Answer:
4 degrees decrease every hour
Step-by-step explanation:
90 - 74 = 24 change in 4 hours
24/6 = 4
Consider the feasible region in the xy-plane defined by the following linear inequalities.
x≥0
y ≥0
x ≤ 10
x +y≥ 5
x + 2y ≤ 18
Part 2 Exercises:
1. Find the coordinates of the vertices of the feasible region. Clearly show how each vertex is determined and which lines form the vertex.
2. What is the maximum and the minimum value of the function Q = 60x+78y on the feasible region?
Answer:
1. (0,5), (0,9), (10,4), (10,0), (5,0)
2. [tex]Q_{max}=912[/tex]
[tex]Q_{min}=300[/tex]
Step-by-step explanation:
1.
In order to determine the coordinates of the vertices of the feasible region, we must first graph each of the inequalities. The feasible region is the region where all the inequalities cross each other. In this case it's the region shaded on the attached picture.
The first point is the intercept between the equations x=0 and x+y=5 so in order to find this first coordinate we need to substitute x=0 and solve for y.
0+y=5
y=5
(0,5)
The next point is the intercept between the equations x=0 and x+2y=18, so again, we substitute x for zero and solve for y:
0+2y=18
[tex]y=\frac{18}{2}[/tex]
y=9
(0,9)
The next coordinate is the intercept between the lines x=10 and x+2y=18, so we substitute x for 10 and solve for y:
10+2y=18
2y=18-10
2y=8
[tex]y=\frac{8}{2}[/tex]
y=4, so the oint is
(10,4)
The next point is the intercept between the lines x=10 and y=0, so the point is:
(10,0)
The final point is the intercept between the equations: y=0 and x+y=5. We substitute y for zero and solve for x:
x+0=5
x=5
so the point is:
(5,0).
2. In order to determine the maximum and minimum value of the function Q=60x+78y on the feasible region, we must evaluate it for each of the points found on part 1.
(0,5)
Q=60(0)+78(5)
Q=390
(0,9)
Q=60(0)+78(9)
Q=702
(10,4)
Q=60(10)+78(4)
Q=912
(10,0)
Q=60(10)+78(0)
Q=600
(5,0)
Q=60(5)+78(0)
Q=300
So now we compare the answers and pick the minimum and maximum results.
We get that:
[tex]Q_{max}=912[/tex]
when x=10 and y=4
and
[tex]Q_{min}=300[/tex]
When x=5 and y=0
The feasible region is the possible set of a constraint
The vertices are: [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]The maximum and the minimum values are 702 and 300, respectively.(a) The coordinates of the vertices at the feasible region
The constraints are given as:
[tex]\mathbf{x \ge 0}[/tex]
[tex]\mathbf{y \ge 0}[/tex]
[tex]\mathbf{x \le 0}[/tex]
[tex]\mathbf{x + y\ge 5}[/tex]
[tex]\mathbf{x + 2y\ge 18}[/tex]
See attachment for the graph of the constraints
From the graph, the vertices are:
[tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex]
(b) The minimum and the maximum values of objective function Q
The objective function is:
[tex]\mathbf{Q=60x +78y}[/tex]
Substitute [tex]\mathbf{(x,y) \to (0,5), (0,9), (5,0)}[/tex] in Q
[tex]\mathbf{Q=60(0) +78(5) = 390}[/tex]
[tex]\mathbf{Q=60(0) +78(9) = 702}[/tex]
[tex]\mathbf{Q=60(5) +78(0) = 300}[/tex]
Hence, the maximum and the minimum values are 702 and 300, respectively.
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Notebooks are priced 3.20 for 4 notebooks Pencils are priced 4.80 for 12 pencils, write a rate
Answer:
$0.80 per notebook
$0.40 per pencil
Step-by-step explanation:
To find the rate, we need to determine how much each item costs. That is, the cost per item.
Given that,
4 notebooks = $3.20
The cost of 1 notebook/rate = [tex] \frac{3.20}{4} = 0.80 [/tex]
Rate = $0.80 per notebook
Given that,
12 pencils = $4.80
The cost of 1 notebook/rate = [tex] \frac{4.80}{12} = 0.40 [/tex]
Rate = $0.40 per pencil.
Two particles are projected simultaneously towards each other from opposite ends of a straight
horizontal tube. One particle travels 97 cm in the 1st 2 seconds, 93 cm in next 2 seconds , 89 cm in
another next 2 seconds, etc. The other particle travels 49 cm in the 1st 2 seconds, 47 cm in the next 2
seconds , 45 cm in another next 4 seconds, etc. Find how long it takes for the particles to meet and
hence, determine the distances travelled by each particle.
Answer:
The problem with this question is that it is missing an important number, which is the length of the tube. Assuming that the tube is 10 meters long (=1,000 centimeters long)
time (in distance traveled distance traveled distance
seconds) by particle A in cms by particle B in cms between both
particles in cms
1 97 49 854
2 93 47 714
3 89 45 580
4 85 43 452
5 81 41 330
6 77 39 214
7 73 37 104
8 69 35 0
After 8 seconds both particles should meet. Particle A traveled 664 centimeters and particle B traveled 336 centimeters.
Factor using the identity:
a3 + b3 = (a + b)(a? - ab + b2)
Z3+8
Question o A car traveled 60 miles in 0.75 hours. How fast was the car traveling in miles per hour? miles per hour At that rate, how long will it take her to go 72 miles? Round your answer to the nearest tenth of an hour. "hours.
Answer:
80miles/hr
0.9hr
Step-by-step explanation:
Given parameters:
Distance traveled = 60miles
Time taken = 0.75hrs
Unknown:
Speed of the car = ?
Time it will take to cover 72miles = ?
Solution:
Speed is the distance divided by time;
Speed = [tex]\frac{distance}{time}[/tex]
Insert the parameters and solve;
Speed = [tex]\frac{60}{0.75}[/tex] = 80miles/hr
Time taken;
Time = [tex]\frac{distance}{speed}[/tex] = [tex]\frac{72}{80}[/tex] = 0.9hr
Which number is additive inverse of -4 1/4
Answer:
4 1/4
Step-by-step explanation:
the additive inverse is a number that when you add it with the number you already had, makes 0
-2 is the additive inverse of 2
so 4 1/4 is the inverse of -4 1/4
Suppose that you are in charge of organizing the music for a school dance. You survey five of your friends about the kinds of music they like. a) Did you use a census or a sample? b) Will your decisions based on this survey be biased? Why or why not? Answer both a) and b) in the space below
Answer:
A. Sample because census is an official count of POPULATION B. No it will not be biased because it is fair.
Step-by-step explanation:
What is the y-intercept of the function fx) = -2/9x + 1/3
O -2/9
O- -1/3
O- 1/3
O-2/9
Answer:
Step-by-step explanation:
The answer is 1/3
Determine the probability p(1 or fewer) for a binomial experiment with trials and the success probability . Then find the mean, variance, and standard deviation.
Complete Question
Determine the probability P(1 or fewer) for a binomial experiment with n = 16 trials and the success probability p = 0.2. Then find the mean, variance, and standard deviation
Answer:
The probability is [tex]P(X \le 1 ) = 0.0484[/tex]
The mean is [tex]\mu = 3.2[/tex]
The variance is [tex]\sigma ^2 =2.56[/tex]
The standard deviation is [tex]\sigma =1.6[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.2
The sample size is n = 16
Generally this experiment follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
and the probability distribution function for binomial distribution is
[tex]P(X = x) = ^{n}C_x * p^x * (1- p)^{n-x}[/tex]
Here C stands for combination hence we are going to be making use of the combination function in our calculators
Generally the the probability P(1 or fewer) is mathematically represented as
[tex]P(X \le 1 ) = P(X = 0 ) + P(X = 1 )[/tex]
=> [tex]P(X \le 1 ) = [^{15}C_0 * (0.2)^0 * (1- 0.2)^{15-0}] + [^{15}C_1 * (0.20)^1 * (1- 0.20)^{15-1} ][/tex]
=> [tex]P(X \le 1 ) = [1 * 1* 0.0352 ] + [15 * 0.20 * 0.0439][/tex]
=> [tex]P(X \le 1 ) = 0.0484[/tex]
Generally the mean for this experiment is mathematically represented as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 16 * 0.2[/tex]
=> [tex]\mu = 3.2[/tex]
Generally the variance is mathematically represented as
[tex]\sigma ^2 = n * p * (1- p )[/tex]
=> [tex]\sigma ^2 = 16 * 0.2 * (1- 0.2)[/tex]
=> [tex]\sigma ^2 =2.56[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\sigma ^2 }[/tex]
=> [tex]\sigma =1.6[/tex]
Which method could be used to prove they are similar?
1.5
3
4.5
Jy
Answer:
Prove what is similar?????
# 6
Write an equation in slope-intercept
form to represent the line
perpendicular to 2x + 10y = 3 passing
through the point (2, 3).
O y = 1/5x+3/10
O y = 5x + 13
y = 5x - 7
O y = -1/5x + 17/5
9514 1404 393
Answer:
y = 5x - 7
Step-by-step explanation:
We can make an equation for the perpendicular line by swapping the x- and y-coefficients, negating one of them. Then we can use that form with the given point to see what the constant is.
10x -2y = ...
Removing a common factor of 2 gives ...
5x -y = 5(2) -(3) = 7 . . . . using (x, y) = (2, 3), we can find the constant
Solving for y, we get ...
5x -7 = y . . . add y-7
y = 5x -7 . . . write in the desired form
Lizzie has 4 pounds of hamburger. She is making her famous 2/3 pound hamburgers for dinner. How many hamburgers can she make? pleeeeeeeeeeeeeease helppppppppppppp
Answer:
6
Step-by-step explanation:
Total meat: 4 lb.
Each hamburger: 2/3 lb.
How many 2/3 lb portions can you make with 4 lb?
This is a division problem.
4 / (2/3) = 4/1 * 3/2 = 12/2 = 6
Answer: 6 hamburgers
Q6 Paul owns a supermarket. He discovered that on average his workers sell 500 pints of milk a
day with a standard deviation of 50 pints.
(a) If the supermarket has 600 pints in stock at the beginning of a day, what is the probability
that it will run out of milk.
(b) How many pints should the supermarket stock if it wants the probability of running out to
be 0.052
What is the constant of proportionality in the equation y=2xy
Answer:
2 is the constant of proportionality in the equation y = 2x .
Step-by-step explanation:
Definition of constant of proportionality
When two variables are directly proportional to each others .
Let us assume that u and v .
u \propto vu∝v
Than the equation becomes u= kv
Where k is called the constant of proportionality .
Thus in the question x and y are proportional variables .
i.e
y \propto xy∝x
y = kx
Where k is called the constant of proportionality .
Compare the equation y = kx with y=2x .
Thus
k = 2
Therefore 2 is the constant of proportionality in the equation y = 2x
the explanation is not mine only the answer
The selling price of lumber at Home Depot is $4,000, percent markup on cost is 30%. Calculate the actual cost. (Round your answer
to the nearest cent.)
Step-by-step explanation:
Selling Price=$4000
Profit Percent=30%
Cost Price;
[tex] \frac{100}{100 + pp} \times 4000 [/tex]
[tex] \frac{100}{100 + 30} \times4000 [/tex]
[tex] \frac{100}{130} \times 4000 [/tex]
[tex] \frac{10}{13} \times 4000[/tex]
[tex] \frac{40000}{13} [/tex]
$3,076.923
=$3,077.000
I am not really Good at rounding forgive me Confirm from someone please.
two walkers 16 miles apart travel toward each other. one travel 3 miles per hour and the other 4 miles per hour. if the latter is delayed 3 hours how many hours before they meet
I WILL REWARD BRAINLIEST OKAY IM BEGGING YOU HELP ME
IN THAT PHOTO WHAT ARE THE X AND Y INTERCEPTS!?! WAIT DON'T LOOK AT THE PHOTO YET!!
PLEASE LOOK AT THIS EXAMPLE:
X intercept: ( ), ( )
Y intercept: ( ), ( )
NOW LOOK. AT THE PHOTO PLEASE!!
Answer:
X-intercept: -10
Y-intercept: -45
(-10),(-45)
Step-by-step explanation:
Hop this helped, Have a Wonderful Day!!
1.23, 1.03, 0.031
from smallest to largest
Answer:
the samllest is 0.031 after that is 1.03 and the largest is 1.23
on a number line 0 comes before 1 so 0.30 will naturally be smaller and between 1 and 2, 1.03 comes before 1.23
A consistent dependent system of equations is a system with
Answer:
Systems of equations can be classified by the number of solutions. , . , . If a consistent system has an infinite number of solutions, it is dependent.
Find the error in the calculations below, if there is one:
Answer:
Between line 1 and 2
Step-by-step explanation:
4x³ +2x²- 6x+ 3 (Line 1)
note that +3 can be written as -(-3), giving us:
4x³ +2x² -6x - (-3)
if we group the first two terms and the last two terms, we will get
(4x³ +2x²) + [ -6x - (-3) ] (factor out 2x from first group and -3 from second group)
= 2x²(2x +1) -3(2x - 1 )
if we compare this with (Line2) we can see that the difference is in the sign of the last term inside the second group. Hence this is where the mistake is made Between line 1 and 2
By applying an straightforward approach we conclude that the error in the calculations shown in the statement occurred from line (1) to line (2).
How to find a procedure error by applying algebra
A straightforward approach consists in applying algebraic definitions and theorems to find any difference with respect to the procedure shown on the statement. Our procedure is shown below:
4 · x³ + 2 · x² - 6 · x + 3 Given2 · x² · (2 · x + 1) - 3 · (2 · x - 1) Associative, commutative and distributive propertiesBy applying an straightforward approach we conclude that the error in the calculations shown in the statement occurred from line (1) to line (2).
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Work out the number of sides of a regular polygon, if the interior angle is 177
Answer:
Let the number of sides be x.
One interior angle is 177°
One exterior angle is 180-177 (linear pair)
= 3°
Exterior angle × Number of sides = 360
3*x = 360
x = 360/3
x = 120
Therefore, the polygon has 120 sides.
If the interior angle of a polygon is 177° then the number of sides is 120.
What is a polygon?A polygon is a closed more than two-sided and can be made up of a finite number of straight line segments and is a type of planar figure in geometry.
Each line of the polygonal circuit's segments are referred to as its edges or sides.
We know, Interior angle = 180(n-2)/n, where 'n' is the number of sides.
Given, A regular polygon has interior angles of 177°.
Therefore,
177 = 180(n-2)/n.
177n = 180n - 360.
- 3n = - 360.
3n = 260.
n = 360/3.
n = 120.
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consider f(x) = x^3 + x^1 would the function be even, odd, neither,or not enough information to determine
Answer:
The function is odd
Step-by-step explanation:
Even functions and odd functions are those which satisfy particular symmetry relations as follows:
f(x) is even if f(-x) = f(x)
f(x) is odd if f(-x) = -f(x)
Not all functions are eligible for being even or odd.
Considering
[tex]f(x)=x^3+x^1[/tex]
Let's find f(-x)
[tex]f(-x)=(-x)^3+(-x)^1[/tex]
Since [tex](-x)^3=(-x)(-x)(-x)=-x^3[/tex]
And [tex](-x)^1=-x:[/tex]
[tex]f(-x)=-(x)^3-(x)^1[/tex]
Factoring by -1:
[tex]f(-x)=-((x)^3+(x)^1)[/tex]
The expression in parentheses if f(x), thus:
[tex]f(-x)=-f(x)[/tex]
And the function is odd.
If a lost male child is found who is 145 cm tall, determine an interval of likely ages for the child. Give whole numbers.
≤ age ≤
We can deduce here that for a height of 145 cm, a likely interval of ages could be: 12 ≤ age ≤ 15
What is inequality?In mathematics, an inequality is a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than or less than another. It represents a comparison or a difference in values.
For a height of 145 cm, a likely interval of ages could be:
12 ≤ age ≤ 15
This range assumes that the child's height falls within the average height range for boys aged 12 to 15 years. However, it's important to consider that individual variations and growth patterns can influence a child's height, so this interval should be interpreted with caution.
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What is the value of x?
Answer:
I believe it is x+3..
Step-by-step explanation:
Answer:
x = 5
which agrees with the first answer option listed
Step-by-step explanation:
Use the proportionality associated with similar triangles, considering that the larger triangle has sides:
x + (x+5) = 2 x + 5
and
(x+1) + (x-2) = 2 x - 1
and the smaller triangle:
x and (x-2)
The we build the following proportionality:
(2 x + 5) / x = (2 x - 1) / (x - 2)
cross multiply to eliminate denominators:
(2 x + 5) (x - 2) = x (2 x - 1)
operate:
2 x^2 - 4 x + 5 x -10 = 2 x^2 - x
combine like terms:
2 x^2 + x -10 = 2 x^2 - x
subtract 2 x^2 from both sides:
x - 10 = - x
add x to both sides:
2 x -10 = 0
add 10 to both sides
2 x= 10
divide both sides by 2:
x = 5
which agrees with the first answer option listed
i need help asap D:
Answer:
F
Step-by-step explanation:
decimals are percentages and then fraction can be reduced into percentages so I did the math on all of them and f is the highest score
Help me plz I need help
1. Lisa is saving 850 that she received from her grandmother. She earns 56 each time she walks her neighbor's dog,
which she also saves
Which function can be used to find 1, the amount of money Lisa Will have saved after walking the neighbor's dog d
times?
A f = 500 + 6
OB. f = -6d + 50
Oc. f = - bd + 44
OD. f = bd + 50
Answer:
d
Step-by-step explanation:
6(d) d=days
50 =how much she already got
6times how many d plus fifty is equal to number d
need someone’s help with this please!!!
Answer:
Option 3
Step-by-step explanation:
Since lines a and b are intersecting, x+5=2x-5. Because they are vertical angles.
x+5=2x-5
2x-x=5+5
x=10
HELP ME FOR 30 POINTS!!!!!!
Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation for the water level, L, after d days.
Answer:26 in 16 days
Step-by-step explanation:
Work out the size of angle z
image included
Answer:
no image
Step-by-step explanation:
