Answer:
9
Step-by-step explanation:
You want the minimum value of objective function C=6x+3y, given the constraints x>1, y≥1, 4x+2y<32, and 2x+8y<56.
MinimumThe objective function has positive coefficients for both x and y, so it will be minimized when x and y are at their minimum values. The constraints tell you these minimum values are x=1 and y=1, so the minimum value of C is ...
C = 6(1) +3(1) = 9
The minimum value of C is 9.
__
Additional comment
The value of x cannot actually be 1, so the value of C cannot actually be 9. However x may be arbitrarily close to 1, so C may be arbitrarily close to 9.
C = 6x +3y ⇒ x = (C -3y)/6
The x-constraint requires ...
x > 1
(C -3y)/6 > 1
C -3y > 6 . . . . . . multiply by 6
C > 6 +3y . . . . . . add 3y
The minimum value of y is exactly 1, so we have ...
C > 6 +3(1)
C > 9
Is -36/6 a integer number
Answer:
Yes
Step-by-step explanation:
-36/6 = -6
Integers are the whole numbers (0.1.2.3.4.5....) and their opposites ...-4,-3,-2,-1
please help me work through this if you can, thank you!
Given:
[tex]C=\frac{x^4}{4}-\frac{4}{3}x^3-\frac{35}{2}x^2+150x[/tex]Let's solve for the following:
• (a). Find C'(x).
Here, we are to find the derivative of C(x).
Apply the sum rule:
[tex]\begin{gathered} C^{\prime}=\frac{d}{dx}(\frac{x^4}{4})+\frac{d}{dx}(-\frac{4}{3}x^3)+\frac{d}{dx}(-\frac{35}{2}x^2)+\frac{d}{dx}(150x) \\ \\ C^{\prime}=x^3-4x^2-35x+150 \end{gathered}[/tex]• (b). The critical numbers of C(x).
The critical numbers will be the points where the graph changes direction.
Using the derivative, let's solve for x.
[tex]x^3-4x^2-35x+150=0[/tex]Factor the left side using the rational root test:
[tex](x-5)(x^2+x-30)=0[/tex]Now factor using the AC method:
[tex]\begin{gathered} (x-5)((x-5)(x+6))=0 \\ \\ (x-5)(x-5)(x+6)=0 \end{gathered}[/tex]Equate each factor to zero and solve for x:
[tex]\begin{gathered} x-5=0 \\ \text{ Add 5 to both sides:} \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x-5=0 \\ x-5+5=0+5 \\ x=5 \\ \\ \\ x+6=0 \\ x+6-6=0-6 \\ x=-6 \end{gathered}[/tex]Therefore, the critical numbers of C(x) are:
x = -6, 5
• (C). Increasing interval.
Use the critical points to find the increasing and decreasing intervals.
Using interval notation, the increasing interval is:
[tex](-6,5)\cup(5,\infty)[/tex]• D. Decreasing interval:
Using interval notation, the decreasing interval is:
[tex](-\infty,-6)[/tex]ANSWER:
(a). C'(x) = x³ - 4x² - 35x + 150
(b). x = -6, 5
(c). Increasing: (-6, 5) U (5,∞)
Decreasing: (-∞, -6)
Solve the trigonometric equation for all values 0 ≤ x < 2π.tan x - 1 = 0
Here’s the question to solve. Just do the question that has the chart
Step 1:
Write the equation
[tex]x^4-x^3+3x^2\text{ - 9x }-\text{ 54 = 0}[/tex]Step 2:
Use trial and error to find one the the factor
x - 3 is a factor
Because when you substitute x = 3, the result is zero
Hence, 3 is zero of the polynomial
Step 3
Use the long division
I don’t know how to find the median and the mode HELPP
First, let's write the data set in crescent order:
[tex]35,35,44,50,50,50,56,60,65,70,86,90,110[/tex]The mean is given by the sum of all values divided by the number of values:
[tex]\begin{gathered} mean=\frac{35+35+44+50+50+50+56+60+65+70+86+90+110}{13}\\ \\ mean=\frac{801}{13}\\ \\ mean=61.62 \end{gathered}[/tex]The median is given by the central value of the set in crescent order. Since this set has 13 values, the median is the 7th value:
[tex]median=56[/tex]The mode is the value that repeats the most. Looking at the set, the value that repeats the most (three times) is 50, so the mode is 50.
7. 200 is the ? th term of 24, 35, 46, 57, ..
200 is the 17th term of the progression
What is arithmetic progression?
Arithmetic progression or arithmetic sequence (AP) is a numerical series in which the difference between subsequent terms is constant. The sequence 5, 7, 9, 11, 13, 15,..., for example, is an arithmetic progression with a common difference of 2. A finite arithmetic progression, or simply an arithmetic progression, is a finite section of an arithmetic progression. An arithmetic series is the sum of a finite arithmetic progression. An arithmetic series is the sum of the elements of a finite arithmetic progression. A closed expression determines the product of the members of a finite arithmetic progression with a beginning element a1, common differences d, and n elements in total.
This can be solved using arithmetic progression
Aₙ = a + (n - 1)d
where, Aₙ = 24, d = 35 - 24 = 11
so, n = (Aₙ - a)/d + 1 = (200-24)/11 + 1 = 17
Hence, 200 is the 17th term of the progression
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An air traffic controller spots two planes flying at the same altitude. Their flight paths form a right angle at point P. One plane is 150 miles from point P and is moving at 440 miles per hour. The other plane is 200 miles from point P and is moving at 440 miles per hour. Write the distance s between the planes as a function of time t.
The distance s as a function of time is s = 50√(162t² -126t +25)
Take miles and hours to be the problem's units.
The distance of the first plane from point p is provided by
x = 150 -450t
The distance of the second plane from point p is given by
y = 200 -450t
The Pythagorean theorem can be used to calculate the distance between them because their flight trajectories are at right angles (s).
s² = x² + y²
s² = (150 -450t) (150 -450t)
² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²
... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)
... s = 50√(162t² -126t +25)
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What is the answer to this question?
The probability of drawing a blue socks and white socks is 1/12.
Given that, a drawer contains 10 red socks, 6 white socks and 8 blue socks.
What is probability of an event?Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.
As we know the probability of an event = Number of favorable outcomes/Total number of outcomes
Total number of outcomes = 10+6+8=24
Probability of getting blue socks = 8/24 = 1/3
Probability of getting white socks = 6/24 =1/4
Now, probability of an event = 1/3 × 1/4 = 1/12
Therefore, the probability of drawing a blue socks and white socks is 1/12.
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Point B is located at (-5, -5) on the coordinate plane. Point B is reflected over thex-axis to create point B'. What ordered pair describes the location of B'?
SOLUTION
If a coordinate is refleted over the x-axis, the formula to apply is
[tex](x,y)\rightarrow(x,-y)[/tex]So for B(-5, -5), this becomes
[tex]\begin{gathered} B\mleft(-5,-5\mright)\rightarrow(-5,-(-5) \\ \\ the\text{ answer becomes } \\ \\ B(-5,-5)\rightarrow B^{\prime}(-5,5) \end{gathered}[/tex]111 pointFind cot(1.570/7.3). Round to 3 decimal places.Type your answer...
What is the volume, in cubic inches, of a rectangular prism with a height of 19in, a width of 8in, and a length of 17in?
The volume of a rectangular prism is given by
[tex]V=L\times W\times H[/tex]Where L is the length, W is the width, and H is the height of the rectangular prism.
For the given case, we have
Length = 17 in
Width = 8 in
Height = 19 in
Let us substitute these values into the above formula
[tex]\begin{gathered} V=L\times W\times H \\ V=17\times8\times19 \\ V=2584\: in^3 \end{gathered}[/tex]Therefore, the volume of the given rectangular prism is 2584 cubic inches.
Find the solution.7 · x = 8412139177
We need to find the value for x using the inverse operation:
Then:
[tex]\begin{gathered} 7-x=84 \\ \end{gathered}[/tex]Let us solve for x:
The x is subtracting, so it will add up to the other side:
[tex]7=84+x[/tex]Now, the 84 is positive, so it will be negative on the other side:
[tex]\begin{gathered} 7-84=x \\ x=-77 \end{gathered}[/tex]Hence, the solution for x is -77.
Why did the turkey volenteer to be the drummer in the popular bird band? only 2.1 section
Answer:
I eat birds tasty
What is 3+2? and add 7 then subtract 4
the answer is 8
add 3+2, that gives u 5, add 7+5 which is 12, do 12-4 its equal to 8
how do I put 5/7-i in standard form?
To put
[tex]\frac{5}{7-i}[/tex]In the standard form, we must multiply the numerator and denominator by the complex conjugate of (7-i), it means
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}[/tex]And now we solve it, therefore
[tex]\frac{5}{7-i}\cdot\frac{7+i}{7+i}=\frac{5(7+i)}{7^2-i^2}[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} \frac{5(7+i)}{7^2-i^2}=\frac{5(7+i)}{49+1} \\ \\ \frac{5(7+i)}{49+1}=\frac{5(7+i)}{50} \end{gathered}[/tex]Now we can simplify it
[tex]\frac{5(7+i)}{50}=\frac{7+i}{10}[/tex]And we have it in the standard form
[tex]\frac{7}{10}+\frac{1}{10}i[/tex]Which of the following hypotheses is not a valid null hypothesis?a.H0: µ = 0b.H0: µ ≥ 0c.H0: µ ≤ 0d.H0: µ < 0
Given:
a. H0: µ = 0
b. H0: µ ≥ 0
c. H0: µ ≤ 0
d. H0: µ
Required:
To choose the hypotheses that is not valid.
Explanation:
The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Here the option d is not valid.
Final Answer:
The option d is not valid.
H0: µ < 0
If translation T maps point A(-3, 1) onto point A'(5, 5),
which is the translation T?
Answer: [tex](x,y) \to (x+8, y+4)[/tex]
==================================================
Explanation:
The x coordinate of A and A' are -3 and 5 respectively.
This is an increase of +8 since -3+8 = 5
Therefore, we shift the preimage 8 units to the right to get the image point.
That explains how x turns into x+8.
-------------
The y coordinates of A and A' are 1 and 5 respectively.
This is an increase of +4, so we shift the preimage up 4 units.
This signals that y turns into y+4
--------------
To recap we found that,
x becomes x+8y becomes y+4Therefore we get to the answer [tex](x,y) \to (x+8, y+4)[/tex]
--------------
To check the answer, let's apply this translation to point A(-3,1) and we should get (5,5) as the result.
[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}+4)\\\\(-3,1)\to(-3+8,1+4)\\\\(-3,1)\to(5,5)\\\\[/tex]
This confirms the answer is correct.
Need some guidance and reassurance because I am not getting full points on my homework. Thanks.
Given the parent function:
[tex]y=x^3[/tex]If y is shifted right by 7 units, we obtain:
[tex]Option\text{ D: }y=(x-7)^3[/tex]If y is compressed horizontally by a factor of 7, we have:
[tex]Option\; E\colon y=(7x)^3=7^3x^3[/tex]If y is stretched vertically by the factor 7, we obtain:
[tex]\text{Option H: }y=7x^3[/tex]A shift downwards by 7 units gives:
[tex]\text{Option A: }y=x^3-7[/tex]Give the standard form of the given equation below. If it is a quadratic equation, then give the a, b, and c coefficients. 3x2-2x-5x(x-7)=(x-2)(x+4)+1
Answer:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]Step-by-step explanation:
The quadratic equation in standard form is represented by:
[tex]ax^2+bx+c=0[/tex]For the following equation;
[tex]\begin{gathered} 3x^2-2x-5x(x-7)=(x-2)(x+4)+1 \\ 3x^2-2x-5x^2+35x=x^2+4x-2x-8+1 \\ -2x^2-2x+35x=x^2+2x-7 \end{gathered}[/tex]Compute all the terms on the left side, equalizing 0:
[tex]\begin{gathered} -3x^2+31x+7=0 \\ \text{Then, the a,b and c coefficeints would be:} \\ a=-3 \\ b=31 \\ c=7 \end{gathered}[/tex]The quadrilateral RSTU is inscribed in the circle shown below. S R U Jake wants to prove the theorem that says that the measure of the quadrilateral's opposite angles add to 180°. He knows that the measure of angle Ris half the measure of are STU and that the measure of angle T is half the measure of arc SRU. Which of the following is an appropriate step to prove that ZR + ZT =180°?
Arc STU and arc SRU can form the complete circle. Therefore
[tex]Therefore,[tex]\begin{gathered} 2R+2T=360^0 \\ \text{factorize left hand side} \\ 2(R+T)=360^0 \end{gathered}[/tex]Dividing both sides by 2, we have
[tex]Hence, the appropriate steps are: Assume that the measure of arcs STU and SRU add up to 360 degreesAlso, substitute 2 m
pick yes in options 2 and 3
pick no in options 1 and 4
Number 6. Find the missing measure and round to nearest 10th
Note that Cosine law can be used if three sides of the triangle are given in order to get the angles.
For example, in getting the measurement of angle C
[tex]\cos C=\frac{a^2+b^2-c^2}{2ab}[/tex]Then take the arccos to get the angle C.
From the problem, we have :
We need to find the measurement of angle F using the same formula above.
[tex]\begin{gathered} \cos F=\frac{16^2+12^2-18^2}{2(16)(12)} \\ \cos F=\frac{19}{96} \end{gathered}[/tex]Taking the arc cosine :
[tex]\begin{gathered} \angle F=\arccos (\frac{19}{96}) \\ \angle F=78.58 \end{gathered}[/tex]The answer rounded to the nearest 10th is
. Which units can be used to measure distance?
A. seconds
B. cubic centimeters
C. meters
D. liters
Answer:
c
Step-by-step explanation:
The metre or meter, symbol m, is the primary unit of length in the International System of Units, though its prefixed forms are also used relatively frequently.
p and q are both prime numbers. They are each less than 22 Give an example where p + q is odd but not prime. You must only write the two numbers in the answer box. Type here to search O RI e Total ma
Answer:
See below
Step-by-step explanation:
2 + 7 = 9 2 and 7 are prime the answer is odd but not prime
please help me out fr
Christian, this is the solution to the problem:
p = 2l + 2w
Solving for l, we have:
2l = p - 2w
Dividng by 2 at both sides:
2l/2 = (p - 2w)/2
l = (p - 2w)/2
The correct answer is D.
Victor earns 19% commission as a salesperson. He sold a microscope that cost $368.84. How much commission did Victor earn? Round your answer to the nearest cent: $
Victor earns 19% commission
He sold a microscope that cost $368.84.
so, the commission = 19% of $368.84 = 0.19 * 368.84 = 70.0796
Rounding to the nearest cent
So,
the commission = $70.08
Help need please!!!!!!!factorize 36a-12b-60c
Solution:
Given:
[tex]36a-12b-60c[/tex]The greatest common factor (GCF) is factored out of the expression.
The GCF is 12.
Hence,
[tex]36a-12b-60c=12(3a-b-5c)[/tex]Therefore, the factorization of the given polynomial 36a - 12b - 60c is;
[tex]12(3a-b-5c)[/tex]If the proportion of the total disposable income spent on consumer goods and services is 91.6 percent and if consumers spend 82.0
percent of each additional dollar, what is
Instructions: Round your responses to three decimal places.
a. the APC?
b. the APS?
c. the MPC?
d. the MPS?
a) The Average Propensity to Consume (APC), rounded to three decimal places, is 0.916.
b) The Average Propensity to Save (APS), rounded to three decimal places, is 0.084.
c) The Marginal Propensity to Consume (MPC), rounded to three decimal places, is 0.820.
d) The Marginal Propensity to Save (MPS), rounded to three decimal places, is 0.180.
What do these economic indexes mean?The average propensity to consume is the ratio of consumption expenditures to the total consumers' disposable income.
The average propensity to save is the inverse of the APC. It shows the rate of or total disposable income reserved instead of being consumed.
The marginal propensity to consume is the ratio of consumption based on additional income.
The marginal propensity to save is the inverse of the MPC, showing the percentage of the additional income saved instead of being consumed.
APC = 91.6%
= 0.916
APS = 1 - APC
= 0.084 (1 - 0.916)
MPC = 82%
= 0.820
MPS = 1 - MPC
= 0.180 (1 - 0.820)
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Solve the problems fill in the blanks show you work I NEED HELP!
The fill in the blanks (that uses division) can be filled as -1.2([tex](\frac{2}{5} )[/tex] ÷ -2, -0.48÷-2 and 0.24.
According to the question,
We have the following information:
-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2
Now, we have to solve this problem and fill the blanks at the same time.
Now, the first step would be to write the question.
So, for the first blank we have:
-1.2 [tex](\frac{2}{5} )[/tex] ÷ -2
Now, the required number is (2/5).
Now, the next step is to multiply -1.2 with 2/5:
-2.4/5
-0.48
So, the second blank can be filled by -0.48.
Now, the third step would be to divide -0.48 by -2:
-0.48÷-2
0.24
So, the next blank can be filled by 0.24.
Hence, the numbers in the blanks are [tex]\frac{2}{5}[/tex], -0.48 and 0.24 respectively.
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Given that f ( x ) = 3 x − 6 f ( x ) = 3 x - 6 and g ( x ) = 2 − x 2 g ( x ) = 2 - x 2 , calculate
If it is given f(x) = 3x− 6 and g(x) = 2- x² then f(g(x)) = -6x².
To solve this problem we have to know more about mathematical functions.
What is a mathematical function?
A mathematical function is a such type of mathematical device as it establishes a special type of relation which provides an output concerning an input.
Example: f(x) = x²+ 2 where f(x) is a function of x where x is the input. If x = 3 then the output value of f(x) = 3²- 2 = 9-2 = 7.
Here we have to calculate, f(g(x)) where f is a function of g(x) and g(x) is a function of x.
g(x) = 2- x².
f(x) = 3x - 6.
Therefore,
f(g(x)) = 3( 2- x² ) - 6. [where g(x) = 2- x²]
So, f(g(x)) = 3( 2- x² ) - 6 = 6 -6x² -6 = -6x²
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The complete question:
Given that f(x) = 3x − 6 and g(x) = 2 - x² , calculate f(g(x))
#3 TV Aspect RatioUsing your knowledge of aspect ratios, find the difference between the actualscreen size or area of an older style TV with an aspect ratio of 4:3 and a newer TVwith an aspect ratio of 16:9. Assume that both TV's are 52 inches in height. Whatis the difference in the areas of the two TV's? (show all work and justify youranswer) (8 points)
3:4 ratio
height: 52 in
width: height * 4/3 = 52*4/3 = 208/3 in
Area of the TV: height*width = 52*208/3 = 3605 1/3 square inches
9:16 ratio
height: 52 in
width: height * 16/9 = 52*16/9 = 832/9 in
Area of the TV: height*width = 52*832/9 = 4807 1/9 square inches
Then, the difference in the areas is: 4807 1/9 - 3605 1/3 = 1201 7/9 square inches