Given:
The objective function, [tex]C=2x+3y[/tex],
Constraints,
[tex]2x+3y\leq 24[/tex]
[tex]3x+y\leq 15[/tex]
[tex]x\geq 2[/tex]
[tex]y\geq 3[/tex]
To find:
The minimum value of the given objective function.
Solution:
We have,
Objective function, [tex]C=2x+3y[/tex] ....(i)
The related equations of given constraints are
[tex]2x+3y=24[/tex] ...(ii)
[tex]3x+y=15[/tex] ...(iii)
[tex]x=2[/tex], it is a vertical line parallel to y-axis and 2 units left from y-axis.
[tex]y=3[/tex], it is a horizontal line parallel to x-axis and 4 units above from y-axis.
Table of value for (i),
x : 0 12
y : 8 0
Table of value for (ii),
x : 0 5
y : 15 0
Plot these points on a coordinate plane and draw these 4 related lines.
The sign of inequality of [tex]2x+3y\leq 24[/tex] and [tex]3x+y\leq 15[/tex] is ≤, it means the related lines are solid lines and the shaded region lie below the related line.
For [tex]x\geq 2[/tex], left side of the line [tex]x=2[/tex] is shaded.
For [tex]y\geq 3[/tex], shaded region is above the line [tex]y=3[/tex].
From the below graph it is clear that the vertices of the feasible (common shaded region) are (2,3), (4,3), (3,6) and (2,6.667).
Points [tex]C=2x+3y[/tex]
(2,3) [tex]C=2(2)+3(3)=4+9=13[/tex] (Minimum)
(4,3) [tex]C=2(4)+3(3)=8+9=17[/tex]
(3,6) [tex]C=2(3)+3(6)=6+18=24[/tex]
(2,6.667) [tex]C=2(2)+3(6.667)=4+20=24[/tex]
Therefore, the objective function is minimum at point (2,3).
Find the value of x. Then find the measure of each angle.
1. x =
2. Angle =
3. Angle =
1. x+(x-26)= 180 (being corresponding angle)
2x-26=180
2x=180-26
2x=154
x=154÷ 2
∴x=77
A
8
B
7
D
С
CD = [?]
Please help meh please
Step-by-step explanation:
Movie pricing per person is $7.75
hockey pricing per person is $7.90
The Movie pricing is less per person because 7.90<7.75
I hope it answers
Answer:
movies
Step-by-step explanation:
im adding a picture of the explination because i worked it out
combine like terms to find the answer.
Answer: 9m + 5y + 1
Step-by-step explanation:
3 + 6m + -2y - 2 + 3m + 7y
3 + -2 = 1
1 + 6m + -2y + 3m + 7y
-2y + 7y = 5y
1 + 6m + 5y + 3m
6m + 3m = 9m
9m + 5y + 1
Answer:
1+9m+5y
Step-by-step explanation:
What is 6% of 15? Use a fraction to solve
Answer:
0.9
Step-by-step explanation:
can't really Explain, its simple mathamatics 6% of 15 = 0.9
Solve 3a – 8= 5a + 12
Show your work. (please)
Answer:
a = - 10
Step-by-step explanation:
3a – 8 = 5a + 12
3a – 8 + 8 = 5a + 12 + 8
3a = 5a + 20
3a - 5a = 5a + 20 - 5a
- 2a = 20
[tex]\dfrac{-2a}{-2}=\dfrac{20}{-2}[/tex]
a = - 10
Name the factors in each of the following problems
What is the best estimate for 82% of 503?
Can somebody please help with this? (Slope)
Answer:
the slope is m= 5/31 :)
Which statement is true of normally distributed data?
A.
Approximately 90% of data falls within 2 standard deviations (±2) of the mean.
B.
Approximately 90% of data falls within 3 standard deviations of (±3) the mean.
C.
Approximately 95% of data falls within 2 standard deviations (±2) of the mean.
D.
Approximately 95% of data falls within 3 standard deviations (±3) of the mean.
Please explain and no answering just for points.
C
have a nice day!!!!!!!!!!!!!!!!!!!!!!!
Approximately 95% of data falls within 2 standard deviations (±2) of the mean. Option D is correct.
What is a normal distribution?A normal distribution is a type of continuous probability distribution for a real-valued random variable such that the values are symmetric about a mean and the curve has bell shape.
Standard deviation is the measure of the randomness of the distribution. The curve has its peak at the mean.
As standard deviation increases, the peak of the curve comes lower and the distribution becomes more and more dispersed.
In a normal distribution 68% of the values falls within 1 standard deviation
and 95% of the values falls within two standard deviations. 99% of the values falls within three standard deviations.
Hence, approximately 95% of data falls within 2 standard deviations (±2) of the mean.
To learn more about normal distribution visit:
https://brainly.com/question/15103234
#SPJ1
Hello! :)
Please help me solve this + explain your answer :)
I will indeed give you Brainlst <3
Answer:
D. (-2, 6)
Step-by-step explanation:
First, isolate a variable in one of the equations (i.e y = or x =)
The first equation already has isolated x.
x = y - 8 or y - 8 = x
5x + y = -4
Substitute the isolated variable into the second equation.
5(y-8) + y = -4
There is now only one variable, y, in the equation. Now you can solve for y.
First, use the distributive property to get the equation
5y - 40 + y = -4
Then, add 40 to both sides.
5y + y = 36
Add like-terms.
6y = 36
Divide.
36 / 6 = 6
So, y = 6.
Now that we have one coordinate, y = 6, you can substitute for y in the first equation.
x = 6 - 8
Subtract.
x = -2
Your coordinates are now x = -2 and y = 6, or (-2, 6).
Let T: P2 → P3 be the transformation that maps a polynomial p(t) into the polynomial (t-2)p(t).
a. Find the image of p(t) = 2-t + t^2
b. Show that T is a linear transformation.
c. Find the matrix for T relative to the bases (1, t,t^2) and (1,t,t^2,t^3).
(a) Applying T to p(t) = 2 - t + t ² gives
T ( p(t) ) = (t - 2) (2 - t + t ²) = -4 + 4t - 3t ² + t ³
(b) T is a linear transformation if for any p(t) and q(t) in P₂ and complex scalars a and b, the image of any linear combination of p and q is equal to the linear combination of the images of p and q. In other words,
T ( a p(t) + b q(t) ) = a T ( p(t) ) + b T ( q(t) )
Let
p(t) = α₀ + α₁ t + α₂ t ²
q(t) = β₀ + β₁ t + β₂ t ²
Compute the images of p and q :
T ( p(t) ) = (t - 2) (α₀ + α₁ t + α₂ t ²)
… = -2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³
Similarly,
T ( q(t) ) = -2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³
Then
a T ( p(t) ) + b T ( q(t) ) = a (-2α₀ + (α₀ - 2α₁) t + (α₁ - 2α₂) t ² + α₂ t ³) + b (-2β₀ + (β₀ - 2β₁) t + (β₁ - 2β₂) t ² + β₂ t ³)
… = c₀ + c₁ t + c₂ t ² + c₃ t ³
where
c₀ = -2 (a α₀ + b β₀)
c₁ = a (α₀ - 2α₁) + b (β₀ - 2β₁)
c₂ = a (α₁ - 2α₂) + b (β₁ - 2β₂)
c₃ = a α₂ + b β₂
Computing the image of a p(t) + b q(t) would give the same result; just multiply it by t - 2 and expand. This establishes that T is indeed linear.
(c) Find the image of each vector in the basis for P₂ :
T (1) = (t - 2) × 1 = t - 2
T (t ) = (t - 2) t = t ² - 2t
T (t ²) = (t - 2) t ² = t ³ - 2t ²
Then
[tex]T=\begin{bmatrix}-2&0&0\\1&-2&0\\0&1&-2\\0&0&1\end{bmatrix}[/tex]
math The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing. If there are 15 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed
Answer:
2730 ways
Step-by-step explanation:
Given that,
There are 15 eligible candidates for these positions.
The newly elected president needs to decide the remaining 3 spots available in the cabinet he/she is appointing.
It is a concept based on permutations.
[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
Put n = 15 and r = 3
[tex]P(15,3)=\dfrac{15!}{(15-3)!}\\\\=\dfrac{15!}{12!}\\\\=\dfrac{15\times 14\times 13\times 12!}{12!}\\\\=15\times 14\times 13\\\\=2730[/tex]
Hence, 2730 ways can the members of the cabinet be appointed
please help me
thank
Answer:
D will round to 18.96
Step-by-step explanation:
18.958, 5+ will get rounded higher so it turns to 18.96, hope this helps you!
What’s is a standard form?
Answer:
Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . ... This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form.
Step-by-step explanation:
Answer:
ax+by=c
Step-by-step explanation:
this is standard for, if that's what you'e asking for
Can someone help solve this?
Answer:
x = 8
y = 18
Step-by-step explanation:
First, it would be easiest to start by drawing a picture. To do so, draw two simple Isosceles triangles. Then, label their points. One having the points F, U, and N while the other has B, A, and T. Now, since both triangles are congruent, that means that F≅B, U≅A, and N≅T. Because of this knowledge, FN would be congruent to BT. So, you would be able to write that 52 = 14x - 60. By solving that, you would get the answer to x. Moving onto y, you would see that since the triangles are congruent, the interior angles are too. So, you would be able to use angles F and N to find A. By adding them to 180°, the equation would look like: 71° + 36° + (3y + 19)° = 180°. So, you would be able to find the answer to y. Hope this helped!
HELPPP MEEEEEEEEEEEEEEEEEEEEEEE
solve the inequality
Answer:
-18>t
Step-by-step explanation:
just move the 7 over the > sign lol
Desiree writes songs for her band. her first song is 3 1/2 minutes long. Her second song is 1 1/2 times as long as her first song. her third song is 2/3 times as long as her second song. How many minutes long are the second and third songs?
A line passes through the point (-8,-5) and has a slope of 3/4. Write an equation in slope intercept form for this line.
Answer:
y = ¾x + 1
Step-by-step explanation:
Point-slope equation for line of slope ¾ that passes through (-8,-5):
y+5 = ¾(x+8)
Put into slope-intercept form:
y = ¾(x+8) - 5 = ¾x + 6 - 5 = ¾x + 1
Find the unit rate. Round to the nearest hundredth, if necessary.
$190 for 16 ft
Answer:
About $11.88 per foot
Step-by-step explanation:
NEED HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Segment DO
Step-by-step explanation:
The first option is not the radius because A is going outside of the circle and it would actually be longer than the radius.
BC is too high up, and it's considered a chord, not the radius.
DE is the diameter, not the radius.
That leaves us with 1 answer remaining.
Can somebody help me with this one thank you.
12x+5y=95
find the x-intercept
Answer:
(95/12,0)
Step-by-step explanation:
Answer:
(7.916, 0)
Step-by-step explanation:
In order to find the X-intercept, let y=0
12x + 5(0) = 95
12x = 95
95/12x = 7.91666...
Therefore, the x intercept is (7.916, 0)
Can somebody help me on this ?
Answer:
drag the protactor so that the the bottom, middle line is centered in point B, and the bottom edge is flat against line BC
the angle will be whatever number AB lines up with on the outer ring (the big numbers)
Step-by-step explanation:
Graphs can only provide a limited view of the data.
a. True
b. False
Answer:
Graphs can only provide a limited view of the data.
b. False
Step-by-step explanation:
On the contrary, graphs present better views of the presented data. Mathematically, graphs are methods of visually illustrating data relationships. The main purpose of using a graph is to present complicated data that show trends or relationships between variables. It has been an important tool for presenting data in a visual and easy-to-understand format, without using too much description.
the first term of a sequence is 13 you take away 5 find out the 4th term
Answer:
a4 = -2
Step-by-step explanation:
a2 = 13 -5 = 8
a3 = 8 -5 = 3
a4 = 3 -5 = -2
Whats the Standard form of 3-7i/2+6i
Answer:
[tex]3+\frac{5i}{2}[/tex]
Step-by-step explanation:
Simplify and write the answer in the standard form, a+bi. Hope this helps!
Quadrilateral RUST has a vertex at R (1,2). U S What are the coordinates of R'after a dilation by a scale factor of 3, centered at the origin, followed by the translation (x, y) - (x + 2, y)?
A. (5,8)
B. (5,2)
C. (9,6)
D. (5,6)
Answer:
D. [tex](5,6)[/tex]
Step-by-step explanation:
Let [tex]R(x,y) = (1,2)[/tex], we proceed to perform all operations described on statement:
1) Dilation
[tex]R'(x,y) = O(x,y) + k\cdot [R(x,y)-O(x,y)][/tex] (1)
Where:
[tex]O(x,y)[/tex] - Point of reference.
[tex]R(x,y)[/tex] - Original point.
[tex]R'(x,y)[/tex] - Dilated point.
[tex]k[/tex] - Scale factor.
If we know that [tex]O(x,y) = (0,0)[/tex], [tex]R(x,y) = (1,2)[/tex] and [tex]k = 3[/tex], then the dilated point is:
[tex]R'(x,y) = (0,0) +3\cdot [(1,2)-(0,0)][/tex]
[tex]R'(x,y) = (0,0) +3\cdot (1,2)[/tex]
[tex]R'(x,y) = (3,6)[/tex]
2) Translation
[tex]R''(x,y) = R'(x,y) + T(x,y)[/tex] (2)
Where:
[tex]R'(x,y)[/tex] - Original point.
[tex]T(x,y)[/tex] - Translation point.
[tex]R''(x,y)[/tex] - Translated point.
If we know that [tex]R'(x,y) = (3,6)[/tex] and [tex]T(x,y) = (2,0)[/tex], then the translated vector is:
[tex]R''(x,y) = (3,6)+(2,0)[/tex]
[tex]R''(x,y) = (5,6)[/tex]
Therefore, the correct answer is D.
Answer:d
Step-by-step explanation:
Which graph represents a linear function?
Answer:
Graph two would be the answer because it is not curving.
Step-by-step explanation: