12. In a library, 50% of total number of books is of Marathi. The books of English are 3 1 rd of Marathi books. The books on mathematics are 25% of the English books. The remaining 560 books are of other subjects. What is the total number of books in the library?​

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)

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

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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 <.

The equation that quickly reveals the y-intercept is f(x) = 3x²+ 36x + 33 and the y- intercept is 33

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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The system of equations for the two plans is:

y = 8x + 25

y = 12x + 5

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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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:

To show that a pattern repeats indefinitely, a bar is put over it. For example, 2.2616161 in bar notation is: 2.26¯.

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¯.

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{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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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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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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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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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.

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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Answer:

f(2)=3x²+2x-10

f(2)=3(2)² +2(2)-10

=12+4-10

=6

Answer:

think its this not sure : Alternate interior angles theorem

Step-by-step explanation:

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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Answer:

djdjdhdudjdhxnfbxi94949495959584748474748494949585858595959585858585858585859696969485858589484748487474747383392929२९३9999४४६५८४९२84८३4६३०२०८४७४94८८४७४९8४८४८४८४८४८48484८5८५८५८४८३९2९२919९२9३76४७४7७४७४7४5959999393939393939494949449494949494998595859303099

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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∫fx(x)dx = 1 over the entire range of x, and fx is indeed a density function.

A random variable X has the normal distribution N(m, o^2), where m and o are both real numbers, if it is an absolutely continuous random variable with density fx(x) = (1/√(2πo^2)) * exp(-(x-m)^2/2o^2).

To verify that fx is indeed a density, we need to check that it satisfies the two properties of a density function:

1) fx(x) >= 0 for all x
2) ∫fx(x)dx = 1 over the entire range of x

First, let's check that fx(x) >= 0 for all x. Since the exponential function is always positive, we can see that fx(x) will always be positive as well. Therefore, fx(x) >= 0 for all x.

Next, let's check that ∫fx(x)dx = 1 over the entire range of x. To do this, we need to integrate fx(x) over the entire range of x, which is from -∞ to ∞:

∫fx(x)dx = ∫(1/√(2πo^2)) * exp(-(x-m)^2/2o^2)dx from -∞ to ∞

Using the substitution u = (x-m)/√(2o^2), we can rewrite the integral as:

∫(1/√(2πo^2)) * exp(-u^2/2) * √(2o^2)du from -∞ to ∞

Simplifying, we get:

∫(1/√(2π)) * exp(-u^2/2)du from -∞ to ∞

This integral is equal to 1, as it is the integral of the standard normal density function. Therefore, ∫fx(x)dx = 1 over the entire range of x, and fx is indeed a density function.

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The approximate diameter of the circle is 8.5 ft.

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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Answer:

D is correct

Step-by-step explanation:

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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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

w |w|-20=-13
w = 7 and w = -33

A. For this equation, we have to solve for the absolute value of w.

An absolute value equation can be thought of as two equations in one, so we need to solve for both cases.

B.

Case 1: w > 0

w - 20 = -13

w = 7

Case 2: w < 0

w + 20 = -13

w = -33

Therefore, the solution to this absolute value equation is w = 7 and w = -33.

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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

Answer: 29%

Step-by-step explanation:

109/360=.294 Then move the decimal to make it a percent

Answer:

Step-by-step explanation:

from top down:

xᵃ⁻ᵇ

xᵃ⁺ᵇ

1

xᵃˣᵇ

1/xᵃ

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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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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