150 - 141 = 9 seniors are not enrolled in any classes.
What is statistics, and how can it be used?The area of mathematics known as statistics is used to gather, analyse, and interpret data. To predict the future, determine the likelihood that a specific event will occur, or learn more about a survey, statistics can be employed.
The Venn diagram reveals the amount of seniors enrolling in at least one of the courses as follows:
80 + 41 + 54 - 10 - 19 - 12 + 7
= 141
Therefore, 150 - 141 = 9 seniors are not enrolled in any classes.
= 9
So, there are 9 seniors taking none of the courses. Answer: 9.
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Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b (3.5). x + 2y = 5 The equation of the line is ____(Type an equation Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer
The equation of the line is y = -1/2 + 13/2.
The point is (3, 5).
An equation of line is x + 2y = 5.
To determine the slope intercept form of the equation using the point and line we first determine the slope of the equation from the given line.
Convert the equation of line in slope intercept form.
x + 2y = 5
Subtract x on both side, we get
2y = -x + 5
Divide by 2 on both side, we get
y = -1/2 x + 5
On comparing with y = mx + c, where m is slope, we get
m = -1/2
Now the equation of the line is;
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 3)
Simplify the bracket
y - 5 = -1/2x + 3/2
Add 5 on both side, we get
y = -1/2x + 3/2 + 5
y = -1/2 + 13/2
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The complete question is:
Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx + b.
(3, 5); x + 2y = 5
The equation of the line is ____ . (Type an equation Type your answer in slope intercept form. Use integers or fractions for any numbers in the equation. Simplify your answer)
what is the half life of a substance that decays at a rate of 2.5% p.a?
Answer:
The half-life of a substance is the amount of time it takes for half of the initial amount of the substance to decay.
We can use the following formula to calculate the half-life (t1/2) of a substance with a decay rate of r:
t1/2 = (ln 2) / r
where ln 2 is the natural logarithm of 2 (approximately 0.693).
In this case, the decay rate is 2.5% per year, or 0.025 per year. Plugging this into the formula, we get:
t1/2 = (ln 2) / 0.025
t1/2 = 27.73 years (rounded to two decimal places)
Therefore, the half-life of the substance is approximately 27.73 years.
Find the local maximum and minimum values of f using both the first and second derivative tests f(x) = x2 / (x - 1). Summary: The local maximum and minimum values of f(x) = x2 / (x - 1) using both the first and second derivative tests is at x = 0 and x = 2.
The value of local maximum and local minimum for the function f(x) = x^2/(x -1 ) is equal to f(0) = 0 at x = 0 and f(2) = 4 at x = 4 respectively.
Local maximum and minimum values of the function
f(x) = x^2 / (x - 1),
Use both the first and second derivative tests.
First, let's find the critical points of the function,
By setting its derivative equal to zero and solving for x,
f'(x) = [2x(x - 1) - x^2] / (x - 1)^2
⇒ [2x(x - 1) - x^2] / (x - 1)^2 = 0
Simplifying this expression, we get,
x(x - 2) = 0
This gives us two critical points,
x = 0 and x = 2.
These critical points correspond to local maxima, local minima, or neither.
Use the second derivative test,
f''(x) = [2(x - 1)^2 - 2x(x - 1) + 2x^2] / (x - 1)^3
At x = 0, we have,
f''(0) = 2 / (-1)^3
= -2
Since the second derivative is negative at x = 0, this critical point corresponds to a local maximum.
f(0) = 0^2/ (0 -1 )
= 0
At x = 2, we have,
f''(2) = 2 / 1^3
= 2
Since the second derivative is positive at x = 2, this critical point corresponds to a local minimum.
f(2) = 2^2/ (2 - 1)
= 4
Therefore, at x = 0, the local maximum value is f(0) = 0, and at x = 2, the local minimum value is f(2) = 4.
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can you help to solve this two questions?
41.
a=?
b=?
42.
slope of the tangent line=?
The equation of the tangent line to the graph of the function at x = 7 is: y = -1/49 x + 50/343, the equation of the normal line to the graph of the function at x = 7 is: y = 49x - (2402/7) and slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.
What is the tangent line to the graph of the function at x = 7a) To find the tangent line to the graph of the function at x = 7, we need to find the slope of the function at that point. We can use the derivative of the function to find the slope:
f(x) = 1/x
f'(x) = -1/x^2
So, at x = 7, the slope of the tangent line is:
m = f'(7) = -1/7^2 = -1/49
To find the equation of the tangent line, we also need a point on the line. We know that the point (7, 1/7) is on the graph of the function, so we can use that as our point. Using the point-slope form of a line, we have:
y - 1/7 = -1/49(x - 7)
Simplifying this equation, we get:
y = -1/49 x + 50/343
So the equation of the tangent line to the graph of the function at x = 7 is:
y = -1/49 x + 50/343
b) To find the normal line to the graph of the function at x = 7, we need to find a line that is perpendicular to the tangent line we found in part (a). The slope of the normal line is the negative reciprocal of the slope of the tangent line:
m(normal) = -1/m(tangent) = -1/(-1/49) = 49
Using the point-slope form of a line again, we can find the equation of the normal line that passes through the point (7, 1/7):
y - 1/7 = 49(x - 7)
Simplifying this equation, we get:
y = 49x - [(2402)/7]
So the equation of the normal line to the graph of the function at x = 7 is:
y = 49x - (2402/7)
Problem 42:
We can use the limit definition of the derivative to find the slope of the tangent line to the graph of y = 5x^3 at the point (2,40).
Using the formula for the derivative:
dy/dx = lim(h→0) [(f(x+h) - f(x))/h]
we can calculate the slope of the tangent line at x = 2.
Plugging in the given function, we get:
[tex]\frac{dy}{dx} = \lim_{h \to 0} [(5(2+h)^3 - 40) / h][/tex]
[tex]= \lim_{h \to 0} [(40 + 60h + 30h^2 + 5h^3 - 40) / h]\\= \lim_{h \to 0} [60 + 30h + 5h^2]\\= 60[/tex]
Therefore, the slope of the tangent line to the graph of y = 5x^3 at the point (2,40) is 60.
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pls helppppppp explain !!!
Answer:
x²
Step-by-step explanation:
[tex]{ \tt{ \frac{ {x}^{ - 3} . {x}^{2} }{ {x}^{ - 3} } }} \\ \\ \dashrightarrow{ \tt{x {}^{( - 3 + 2 - ( - 3))} }} \\ \dashrightarrow{ \tt{ {x}^{( - 3 + 2 + 3)} }} \: \: \: \: \\ \dashrightarrow{ \boxed{ \tt{ \: \: \: \: {x}^{2} \: \: \: \: \: \: }}} \: \: \: \: [/tex]
please help!! Given m∥n - find the value of x and y.
(x+19)°
(9x+1)°
(3y+8)°
Answer: x=16, y=9
Step-by-step explanation: Find x first. The unmarked angle underneath the x + 19 is 9x + 1 (corresponding angles so congruent so same measure as the angle below)
So the two angles add up to 180°
x+19 + 9x + 1 = 180°
combine like terms
10x + 20 = 180
subtract 20
10x = 160
divide by 10
x = 16
Now you can find the measure of the angle marked 9x+1.
9(16) + 1
= 144 + 1
= 145
Now find y. The angle marked 9x+1 is now known to be a 145° angle. So that angle with the angle marked 3y+8 must make 180°
3y + 8 + 145 = 180
combine like terms
3y + 153 = 180
subtract 153
3y = 27
divide by 3
y = 9
-Hope this helps! Thanks, have a good day :-)
Find all the values of
arcsin −√3/2
Select all that apply:
a.π3
b.5π6
c.11π6
d.5π3
e.2π3
f.7π6
g.4π3
Answer:
g
Step-by-step explanation:
The given expression is arcsin (-√3/2), which represents the angle whose sine is equal to -√3/2. Recall that the range of the arcsin function is from -π/2 to π/2 radians, so we can narrow down the possible solutions to the second and third quadrants.
Since the sine function is negative in the third quadrant, we can start by considering the angle 4π/3, which is in the third quadrant and has a sine of -√3/2:sin(4π/3) = -√3/2
However, we need to check if there are any other angles in the second or third quadrants that satisfy the equation. Recall that sine is periodic with a period of 2π, so we can add or subtract any multiple of 2π to the angle and still obtain the same sine value.
In the second quadrant, we can use the reference angle π/3 to find the corresponding angle with a negative sine:
sin(π - π/3) = sin(2π/3) = √3/2
This angle does not satisfy the equation, so we can eliminate it as a possible solution.In the third quadrant, we can use the reference angle π/3 to find another possible solution:
sin(π + π/3) = sin(4π/3) = -√3/2
This confirms our initial solution of 4π/3, so the answer is (g) 4π/3.
Let me know if this helped by hitting brainliest! If you have a question, please comment and I"ll get back to you ASAP!
Answer:
We know that sin(π/3) = √3/2, so we can write:
arcsin(-√3/2) = -π/3 + 2nπ or π + π/3 + 2nπ
where n is an integer.
Therefore, the values of arcsin(-√3/2) are:
a. π/3 + 2nπ
c. 11π/6 + 2nπ
e. 2π/3 + 2nπ
f. 7π/6 + 2nπ
So, options a, c, e, and f are all correct.
what is the second derivative of x^n when n= greater than or equal to 2
Answer:
The second derivative of x^n when n is greater than or equal to 2 is n(n-1)x^(n-2).By what like amount does the length and width of 6 by 4 rectangle need to be increased for its area to be doubled
Answer:
Step-by-step explanation:
Area = 8 x 4 =24
Area doubled = 48
Let x be the amount we increase width and length to get area =48.
[tex](6+x)\times (4+x)=48[/tex]
[tex](x+6)(x+4)=48[/tex]
[tex]x^2+10x+24=48[/tex]
[tex]x^2+10x-24=0[/tex]
[tex](x+12)(x-2)=0[/tex]
[tex]\text{gives }x=-12,2[/tex]
But [tex]x=-12[/tex] is not a practical solution.
So [tex]x=2[/tex] is the required solution.
We must increase the length and width by 2.
An organization wishing to attract more people decides to base its
membership fees on the age of the member. Also, wanting members to
attend more activities, it gives a reduction on the membership fee for each
activity attended in the previous year.
The following table depicts the corresponding fee and reductions. The
minimum membership fee is $1, even if the member attended a lot of
activities.
Age
6 years or less
7-12 years
13-18 years
Over 18 years
Membership
Fee Reduction per Activity
$0.75
$1.25
$2
$5
$10
$15
$25
$2
Write a program that asks the user to input their age and the number of
activities attended and then displays the corresponding membership fee.
Input Validation: Do not accept a negative value for either the age or the
number of activities
C++
1. Begin the program by including the header file <iostream> which includes basic input/output library functions as well as the <vector> library which is needed for this program.
2. Declare a vector of integer type named 'ageGroups' which will store the age groups and the corresponding membership fee and reductions.
3. Create a void function named 'calculateFee()' which will take a parameters age and activities attended.
4. In the calculateFee() function, use the switch statement for the age group and store the corresponding membership fee and reduction value in variables.
5. Use an if statement to check that the number of activities attended is non-negative.
6. Calculate the membership fee using the variables and store it in a variable named 'fee'.
7. Use an if statement to check if the fee is less than 1 and if yes, assign the fee to 1.
8. Print the fee to the user.
9. End the program.
Can anyone help thanks!!!!
Answer:
B
Step-by-step explanation:
5^2 is the small square, 4(3x4x1/2) are the 4 triangles
Answer: The answer would be B.
Step-by-step explanation:
Hello.
First, we know that the smaller square is 5, and to find the area of the big square, we need to square 5 to get the area. We also know that C wouldn't be a viable option, so, our only remaining choices are A and B. We know that without the smaller square, there are 4 triangles, and the Area of a Triangle is: 1/2*b*h. So, this also takes A out as an option as well. After this, you will have your answer as B; 5^2 + 4(3 * 4 * 1/2)
(Or, you could have found the Area of the Triangles, and realize that neither A, nor C have those options, making B the answer by default.)
Hope this helps, (and maybe brainliest?)
Martin Pincher purchased a snow shovel for $28.61, a winter coat for $23.27, and some rock salt for $7.96. He must pay the state tax of 5 percent, the county tax of 0.5 percent and the city tax of 2.5 percent. What is the total purchase price?
Hi Martin,
To calculate the total purchase price of your items, you'll need to apply the state, county, and city taxes to the total purchase cost of all three items.
The total purchase cost of all three items is:
Snow shovel: $28.61
Winter coat: $23.27
Rock salt: $7.96
Total purchase cost: $59.84
Now, we apply the applicable taxes:
State tax: 5% of $59.84 = $2.99
County tax: 0.5% of $59.84 = $0.30
City tax: 2.5% of $59.84 = $1.49
Total taxes: $2.99 + $0.30 + $1.49 = $4.78
Therefore, the total purchase price is:
Total purchase cost + Total taxes = $59.84 + $4.78 = $64.62
Question 20 (2 points)
Suppose a survey was given to students at WCC and it asked them if they voted for
the Democrat or Republican in the last election. Results of the survey are shown
below:
Democrat Republican
Male. 50. 75
Female. 125. 50
If a student from the survey is selected at random, what is the probability they voted
for the republican?
75/50
50/75
75/300
125/300
Answer:
The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.
The total number of students in the survey is:
50 + 75 + 125 + 50 = 300
The number of students who voted for the Republican party is:
75 + 50 = 125
Therefore, the probability of selecting a student who voted for the Republican party is:
125/300 = 0.4167 (rounded to four decimal places)
So, the answer is option D: 125/300
(please mark my answer as brainliest)
The points (-2, -2) and (5,5) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer:
Step-by-step explanation:
[tex]diameter=\sqrt{(5+2)^2+(5+2)^2} \\=\sqrt{49+49} \\=\sqrt{98} \\=7\sqrt{2} \\radius=\frac{7\sqrt{2} }{2} \\\approx 4.95[/tex]
porrect
Question 2
Individuals who identify as male and female were surveyed regarding their diets.
Vegetarian
Pescatarian
Vegan
18
27
45
Male
Female
Total
Meat-eater
0.21
35
37
72
12
23
35
24
14
38
Total
89
101
190
0/1 pts
What is the probability that a randomly selected person is a pescatarian or vegetarian?
Round your answer to the hundredths place.
Answer:
0.38
Step-by-step explanation:
There are a total of 38 pescatarians and 35 vegetarians. This is obtained by looking at the column totals for those categories and includes both males and females
There are a total of 190 participants in the survey
P(pescatarian) = 38/190
P(vegetarian) = 35/190
P(pescatarian or vegetarian)
= P(pescatarian) + P(vegetarian)
= 38/190 + 35/190
= 73/190
= 0.3842
= 0.38 (rounded to hundredths place)
A person invests 5,500 dollars in a bank. The bank pays 4.5% interest compounded annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches $6,700 dollars?
Work Shown:
A = P*(1+r/n)^(n*t)
6700 = 5500*(1+0.045/1)^(1*t)
6700/5500 = (1.045)^t
1.218182 = (1.045)^t
log( 1.218182 ) = log( (1.045)^t )
log( 1.218182 ) = t*log( 1.045 )
t = log(1.218182)/log(1.045)
t = 4.483724
t = 4.5
It takes about 4.5 years to reach $6700
Please help me with number 9 and 10!??? Thank you for help anyone who help me ((:!!!
Answer:
9. $18
10. 68
Step-by-step explanation:
$8 + $2 + $3 + $5= $18
104 - 36= 68
In the given figure, mHJ = 106° and F H G Figure not drawn to scale FH ~JH. Which statement is true? K 106° J OA. The measure of ZG is 21°, and triangle FGH is isosceles. OB. The measure of ZG is 56°, and triangle FGH is isosceles. OC. The measure of ZG is 21°, and triangle FGH is not isosceles The measure of ZG is 56°, and triangle FGH is not isoscelesd D.
Check the picture below.
[tex]\measuredangle G=\cfrac{\stackrel{far~arc}{148}-\stackrel{near~arc}{106}}{2}\implies \measuredangle G=21^o \\\\\\ \hspace{6em}\measuredangle F=\cfrac{106}{2}\implies \measuredangle F=53^o\hspace{8em}\measuredangle G=106^o \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle FGH\textit{ is not an isosceles}~\hfill[/tex]
A bag with 6 marbles has 2 blue marbles and 4 yellow marbles. A marble is chosen from the bag at random. What is the probability that it is red?
Write your answer as a fraction in simplest form.
Step-by-step explanation:
Hey mate, if there are no red balls inside the bag then the probabililty will be obviously 0
Please help! 20 points
Order the simplification steps of the expression below using the properties of rational exponents.
Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]
Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]
Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex] [break the cube root as power [tex]1/3[/tex]]
Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex] [break [tex]875=125\times7[/tex]]
[tex]125=5^3[/tex]
Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex] [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]
Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex] [break the power of [tex]x[/tex]]
Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]
Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]
Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]
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If m∠ADB = 110°, what is the relationship between AB and BC? AB < BC AB > BC AB = BC AB + BC < AC
The relationship between AB and BC is given as follows:
AB > BC.
What are supplementary angles?Two angles are defined as supplementary angles when the sum of their measures is of 180º.
The supplementary angles for this problem are given as follows:
<ADB = 110º. -> given<CDB = 70º. -> sum of 180º.By the law of sines, we have that:
AB/sin(110º) = BC/sin(70º).
As sin(110º) > sin(70º), the inequality for this problem is given as follows:
AB > BC.
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Answer:
AB>BC
Step-by-step explanation:
AI-generated answer
Based on the given information, the relationship between AB and BC depends on the measure of angle ZADB. If mZADB is 110°, we can determine the relationship as follows:
Since triangle ABD and triangle CBD share side AB, the larger the angle ZADB, the longer the side AB will be compared to side BC. Therefore, if mZADB is 110°, we can conclude that AB is greater than BC.
In summary, when mZADB is 110°, the relationship between AB and BC is:
AB > BC.
4. A pet store has eight dogs and cats. Three are dogs. What fraction represents the number of cats?
A. 1/4
B. 3/8
C. 1/2
D.5/8
Answer:
Step-by-step explanation:
Number of cats = 8 - 3 = 5
Fraction that are cats [tex]=\frac{5}{8}[/tex]
A mountain is 13,318 ft above sea level and the valley is 390 ft below sea level What is the difference in elevation between the mountain and the valley
Answer: 13,708 ft
Step-by-step explanation:
To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:
13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft
Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.
Answer: The difference is 13,708 ft.
Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].
Given that a valley is 390 feet below sea level.
So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].
So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]
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Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.
Answer:
[tex]\dfrac{4096\pi}{5}\approx 2573.593\; \sf (3\;d.p.)[/tex]
Step-by-step explanation:
The shell method is a calculus technique used to find the volume of a solid revolution by decomposing the solid into cylindrical shells. The volume of each cylindrical shell is the product of the surface area of the cylinder and the thickness of the cylindrical wall. The total volume of the solid is found by integrating the volumes of all the shells over a certain interval.
The volume of the solid formed by revolving a region, R, around a vertical axis, bounded by x = a and x = b, is given by:
[tex]\displaystyle 2\pi \int^b_ar(x)h(x)\;\text{d}x[/tex]
where:
r(x) is the distance from the axis of rotation to x.h(x) is the height of the solid at x (the height of the shell).[tex]\hrulefill[/tex]
We want to find the volume of the solid formed by rotating the region bounded by y = 0, y = √x, x = 0 and x = 16 about the y-axis.
As the axis of rotation is the y-axis, r(x) = x.
Therefore, in this case:
[tex]r(x)=x[/tex]
[tex]h(x)=\sqrt{x}[/tex]
[tex]a=0[/tex]
[tex]b=16[/tex]
Set up the integral:
[tex]\displaystyle 2\pi \int^{16}_0x\sqrt{x}\;\text{d}x[/tex]
Rewrite the square root of x as x to the power of 1/2:
[tex]\displaystyle 2\pi \int^{16}_0x \cdot x^{\frac{1}{2}}\;\text{d}x[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^b \cdot a^c=a^{b+c}[/tex]
[tex]\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x[/tex]
Integrate using the power rule (increase the power by 1, then divide by the new power):
[tex]\begin{aligned}\displaystyle 2\pi \int^{16}_0x^{\frac{3}{2}}\;\text{d}x&=2\pi \left[\dfrac{2}{5}x^{\frac{5}{2}}\right]^{16}_0\\\\&=2\pi \left[\dfrac{2}{5}(16)^{\frac{5}{2}}-\dfrac{2}{5}(0)^{\frac{5}{2}}\right]\\\\&=2 \pi \cdot \dfrac{2}{5}(16)^{\frac{5}{2}}\\\\&=\dfrac{4\pi}{5}\cdot 1024\\\\&=\dfrac{4096\pi}{5}\\\\&\approx 2573.593\; \sf (3\;d.p.)\end{aligned}[/tex]
Therefore, the volume of the solid is exactly 4096π/5 or approximately 2573.593 (3 d.p.).
[tex]\hrulefill[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Power Rule of Integration}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}(+\;\text{C})$\\\end{minipage}}[/tex]
which of the following is the most appropriate documentation to appear with the calculate procedure?
The documentation "Prints all positive odd integers that are less than or equal to max" is the most appropriate documentation for the printNums procedure, as it accurately describes the behavior of the procedure. so, the option C) is correct.
This procedure uses a loop to display all positive odd integers less than or equal to the input parameter max. It starts by initializing a count variable to 1, and then uses a repeat-until loop to display the current value of count and increment it by 2 until count is greater than max.
The documentation provided is concise, clear, and accurately describes what the procedure does, making it easy for users to understand the purpose and behavior of the procedure. So, the correct answer is C).
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_____The given question is incomplete, the complete question is given below:
In the following procedure, the parameter max is a positive integer.
PROCEDURE printNums(max)
{
count ← 1
REPEAT UNTIL(count > max)
{
DISPLAY(count)
count ← count + 2
}
}
Which of the following is the most appropriate documentation to appear with the printNums procedure?
a, Prints all positive odd integers that are equal to max.
b, Prints all negative odd integers that are less than or equal to max.
c, Prints all positive odd integers that are less than or equal to max.
d, Prints all negative odd integers that are less than or equal to max.
In each case either show that the statement is true, or give an example showing it is false. a. If a linear system has n variables and m equations, then the augmented matrix has n rows.
The given statements are true or false are shown below, about linear system has n variables and m equations, then the augmented matrix has n rows.
First, let's write how A and C look like.
A = [C|b], where b is the constant matrix.
(a) False.
Example
[tex]\left[\begin{array}{ccc}1&0&2\\0&1&3\\\end{array}\right][/tex]
We can see that z = t and so we have infinitely many solutions but there's no row of zeros.
(b) False.
Example
[tex]\left[\begin{array}{cc}1&0&0\1&1&0&0\\\end{array}\right][/tex]
Here; x1 = 1 and x2 = 1 is a unique solution and we have a row of zeros.
(c) True.
In the row-echelon form, the last row is either a row of zeros or a row that contains a leading 1. If the row has a leading 1, then there is a solution. Since we assume there is no solution, then the row must be a row of zeros.
(d) False.
Example
[tex]\left[\begin{array}{cc}1&3\\0&0\end{array}\right][/tex]
Here; x₁ = 1 − 3t and x2 = t. Thus, the system is consistent.
(e) True.
Suppose we have a typical equation in a system
а1x1 + A2X2 + ··· + anxn = b
Now, if b≠0 and x1 = x2 = ··· = x₂ = 0, then the system is Xn inconsistent. But, if b = 0, then we have a solution.
(f) False.
Example
[tex]\left[\begin{array}{cc}1&2&0&0\end{array}\right][/tex]
If a = 0, then it's consistent(infinitely many solutions) but if a 0, then it's inconsistent.
(g) Ture.
Since the rank would be at most 3 and this will lead to a free variable (4 columns in C and the rank is 3, so there is at leat 1 free variable). Thus, the system has more thatn one solution.
(h) True.
Because the rank is the number of leading 1's lying in different rows and A has 3 rows. Thus, the rank ≤ 3.
(i) False.
Because we could have a row of zeros in C and a leading 1 in A. In other words, a31 = a32 = A33 = A34 = 0 and c3 1. This makes the system inconsistent.
(j) True.
If the rank of C = 3, then there will be a free variable and this means the system is consistent.
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Complete question:
In each case either show that the statement is true, or give an example showing it is false. (a) If a linear system has n variables and m equations, then the augmented matrix has n rows. quations • ( *b) A consistent linear system must have infinitely many solutions. . (c) If a row operation is done to a consistent linear system, the resulting system must be consistent. (d) If a series of row operations on a linear system results in an inconsistent system, the original system is inconsistent.
What is the measure of angle ABC?
rewrite each equation without absolute value for the given conditions
y=|x-3|+|x+2|-|x-5| if 3
Answer:
Step-by-step explanation:
|x-3|=x-3,if x-3≥0,or x≥3
|x-3|=-(x-3),if x-3<0 ,or x<3
which of the following equations represent the profit-maximizing combination of resources for a firm?
The profit-maximizing combination of resources for a firm is MRPl / Pl = MRPc / Pc = 10/2 = 5/1 . The correct option is D).
The profit-maximizing combination of resources for a firm is determined by the equality of the marginal revenue product (MRP) per unit of input (labor, L, or capital, C) to the price per unit of input.
Therefore, the equation that represents the profit-maximizing combination of resources for a firm is:
MRPl / Pl = MRPc / Pc
where MRPl is the marginal revenue product of labor, Pl is the price of labor, MRPc is the marginal revenue product of capital, and Pc is the price of capital.
Among the given options, only option D satisfies the above equation. Therefore, option D represents the profit-maximizing combination of resources for a firm.
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_____The given question is incomplete, the complete question is given below:
Which of the following equations represent the profit-maximising combination of resources for a firm?
A. MRPl / Pl = MRPc / Pc = 1
B. MRPl / Pl = MRPc / Pc = 5
C. MRPl / Pl = MRPc / Pc = 10/10 = 5/5
D. MRPl / Pl = MRPc / Pc = 10/2 = 5/1
In a school district, 57% favor a charted school for grades K to 5. A random sample of 300 are surveyed and proportion of those who favor charter school is found. Let it be X. What is the probability that less than 50% will favor the charter school? Assume central limit theorem conditions apply.