The value of the linear correlation coefficient r is of:
m = -1.
What is a linear function?A linear equation is a special function that has the format of the equation given as follows:
y = mx + b.
The coefficients of the equation y = mx + b are given as follows:
m is the slope, representing the rate of change of y relative to x, which is also the correlation coefficient of the linear function.b is the y-intercept, representing the value of y when x = 0.In this problem, the points of the function are listed as follows:
(1 , 6) , (3 , 4) and (5 , 2)
From these three points, we can gather that when x increases by 2, y decays by 2, hence the slope of the linear function is given as follows:
m = -2/2 = -1.
Meaning that the linear correlation coefficient r of the linear function is of r = -1.
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See picture-multiple choice.
A camp counselor and four campers are to be seated along a picnic bench. In how many ways can this be done if the counselor must be seated in the fourth and a camper who has a tendency to engage in food fights must sit to the counselor's immediate ?
Answer: 6 ways
Step-by-step explanation:
(a - 2b)3 when a = 3 and b = -1/2
Answer:
64
Step-by-step explanation:
Substitute the values so (3-2(-1/2))3
Then distribute so (3-(-1))3
Add since it's a double negative to get (4)3
And 4 cubed is 64
solve for missing angle 20 degrees + 40 degrees + 39 degrees + x
The sum of angles at a point is equal 360 degrees and using that, the value of x is 261 degrees.
Angle At a PointAngles around a point describes the sum of angles that can be arranged together so that they form a full turn. Angles around a point add to 360°.
In this question, when we sum all angles up, it will give us the sum of 360 degrees.
20 + 40 + 39 + x = 360
x + 99 = 360
x = 360 - 99
x = 261
x has a value of 261 degrees.
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dentify on which quadratic function is positive.
Y = 2x^2 - 17x + 30
Identify on which quadratic function is negative.
Y = - x^2 - 6x - 8
A explanation on the answers would be appreciated!
(Lots of points!)
Step-by-step explanation:
Let us identify which quadratic function is positive. Yeah, let's start.
Y = [tex]{ \red{ \sf{2 {x}^{2} - 17x + 30}}}[/tex]
By using factorisation method,
[tex]{ \red{ \sf{2 {x}^{2} - 12x - 5x + 30}}}[/tex]
Take common factors
[tex]{ \red{ \sf{2x(x - 6) - 5(x - 6)}}}[/tex]
[tex]{ \red{ \sf{(2x - 5)}}} \: \: \: \: \: \: \: || \: \: \: \: \: { \red{ \sf{(x - 6)}}}[/tex]
[tex]{ \red{ \sf{2x - 5 = 0}}} \: \: || \: \: { \red{ \sf{x - 6 = 0}}}[/tex]
[tex]{ \red{ \sf{2x = 5}}} \: \: \: \: \: \: \: \: \: || \: \: \: \: { \red{ \boxed{ \green{ \sf{x = 6}}}}}[/tex]
[tex]{ \red{ \sf{{ \frac{ \cancel2}{ \cancel2}x}}}} = { \red{ \sf{ \frac{5}{2}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{5}{2}}}}}} [/tex]
____________________________________
Y = [tex]{ \blue{ \sf {{ - x}^{2} - 6x - 8}}}[/tex]
By using factorisation method,
[tex]{ \blue{ \sf{ - {x}^{2} - 2x - 4x - 8}}}[/tex]
Take common factors
[tex]{ \blue{ \sf{ - x(x + 2) - 4(x + 2)}}}[/tex]
[tex]{ \blue{ \sf{( - x - 4)}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{(x + 2)}}}[/tex]
[tex]{ \blue{ \sf{- x - 4 = 0}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \sf{x + 2 = 0}}}[/tex]
[tex]{ \blue{ \boxed{ \green{ \sf{x = -4}}}}} \: \: \: \: \: || \: \: \: \: \: { \blue{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]
Hence, the first quadratic function is positive and second quadratic function is negative.
Answer:
[tex]\textsf{$y = 2x^2 - 17x + 30$: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}[/tex]
[tex]\textsf{$y = - x^2 - 6x - 8$: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}[/tex]
Step-by-step explanation:
A function is positive when it is above the x-axis, and negative when it is below the x-axis.
---------------------------------------------------------------------------------
Given quadratic equation:
[tex]y = 2x^2 - 17x + 30[/tex]
Factor the equation:
[tex]\implies y = 2x^2 - 17x + 30[/tex]
[tex]\implies y = 2x^2 - 5x-12x + 30[/tex]
[tex]\implies y=x(2x-5)-6(2x-5)[/tex]
[tex]\implies y=(x-6)(2x-5)[/tex]
The x-intercepts of the parabola are when y = 0.
To find the x-intercepts, set each factor equal to zero and solve for x:
[tex]\implies x-6=0 \implies x=6[/tex]
[tex]\implies 2x-5=0 \implies x=\dfrac{5}{2}[/tex]
Therefore, the x-intercepts are x = ⁵/₂ and x = 6.
The leading coefficient of the given function is positive, so the parabola opens upwards.
The function is positive when it is above the x-axis.
Therefore, the function is positive for the values of x less than the smallest x-intercept and more than the largest x-intercept:
[tex]\textsf{Solution: \quad $x < \dfrac{5}{2}$ \;and \;$x > 6$}[/tex][tex]\textsf{Interval notation: \quad $\left(-\infty, \dfrac{5}{2}\right) \cup (6, \infty)$}[/tex]---------------------------------------------------------------------------------
Given quadratic equation:
[tex]y = - x^2 - 6x - 8[/tex]
Factor the equation:
[tex]\implies y = - x^2 - 6x - 8[/tex]
[tex]\implies y = -(x^2 +6x +8)[/tex]
[tex]\implies y = -(x^2 +4x +2x+8)[/tex]
[tex]\implies y = -((x(x+4)+2(x+4))[/tex]
[tex]\implies y = -(x+4)(x+2)[/tex]
The x-intercepts of the parabola are when y = 0.
To find the x-intercepts, set each factor equal to zero and solve for x:
[tex]\implies x+4=0 \implies x=-4[/tex]
[tex]\implies x+2=0 \implies x=-2[/tex]
Therefore, the x-intercepts are x = -4 and x = -2.
The leading coefficient of the given function is negative, so the parabola opens downwards.
The function is negative when it is below the x-axis.
Therefore, the function is negative for the values of x less than the smallest x-intercept and more than the largest x-intercept:
[tex]\textsf{Solution: \quad $x < -4$ \;and \;$x > -2$}[/tex][tex]\textsf{Interval notation: \quad $\left(-\infty, -4\right) \cup (-2, \infty)$}[/tex]The equity sections for Atticus Group at the beginning of the year (January 1) and end of the year (December 31) follow.
Stockholders’ Equity (January 1)
Common stock—$4 par value, 100,000 shares authorized, 35,000 shares issued and outstanding $ 140,000
Paid-in capital in excess of par value, common stock 100,000
Retained earnings 360,000
Total stockholders’ equity $ 600,000
Stockholders’ Equity (December 31)
Common stock—$4 par value, 100,000 shares authorized, 41,000 shares issued, 5,000 shares in treasury $ 164,000
Paid-in capital in excess of par value, common stock 148,000
Retained earnings ($50,000 restricted by treasury stock) 440,000
752,000
Less cost of treasury stock (50,000)
Total stockholders’ equity $ 702,000
The following transactions and events affected its equity during the year.
January 5 Declared a $0.50 per share cash dividend, date of record January 10.
March 20 Purchased treasury stock for cash.
April 5 Declared a $0.50 per share cash dividend, date of record April 10.
July 5 Declared a $0.50 per share cash dividend, date of record July 10.
July 31 Declared a 20% stock dividend when the stock’s market value was $12 per share.
August 14 Issued the stock dividend that was declared on July 31.
October 5 Declared a $0.50 per share cash dividend, date of record October 10.
3. What is the amount of retained earnings transferred to paid-in capital accounts (capitalized) for the stock dividend?
4. What is the per share cost of the treasury stock purchased? (Round your answer to 2 decimal places.)
5. How much net income did the company earn this year?
3. The amount of retained earnings transferred to the paid-in capital accounts (capitalized) for the stock dividend is $72,000.
4. The per-share cost of the treasury stock purchased is $10.
5. The net income earned by the Atticus Group this year was $217,500.
How are stock dividends capitalized?Stock dividends do not affect the cash account, unlike cash dividends.
Instead, the deduction is made from the retained earnings.
When the stock dividends are distributed, they are capitalized to the paid-in capital accounts (common stock and additional paid-in capital).
Transaction Analysis:January 5 Dividend $17,500 Dividends Payable $17,500 (35,000 x $0.50)
Retained Earnings $17,500 Dividend $17,500
March 20 Treasury Stock $20,000 Paid-in Capital in Excess $30,000 Cash $50,000 ($50,000/5,000)
April 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)
Retained Earnings $15,000 Dividend $15,000
July 5 Dividend $15,000 Dividends Payable $15,000 (30,000 x $0.50)
Retained Earnings $15,000 Dividend $15,000
July 31 Stock Dividend $72,000 Dividends Issuable $72,000 (30,000 x 20% x $12)
Retained Earnings $72,000 Stock Dividend $72,000
August 14 Dividends Issuable $72,000 Common Stock $24,000 Paid-in Capital in excess of par value $48,000
October 5 Dividend $18,000 Dividends Payable $18,000 (36,000 x $0.50)
Retained Earnings $18,000 Dividend $18,000
5) Retained earningsEnding balance $440,000
Add:
Dividend $17,500
Dividends $15,000
Dividends $15,000
Dividends $72,000
Dividends $18,000 $137,500
Less Beginning balance $360,000
Net income = $217,500
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Is 49 prime or composite?
Can Mario organize his marbles into aqual piles?
The number 49 is a composite number because it has more than two factors.
What is a prime number?A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime. 5 is prime, for example, because the only ways to write it as a product, 1 5 or 5 1, involve 5 itself.
Numbers with more than two factors are known as composite numbers. Non-prime numbers are composite numbers because they can be divided by more than two numbers.
A positive integer is a composite number. which is not the case (i.e., which has factors other than 1 and itself). The first few composite numbers (sometimes abbreviated as "composites") are 4, 6, 8, 9, 10, 12, 14, 15, and 16.
A composite number is one that can be formed by multiplying two smaller positive integers. It is a positive integer with at least one divisor other than 1 and itself. Every positive integer is either composite, prime, or the unit 1, so composite numbers are those that are neither prime nor a unit.
In this case, the factor of 49 are 1, 7 and 49. Therefore, it's a composite number.
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The sum of two numbers is 12. The difference of the two numbers is 6. What are the two numbers?
Answer:
3 and 9
Step-by-step explanation:
x+y=12
y-x=6
y-x=6
+x. +x
y=6+x
x+(6+x)=12
6+2x=12
-6. -6
2x=6
/2. /2
x=3
3+y=12
-3. -3
y=9
Hopes this helps please mark brainliest
A biologist is studying a particular species of flower. She writes the following equation to
show the length of the flower petal f(w), in cm, after w weeks:
f(w) = 3(1.03)
Part A (3pts): Complete
the table using the
function.
0
1
2
3
4
5
f(w)
Part B (1pt) Highlight the data
needed to solve this from the
table in Part A.
(2pts): What is an average
rate of change of the function
f(w) when w = 2 to
w = 5?
Rate of change formula =
y₂-y₁
x₂-x
3.03
Part C (2pts): What does the y-intercept of
the graph of the function f(w) represent?
(Circle the correct answer.)
a.) initial length of the petal
b.) length of the petal after w weeks
c.) time it took for the flower to stop growing
d.) percentage of growth each week
Part D (2pts): At the end of the study the
length of the petal was 3.48 cm. What is a
reasonable domain to plot the growth
function?
Sws
A. The lengths of the flower petals corresponding to the weeks 0, 1, 2, 3, 4, and 5 are 0, 3.09, 6.18, 9.27, 12.36, and 15.45, respectively.
B. The average rate of change of the function f(w) from week two to week five is 3.09.
C. The y-intercept of the function f(w) represents the initial length of the petal.
D. The reasonable domain to plot the growth function is week 0 to week 2.
The length of the flower petal and the weeks passed are denoted by f(w) and w. The equation of the function is given below.
f(w) = 3(1.03)w
The simplified function is f(w) = 3.09w.
The rate of change of the function from weeks 2 to 5 is calculated below.
R = [f(5) - f(2)]/(5 - 2)
R = [3.09*5 - 3.09*2]/3
R = 3.09*(5 - 2)/3
R = 3.09
The length of the flower petal at the end of the study was 3.48 cm. The length lies between the week 0 and the week 2.
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Which diagram matches the following situation? The function h relates Kami's age in years to her height in inches on her birthday that year.
The diagram that matches the given situation is as shown below.
The correct answer is an Option C
We know that, in the mapping of functions, we map certain parameters to a set of other parameter functions.
In this question, we have been given the function h relates Kami's age in years to her height in inches on her birthday that year.
It means that her ages would be one-one the left to map her height. that means there were 2 times were despite her age difference, her height remained the same.
From the given options, the correct one that represents the required mapping is:
h(14) = 64
h(15) = 64
Therefore, the diagram that matches the given situation is as shown below.
The correct answer is an Option C
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Out of 45 times at bat, Raul got 27 hits. Write the decimal that represents the times Raul didn't
get a hit.
Answer:
0.6
Step-by-step explanation:
The curve with equation y = x³ +3 has two tangents parallel to the line with equation
y = 12x-1. Find the co-ordinates of the two points.
Answer:
(-2, -5), (2, 11)
Step-by-step explanation:
You want the coordinates of the points on the curve y = x³ +3 where the tangent lines are parallel to y = 12x -1.
SlopeThe slope of the tangent line is the x-coefficient in its equation: 12.
The slope of the curve is given by its derivative:
y' = 3x²
We want the x-values where the slope is 12. These are the solutions to ...
12 = 3x²
4 = x² . . . . . . . . . . divide by 3
x = ±√4 = ±2 . . . . . take the square root
CoordinatesThe coordinates of the points with x = ±2 are ...
y = (±2)³ +3 = ±8 +3 = {-5, 11}
The tangent points are (-2, -5) and (5, 11).
__
Additional comment
The attached graphs and table show the solutions to y'=0 and the corresponding point locations. It also shows the tangent line equations (in point-slope form).
A single serving of hot chocolate requires 0.75 cups of milk. Nina used 7 cups of milk to make hot chocolate for her 9 friends. Did she make enough for each friend to get a serving of hot chocolate?
Answer:
nik
Step-by-step explanation:
<7 and <8 are vertical angles can you shoe me how to draw this please
Vertical angles are opposite of each othe. Attached is a picture of how it looks:
I hope this helps!
A. x² +5
B. +5X
C.X + 5
D.5X
The expression that represents the quotient of the given model is x + 5. The correct option is C. x + 5
Determining the expression that represent the quotient of a modelFrom the question, we are to determine the expression that represent the quotient of the given model
From the given model, we can write that
x | x² + x + x + x + x + x
Dividing by using the long division
x + 1 + 1 + 1 + 1 + 1
x | x² + x + x + x + x + x
Thus, the quotient of the expression is
x + 1 + 1 + 1 + 1 + 1
Further simplification,
NOTE: 1 + 1 + 1 + 1 + 1 = 5
Then,
The expression x + 1 + 1 + 1 + 1 + 1 becomes
x + 5
Hence, the expression is x + 5
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Find a formula for the polynomial of least degree that is graphed below Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4).
Answer: y=-2x²-6x
Step-by-step explanation:
Its x-intercepts are 0 and -3, and the graph goes through the point (-1,4)
Hence we have three coordinates of the equation y=ax²+bx+c (1):
(0,0) (-3,0) (-1,4)
Let's substitute these coordinates into formula (1):
[tex]0=a(0)^2+b(0)+c\\0=a(-3)^2+b(-3)+c\\4=a(-1)^2+b(-1)+c\\\\0=0+0+c\\0=9a-3b+c\\4=a-b+c\\\\0=c\\0=9a-3b+0\\0=a-b+0\\\\c=0\\9a-3b=0\ \ (1)\\a-b=4\ \ \ \ \ (2)\\\\c=0\\\\[/tex]
Divide both parts of the equation (1) by 3 and multiply both parts of the equation (2) by -1: :
[tex]3a-b=0\\-a+b=-4\\\\[/tex]
Sum these equations:
[tex]2a=-4[/tex]
Divide both parts of the equation by 2:
[tex]a=-2[/tex]
We substitute the value of a=-2 into equation (2):
[tex]-2-b=4\\[/tex]
Divide both parts of the equation by -1:
[tex]2+b=-4\\\\2+b-2=-4-2\\\\b=-6[/tex]
[tex]Thus, \\\\y=-2x^2-6x+0\\\\y=-2x^2-6x[/tex]
The height of the blade of a wind turbine as it turns through an angle of is given by the function h()=8.5sin(+180⁰) + 40, with height measured in meters.
Find the maximum and minimum positions of the blade.
Explain what the value of 40 in the equation represents.
What is the amplitude? Explain what it represents.
Sketch the function over two cycles.
Considering the sine function in this problem, we have that:
The minimum position in the table is of: 31.5The maximum position in the table is of: 48.5.The value of 40 is the vertical shift of the function.The amplitude is of 8.5.The graph of two cycles is given by the image at the end of the answer.How is the sine function defined?
The general sine function has the definition presented as follows:
f(x) = asin(b(x+c))+d.
The coefficients are given as follows:
a is the amplitude of the sine function.b: The period of the sine function is of 2π/b.c is the phase shift of the sine function.d is the vertical shift of the sine function.For this problem, the function is:
h(θ ) = 8.5 sin (θ + 180°) + 40
The amplitude is of:
a = 8.5.
The function should oscillate between:
-8.5 and 8.5.
However, with the vertical shift of 40, the minimum and maximum values are given as follows:
Minimum value: -8.5 + 40 = 31.5.Maximum value: 8.5 + 40 = 48.5.The measure of each cycle of the cosine function is of:
2π = 360º.
The function has a phase shift to the right of 180º, hence the graph is given by the image at the end of the answer, for two cycles, that is, between 0 and 4π.
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find the value of x.....
Answer:
Below
Step-by-step explanation:
All of the angles labeled sum up to a right angle = 90 °
x+4 + x+4 + x+4 = 90
3x + 12 = 90
3x = 78
x = 26°
Answer:
x = 26
Step-by-step explanation:
from the diagram
∠ BFC + ∠ CFD + ∠ DFE = ∠ BFE , that is
x + 4 + x + 4 + x + 4 = 90
3x + 12 = 90 ( subtract 12 from both sides )
3x = 78 ( divide both sides by 3 )
x = 26
Maria is applying for a summer job. Six employees who do various jobs at the company earn $8.00, $8.50, $9.00, $9.50, $10.00, and $23.50 per hour. In the interview, the boss tells Maria that the median of the hourly wages is $9.25. Is the boss’s statement misleading? Why or why not?
Answer:
Boss's statement is not misleading.
Explanation:
To find the median, we need to find the middle number.
8.00, 8.50, 9.00, 9.50, 10.00, 23.50
9.00 and 9.50 are in the middle.
And in the middle of those two is 9.25.
Truck Transport
A truck driver is beginning her haul across the country. The warehouse is 15 miles
from the highway. Once she gets on the highway she maintains a constant rate for
several hours. Complete the table of values for the sequence below that relates hours on
the highway and distance from the warehouse in miles.
Refer to the attachment for the required table:
What is the unit rate?
A unit rate is a cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
From the table,
For 0 hours, distance = 15 miles
For 1 hour, distance = 80 miles
Difference between distances= 80-15=65 miles
Since it is given that, it is at a constant rate, for every hour there is an increase of 65 miles in distance.
The completed table is shown in the attachment.
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Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = (x + 6) (5x² + 2)(x − 3)
The y-coordinate of the y-intercept of the polynomial function is -36.
Given:
polynomial function defined below.
f(x) = (x + 6) (5x² + 2)(x − 3)
To find y intercept put x = 0 in the function.
y = (0+6)(5*0^2+2)(0-3)
= 6*(5*0+2)*(-3)
= 6*(0+2)(-3)
= 6*2*(-3)
= 12(-3)
= -36
Therefore The y-coordinate of the y-intercept of the polynomial function is -36.
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HELP NOW
Which variables would the scatter plot at the right be most likely to represent?
A.The number of people at a concert and the total concession sales
B.The number of guests at a hotel and the total water consumption
C.The number of siblings a person has and the person's GPA
D.The total number of miles driven and the total gallons of gas used
15=2m+3
solving two step equations
Answer:
[tex]m=6[/tex]
Step-by-step explanation:
Start by subtracting 3 from both sides
[tex]15=2m+3\\15-3=2m+3-3\\12=2m[/tex]
Now, divide both sides by 2!
[tex]\frac{12}{2}=\frac{2}{2}m\\ 6=m\\ m=6[/tex]
Answer:
m=6
i think this help you
what's the skskksks of slskksksk
Find the cardinal number of a set B={Q,R,S,T,U,V}.
Answer:
6
Step-by-step explanation:
The cardinal number of a finite set is the number of elements of the set.
cardinal number = 6
In a town 100 people need 700 liters of water to drink everyday at a festival time how many liters of water do they need to drink with their 30 guest
Answer: 210 liters
Step-by-step explanation:
Piece of rope is 24 1/2 feet long how many 1/4 foot sections will there be?
By taking a quotient between the lengths, we will see that 98 pieces of 1/4 foot can be made.
How many 1/4 foot sections are in the piece of rope?We know that the total length of the rope is (24 + 1/2) ft, to see how many pieces of 1/4 feet we can take from that rope, we need to take the quotient between the total length and the length of the pieces.
It gives:
Q = (24 + 1/2)ft/(1/4)ft = 4*(24 + 1/2)
Q = 4*24 + 4*(1/2)
Q = 96 + 4/2
Q = 96 + 2 = 98
So 98 pieces of 1/4 foot can be made.
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I need help with this please help me
From the given figure
a) The value of y = 6
b) The length of the line RS = 39 units
The length of the line ST = 38 units
The length of the line RS = 6y + 3
The length of the line ST = 5y + 8
The length of the line RT = 77
From the line we can say that
RT = RS + ST
77 = 6y + 3 + 5y + 8
Add the like terms
11y + 11 = 77
11y = 77 - 11
11y = 66
y = 66/11
y = 6
The value of y = 6
The length of RS = 6y + 3
= 6×6 + 3
= 36 + 3
= 39 units
The length of the line ST = 5y + 8
= 5×6 + 8
= 30 + 8
= 38 units
Hence, from the given figure
a) The value of y = 6
b) The length of the line RS = 39 units
The length of the line ST = 38 units
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Solve the linear programming problem.
On the coordinate (0,7) the value of P is maximum 280.
What is a Linear Inequality?
In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.
Solution:
First of all to solve the Linear Inequality we need to plot the graph of the given equations.
Kindly find the attached graph
To maximise the equation P = 30x + 40y
we need to find the corner values of x and y.
According to the graph, the corner values of (x,y) are
(5,0), (3,4) and (0,7)
putting the values in the equation P = 30x + 40y
at x = 5 and y = 0
P = 150
at x = 3 and y = 4
P = 250
at x = 0 and y = 7
P = 280
So, on the cordinate (0,7) the value of P is maximum i.e. 280.
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Which of the following could be used as a statement in a two-column proof?
A statement of given information can be used in a two column proof
What is two column proof ?Among the many methods available to mathematicians are proofs, or logical arguments, that begin with premises and reach conclusions through the presentation of facts. The proof is hard to write because you have to put each part in the correct order.While paragraphs and flow charts are enough to outline the various steps, nothing beats a two-column proof for purity and clarity. A two-column proof uses a table to represent a logical argument and assigns a task to each column.The two columns then work in lockstep, leading the reader from the premise to the conclusion. Paragraph proofs tell a story by chronologically listing each fact and reason. This means you have to be very organized and have to rewrite paragraphs over and over until you get it right. Flowchart proofs can be difficult to follow, but at least they provide a clean separation between mathematics and reasoningIn light of the question -The two-column proof is summarized in the statement and reason columns, and each statement must have a verified reason. Two-column proof reasons are usually given information, vocabulary definitions, hypotheses, and previously proven theorems.
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