Therefore, the probability that the average weight of the sample of 39 Goliath Grouper is within 14 pounds of the average weight of all Goliath Grouper caught on the Treasure Coast is approximately 0.2342 or 23.42%.
What is mean?In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data. It is also known as the arithmetic mean or average, and is calculated by summing up all the values in the dataset and then dividing by the number of values. The mean provides a useful summary of the data as it gives an idea of the typical or average value in the dataset. It is commonly used in various fields, including finance, science, and social sciences, to analyze and interpret data. However, the mean can be sensitive to extreme values or outliers in the dataset, so it is important to consider other measures of central tendency, such as the median and mode, in addition to the mean.
Here,
We can approach this problem using the central limit theorem, which states that the distribution of sample means will be approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Let's first calculate the standard error of the mean:
standard error of the mean = standard deviation / sqrt(sample size)
= 74 / √(39)
≈ 11.83
Next, we need to find the z-score corresponding to a sample mean within 14 pounds of the population mean:
z = (sample mean - population mean) / standard error of the mean
= (418 - 14 - 418) / 11.83
= -1.19
Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than -1.19 is about 0.1171. Since we're interested in the probability that the sample mean is within 14 pounds of the population mean, we can multiply this probability by 2 to account for the area under the curve in both tails:
P(sample mean within 14 pounds of population mean) ≈ 2 * 0.1171 ≈ 0.2342
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HELPPPPP???????? PLEASEEE
Answer:
(1,2)
Step-by-step explanation:
The solution to a system of equations is the point at which the lines defined by the equations intersect.
On this graph, we can see that the lines meet a point on the graph that is at 1 on the x-axis (horizontal axis) and at 2 on the y-axis (vertical axis).
In Cartesian coordinates, this is written in the format (x, y):
(1, 2)
The graph of a function g is shown below. Find g (-2). g (-2) = 0
Hence, in answering the stated question, we may say that As a result, graphs P75 equals 80.375.
What is graphs?Mathematicians use graphs to visually explain or chart events or variables. A graph point often indicates a connection between one thing and another. A graph, a non-linear data structure, is constituted of nodes (vertices) and edges. Glue the nodes, which are also called as vertices. This graph has E=1, 2, 1, 3, 2, 4, and (2.5) edges and V=1, 2, 3, 5. (3.5). (4.5). Graphical representations of exponential growth in analytical charts (bar charts, pie charts, line charts, and so on). a graph of a logarithmic triangle.
To get the value of P75, the 75th percentile, we need to discover the score where 75% of the scores fall below it.
z = (x - μ) / σ
where x is the score to be converted, is the mean, and is the standard deviation.
So we can write:
0.75 = P(Z ≤ 0.675)
where Z is the standard normal variable with a mean of 0 and a standard deviation of 1.
We can now rearrange the formula for the z-score to solve for the score x:
x = μ + zσ
Plugging in the values we have:
x = 77.4 + (0.675)(5) (5)
x = 80.375
As a result, P75 equals 80.375.
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need help with this , 13 × y z + 9 +2 × y z + 3
Answer:
simplified expression: 15yz + 12
The ACT is a college entrance exam. ACT has determined that a score of 22 on the mathematics portion of the ACT suggests that a student is ready for college- level mathematics. To achieve this goal, ACT recommends that students take a core curriculum of math course: Algebra 1, Algebra 2, and Geometry. Suppose a random sample of 200 students who completed this core set of courses results in a mean ACT math of 22.6 with a standard deviation of 3.9. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 22 on the math portion of the ACT?
a) State the appropriate null and alternative hypotheses.
b) Use the classical and p-value approach at the = . level of
significance to test the hypotheses in part (a).
c) Write a conclusion based on your result to part (b)
Using null hypothesis,
a. Hzero : μ = 22
Hone : μ > 22
b. All requirements are satisfied.
c. Reject Hzero
d. There is sufficient evidence to support the claim that the students who complete the core curriculum are ready for college-level mathematics. (Score above 22 on average).
What is null hypothesis?The null hypothesis is used to make decisions when employing data and statistical tests. The null hypothesis, or Hzero, claims that there is no difference in the characteristics of the two samples. A null hypothesis is, in general, a statement of no difference. The null hypothesis must be rejected in order to accept the alternative hypothesis.
a. Given,
μzero = 22.
n = 200
x = 22.6
s = 3.9
α = 0.05
Claim is mean is more than 22.
The claim is either null or alternative hypothesis. The null hypothesis states that the population mean is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.
Hzero : μ = 22
Hone : μ > 22
b. Requirements t-distribution hypothesis test: Simple random sample, sampling distribution of the sample mean is approximately normal & independent sample results.
Simple random sample: Satisfied, because exercise prompt states that the sample is a random sample.
All requirements are satisfied.
c. Classical approach:
Determine the value of test statistics,
t = 2.176
Determine the critical values from the students' T-distribution table with
df = n - 1 = 200 -1 = 199 > 100
t = 1.660
2.176>1.660
⇒ Reject Hzero
d. There is sufficient evidence to support the claim that the students who complete the core curriculum are ready for college-level mathematics. (Score above 22 on average).
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2.5% of x is = 17
what is x??
Answer: 680
Step-by-step explanation:
Theoretical propobility
Theoretical probability is the likelihood of an event occurring based on mathematical reasoning or analysis, rather than on empirical or experimental data.
What is probability?Probability refers to the likelihood of a particular event or outcome occurring. It is a measure of the chance of an event happening, and is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, physics, engineering, and finance, to make predictions and inform decision-making.
Here,
It is calculated using the laws of probability and assumes that all outcomes are equally likely to occur. Theoretical probability is often used in situations where it is not possible or practical to conduct experiments or collect data, such as in mathematical or statistical modeling.
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An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240 engines and the mean pressure was 4.6 lbs/square inch. Assume the variance is known to be 0.81 . If the valve was designed to produce a mean pressure of 4.7 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.
We reject the null hypothesis and come to the conclusion that there is adequate evidence at the 0.02 level.
What does hypothesis testing's Type I error and Type II error mean?The rejection of a correct null hypothesis during hypothesis testing is referred to as a Type I mistake. As a result, we get the incorrect conclusion that there is a large difference between two groups or variables. A false positive is another name for a Type I mistake.
Failure to reject a faulty null hypothesis is a Type II mistake. This means that we get the incorrect conclusion that there is no difference between two groups or variables when there actually is one. False negative is another name for a Type II mistake.
The valve generates a mean pressure of 4.7 lbs/square inch, which is the null hypothesis:
H0: μ = 4.7
The other possibility is that the valve does not generate 4.7 lbs/square inch of mean pressure:
Ha: μ ≠ 4.7
Since we are comparing the single sample mean to a known population mean and we are aware of the population variance, we can test this hypothesis using a one-sample t-test. The test statistic is determined by dividing the sample mean (x) by the population mean, the sample size (n), and the population standard deviation (s).
We obtain the following by plugging in the values:
t = (4.6 - 4.7) / (0.9 / √(240))
t = -4.15
Using a two-tailed test and a t-distribution table with 239 degrees of freedom (240 - 1), we can get the crucial t-value as follows:
T critical equals 2.571
We reject the null hypothesis and come to the conclusion that there is adequate evidence at the 0.02 level that the valve does not operate in accordance with specifications since our computed t-value (-4.15), which is in the rejection area (t -2.571 or t > 2.571), falls within this range.
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Use the given information to find the unknown value.
2. y varies
1. y varies directly as the square root
inversely with the cube of x.
of x. When x = 16, then y = 4. Find y
y = 1. Find y when x = 1.
when x = 36.
When x = 3, then
3. The distances that an object falls varies directly with the
square of the time, t, of the fall. If an object falls 16 feet in one
second, how long for it to fall 144 feet?
4. The rate of vibration of a string under constant tension varies
inversely with the length of the string. If a string is 24 inches long
and vibrates 128 times per second, what is the length of a string
that vibrates 64 times per second?
The proportional and inverse relationships can be presented as follows;
1. The value of y when x = 36 is 6
2. The value of y when x = 1 is 27
3. The time of fall of an object that falls 144 feet is 3 seconds
4. The length of the string that vibrates 64 times per second is 48 inches long
What is a proportional relationship?A proportional relationship is one that can be expressed in the form; y = k × x.
The possible questions, obtained from a similar question posted online, are presented as follows;
1. y varies directly as the square root of x, when y = 4, x = 16, to find y when x = 36;
The value of y can be found by expressing the relationship between y and x using a proportional relation as follows;
y ∝ √x
y = c·√x
4 = c·√(16) = 4·c
Therefore;
c = 4/4 = 1
c = 1
When x = 36, we get;
y = 1 × √(36) = 6
Therefore, when x = 36, y = 62. The variation of y and x can be presented as follows;
y ∝ 1/x³
y = c/x³
y = 1, when x = 3, therefore;
1 = c/3³ = c/27
c = 27 × 1 = 27
c = 27
The value y when x = 1, can be found as follows;
y = 27/1³
y = 27/1³ =27
When x = 1, y = 273. The relationship between the distance and the time duration the ball can be presented as follows;
Let s represent the distance the ball falls, and let t represent the time the ball falls, we get;
s = k·t²
The distance an object falls in one second = 16 feet
Therefore, we get;
When s = 16, t = 1
16 = k × 1²
k = 16/1² = 16
k = 16
s = 16·t²
When s = 144 feet, we get;
144 = 16 × t²
t² = 144/16 = 9
t = √9 = 3
The time the object will take to fall 144 feet is 3 seconds4. The relationship between the vibration of a string and the tension in the string can be presented as follows;
Let f represent the vibration of the string, and let l represent the length in the string, we get;
f ∝ 1/l
f = c/l
When l = 24, f = 128, we get;
128 = c/24
c = 128 × 24 = 3,072
Therefore, if the string vibrates 64 times per second, we get;
64 = 3,072/l
l = 3,072/64 = 48
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There are 700 houses in Toby's town. Last summer, 651 of the houses were for sale. What percentage of the houses in the town were for sale last summer? Write your answer using a percent sign (%).
Answer:
93%
Step-by-step explanation:
651/700 houses were for sale. Write that as a percentage.
651/700=0.93
0.93=93%
Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 6.6 per year.
a. Find the probability that, in a year, there will be 4 hurricanes.
b. In a 35-year period, how many years are expected to have 4 hurricanes?
c. How does the result from part (b) compare to a recent period of 35 years in which 3 years had 4 hurricanes? Does the Poisson distribution work well here?
The probability of having 4 hurricanes in a year is approximately 0.118 or 11.8%.
What is probability?It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
According to question:a. To find the probability of having exactly 4 hurricanes in a year, we use the Poisson distribution with a mean of 6.6:
P(X=4) = (e^-6.6)×(6.6^4)/(4!) ≈ 0.118
Therefore, the probability of having 4 hurricanes in a year is approximately 0.118 or 11.8%.
b. In a 35-year period, the expected number of years with 4 hurricanes is:
μ = λt = 6.635 ≈ 231
Therefore, we can expect to have 231 years with 4 hurricanes in a 35-year period.
c. If in a recent period of 35 years, only 3 years had 4 hurricanes, this is less than what the Poisson distribution would predict (231 years). However, this doesn't necessarily mean that the Poisson distribution doesn't work well here. The Poisson distribution is a theoretical model that assumes certain conditions, and it's possible that those conditions weren't met in this specific case. It's also possible that this was just a rare event that can happen due to chance. Further analysis would be needed to determine whether the Poisson distribution is a good fit for this data.
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How do you determine area of a circle
Step-by-step explanation:
it's radius squared timesed by pi (π)
r^2×π
if u don't have a radius but a diameter then half the diameter to get the radius
Answer:
There are two common formulas that can be used to calculate the area of a circle. Here they are:
1. Diameter based formula: [tex]\frac{\pi d^{2} }{4}[/tex].Where [tex]\pi[/tex] is the universal value for all circles that expresses the ratio between the length of circumference and the diameter of any circle. It's a rational number and its value is about 3.141592653589793238462643383279502884197..., so you may want to just 3.14.
2. Radius based formula: [tex]\pi r^{2}[/tex].This is the easiest and simplest formula. Letter "r" represents the length of radius of the circle,
3. Circumference based formula: [tex]\frac{C^{2} }{4\pi }[/tex].Rarely used formula. In this equation, "C" represents the length of circumference of the circle.
Check the attached image to better understand the meaning of radius, diameter and circumference. Also, provided a second image with all the formulas for the area of a circle.
Create a pattern for the rule a +4.
As you can see, each number in the pattern is obtained by adding 4 to the previous number.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
Sure, here's a pattern for the rule a + 4:
a = 1: 1 + 4 = 5
a = 2: 2 + 4 = 6
a = 3: 3 + 4 = 7
a = 4: 4 + 4 = 8
a = 5: 5 + 4 = 9
a = 6: 6 + 4 = 10
a = 7: 7 + 4 = 11
a = 8: 8 + 4 = 12
a = 9: 9 + 4 = 13
a = 10: 10 + 4 = 14
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Write two numbers that multiply to the value on top and add to the value on bottom
Submit Answer
45
X
-14
Answer:
-9 and -5
Step-by-step explanation:
-9 + -5 = -14
-9 * -5 = 45
Answer:
- 9 and - 5
Step-by-step explanation:
- 9 × - 5 = 45 and - 9 + (- 5) = - 9 - 5 = - 14
There are 6 adults in this class. Mary wants to give 5/8 of a doughnut to each person. How many doughnuts will he need?
Step-by-step explanation:
Divide.
Calculus(Question in picture)
The absolute maximum value occur (3, 4.033) at point x = 3
How to find the absolute value of the functionThe function given in the problem is g(x) = 3x³e⁻ˣ
differentiating the function
g(x) = 3x³e⁻ˣ
g'(x) = 3x³(-e⁻ˣ) + e⁻ˣ(9x²)
g'(x) = e⁻ˣ(-3x³ + 9x²)
equating to zero
0 = e⁻ˣ(-3x³ + 9x²)
0 = -3x³ + 9x²
3x³ = 9x²
x = 3
checking intervals close to 3: the check is done using numbers at the left and right to 3 and this numbers will be sufficiently close.
We choose 1 and 5, when the value of g'(x) increases from positive to negative then maximum value occurs
at x = 1, g'(1) = e^(-1)(-3(1)³ + 9(1)²) = 2.2073
at x = 3, g'(3) = e^(-3)(-3(3)³ + 9(3)²) = 0
at x = 5, g'(5) = e^(-5)(-3(5)³ + 9(5)²) = -1.0107
We can say that x = 3 is point of local maxima
g(3) = 3(3)³e^(-3) = 4.03275 = 4.033
from calculation the absolute maximum value occurs at (3, 4.033)
From the graph the absolute maximum value for the domain -1 ≤ x ≤ 5 occurs at (3, 4.033)
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Find the equation of the line shown.
Answer: y=1x+6
Step-by-step explanation:
goign up by 1/1 y intercpt is 6
Which dilation of △ RST would result in a line segment with a slope of 2 that passes through ( − 4 , 2 ) ?
Answer:
The location of the point (4, 2) is to the right of the triangle RST, therefore,
a dilation from the left or a contraction from the right is required.
The dilation of ΔRST that would result in a line segment with slope of 2
that passes through (4, 2) is C. A dilation with a scale factor of 0.5 centered 12,2
Step-by-step explanation:
Corresponding Angles are congruent. Which angle corresponds with 3? 1/2 3/4 fine 7/8 5 6 [?]
Answer:
5, 8 and 2
Because it has the same angel as 3 there for it's 5 , 8 and 2
If the perimeter of the isosceles triangle is at most 45 centimeters, which inequality could be used to find the value of p
Inequality to find the value of p is 7p - 12 ≤ 45. So correct option is C. The value of p is at most 8.14 centimeters.
Describe Inequality?Inequalities can be solved in a similar way to equations, but with some important differences. To solve an inequality, one must find the set of values that satisfy the inequality. This set of values is often expressed as an interval, which is a range of values between two endpoints. For example, the solution to the inequality x < 5 is the interval (-∞, 5), which includes all values of x that are less than 5. The solution to an inequality may also be expressed graphically on a number line or coordinate plane.
The perimeter of an isosceles triangle with sides of length 3p-6, 3p-6, and p is:
Perimeter = (3p-6) + (3p-6) + p
= 7p - 12
We are given that the perimeter is at most 45 centimeters. Therefore, we can write the following inequality to find the value of p:
7p - 12 ≤ 45
Adding 12 to both sides, we get:
7p ≤ 57
Dividing both sides by 7, we get:
p ≤ 8.14
Therefore, the value of p is at most 8.14 centimeters.
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Mio deposits money in his bank account from a summer job and doesn’t spend any of it. After working 3 hours total, he has $71. After working 12 hours total, he has $134. How much money does Mio earn per hour?
Answer:
Step-by-step explanation:
because we know 1 hour is 60 min so 3 hours would be 60x3=180 then you do 3x23.7=71 12x11.2=134 so in total he has 23.7 per hour and 11.2 for 3 hours
The width of a rectangle is 16 feet less than 3 times the length, and the area is 35 square feet.
Part a: Write an equation that can be used to determine the length and width of the rectangle. Express your answer as a quadratic equation set equal to zero
A rectangle has a width that is 16 feet shorter than its length and an area that is 35 square feet. The rectangle's length and breadth can be calculated using the equation [tex]3x^2[/tex] - 16x - 35 = 0.
Assume that the rectangle measures "x" feet in length. Then, according to the problem:
The width is 16 feet less than 3 times the length, so the width is 3x - 16 feet.
The area of the rectangle is 35 square feet, so we can write:
Area = Length x Width
35 = x(3x - 16)
To solve for x, we can simplify this quadratic equation by expanding the right-hand side and moving all the terms to one side:
35 = [tex]3x^2[/tex] - 16x
[tex]3x^2 - 16x - 35 = 0[/tex]
The rectangle's length and breadth can be calculated using the quadratic equation shown above.
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Eric invested $10,000 in a 6-years certificate of deposit that pays 8% simple interest.
a) How much will he receive after the 6 years?
b) What is the total interest that he will earn?
Please help !!!!! My test is timed
Step-by-step explanation:
a) To calculate the amount that Eric will receive after the 6 years, we need to use the formula for simple interest:
I = P * r * t
Where:
- I is the interest earned
- P is the principal amount (the initial investment)
- r is the interest rate (as a decimal)
- t is the time period (in years)
In this case, Eric invested $10,000 at an interest rate of 8% for 6 years. So we can plug in these values:
I = 10,000 * 0.08 * 6
I = 4,800
The interest earned is $4,800. To find the total amount that Eric will receive after the 6 years, we need to add the interest to the principal:
Total = P + I
Total = 10,000 + 4,800
Total = 14,800
Therefore, Eric will receive $14,800 after the 6 years.
b) The total interest that Eric will earn is already calculated in part a) and it is $4,800.
Help would be appreciated a lot!!
In ALMN, LM || OP. Given that NL = 33, NM=44, and NP = 24, find NO.
0
M
NO= =
0
Answer:
NO= 18
Step-by-step explanation:
If we dissect the image, we can see that triangle LMN there are two similar triangles; triangle LMN and smaller triangle OPN. By definition of similar triangles, corresponding parts of similar triangles will have the same ratios. So, as we can see, sides NP and NM are corresponding. The ratio of the two sides is 24/44 (just put the smaller side over the longer side). Simplified, the ratio is 6/11. So, we know that the opposite sides' ratio will also be 6/11. So, all we have to do is multiply NL (33) by 6/11, which equals 18.
Check:
24/44=6/11, and 18/33=6/11, so the ratios are the same.
Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 24 gallons of gasoline to travel 552 miles.
Write a direct variation equation to represent the relationship. Use d for the distance the car travels (in miles) and g for amount of gasoline it uses (in gallons)
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{D varies directly with G}}{D = k(G)}\hspace{5em}\textit{we also know that} \begin{cases} G=24\\ D=552 \end{cases} \\\\\\ 552=k(24)\implies \cfrac{552}{24}=k\implies 23=k\hspace{5em}\boxed{D=23G}[/tex]
Can someone please help
Answer:
34
Step-by-step explanation:
16x-12= 9x-11 + 9x-11
16×-12=18x-22
10=2x
5=x
WT= 9x-11=9(5)-11
WT=45-11
WT=34
Which graph represents the function g(z)=√2-1+1?
In response to the given question, we can state that Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.
what is function?Mathematicians examine numbers and complex variations, equations and associated structures, forms and their locations, and prospective positions for these things. The term "functioning" signifies the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and results in which each input leads to a single, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used this to denote functions (x). The symbol for admission is an x. The four primary types of usable functions are on operations, one-to-one capabilities, so multiple functionality, in capabilities, and then on functions.
Because it is independent of z, the function g(z) is a constant function. In particular, g(z) equals 2 - 1 + 1 = 2.
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I will mark you brainiest!
The sum of all of the exterior angles of an octagon is:
A) 180º.
B) 360º.
C) 1080º.
D) 36º.
Answer:
The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees. Each exterior angle of a regular octagon measures 45 degrees, because the sum of the interior and exterior angles at each vertex is 180 degrees, and the octagon has 8 vertices. Therefore, the sum of all the exterior angles of an octagon is:
8 × 45º = 360º
So the answer is option B) 360º.
Solve for the value of e.
(pls help me)
Answer:
e = 10
Step-by-step explanation:
Vertically opposite angles are the angles formed opposite to each other when two lines intersect.
Vertically opposite angles are equal.
9e - 8 = 8e + 2
Add 8 to both sides,
9e = 8e + 2 + 8
9e = 8e + 10
Subtract '8e' from both sides,
9e - 8e = 10
[tex]\boxed{\bf e = 10}[/tex]
Answer:
e = 10
Step-by-step explanation:
According to the Vertical Angle Theorem, when two straight lines intersect, the opposite vertical angles are congruent.
Since the two given angles are vertical angles, they are congruent.
Therefore, we can set them equal to each other:
[tex]\implies (9e - 8)^{\circ} = (8e + 2)^{\circ}[/tex]
[tex]\implies 9e - 8= 8e + 2[/tex]
To solve for e, begin by subtracting 8e from both sides of the equation:
[tex]\implies 9e - 8-8e= 8e + 2-8e[/tex]
[tex]\implies e - 8= 2[/tex]
Add 8 to both sides of the equation:
[tex]\implies e - 8+8= 2+8[/tex]
[tex]\implies e=10[/tex]
Therefore, the value of e is 10.
1. ALUMMUNI PLC. Produces three models of tractors: Metakeb, Mewesson, Metekem Each unit of Metakeb, Mewesson and Metekem requires the following amounts of time in minumtes in each of the indicated departments.
Machining dep't
Inspection dep't
(in minutes)
(in minutes)
(in minutes)
Metakeb
1200
2400
600
Mewesson
1800
1200
3000
Metekem
3000
Assembly dep't
2400
1200
Suppose the total time available per month in machining, assembly and inspection departments are 1050, 1160 and 830 hours respectively.
Required:
Determine the number of units of each product to be produced in a month to use up all the available resources (use Gaussaian method)
The company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.
What is the Gaussian method?
The Gaussian method, also known as Gaussian elimination or row reduction, is a technique for solving systems of linear equations. It involves performing a sequence of operations on the rows of a matrix to transform it into an equivalent matrix that is in row echelon form or reduced row echelon form.
To use the Gaussian method, we need to set up a system of linear equations based on the given information. Let x, y, and z be the number of units of Metakeb, Mewesson, and Metekem produced per month, respectively. Then we have:
Machining department: 1200x + 1800y + 3000z = 1050(60)
Inspection department: 2400x + 1200y = 1160(60)
Assembly department: 600x + 3000y = 830(60)
Simplifying these equations, we get:
Machining department: 20x + 30y + 50z = 3150
Inspection department: 8x + 4y = 232
Assembly department: x + 5y = 139
Now we can use the Gaussian method to solve for x, y, and z:
Step 1: Write the augmented matrix:
| 20 30 50 | 3150 |
| 8 4 0 | 232 |
| 1 5 0 | 139 |
Step 2: Use row operations to get the matrix in row echelon form:
R2 → R2 - 4/5 R3
R1 → R1 - 20R3
| 0 -2 50 | 850 |
| 0 2 -4 | -28 |
| 1 5 0 | 139 |
R2→ -1/2 R2
R1 → R1 + R2
| 0 1 -25 | 407 |
| 0 1 -2 | 14 |
| 1 5 0 | 139 |
R1→ R1 - R2
| 0 0 -23 | 393 |
| 0 1 -2 | 14 |
| 1 5 0 | 139 |
R3→ R3 - 5R2
| 0 0 -23 | 393 |
| 0 1 -2 | 14 |
| 1 0 10 | 65 |
R1→ -1/23 R1
| 0 0 1 | -17 |
| 0 1 -2 | 14 |
| 1 0 10 | 65 |
R2 → R2 + 2R3
| 0 0 1 | -17 |
| 0 1 0 | 96 |
| 1 0 10 | 65 |
R3 → R3 - 10R1
| 0 0 1 | -17 |
| 0 1 0 | 96 |
| 1 0 0 | 235 |
Step 3: Read off the solution from the row echelon form:
z = -17
y = 96
x = 235
Therefore, the company should produce 235 units of Metakeb, 96 units of Mewesson, and 17 units of Metekem per month to use up all the available resources.
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A vending machine takes only nickels and dimes. There are 8 times as many nickels as dimes in the machine. There is a total of $3.00 in the machine. How many of each coin are there? (Show steps)
In response to the question, we may say that Value total: 60 cents plus equation 240 cents plus 300 cents equals $3.00.
What is equation?The equals symbol (=), which indicates equivalence, connects two statements in a mathematical equation. An algebraic equation's mathematical assertion proves the equality of two mathematical propositions. The equal sign, for instance, places a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. Use a mathematical formula to understand how the two sentences on opposite sides of a letter relate to one another. Usually, the logo corresponds to the particular programme. An example would be 2x - 4 = 2.
Let's define our variables first:
Let x represent the amount of quarters in the machine.
10x + 5(8x) = 300
When we simplify and find x, we obtain:
10x + 40x = 300
50x = 300\sx = 6
Hence, the machine has six dime coins. We may determine the quantity of nickels by using the connection between the number of dimes and nickels:
8x = 8(6) = 48
There are 48 nickels in the machine as a result.
Verifying our response:
6 dime is 6 times 10 cents, or 60 cents.
48 nickels is 48 x 5 cents, or 240 cents.
Value total: 60 cents plus 240 cents plus 300 cents equals $3.00.
The vending machine has 48 nickels and 6 dimes, thus our answer is right.
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