Answers
Answer:
The maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Step-by-step explanation:
Given;
F = 4y - 3x
The function is subject to y ≤ 2x - 1,
y ≥ -2x + 3,
x ≤ 3
y ≤ 2x - 1
- ( y ≥ -2x + 3)
-------------------
0 ≤ 4x - 4
4 ≤ 4x
1 ≤ x
thus, 1 ≤ x ≤ 3
When x = 3
y ≤ 2x - 1 ⇒ y ≤ 2(3) - 1, ⇒ y ≤ 5
y ≥ -2x + 3, ⇒ y ≥ -2(3) + 3, ⇒ y ≥ - 3
thus, -3 ≤ y ≤ 5
When x = 1
y ≤ 2x - 1 ⇒ y ≤ 2(1) - 1, ⇒ y ≤ 1
y ≥ -2x + 3, ⇒ y ≥ -2(1) + 3, ⇒ y ≥ 1
when x = 1 and y = 1
F = 4(1) - 3(1)
F = 1
when y = -3, and x = 3
F = 4(-3) - 3(3)
F = -12 - 9
F = - 21
When y = 5 and x = 3
F = 4(5) - 3(3)
F = 20 - 9
F = 11
Therefore, the maximum value of the function = 11, at x = 3 and y = 5
The minimum value of the function = -21, at x = 3 and y = -3
Related Questions
convert 1.5% to decimal and a fraction. Show and explain your method
Answers
Answer:
0.015 and 3/200.
Step-by-step explanation:
1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.
0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.
A rectangle is drawn so the width is 6 inches longer than the height. If the rectangle's diagonal measurement is 27 inches, find the height.
Give your answer rounded to 1 decimal place.
Answers
Answer:
height = 3
Step-by-step explanation:
x(x+6) = 27
x^2 + 6x - 27 = 0
(x+9)(x-3) = 0
x = 3
Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1800 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 2004?
Answers
Answer:
The people dies in 2004 by aids are 413042853.4
Step-by-step explanation:
growth factor = 1.8
People died in 1983 = 1800
Let the people dies in 2004 is P.
Time, t = 2004 - 1983 = 21
So,
[tex]P = 1800 \times (1.8)^{21}\\\\P = 413042853.4[/tex]
Use the discriminant to determine how many and what kind of solutions the quadratic equation 2x^2 - 4x = -2 has.
Answers
Answer:
We can use three solution and they are
(1)completing the square
(2)quadratic formula
(3) factorisation method
The quadratic equation 2x^2 - 4x = -2 has two values .
What is quadratic equation ?According to our definition, a quadratic equation is one with degree 2, implying that its maximum exponent is 2. A quadratic has the standard form y = ax2 + bx + c, where a, b, and c are all numbers and a cannot be zero. All of these are examples of quadratic equations: y = x^2 + 3x + 1.Kind of solutions -(1)completing the square
(2)quadratic formula
(3) factorization method
Given,
quadratic equation 2x^2 - 4x = -2
2x² - 4x + 2 =0
Now solve this equation by factor,
2x² - 4x + 2 = 0
2x² - ( 2+2)x +2 = 0
2x² - 2x -2x + 2 = 0
2x(x- 1 ) -2 ( x -1) = 0
(2x - 2) ( x- 1) =0
2x - 2 = 0 or x - 1 = 0
x = 1 or x = 1
So, this equation has 2 value of x.
Learn more about quadratic equation brainly.com/question/2263981 here
#SPJ2
A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5 with known variance σ. What is the critical value for the test statistic for the significance level of 0.010
Answers
Answer:
The critical value is [tex]Z_c = -2.327[/tex]
Step-by-step explanation:
A hypothesis will be used to test that a population mean equals 5 against the alternative that the population mean is less than 5
Test if the mean is less than a value, so a one-tailed hypothesis test is used.
Known variance σ.
This means that the z-distribution is used to solve this question.
What is the critical value for the test statistic for the significance level of 0.010?
Z with a p-value of 0.01, so, looking at the z-table, [tex]Z_c = -2.327[/tex]
Identify the domain of the table of values shown
Answers
Answer:
{-6,0,2,4}
Step-by-step explanation:
evaluate the expression when x=7 and y= -2 -x+8y
Answers
Answer:
y=-2
Step-by-step explanation:
y=-2*-7*+8y
y= 14+8y
-7y=14
y=-2
In a survey of 302 registered voters, 167 of them wished to see Mayor Waffleskate lose her next election. Find a point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated.
Answers
Answer:
A point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated is of 0.553.
Step-by-step explanation:
Point estimate:
The point estimate of a proportion is the sample proportion(number of desired outcomes divided by the number of total outcomes).
Find a point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated.
167 out of 302. So
[tex]p = \frac{167}{302} = 0.553[/tex]
A point estimate for the proportion of registered voters who wish to see Mayor Waffleskate defeated is of 0.553.
Please help!! Picture included!
Answers
Answer: the answer is c
Step-by-step explanation:brainlist [tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
the amount of mil available per child in a day care centrr is given by the function m(x) =25/x, where x is the number of children and m is the quantity of available milk in liters. if 50 children are present on a day how much milk is available per child
Answers
Answer:
0.5 liters of milk are available per child.
Step-by-step explanation:
Amount of milk available per children:
The amount of milk, in liters, available for x children is given by:
[tex]m(x) = \frac{25}{x}[/tex]
50 children are present on a day
This means that [tex]x = 50[/tex]
How much milk is available per child?
This is m(50). So
[tex]m(50) = \frac{25}{50} = 0.5[/tex]
0.5 liters of milk are available per child.
Which operation will solve the following word problem? Andrea's class has 20 students and half of the students are studying math, half of these are studying word problems. How many are studying word problems?
Addition
Subtraction
Division
Multiplication
Answers
divide .2÷20 =10 10 students are Studing word problems
John's age 4 years ago, if he will be y years old in 5 years
Answers
9514 1404 393
Answer:
y -9
Step-by-step explanation:
From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.
John's age 4 years ago is y-9 years.
HELP PLEASSSSSS I will give brainlyest!!!!!!!!!!!!!!!!!!
Answers
Answer:
1/2
Step-by-step explanation:
Convert 2/3 to 4/6
Subtract: 4/6 - 1/6
You get 3/6
Simplify: 1/2
Hope this helps!
Answer: The answer is 1/2
The solution of this equation has an error. Which of the following steps has the error? 18 − (3x + 5) = 8
Step 1: 18 − 3x + 5 = 8
Step 2: -3x + 23 = 8
Step 3: -3x = -15
Step 4: x = 5
Step 1 Step 2 Step 3 Step 4. ?
Answers
Answer:
Step 1
Because the number in front of the bracket is 1 and it is also affected by the negative sign(-),5 is supposed to be negative not positive because (negative by positive is negative)
And since the first step has an error in it,the remaining steps would also be wrong.
In order to win a prize, Heather randomly draws two balls from a basket of 40. There are 25 blue balls, and the rest are green balls. Of the blue balls, 12% are winning balls. Of the green balls, 20% are winning balls. Calculate the expected number of winning balls that Heather draws.
Answers
Answer:
The expected number of winning balls that Heather draws is 0.3.
Step-by-step explanation:
The balls are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Expected value of the hypergeometric distribution:
The expected value is given by:
[tex]E(X) = \frac{nk}{N}[/tex]
Expected number of blue and green balls:
40 balls, which means that [tex]N = 40[/tex]
2 are chosen, which means that [tex]n = 2[/tex]
25 are blue, which means that [tex]k = 25[/tex]
So
[tex]E(X) = \frac{nk}{N} = \frac{25(2)}{40} = 1.25[/tex]
1.25 balls are expected to be blue and 2 - 1.25 = 0.75 green.
Of the blue balls, 12% are winning.
Of the green balls, 20% are winning.
Calculate the expected number of winning balls that Heather draws.
[tex]E_w = 1.25*0.12 + 0.75*0.2 = 0.3[/tex]
The expected number of winning balls that Heather draws is 0.3.
PRACTICE
Find and circle the verb to be in the text about
Sean Canty.
2 a Practice the verb to be.
5 b
2. We are
1.1
.... at home.
in the classroom.
3. My father ............. at work now.
4. My grandmother ....... alive.
5. It ............. Saturday today.
1. What
2
-
3. Whe
4. How
5. Wha
2h
Answers
jvdhvfggvvvbbbbbbbbb
What is the average rate of increase in enrollment
per
decade between 1950 and 2000?
Answers
Given:
The graph that represents the enrollment for college R between 1950 and 2000.
To find:
The average rate of increase in enrollment per decade between 1950 and 2000?
Solution:
The average rate of change of function f(x) over the interval [a,b] is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
So, the average rate of increase in enrollment per year between 1950 and 2000 is:
[tex]m=\dfrac{f(2000)-f(1950)}{2000-1950}[/tex]
[tex]m=\dfrac{7-4}{50}[/tex]
[tex]m=\dfrac{3}{50}[/tex]
[tex]m=0.06[/tex]
It is given average rate of increase in enrollment per year between 1950 and 2000 is 0.06.
We need to find the average rate of increase in enrollment per decade between 1950 and 2000, So, multiply the average rate of increase in enrollment per year by 10.
[tex]0.06\times 10=0.6[/tex]
Therefore, the average rate of increase in enrollment per decade between 1950 and 2000 is 0.6.
Tom's graduation picnic costs $4 for every attendee. At most how many attendees can there be if Tom budgets a total of $36 for his graduation picnic?
Answers
If Tom budgets $36 for his graduation, means that was how much that was earned.
x = log e square root e
x=
Answers
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
By definition, we have [tex]\log_a b=c\implies c^a=b[/tex].
Therefore, given [tex]\log_e \sqrt{e}=x[/tex], we have:
[tex]e^x=\sqrt{x}[/tex]
Solving, we have:
[tex]x=\boxed{\frac{1}{2}}[/tex]
(Recall that [tex]a^{(\frac{b}{c})}=\sqrt[c]{a^b}[/tex]).
Answer:
1/2
Step-by-step explanation:
Given :-
log e √e log e e ^½ 1/2 log e e 1/2 * 11/2There are 4 routes from Danbury to Hartford and 6 routes from Hartford to Springfield. You need to drive from Danbury to Springfield for an important meeting. You don’t know it, but there are traffic jams on 2 of the 4 routes and on 3 of the 6 routes. Answer the following:
a. You will miss your meeting if you hit a traffic jam on both sections of the journey. What is the probability of this happening?
b. You will be late for your meeting if you hit a traffic jam on at least one, but not both sections of the trip. What is the probability of this?
c. What is the probability that you will hit no traffic jam?
Answers
Answer:
a. P) = 0.25
b. P) = 0.25
c. P) = 0.5
Step-by-step explanation:
a) 1/4 as 1/2 x 1/2 = 1/4 = 0.25 This becomes reduced as we are multiplying one complete probability journey by another complete probability journey.
b) see above as 1/2 x 1/4 and 1/4 x 1/2 = 2.5 = 1/4 = 0.25
or we can Set to 1 and 1 - 3/4 = 1/4. = 0.25.
c) 1/2 as half of the journeys have traffic jams so its 1 - 1/2 = 1/2 = 0.5
A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 51.25 and 51.5 minutes.
Answers
Answer:
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Uniformly distributed between 47.0 and 57.0 minutes.
This means that [tex]a = 47, b = 57[/tex]
Find the probability that a given class period runs between 51.25 and 51.5 minutes.
[tex]P(c \leq X \leq d) = \frac{51.5 - 51.25}{57 - 47} = 0.025[/tex]
0.025 = 2.5% probability that a given class period runs between 51.25 and 51.5 minutes.
The function c(r)=2r+12.5 represents the cost c, in dollars, of riding r rides
at a carnival. How much does it cost to get into the carnival? *
1 point
A.$2
B. $12.50
C. $14.50
D.r
Answers
The following data were collected from a simple random sample from an infinite population.
13 15 14 16 12
The point estimate of the population standard deviation is _____.
Answers
Answer:
15
Step-by-step explanation:
HELP FAST PLEASEEEEEE
Which of the tables represents a function?
Table AInput
Output
3
1
3
4
2
3
Table BInput
Output
2
7
5
6
2
9
Table CInput
Output
1
5
7
2
7
3
Table DInput
Output
3
4
1
5
8
5
Select one:
a. Table A
b. Table B
c. Table C
d. Table D
Answers
Answer:
d.......................
The area of a rectangle is (4x2 − 49y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely.
Answers
Answer:
8x
Step-by-step explanation:
[tex](4x^{2} - 49y^{2} ) = (2x+7y)(2x-7y)[/tex]
How to find the surface area of a cuboid
Answers
if an angle is bisected to form two new 20 degree angles, what was the measure of the original angle?
Answers
Answer:
10 degrees
Step-by-step explanation:
The angle bisected so that mean it was divided into 2 parts, so if it's 20 degree angles bisected it's divided by 2:
20/2= 10°
So the measure of the original angle is 10° degrees!
Answer:40
Step-by-step explanation: i took the lesson this was the answer
Question 4 of 10
Is the graph increasing, decreasing, or constant?
O A. Decreasing
O B. Constant
O C. Increasing
Answers
is this right? PLEASE HELP ILL MARK
Answers
Answer:
yeah u r correct...hope it helps ..stay safe healthy and happy.Janelle says that lines l and m are skew lines.
Planes B and A intersect. Plane B is vertical and contains vertical line n. Plane A is horizontal and contains horizontal line m. Line m and n are perpendicular. Line l is on plane A and it is slightly diagonal.
Is Janelle correct?
Answers
B.. No, because the lines are in the same plane.
Remember to take breaks. It can be really really skew but its going to be their tm. Maybe with more assignments but still. happy learning.
Ayo whats good
the answer's C Line p must be drawn so that it can lie in the same plane as line l.
explination