The maximum value of the objective function is 33, which occurs at the corner point (3, 3)
According to the question we have to maximize 6x+5y (OBJ)Subject tox+y≤6 (1)2x+y≤8 (2)y≤5 (3).Linear programming is a mathematical method that aims to maximize or minimize an objective function subject to a set of linear constraints. In this problem, we are asked to maximize the objective function 6x + 5y subject to the constraints given by the inequalities 1, 2, and 3.
The inequalities 1, 2, and 3 define a feasible region in the xy-plane, which is a region that satisfies all the constraints. The feasible region can be found by graphing the three inequalities and shading in the region that satisfies all of them.
In this case, the feasible region is a triangle with vertices (0, 0), (3, 3), and (4, 1), as shown below:
The objective function 6x + 5y is evaluated at each corner point as follows:
At (0, 0), 6(0) + 5(0) = 0, At (3, 3), 6(3) + 5(3) = 33, At (4, 1), 6(4) + 5(1) = 29. Thus, the optimal solution is x = 3 and y = 3, and the maximum value of the objective function is 33.
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In one day, a store sold 2/3 as many DVDs as Blu-Ray discs. the total number of DVDs Blu-ray discs sold that day was 280, how many DVDs were sold?
Answer: Let's start by representing the number of Blu-Ray discs sold as x.
According to the problem, the store sold 2/3 as many DVDs as Blu-Ray discs. So the number of DVDs sold is 2/3 of x, or (2/3)x.
We also know that the total number of DVDs and Blu-Ray discs sold was 280. So we can set up an equation:
(2/3)x + x = 280
To solve for x, we can simplify the equation by combining like terms:
(5/3)x = 280
Multiplying both sides by 3/5, we get:
x = 168
So the number of Blu-Ray discs sold was 168.
To find the number of DVDs sold, we can use the expression we derived earlier:
(2/3)x = (2/3) * 168 = 112
Therefore, the store sold 112 DVDs on that day.
Step-by-step explanation:
a geology class is studying a sample of rock and a sample of dry sponge the rock sample has a mass of 1 x 10¹ kg. The dry sponge sample has a mass of 2x 10⁻³ kg. Which sample has a greater mass? How many times greater?
The sample that has a greater mass is given as follows:
The sample of rock.
The sample of rock has a mass that is 5000 times the mass of the sample of dry sponge.
What is scientific notation?A number in scientific notation is given by the notation presented as follows:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex], meaning that it can assume values from 1 to 10, with an open interval at 10 meaning that for 10 the number is written as 10 = 1 x 10¹, meaning that the base is 1, justifying the open interval at 10.
To obtain which amount is greater, we must verify the bases when the exponent is the same, hence:
Rock: 1 x 10¹ kg = 10 kg.Sponge: 2 x 10^-3 kg = 0.2 x 10^-2 kg = 0.02 x 10^-1 kg = 0.002 kg.Hence the rock has the greater mass, and the ratio is given as follows:
10/0.002 = 5000.
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In a study in 1998, the following equation for predicting baby birth weight in grams (Y) given mothers age in years (X): = -1163.45 + 245.15.X. If the RMS=589.3 grams, about 95% of the babies born to a 22-year-old mothers will weigh between grams and _______grams. Hint: make sure to carry calculations to at least 4 places past the decimal. OA) (1726.5, 5262.3) OB) (4687.55, 5866.15) OC) (3051.25, 5408.49) OD) (6508.95, 7044.75) OE) (2315.8, 4673.0).
The 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).
To get started, let's put the mother's age into the given equation to determine the mean birth weight. Then, we'll use the RMS value to calculate the standard deviation.The equation for predicting baby birth weight in grams given the mother's age is: Y = -1163.45 + 245.15XWhere X is the mother's age, and Y is the baby's birth weight. We are given X=22, so let's use that to find the predicted mean birth weight:Y = -1163.45 + 245.15(22) = 4486.95 gramsThe RMS is given to be 589.3 grams. Because we're told that the distribution is approximately normal, we can use the 68-95-99.7 rule to find the 95% prediction interval. Here are the steps:Subtract the RMS from the mean to find the lower endpoint of the interval:4486.95 - (2 x 589.3) = 3308.35Add the RMS to the mean to find the upper endpoint of the interval:4486.95 + (2 x 589.3) = 5665.55Round both values to four decimal places, as instructed in the problem:3308.35 rounds to 3308.4 grams5665.55 rounds to 5665.6 gramsTherefore, about 95% of the babies born to 22-year-old mothers will weigh between 3308.4 grams and 5665.6 grams.The correct answer is option C) (3051.25, 5408.49).
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? → Find the pressure in kN/m2 exerted by a force of 60 kN on an area of 12 m². kN/m²
Therefore , the solution of the given problem of area comes out to be the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².
Explain area.Calculating how much room is needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal shape's surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capability of a cuboid is given by the total of the borders connected to each of its six rectangular edges.
Here,
The following method determines the pressure P that a force F exerts on an area A:
=> P = F/A
Inputting the numbers provided yields:
=> P = 60 kN / 12 m²
If we simplify, we get:
=> P = 5 kN/m²
As a result, the force of 60 kN applies 5 kN/m2 of pressure to a 12 m² is 5 kN/m².
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Find all holes of the following function. Write your answer as a coordinate point in
simplest form. If no hole exists, press the icon to indicate there is no solution.
ƒ(x) =x-1/x² - 4x +3
PLEZZZZZZ help
Answer:
Step-by-step explanation:
In order to find a hole, you have to factor the denominator to see if it matches an expression in the numerator and can therefore be crossed out.
The factored form of the denominator is shown below:
[tex]f(x)=\frac{x-1}{(x-3)(x-1)}[/tex]
Because the term x-1 is in both the numerator and the denominator, it is a hole, or removeable discontinuity. To find the hole, we plug in a 1 to the fraction that remains after we cancel the hole:
[tex]f(1)=\frac{1}{1-3}=-\frac{1}{2}[/tex]
The hole is found at (1, -1/2)
Find the distance between the points (-3, -6) and (1, -2).
Answer:
4*sqrt(2)
Step-by-step explanation:
To find the distance between two points, we use the distance formula, which is the following:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the values for the given points, we get the following:
d = sqrt((1 - (-3))^2 + (-2 - (-6))^2)
= sqrt((1 + 3)^2 + (-2 + 6)^2)
= sqrt(4^2 + 4^2)
= sqrt(32)
= 4*sqrt(2)
Therefore, the distance between the points (-3, -6) and (1, -2) is 4*sqrt(2).
Please HELP ASAP Quick
Which are strategies to manage risk that comes with investing?
Spread investments over time
Invest in British pound
Hold your investments for a long time
Diversify your investments
Therefore , the solution of the given problem of unitary comes out to be each asset class as part of the diversification plan.
What is an unitary method?By combining the information obtained using this nanosection technique with all variable additional data from two individuals who used a specific strategy, the task can be completed. Simply put, this mean that, if the desired outcome materialises, either the specified entity will be known or, actually, the colour from both enormous processes will be skipped. For forty pens, a refundable charge of Rupees ($1.01) might be required.
Here,
The next two are methods for reducing the danger associated with investing out of the four you offered:
Dollar-cost averaging is the term used to describe this method of spreading investments out over time. Regardless of the investment's price, it entails making a set amount of investments at regular intervals over a length of time.
Spread your investments across various asset classes (such as stocks, bonds, real estate, etc.) and/or various companies within each asset class as part of the diversification plan.
Since currency values can be influenced by a number of variables and are sometimes unpredictable, investing in a particular currency (such as the British pound) is not always a risk management plan.
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ind the complex zeros of the following polynomial function. Write f in factored form: f(x) = x^4 + 170x^2 + 169 The complex zeros of f are. (Simplify your answer. Type an exact answer, using radicals and i as needed. Use Use the complex zeros to factor f f(x) = (Type your answer in factored form. Type an exact answer, using radicals and i as
The complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169 are [-i\sqrt{2}, i\sqrt{2}, -1, 1].
To find the complex zeros of the given polynomial function f(x) = x^4 + 170x^2 + 169, we can start by noting that this polynomial is a perfect square of a binomial. Specifically, we have:
f(x) = (x^2 + 13)^2
Therefore, the zeros of f(x) are the values of x that satisfy f(x) = 0. In other words, we need to solve the equation:
(x^2 + 13)^2 = 0
Taking the square root of both sides, we get:
x^2 + 13 = 0
Solving for x, we get:
x = ±i√13
However, we need to find the complex zeros of f(x), which are the roots of the equation f(x) = 0. Since f(x) = (x^2 + 13)^2, the zeros of f(x) are exactly the same as the zeros of x^2 + 13, namely ±i√13.
But this is not the end of the story. Since x^2 + 13 has only two distinct roots, namely ±i√13, each of these roots must occur with multiplicity 2 in f(x). This means that f(x) has a repeated root at each of the values ±i√13.
Finally, we note that x^2 + 13 can be factored as:
x^2 + 13 = (x + i√13)(x - i√13)
Therefore, we can write f(x) as:
f(x) = (x^2 + 13)^2 = (x + i√13)^2(x - i√13)^2
This gives us the factored form of f(x), and we can see that it has four roots, namely -i√13, i√13, -i√13, and i√13, which can be simplified to -i√2, i√2, -1, and 1.
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Which describes the correct method? Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent
The option D "Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent." describes the correct method. So the option D is correct.
The substitution method is a method of solving a system of linear equations by expressing one variable in terms of the other and then substituting the expression into the other equation. This method can be used when the system of equations consists of two linear equations with two unknowns.
The elimination method is a technique used to solve systems of linear equations. It involves transforming the given system into an equivalent system of equations in which the coefficients of one of the variables are the same in each equation, and then eliminating that variable by addition or subtraction. So the option D is correct.
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Which describes the correct method?
A. Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent.
B. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
C. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent.
D. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
If k(x) = 2x² - 3√x, then what is the value of k(9)?
Answer: To find the value of k(9), we need to substitute x=9 into the given function k(x):
k(9) = 2(9)² - 3√(9)
k(9) = 2(81) - 3(3)
k(9) = 162 - 9
k(9) = 153
Therefore, the value of k(9) is 153.
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All original content anything provided above is not copy and pasted. IT was typed by hand.
help would be appreciated
The graph that shows the horizontal compression is graph A.
Which graph shows the transformed function?For a function f(x), we define a horizontal compression of scale factor k as :
g(x) =f(x*k)
In this case, the function f(x) is graphed at the top, and we want to identify the graph of f(4*x).
So we have a compression of scale factor k = 4.
This only changes the values in the horizontal axis, and the vertical axis remains unchanged, so option D and C can be discarded.
Now, B is a dilation and A is a compression, so the correct option is graph A.
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What is the measures
Answer:
<COA MESURES = 61
<AOH MESURES = 46
<HOG MESURES = 73
<FOE MESURES = 73
Step-by-step explanation:
reduce fraction
17/68
Answer:
The reduced answer is 1/4
Noah and his children went into a grocery store and where they sell apples for $1 each and mangos for $2 each. Noah has $20 to spend and must buy at least 9 apples and mangos altogether. If Noah decided to buy 4 apples, determine the maximum number of mangos that he could buy. If there are no possible solutions, submit an empty answer.
Answer:
8 Mangoes
Step-by-step explanation:
Since he decides to buy 4 apples, that would cost him: 4 × $1 = $4
That leaves him: $20 - $4 = $16.
So, how many mangoes can Noah possibly buy with $16?
That is: $16/$2 = 8(We divide by $2 because it is the cost of one mango)
what is the maximum value of the probability of a event
The maximum value οf the prοbability οf any event cannοt exceed 1.
What is the maximum value οf the prοbability?The maximum value οf the prοbability οf an event is 1. The prοbability οf an event represents the likelihοοd οr chance that the event will οccur, and it is always expressed as a number between 0 and 1. A prοbability οf 0 means the event is impοssible, while a prοbability οf 1 means the event is certain tο οccur.
Prοbabilities between 0 and 1 represent the degree οf uncertainty οr likelihοοd οf the event. Since the sum οf prοbabilities οf all pοssible οutcοmes is always 1, the maximum value οf the prοbability οf any event cannοt exceed 1.
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A laptop costs $550.
You get a coupon in the mail for 30% off.
If you use the coupon, what is the sale price for the laptop?
The sale price of the laptop is $414 after the use of the coupon.
Answer:
$385.00
Step-by-step explanation:
Original Price - Discount = Sale price
Since the discount is 30%, we would multiply 0.30(550) to get the amount of the discount.
0.30(550) = 165
550 - 165 = $385
please help with this!
Answer:
m = - 6.5
Step-by-step explanation:
the remainder theorem states
if a function f(x) is divide by (x - a) then the remainder is equal to f(a)
given
p(x) is divided by (x - 2) then p(2) = 2 ( the remainder )
then
2[tex](2)^{4}[/tex] - 5(2)² + 2m + 3 = 2
2(16) - 5(4) + 2m + 3 = 2
32 - 20 + 2m + 3 = 2
15 + 2m = 2 ( subtract 15 from both sides )
2m = - 13 ( divide both sides by 2 )
m = - 6.5
Solve the equation.
5(y+25)=−13
y =?
Answer:
y=-27+3/5 or 138 or 5 if need as a fraction
Step-by-step explanation:
5(y+25)-(-13)=0
add all the numbers together and all the variables
5(y+25)+13=0
multiply parentheses to get
5y+125+13=0
add all the numbers together n all the variables together to
5y+138=0
Then move all terms hat have y to the left and terms to the right
so 125 basiclly
5y=-138
y=-138/5
y=-27+3/5 aslo could be known as - 138 over 5 (fraction )
Pls help 100 pts
If u could pls answer question a
Answer:
Step-by-step explanation:
The initial height is the beginning of the graph, or in this case, x=0. So the initial height is 1.5.
Many historians agree that there is about 1 chance in 4 that Jones wrote the ‘Q document’ and 3 chances in 4 that Smith wrote it. In a new analysis of the 10,000-word document, the word ‘that’ is found to occur 27 times. From the known writings of Smith and Jones, experts assess a probability of 0. 0084 that this frequency of ‘that’ would be observed if Jones were the author, whilst the probability for Smith would be 0. 4. In the light of this new evidence, what now is the probability that Jones is the author?
The probability of Jones being the author is 0.0275.
The new evidence updates the probability of Jones being the author from 1 in 4 to 0.0084. The probability of Smith being the author is 0.4.
To calculate the new probability, we need to use Bayes' theorem.
P(Jones|that) = P(that|Jones) x P(Jones) / (P(that|Jones) x P(Jones) + P(that|Smith) x P(Smith))
P(Jones|that) = 0.0084 x 0.25 / (0.0084 x 0.25 + 0.4 x 0.75)
P(Jones|that) = 0.0084 / (0.0084 + 0.3)
P(Jones|that) = 0.0084 / 0.3084
P(Jones|that) = 0.0275
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400 ml of squash is made by mixing 50 ml of cordial with water. What fraction of the drink is water?
Answer:
If 400 ml of squash is made by mixing 50 ml of cordial with water, then the remaining volume is water.
The volume of water used in making the squash = 400 ml - 50 ml = 350 ml
The fraction of the drink that is water is:
Water volume / Total volume = 350 ml / 400 ml = 7/8
Therefore, 7/8 of the drink is water.
Answer:
[tex]\frac{7}{8}[/tex]
Step-by-step explanation:
We know that 400ml squash = 50ml of Cordial With Water.
Therefore in 400ml of squash, amount of water will be 400ml - 50ml = 350ml of water.
In fraction form, this will be [tex]\frac{350}{400} =\frac{7}{8}[/tex]
Hope it helps
Gracie is rewriting the expression (24 + 40) as an integer times the sum of two integers. By factoring out a 2, she knows she can rewrite the expression as 2 times the sum of two integers. What are all the other numbers greater than 2 that Gracie can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers?
Step-by-step explanation:
To rewrite (24 + 40) as an integer times the sum of two integers, Gracie first factored out 2, obtaining:
(24 + 40) = 2 × (12 + 20)
We can check that this is true by distributing the 2:
2 × (12 + 20) = 2 × 12 + 2 × 20 = 24 + 40
Now, Gracie is looking for other numbers greater than 2 that she can factor out of (24 + 40) to rewrite the expression as an integer times the sum of two integers.
One way to approach this is to look for other common factors between 24 and 40. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The common factors of 24 and 40 are 1, 2, 4, 8, and the largest factor is 8.
Therefore, Gracie can factor out 4 or 8 to rewrite the expression as an integer times the sum of two integers. For example:
(24 + 40) = 4 × (6 + 10)
(24 + 40) = 8 × (3 + 5)
Note that we can also factor out 1 or 2, but that would not change the expression in any meaningful way.
To have $6,000 for a child’s education in 10 years, what amount should a parent deposit in a savings account that earns 12% compounded quarterly?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 6000\\ P=\textit{original amount deposited}\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]6000 = P\left(1+\frac{0.12}{4}\right)^{4\cdot 10} \implies 6000=P1.03^{40} \\\\\\ \cfrac{6000}{1.03^{40}}=P\implies 1839.34\approx P[/tex]
Problem 2 Lanny got a short term job selling computers. He is paid on
commission. In order to impress customers, he bought a few nice suits. If he has
$20 000 in sales, he will lose $140. If he has$30 000 in sales, he will make a $90
profit. Determine the:
a. rate of change and initial value
b. the amount he needs to sell to break even
c. The amount he needs to sell in order to make $1000 profit
Answer:
Step-by-step explanation:
A. the rate of change is 50
i need help solving this
Use the graphs to make predictions about the relationship between the number of homeless Pit Bulls and the number of homeless Chihuahuas
Answer:
the answer to ur question is 6
Answer:
25
Step-by-step explanation:
Santa Claus has 3h+11 red presents and h+5 white presents in his stocking. Ethan selects a present at random from the stocking.
The value of h is 1.89. The solution involves setting up and solving an equation involving the probabilities of selecting a red or white present.
Santa Claus has a total of 3h+11 red presents and h+5 white presents in his stocking. If Ethan selects a present at random from the stocking, the probability of obtaining a red present is given as 19/26. Using this information, we can form an equation (3h+11)/(4h+16) = 19/26 and solve for h. Cross-multiplying and simplifying, we get 494h = 936, which leads to h = 1.89. Therefore, the value of h that satisfies the given conditions is approximately 1.89.
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Complete question:
Santa Claus has 3h+11 red presents and h+5 white presents in his stocking. Ethan selects a present at random from the stocking. Given that the probability that he obtains a red present is 19/26, find the value of h.
A chemical equation is given
below. How would you classify
this reaction?
4C5H₂O + 270220CO2 + 18H₂O
Find the value of x.
Answer:
116
Step-by-step explanation:
We can see that the two lines in between the triangle are the same size. This must mean that if we were to move the inner triangle and line it up to the triangle on the edge it must be the same size. We are also told that one of the angles on the side is 116. This means that the value of x must also be 116!
Hope this helps, have a lovely day! :)
Which graph represents the solution for the equation
2/3 x - 2 = -5x + 1?
Answer:
B
Step-by-step explanation:
The answer is B because for the slope of the first part of the equation, it's 2/3 up 2 over 3. The starting point for that part of the equation is -2, so that's where your starting point is. For the second part of the equation, your starting point is on 1, and the slope is -5, so moving to the right 1 and down 5.