To find the number of machines that minimize the unit cost, we need to find the value of x that minimizes the function C(x). We can do this by finding the critical points of C(x) and determining which one corresponds to a minimum.
First, we take the derivative of C(x) with respect to x:
C'(x) = 1.2x - 372
Then, we set C'(x) equal to zero and solve for x:
1.2x - 372 = 0
1.2x = 372
x = 310
So the critical point is x = 310.
To determine whether this critical point corresponds to a minimum or a maximum, we need to examine the second derivative of C(x):
C''(x) = 1.2
Since C''(x) is positive for all values of x, we know that the critical point x = 310 corresponds to a minimum.
Therefore, the number of machines that must be made to minimize the unit cost is 310.
suppose vi pays its phone reps $12 per hour. how many phone reps should it employ if it wants to maximize profit?
Therefore , the solution of the given problem of unitary method comes out to be hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
An unitary method is what?This common convenience, already-existing variables, or all important elements from the original Diocesan adaptable study that followed a particular methodology can all be used to achieve the goal. Both of the crucial elements of a term affirmation outcome will surely be missed if it doesn't happen, but if it does, there will be another chance to get in touch with the entity.
Here,
The formula below can be used to determine the ideal amount of phone representatives:
=> MR = MC
Where n is the amount of phone reps and 12 is their hourly wage, the cost is given by C = 12n.
The following results are obtained by taking the derivative of revenue and cost with regard to n:
=> MR=dR/dn = k
=> dC/dn = 12 for MC.
When we set MR equal to MC, we obtain:
=> k = 12
Accordingly, Vi should hire as many phone representatives as are required to produce an hourly salary of $144, or 12 times the average hourly wage of $12 for phone reps.
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A pharmacist has an 18% alcohol solution and a 40% alcohol solution. How much of each should he mix together to make 10L of a 20% alcohol solution? Pls help
0.18x + 4 - 0.40x = 2
-0.22x = -2
x = 9.09
Therefore, the pharmacist should mix 9.09 liters of 18% alcohol solution and 0.91 liters of 40% alcohol solution to make 10 liters of 20% alcohol solution.
[tex]x=\textit{Liters of solution at 18\%}\\\\ ~~~~~~ 18\%~of~x\implies \cfrac{18}{100}(x)\implies 0.18 (x) \\\\\\ y=\textit{Liters of solution at 40\%}\\\\ ~~~~~~ 40\%~of~y\implies \cfrac{40}{100}(y)\implies 0.4 (y) \\\\\\ \textit{10 Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~10\implies \cfrac{20}{100}(10)\implies 2 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{alcohol only}}&\stackrel{\textit{Liters of}}{\textit{alcohol only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.18&0.18x\\ \textit{2nd Sol'n}&y&0.4&0.4y\\ \cline{2-4}&\\ mixture&10&0.2&2 \end{array}~\hfill \begin{cases} x + y = 10\\\\ 0.18x+0.4y=2 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=10\implies y=10-x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation from above}}{0.18x+0.4(10-x)=2}\implies 0.18x+4-0.40x=2 \\\\\\ -0.22x+4=2\implies -0.22x=-2\implies x=\cfrac{-2}{-0.22}\implies \boxed{x\approx 9.09} \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y\approx 10-9.09\implies \boxed{y\approx 0.91}[/tex]
2 people - 0 people = ? people
Given a line with the equation: 4x + 4y = 4.
1) Write the equation of a line that is parallel to this line.
2) Write the equation of a line that is perpendicular to this line.
3) Write the equation of a line that is neither parallel nor perpendicular to this line.
An equation of a line that is parallel to this line is y = -x + 3.
An equation of a line that is perpendicular to this line is y = x + 3.
An equation of a line that is neither parallel nor perpendicular to this line is y = 3x + 3.
How to write the required equations?Based on the information provided about this line, an equation that models it is given by:
4x + 4y = 4.
4y = -4x + 4
y = -x + 1
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -1 = -1
Slope (m) = -1
Therefore, the required equation is y = -x + 3
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
-1 × m₂ = -1
m₂ = 1
Slope, m₂ = 1
Therefore, the required equation is y = x + 3
By using a line with a different slope other than 1 and -1 would produce a line that is neither parallel nor perpendicular to the given line.
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GM is tangent to circle O at point G, and GS
is a secant line. If mGS = 84°, find
m/SGM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.
What is secant line?Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.
the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:
m∠MGS = 90°
Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.
m∠SGM = 1/2 (mSE - mGE)
where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.
mSE = 2mGS
mSE = 2(84°) = 168°
m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°
Therefοre, m∠SGM = 84°.
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Sarah has 43 bananas, she gives Steve 10. How many bananas does she have left?
Answer:
33
Step-by-step explanation:
43-10=33 sarah has 33 bananas ledt
someone please help meee!! ASAPPP
Hi so you have to do grid for the equation
helppppp!! For #19-20, solve for x. Simplify all radicals.
math hw please helpppp
The characteristics of each function has been explored based on the table below.
The graph of each function is shown in the image attached below.
How to complete the table and graph the functions?In order to use the given functions to complete the table, we would have to substitute each of the values of x (x-values) into the function and then evaluate as follows;
A. f(x) = 2x
x process f(x)
-2 f(-2) = 2(-2) -4
-1 f(-1) = 2(-1) -2
0 f(0) = 2(0) 0
1 f(1) = 2(1) 2
2 f(2) = 2(2) 4
B. G(x) = x²
x process f(x)
-2 f(-2) = (-2)² 4
-1 f(-1) = (-1)² 1
0 f(0) = (0)² 0
1 f(1) = (1)² 1
2 f(2) = (2)² 4
B. H(x) = 2ˣ
x process f(x)
-2 f(-2) = (2)⁻² 1/4
-1 f(-1) = (2)⁻¹ 1/2
0 f(0) = (2)⁰ 1
1 f(1) = (2)¹ 2
2 f(2) = (2)² 4
In this scenario and exercise, we would use an online graphing calculator to plot each of the given functions as shown in the graph attached below.
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you glass of orange is 1/2 full. Your friends glass is 1/3 full. your friend has more orange juice explain how this is possible
Answer:
Step-by-step explanation:
It is possible if your friend has a bigger glass than you.
how can you make two pairs of adjacent and vertical angles but explained in a simple way.
Answer:
there
Step-by-step explanation:
There are 80 people in a choir.
Half the people in the choir are women.
The number of men in the choir is one quarter of the number of women.
The rest of the people in the choir are children.
the number of children in the choir: the number of men in the choir = n: 1
Work out the value of n.
You must show how you get your answer.
Answer:
3
Step-by-step explanation:
Number of people in the choir = 80
Number of women = half of 80 = 40
Number of men in the choir is ¼ of the women = 40/4 = 10
Number of men plus women = 10 +40 = 50
Number of children = 80 - 50 = 30
Ratio of children to men = n:1 = 30:10
Divide both sides by 10
30:10 = 3:1
n = 3
When comparing the given value to −12, which is a TRUE statement?
Select the statement that shows equivalent measurements.
5.2 meters = 0.52 centimeters
5.2 meters = 52 decameters
52 meters = 520 decimeters
5.2 meters = 5,200 kilometers
None of these options
Option A
Conversion of measurement of Metres to Centimetres can be done by multiplying the number by 100
1 metre = 100 centimetres
5.2 metres = 520 centimetres
Option B
Conversion of measurement of Metres to Decametres can be done by multiplying the number by 0.1
1 metre = 0.1 decametres
5.2 metres = 0.52 decametres
Option C
Conversion of measurement of Metres to Decimetres can be done by multiplying the number by 10
1 metre = 10 decimetres
5.2 metres = 52 decimetres
Option D
Conversion of measurement of Metres to Kilometres can be done by multiplying the number by 0.001
1 metre = 0.001 kilometres
5.2 metres = 0.0052 kilometres
Therefore,
5.2 metres = 520 centimetres
5.2 metres= 0.52 decametres
5.2 metres= 52 decimetres
5.2 metres= 0.0052 kilometres
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a postal employee is counting how many houses on the route have dogs. statistically, 48\% of homes have dogs, according to the postal employees research. on the route of 30 homes, the postal employee encounters 12 dogs. what is the variance?
The variance is 7.2.
We can use the binomial distribution formula to calculate the variance. The formula for the variance of a binomial distribution is
Variance = n × p × (1 - p)
where n is the number of trials, p is the probability of success on each trial, and (1 - p) is the probability of failure on each trial.
In this case, n = 30 (the number of homes on the route), p = 0.48 (the probability of a home having a dog), and (1 - p) = 0.52 (the probability of a home not having a dog).
The postal employee encountered 12 dogs, which means there were 18 homes without dogs. So, the actual probability of success in this case is
P(dogs) = 12/30 = 0.4
Using the formula above, we can calculate the variance
Variance = n × p × (1 - p)
= 30 × 0.4 × 0.6
= 7.2
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in a gambling game a person draws a single card from an ordinary 52-card playing deck. a person is paid $19 for drawing a jack or a queen and $5 for drawing a king or an ace. a person who draws any other card pays $2. if a person plays this game, what is the expected gain? (round your answer to the nearest cent.)
the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.
There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.
The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:
Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)
Expected gain = 38/13 - 10/13 - 18/13
Expected gain = 10/13 ≈ 0.77
Therefore, the expected gain is $0.77, rounded to the nearest cent.
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about 4% of the population has a particular genetic mutation. 1000 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 1000.
The standard deviation for the number of people with the genetic mutation in a group of 1000 individuals is approximately 4.89.
To find the standard deviation for the number of people with a particular genetic mutation in a group of 1000 individuals, we first need to understand the concept of binomial distribution.
Binomial distribution is a statistical probability distribution that represents the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).
In this case, the probability of success (having the genetic mutation) is 0.04, and the probability of failure (not having the mutation) is 0.96. Thus, we can model the number of people with the mutation in a group of 1000 individuals using a binomial distribution with n = 1000 and p = 0.04.
The formula for the standard deviation of a binomial distribution is:
σ = √(np(1-p))
Where σ is the standard deviation, n is the number of trials, and p is the probability of success. Plugging in the values, we get:
σ = √(1000 x 0.04 x 0.96) = 4.89
In other words, we can expect that the number of people with the genetic mutation in a group of 1000 individuals will vary around the mean of 40 (1000 x 0.04) by about 4.89, with about 68% of the observations falling within one standard deviation of the mean.
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for each of the number lines, write an absolute value equation in the form |x-c|=d, where c and d are some numbers, to satisfy the given solution set.
PLEASE HELP!!!!!!!!! ASAP!!!!!!
Here are some examples:
Distance to endpoint: |2 - (-2)| = 4
Equation: |x - 2| = 4
When answering questions on Brainly, you should always be factually accurate, professional, and friendly. You should be concise and not provide extraneous amounts of detail. You should also use the following terms in your answer, if they are relevant to the question being asked.
In order to write an absolute value equation in the form |x-c|=d to satisfy a given solution set on a number line, you need to do the following:First, identify the number c, which is the midpoint of the solution set. This is because the absolute value of x-c is equal to the distance between x and c on the number line.
Next, identify the number d, which is equal to the distance between the midpoint c and one of the endpoints of the solution set. This is because the absolute value of x-c can never be greater than the distance between x and c, so the maximum value of x that satisfies the equation is c+d and the minimum value is c-d.Finally, write the equation in the form |x-c|=d using the values of c and d that you identified.
Set of solutions (-3, 1) In the middle: (-3 + 1)/2 = -1
Endpoint distance: |-1 - (-3)| = 2
Formula: |x + 1| = 2
Set of solutions (-4, 4)
Center: (-4 + 4)/2 = 0.
Endpoint distance: |0 - (-4)| = 4
Equation: 4 for |x| Set of solutions (-2, 6)
Center: (-2 + 6)/2 = 2
Endpoint distance: |2 - (-2)| = 4
Equation: 4 for |x - 2|
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8. A rectangular room is shown.
4x - 1
--x
2
3x + 6
A. (4x-1)-2x
B. (3x2+6) + (4x - 1) + x
C. (4-1)-(3x² + 6)
(3x2+6) + 2(4x - 1) + 2x
Door
X
4x - 1
Port A: Which of the following expressions represents the perimeter of the room without th
door?
(3x²+6)+(x-1)x2+²x = (3x²+6) + 2(9x-=
Port B: What is the perimeter of the room without the door in simplest form? Show you
work.
I only need part b
Answer: 14x + 10
Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:
Perimeter = 2(4x-1) + 2(3x+6)
Simplifying and combining like terms, we get:
Perimeter = 14x + 10
Therefore, the perimeter of the room without the door in simplest form is 14x + 10.
one number is four more than a second number. two times the first number is 2 more than four times the second number. what are the two numbers?
The two numbers are 6 and 2.
Let's assume the first number is x and the second number is y.
From the first statement, we can write the equation x = y + 4.
From the second statement, we can write the equation 2x = 4y + 2.
Now, we can substitute x in terms of y from the first equation into the second equation:
2(y + 4) = 4y + 2
Simplifying this equation, we get:
2y + 8 = 4y + 2
2y = 6
y = 3
Substituting y = 3 in the first equation, we get:
x = y + 4 = 3 + 4 = 7
Therefore, 6 and 2 are the two numbers,
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let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. which of the following is a possible graph of y=f(x)?
First, note that the degree of the polynomial is the highest power of x that appears in the expression. In this case, the degree is max(n, 5, m, 2).
How to determine graph?Next, consider the leading coefficient of the polynomial, which is the coefficient of the term with the highest power of x. In this case, the leading coefficient is a.
Based on this information, here are some possible general shapes of the graph of y=f(x):
If n is even and a > 0, the graph of y=f(x) looks like a "U" shape, with both ends pointing upwards.
If n is even and a < 0, the graph of y=f(x) looks like an upside-down "U", with both ends pointing downwards.
If n is odd and a > 0, the graph of y=f(x) looks like a "v" shape, with the vertex pointing upwards.
If n is odd and a < 0, the graph of y=f(x) looks like an upside-down "v", with the vertex pointing downwards.
Note that these are just general shapes, and the actual graph could be modified by the other terms in the polynomial. Additionally, the values of b, c, d, and the constants could also affect the shape and behavior of the graph.
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Complete Question is : let f(x)=ax^n+bx^5+36/cx^m-dx^2+9 where m and n are integers and a,b,c and d are unknown constants. what is the possible graph of the function?
in a normal distribution, 95.4% of the values fall between 5.8 and 10.6. compute the mean of the distribution.
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%
The mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values are between 5.8 and 10.6, and the total number of values is 95.4%.
To calculate the mean, we must first calculate the sum of all the values. To do this, we will use the following formula:
sum of values = (lowest value + highest value) / 2
In this case, the lowest value is 5.8 and the highest value is 10.6, so the sum of values is 8.2.
We now have the sum of all the values, so we can calculate the mean by dividing the sum by the total number of values. The total number of values is 95.4%, so the mean is 8.2 / 0.954 = 8.57.
Therefore, the mean of the normal distribution is 8.57.
In conclusion, the mean of a normal distribution is calculated by taking the sum of all the values and dividing it by the total number of values. In this case, the values were between 5.8 and 10.6, and the total number of values was 95.4%. When the sum of all the values (8.2) was divided by the total number of values (0.954), the mean was calculated to be 8.57.
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a subset of the integers 1, 2, . . . , 100 has the property that none of its members is 5 times another. what is the largest number of members such a subset can have? (a) 72 (b) 77 (c) 84 (d) 85 (e) 86
Answer:
Let's assume that the subset contains as many numbers as possible. We start by including all the numbers from 1 to 100 that are not divisible by 5. These are the numbers 1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 86, 87, 88, 89, 91, 92, 93, 94, 96, 97, 98, 99.
This gives us a subset of 81 numbers. However, we need to remove any numbers that are multiples of other numbers in the subset. For example, if we include the number 6, we must remove 12, 18, 24, etc. Similarly, if we include the number 9, we must remove 18, 27, 36, etc. We can see that the only numbers that have multiples in the subset are 2, 3, 7, 8, 13, 17, 18, 19, 27, 28, 37, 38, 39, 52, 53, 54, 57, 58, 59, 68, 69, 73, 74, 78, 79, 83, 84, 87, 88, 89, 92, 93, 94, and 98.
Therefore, we need to remove these 34 numbers from the subset. This leaves us with a subset of 81 - 34 = 47 numbers.
However, we can still include the number 5, since it is not a multiple of any other number in the subset. This adds one more number to the subset, giving us a total of 48 numbers.
Therefore, the largest number of members that such a subset can have is 48, which corresponds to answer choice (e).
a. is w in fv1; v2; v3g? how many vectors are in fv1; v2; v3g? b. how many vectors are in span fv1; v2; v3g? c. is w in the subspace spanned by fv1; v2; v3g? why?
a. No, w is not in fv1; v2; v3g. There are three vectors in fv1; v2; v3g.
b. There are three vectors in the span of fv1; v2; v3g.
c. No, w is not in the subspace spanned by fv1; v2; v3g. This is because the subspace is the set of all linear combinations of the vectors in the span, and w does not have to be a linear combination of the vectors in the span.
To prove this, we first need to recall the definition of the span: it is the set of all linear combinations of a set of vectors. A linear combination is a sum of the vectors, multiplied by constants. For example, if we have a vector v1, and two constants a and b, then the linear combination of a*v1 and b*v1 is (a + b)*v1. If a vector w is not a linear combination of v1, then w is not in the span of v1.
The same logic applies to the vectors fv1; v2; v3g. If w is not a linear combination of these three vectors, then w is not in the subspace spanned by these three vectors. We can prove this by showing that w cannot be a linear combination of fv1; v2; v3g. This is because the only way to create a linear combination of these vectors is to multiply them by constants, and since w is not one of the vectors, it cannot be multiplied by a constant. Therefore, w is not in the subspace spanned by fv1; v2; v3g.
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8. describe the center and spread of the chi-square distributions. 9. what is the chi-square test statistic? is it on the formula sheet? what does it measure? 10. how many degrees of freedom does the chi-square distribution have? 11. what is the rule of thumb for all expected counts in a chi-square goodness of fit test?
8. Spread = SD = sqrt(2*df)
9. The difference between the observed and expected frequencies of the outcomes of a set of events or variables.
10. Degrees of 1 freedom does the chi-square distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
8. Describe the center and spread of the chi-square distributions.
Shape - skewed right because can't be zero
µ = df = tipping point
mode = df - 2 = peak
spread = SD = sqrt(2*df)
9. Chi-square test is a non-parametric test (a non-parametric statistical test is a test whose model does not specify conditions about the parameter of the population from which the sample is drawn.). It is used for identifying the relationship between a categorical variable and denoted by χ2.
10. A chi-squared distribution constructed by squaring a single standard normal distribution is said to have 1 degree of freedom. Thus, as the sample size for a hypothesis test increases, the distribution of the test statistic approaches a normal distribution.
11. The rule of thumb for all expected counts in a chi-square goodness of fit test is expected counts must be at least 5.
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Can someone tell me the answer to this question is please?
Each student should receive 1/2 kg of soil.
How to distribute same amount of soil?To find out how much soil each student will have, we need to first add up the total amount of soil collected and then divide it equally among the 10 students.
Let's start by converting all the amounts of soil to a common unit, such as kilograms:
3 students brought 1/4 kg each, so they brought a total of 3/4 kg.
4 students brought 1/2 kg each, so they brought a total of 2 kg.
3 students brought 3/4 kg each, so they brought a total of 2 1/4 kg.
Adding up these amounts, we get:
3/4 + 2 + 2 1/4 = 5 kg
So the total amount of soil collected is 5 kg.
To redistribute this soil equally among the 10 students, we need to divide it by 10:
5 kg ÷ 10 = 1/2 kg per student
Therefore, each student should receive 1/2 kg of soil.
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a pwr core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores
The probability of finding 10 defective cores in a sample of 10 power cores is approximately 0.0000161, or about 0.0016%.
Assuming that each fuel rod is independent of each other and that the probability of finding a defective fuel rod is constant at 0.1%, we can model the number of defective fuel rods in a power core with a binomial distribution. Let X be the number of defective fuel rods in one power core, then X follows a binomial distribution with parameters n = 50000 and p = 0.1/100 = 0.001.
To find the probability of finding 10 defective cores, we can use the binomial distribution again, but with a different set of parameters. Let Y be the number of defective cores in a sample of 10 power cores, then Y follows a binomial distribution with parameters n = 10 and p = P(X ≥ 1), where P(X ≥ 1) is the probability of finding at least one defective fuel rod in one power core. We can find P(X ≥ 1) using the complement rule:
P(X ≥ 1) = 1 - P(X = 0)
= 1 - (1 - 0.001)^50000
≈ 0.3935
So, the probability of finding 10 defective cores in a sample of 10 power cores is:
P(Y = 10) = (10 choose 10) * (0.3935)^10 * (1 - 0.3935)^(10 - 10)
≈ 0.0000161
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Complete Question:
a power core contains about 50000 fuel rods. if the probability to find one defective fuel rod is 0.1%, what is the probability to find 10 defective cores.
The difference of -12 - 45 will be?? postive or negitive or equle
Answer:33
Step-by-step explanation:45-12=33
does anyone know the answer??
The point that partitions segment AB in a 1:4 ratio is (-1, -0.4).
How to determine the coordinates of point Q?In this scenario, line ratio would be used to determine the coordinates of the point Q on the directed line segment AB that partitions the segment into a ratio of 1 to 4.
In Mathematics, line ratio can be used to determine the coordinates of Q and this is modeled by the following mathematical expression:
Q(x, y) = [(mx₂ + nx₁)/(m + n)], [(my₂ + ny₁)/(m + n)]
Substituting the given parameters into the line ratio formula, we have;
Q(x, y) = [(1(7) + 4(-3))/(1 + 4)], [(1(-10) + 4(2))/(1 + 4)]
Q(x, y) = [(7 - 12)/(5)], [(-10 + 8)/5]
Q(x, y) = [-5/5], [(-2)/(5)]
Q(x, y) = [-1, -2/5]
Q(x, y) = [-1, -0.4]
Read more on line ratio here: brainly.com/question/14457392
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