Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
2071 Old Q.No.5 Person's coefficient of skewness for a distribution is 0.4 and its coefficient of variation is 30%. If mode is 88, find mean and median.
Answer:
[tex]Mean = 100[/tex]
[tex]Median = 96[/tex]
Step-by-step explanation:
Given
[tex]C_v = 30\%[/tex] --- coefficient of variation
[tex]mode = 88[/tex]
[tex]Skp = 0.4[/tex]
Required
The mean and the median
The coefficient of variation is calculated using:
[tex]C_v = \frac{\sigma}{\mu}[/tex]
Where:
[tex]\mu \to[/tex] mean
So:
[tex]30\% = \frac{\sigma}{\mu}[/tex]
Express percentage as decimal
[tex]0.30 = \frac{\sigma}{\mu}[/tex]
Make [tex]\sigma[/tex] the subject
[tex]\sigma = 0.30\mu[/tex]
The coefficient of skewness is calculated using:
[tex]Skp = \frac{\mu - Mode}{\sigma}[/tex]
This gives:
[tex]0.4 = \frac{\mu - 88}{\sigma}[/tex]
Make [tex]\sigma[/tex] the subject
[tex]\sigma = \frac{\mu - 88}{0.4 }[/tex]
Equate both expressions for [tex]\sigma[/tex]
[tex]0.30\mu = \frac{\mu - 88}{0.4 }[/tex]
Cross multiply
[tex]0.4*0.30\mu = \mu - 88[/tex]
[tex]0.12\mu = \mu - 88[/tex]
Collect like terms
[tex]0.12\mu - \mu = - 88[/tex]
[tex]-0.88\mu = - 88[/tex]
Divide both sides by -0.88
[tex]\mu = 100[/tex]
Hence:
[tex]Mean = 100[/tex]
Calculate [tex]\sigma[/tex]
[tex]\sigma = 0.30\mu[/tex]
[tex]\sigma = 0.30 * 100[/tex]
[tex]\sigma = 30[/tex]
So:
Also, the coefficient of skewness is calculated using:
[tex]Skp = \frac{3 * (Mean - Median)}{\sigma}[/tex]
[tex]0.4= \frac{3 * (100 - Median)}{30}[/tex]
Multiply both sides by 30
[tex]0.4*30= 3 * (100 - Median)[/tex]
Divide both sides by 3
[tex]0.4*10= 100 - Median[/tex]
[tex]4= 100 - Median[/tex]
Collect like terms
[tex]Median = 100 - 4[/tex]
[tex]Median = 96[/tex]
Can someone answer this please
Answer:
[tex]336m^2[/tex]
Step-by-step explanation:
[tex]6*8=48[/tex]
[tex]10*12=120[/tex]
[tex]8*12=96[/tex]
[tex]6*12=72[/tex]
Add all these up
[tex]48+120+96+72=336[/tex]
Hope this helps
12y^2+12y-3y^3 = 124-(y+5)
Answer:
[tex]{ \tt{12 {y}^{2} + 12y - 3 {y}^{3} = 124 - (y + 5)}} \\ 3 {y}^{3} - 12 {y}^{2} - 12y = - 124 + (y + 5) \\ {3y}^{3} - 12 {y}^{2} - 12y = - 124 + y + 5 \\ { \tt{3 {y}^{3} - {12y}^{2} - 11y + 119 = 0 }}[/tex]
Kaya babysits to add money to her savings. She draws a graph to show how much she can earn by babysitting. What is the equation of Kaya's line in slope-intercept form
Answer:
Step-by-step explanation:
!pls help!
Use a net to find the surface area
Answer:
336 square inches
Step-by-step explanation:
Nets are the spreaded out version/outline of 3d figures. It shows the faces of the figure. The figure in this case is actually a triangular prism.
find the area of each shape in the net:
Triangle A (1/2 x base x height)
1/2 • 8 x 6 = 24 square inches
Rectangle B (length x width):
6 x 12 = 72 square inches
Rectangle C:
8 x 12 = 96 square inches
Rectangle D:
10 x 12 = 120 square inches
Triangle E:
1/2 x 6 x 8 = 24 square inches
Add up all the areas of all shapes:
24 + 24 + 120 + 72 + 96 = 336
Surface area is measured in square inches
(Inches in this case)
Hope this helps
f(X)=X^3 + 4 X^2-10=0 (between X=1 , X=2) بطريقه ال Bisection method
please fast
I hope it's helpful for u but I am not sure my answer is right !
l[tex]\lim_{n \to \0} \frac{sin x}{x}[/tex]
1
Step-by-step explanation:
[tex]\displaystyle \lim_{x \to 0}\dfrac{\sin x}{x}[/tex]
Let
[tex]f(x)= \sin x[/tex]
[tex]g(x)=x[/tex]
We are going to use L'Hopital's Rule here that states
[tex]\displaystyle \lim_{x \to c}\dfrac{f(x)}{g(x)}=\lim_{x \to c}\dfrac{f'(x)}{g'(x)}[/tex]
We know that
[tex]f'(x) = \cos x[/tex] and [tex]g'(x)=1[/tex]
so
[tex]\displaystyle \lim_{x \to 0}\dfrac{\sin x}{x}=\lim_{x \to 0}\dfrac{\cos x}{1}=1[/tex]
...................
thnx If solved....XD
$4825.70
Step-by-step explanation:
Cost for Fans: 4 x 675 = $2700
Cost for Lamps: 2 x 110 = $220
Cost for Switches: 5 x 41 = $205
Cost for Tubes: 6 x 135 = $810
Cost for Electric Wire: 230 x 2.50 = $575
Total cost: 2700 + 220 + 205 + 810 + 575 = $4510
Tax: Total cost x Tax rate = 4510 x 0.07 = $315.70
Total paid: Total cost + Tax = 4510 + 315.70 = $4825.70
1. My number has two digits
2. I am greater than 30
3. I am less than 90
4. My second digit is greater than 3
5. My first digit is divisible by 2
6. Both of my digits add up to either 11 or 12
7. I am the smallest number of
the four numbers that are left.
Answer:
47
Step-by-step explanation:
1. #2 and #3 reveal that it must be between 31 to 89
2. #4 and #5 reveals that the answer is one of these numbers:
44, 45, 46, 47, 48, 49
64, 65, 66, 67, 68, 69
84, 85, 86, 87, 88, 89
This is because only 4, 6, and 8 are divisible by 2
3. You must add up all the numbers to see which ones add up to either 11 or 12.
4 + 7 = 11
4 + 8 = 12
6 + 5 = 11
6 + 6 = 12
8 + 4 = 12
This means that these are the following numbers: 47, 48, 65, 66, 84
4. #7 says that you must find the smallest number. The smallest number left is 47.
p = 4x + qx - 5 SOLVE FOR X
[tex]\sf \bf {\boxed {\mathbb {\: x = \frac{(p + 5)}{(4 + q)} }}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]p = 4x + qx - 5 \\ [/tex]
[tex]➺ \: p = x \: (4 + q) - 5 \\ [/tex]
[tex]➺ \: x \: (4 + q) = p + 5 \\[/tex]
[tex]➺ \: x = \frac{(p + 5)}{(4 + q)} \\ \\ [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
Determine the value of x for which r is parallel to s if m angle 1 = 60-2x and m angle 2=70-4x
Answer: r = 5
Step-by-step explanation:
Ibrahim heeft een bijbaantje op de markt. Hij berekent zijn inkomsten met de formule
inkomsten in €=5+3,50 x tijd in uren. Leg de formule uit.
Answer:
Ibrahim gets 5 fixed and 3.5 per hour.
Step-by-step explanation:
Ibrahim has a side job at the market. He calculates his income with the formula income in € = 5 + 3.50 x, time in hours. Explain the formula.
Here, the fixed income is 5.
the income per hour is 3.5.
So, Ibrahim gets 5 fixed and 3.5 per hour.
Which number line represents the solution set for the inequality -1/2x >= 4
Answer:
x≤-8
Step-by-step explanation:
-1/2x ≥ 4
Multiply each side by -2, remembering to flip the inequality
-2*-1/2x≤ 4*-2
x≤-8
Answer:
Step-by-step explanation:
Note: by the rule of order of operations, -1/2x == -1/2*x = -x/2
-x/2 >= 4
-x >= 4*2 = 8
x <= -8
The number line looks like this:
<============================O--------------------------------------
where the circle should be filled and at x= -8
The valid part of the number line is to the left of the circle but INCLUDING the circle (solid dot).
Type your answers into the boxes.
Complete the following questions.
4x5-(22 - 2) =
(18= 3) + (32 - 7) =
Answer:
0 and 40
Step-by-step explanation:
First expression: 4*5 - (22 - 2). We must do work inside parentheses before any other work. This, we have 4*5 - (20), which simplifies to 20 - 20 = 0
Second expression: (18 - 3) + (32 - 7 becomes (15) + 25, or 40.
The function f(x) = x² is transformed to f(x) = 0.4(x + 1)? Which statement describes the effect(s) of the transformation on the
graph of the original function?
A)
The parabola is wider and shifted 1 unit to the left.
B)
The parabola is wider and shifted 1 unit to the right.
The parabola is narrower and shifted 1 unit to the left.
D)
The parabola is narrower and shifted 1 unit to the right.
Answer:
D) The parabola is narrower and shifted 1 unit to the right.
SERIOUS ANSWERS ONLY WILL GIVE BRAINLIEST
Use the function f(x) to answer the questions:
f(x) = 4x2 + 8x − 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Hello,
Part A:
[tex]f(x)=4x^2+8x-5\\=4(x^2+2x)-5\\=4(x^2+2x+1-1)-5\\=4(x+1)^2-9\\=(2(x+1)-3)(2(x+1)+3)\\=(2x-1)(2x+5)\\x-intercepts\ are\ x=\frac{1}{2} \ and\ x=-\frac{5}{2} \\[/tex]
Part B:
x² coefficient is 4 >0 thus a minimun
as y=4(x+1)²-9 : vertex is (-1,-9)
Proof: see picture
Sorry for Part c: I don't know
In France, we make an array of (x,f(x)) and then plot the severals points.
what is a proof
PLS PLS PLS HELP GELP HELPPPPPPPP
A. Definition = (the third meaning.)
B. Postulate (axiom) = (the first meaning.)
C. Common notion = (the last meaning.)
D. Theorem = (The second meaning.)
E. Corollary = (the fourth meaning.)
Proof is evidence or an argument that helps to establish a fact or the truth of a statement. For example, most people won't accept new concepts or ideas without proof of its existence.
let's tick to the well defined collection
Answer:
the answer should be B, because I think the collection of fruits is right
Answer:
i think its b
Step-by-step explanation:
please help me please i really need help please
Answer:
3053.63 inches cube
Step-by-step explanation:
V =4 3
------nr
3
4/3×22/7×9×9×9
=
3053.63
please mark as brainliest answer as it will also give you 3 pts
Please look below and answer (No links) please explain. I will give brainiest
Answer:
The slope is 1/2 because for every y value that it goes down, the x value goes down by 2. The y-intercept is 4 because when x is 0, y is equal to 4.
I’ve been stuck on this problem I can’t seem to get 7 9/4 into the ABC form
Answer:
7 square root 9^4
Step-by-step explanation:
what is the average rate of change between:
x=1 and x=2
x=2 and x=3
x=3 and x=4
Rate of change = RΔ = (y2-y1)/(x2-x1) = Δy/Δx
(X1,Y1)(X2,Y2)
(1, 2) (2, 4)
RΔ = Δy/Δx
= (4-2)/(2-1)
RΔ = 2
(2, 4) (3, 8)
RΔ = (8-4)/(3-2)
RΔ = 4
(3, 8) (4, 16)
RΔ = (16-8)/(4-3)
RΔ = 8
Compute ∬_R〖(7xy-5-2y^2)dxdy〗 where the domain of integration R is bounded by the lines y=0, y=4-2x and y=2x^2
Attached you'll find the region of interest, which is captured by the set of points
R = {(x, y) | √(y/2) ≤ x ≤ (4 - y)/2 and 0 ≤ y ≤ 2}
Written in this way, it's convenient to integrate with the order dx dy (that is, with respect to x first). In particular, we have
[tex]\displaystyle\iint_R(7xy-5-2y^2)\,\mathrm dx\,\mathrm dy = \int_0^2 \int_{\sqrt{\frac y2}}^{\frac{4-y}2} (7xy-5-2y^2)\,\mathrm dx\,\mathrm dy[/tex]
[tex]\displaystyle = \int_0^2 \int_{\sqrt{\frac y2}}^{\frac{4-y}2} \left(\frac72 x^2y-5x-2xy^2\right)\bigg|_{\sqrt{\frac y2}}^{\frac{4-y}2}\,\mathrm dy[/tex]
[tex]=\displaystyle\int_0^2\left(\frac{15}8y^3-11y^2+\frac{33}2y-10 +\sqrt2 y^{\frac52}-\frac74y^2+\frac5{\sqrt2}y^{\frac12}\right)\,\mathrm dy[/tex]
[tex]=\displaystyle\left(\frac{15}{32}y^4+\frac{2\sqrt2}7y^{\frac72}-\frac{17}4y^3+\frac{33}4y^2+\frac{5\sqrt2}3y^{\frac32}-10y\right)\bigg|_0^2[/tex]
[tex]=\boxed{-\dfrac{95}{42}}[/tex]
The numbers 1, 2, 3 , and 4 are drawn one at a time from the set {0, 1, 2, …, 9}. If these four numbers are drawn with replacement, what is the probability that 14 − 23 is an even number?
Find the distance (-2,4) and (-5,-0)
Answer:
d=√65 units
Step-by-step explanation:
Using the distance formula :
d=√((−5)−(2))2+((0)−(4))2 units
d=√(−7)2+(−4)2 units
d=√49+16 units
d=√65 units
If this helps you, please mark brainliest!
Have a nice day!
William is an electrician. He charges an initial fee of $44 per visit. If he charges $30 for every hour he works, which explicit
expression and recursive process can be used to find out how much he will charge for working n hours?
O A. Explicit Expression: 30n - 44
Recursive Process: To find out how much William will charge for working n hours, subtract $30 from how much he
charges for working n - 1 hours.
W = Wn-1 - $30, Wo = $44
OB. Explicit Expression: 30n +44
Recursive Process: To find out how much William will charge for working hours, add $30 to how much he charges for
working n - 1 hours.
W = Wn-1 + $30, Wo = $44
OC. Explicit Expression: 44n - 30
Recursive Process: To find out how much William will charge for working n hours, subtract $44 from how much he
charges for working n - 1 hours.
Wn = Wn-1 - $44, Wo = $30
OD. Explicit Expression: 44n+ 30
Recursive Process: To find out how much William will charge for working n hours, add $44 to how much he charges for
working n - 1 hours.
Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $52 for 180 miles. On another day she rented a car from the same agency and paid $77.50 for 350 miles. Find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.
f(x) =
9514 1404 393
Answer:
f(x) = 0.15x +25
Step-by-step explanation:
We are given two points:
(x, y) = (180, 52) or (350, 77.50)
The slope is given by ...
m = (y2 -y1)/(x2 -x1)
m = (77.50 -52)/(350 -180) = 25.50/170 = 0.15
The y-intercept is given by ...
b = y -mx
b = 52 -0.15×180 = 25
Then the equation for the linear function is ...
f(x) = mx +b
f(x) = 0.15x +25
Which recursive sequence would produce the sequence 6, 20, 62, …
Step-by-step explanation:
Using an online calculator, I was able to find that one pattern is
[tex]a_{n} = a_{n-1} + 14 * 3^{n-1}[/tex] . Finding a recursive sequence is generally based on guess and check, so there isn't much explanation to obtaining one
Find a value of 0 in the interval 0° < 0 < 90° that satisfies the given statement.
tan = 0.85088446
Answer:
That Satisfies The Given Statement. Tan 0 = 0.78879988 (Simplify Your Answer. Type An Integer Or A Decimal.
Step-by-step explanation:
5.
An object has a constant acceleration of 40 ft/sec2, an initial velocity of -20 ft/sec, and an initial position of 10 ft. Find the position function, s(t), describing the motion of the object. (10 points)
You can solve for the velocity and position functions by integrating using the fundamental theorem of calculus:
a(t) = 40 ft/s²
v(t) = v (0) + ∫₀ᵗ a(u) du
v(t) = -20 ft/s + ∫₀ᵗ (40 ft/s²) du
v(t) = -20 ft/s + (40 ft/s²) t
s(t) = s (0) + ∫₀ᵗ v(u) du
s(t) = 10 ft + ∫₀ᵗ (-20 ft/s + (40 ft/s²) u ) du
s(t) = 10 ft + (-20 ft/s) t + 1/2 (40 ft/s²) t ²
s(t) = 10 ft - (20 ft/s) t + (20 ft/s²) t ²