Let a[0 . . . n] be an array of n + 1 natural numbers not exceeding n. let k < n be an integer such that the values of any two successive entries of a differ at most by k, i.e., |a[j] − a[j + 1]| ≤ k for all j ∈ {0, . . . , n − 1}. 1. prove that there exist an index j such that |a[j] − j| ≤ (k + 1)/2. 2. given the number k, find an o(log n) divide and conquer algorithm that finds such an index.

Answer:

The required paint for a total of [tex]1.404\ ft^{2}[/tex] is approximate 6 gallons

Step-by-step explanation:

we know that

To find how much paint would I need to buy to paint the walls of all three bedrooms, calculate the area of all three bedrooms

Master Bedroom

The area is equal to

[tex]A1=(16+16+12+2+18)*9=576\ ft^{2}[/tex]

2 Bedroom

The area is equal to

[tex]A2=(12+14+10+10)*9=414\ ft^{2}[/tex]

3 Bedroom

The area is equal to

[tex]A3=(10+10+14+10+2)*9=414\ ft^{2}[/tex]

The total area is equal to

A=A1+A2+A3

[tex]A=576+414+414=1.404\ ft^{2}[/tex]

Approximate one gallon of paint covers 250 square feet

so

[tex]1.404/250=5.6\ gal[/tex]

Answer:

a = -8

b = -2

Step-by-step explanation:

We have been given the following radical expression;

[tex]\sqrt[3]{x^{10} }[/tex]

The radical can be expressed using the law of exponents;

[tex]\sqrt[n]{x}=x^{\frac{1}{n} }[/tex]

The radical can thus be re-written as;

[tex]\sqrt[3]{x^{10} }=(x^{10})^{\frac{1}{3} }[/tex]

Using the law of exponents;

[tex](a^{b})^{c}=a^{bc}[/tex]

The last expression becomes;

[tex](x^{10})^{\frac{1}{3} }=x^{\frac{10}{3} }=x^{3}*x^{\frac{1}{3} }\\\\=x^{3}\sqrt[3]{x}[/tex]

substituting x with -2 yields;

[tex]-2^{3}\sqrt[3]{-2}=-8\sqrt[3]{-2}[/tex]

Answer:

The correct answer option is D. 17/50.

Step-by-step explanation:

We are given that a jelly bean machine has 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans and 26 purple jelly beans.

We are to find the probability of getting a blue jelly bean chosen at random.

Total number of jelly beans = 16 + 34 + 24 + 26 = 100

Number of blue jelly beans = 34

P (getting a blue jelly bean) = 34/100 = 17/50

Answer:

by 5

Step-by-step explanation: because tgey wou;d nred help

Answer:

C.) If events A and B are DEPENDENT, then A's occurrence can affect the probability of B's occurrence. For example, when two cards are chosen from a deck without replacement, the possibilities change for the second card.

Answer:

The answer is confirmed 1.  Just took it.

Step-by-step explanation:

Answer:

Company 1 is greater.

Step-by-step explanation:

Given,

The function that shows the production cost of company 1,

[tex]f(x)=0.15x^2-6x+400[/tex]

Differentiating with respect to x,

We get,

[tex]f'(x)=0.30x-6[/tex]

Again differentiating,

[tex]f''(x)=0.30[/tex]

For minimum or maximum,

f'(x) = 0,

[tex]\implies 0.3x-6=0[/tex]

[tex]\implies x = 20[/tex]

Since, at x = 20, f''(x) = Positive,

So, f(x) is minimum at x = 20,

⇒ Minimum cost in company 1 is,

[tex]f(20)=0.15(20)^2-6(20)+400[/tex]

[tex]=340[/tex]

Also, by the given table,

The minimum cost of company 2 is at x = 70,

g(70) = 55,

Since, 340 > 55,

Hence, Based on the given information, the minimum production cost for company 1 is greater.

Answer:

D

Step-by-step explanation:

[tex]\frac{5x}{20} =\frac{45}{36}[/tex]

Cross multiply:

(5x)(36)=(20)(45)

180x = 900

divide by 180.

x=5

The value of x is 5.

Δ ACE ≅ Δ BCD    (by AAA property)

Therefore

[tex]\frac{CD}{CE} = \frac{CB}{CA}[/tex]         ( Similar triangle property)

[tex]\frac{20}{36} = \frac{5x}{45}[/tex]

5x = [tex]\frac{20 * 45}{36}[/tex]

5x = 25

x = 5

Therefore, option D. 5 is the correct answer

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C. shifted 4 units left and 3 units up

If you compare the graphs (ABCD=Blue; A’B’C’D’=Red), you see that ABCD was moved left 4 and up 3 to become A’B’C’D’.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is A.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

To know the steps that were applied to ABCD to obtain A'B'C'D, we need to observe the coordinates of any one point of the polygon given.

Now, if we look at the coordinates of the points D and D', then it can be observed that point D is shifted 3 units left and 3 units up to form A'B'C'D.

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Answer:

B

Step-by-step explanation:

If a sinusoidal function is given in the form y = B Sin x or y = B Cos x, then,

B is called the amplitude of the function. It will define minimum and maximum.

The minimum & maximum of this form of a cos function is B and -B.

The function given is y = 7 Cos x, so the Maximum is 7 and Minimum is -7

Correct answer is B.

Answer:

P = 1/2 = 0.5

Step-by-step explanation:

Total amount of cans = 100

Cans of cola = 34

Cans of orange soda = 50

Cans of ginger ale = 12

Cans of root beer = 4

Probability of selecting

- a can of cola = 34/100 = 0.34

- a can of orange soda = 50/100 = 0.5

- a can of ginger ale = 12/100 = 0.12

- a can of root beer = 4/100 = 0.04

Since we are asked the probability that the can selected is a root beer​, cola, or ginger ale, we need to add together the probabilities of each.

P = 0.04 + 0.34 + 0.12 = 0.5 = 1/2

Answer:

V=2197

Step-by-step explanation:

Equation for volume of a cube:

V= side length cubed

V=(13)(13)(13)

V=2197

Answer:

V = 2,197 ft3

Step-by-step explanation:

Your welcome ;)

For this case we have to:

[tex]cos (F) = \frac {h} {27}[/tex]

That is, the cosine of the angle F, will be equal to the adjacent leg on the hypotenuse.

So, by clearing h we have:

[tex]h = 27 * cos (54)\\h = 27 * 0.58778525\\h = 15.87020175[/tex]

Rounding out the value of h we have:

[tex]h = 15.9[/tex]

Answer:

Option B

Answer:

The correct answer is option b.   15.9

Step-by-step explanation:

Points to remember:-

Trigonometric ratio

Cos θ = adjacent side/Hypotenuse

From the figure we can see a right triangle triangle FGH.

To find the value of h

It is given that, g=27 and F=54°

Cos F =  adjacent side/Hypotenuse

Cos 54 =  adjacent side/Hypotenuse

     = FG/FH = h/g

h = g * Cos F = 27 * Cos 54 = 27 * 0.5878 = 15.87 ≈ 15.9

Therefore the correct answer is option b.  15.9

The depth of the lake is 1.4 kilometers after converting the result to kilometers.

To find the depth of the lake in kilometers when it is 100 centimeters less than 1401 meters, first convert the depth difference to meters.

Since 100 centimeters is equivalent to 1 meter, the actual depth of the lake in meters is 1400 meters (which is 1401 meters - 1 meter).

To convert this depth into kilometers, we divide by 1000, since there are 1000 meters in one kilometer.

Hence, the depth is 1.4 kilometers.

Answer:

[tex]\dfrac{11}{30}[/tex]

Step-by-step explanation:

Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.

The probability to select red marble is [tex]\dfrac{3}{5}=0.6.[/tex]

Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.

The probability to select red marble is [tex]\dfrac{3}{10}=0.3.[/tex]

Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.

The probability to select red marble is [tex]\dfrac{1}{5}=0.2.[/tex]

The probability to choose each urn is the same and is equal to [tex]\frac{1}{3}.[/tex]

Thus, the probability that the marble is red is

[tex]\dfrac{1}{3}\cdot 0.6+\dfrac{1}{3}\cdot 0.3+\dfrac{1}{3}\cdot 0.2=\dfrac{1.1}{3}=\dfrac{11}{30}.[/tex]

Answer:

A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)

Step-by-step explanation:

Before the rotation:

A (-4, 4), B (6, 2), C (1, 1), D(-5, 3)

270° rotation clockwise is the same as 90° counterclockwise.  To do that transformation:

(x, y) → (-y, x)

Therefore, the coordinates of the rotated figure are:

A (-4, -4), B (-2, 6), C (-1, 1), D(-3, -5)

The coordinates of the image are:

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

This question is solved applying a 270° clockwise about the origin, which has the following rule:

[tex](x,y) = (-y,x)[/tex]

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

Coordinate A:

At the Figure, coordinate A is A(-4,4). Applying the rule:

[tex](-4,4) = (-4, -4)[/tex]

So the image of A is A'(-4,-4).

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

Coordinate B:

At the Figure, coordinate B is B(6,2). Applying the rule:

[tex](6,2) = (-2, 6)[/tex]

So the image of B is B'(-2,6).

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

Coordinate C:

At the Figure, coordinate C is C(1,1). Applying the rule:

[tex](1,1) = (-1, 1)[/tex]

So the image of C is C'(-1,1).

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

Coordinate D:

At the Figure, coordinate C is D(-5,3). Applying the rule:

[tex](-5,3) = (-3,-5)[/tex]

So the image of D is D'(-3,-5).

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ANSWER

B.) 72

EXPLANATION

Recall the expansion for the factorial notation:

[tex]n! = n \times (n - 1) \times (n - 2) \times ...3 \times 2 \times 1[/tex]

We want to simplify

[tex] \frac{9!}{7!} [/tex]

Let us expand the numerator up to 7! while maintaining the denominator.

[tex] \implies \: \frac{9 \times 8 \times 7!}{7!} [/tex]

When we cancel out the common factors,we obtain:

[tex]\implies \: \frac{9 \times 8 \times 1}{1} [/tex]

This simplifies to

[tex]\implies \: \frac{72}{1} = 72[/tex]

The correct answer is B.

C seem reasonable to me

Answer:

0 Kesha is already home 8+4 is 12 and it's 12 miles from the store to her house .-.

Step-by-step explanation:

Answer:

0 more miles.

Step-by-step explanation:

If 12 miles is the total distance from her house to the store the answer should be 0.  She should be at home because 8 miles on the bike + the 4 walked = 12 miles, which is how many she rode to the store in the first place.

Answer:

Tangent is positive in Quadrant III.

Step-by-step explanation:

All trigonometric functions are positive in QUADRANT I

The Sine function is positive in QUADRANT II

The Tangent function is positive in QUADRANT III

The Cosine function is positive IN QUADRANT IV

*ASTC JUST REMEMBER THAT :)*

There are four quadrants in a plane, and the true statement is (b) Tangent is positive in Quadrant III.

There are four quadrants in a coordinate plane, and they have the following properties

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

The above means that the true statement is (b) Tangent is positive in Quadrant III.

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Answer:

13.3 cm

Step-by-step explanation:

Apply the Pythagorean Theorem:

hyp² = (2nd longest side)² + (shortest side)².  Here the numbers are:

(24 cm)² = (20 cm)² + (shortest side)², or

576 - 400 = 176 = hyp²

Taking the square root of both sides, we get (shortest side) = 13.3 cm

Answer: the answer is 13.3

Answer:

The same number was not added to both sides.

Step-by-step explanation:

The same number was not added to both sides.

In line 2,  6 was added to the left side  and 78 was added to the right side.

The best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved as shown below.

t - 6 = 78

t - 6 + 6 = 78 + 6

t = 84

Now, if we compare it with the given equation, we can find that the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

Hence, the best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.

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Answer:

The coordinates of the solution that lies in quadrant IV are (2, -5)

Step-by-step explanation:

We have 2 equations, the first of an ellipse and the second of a circumference.

[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]

To solve the system solve the second equation for x and then substitute in the first equation

[tex]x^2+y^2+2y=19\\\\x^2 = 19 -y^2 -2y[/tex]

So Substituting in the first equation we have

[tex]x^2 = 19 -y^2 -2y\\\\2(19 -y^2 -2y)+y^2=33\\\\38 -2y^2-4y +y^2 = 33\\\\-y^2-4y+5=0\\\\y^2 +4y-5 = 0[/tex]

Now we must factor the quadratic expression.

We look for two numbers that multiply as a result -5 and add them as result 4.

These numbers are -1 and 5.

Then the factors are

[tex]y^2 +4y-5 = 0\\\\(y-1)(y+5) = 0[/tex]

Therefore the system solutions are:

[tex]y = 1[/tex]; [tex]y = -5[/tex]

In the 4th quadrant the values of x are positive and the values of y are negative.

So we take the negative value of y and substitute it into the system equation to find x

[tex]y=-5\\\\2x^2+(-5)^2=33\\\\2x^2 = 33-25\\\\2x^2 = 8\\\\x^2 = 4[/tex]

[tex]x = 2[/tex], and [tex]x= -2[/tex]

In the 4th quadrant the values of x are positive

So we take the positive value of x

the coordinates of the solution that lies in quadrant IV are (2, -5)

Check the picture below.

Answer:

Step-by-step explanation:

55

FED is 5/4 times bigger than CBA. So, 44×1.25 is 55. 40×1.25 is 50. The perimeter is 125

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \stackrel{\stackrel{\textit{ratio of the }}{\textit{sides}}}{\cfrac{3}{6}}= \stackrel{\stackrel{\textit{ratio of the }}{\textit{volumes}}}{\cfrac{\sqrt[3]{V}}{\sqrt[3]{V}}}\implies \cfrac{3}{6}=\sqrt[3]{\cfrac{1000}{V}}\implies \left( \cfrac{3}{6} \right)^3=\cfrac{1000}{V} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{1000}{V}\implies \cfrac{1^3}{2^3}=\cfrac{1000}{V}\implies \cfrac{1}{8}=\cfrac{1000}{V}\implies V=8000[/tex]

Answer:

C2 + a2 +2 = b

Would be the new formula

Answer:

the correct answer is:

a =  √ c^2 − b^2

Step-by-step explanation:

a^2 + b^2 = c^2

Explanation:

a^2 + b^2 = c^2

a^2 = c^2 − b^2

a =  √ c^2 − b^2

Answer:

S =  264π m²

Step-by-step explanation:

Left cone

= π(6)(8)

= 48π m²

Central cylinder

= 2π(6)(14)

= 168π m²

Right cone

π(6)(8)

= 48π m²

Surface area = 48π + 168π + 48π = 264π m²

The surface area of the composite figure is 264π [tex]m^{2}[/tex]

r = 6m

h = 14m

l = 8m

The curved surface area of the cylinder = 2πrh

= 2*[tex]\pi[/tex]*6*14

=168π [tex]m^{2}[/tex]

The curved surface area of the cone = πrl

=π*6*8

=48π [tex]m^{2}[/tex]

The total surface area of the composite figure  

= CSA of cylinder + 2( CSA of cone )

= 168π + 2*48π

=168π + 96π

= 264π [tex]m^{2}[/tex]

Therefore, option S =  264π [tex]m^{2}[/tex]  is the correct answer

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Answer:

See below.

Step-by-step explanation:

4x + 3y = -24

We convert to slope/intercept form ( y = mx + b):

3y = - 4x - 24

Divide through by 3:

y = (-4/3)x - 8

Comparing this with y = mx + b:

we see that b ( the y-intercept) is -8.

To find the x -intercept solve (-4/3)x - 8 = 0

(-4/3)x = 8

Multiplying through by -3/4:

x = 8 * -3/4 = -6 = x-intercept.

To draw the graph  draw a line through the points (-6,0) and (0, -8).

Answer:

  -3/4 y-6

Step-by-step explanation:

False.

Replace x with -2 and simplify. 5(-2) + 3 = 13

Multiply. -10 + 3 = 13

Add. -7 = 13

This is not true, so -2 is not a solution, therefore the answer to the question is false.

ANSWER

Period: 2π , amplitude: 4

EXPLANATION

The graphed function is

[tex]y = 4\cos(x) [/tex]

The amplitude of this function is

[tex] |4| = 4[/tex]

The period is 2π because there is no phase shift hence the period is still equal to the parent function.

Period: 2π , amplitude: 4

Answer:

The correct option is 3.

Step-by-step explanation:

The general form of a cosine function is

[tex]f(x)=A\cos (Bx+C)+D[/tex]

where, A is amplitude, 2π/B is period, C is phase sift and D is midline.

[tex]A=midline=\frac{Maximum-Minimum}{2}[/tex]

[tex]A=midline=\frac{4-(-4)}{2}[/tex]

[tex]A=midline=4[/tex]

The amplitude of the function is 4.

The given graph complete a cycle in the interval [0,2π], therefore the period of the graph is 2π.

Therefore the correct option is 3.

Answer:

  the correct answers are marked in green below

Step-by-step explanation:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

  ║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Answer:

As with any right triangle, the length of the hypotenuse is equal to the root of the sum of the squares of the legs. That root is less than the sum of the leg lengths and greater than the longest leg (for non-zero leg lengths).

_____

Comment on the choices

The relationship is actually ...

 ║u+v║ ≤ ║u║ + ║v║

That makes the first selection possibly correct. It will only be correct if ║u║ or ║v║ is zero. The problem statement does not rule out that case.

Step-by-step explanation: