Suppose you want to fill nine 1-lb tins with a snack mix. You have 15 and plan to buy almonds for 2.45 per lb, hazelnuts for 1.85 per lb, and raisins for .80 per lb. You want the mix to contain an equal amount of almonds and hazelnuts and twice as much of the nuts as the raisins by weight.
x + y + z = 9 2.45x + 1.85y + 0.8z = 15 x+y = 2z.
a. Explain how each equation to the right relates to the problem. What does each variable represent?
Answers
We can determine the specific values of x, y, and z, which represent the number of tins filled with almonds, hazelnuts, and raisins, respectively, to meet the given constraints and budget limitations.
Let's analyze each equation and understand how they relate to the problem:
x + y + z = 9
This equation represents the total number of tins (nine in this case) we want to fill. The variables x, y, and z represent the number of tins filled with almonds, hazelnuts, and raisins, respectively. The sum of these variables should equal the total number of tins, which is nine.
2.45x + 1.85y + 0.8z = 15
This equation represents the budget constraint of $15. The variables x, y, and z represent the pounds of almonds, hazelnuts, and raisins, respectively. The equation is formed by multiplying the price per pound of each ingredient by the respective quantity and ensuring that the total cost does not exceed the budget.
x + y = 2z
This equation represents the ratio constraint between almonds, hazelnuts, and raisins. It states that the total weight of almonds and hazelnuts combined should be twice the weight of the raisins. This constraint ensures a specific ratio of the ingredients in the snack mix.
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Related Questions
Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount remains after 900 years? (Round your answer to two decimal places.)
Answers
64.77% of a given amount remains after 900 years.
To determine the percentage of radioactive radium remaining after 900 years, we'll use the half-life formula:
Final Amount = Initial Amount * \(1/2^{(time elapsed / half-life)}\)
In this case, the half-life is 1599 years and the time elapsed is 900 years. We want to find the percentage remaining, so let's assume the initial amount is 100%.
Final Amount = 100 * \((1/2)^{(900 / 1599)}\)
Now, we'll calculate the exponent:
Exponent = 900 / 1599 ≈ 0.5635
Then, we'll compute the final amount:
Final Amount ≈ 100 * \((1/2)^{0.5635}\) ≈ 100 * 0.6477 ≈ 64.77%
After 900 years, approximately 64.77% of the initial radioactive radium remains. This percentage was found using the half-life formula, which accounts for the exponential decay of radioactive substances over time.
The formula shows how the remaining amount of a substance decreases as time progresses based on its half-life, which is the time it takes for half of the substance to decay. In this scenario, radium's half-life of 1599 years and the 900-year time frame were used to determine that roughly 64.77% of the initial radium remains.
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Determine the equation of the tangent plane and normal line of
the curve f(x,y,z)=x2+y2-2xy-x+3y-z-4 at p(2,
-3, 18)
Answers
To determine the equation of the tangent plane and normal line of the given curve at the point P(2, -3, 18), we need to find the partial derivatives of the function f(x, y, z) = x^2 + y^2 - 2xy - x + 3y - z - 4.
Taking the partial derivatives with respect to x, y, and z, we have:
fx = 2x - 2y - 1
fy = -2x + 2y + 3
fz = -1
Evaluating these partial derivatives at the point P(2, -3, 18), we find:
fx(2, -3, 18) = 2(2) - 2(-3) - 1 = 9
fy(2, -3, 18) = -2(2) + 2(-3) + 3 = -7
fz(2, -3, 18) = -1
The equation of the tangent plane at P is given by:
9(x - 2) - 7(y + 3) - 1(z - 18) = 0
Simplifying the equation, we get:
9x - 7y - z - 3 = 0
To find the equation of the normal line, we use the direction ratios from the coefficients of x, y, and z in the tangent plane equation. The direction ratios are (9, -7, -1).Therefore, the equation of the normal line passing through P(2, -3, 18) is:
x = 2 + 9t
y = -3 - 7t
z = 18 - t
where t is a parameter representing the distance along the normal line from the point P.
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7 (b)
Rashid spent 30 minutes on each piece of homework.
Work out the total time he spent on homework for these three subjects.
Give your answer in hours and minutes.
13
Answers
Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.
If Rashid spent 30 minutes on each piece of homework for three subjects, we can calculate the total time he spent by multiplying the time spent per subject (30 minutes) by the number of subjects (3).
30 minutes * 3 = 90 minutes.
To convert this into hours and minutes, we divide 90 minutes by 60 since there are 60 minutes in an hour.
90 minutes ÷ 60 = 1 hour and 30 minutes.
Therefore, Rashid spent a total of 1 hour and 30 minutes on homework for these three subjects.
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The blank is the number that tell how many times a base number is used as a factor
Answers
Answer:
exponent
Step-by-step explanation:
Students are building rectangular wooden frames for the set
Answers
The length of the braces are then the hypotenuses
DE is parallel to AC. Find the lengths of AC and AD. FAST!!!
Answers
Answer:
we have:
∆BDE is similar to ∆BAC
so their side are proportional :
BD/BD=BE/BC
2/BD=4/(6+4)
BD=2×10/4
BD=5
again
BE/BC=DE/AC
4/10=5/AC
AC=5×10/4
AC=25/2
Now,
AC=25/2 or 12.5.
AD=BA-BD=5-2=3.
is your answer.
Answer:
AC = 12.5, AD = 3
Step-by-step explanation:
A line parallel to a side of a triangle and intersecting the other 2 sides, divides those sides proportionally, that is
\(\frac{BD}{BE}\) = \(\frac{AD}{CE}\) , substitute values
\(\frac{2}{4}\) = \(\frac{AD}{6}\) ( cross- multiply )
4 AD = 12 ( divide both sides by 4 )
AD = 3
-----------------------------------------
Δ BDE and Δ BAC are similar, so the ratios of corresponding sides are equal, that is
\(\frac{DE}{AC}\) = \(\frac{BD}{BA}\) , substitute values
\(\frac{5}{AC}\) = \(\frac{2}{5}\) ( cross- multiply )
2 AC = 25 ( divide oth sides by 2 )
AC = 12.5
.
A scale drawing of a town park has a scale of 2 inches : 300 feet. What is the actual length of each foot in the drawing?
Answers
Answer:
three hundred divided by two
Answer:
i think 450
Step-by-step explanation:
Calculate the Curved Surface area of a Cone whose height IS 8Cm and radius is 5cm
Answers
The curved surface area of the cone is 148.19 square cm
Calculating the curved surface area of the coneFrom the question, we have the following parameters that can be used in our computation:
Radius, r = 5 cm
Height, h = 8 cm
The slant height l of the cone is calculated as
l² = 8² + 5²
So, we have
l² = 89
This gives
l = √89
The curved surface area of the cone is then calculaed as
Area = πrl
So, we have
Area = π * 5 * √89
Evaluate
Area = 148.19
Hence, the curved surface area of the cone is 148.19 square cm
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Will give brainliest and ten points
t+7.45=13 3/4
Answers
Answer:
t = 6.3
Step-by-step explanation:
t = 13\(\frac{3}{4}\) - 7.45
t = \(\frac{55}{4}\)-7.45
t= 13.75 - 7.45
t = 6.3
Answer:
T would equal 6.3
Step-by-step explanation:
You can start out by converting 13 3/4 to a decimal, which would be 13.75.
Therefore leaving you with this equation:
t + 7.45 = 13.75
Next, you subtract.
t + 7.45 = 13.75
-7.45 -7.45
---------------------------
Therefore leaving you with your answer of 6.3 or 6 3/10. I hope this helps! :)
an agency for the us government spends millions of dollars funding research on cancer. in particular, 20 research projects are funded to test a drug used to reduce pancreatic tumors. in one of these projects (project number 11) researchers find that the drug significantly reduces the size of tumors with a p-value of 0.027. there are no significant effects found in the other 19 projects (p-values all greater than 0.05) for the drug. given the entirety of this information, would it be proper to conclude that the drug is effective in reducing the size of pancreatic tumors?
Answers
The result from project number 11 suggests that the drug may be effective in reducing the size of pancreatic tumors, but it is not sufficient to conclude definitively that the drug is effective using hypothesis.
The p-value of 0.027 indicates that if there were truly no effect of the drug, the probability of observing a result as extreme as or more extreme than what was observed in project number 11 would be 0.027. This suggests that the result is unlikely to have occurred by chance alone. However, it is possible that the result is a false positive or due to chance variation, especially given that 20 research projects were conducted. It would be important to replicate the result in additional studies and consider the overall body of evidence before concluding definitively that the drug is effective.
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Jayden folded a 66cm strip of paper into 6 equal parts to model a honeycomb cell's. Each part was one side of the model. What is the length of one side of the model?
Answers
Answer:
11 cm
Step-by-step explanation:
The strip of paper is 66 cm and it is folded into 6 different parts. It is used to form a model of a honeycomb cell.
To find the length of one side of the model, all we have to do is divide 66 cm by 6. That is:
66 / 6 = 11 cm
The length of one side of the model is 11 cm.
I will mark you BRAINLIEST for the correct answer
Answers
Answer:
8:56 which simplified would be 1:7
Step-by-step explanation:
What is the radius of convergence of a power series function?
Answers
The radius of convergence of a power series function is a positive real number R that determines the interval of values for which the power series converges.
It represents the distance from the center of the power series expansion, within which the series converges. The radius of convergence is determined by the properties of the coefficients in the power series. Specifically, it is defined as the reciprocal of the limit superior of the absolute values of the coefficients. Mathematically, if we have a power series function of the form:
f(x) = ∑(n=0 to ∞) aₙ(x - c)ⁿ
where aₙ represents the coefficients and c is the center of the series, then the radius of convergence R is given by:
R = 1 / lim sup |aₙ|^(1/n)
The power series converges for all values of x within the interval (c - R, c + R). If |x - c| > R, the series diverges.
It's important to note that the radius of convergence can be zero, indicating that the power series only converges at the center point (x = c), or it can be infinite, indicating that the series converges for all values of x.
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fx=4(3)^(x)
The function represents exponential growth.
The function represents exponential decay .
The y-intercept is _______
Answers
The function represents exponential growth and the y-intercept is 4
How to determine the type of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 4(3)^x
An exponential function is represented a
f(x) = ab^x
Where
y-intercept = a
rate = b
This means that
y-intercept = 4
b = 3
Since the value of b is greater than 1, then the function is a growth function
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1. Luzcel real estate owns 8000 square meters of lot area and decides to construct two different styles of houses, B and C. The lot area of house B is 250 sq. m. and house C lot area is 200 sq. m. The construction engineer has a maximum of 6400 man-hours of labor for the construction. Let your variables be the number of units of house B and the number of units of house C to be constructed. a) Write an inequality which states that there are 8000 sq. m. of land available. b) A unit of house B requires 160 man-hour and a unit of house C requires 256 man-hour. Write an inequality that the engineer has at most 6400 man-hour available for construction. c) If material cost 600 thousand pesos for a unit of house B and 800 thousand for a unit of house C, write an inequality stating that the engineer has at least 12 million pesos to spend for materials. d) Labor cost 1.1 million pesos for constructing a unit of house B and 1.3 million pesos for constructing a unit of house C. If a unit of house B sells for 3.5 million and a unit of house C selis for 4 million, how many units of house B and house C should be constructed to obtain the maximum profit? Show the graph.
Answers
Inequality stating that there are 8000 sq. m. of land available: Let B be the number of units of house B and C be the number of units of house C.
Therefore,B+C ≤ 8000/200 [Reason: House C requires 200 sq. m. of land]⇒B+C ≤ 40b. Inequality that the engineer has at most 6400 man-hour available for construction:
160B + 256C ≤ 6400c
Inequality stating that the engineer has at least 12 million pesos to spend for materials:
600B + 800C ≤ 12000d
. Let us write down a table to calculate the cost, income and profit as follows:Units of house BLabor Hours per unit of house BUnits of house CLabor Hours per unit of house CTotal Labor HoursMaterial Cost per unit of house BMaterial Cost per unit of house CTotal Material CostIncome per unit of house BIncome per unit of house C
Total IncomeTotal ProfitBC=8000/200-B160CB+256C600000800000+256C12,000,0003,500,0004,000,0003,500,000B+C ≤ 40 160B + 256C ≤ 6400 600B + 800C ≤ 12000 Units of house B requires 160 man-hour and a unit of house C requires 256 man-hour.
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the body mass of a man is xkg.thebody mass of his two children are five-sixth and four_fifths of their father5 x over 6 + 4 x over 5 5 x over 6 + 4 x over 5
Answers
56/120
Step-by-step explanation:
The body masses of the two children in terms of their father's body mass, x, are:
First child's body mass = 5x/6 kg
Second child's body mass = 4x/5 kg
To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.
Let the body mass of the man be x kg.
The first child's body mass is five-sixths of their father's body mass:
Body mass of the first child = (5/6) * x
= 5x/6 kg.
The second child's body mass is four-fifths of their father's body mass:
Body mass of the second child = (4/5) * x
= 4x/5 kg.
Therefore, the body masses of the two children in terms of their father's body mass, x, are:
First child's body mass = 5x/6 kg
Second child's body mass = 4x/5 kg
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Pleaseeeee helpppp !!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
Square root of 56 so in simplest radical form 4 root 4
Step-by-step explanation:
hope this helped!
(Leve
A manufacture manufactures a car for a fixed cost
The car show room determines the selling price to be 55% above the manufacturing
The car show room currently has a sale, reducing all cars be 16%
The sale price of the car is £12,369
Calculate the manufacturing cost of the car.
Answers
Answer:
20068
Step-by-step explanation:
mmm
which statement describes the solutions of the equation? 4x/3x+1 = x/2x+10
A) the equation has one valid solution and no extraneous of solutions.
B. the equation has one valid solution and one extraneous of solutions.
C. the equation has two valid solution and no extraneous of solutions.
D. the equation has no valid solution and two extraneous of solutions.
Answers
Answer:
The equation has one valid solution and no extraneous of solutions.Step-by-step explanation:
Given the expression;
4x/3x+1 = x/2x+10
We are to get the nature of the value of x
Cross multiply;
x(3x+1) = 4x(2x+10)
3x²+x = 8x²+40x
Collect like terms;
3x²-8x² + x - 40x = 0
-5x²+x -40x = 0
-5x²-39x = 0
-5x² = 39x
-5x = 39
x = -39/5
Since we have just one value of x hence, the equation has one valid solution and no extraneous of solutions.
The equation has one valid solution and no extraneous of solutions. The correct option is A.
What is equation?An equation is a mathematical expression in terms of one or more unknown variable.
Given the equation : 4x/3x+1 = x/2x+10
Simplify by Cross multiplication, we get
x(3x+1) = 4x(2x+10)
3x²+x = 8x²+40x
3x²-8x² + x - 40x = 0
-5x²+x -40x = 0
-5x²-39x = 0
Simplifying further and solving for x
-5x² = 39x
-5x = 39
x = -39/5
We have just one value of x.
Hence, the equation has one valid solution and no extraneous of solutions.
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Fred makes $750 a week working 5 days .How much does he make in one day
Answers
Answer:
$150
Step-by-step explanation:
750/5 = 150
Part B
Write a numerical expression that represents the area Sabrina painted the second weekend. Using this numerical expression, find the area that Sabrina painted the second weekend.
Answers
Step-by-step explanation:
she painted half of the still to be painted area.
after the first weekend there were 800 of 1600 ft² painted, and therefore 1600 - 800 = 800 ft² left to be painted.
on the second weekend she then painted half of that :
800 / 2.
that means she painted 800/2 = 400 ft², and that left 800 - 400 = 400 ft² to be painted on the following weekends.
if we look in detail, we find the starting 800 ft² of the second weekend are already the result of the first weekend.
800 = 1600 / 2
so,
800 / 2 = 1600 / 2 / 2 = 1600 / 2² = 1600 / 4.
and the same principle goes on weekend after weekend.
therefore, the expression for the nth weekend could be
1600 × (1/2)^n ft²
that means, she painted
on the 1st weekend : 1600 × 1/2 = 800 ft²
on the 2nd weekend : 1600 × 1/4 = 400 ft²
on the 3rd weekend : 1600 × 1/8 = 200 ft²
on the 4th weekend : 1600 × 1/16 = 100 ft²
...
that also means : she will never be finished, as she always paints only half of what is still left open, and that leaves always some part open. it will be tinier and tinier over time, but never 0.
an oil tank has to be drained for maintenance. The tank is shaped like a that is ft long with a diameter of 2.2 Suppose is drained at a rate of 2.1 ft ^ 3 per minutethe tank starts completely full , how many minutes will it take to empty the tank? Use the value 3.14 for and round your answer to the nearest minutenot round any intermediate computations
Answers
The given information is:
- The tank has the shape of a cylinder
- The dimensions of the cylinder are 5 ft long and diameter 2.2 ft.
- The tank is drained at a rate of 2.1 ft^3 per minute.
The volume of the tank is given by the formula:
\(V=\pi *(\frac{d}{2})^2*h\)Where d is the diameter and h is the height.
By replacing the known values we obtain the initial volume:
\(\begin{gathered} V=3.14*(\frac{2.2ft}{2})^2*5ft \\ V=3.14*(1.1ft)^2*5ft \\ V=3.14*1.21ft^2*5ft \\ V=18.997ft^3 \end{gathered}\)As the drain rate is 2.1 ft^3 per minute, the time that is needed to empty the tank is:
\(\frac{18.997ft^3}{2.1ft^3\text{ / min}}=9.04\text{ min}\)The answer is 9 minutes.
If the equation 2x
2 – 8x – 42 = 0 is solved by factoring, what is its positive
solution set?
A. {-3} B. {5} C. {6} D. {7}
Answers
Answer:
B.{5}
Step-by-step explanation:
2-8x-42=0
(÷2), we get,
1-4x-21=0
-4x-20=0
-4x=20
x=20÷(-4)
x=(-5)
since the question asks for a positive set, the answer is [x=5]
The positive solution set is D. {7}.
What is a set ?A set is a well defined collection of objects written by commas and closed by second brackets.
According to the given question the equation 2x² - 8x - 42 = 0 have two factors and we have write the positive factor in form of a set.
2x² - 8x - 42 = 0
x² - 4x - 21 = 0
x² -7x + 3x - 21 = 0
x(x-7) + 3(x - 7) = 0
(X+3) = 0 OR (x-7) = 0
x = -3 OR x = 7.
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- I will give brainliest
Find the area of this shape. Include units of measure in your answer.
Answers
21 inch²
we splitthe two shapes, find the areas by multiplying the two sides and we add both of the answers, 15+6
Answer:
2(3) + 2(6) = 6 + 12 = 18 square feet
Factor this expression completely, then place the factors in the proper location on the grid.
x3 - 1
Answers
Answer:
(x - 1)(x^2 + x + 1)
Step-by-step explanation:
they said it was the answer.
i need help please! How do i know which is the correct answer.
Answers
Answer:
C
Step-by-step explanation:
since there cant be technically half of someone (i hope not) the domain has to be "whole numbers". hours can be split, so they are "all numbers". well, looking at it again, it is C, since the others can not possibly be correct.
2+6k-18=-3k+11
show work
thanks!! :)
Answers
Answer:
k=3
Step-by-step explanation
1.)Group like terms 2+6k-18= -3k+11
2.)Add/Subtract the numbers 2-18=-16 6k-16= -3k+11
3.)Add 16 to both sides
4.)Simplify 6k=-3k+27
5.)Add 3k to both sides
6.)Simplify 9k=27
7.)Divide both sides by 9
8.)Simplify k=3
:)Hope you enjoy this:)
2d a researcher wanted to know if there was a significant difference in cyber security breaches between cities on two different continents. what test should he conduct to determine if there is a significant difference in cyber security breaches between the continents? write up the results and determine what do the results mean? here is the data set: asia europe 40 25 52 35 63 20 70 18 25 19 19 14 11 9
Answers
There is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
We use two sample t-test to check for the significance.
We take the sample of Asia as treatment 1 and that of Europe as treatment 2
Treatment 1
\(N_{1}\): 5
\(df_{1}\) = N - 1 = 5 - 1 = 4
\(M_{1}\): 24.6
\(SS_{1}\): 77.2
\(S^{2} _{1}\) = \(SS_{1}\)/(N - 1) = 77.2/(5-1) = 19.3
Treatment 2
\(N_{2}\): 6
\(df_{2}\) = N - 1 = 6 - 1 = 5
\(M_{2}\): 23.5
\(SS_{2}\): 1051.5
\(S^{2} _{2}\) = \(SS_{2}\)/(N - 1) = 1051.5/(6-1) = 210.3
T-value Calculation
\(S^{2} p_{}\) = (( df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((4/9) * 19.3) + ((5/9) * 210.3) = 125.41
s2M1 = s2p/N1 = 125.41/5 = 25.08
s2M2 = s2p/N2 = 125.41/6 = 20.9
t = (M1 - M2)/√(s2M1 + s2M2) = 1.1/√45.98 = 0.16
The t-value is 0.16221. The p-value is .874721. The result is not significant at p < .05
Hence the answer is there is no significant difference between the cyber security breaches of the two destinations and the values are t-value is 0.16221, the p-value is .874721.
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Fritz can build a bookcase in 8 hours and Holly can build the same bookcase in 10 hours. After working together for 3 hours, Fritz leaves how long will it take holly to finish the bookcase by herself?
Answers
Holy will take 13/5 or 2.6 hours to finish the bookcase.
What is relation between time and work?The relation between time and work is
Work Done = Time Taken × Rate of Work ·
or, Rate of Work = 1 / Time Taken ·
or, Time Taken = 1 / Rate of Work ·
Now it is given that,
Time taken by Fritz to build a bookcase = 8 hours
So, Bookcase build by Fritz in 1 hour = 1/8
Similarly,
Time taken by Holly to build a bookcase = 10 hours
So, Bookcase build by Holly in 1 hour = 1/10
So, bookcase build in 3 hours
Fritz = 3/8
Holly = 3/10
Total bookcase build in 3 hours = 3/8 + 3/10 = 27/40
So. remaining work = 1 - 27/40 = 13/40
Thus, Time taken by Fritz to complete the bookcase = 8 * (13/40) hours
= 13/5 or 2.6 hours
Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.
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orange squash diluted 1 part squash to 7 parts water. Making 2 litres of diluted squash. How much water is needed?
Answers
We need 1.75 litres of water to make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water
The number of waterTo make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water, we need to calculate how much water is needed.
We can do this by using the following formula:
Water = Diluted Squash - Squash First, we need to find out how much squash is in 2 litres of diluted squash.
Since the ratio is 1:7, we can divide 2 litres by the total number of parts (1 + 7 = 8) to find out how much squash is in 2 litres of diluted squash: Squash = 2 litres / 8 = 0.25 litres
Now we can use the formula to find out how much water is needed:
Water = 2 litres - 0.25 litres = 1.75 litres
Therefore, we need 1.75 litres of water to make 2 litres of diluted squash with a ratio of 1 part squash to 7 parts water.
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