Preethi writes fifteen 1s in a row and randomly writes + and - between each pair of consecutive 1s. Find the probability that the expression that preethi wrote has value 7.

Answer: Because of the total number of DVDs given (36)the number of  individual type of DVD are coming in decimals such that

Number of comedy films =11.07

Number of Action films =22.15

and Number of horror  films =2.78

I also solved using total number of DVDs as 26 and the results were as follows

Number of comedy films =8

Number of acton films =16

and Number of horror  films =2

Step-by-step explanation:

Total number of DVD collection = 36

ratio of the type of DVD =comedy films to action to horror = 4:8: 1

Total ratio =4+8+1 = 13

Number of comedy films = ratio of comedy films/ total ratio x Total DVD collection

= 4/13 x 36= 11,.07 rounded to 11 comedy films

Number of action films = ratio of action films/ total ratio x Total DVD collection

= 8/13 x 36= 22.15 rounded to 22 action films

Number of horror films = ratio of horror films/ total ratio x Total DVD collection

1/13 x 36=2.78 rounded t0 3 Horror movies .

The numbers of each DVD are giving decimal numbers .

Using

Total number of DVD collection  as 26.

we have that

Number of comedy films= 4/13 x 26 = 8

Number of action films= 8/13 x 26= 16

Number of Horror films = 1/13 x 26 = 2

Answer:

The value of x is 30 and y is 14

Step-by-step explanation:

Here, In given triangle,

∆JLK is similar to ΔPQR

JL is corresponds to PQ.

So, we have the ratio, 21/y ...(1)

Now,

LK is corresponds to QR.

So, we have the ratio, 18/12 = 3/2 ...(2)

Now,

JK is corresponds to PR.

So, we have the ratio, x/20 ...(3)

Then, (1) = (2) = (3)

21/y = 3/2 = x/20 ...(*)

Now, Cross Multiply by (1) and (2) we get,

21 × 2/y × 3

42 = 3y

3y = 42

y = 42/3

y = 14

Here, we get the value of y is 14. So, we will put the value of y in (1) we get,

21/y = 21/14

So, by (*) we get

21/14 = 3/2 = x/20

Then, Cross Multiply with (2) and (3) we get,

3/2 = x/20

20 × 3 = 2 × x

60 = 2x

2x = 60

x = 60/2

x = 30

Thus, The value of x is 30 and y is 14

21/y = 3/2 = x/20

21/14 = 3/2 = 30/20

3/2 = 3/2 = 3/2

-TheUnknownScientist

The standard deviation of the given data can be calculated using the formula for the population standard deviation:

Standard deviation = √[∑(X - μ)² * f / N]

where X is the data value, μ is the mean, f is the frequency, and N is the total number of observations.

Given the data:

X: 3 4 5 6 7 8 9

f: 37 8 10 12 4 3 2

Assumed mean (μ) = 6

To calculate the standard deviation, we need to calculate the squared difference between each data value and the mean, multiply it by the frequency, and sum up these values. Then divide the sum by the total number of observations (N) and take the square root of the result.

Let's calculate it step by step:

(X - μ)² * f:

(3 - 6)² * 37 = 111

(4 - 6)² * 8 = 32

(5 - 6)² * 10 = 10

(6 - 6)² * 12 = 0

(7 - 6)² * 4 = 4

(8 - 6)² * 3 = 12

(9 - 6)² * 2 = 18

Sum of (X - μ)² * f = 187

Now divide the sum by the total number of observations (N = 37 + 8 + 10 + 12 + 4 + 3 + 2 = 76) and take the square root of the result:

Standard deviation = √(187 / 76) ≈ 1.82

Therefore, the standard deviation of the given data is approximately 1.82.

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9514 1404 393

Answer:

  400

Step-by-step explanation:

If x represents the number of employees a year ago, the current number is ...

  x + 0.33x = 53,200

  x = 53,200/1.33 = 400

The company had 400 employees a year ago.

Answer:

-ab^2

Step-by-step explanation:

7b^2a - 5b^2a - 3ab^2

= 2b^2a - 3ab^2

= (2 × b^2 × a) - (3 × a × b^2)

= -ab^2

b^2a and ab^2 is the same thing. hope it helps!

Answer:

3 should be the answer to your question

The weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, but using mathematical induction, the basis step works, although the inductive step fails.

a) If we try to prove the inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) using mathematical induction, we can see that the basis step works. When n = 1, we have 1/2 < 1/√3, which is true.

Now, let's consider the inductive step. Assuming that the inequality holds for some positive integer k, we need to show that it also holds for k+1, i.e., we assume 1/2 · 3/4 ··· 2k-1/2k < 1/√(3k) and we want to prove 1/2 · 3/4 ··· 2k-1/2k · (2k+1)/(2k+2) < 1/√(3k+3).

If we attempt to manipulate the expression, we can simplify it to (2k+1)/(2k+2) < 1/√(3k+3). However, we cannot proceed further to prove this inequality, as it is not necessarily true. Therefore, the inductive step fails, and we cannot establish the original inequality using mathematical induction.

b) However, mathematical induction can still be used to prove the stronger inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n+1) for all integers greater than 1. We can start by verifying the case where n = 1, which gives us 1/2 < 1/√4, which is true.

Now, assuming the inequality holds for some integer k, we can multiply both sides of the inequality by (2k+3)/(2k+2) to get:

(1/2 · 3/4 ··· 2k-1/2k) · (2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

Simplifying the expression on both sides, we have:

(2k+3)/(2k+2) < 1/√(3k+1) · (2k+3)/(2k+2).

We can observe that the right side of the inequality is less than 1/√(3k+3) by multiplying the denominator of the right side by (2k+3)/(2k+3). Hence, we obtain:

(2k+3)/(2k+2) < 1/√(3k+3).

This establishes the inequality for k+1, and thus, we have proven the stronger inequality using mathematical induction.

By verifying the case where n = 1 separately, we can conclude that the weaker inequality 1/2 · 3/4 ··· 2n-1/2n < 1/√(3n) holds for all positive integers n, as it follows from the proven stronger inequality using mathematical induction.

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Answer:

0

Step-by-step explanation:

the equation on finding slope is y2 - y1/x2 - x1

so it is...

6 - 6 = 0

6 - -5 = 11

0/11 but that doesnt work so I believe the slope is zero because the denominator is not the one being a 0

hope I helped ;)

Answer: its a zero slope

Step-by-step explanation: i just put them on a graph - uh i think there is another way to do it but i forgot

Answer:

20

Step-by-step explanation:

One pattern is that we are adding one row and one column for each step.

The first step has 1 row and 2 columns,

the second one has 2 rows and 3 columns,

and the third has 3 rows and 4 columns.

Thus, it would make sense for the fourth step to have 4 rows and 5 columns. This makes a rectangle with a length and a width, with the area of the rectangle being length * width. 4 * 5 = 20 as our number of dots

Answer:

x > 7

Step-by-step explanation:

Step 1: Divide both sides of the inequality by 7.

Therefore, the answer is x > 7.

Using the properties of remainder theorem we calculate that Luisa can get 8 toys and 5 coupons will be left over.

The Remainder Theorem is a method for dividing polynomials in Euclidean space. According to this theorem, reducing a polynomial P(x) by a factor (x - a) that is not an ingredient of the polynomial results in a smaller polynomial and a remainder.

Luisa has 85 coupons.

Each toy can be traded for 10 coupons .

So number of toys that can be bought = 85 ÷ 10

This given 8 quotient and 5 remainder.

This deduced remainder is a magnitude of P(x) at x = a, more precisely P (a). When and only when P(a) = 0, x -a is thus a component of P(x). It is used to factor polynomials of any degree in a visually appealing manner.

Hence we calculate that Luisa can get 8 toys and 5 coupons will be left over.

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Answer:

75/25= 3 wholes

Step-by-step explanation:

Because 25*3=75 so it would be 3 wholes

To know the best deal, we have to know which one gives us the least cost per gallon.

To do that we divide the price by the quantity or volume.

A) $56 for 25 gallons

B) $32.05 for 15 gallons

C) $51.29 for 23 gallons

D) $22.50 for 10 gallons

The best deal is B: $32.05 for 15 gallons, because it offers a price per gallon that is lower than the others.

Answer:

8x^12 y^3

Step-by-step explanation:

8x^12 y^3

Answer:

y = 1

x = 3

Step-by-step explanation:

y = 7 - 2x

x - 2y = 1

5x - 14 = 1

y = 7 - 2x

x = 3

y = 7 - 2x

y = 1

Answer: - 1/3

Step-by-step explanation:

To solve this algebraic expression, you will need to evaluate the equation like this:

13(9x + 3) = 3x + 1

117x + 39 =  3x + 1

117x + 39 - 39 =  3x + 1 - 39

117x = 3x - 38

117x - 3x = 3x - 38 - 3x

114x = -38

 x =  - 1/3

Therefore, the solution to this equation is -1/3. Hope this helps!

Answer:

y = 1/2x + 7/6

Step-by-step explanation:

Answer:

The answer is b

Step-by-step explanation:

The distance traveled by the passenger train and the cattle train is equal to the total distance between them, which is 960 miles. Let x be the time (in hours) traveled by the passenger train and cattle train. Then, the equation that represents this situation is:

55x + 65x = 960

Simplifying the left-hand side of the equation, we get:

120x = 960

Dividing both sides by 120, we get:

x = 8

Therefore, the correct equation is:

B - 65x - 55x = 960

The calculated value of x in the pentagon is 121

From the question, we have the following parameters that can be used in our computation:

The pentagon (see attachment)

The sum of angles in a pentagon is

Sum = 180 * (n - 2)

Where

n = 5

So, we have

Sum = 180 * (5 - 2)

Evaluate

Sum =  540

Algebraically, we have

x + 87 + 92 + 105 + 135 = 540

So, we have

x + 419 = 540

Subtract 419 from both sides

x = 121

Hence, the value of x is 121

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Answer:

42.35

Step-by-step explanation:

hope it helps po.

Answer:

The number is 140

Step-by-step explanation:

Let n be the unknown number

of means multiply, is means equals

55% * n = 77

Change to decimal form

.55n = 77

Divide by .55

.55n/.55 = 77/.55

n =140

The number is 140

Answer:

7.03, 6.75, 6.72, 6.08, 6.4

Step-by-step explanation:

The first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3. (Option C)

In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like ^n for a nonnegative integer n. For a binomial series, the formula for the expansion of any terms is given by

(1+x)^m=1+mx+  m(m-1)/2! x^2+  m(m-1)(m-2)/3! x^3+⋯.

For the given function (1+ x/4)^(-2)

m = -2

x = x/4

Hence, using the above expansion formula

The first term = 1

The second term = mx = (-2)(x/4) = -x/2

The third term =m(m-1)/2! (x/4)^2=  (-2(-2-1))/(2*1*16) x^2=3/16 x^2

The fourth term = m(m-1)(m-2)/3! (x/4)^3=(-2(-2-1)(-2-2))/(3*2*1*64) x^3=-1/16 x^3

Hence, the first four terms of the binomial series are 1-  1/2 x+  3/16 x^2-  1/16 x^3.

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The amount needed to purchase materials needed to cover the area of the triangular flag is: $54.

Area of a triangle = 1/2(bh)

Given the dimensions of the flag as the following:

base (b) = 18 in.

height (h) = √(41² - 9²) = 40 in.

Area of the flag = 1/2(18)(40) = 360 in.²

Cost of material needed = (360)(0.15) = $54

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Answer:

360 and $54

Step-by-step explanation:

The value of the integral ∫\(e^{cos(t)\) sin(2t) dt over the interval [0, π] is 0.

The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.

To evaluate the integral ∫\(e^{cos(t) sin(2t)} dt\) over the interval [0, π], we can use integration by parts with the substitution u = sin(t) and dv = \(e^{cos(t)cos(t)}dt\). Then, du = cos(t)dt and \(v = e^{cos(t)\).

Using this substitution and the formula for integration by parts:

∫\(e^{cos(t) sin(2t)} dt\) = \(-e^{cos(t) sin(t)}\) + ∫\(e^{cos(t) cos(t)} dt\)

We can use another substitution, z = cos(t), to simplify the integral on the right-hand side:

∫\(e^{cos(t) cos(t)} dt = \int e^{z} dz = e^z + C\)

Substituting back to the original integral, we get:

∫\(e^{cos(t) sin(2t)} dt = -e^{cos(t) sin(t)} + e^{cos(t)} + C\)

Evaluating the definite integral over the interval [0, π], we get:

∫[0,π] \(e^{cos(t) sin(2t)} dt = -e^{cos(\pi ) sin(\pi )} + e^{cos(\pi )} - (-e^{cos(0) sin(0)} + e^{cos(0)})\)

Simplifying the trigonometric terms sin(π) = 0 and sin(0) = 0, and using the fact that cos(π) = -1 and cos(0) = 1, we get:

∫[0,π] \(e^{cos(t)\) sin(2t) dt = \(-e^{-1} + e^{-1} = 0\)

Therefore, the value of the integral ∫\(e^{cos(t)\) sin(2t) dt over the interval [0, π] is 0.

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Incomplete question. I inferred you want to know the properties of parallel and perpendicular lines. Which I provided below.

Explanation:

In geometry, parallel lines are two lines that are always drawn at the same distance apart and never touch each other. Parallel lines are usually denoted by the symbol ∥.

Here are some of their properties;

When a transversal intersects two parallel lines:

Perpendicular lines are two lines that meet at a right angle (90 degrees) to each other.

Properties: two lines that meet, implies all four angles are right angles.

(i) The dual of the given LP problem can be found by following these steps:

1. For each constraint in the primal problem, create a dual variable. In this case, we have three constraints, so we'll have three dual variables: y1, y2, and y3.
2. The objective function of the dual problem will be the sum of the products of the primal variables and their corresponding dual variables. So, the dual objective function is:
  Maximize w = 3y1 + 2y2 + y3.
3. For each primal variable x, create a constraint in the dual problem with the coefficient of the corresponding dual variable equal to the coefficient of x in the primal objective function. So, the dual constraints are:
  y1 + 2y2 - y3 ≤ -2
  y1 + y2 + y3 ≤ -1
  y1, y2, y3 ≥ 0.

(ii) To find the optimal solution to the dual problem, we need to solve the optimal tableau of the dual problem. From the given information, we know that Row 0 of the optimal tableau is:
  w = 4x1 + e2 + (M-1)a2 + (M+2)a3 = 0.
 
  However, the given information does not provide any details about the values of x1, e2, a2, or a3. Therefore, without this information, we cannot determine the specific optimal solution to the dual problem.

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the equation of the parabola will be y=3/4 (x²-1).

What is parabola ?

A parabola is a curve whose equation places a point on it at a same distance from both a fixed point and a fixed line. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. The fixed point does not lie on the fixed line, which is another crucial factor to remember. A parabola is a locus of any point that is equally distant from both the focus and directrix of two supplied points. The point where a parabola makes its sharpest turn is known as the vertex. If a parabolic function has the shape of a "," it has a maximum value; otherwise, it has a minimum value.

A parabola has a vertex at (0, -1)  

passes through point (2, 2). Which of the following is the equation of

this parabola in the form y = a(x-h)² +k.

The equation will be (2,2)

x=2, y=2

2=a(2²)-1

2=a(4)-1

3=a(4)

a = 3/4

the equation is

y=3/4 (x²-1)

Hence the equation of the parabola will be y=3/4 (x²-1).

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