Answer:
a. These four vectors are dependent because there are columns of 3 by 4 matrix with one free variable.
b. If one is a multiple of other
c. c1v1 + c20 = 0 has nontrivial solution.
Step-by-step explanation:
Any set of 4 or more vectors must be linearly dependent. The non trivial combination of vector may produce zero as the set is linearly dependent. The vector v1 and v2 will be dependent if one is the multiple of the other.
Angle Sum Theorem Acellus
20 120 y = ?
We know
Sum of two interior angles=exterior angle
[tex]\\ \sf\longmapsto 20°+120°=<y[/tex]
[tex]\\ \sf\longmapsto <y=20°+120°[/tex]
[tex]\\ \sf\longmapsto <y=140°[/tex]
Hope it helps
$26,876 is invested, part at 9% and the rest at 5%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 5% by $720.78, how much is invested at each rate? (Round to two decimal places if necessary.)
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Answer:
$14,747 at 9%$12,129 at 5%Step-by-step explanation:
Let x represent the amount invested at 9%. Then the difference in interest amounts is ...
(9%)x -(5%)(26876 -x) = 720.78 . . . . . assuming a 1-year investment
0.14x -1343.80 = 720.78 . . . . . . . . . simplify
0.14x = 2064.58 . . . . . . . . . . . . . . add 1343.80
x = 14,747 . . . . . . . . . . . . . . . . divide by 0.14
$14,747 is invested at 9%; $12,129 is invested at 5%.
Please help.........
Answer:
a
Step-by-step explanation:
If you were asked to measure the success of a campaign to fight for human rights, what criteria would you use?
Step-by-step explanation:
Many factors would be used to assess the effectiveness of a human rights campaign, including the following:
Social Influence. Direct Interpersonal Reach. Participant Observation. Reputation. Volume of Search & Interest. Website Traffic.
National Research.
Please Help!
What is the locus of the midpoints of all chords that can be drawn from a given point on a circle with a radius of 6.
The locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Given: A circle of radius 6 units
To find: The locus of the midpoint of all chords that can be drawn from a given point on the circle.
To find the required locus, we need to know the following:
Locus of a moving point is the trajectory of that point. It is the geometrical figure represented by the equation which is satisfied by the coordinates of the moving point.A chord of a circle is a line segment joining any points of a circle.Equation of a circle with center at origin and radius of [tex]r[/tex] units is [tex]x^{2} +y^{2} =r^{2}[/tex] According to the midpoint formula, the coordinates of the midpoint of the line segment joining the points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex](\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )[/tex]Let, without loss of generality, the given circle be centered at the origin. Even if it is not, we can shift the origin to the center of the given circle with coordinate transformation.
Then, the equation of the given circle is [tex]x^{2}+y^{2} =6^{2}[/tex], that is, [tex]x^{2}+y^{2} = 36[/tex]
Let the coordinates of the given fixed point be [tex](a,b)[/tex]
Let the coordinates of any point on the circle be [tex](p,q)[/tex] and let the coordinates of the midpoint of the chord joining the points [tex](a,b)[/tex] and [tex](p,q)[/tex] be [tex](h,k)[/tex]
We have to find the locus of [tex](h,k)[/tex]
Then, using the midpoint formula,
[tex](h,k)=(\frac{a+p}{2} ,\frac{b+q}{2})[/tex]
On solving, we get,
[tex]p=2h-a,q=2k-b[/tex]
Since [tex](a,b)[/tex] and [tex](p,q)[/tex] are both points on the given circle, they satisfy the equation of the circle, [tex]x^{2}+y^{2} = 36[/tex]
Then,
[tex]a^{2} +b^{2} =36[/tex]
[tex]p^{2} +q^{2} =36[/tex]
Substituting [tex]p=2h-a,q=2k-b[/tex] in [tex]p^{2} +q^{2} =36[/tex], we have,
[tex](2h-a)^{2} +(2k-b)^{2} =36[/tex]
[tex](2(h-\frac{a}{2}) )^{2} +(2(k-\frac{b}{2}))^{2} =36[/tex]
[tex]4(h-\frac{a}{2})^{2} +4(k-\frac{b}{2})^{2} =36[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =\frac{36}{4}[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =9[/tex]
[tex](h-\frac{a}{2})^{2} +(k-\frac{b}{2})^{2} =3^{2}[/tex]
This is the locus of the point [tex](h,k)[/tex]
Replace [tex](h,k)=(x,y)[/tex] to get,
[tex](x-\frac{a}{2})^{2} +(y-\frac{b}{2})^{2} =3^{2}[/tex]
This is the equation of a circle with center at [tex](\frac{a}{2} ,\frac{b}{2} )[/tex] and radius 3 units.
Thus, we can conclude that the locus of the midpoints of all chords that can be drawn from a given fixed point [tex](a,b)[/tex] on a circle with a radius of 6 units, is a circle of radius 3 units with center at a point whose x & y coordinates are shifted from the center of the given circle by [tex]\frac{a}{2}[/tex] and [tex]\frac{b}{2}[/tex] respectively.
Learn more about locus here:
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in how many ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies?
Answer:
5880 ways
Step-by-step explanation:
For selections like this, we solve using the combination theory. Recall that
nCr = n!/(n-r)!r!
Hence given to find the number of ways 6 gentleman and 4 ladies can be choosen out of 10 gentleman and 8 ladies,
= 10C6 * 8C4
= 10!/(10-6)!6! * 8!/(8-6)!6!
= 10 * 9 * 8 * 7 * 6!/4 *3 *2 * 6! * 8 * 7 * 6!/2 * 6!
= 210 * 28
= 5880 ways
The arrangement can be done in 5880 ways
In the graph above, which vertical line (V) and horizontal line (H) can be used to graph point A?
A)
V: x = 1; H: y = 4
B)
V: x = 4; H: y = 1
C)
V: y = 4; H: x = 1
D)
V: x = 1; H: y = –4
Answer:
V: x = 1; H: y = 4
Step-by-step explanation:
Point A is at x = 1 and y = 4
A vertical line at x=1 and a horizontal line at y = 4
[tex]-3x^{2} -4y^{2} -z^{2}+6xy-6x+4z[/tex]
If total sales are $54000 your food service total is 42% of your total sales what is your dollar target for food service
Answer:
Your dollar target for food service is $22,680
Step-by-step explanation:
It is given in the question that total sales are = $54,000
your food service is 42% of your total sales = 42% × $54,000
= × 54,000
= 0.42 × 54,000
= $22,680
BRAINLIEST FOR ANSWER
A cylinder of water was holding a volume of 2 mL of water. An irregularly shaped stone was put into the cylinder and the volume rose to 8 mL. If the mass of the stone was 21 g, what was its density?
Answer:
3.5g/ml or 3.5g/cm³
Step-by-step explanation:
1cm³=1ML
Volume of the irregular shaped stone = New Volume of water in cylinder -initial Volume of water in cylinder
Volume of irregular shaped stone = 8ml-2ml
Volume of irregular shaped stone =6ml
Denisty =Mass/Volume
Density = 21g/6ml
Density = 3.5g/ml
Help!!????
Please!!!????
Answer:
true
mark me brainist if it comes out to be true
Answer:
The answer is TRUE.
Step-by-step explanation:
The equation of a parabola in standard form is
y = mx + b
y = mx2 + b
y = ax2 + bx + c
y = a(x - h)2 +k
Answer: y = ax2 + bx + c
looks like a slightly trick question...
y = ax2 + bx + c is the standard form...
y = a(x - h)2 +k is the graphing form
Step-by-step explanation:
jope works 42 hours in a 6 day week, calculate the number of hours in a week he is not at work
Answer:
the number of hours in a week Jope, who is not at work, is 102 hours
Step-by-step explanation:
call X is the number of hours in a week Jope is not at work.
=> the number of hours in a week = X + the number of work hours in a week
=> 6*24 = X + 42
=> X = 6*24 - 42
=> X = 102 hours
PLEASE HELP URGENT!!!
Janine determines that the total resistance in her circuit is 80 ohms. Using the inverse equation modeling this situation, find the resistance of the second lightbulb.
The resistance of the second lightbulb is ohms.
A. 120
B. 240
C. 300
D. 40
The sum of resistors arranged in parallel is the inverse of the sum of the inverses of the magnitudes of the individual resistances
The correct option for the resistance of the second light bulb in ohms (Ω) is option B;
B. 240
The reason why option B is the correct answer is s follows:
Known parameters:
Based on a online search, the question appears to have some parts missing which can be as follows;
The resistance of the first light bulb = 120 Ω
Janine's model of the total resistance of the circuit, [tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]
Where;
r = The resistance of the second light bulb
The unknown parameter:
Resistance of the second light bulb
Method:
Find r using Janine's model of the total resistance, which is the equation of total resistances in parallel arrangement
The inverse relationship modelling the sum, t, of resistances, r, and 120, arranged in parallel, presented as follows;
[tex]\mathbf {\dfrac{1}{t} } =\dfrac{1}{120} + \dfrac{1}{r}[/tex]
∴ [tex]\mathbf {\dfrac{1}{t}} = \dfrac{r + 120 }{120 \cdot r}[/tex]
Therefore, by finding the inverse of both sides of the above equation, we get Janine's model as follows;
[tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]
The above equation is the inverse equation modelling the total resistance of the parallel arrangement of the resistances in the lightbulb
The question details include:
The total resistance in her circuit, t = 80 Ω
Solution:
Plugging in t = 80 in [tex]t = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex], gives;
[tex]80 = \mathbf {\dfrac{120 \cdot r }{r + 120} }[/tex]
Therefore, we get;
80·(r + 120) = 120·r
80·r + 80 × 120 = 120·r
∴ 120·r - 80·r = 80 × 120 = 9,600
120·r - 80·r = 40·r
∴ 40·r = 9,600
r = 9,600/40 = 240
The resistance of the second light bulb, r = 240 Ω
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Answer:240
Step-by-step explanation:
i watched the walk through
Find the area of the shaded part !
Answer:
Step-by-step explanation:
Semicircle:
Shaded area of semicircle = area of outer semicircle - area of inner semicircle
Outer semicircle:
d = 40 m r = 40/2 = 20m
Area of outer semicircle = πr²
= 3.14*20*20
= 1256 m²
Inner semicircle:
d = 30 m r = 30/2 = 15 m
Area of outer semicircle = πr²
= 3.14*15*15
= 706.5 m²
Shaded area of semicircle = 1256 - 706.5 = 549.5 m²
Shaded area of semicircle in both sides = 2 * 549.5 = 1099 m²
Rectangle on both sides:
Length = 50 m
width = 30 m
Area of shaded rectangles on both sides = 2* (length *width)
= 2* 50 * 30
= 3000 m²
Shaded area = 1099 + 3000 = 4099 m²
CAN YOU GUYS PLEASE HELP ME? THANK YOU!
Answer:
60
step by step explanitation
SCALCET8 4.7.011. Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens
Answer:
For any rectangle, the one with the largest area will be the one whose dimensions are as close to a square as possible.
However, the dividers change the process to find this maximum somewhat.
Letting x represent two sides of the rectangle and the 3 parallel dividers, we have 2x+3x = 5x.
Letting y represent the other two sides of the rectangle, we have 2y.
We know that 2y + 5x = 750.
Solving for y, we first subtract 5x from each side:
2y + 5x - 5x = 750 - 5x
2y = - 5x + 750
Next we divide both sides by 2:
2y/2 = - 5x/2 + 750/2
y = - 2.5x + 375
We know that the area of a rectangle is given by
A = lw, where l is the length and w is the width. In this rectangle, one dimension is x and the other is y, making the area
A = xy
Substituting the expression for y we just found above, we have
A = x (-2.5x+375)
A = - 2.5x² + 375x
This is a quadratic equation, with values a = - 2.5, b = 375 and c = 0.
To find the maximum, we will find the vertex. First we find the axis of symmetry, using the equation
x = - b/2a
x = - 375/2 (-2.5) = - 375/-5 = 75
Substituting this back in place of every x in our area equation, we have
A = - 2.5x² + 375x
A = - 2.5 (75) ² + 375 (75) = - 2.5 (5625) + 28125 = - 14062.5 + 28125 = 14062.5
Step-by-step explanation:
My friend needs help on this sorry!
A group of 6 children and 6 adults are going to the zoo. Child tickets cost $10, and adult tickets cost $14. How much will the zoo tickets cost in all?
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Answer:
$144
Step-by-step explanation:
Multiplication is used to simplify repeated addition. To find the total cost, add up the costs of each of the tickets.
6 child tickets will cost $10 +10 +10 +10 +10 +10 = 6×$10 = $60
6 adult tickets will cost $14 +14 +14 +14 +14 +14 = 6×$14 = $84
Then the total cost of all of these tickets will be ...
$60 +84 = $144 . . . . cost of zoo tickets in all
Identify the most relevant source of bias in this situation: A study seeks to investigate whether a new pain medication is safe to market to the public. They test by randomly selecting 300 men from a set of volunteers.
Answer:
The bias is they only picked men to test the new medication on to see if it was ready for the general public to use.
Step-by-step explanation:
Find the missing segment in the image below
Answer:
x = 42
Step-by-step explanation:
24+8 = 32
[tex]\frac{x}{24}[/tex] = [tex]\frac{x+14}{32}[/tex]
32x = 24(x+14)
32x = 24x+336
8x = 336
x = 42
10
8
12
10
14
?
a. 16
b. 10
c. 12
d. 18
Answer:
12
Step-by-step explanation:
10 8 subtract 2
8 12 add 4
12-10 subtract 2
10 14 add 4
Now we subtract 2
14-2 = 12
help everyone!!!!!!..........
Answer:
a-648²
b-4.2²
Step-by-step explanation:
least 108*48 = 648²
An equal number of juniors and seniors are trying out for six spots in this year's decathlon
team. If the team must consist of four seniors and two juniors, then how many different
possible decathlon teams could result if five juniors try out?
50
55
75
100
There are 50 different possible debating teams that could be selected as obtained using COMBINATION.
Since there are EQUAL number of juniors and seniors ;
Then we have 5 of each.
Here, the order of arrangement DOES NOT matter, Hence, we use COMBINATION
since the team MUST contain 4 SENIORS and 2 JUNIORS
4 Seniors from 5 = 5C4 = 5
2 Juniors from 5 = 5C2 = 10
Hence, (5C4 * 5C2) = 5 * 10 = 50
Hence, there are 50 different possible debating teams that could be selected.
Learn more about COMBINATION :
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Tìm vi phân toàn phần của các hàm số sau:
ln(x+√(x^2+y^2 ) ) ln(sin(y/x))
Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).
Then the total differential is
[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]
[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]
Write the English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. Six times the sun of 4 and a number
Answer:
6x + 24
Step-by-step explanation:
6 * (4 + x) = 6 * 4 + 6 * x = 6x + 24
I'm not sure how to do this
Answer:
1 and 5 sevenths of a bag
Step-by-step explanation:
2/7 males half to it takes 4/7 to make a full one multiply 4 by 3 and you get 12/7 so that makes 1 and 5/7
May I get help with this question?
Answer:
C. <F
Step-by-step explanation:
The angle that sees the largest side length has the largest measurement.
Amongst the given side lengths the one that sees <F has the longest length so the answer is C
An angle, Theta. is in standard position. The terminal side of the angle passes through the point (6.-5).
Find sin Theta
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Answer:
sin(θ) = (-5√61)/61
Step-by-step explanation:
The distance from the origin to the given point is ...
d = √(6² +(-5)²) = √61
The sine of the angle is the ratio ...
sin(θ) = y/d = -5/√61
Rationalizing the denominator gives us ...
sin(θ) = (-5√61)/61
A clothing manufacturer purchased 50 yd of cotton and 80 yd of wool for a total cost of $1,330. Another purchase, at the same prices, included 75 yd of cotton and 20 yd of wool for a total cost of $895. Find the cost per yard of the cotton and of the wool.
Answer:
The cotton is $9 per yard and the wool is $11 per yard
Step-by-step explanation:
Create a system of equations where c is the cost per yard for the cotton and w is the cost per yard for the wool.
50c + 80w = 1330
75c + 20w = 895
Solve by elimination by multiplying the bottom equation by -4:
50c + 80w = 1330
-300c - 80w = -3580
Add these together and solve for c:
-250c = -2250
c = 9
Plug in 9 as c into one of the equations, and solve for w:
50c + 80w = 1330
50(9) + 80w = 1330
450 + 80w = 1330
80w = 880
w = 11
The cotton is $9 per yard and the wool is $11 per yard.
A random sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 9. An independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 11. Test the claim that the population means are different. Use level of significance 0.01.
Compute the corresponding sample distribution value. (Test the difference μ1 − μ2. Round your answer to two decimal places.)
Answer:
The answer is "-3.04"
Step-by-step explanation:
[tex]\to \bar{x_1}-\bar{x_2}=9-11=-2[/tex]
Sample distribution:
[tex]z=\frac{\bar{x_1}-\bar{x_2}- \bar{\mu_1}-\bar{\mu_2}}{\sqrt{\frac{\sigma_{1}^2}{n_1}+\frac{\sigma_{2}^2}{n_2}}}\\\\[/tex]
[tex]=\frac{(-2)-0}{\sqrt{\frac{3^2}{49}+\frac{4^2}{64}}}\\\\=\frac{-2}{\sqrt{\frac{9}{49}+\frac{16}{64}}}\\\\=\frac{-2}{\sqrt{\frac{576+784}{3136}}}\\\\=\frac{-2}{\sqrt{\frac{1360}{3136}}}\\\\=\frac{-2}{\sqrt{0.433}}\\\\=\frac{-2}{0.658}\\\\=-3.039\\\\=-3.04[/tex]
