how many ways can six books be arranged on a shelf if one of the books is a dictionary and it must be on an end?

Answer:

1.17

Step-by-step explanation:

1 £ = 1.25 dollars

1 Euro = 1.07 dollars

=> 1 £ = (1.25/1.07) Euros = 1.17 Euros

Answer:

have you missed out any option cause i doeant match with any of your options

For the first equation you add 2 on both sides to get m < -6.

For the second you multiply by 8 on both sides to get m > 8

The answer is C.

Hope this helps

The following inequality of m - 2 < -8 or m/8 > 1 is m < -6 or m > 8.

Option C is the correct answer.

It is a statement of an ordered relationship

- greater than,

- greater than or equal to,

- less than,

- less than or equal to between two numbers or algebraic expressions.

We have,

m - 2 < -8 or m/8 > 1

Let's find m for each inequality.

m - 2 < -8

Adding 2 on both sides.

m - 2 + 2 < -8 + 2

m < -6 _____(1)

m/8 > 1

Multiply 8 on both sides.

8 x m/8 > 8 x 1

m > 8 _____(2)

From (1) and (2) we get,

m < -6 or m > 8

Thus,

The following inequality of m - 2 < -8 or m/8 > 1 is m < -6 or m > 8.

Option C is the correct answer.

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Answer:

18245

Step-by-step explanation:

We have to use L.C.M,

L.C.M(20,24,32,38)

2|20,24,32,38

2| 10 ,12 ,16 ,19

2| 5 , 6 , 8 , 19

2| 5 , 3 , 4 , 19

2| 5 , 3 , 2 , 19

L.C.M = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 3 x 19

          = 18240

Now for each case remainder is 5,

So the number is 18240+5

=> 18245

(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.

(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.

(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.

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Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

The value of the line integral ∫c (11y dx + 7x dy) is -4π. To evaluate the line integral ∫c (11y dx + 7x dy) using Green's theorem, we need to follow these steps:

1. Recognize that the given circle is x² + y² = 1, with a positive (counter-clockwise) orientation.

2. Green's theorem states that for a positively oriented, simple, closed curve C, ∫c (P dx + Q dy) = ∬D (Qx - Py) dA, where D is the region bounded by C, and P and Q are functions of x and y.

3. In our case, P = 11y and Q = 7x. So, we need to compute Py and Qx.
Py = ∂(11y)/∂y = 11, and Qx = ∂(7x)/∂x = 7.

4. Apply Green's theorem: ∫c (11y dx + 7x dy) = ∬D (7 - 11) dA = -4∬D dA.

5. Now, we need to find the area of the circle. The area of a circle is given by A = πr². Since the circle is x² + y² = 1, the radius r is 1. Thus, A = π(1)² = π.

6. The final step is to multiply the area by the constant factor from step 4: -4∬D dA = -4A = -4π.

So, the value of the line integral ∫c (11y dx + 7x dy) is -4π.

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1/5 is the slope and we can use (-4,0) as a starting point.

Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.

A number written as a superscript over another number is known as an exponent. In other words, it means that the base has been elevated to a particular level of power. Other names for the exponent are index and power. mn indicates that m has been multiplied by itself n times if m is a positive number and n is its exponent.

Given,

Adding and subtracting to multiplying and dividing bases with different exponents.​

Exponent rules for addition and subtraction are identical to one another. As a reminder, all terms' bases must be the same in order to remove terms with exponents. All terms' exponents must be equal.

The exponents and variables must match in order to add exponents. The exponents are left constant while the variable coefficients are added. The addition only includes terms with the same variables and powers. Exponents can be multiplied and divided according to this rule.

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Answer:

118

Step-by-step explanation:

inscribed angle = 1/2 intercepted arc, therefore an intercepted arc is twice its inscribed angle

\(59 \times 2 = 118\)

Answer:

SA = 10,800 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 40

w = 60

h = 30

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 60(40) + 30(40) + 30(60) )

SA = 2 ( 2400 + 1200 + 1800 )

SA = 2 ( 5400 )

SA = 10,800 ft²

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Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

C 3.5t + 15, where t is the number

of days

The  values of x will f(x) > 0 for x < 0, and f(x) < 0 for -6 < x < 0 and x > -6.

To determine the values of x for which f(x) > 0, we need to find the intervals where the function is positive. Let's analyze the function f(x) = x*-x³-6x².

First, let's factor out an x from the expression to simplify it: f(x) = x(-x² - 6x).

Now, we can observe that if x = 0, the entire expression becomes 0, so f(x) = 0.

Next, we analyze the signs of the factors:

1. For x < 0, both x and (-x² - 6x) are negative, resulting in a positive product. Hence, f(x) > 0 in this range.

2. For -6 < x < 0, x is negative, but (-x² - 6x) is positive, resulting in a negative product. Therefore, f(x) < 0 in this range.

3. For x > -6, both x and (-x² - 6x) are positive, resulting in a negative product. Thus, f(x) < 0 in this range.  

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Answer:

-10.50*3

=-31.5

The coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).

The picture M', whose coordinates are in the fourth quadrant and created when point M is mirrored in the x-axis, is (h, -k). As a result, we deduce that when a point is reflected along the x-axis, the x-coordinate stays constant while the y-coordinate changes to the negative.

As a result, M'(h, -k). is the image for point M (h, k)

Given data:

coordinates of the vertices before reflection:

B(1,7), D(1,6) and C(10, 7).

Reflection about x = 1.

As Point B and D lies on the line x = 1, their coordinates will  not change.

C is 9 units to the right of the line x = 1 at (10, 7)

Thus, after reflection C will be 9 units to the left of the line x = 1 at (-8, 7).

Therefore, the coordinates of the vertices B, D and C after a reflection over the line x = 1 are B'(1,7), D'(1,6) and C'(-8, 7).

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Answer:

negative 5 and 3/5

Step-by-step explanation:

-4-1&3/5

-5&3/5

negative 5 and 3/5(three fifths)

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Answer:

negative 5 and 3/5

Step-by-step explanation:

-4-1&3/5

-5&3/5

negative 5 and 3/5(three fifths)

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Step-by-step explanation:

Answer:

Currently, the RED team has a higher mean.

The difference between the means is HIGHER than the mean absolute deviation of either team.

There is SOME overlap between sales in the teams.

The number of hours they can play the video games before the weekend, then the inequality that represents the situation will be:

8 - t ≤ 4

An inequality is a mathematical statement that compares two quantities or expressions that are not equal using the inequality signs such as:

We are give that:

Total hours Dominique is allowed to play is 8 hours, this means 8 hours is the maximum number of hours he can play in a week.

Number of hours to be played during for the weekend is given as, at least 4 hours. This means, the number of hours to play at weekend can be 4 hours or more.

If t represents the number of hours they can play the video games before the weekend, then the inequality that represents the situation will be:

8 - t ≤ 4

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Answer:

x = 6

Step-by-step explanation:

Segment representing 2x - 1 is the mid segment of the given triangle.

Therefore, by mid segment theorem:

2(2x - 3) = 18

2x - 3 = 18/2

2x - 3 = 9

2x = 9 + 3

2x = 12

x = 12/2

x = 6

Answer:

x = 6

Step-by-step explanation:

D is the mid-point of AB (given)

E is the mid-point of AC (given)

Therefore, by mid-point theorem,

DE = 1/2 BC

=> 2x - 3 = 1/2 × 18

=> 2x - 3 = 9

=> 2x = 12

=> x = 6

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By using the concept of compact set, it can be proved that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

What is compact set?

A set K is said to be compact if every open cover of K has a finite subcover.

Let K⊆Rn is compact  f:K→R is continuous, and ϵ>0

Let there exist \(x_n, y_n\) ∈ K such that |f(\(x_n\))−f(\(y_n\))| > n∥\(x_n\)−\(y_n\)∥+ϵ,

Since K is compact there is a subsequence \(x_{nk}\) and \(y_{nk}\) of \(x_n, y_n\) respectively such that \(x_{nk}\) converges to x and \(y_{nk}\) converges to y.

So,  |f(\(x_{nk}\))−f(\(y_{nk}\))| > \(n_k\)∥\(x_{nk}\)−\(y_{nk}\)∥+ϵ,

Since f is continuous,

We can write

|f(x)−f(y)| > \(n_k\)∥x - y∥+ϵ,

This is true for infinite many \(n_k\)

So ||x - y|| = 0

|f(x) - f(y)| > ϵ, a contradiction since f is continuous

So,  there is a number A>0 such that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

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The reflected coordinates of triangle ABC across the x-axis are:

A'(2, -4), B'(9, -4), and C'(4, -7).

Coordinate the given triangle ABC as per the given figure is,

A(2, 4), B(9, 4), and C(4, 7)

When a triangle is reflected across the x-axis, the y-coordinates of its vertices are negated while the x-coordinates remain the same.

For the given triangle ABC:

A(2, 4), B(9, 4), and C(4, 7)

If we reflect the triangle across the x-axis, the new coordinates will be:

A'(2, -4)

B'(9, -4)

C'(4, -7)

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Answer:(6, -1)

Step-by-step explanation:

a. The expressions to show how much kite string Jordyn and Teri have, respectively, are 2x + y and x + y

b. The expression to show how much kite string Morgan has is 3x + y

c. The inequality representing is x > 3x + y.

d. The inequality representing  is 3x + y > 2x + y.

e. For the girls' kites to fly at the same height, the length of a roll of string (x) would need to be equal for both Jordyn and Teri and Morgan. Therefore, x = 2x + y = 3x + y.

a. Jordyn and Teri each have one roll of kite string, so their expressions would be 2x + y (representing Jordyn's string) and x + y (representing Teri's string). The variable x represents the number of yards of string on one roll, and y represents the yards of extra string they have.

b. Morgan has three rolls of kite string plus extra string. Hence, the expression representing the amount of kite string Morgan has is 3x + y, where x represents the number of yards of string on one roll, and y represents the yards of extra string she has.

c. To fly their kite higher than Morgan's, the combined string length of Jordyn and Teri (2x + y) should be greater than the string length of Morgan (3x + y). This can be represented as the inequality x > 3x + y.

d. For Morgan to fly her kite higher than Jordyn and Teri's, the string length she has (3x + y) should be greater than the combined string length of Jordyn and Teri (2x + y). This can be represented as the inequality 3x + y > 2x + y.

e. For the girls' kites to fly at the same height, the length of a roll of string (x) should be equal for both Jordyn and Teri and Morgan. This means that the expressions 2x + y and 3x + y should be equal. Therefore, x = 2x + y = 3x + y.

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Answer:

4 bowls

Step-by-step explanation:

Conversion rate :

1 liquid pint = 16 fluid ounces

From the question, we are told that :

4 fluid ounces of bubble mix = 1 bowl

16 fluid ounces of bubble mix(1 liquid pint) = y bowl

Cross Multiply

4 fluid ounces × y bowl = 16 fluid ounces × 1bowl

y bowl = 16 fluid ounces × 1bowl/4 fluid ounces

= 4 bowls

Therefore, he can fill 4 bowls with 1 pint of bubble mix

Answer:

AC ≈ 11.0 cm

Step-by-step explanation:

Using Pythagoras' identity in Δ CDE and Δ ADE

CE² + DE² = DC²

CE² + 7² = 8²

CE² + 49 = 64 ( subtract 49 from both sides )

CE² = 15 ( take the square root of both sides )

CE = \(\sqrt{15}\)

-------------------------------------------------------

AE² + DE² = DA²

AE² + 7² = 10²

AE² + 49 = 100 ( subtract 49 from both sides )

AE² = 51 ( take the square root of both sides )

AE = \(\sqrt{51}\)

Then

AC = AE + CE = \(\sqrt{15}\) + \(\sqrt{51}\) ≈ 11.0 cm ( to the nearest tenth )