The point in the feasible region maximizes the objective function is (5, 1)
How to determine the feasible region?The given parameters are
Objective function: C = 2x + y
Subject to (i.e. the constraints)
x >= 0, y >= 0
y <= x - 4, x + y <= 6
Represent y <= x - 4, x + y <= 6 as equations
y = x - 4 and x + y = 6
Substitute y = x - 4 in x + y = 6
So, we have
x + x - 4 = 6
Evaluate the like terms
2x = 10
This gives
x = 5
Substitute x = 5 in y = 6 - x
y = 6 - 5
Evaluate
y = 1
So, we have
(x, y)= (5, 1)
Hence, the coordinates is (5, 1)
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Given that angle A lies in Quadrant IV and cos(A)= 7/10, evaluate sin(A).
The value of the trigonometric function is; sin(A) =√51/10.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
We have been given that angle A lies in Quadrant IV and cos(A)= 7/10 then;
cos(A)= 7/10
Hence, base = 7
hypotenuse = 10
Therefore, perpendicular
h² = b² + p²
10² = 7² + p²
100 = 49 + p²
p = √51
Then sin(A = perpedicular/ hypotenuse
sin(A) = √51/10
Hence, the value of the trigonometric function is; sin(A) =√51/10.
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Can someone pls help me . Thank you so much .FIRST PROBLEM
Answer:
Step-by-Step explanation:
We are given the following equation:
A local dairy has three machines to fill half-gallon milk cartons. The machines can fill the daily quota in 3 hrs, 14 hrs, and 10.5 hrs, respectively. Find how long it takes to fill the daily quota if all three machines are running.
Answer
It will take 2 hours to fill the daily quota if all the machines are running.
Explanation
To find how long it takes to fill the daily quota if all the machines are running, we use the relation below:
Rate of machine 1 + Rate of machine 2 + Rate of machine 3 = Total rate of the machines
[tex]\begin{gathered} \Rightarrow\frac{1}{3}+\frac{1}{14}+\frac{1}{10.5}=\frac{1}{x} \\ \text{Where x is the }time\text{ it takes to fill the daily quota} \\ \frac{1}{3}+\frac{1}{14}+\frac{2}{21}=\frac{1}{x} \\ \text{Multiply all through by 42x} \\ 42x(\frac{1}{3})+42x(\frac{1}{14})+42x(\frac{2}{21})=42x(\frac{1}{x}) \\ 14x+3x+4x=42 \\ 21x=42 \\ x=\frac{42}{21} \\ x=2 \\ \text{Therefore it will take 2 hours to fill the daily quota} \end{gathered}[/tex]The revenue function R in terms of the number of units sold, a, is given as R = 300x - 0.4x^2where R is the total revenue in dollars. Find the number of units sold a that produces a maximum revenue?Your answer is x =What is the maximum revenue?
1) Considering the Revenue function in the standard form:
[tex]R(x)=-0.4x^2+300x[/tex]2) Since this is a quadratic function, we can write out the Vertex of this function:
[tex]\begin{gathered} x=h=-\frac{b}{2a}=\frac{-300}{2(-0.4)}=375 \\ k=f(375)=-0.4(375)^2+300(375)\Rightarrow k=56250 \end{gathered}[/tex]3) So, we can answer this way:
[tex]x=375\:units\:yield\:\$56,250[/tex]At a point on the ground 35 ft from base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree. The height of the tree is ___. (ft^3, ft^2, or ft)(Simply your answer. Round to the nearest foot as needed)
At a point on the ground 35 ft from the base of a tree, the distance to the top of the tree is 1 ft more than 3 times the height of the tree. Find the height of the tree
see the attached figure to better understand the problem
Applying the Pythagorean Theorem
(3h+1)^2=h^2+35^2
9h^2+6h+1=h^2+1,225
solve for h
9h^2-h^2+6h+1-1,225=0
8h^2+6h-1,224=0
Solve the quadratic equation
Using a graphing tool
the solution is
h=12 ftWhich answer choice below is a solution to this equation?7x + 5 – 2x = 2x – 7A. 2B. 0C. -4D. 8
SOLUTION:
Step 1:
In this question, we are given the following:
[tex]7x\text{ + 5 - 2 x = 2 x- 7}[/tex]Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} 7\text{ x - 5 - 2 x = 2 x - 7} \\ 5x\text{ - 5 = 2x - 7} \\ collecting\text{ like terms, we have that:} \\ 5\text{ x - 2x = - 7 - 5} \\ 3\text{ x = - 12} \\ Divide\text{ both sides by 3, we have that:} \\ x\text{ =}\frac{-12}{3} \\ x\text{ = - 4 \lparen OPTION C \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]x\text{ = - 4 \lparen OPTION C\rparen}[/tex]
The Neckware association of America reported that 3% of ties sold in the United States are bow ties. If 4 customers who purchased a tie randomly selected,find the probability that at least 1 purchased a bow tie
Pr (people with bow ties) = 3% = 0.03
p = 0.03
Pr (people without bow tie) = 1 - 0.03 = 0.97
q = 0.97
n = 4 customers
[tex]Pr(at\text{ least 1 purchased a bow tie) = 1 - Pr(none purchased a bow tie)}[/tex]To find the probability that at least 1 purchased a bow tie, we will use a binomial probability formula:
[tex]p(x=^{}X)=^nC_xp^xq^{n\text{ - x}}[/tex][tex]\begin{gathered} \text{Pr(none purchased a bow tie) = p(x = 0)} \\ \text{p(x = 0) = }^4C_0\times p^0\times q^{4\text{ - }0} \\ \text{p(x = 0) = 1 }\times\text{ 1}\times q^4=(0.97)^4 \\ \text{p(x = 0) = }0.8853 \\ \\ \text{Pr(none purchased a bow tie) = }0.8853 \end{gathered}[/tex][tex]\begin{gathered} Pr(at\text{ least 1 purchased a bow tie) = 1 - 0.8853} \\ Pr(at\text{ least 1 purchased a bow tie) = 0.1147} \end{gathered}[/tex]On the desmos app can you have more standard forms or only one?
Answer: I am pretty sure you can only have one.
Step-by-step explanation:
Find the missing side of this righttriangle.x816x= V[?]=Enter the number that belongs in the green box.Enter
As gien by the question
There are given that the right angle triangle.
Now,
To find the value of x, use Pythagoras theorem:
So,
From the Pythagoras theorem;
[tex]\begin{gathered} x^2+8^2=16^2 \\ x^2+64=256 \\ x^2=256-64 \\ x=\sqrt[]{192} \end{gathered}[/tex]Hence, the value of x is shown below:
[tex]x=\sqrt[]{192}[/tex]15. I need help on this question. How do you do it?
Solution:
Given the expression:
[tex]-5^2[/tex]This expression is evaluated as
[tex]\begin{gathered} -5\text{ multiplied in 2 places} \\ \Rightarrow-5\times-5 \\ =25 \end{gathered}[/tex]Hence,
[tex]-5^2[/tex]is evaluated to be 25
Write an expression for the sequence of operations described below.1)) multiply 7 by 8, then divide f by the resultDo not simplify any part of the expression.Submit
We need to write an expression for the operations:
[tex]\begin{gathered} \text{ multiply 7 by 8} \\ \\ \text{dived f by the result} \end{gathered}[/tex]The first operation (multiplication) can be represented as:
[tex]7\cdot8[/tex]The second operation (the division of f by the previous result) can be represented as:
[tex]f\div(7\cdot8)[/tex]Notice that we need the parenthesis to indicate that the product is the first operation to be done.
Answer:
[tex]f\div(7\cdot8)[/tex]a line passes through the points (2,5) and (-6,4). What is it's equation in point-slope form?
Answer:
y-5=⅛(x-2)
Explanation:
Given the points (2,5) and (-6,4).
To find the equation of the line joining these points in point-slope form, we begin by finding its slope.
[tex]\begin{gathered} \text{Slope,m}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{5-4}{2-(-6)} \\ =\frac{1}{2+6} \\ m=\frac{1}{8} \end{gathered}[/tex]Next, we substitute the slope and any of the given points into the point-slope form below:
[tex]y-y_1=m(x-x_1)[/tex]We use the point (2,5).
• x1=2, y1=5
[tex]y-5=\frac{1}{8}(x-2)[/tex]The equation in point-slope form is y-5=⅛(x-2).
What is the probability that a random selected yard will have fewer than 6 trees
Based on the given histogram on yards and the number of trees they have, the probability that a random selected yard will have fewer than 6 trees is 60%
How to find the probability?The probability that in a random yard, the number of trees would be less than 6 trees can be found by the formula:
= Proportion of yards with 0 - 2 trees + Proportion of yards with 2 - 4 trees + Proportion of yards with 4 - 6 trees
The probability that a random yard would have fewer than six trees is therefore:
= 0.35 + 0.20 + 0.05
= 0.60
= 60%
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Find the quotient32 divided by 517 what is quotient and what is remainder
Calculate the division as shown below
Therefore, the quotient is 16 and the remainder is 5
The answer is 16R5A teacher determines the linear equation y=12x + 40 best models the number of points a student should earn on a test, y, if the student studies for x hours. Which statement is true
Given the equation:
y = 12x + 40
Where x represents the number of hours and y represents the number of points the student should earn.
To find the correct statement substitute the number of hours and points given for x and y respectively. If the left hand side of the equation equals the right hand side then the statement is the true.
We have:
1. A student who studies for 3 hours should earn about 76 points.
x = 3
y = 76
Substitute 3 for x and 76 for y.
y = 12x + 40
76 = 12(3) + 40
76 = 36 + 40
76 = 76
This statement is true.
2.
The entire company went in together to buy lottery tickets. Inside the safe are two different types of lottery tickets. The Mega Million Tickets cost $5 each and the Scratch Off Tickets cost $2 each. They bought 60 tickets totaling $246. what are my x and y variables?x=y=
we have the following system
[tex]\begin{gathered} \begin{cases}x+y=60 \\ 5x+2y=246\end{cases} \\ \end{gathered}[/tex]where x is the number of mega million ticktets and y the number of scratch off tickets, so we have that y=60-x and we get that
[tex]\begin{gathered} 5x+2(60-x)=246 \\ 5x-2x+120=246 \\ 3x=126 \\ x=\frac{126}{3}=42 \end{gathered}[/tex]so they bought 42 mega million tickets and 18 scratch off
how do you find the sale price of the item if original price $71 and mark down to 34% the sale price is
Answer:
The sale price is $46.86
Explanation:
Given an original price of $71, and a markdown of 34%
The sale price is:
$71 - (34% of $71)
= $71 - (0.34 * $71)
= $71 - $24.14
= $46.86
Answer:
The sale price is $46.86
Explanation:
Given an original price of $71, and a markdown of 34%
The sale price is:
$71 - (34% of $71)
= $71 - (0.34 * $71)
= $71 - $24.14
= $46.86
Sue wants to plant 545 acres of wheat. She has planted a 128 acre field near the river. Whatpercent of her wheat crop has she planted?
Percentage of the wheat crop planted = 128/ 545 x 100
= 12800/545
= 23.4 percent
You are looking for summer work to help pay for college expenses. Your neighbor is interested in hiring you to do yard work and other odd jobs. You tell them that you can start right away and will work all day July 1 for 3 cents. This gets your neighbor's attention, but they is wondering if there is a catch. You tell them that you will work July 2 for 9 cents, July 3 for 27 cents, July 4 for 81 cents, and so on for every day in the month of July. Which equation will help you determine how much money you will make in July?
Answer:
y=3^x
Explanation:
The expected payments (in cents) beginning from July 1 are given below:
[tex]3,9,27,81,\cdots[/tex]Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.
We can rewrite the payment as a power of 3 as follows:
[tex]3^1,3^2,3^3,3^4,\cdots[/tex]Therefore, the equation will help you determine how much money you will make in July will be:
[tex]y=3^x[/tex]The first option is correct.
Teresa has a bookcase with 8 shelves. There are n books on each shelf. Using n, write an expression for the total number of books.
Answer:
8*n
Step-by-step explanation:
You solve this question by multiplying the number of shelves by the number of books to find the total number of books on the shelves.
Line Graph: This time you will not have the numbers on the x and y axis. You will need to decide which number to use (1, 2, 3... or 2,4,5.... Or 5, 10, 15...) 3: Creating Graphs Create a single line graph using the following table. Time goes on the x axis Rainfall goes on the y axis Make sure to do the following: Label the x and y axis Create a title 10 15 20 Time (minutes) 25 30 35 40 25 55 45 60 50 35 40 Speed (of car) (km/min)
Line Graph:
A line graph is used to show how the data points are changing with respect to time.
For Example:
A line graph may be used to show the average rainfall over the entire month.
For the given scenario we have,
X-axis = Time in minutes
Y-axis = Speed of car in km/min
Title of graph = Speed of Car Vs Time
Data points for time = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Data points for speed = 25, 30, 35, 40, 25, 55, 45, 60 50 35 40
This is how the line graph looks like.
It is showing the speed of the car in km/min over an interval of 60 minutes in steps of 5 minutes.n steps of
Procedure:
• Draw and label the x-axis and y-axis.
,• Label the data points on both axis.
,• Draw the data points.
,• Join the data points with a line.
,• We are done.
,•
The triangles are similar, solve for the question mark. A Z с ? 15 10 12 B X D E 8 8 18 12.5 0 24
Answer:
18
Explanation:
The triangles are similar if their sides are proportional. It meant that the ratio of AB to CD is equal to the ratio of AE to CE, so we can write the following equation:
[tex]\begin{gathered} \frac{AB}{CD}=\frac{AE}{CE} \\ \frac{15}{10}=\frac{AE}{12} \end{gathered}[/tex]So, we can solve for AE as:
[tex]\begin{gathered} \frac{15}{10}\cdot12=\frac{AE}{12}\cdot12 \\ 18=AE \end{gathered}[/tex]Therefore, the measure of AE is 18
1 a) is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
First, we count the number of boxes.
We have: 4,8,12,16
(a)Now:
• 8-4=4
,• 12-8=4
,• 16-12=4
Since the difference is the same, the sequence is an arithmetic sequence.
(b)In the sequence
First term, a =4
Common difference, d=4
The nth term of an arithmetic sequence is:
[tex]\begin{gathered} U_n=a+(n-1)d \\ =4+4(n-1) \\ =4+4n-4 \\ =4n \end{gathered}[/tex]The explicit formula for the above sequence, f(n)= 4n.
(c)18th term
f(18)= 4 x 18
=72
The 18th term is 72.
Find the sum of the arithmetic series given a₁ =A. 650B. 325C. 642D. 1266Reset SelectionPrevious Jixt45, an=85, and n = 5.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: write the given details
[tex]a_1=45,a_n=85,n=5[/tex]STEP 2: Write the formula for calculating the sum of arithmetic series
STEP 3: Find the sum
By substitution,
[tex]\begin{gathered} S_n=5(\frac{45+85}{2}) \\ S_n=5(\frac{130}{2})=5\times65=325 \end{gathered}[/tex]Hence, the sum of the series is 325
I need to use substitution to solve each system of equations then use ordered pairs
From the given question
There are given that the equation
[tex]\begin{gathered} 2x+5y=38\ldots(1) \\ x-3y=-3\ldots(2) \end{gathered}[/tex]Now,
From the equation (1)
[tex]\begin{gathered} 2x+5y=38 \\ 2x=38-5y \\ x=\frac{38}{2}-\frac{5}{2}y \\ x=19-\frac{5}{2}y\ldots(3) \end{gathered}[/tex]Then,
Put the equation (3) into the equation (2)
So,
[tex]\begin{gathered} x-3y=-3 \\ 19-\frac{5}{2}y-3y=-3 \\ 38-5y-6y=-6 \\ 38-11y=-6 \\ -11y=-6-38 \\ -11y=-44 \\ y=4 \end{gathered}[/tex]Then,
Put the value of y into the equation (3)
So,
[tex]\begin{gathered} x=19-\frac{5}{2}y \\ x=19-\frac{5}{2}(4) \\ x=19-\frac{20}{2} \\ x=19-10 \\ x=9 \end{gathered}[/tex]Hence, the value of x is 9 and y is 4.
help meeeee pleaseeeee!!!
thank you
Step-by-step explanation:
what is the problem ?
first you need to put "1" in place of the x and calculate, and then you need to put "2" in place of the x and calculate.
just simple calculation !
(a)
R(1) = 1000×1² / (1² + 4) = 1000 / 5 = 200
$200 million
(b)
R(2) = 1000×2² / (2² + 4) = 4000 / 8 = 500
$500 million
there ! that's all that was needed.
the sum of interior angle measures of a polygon with n sides is 2340 degrees. find n15
the measure of each angle will be 2340/n then if n=15 the measure of each one of the angles will be 2340/15=156 degrees
Find seco, coso, and coto, where is the angle shown in the figure.Give exact values, not decimal approximations.
step 1
Find out the value of cosθ
cosθ=8/17 ------> by CAH
step 2
Find out the value of secθ
secθ=1/cosθ
secθ=17/8
step 3
Find out the length of the vertical leg in the given right triangle
Applying the Pythagorean Theorem
17^2=8^2+y^2
y^2=17^2-8^2
y^2=225
y=15
step 4
Find out the value f cotθ
cotθ=8/15 -----> adjacent side divided by the opposite side
therefore
secθ=17/8cosθ=8/17cotθ=8/15Which ordered pair is a solution set for the linear equation, x + 16 = 6y? A (16,4) B (2, 3) C (-4,-2) D (-10,-1)
Explanation
to figure out if a pair is a solution, just replace x and y values and check if the equation is true,then
Step 1
[tex]\begin{gathered} x+16=6y \\ A)(16,4)\rightarrow when\text{ x=16 and y =4} \\ \text{replace} \\ 16+16=6\cdot4 \\ 32=24\rightarrow False,then\text{ A is not a solution} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} B)(2,3)\rightarrow whenx=\text{ 2 and y=3} \\ x+16=6y \\ \text{replace} \\ 2+16=6\cdot3 \\ 18=18\rightarrow true \\ so\text{ B is a solution} \end{gathered}[/tex]Step 3
[tex]undefined[/tex]Evaluate 1312e 4 Sov? 3x²x3 dx (Type an exact answer.)
We have to solve the integral:
[tex]\int ^4_03x^2e^{x3}dx[/tex]We will apply a variable substitution in order to simplify the solution. We have a hint when we see that the derivative of x^3 is 3x^2, that is part of the factors.
[tex]\begin{gathered} u=x^3\Rightarrow du=(3x^2)dx \\ x=0\Rightarrow u=0^3=0 \\ x=4\Rightarrow u=4^3=64 \end{gathered}[/tex]Then, we can write:
[tex]\int ^4_03x^2e^{x3}dx=\int ^4_0e^{x3}(3x^2)dx=\int ^{64}_0e^udu[/tex]Then, we have a simpler integral to solve:
[tex]\int ^{64}_0e^udu=e^u+C=e^{64}-e^0=e^{64}-1[/tex]The exact solution is e^64-1.
