By graphing the system of constraints, find the values of x and y that maximize the objective function. 25<=x<=75 y<=110 8x+6y=>720 y=>0 minimum for c=8x+5y a. c=100 b. c=225 2/3 c. c=633 1/3 d. c=86 2/3
Answers
x = 25
x = 75
y = 110
6y = 720 - 8x
and C = 8x + 5y
The minimum point for C is the point of intersection between 8x + 6y = 720 and x = 25
Substitute x = 25 into 8x + 6y = 720 we have:
8(25) + 6y = 720
200 + 6y = 720
6y = 720-200
6y = 520
y = ²⁶⁰/₃
Substitute x = 25 and y = ²⁶⁰/₃ into C
C = 8(25) + 5(²⁶⁰/₃) = 633¹/₃
Answer: Option C
Related Questions
Deangelo has $7 worth of dimes and quarters in a jar. He has 7 more quarters than dimes. How many of each coin does he have? Enter your answers in the boxes. _dimes and _ quarters
Answers
q = d + 7
0.10d + 0.25(d + 7) = 7
0.10d + 0.25d + 1.75 = 7
0.35d = 7 - 1.75
0.35d = 5.25
d = 5.25 / 0.35
d = 15 <=== there are 15 dimes
q = d + 7
q = 15 + 7
q = 22 <== there are 22 quarters
Answer:
There are 15 dimes and 22 quarters in the jar.
Step-by-step explanation:
Deangelo has $7 worth of dimes and quarters in a jar.
Let he has d number of dimes and q number of quarters in a jar.
0.10d + 0.25q = 7 -------(1)
He has 7 more quarters than dimes.
q = d + 7 -------(2)
We replace the value of y from equation 2 in the equation 1
0.10d + 0.25(d + 7) = 7
0.10d + 0.25d + 1.75 = 7
0.35d = 7 - 1.75
0.35d = 5.25
d = [tex]\frac{5.25}{0.35}=15[/tex] dimes
Now we put this value in the equation number 2
q = 15 + 7 = 22
Therefore, number of dimes and quarters are 15 and 22 respectively.
How many feet does it take to go from 0 to 60?
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Calculus: Help ASAP
Using n = 4 equal-width rectangles, approximate the integral from negative 2 to 2 of the quantity x cubed plus 8, dx. Use the mid-point of each sub-interval to determine the height of each rectangle.
Answers
Answer:
32
Step-by-step explanation:
To solve this, you need to start by finding the width of the rectangles and the midpoints. If n=4, b=2, a=-2, and the width of each triangle is delta x = b-a / n, then each width is equal to 1 and there will be four midpoints (you can also tell the amount of midpoints by n=4). These midpoints are -1.5, -0.5, 0.5, and 1.5. The height of each of the rectangles is going to be equal to f(x*k), where x*k is the specific mid point. This means that you need to find f(-1.5), f(-0.5), f(0.5), and f(1.5). When putting these into the function you will get 4.625, 7.875, 8.125, and 11.375. Seeing as the Riemann Sum formula says the summation of f(x*k) * delta x, multiply each of the heights by the width of 1 and then add all of the values together. When you do this you will get 4.625 + 7.875 + 8.125 +11.375 which all totals to 32. This means that the approximation of the given integral is 32.
Which of the following statements must be true about this diagram? Check all that apply.
A. m1 + m2 = m4
B. m1 + m2 = m3
C. m4 is greater than m2
D. m4 is greater than m1
E. m3 is greater than m2
F. m2 + m3 = m4
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What is the probability that the next flood will occur four years from now?
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3x+1<2x-3 what is x
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3x less 2x-4
x less -4
Rita had $300.she spent 1/3 of her money on notebooks and 1/4 of the remainder on staionary items.how much money does she have left
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The sum of two numbers is 28 and their difference is 4. What are the numbers?
Answers
x-y=4----(b)
(a)-(b)
2y=24
y=24/2=12----(c)
use (c) in (b)
x=4+12=16
All the best
Betsy, a recent retiree, requires $ 6 comma 000 6,000 per year in extra income. She has $ 60 comma 000 60,000 to invest and can invest in B-rated bonds paying 15 15% per year or in a certificate of deposit (CD) paying 5 5% per year. How much money should be invested in each to realize exactly $ 6 comma 000 6,000 in interest per year?
Answers
Then,
x + y = 60,000 . . . . . . . (1)
0.15x + 0.05y = 6,000 . (2)
Multiplying the first equation by 0.15 gives:
0.15x + 0.15y = 9,000 . (3)
Subtracting equation (2) from equation (3) gives:
0.1y = 3,000
y = 3,000 / 0.1 = 30,000
From equation (1):
x + 30,000 = 60,000
x = 60,000 - 30,000 = 30,000
Therefore, the amount of money that should be invested in each to realize exactly $6,000 in interest per year is $30,000 each.
plzz help me i hate word problems
Answers
Convert the base-6 number 12345 to decimal
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A decimal is a way of expressing numbers that are not whole numbers, but rather include a fractional or decimal part. The decimal equivalent of the base-6 number 12345 is 1415.
To convert a base-6 number to decimal, we multiply each digit by its corresponding weight and add the products together. The weights are 6 to the power of the digit's position, starting from the rightmost digit.
For example, to convert the base-6 number 12345 to decimal, we would do the following:
(1 * 6^4) + (2 * 6^3) + (3 * 6^2) + (4 * 6^1) + (5 * 6^0)
= 1296 + 72 + 18 + 24 + 5
= 1415
Therefore, the decimal equivalent of the base-6 number 12345 is 1415.
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An experimenter is randomly sampling 3 objects in order from among 48 objects. what is the total number of samples in the sample space?
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Thanks (:
Need help with perfect square! 40 points
Answers
to be a perfect square C needs to be a number that can be squared
and the middle term needs to be able to be multiplied by 2 or -2 of the square of the 3rd term (C)
so in this case C = 25
25 can be squared ( square root of 25 is 5)
square root of 25 (5) times 2 = 10 ( 2nd term)
C = 25
It is the morning of the sandcastle-building competition at the beach. Dory has been looking forward to this event for months. According to her weather app, there is an 80% probability of high winds in her area today. Which of the following BEST describes the MOST likely way the probability was determined?
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Answer:
B) Historically, in this area, high winds occur 80% of the time on days with similar meteorological conditions as today.
Explanation:
Meteorologists calculate the probability of certain weather conditions by dividing specific outcomes by the total number of possible outcomes. For example, to find out the probability of raining on a certain date, meteorologists use a large database which contains information about how many times it rained when the meteorological conditions were similar. If historically it rained during 5,000 days out of 8,000 total days that had a similar meteorological condition, then the probability of rain will be 5,000 / 8,000 = 62.5%
The correlation coefficient (r) between the number of miles driven x and the number of gallons of gasoline used y is 0.925
What percent of the variation in the number of gallons of gasoline can be explained by differences in the number of miles driven?
7.5%
14.4%
85.6%
92.5%
Answers
Answer:
OptionC
Step-by-step explanation:
Given that the correlation coefficient (r) between the number of miles driven x and the number of gallons of gasoline used y is 0.925
Coefficient of determination = square of r
= 0.8556
=85.6%
Hence the percent of the variation in the number of gallons of gasoline can be explained by differences in the number of miles driven is 85.6%
Option C
For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 7, then x2 = 49.
a. If x2 = 49, then x = 7. True; x^2 = 49 if and only if x = 7.
b. If x2 = 49, then x = 7. True; x = 7 if and only if x^2 = 49.
c. If x2 = 49, then x = 7. False
d. If x2 = 7, then x = 49. False
Answers
The converse of 'If x = 7, then x^2 = 49' is 'If x^2 = 49, then x = 7' which is considered true in the real number system. So, these can be combined as a biconditional: 'x = 7 if and only if x^2 = 49.'
The problem involves understanding the conditional, converse, and biconditional statements in mathematics logic. The initial conditional statement is 'If x = 7, then x^2 = 49.' We then need to assess the converse of this, which would be 'If x^2 = 49, then x = 7.' This converse statement is actually true, though it’s implied that we are dealing with real numbers. That’s because, in the real number system, when x^2 = 49, then x could technically be either 7 or -7.
However, because the original statement specified that x = 7 directly, we can say that both the conditional and converse are true. Therefore, these two statements can be combined as a biconditional. The biconditional statement, which is a statement that is accurate if both the conditional and converse are true, would be: 'x = 7 if and only if x^2 = 49.'
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There are 15 boys and 20 girls in ms.smith's algebra class. what is the ratio of boys to girls
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HELP PLEASE!
Which of the following possibilities will form a triangle?
Side = 10 cm, side = 5 cm, side = 6 cm
Side = 10 cm, side = 6 cm, side = 3 cm
Side = 11 cm, side = 5 cm, side = 6 cm
Side = 11 cm, side = 5 cm, side = 5 cm
Answers
Answer:
d
Step-by-step explanation:
Side = 11 cm, side = 5 cm, side = 5 cm
If a car travels 30 mph for 1 hour, and 40 mph for 1 hour, what is the average velocity of the trip?
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Can we obtain a diagonal matrix by multiplying two non-diagonal matrices? give an example
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Consider the matrix multiplication below
[tex] \left[\begin{array}{cc}a&b\\c&d\end{array}\right] \left[\begin{array}{cc}e&f\\g&h\end{array}\right] = \left[\begin{array}{cc}a e+b g&a f+b h\\c e+d g&c f+d h\end{array}\right] [/tex]
For the product to be a diagonal matrix,
a f + b h = 0 ⇒ a f = -b h
and c e + d g = 0 ⇒ c e = -d g
Consider the following sets of values
[tex]a=1, \ \ b=2, \ \ c=3, \ \ d = 4, \ \ e=\frac{1}{3}, \ \ f=-1, \ \ g=-\frac{1}{4}, \ \ h=\frac{1}{2}[/tex]
The the matrix product becomes:
[tex] \left[\begin{array}{cc}1&2\\3&4\end{array}\right] \left[\begin{array}{cc}\frac{1}{3}&-1\\-\frac{1}{4}&\frac{1}{2}\end{array}\right] = \left[\begin{array}{cc}\frac{1}{3}-\frac{1}{2}&-1+1\\1-1&-3+2\end{array}\right]= \left[\begin{array}{cc}-\frac{1}{6}&0\\0&-1\end{array}\right][/tex]
Thus, as can be seen we can obtain a diagonal matrix that is a product of non diagonal matrices.
[tex] \left[\begin{array}{ccc}1&3&4\\0&-8&-9\\0&0&- \frac{55}{8} \end{array}\right] \cdot \left[\begin{array}{ccc}1&-3&- \frac{5}{8} \\0&1&- \frac{9}{8} \\0&0&1\end{array}\right] = \left[\begin{array}{ccc}1&0&0\\0&-8&0\\0&0&- \frac{55}{8} \end{array}\right] [/tex]
Jessica can paint a room in 12 hours. If Mary helps, it takes them 10 hours. Without help how long would it take for mary to finish this job?
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Which statement is always true for any parallelogram?
a. all four angles are right angles
b. the diagonals bisect each other
c. all four sides are congruent
d. the diagonals are congruent
Answers
the diagonals bisect each other- correct
all four sides are congruent - wrong that would be a Rhombus
the diagonals are congruent - wrong, this is the case in a rectangle, but in a parallelogram, because of the angle one side has to be shorter than the other
so b. the diagonals bisect each other is always true and therefore the solution
The statement that is always true for any parallelogram is that the diagonals bisect each other.
Explanation:The statement that is always true for any parallelogram is b. "the diagonals bisect each other". To bisect means to divide into two equal parts. In a parallelogram, the diagonals (the line segments connecting opposite corners) will always divide each other into two equal parts. This can be proven by using properties of parallel lines and alternate interior angles.
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Jeff bought 10 cookies and ate 4 of them. He ate what percent of the cookies.
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10-4=6
4=40%
[tex] \frac{4}{10} = \frac{x}{100} \ To\ help\ us\ find\ the\ percentage.\\ Cross\ multiply\ to\ give\ you\ 400 = 10x\\ Divide.\ 400/10 = x\\ X = 40.\\ [/tex]
So, 40% was eaten
If a barber is capable of cutting the hair of 35 people per day and he works 7 days per week, how many haircuts could he give during the months of april, may, and june?
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April=1,225
May=1,225
All June April and May is 3,675 haircuts
a group of 150 students were asked to identify 55 flowers. the relative frequency table shows the results. about how many students identified at least 35 flowers?
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Answer:
55 Students identified at least 35 flowers.
Step-by-step explanation:
Here we have to ask at least 35 flowers, so there are only 3 classes. i.e. 35 - 41, 42 - 48, 49 - 55.
Thus, Number of Students identified at least 35 flowers is: 5 + 31 + 19 = 55
Further, Frequency is the number of repetitions of particular observation or class.
Relative frequency is the proportion of frequency. For finding the Relative Frequency divide the frequency of that observation or class to the total frequencies.
Louisa's savings change by -$9 each time she goes bowling.in all it changed by -$99 during the summer.how many times did she go bowling in the summer?
Answers
Answer:
She went 11 times.
Step-by-step explanation:
Given,
The change in saving in each time she goes bowling = -$ 9,
If she goes t times,
The change in saving for going t times = t × change in saving in each time
= t × -9
= -9t dollars,
According to the question,
-9t = -99
[tex]\implies t=\frac{-99}{-9}=11[/tex]
Hence, she went 11 times to bowling.
What is the length of the hypotenuse of a right triangle if each of the two legs is 6 units?
Square root of 12
6
Square root of 72
36
Question
Answers
It can't be 6 because the hypotenuse cannot equal the same as the legs
It can't be 36 because then one of the legs would have to be 35.5 in length
It can't be the square root of 12 because that would mean its length is 3.46
how to determine if a number is prime or composite
Answers
Answer:
Look at how many factors it has.
If it has 2, it's prime.
If it has 3 or more, it's composite.
Step-by-step explanation:
I hope it helps!
An equilateral triangle is also a(n) _____ triangle. obtuse right isosceles scalene
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Figure JKLM is a kite. What is the measure of angle K?
Answers
118 + 78 + 46 = 242
3 inside angles should equal 360 degrees
so angle K = 360 - 242 = 118 degrees
Answer:
(B) the measure of angle K=118°
Step-by-step explanation:
From the given figure, ∠KJM=78°, ∠JML=118°,∠MLK=46°
Now,since JKLM is a quadrilateral and we know that sum of all the angles of a quadrilateral is =360°, thus
∠KJM+∠JML+∠MLK+∠JKL=360°
⇒78°+118°+46°+∠JKL=360°
⇒242°+∠JKL=360°
⇒∠JKL=360°-242°
⇒∠JKL=118°
Thus, the measure of angle K=118°