Step-by-step explanation:
remember,
100% = 1
1% = 100%/100 = 1/100 = 0.01
as decimal
2/5 % = 1% × 2/5 = 0.01 × 0.4 = 0.004
as fraction
1% × 2/5 = 1/100 × 2/5 = 2/500 = 1/250
Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4,
and 2A^TB^-1 = C. Find det(B)
Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4, and 2A^TB^-1 = C the determinant of matrix B is 4.
To find the determinant of matrix B, we can use the property of determinants that states that det(AB) = det(A)det(B). We can rearrange the given equation 2A^TB^-1 = C to get B = 2A^T C^-1. Then, we can take the determinant of both sides to get det(B) = det(2A^T C^-1).
Using the property of determinants, we can expand the right side of the equation to get det(B) = det(2)det(A^T)det(C^-1). Since the determinant of a scalar multiple of a matrix is the scalar multiple of the determinant, det(2) = 2^3 = 8. Also, the determinant of the transpose of a matrix is the same as the determinant of the original matrix, so det(A^T) = det(A) = 2.
Finally, the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix, so det(C^-1) = 1/det(C) = 1/4.
Substituting these values back into the equation, we get det(B) = 8*2*(1/4) = 4. Therefore, the determinant of matrix B is 4.
det(B) = 4.
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I need help with these point + brainliest if 80% of them are anwered
Answer:Answer:
1) SA = 2(wl + hl + hw) = 2(12*2 + 12*6 + 6*2) = 2(24 + 72 + 12) = 2(108) = 216
2) SA = (6*4)/2 + 6*11 + 2(5*11) = 12 + 66 + 110 = 188
3) SA = 2(6*12 + 14*12 + 6*14) = 648
4) (9*12)/2 + 15*6 + 9*6 + 12*6 = 54 + 90 + 54 + 72 = 270
5) 2(16*9 + 4*9 + 16*4) = 488
6) SA = 2πrh+2πr^2 = 2*3.14*10*16 + 2*3.14*10^2 = 1004.8 + 628 = 1632.8
7) SA = 2(7*7 + 14*7 + 7*14) = 490
8) SA = 2πrh+2πr^2 = 2*3.14*7*11 + 2*3.14*7^2 = 483.56 + 307.72 = 791.28
9) (12*10)/2 + 2(14*13) + 14*10 = 60 + 364 + 140 = 564
Step-by-step explanation:
A small company has the marketing information that 35 units will sell daily at a price of $34.75 per unit, and that sales will rise to 36 units per day at a price of $33.06 per unit. Use this information to create a linear demand function, then create the associated revenue function and find the price that will yield the maximum revenue.
The linear demand function is given by Q = -1.09P + 76.4, the revenue function is R = -1.09P^2 + 76.4P, and the price that yields maximum revenue is $34.95.
To create the linear demand function, we use the two points given: (35, 34.75) and (36, 33.06). We can find the slope of the line between these two points using the slope formula: (33.06 - 34.75)/(36 - 35) = -1.69. This slope represents the change in quantity demanded per dollar change in price. To find the intercept, we can use either of the points and solve for it: 35 = -1.69(34.75) + b, giving us b = 131.15. Thus, the demand function is Q = -1.69P + 131.15, which we can simplify to Q = -1.09P + 76.4.
To find the revenue function, we multiply the demand function by the price: R = P(Q) = P(-1.09P + 76.4) = -1.09P^2 + 76.4P. To find the price that yields maximum revenue, we can take the derivative of the revenue function with respect to price and set it equal to zero: dR/dP = -2.18P + 76.4 = 0, giving us P = $34.95. Therefore, the price that yields maximum revenue is $34.95.
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solve the simultaneous equation
a)
5x+3y=41
2x+3y=40
b)
x+7y=64
x+3y=28
HELPPP
Answer:
a) (0.333, 13.11)
b) (1, 9)
Step-by-step explanation:
a)
5x+3y=41
2x+3y=40
[The steps are labelled so they can be referenced in the subsequent problems]
A. Rearrange one of the two equations so as to isolate the x or y to one side. I'll use 2x+3y=40:
2x+3y=40
2x = 40-3y
x = (40-3y)/2
B. Now use that expression of x in the other equation:
5x+3y=41
5((40-3y)/2)+3y=41
(200-15y)/2 +3y = 41
100 - 7.5y + 3y = 41
-4.5y = - 59
y = 13.11
C. Now use y=13.11 in either equation to find x:
2x+3y=40
2x+3*(13.11)=40
2x + 39.33 = 40
2x = 0.67
x = 0.333
D. Answer: The lines intersect at (0.333, 13.11)
b)
x+7y=64
x+3y=28
A.
x+7y=64
x=64-7y
B.
x+3y=28
(64-7y)+3y=28
64-4y = 28
-4y = -36
y = 9
C.
x=64-7y
x=64-7*9
x = 1
D. Answer: The lines intersect at (1, 9)
See the attached graph for proof of the points of intersection.
HELPPP PROVIDED (I hope)
Which side lengths form a triangle? (Choose all that apply.)
1
2
3
4
5
6
7
8
Answer:
djdjdhdudjdhxnfbxi94949495959584748474748494949585858595959585858585858585859696969485858589484748487474747383392929२९३9999४४६५८४९२84८३4६३०२०८४७४94८८४७४९8४८४८४८४८४८48484८5८५८५८४८३९2९२919९२9३76४७४7७४७४7४5959999393939393939494949449494949494998595859303099
Help with geometry on parallelograms.
x and y must have values of 3 and 11, respectively.
What is a Parallelogram?
A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.
The angles in a parallelogram are given in the diagram.
As opposite sides are equal and parallel in a parallelogram, the alternate interior angles must also be the same.
This gives:
5y - x = 52 ...(i)
6y - 18 = 48 ...(ii)
Solving (ii)
6y = 66
y = 11
Substituting in (i)
5(11) - x = 52
x = 3
The values of x and y must be 3 and 11 respectively.
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Rochelle has 6 pounds of grass seed. She
uses
1 1/3 pounds on the front yard and
1 4/9 pounds on the side yard. How many
pounds are left?
Answer:
6 - (1 1/3 + 1 4/9)
6 - 2 7/9
= 29/9
= 3 2/9
Therefore, 3 2/9 pounds of grass seed are left.
An online video streaming service offers two plans for unlimited streaming.
Plan A has a one-time $8 membership fee and is $25 per month.
Plan B has a $12 membership fee and is $5 per month.
Write a system of equations that represents the two plans.
The system of equations for the two plans is:
y = 8x + 25
y = 12x + 5
How to Write a System of Equations?To write a system of equations for each plan, let:
x = number of month
y = Total amount
Equation of plan A:
one-time membership fee = initial value or y-intercept (b) = 8
Monthly fee per month = slope/unit rate (m) = 25
The equation would be y = 8x + 25
Equation of plan B:
one-time membership fee = initial value or y-intercept (b) = 12
Monthly fee per month = slope/unit rate (m) = 5
The equation would be y = 12x + 5
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Let \( f(x)=\frac{x-3}{x^{2}+2} \) (a) What is the value of \( f(-2) \) ? (b) Find \( f(-2 x-5) \). Simplify your \[ \frac{-2 x-8}{4 x-27} \]
Therefore, f(-2x-5) is \[ \frac{-2(x+4)}{4(x+3)^{2}}=\frac{-2 x-8}{4 x^{2}+24 x+36} \]
(a) To find the value of f(-2), we simply substitute -2 for x in the given function:
\[ f(-2)=\frac{-2-3}{(-2)^{2}+2}=\frac{-5}{6} \]
Therefore, the value of f(-2) is -5/6.
(b) To find f(-2x-5), we substitute -2x-5 for x in the given function:
\[ f(-2x-5)=\frac{-2x-5-3}{(-2x-5)^{2}+2}=\frac{-2x-8}{4x^{2}+20x+27} \]
Simplifying the numerator and denominator, we get:
\[ f(-2x-5)=\frac{-2(x+4)}{4(x+3)(x+3)}=\frac{-2(x+4)}{4(x+3)^{2}} \]
Therefore, f(-2x-5) is \[ \frac{-2(x+4)}{4(x+3)^{2}}=\frac{-2 x-8}{4 x^{2}+24 x+36} \]
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(4) Let ((2) = ve
- 4 and g(2) =
12
11r + 30. Find 1 and & and state their domains.
Let f(x) = Va - 4 and g(x) = 2?
- 11r +30. Find 1 and 9 and state their domains.
Let ((2) = ve- 4 and g(2) = 12 11r + 30. Then f(1) = i√3, g(1) = 21, Domain of f(x) = [4, ∞) and Domain of g(x) = (-∞, ∞)
First, let's find f(1) and g(1). To do this, we simply substitute x = 1 into the equations for f(x) and g(x):
f(1) = √(1 - 4) = √(-3) = i√3
g(1) = 2(1) - 11(1) + 30 = 2 - 11 + 30 = 21
Now, let's find the domains of f(x) and g(x). The domain of a function is the set of all values of x for which the function is defined.
For f(x) = √(x - 4), the expression inside the square root must be greater than or equal to 0 in order for the function to be defined. This means that:
x - 4 ≥ 0
x ≥ 4
So the domain of f(x) is [4, ∞).
For g(x) = 2x - 11x + 30, there are no restrictions on the domain, so the domain of g(x) is (-∞, ∞).
So the final answers are:
f(1) = i√3
g(1) = 21
Domain of f(x) = [4, ∞)
Domain of g(x) = (-∞, ∞)
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The median price of a single family home in a given town is $250,000 in 2018. A real estate broker believes the price value of homes has increased since then. State the null and alternative hypothesis for the scenario using math symbols and words.
Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.
H0: μ = $250,000
Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.
Ha: μ > $250,000
What is represent the null hypothesis?The null hypothesis assumes that there has been no change in the median price since 2018, while the alternative hypothesis assumes that the median price has increased. The alternative hypothesis is one-sided, as the broker is interested in testing whether the price has increased, rather than testing whether there has been any change (i.e., a two-sided test).
The null and alternative hypotheses for the scenario can be stated as follows:
Null hypothesis (H0): The population median price of single-family homes in the town has not changed since 2018.
H0: μ = $250,000
Alternative hypothesis (Ha): The population median price of single-family homes in the town has increased since 2018.
Ha: μ > $250,000
In the above hypotheses, μ represents the population median price of single-family homes in the town.
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I dont know what the answer is and well im quite confused.
Answer:
C
Step-by-step explanation:
They are not proportional
If 3 pie cost $12, one pie will be $4
If 10 pie cost $25, then 1 pie is $2.5
$4 is not proportional to $2.5
Hence 12/3 is not proportional to 25/10
I'd really like some help with this. Please...Please! What's the probability that the point ends in the shaded region?
Answer: 29%
Step-by-step explanation:
109/360=.294 Then move the decimal to make it a percent
(1 point) Given the function f(x)=x+3x−8 find the following. (a)
the average rate of change of f on [−3,1]: (b) the average rate of
change of f on [x,x+h]:
a) The average rate of change of f on [−3,1] is 4.
b) The average rate of change of f on [x,x+h] is 3+16/h.
The average rate of change of a function f(x) on an interval [a,b] is given by the formula:
Average rate of change = (f(b)-f(a))/(b-a)
(a) To find the average rate of change of f on [−3,1], we plug in the values of a=-3 and b=1 into the formula:
Average rate of change = (f(1)-f(-3))/(1-(-3))
= (f(1)-f(-3))/4
Now, we need to find the values of f(1) and f(-3) by plugging in the values of x into the given function:
f(1)=1+3(1)-8=-4
f(-3)=-3+3(-3)-8=-20
Plugging these values back into the formula, we get:
Average rate of change = (-4-(-20))/4
= 16/4
= 4
Therefore, the average rate of change of f on [−3,1] is 4.
(b) To find the average rate of change of f on [x,x+h], we plug in the values of a=x and b=x+h into the formula:
Average rate of change = (f(x+h)-f(x))/(x+h-x)
= (f(x+h)-f(x))/h
Now, we need to find the values of f(x+h) and f(x) by plugging in the values of x and x+h into the given function:
f(x+h)=x+h+3(x+h)-8
=4x+3h-8
f(x)=x+3x-8
=4x-8
Plugging these values back into the formula, we get:
Average rate of change = (4x+3h-8-(4x-8))/h
= (3h+16)/h
= 3+16/h
Therefore, the average rate of change of f on [x,x+h] is 3+16/h.
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Workspace: Given pardlelogram WxY 2, where Wxx =2x+15,xY= x+27 and yz=4x-21, delemine the length of 2W in inches.
The length of 2W in inches can be calculated by using the measurements of the parallelogram. Wxx is 2x+15, and xY is x+27. Since the length of W xx and xY is referring to the same line, x+27=2x+15. Solving for x, x=12. Knowing the value of x, Wxx=2(12)+15=39 inches and xY=12+27=39 inches. Therefore, 2W=2(39)=78 inches.
The length of a line in a parallelogram can be calculated by adding the two measurements of the two lines containing the same point. Since the line containing point W is the same line containing point x, the two measurements can be solved for the same variable, x. Once the variable is determined, the value of the two lines containing the same point can be determined. The value of the two lines can then be multiplied by 2 to determine the length of the line in the parallelogram.
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Two values of x that would make this inequality true.
Answer:-12&-8
Step-by-step explanation:
since 3x is negative the -12 and -8 become positive to combine with 5 to either become 41 or 37
please help me asap!!
What is the missing reason in the following proof?
Answer:
think its this not sure : Alternate interior angles theorem
Step-by-step explanation:
What is the surface area of the cube? (10 Points)
Drag and drop the correct surface area to match the cube.
Cube with edge length = 3.2 m
Options:
A) 12.8 m2
B) 19.2 m2
C) 51.2 m2
D) 61.44 m2
HURRY!!!
Answer:
D is correct
Step-by-step explanation:
Determine whether the ordered pair is a solution of (5,6) {(x+y=11),(x-y=-1):} No Yes
Yes, the ordered pair (5,6) is a solution of the system of equations {(x+y=11),(x-y=-1):}.
To check if an ordered pair is a solution of a system of equations, we can plug the values of the ordered pair into the equations and see if they are true.
For the first equation, x + y = 11, we can plug in 5 for x and 6 for y:
5 + 6 = 11
This is true, so the ordered pair satisfies the first equation.
For the second equation, x - y = -1, we can again plug in 5 for x and 6 for y:
5 - 6 = -1
This is also true, so the ordered pair satisfies the second equation.
Since the ordered pair satisfies both equations, it is a solution of the system of equations.
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Can somebody tell me If this is right or wrong because I don’t know.
The simple interest values are all wrong
What is simple interest?Simple Interest (S.I) is a method of charging or yielding a specific percentage on the principal amount borrowed/deposited in a particular period. It is calculated using the formula
SI = (Principal*Rate*Time)/100,
a) SI = (450*25.2*3)/100,
SI = %70.2
2) SI = (Principal*Rate*Time)/100,
SI = (250*3.75*5)/100,
$46.875
(3) SI = (Principal*Rate*Time)/100,
SI = (1800*2.1*2)/100,
SI = $75.6
4) SI = (Principal*Rate*Time)/100,
SI = (1500*2.9*2)/100,
SI = $87
5) SI = (Principal*Rate*Time)/100,
SI = (50*1.9*10)/100,
SI =$9.5
6) SI = (Principal*Rate*Time)/100,
SI = (8*0.7*300)/100,
SI = $16.8
7) SI = (Principal*Rate*Time)/100,
SI = (125*2.03*4)/100,
SI = $10.15
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The circumstance of a circle is 26 5/7ft
What is the approximate diameter of the circle?
The approximate diameter of the circle is 8.5 ft.
What is area of a circle?The space a circle takes up on a two-dimensional plane is known as the area of the circle. Alternately, the area of the circle is the area included inside the circumference or perimeter of the circle. For measuring the area occupied by a circular field or plot, use the area of a circle formula. The area formula will allow us to determine how much fabric is required to completely cover a circular table, for example. The area formula will also enable us to determine the circle's circumference, or the border length.
The circumference of the circle is given as:
C = 2 πr
We can also write this as:
C = πd
as, 2r = d.
The circumference is given as 26 5/7ft. To convert this to a decimal, we can multiply the fractional part by 7/7 to get:
5/7 * 7/7 = 35/49
So the circumference is approximately:
26 + 35/49 = 26.71 ft
Now we can use the formula to find the diameter:
d = 26.71 / 3.14 ≈ 8.5 ft
Therefore, the approximate diameter of the circle is 8.5 ft.
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Skydiving, anyone? A humor piece published in the British Medical Journal ("Parachute use to prevent death and major trauma related to gravitational challenge: Systematic review of randomized control trials," Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can’t tell for sure whether parachutes are safe and effective because there has never been a properly randomized, double-blind, placebo-controlled study of parachute effectiveness in skydiving. (Yes, this is the sort of thing statisticians find funny. . . .) Suppose you were designing such a study:
a) What is the factor in this experiment?
b) What experimental units would you propose?10
c) What would serve as a placebo for this study?
d) What would the treatments be?
e) What would the response variable be?
f) What sources of variability would you control?
a) The factor in this experiment would be the use of a parachute during skydiving.
b) The experimental units would be individuals who are participating in skydiving.
c) A placebo for this study would be a dummy or fake parachute that is identical in appearance to a real parachute, but does not actually function as a parachute.
d) The treatments would be the use of a real parachute and the use of the placebo or fake parachute.
e) The response variable would be the incidence of injury or death during the skydiving experience.
f) Some sources of variability that would be controlled include
the location of the skydiving activitythe weather conditionsthe experience level of the individuals participating in the study,the safety measures or precautions during skydiving experience.Read more about experiment
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H + 11 < 16 what do u divide by and what would be the answer?
Step-by-step explanation:
please answer this question quickly
Answer:
H<5
Step-by-step explanation:
u solve it as a normal equation but with the symbol <.
Computations In Exercises 1 through 6, list the elements of the subgroup generated by the given subset. 1. The subset{2,3}ofZ122. The subset{4,6}ofZ123. The subset{8,10}ofZ18(4.) The subset{12,30}ofZ365. The subset{12,42}ofZ6. The subset{18,24,39}ofZ
{18, 36, 24, 48, 39, 72}
In Exercises 1-6, the subgroup generated by the given subset is a set of elements that are all powers of the same element.
1. The subset {2,3} of Z12 generates the subgroup {2, 4, 8, 3, 9, 6, 12}.
2. The subset {4,6} of Z12 generates the subgroup {4, 8, 6, 12}.
3. The subset {8,10} of Z18 generates the subgroup {8, 16, 10, 18}.
4. The subset {12,30} of Z36 generates the subgroup {12, 24, 30, 36}.
5. The subset {12,42} of Z6 generates the subgroup {12, 6}.
6. The subset {18,24,39} of Z generates the subgroup {18, 36, 24, 48, 39, 72}.
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Could use some help problem is in picture thanks!!
The equation that quickly reveals the y-intercept is f(x) = 3x²+ 36x + 33 and the y- intercept is 33
What are intercepts?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
This shows that the y-intercept is gotten when x is 0
Therefore amongst the equation above equation 1 is the equation that easily shows the y-intercept.
The equation f(x) = 3x²+ 36x + 33 is presented in a standard form of quadratic equation.
when x= 0
f(x) = 3x²+ 36x + 33
f(x) = 3(0)²+ 36(0) + 33
f(x) = 0+ 0+ 33
= 33
therefore the y-intercept is 33
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Diana is a junior counselor at cactusville craft camp. One day, diana's campers make lanyard keychains out of plastic string. For each keychain, diana cuts a long piece of string into 8 equal pieces. Each piece is 1. 25 feet long. Which equation can you use to find the length s of the long piece of string before diana cuts it?
Answer:777
Step-by-step explanation:888
The equation which we can use to find the length "s" of long piece of string before Diana cuts it is (a) 8s = 1.25.
In order to find the length "s" of the long piece of string, we need to multiply the length of each of the 8 equal pieces of string by 8, because they are all cut from the same long piece of string.
So, the equation we can use to find the length s of the long piece of string before Diana cuts it is:
⇒ 8 × 1.25 = s,
Simplifying the equation:
We get,
⇒ 10 = s
Therefore, the correct equation is option(a) 8s = 1.25.
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The given question is incomplete, the complete question is
Diana is a junior counselor at Cactus Ville craft camp. One day, Diana's campers make lanyard keychains out of plastic string. For each keychain, Diana cuts a long piece of string into 8 equal pieces. Each piece is 1. 25 feet long.
Which equation can you use to find the length s of the long piece of string before Diana cuts it?
(a) 8s = 1.25
(b) s - 8 = 1.52
(c) s + 8 = 1.25
(d) s/8 = 1.25
(a) Find all solutions for x =
[[
x1
x2
x3
]] of the equation system Ax = 3x
where
A =[
[
3 4 3
2 5 3
0 2 6
]]
(b) What is the dimension of the solution set of Ax = 3x?
Note that, in order to answer this question you need first to argue
why it is allowed to speak about the dimension of the solution set
of Ax = 3x
In the following question, among the various parts to solve- a- "x = [[3/2x3-3/2x3x3]]", b- the dimension of the solution set of Ax = 3x is 1.
(a) To find all solutions of the equation system Ax = 3x, we need to solve the following system of linear equations:
(3 4 3) (x1) (3x1)
(2 5 3) (x2) = (3x2)
(0 2 6) (x3) (3x3)
This can be written as (A - 3I)x = 0, where I is the identity matrix. To find the solutions, we need to find the null space of A - 3I.
(A - 3I) = [[0 4 3 2 2 3 0 2 3]]
To find the null space of this matrix, we row-reduce it to obtain:
[[1 0 -3/2 0 1 3/2 0 0 0]]
The last row tells us that x3 is a free variable, while the first two rows give us:
x1 = (3/2)x3
x2 = (-3/2)x3
Therefore, the general solution to Ax = 3x is:
x = [[3/2x3-3/2x3x3]]
where x3 is any real number.
(b) We can speak about the dimension of the solution set of Ax = 3x because it is a linear homogeneous equation. In this case, the solution set is a subspace of the vector space R^3, and the dimension of this subspace is the number of linearly independent solutions. Since we have one free variable in the solution, the set of solutions is a line in R^3, and its dimension is 1. Therefore, the dimension of the solution set of Ax = 3x is 1.
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what is the rule dividing integers with different signs
So far in this course, you have solved single-variable equations like 3x+7=-x-3. Consider this change to that equation: 3(x+7)=-x-3. What is different about the equations? How will the changes made to the original equation change the steps needed to solve the equation?
Answer below
Step-by-step explanation:
For the first 3x+7=-x-3 you will get 4x=-10 and the final answer is x=-5/2
The second is 3(x+7)=-x-3 which is different since it will equal 3x+21=-x-3 then 4x=-24 and you get x=-6
2.2616161 using bar notation
To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.
what is significant figures ?The meaningful numbers in a number are known as significant figures, also known as significant digits. They are the digits that indicate the level of measurement uncertainty and add to the precision of a number. In other words, important figures are one digit that is either uncertain or estimated in addition to the digits that are known for sure.
given
Repeating digits are represented using the bar notation.
We must recognise the repetitive pattern in the decimal before we can represent 2.2616161 as a repeating decimal using bar notation.
The repetitive pattern is 6161, as can be seen by looking at the decimal. As a result, we can write 2.2616161 as:
2.26 16161...
To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.
To know more about significant figures visit:
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