probability of ripe = 30/50
Probability of ripe = 0.6
40 mangoes of which 15 are unripe In the second basket
Number of riped= 40-15= 25
Probability of unriped= 15/40
Probability of unriped= 0.375
Probability of riped= 25/40
Probability of riped= 0.625
probability of getting both are unripe
= 0.4*0.375
probability of getting both are unripe
= 0.15
probability of getting both are ripe
= 0.6*0.625
= 0.375
Probability of one ripe and one unripe
= 0.625*0375
= 0.234375
Probability of at least one unripe
= 1- probability of no unripe
= 1 - probability of both ripe
= 1-0.375
= 0.625
PLEASE ANSWER QUICK A manufacturing facility pays its employees an average wage of $4.50 an hour with a standard deviation of 50cents. If the wages are normally distributed, what is the percentage of workers getting paid between #3.75 and $5.00 an hour? A. 80.4% B.77.4% C.70.5% D.65.4%
Answer:
B.77.4%
Step-by-step explanation:
Mean wage (μ) = $4.50
Standard deviation (σ) = $0.50
For nay given salary X, the z-score is given by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $3.75, the z-score is:
[tex]z=\frac{3.75-4.50}{0.50}\\z=-1.5[/tex]
For X = $5.00, the z-score is:
[tex]z=\frac{5.00-4.50}{0.50}\\z=1[/tex]
A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:
[tex]P=84.13-6.68\\P=77.45\%[/tex]
The answer is alternative B.77.4%
Consider the inequality x3 + 4x2 - 5x < 0.
Select all intervals for which the statement is true.
There may be more than one correct answer. Select all correct answers.
Answer:
Interval notation is
[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]
Solutions:
[tex]\left(-\infty, -5\right)[/tex]
[tex]\left(0,1)[/tex]
Step-by-step explanation:
[tex]x^3 + 4x^2 - 5x < 0[/tex]
In this inequality, luckly we can easily factor it.
[tex]x^3 + 4x^2 - 5x[/tex]
[tex]x(x^2+4x-5)[/tex]
[tex]x(x-1)(x+5)[/tex]
So we have
[tex]x(x-1)(x+5)<0[/tex]
In exercises of this kind I usually do in my mind, but just to make it clear, let's do a table to organize. This table represents the x-intercepts in order to evaluate the inequality.
Consider [tex]x(x-1)(x+5)=0[/tex]. Here, those are the possible values for [tex]x[/tex] for each factor to be 0:
The first step to complete the table is the x value where the factor will be equal to zero.
[tex]x<-5[/tex] [tex]x=5[/tex] [tex]-5<x<0[/tex] [tex]x=0[/tex] [tex]0<x<1[/tex] [tex]x=1[/tex] [tex]x>1[/tex]
[tex]x[/tex] 0
[tex]x-1[/tex] 0
[tex]x+5[/tex] 0
Then, just consider the signal:
[tex]x<-5[/tex] [tex]x=5[/tex] [tex]-5<x<0[/tex] [tex]x=0[/tex] [tex]0<x<1[/tex] [tex]x=1[/tex] [tex]x>1[/tex]
[tex]x[/tex] - - - 0 + + +
[tex]x-1[/tex] - - - - - 0 +
[tex]x+5[/tex] - 0 + + + + +
[tex]x(x-1)(x+5)[/tex] - 0 + 0 - 0 +
When [tex]x(x-1)(x+5)<0[/tex] ?
It happens when [tex]x<-5[/tex] and when [tex]0<x<1[/tex]
The solution is
[tex]\{x \in \mathbb{R} | x<-5 \text{ or } 0<x<1 \}[/tex]
[tex]\left(-\infty, -5\right)\cup \left(0,1)[/tex]
Ten thousand raffle tickets are sold for $1 each. One first prize of $2000, 4 second prizes of $700 each, and 8 third prizes of $300 each are to be awarded, with all winners selected randomly. If you purchase one ticket, what are your expected winnings? 132 cents -$0.28 72 cents -$0.88
Answer:
72 cents.
Step-by-step explanation:
The expected winnings is the amount times the probability that you will get that amount.
2,000 * (1/10,000) = 2,000 / 10,000 = 2 / 10 = 0.2.
700 * (4 / 10,000) = 2,800 / 10,000 = 28 / 100 = 0.28.
300 * (8 / 10,000) = 2,400 / 10,000 = 24 / 100 = 0.24.
0.2 + 0.28 + 0.24 = 0.72.
Hope this helps!
Evaluate the following integrals
Answer:
a. (24 ln 2 − 7) / 9
b. x tan x + ln|cos x| + C
Step-by-step explanation:
a. ∫₁² x² ln x dx
Integrate by parts.
If u = ln x, then du = 1/x dx.
If dv = x² dx, then v = ⅓ x³.
∫ u dv = uv − ∫ v du
= (ln x) (⅓ x³) − ∫ (⅓ x³) (1/x dx)
= ⅓ x³ ln x − ∫ ⅓ x² dx
= ⅓ x³ ln x − ¹/₉ x³ + C
= ¹/₉ x³ (3 ln x − 1) + C
Evaluate between x=1 and x=2.
[¹/₉ 2³ (3 ln 2 − 1) + C] − [¹/₉ 1³ (3 ln 1 − 1) + C]
⁸/₉ (3 ln 2 − 1) + C + ¹/₉ − C
⁸/₉ (3 ln 2 − 1) + ¹/₉
⁸/₃ ln 2 − ⁸/₉ + ¹/₉
⁸/₃ ln 2 − ⁷/₉
(24 ln 2 − 7) / 9
b. ∫ x sec² x dx
Integrate by parts.
If u = x, then du = dx.
If dv = sec² x dx, then v = tan x.
∫ u dv = uv − ∫ v du
= x tan x − ∫ tan x dx
= x tan x + ∫ -sin x / cos x dx
= x tan x + ln|cos x| + C
I need help with this quickly, it would be very much appreciated.
Answer:
complementary because 2 angles that add up to 90º is a complementary angle and x=9 :)
Step-by-step explanation:
90=46+5x-1
45=5x
x=9
Answer:
x = 9 Complementary
Step-by-step explanation:
The angles are compplementary cause the angle add up to 90°
Well to find x we need to make the following equation,
46 + (5x - 1) = 90
We need to simplify and combine like terms,
46 - 1 = 45
45 + 5x = 90
-45 to both sides
5x = 45
Divide 5 by both sides
x = 9
Thus,
x is 9.
Hope this helps :)
A system of linear equations includes the line that is created by the equation y = 0.5 x minus 1 and the line through the points (3, 1) and (–5, –7), shown below. On a coordinate plane, points are at (negative 5, negative 7) and (3, 1). What is the solution to the system of equations? (–6, –4) (0, –1) (0, –2) (2, 0)
Answer:
(2,0)
Step-by-step explanation:
From the information the first equation is y = 0.5 x - 1 and the the line through (3,1) and (-5,-7) is
y = x - 2 . From those two equations you get
x - 2 = 0.5 x -1 and x = 2 , y = 0. So it is the last point. (2,0)
Answer:
D. (2,0)
Step-by-step explanation:
1. An architect is designing a house for the Mullet family. In the design he
must consider the desires of the family and the local building codes. The
rectangular lot on which the house will be built has 91 feet of frontage
on a lake and is 158 feet deep.
Answer:
An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
-------------------------------
The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
hope it helpsss
Step-by-step explanation:
Answer: An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
-------------------------------
The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 422 422 425 429 431 434 437
439 446 447 449 452 457 461 465
Calculate a two-sided 95% confidence interval for true average degree of polymerization.
Answer:
The 95% confidence interval for true average degree of polymerization is (431, 446).
Step-by-step explanation:
The data provided for the degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range is:
S = {418, 421, 422, 422, 425, 429, 431, 434, 437, 439, 446, 447, 449, 452, 457, 461, 465}
Compute the sample mean and sample standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{7}\times 7455=438.5294\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{17-1}\times 3594.2353}=14.988[/tex]
As the population standard deviation is not provided use the t-statistic to compute the two-sided 95% confidence interval for true average degree of polymerization.
[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]
The critical value of the t is:
[tex]t_{\alpha /2, (n-1)}=t_{0.05/2, (17-1)}=t_{0.025, 16}=2.12[/tex]
*Use a t-table.
Compute the 95% confidence interval for true average as follows:
[tex]CI=438.5294\pm 2.12\cdot\frac{14.988}{\sqrt{17}}[/tex]
[tex]=438.5294\pm 7.7065\\=(430.8229, 446.2359)\\\approx (431, 446)[/tex]
Thus, the 95% confidence interval for true average degree of polymerization is (431, 446).
A rectangular piece of sheet metal has an area of 1200 in2. It is going to be bent into a cylinder with volume 600 in3. What are the dimensions of rectangular piece of sheet metal
Answer:
x=6.28 inches
y=191.08 inches
Step-by-step explanation:
Let the dimensions of the rectangle be x and y
Area of the rectangular sheet
x*y=1200 in^2}
x = circumference of the cylinder
This means x=2πr
Volume of a cylinder=πr^2h
h=y
Volume of the cylind=πr^2(y)=600 in^3
From x=2πr
r=x/2π
Substitute r=x/2π into Volume=πr^2(y)=600 in^3
We have,
Volume of the cylinder=πr^2(y)=600 in^3
π*(x/2π)^2(y)=600
(x^2/4π)y=600
Recall, x*y=1200
y=1200/x
Substitute y=1200/x into (x^2/4π)y=600
(x^2/4π)y=600
(x^2/4π)(1200/x)=600
1200x/4π=600
Multiply both sides by 4π
(x^2/4π)(1200/x)(4π)=600*4π
1200x=2400π
Divide both sides by 1200
1200x/1200 = 2400π/1200
x=2π
Substitute x=2π into y=1200/x
We have,
y=1200/2π
y=600/π
The dimensions are x=2π and y=600/π
Let π=3.14
x=2π
=2(3.14)
=6.28 inches
y=600/π
=600/3.14
=191.08 inches
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
objective: central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds is/are
Answer:
Sample size
Step-by-step explanation:
Central Limit Theorem states that population with mean and standard deviation and if the sample size is large then the distribution of sample mean will be will be normally distributed. The central limit theorem holds assumptions that the factors to be considered when assessing central limit theorem is sample size.
The CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
It is given that the objective that central limit theorem assumptions. the factor(s) to be considered when assessing if the central theorem holds.
It is required to describe the above theorem.
What is the central limit theorem?It is defined as the in statistics the assumption holds that the sample means distribution of arbitrary variables follows a normal distribution or close to normal distribution if the sample size is big.
We have an objective:
The CLT is the factor to be considered when assessing if the CLT holds a large sample size.
If we draw the random sample data and its measures, the Central limit theorem explains the distribution will explain the normal bell curve, the mean of the parameters and the distribution will be the same.
Thus, the CLT is the factor(s) to be considered when assessing if the central theorem holds are sample.
Learn more about the Central limit theorem here:
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An open-top rectangular box is being constructed to hold a volume of 350 in3. The base of the box is made from a material costing 8 cents/in2. The front of the box must be decorated, and will cost 10 cents/in2. The remainder of the sides will cost 4 cents/in2. Find the dimensions that will minimize the cost of constructing this box.
Answer:
the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
Step-by-step explanation:
From the information given :
Let a be the base if the rectangular box
b to be the height and c to be the other side of the rectangular box.
Then ;
the area of the base is ac
area for the front of the box is ab
area for the remaining other sides ab + 2cb
The base of the box is made from a material costing 8 ac
The front of the box must be decorated, and will cost 10 ab
The remainder of the sides will cost 4 (ab + 2cb)
Thus ; the total cost C is:
C = 8 ac + 10 ab + 4(ab + 2cb)
C = 8 ac + 10 ab + 4ab + 8cb
C = 8 ac + 14 ab + 8cb ---- (1)
However; the volume of the rectangular box is V = abc = 350 in³
If abc = 350
Then b = [tex]\dfrac{350}{ac}[/tex]
replacing the value for c in the above equation (1); we have :
[tex]C = 8 ac + 14 a(\dfrac{350}{ac}) + 8c(\dfrac{350}{ac})[/tex]
[tex]C = 8 ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]
Differentiating C with respect to a and c; we have:
[tex]C_a = 8c - \dfrac{2800}{a^2}[/tex]
[tex]C_c = 8a - \dfrac{4900}{c^2}[/tex]
[tex]8c - \dfrac{2800}{a^2}=0[/tex] --- (2)
[tex]8a - \dfrac{4900}{c^2}=0[/tex] ---(3)
From (2)
[tex]8c =\dfrac{2800}{a^2}[/tex]
[tex]c =\dfrac{2800}{8a^2}[/tex] ----- (4)
From (3)
[tex]8a =\dfrac{4900}{c^2}[/tex]
[tex]a =\dfrac{4900}{8c^2}[/tex] -----(5)
Replacing the value of a in 5 into equation (4)
[tex]c = \dfrac{2800}{8*(\dfrac{4900}{8c^2})^2} \\ \\ \\ c = \dfrac{2800}{\dfrac{8*24010000}{64c^4}} \\ \\ \\ c = \dfrac{2800}{\dfrac{24010000}{8c^4}} \\ \\ \\ c = \dfrac{2800*8c^4}{24010000} \\ \\ c = 0.000933c^4 \\ \\ \dfrac{c}{c^4}= 0.000933 \\ \\ \dfrac{1}{c^3} = 0.000933 \\ \\ \dfrac{1}{0.000933} = c^3 \\ \\ 1071.81 = c^3\\ \\ c= \sqrt[3]{1071.81} \\ \\ c = 10.234[/tex]
From (5)
[tex]a =\dfrac{4900}{8c^2}[/tex] -----(5)
[tex]a =\dfrac{4900}{8* 10.234^2}[/tex]
a = 5.8481
Recall that :
b = [tex]\dfrac{350}{ac}[/tex]
b = [tex]\dfrac{350}{5.8481*10.234}[/tex]
b =5.848
Therefore ; the dimensions that will minimize the cost of constructing the box is:
a = 5.8481 in ; b = 5.848 in ; c = 10.234 in
The dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches and this can be determined by using the given data.
Given :
An open-top rectangular box is being constructed to hold a volume of 350 inches cube.The base of the box is made from a material costing 8 cents/inch square.The front of the box must be decorated and will cost 10 cents/inch square. The remainder of the sides will cost 4 cents/inch square.According to the given data the total cost is given by:
C = 8ac + 14ab + 8cb --- (1)
The volume of the rectangular box is (V = abc = 350 inch cube). So, the value of b is given by:
[tex]\rm b = \dfrac{350}{ac}[/tex]
Now, substitute the value of 'b' in the equation (1).
[tex]\rm C = 8ac + \dfrac{4900}{c}+\dfrac{2800}{a}[/tex]
First differentiating the above equation with respect to c.
[tex]\rm C_c = 8a-\dfrac{4900}{c^2}[/tex] --- (2)
Now, differentiating the above equation with respect to a.
[tex]\rm C_a = 8c-\dfrac{2800}{a^2}[/tex] --- (3)
Now, equate equation (2) and equation (3) to zero.
From equation (2):
[tex]\rm a=\dfrac{4900}{8c^2}[/tex] ----- (4)
From equation (3):
[tex]\rm c=\dfrac{2800}{8a^2}[/tex] ----- (5)
Now, from equations (4) and (5).
[tex]\rm c = \dfrac{2800}{8\left(\dfrac{4900}{8c^2}\right)^2}[/tex]
Now, simplifying the above expression in order to get the value of c.
c = 10.234
Now, put the value of 'c' in equation (5) in order to get the value of 'a'.
a = 5.8481
The value of 'b' is given by:
[tex]\rm b = \dfrac{350}{5.8481\times 10.234}[/tex]
b = 5.848
So, the dimensions that will minimize the cost of constructing this box are: a = 5.8481 inches, b = 5.848 inches, and c = 10.234 inches.
For more information, refer to the link given below:
https://brainly.com/question/19770987
A dollar bill weighs one gram. How many pounds do one million dollar bills weigh? (1000 grams
is equal to 1 kilogram and 1 kilogram is equal to about 2.205 pounds.)
Hey there! I'm happy to help!
First of all, if one bill weighs on gram, a million would weigh one million grams. Let's divide this by 1,000 to see how many kilograms it is.
1,000,000/1,000=1,000
Now, we need to convert 1,000 kilograms into pounds. We see that 1 kilogram is equal to about 2.205 pounds, so we multiply 1,000 kilograms by 2.205 to get our pounds.
1,000*2.205=2205
Therefore, one million dollar bills weigh about 2205 pounds.
Have a wonderful day! :D
The lowest temperature ever
recorded on earth was -89°C
in Antarctica. The average
temperature on Mars is about
-55°C. Which is warmer?
Write an inequality to support
your answer
Answer:
Mars
Step-by-step explanation:
America
How many games are played in a 4 team round robin tournament? (Each team
plays every other team only once.)
Answer: 6
Step-by-step explanation:
If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.
We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total
Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.
Now we have already included D playing every other team so we don't include any other pairings.
In total, now every team has played every other team giving a total of 6.
(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.
Answer:
6 games.
Step-by-step explanation:
The answer is the number of combinations of 2 from 4
= 4*3 / 2*1
= 6.
what's the thickness of a rectangle prism with a height of 12 inches, a width of 8 inches and surface area 992 square inches?
Answer:
Thickness of rectangle prism is 20 inches.
Step-by-step explanation:
Given:
Surface area of rectangular prism, A = 992 sq inches.
Height, h = 12 inches
Width, w = 8 inches
To find:
Thickness / length of prism, [tex]l[/tex] = ?
Solution:
First of all, let us learn the formula for surface area of a rectangular prism.
Formula for surface area of a prism is given as:
[tex]A=2(wl+hl+hw)[/tex]
As there are 6 faces, each face is a rectangle and area of all the faces is considered in the formula. It is just like a cuboid like structure.
Putting all the given values in the formula to find the value of [tex]l[/tex]:
[tex]992=2(8l+12l+8 \times 12)\\\Rightarrow 496 = 20l + 96\\\Rightarrow 20 l =496-96\\\Rightarrow 20 l =400\\\Rightarrow l = \dfrac{400}{20}\\\Rightarrow l = 20\ inches[/tex]
So, the answer is Thickness of rectangle prism is 20 inches.
What is the solution to the quadratic equation x2 + x - 30 = 0?
Answer:
try 3x=30 or 10
Step-by-step explanation:
plS I really need this question
Mai is making friendship bracelets. Each bracelet is made from 24.3 cm of string. If she has 170.1 cm of string, how many bracelets can she make? Explain or show your reasoning.
Answer:
❄️The answer is 7.0 or 7❄️
Step-by-step explanation:
It mostly depends on how many zeros will you put in 7.0
It actually doesn’t matter how many zeros you put after the decimal point.
Below I attached a picture of how to solve this kinds of problem.
Hope this helps! ^-^
By:❤️BrainlyMagic❤️
Note:if you ever need help, you can always ask me!
Answer:
It’s 7.0 or 7
Step-by-step explanation:
Trust me I got it right in my homework.
This table shows values that represent an exponential function. What is the average rate of change for this function for the interval from x=3 to x=5?
Answer: The average rate of change for this function for the interval from x=3 to x=5 is 12.
Step-by-step explanation:
Complete question is provided in the attachment below.
Formula: The average rate of change for this function y=f(x) for the interval from x= a to x= b :
[tex]Rate =\dfrac{f(b)-f(a)}{b-a}[/tex]
Let y= f(x) for the given table:
At x= 3 , f(3)=8 and f(5)=32
Then, the average rate of change for this function for the interval from x=3 to x=5:
[tex]Rate=\dfrac{f(5)-f(3)}{5-3}\\\\=\dfrac{32-8}{2}\\\\=\dfrac{24}{2}=12[/tex]
Hence, the average rate of change for this function for the interval from x=3 to x=5 is 12. (Option A is correct.)