how many different makes and models of commercial aircraft are currently in service by the world's airlines

The probability of selecting a white marble from the box is 0.5 or 50%.

We have,

To calculate the probability of selecting a white marble from the box, we need to determine the total number of marbles and the number of white marbles in the box.

In this case, the box contains a total of 2 black marbles, 4 red marbles, and 6 white marbles.

The probability of selecting a white marble can be calculated as:

Probability of selecting a white marble = (Number of white marbles) / (Total number of marbles)

Probability of selecting a white marble = 6 / (2 + 4 + 6)

Probability of selecting a white marble = 6 / 12

Probability of selecting a white marble = 0.5

Therefore,

The probability of selecting a white marble from the box is 0.5 or 50%.

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The proof for the given condition S ≤ T is justified using the product rule of differentiation.

The given function is given by f(x) = A sin(x) + B cos(2x).

Let us first find the derivative of this function.

Using product rule, we getf′(x) = A cos(x) – 2B sin(2x)

Now, let us calculate the second derivative of the function

f′′(x) = -A sin(x) – 4B cos(2x)

Now, we need to check if the function is concave or convex over the interval [0, π/2].

In order to do that, we will check the sign of the second derivative on this interval. We note that A is non-zero.

Hence, if we multiply the second derivative by A, we get

-A² sin(x) – 4AB cos(2x).

We observe that cos(2x) is greater than or equal to -1 for all real values of x.

Hence, -4AB cos(2x) is less than or equal to 4AB.

This implies that -A² sin(x) – 4AB cos(2x) is less than or equal to -A² sin(x) + 4AB.

Now, we need to find the maximum value of this expression for x between 0 and π/2.

Let us differentiate this expression w.r.t. x.

A² cos(x) + 8AB sin(x) = 0sin(x)/cos(x)

= -A²/8AB

= -A/8Btan(x)

= -A/8B or

x = -arctan(8B/A)

Let x = -arctan(8B/A).

Then sin(x) = -A/√(A² + 64B²) and cos(x) = 8B/√(A² + 64B²).

Putting these values in the expression, we get

Maximum value of the expression = √((A² + 64B²)/(A²))

= √(1 + (64B²)/(A²))

Hence, we have that for any function f in F,

f(x) ≤ f(a) + f′(a)(x-a) + (√(1 + (64B²)/(A²)) / 2)

f′′(a)(x-a)² for x between 0 and π/2.  

The equation  √√√((a) - arctan (2))³²dr ≤√√√ (f(a) — arctan(a))³d.r can be expressed as ∫ √(a - arctan2(x)) dx ≤ ∫ √(f(a) - arctan(a)) dx  over the interval (0, π/2).

Now, we just need to evaluate the integrals on both sides. We can do this numerically. We will use the trapezoidal rule for this. We will divide the interval into n subintervals of equal length.

Let xi be the point where the ith subinterval starts and let f(xi) be the value of the function at that point.

Then, the integral can be approximated by

∫ √(a - arctan2(x)) dx ≈ (π/(2n))(√(a - arctan2(0)) + 2

∑i=1n-1 √(a - arctan2(xi)) + √(a - arctan2(π/2)))

Similarly,

∫ √(f(a) - arctan(a)) dx ≈ (π/(2n))(√(f(a) - arctan(a)) + 2

∑i=1n-1 √(f(a) - arctan(a)) + √(f(a) - arctan(a)))

Let S = √√√((a) - arctan (2))³²dr and T = √√√ (f(a) — arctan(a))³d.r.

Then, we just need to show that S ≤ T. This can be done by choosing appropriate values of A and B.

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The slope of the line is the ratio of the rise to the run, or rise divided by the run. Yes i can agree with both of their statements.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

As we know that the slope of a line will be always same on a given line. If slope triangle A has slope 6/4. Then triangle B will be also have the same slope.

As both triangles are connected to the same line. These two triangles A and B  will have same slopes.

Mai uses Triangle A and says the slope of this line is 6/4.

If we convert fraction 6/4 to decimal we get 1.5 value.

So i agree with both of their statements.

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Answer:

5/7 this is the answer. I hope it is helpful

Answer:

Step-by-step explanation:

2/3+3/4=8/12+9/12=17/12

The time taken by the Cadesia to cover 12 laps is 30 minutes.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Cadesia swims 2 laps every 5 minutes. If she continues to swim at a constant rate.

The time taken by the Cadesia will be calculated as,

2 laps = 5 minutes

1 lap = 5 / 2 minutes

12 lap = (5 x 12 ) / 2

12 lap = 30 minutes

Therefore, the time taken by the Cadesia to cover 12 laps is 30 minutes.

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Answer:

2 2/3 kg

Step-by-step explanation:

Total tomatoes picked = 4 kg

Tomatoes thrown out = 1 1/3 kg into

How much kg of good tomatoes did he keep?

Total tomatoes remaining = Total tomatoes picked - Tomatoes thrown out

= 4 kg - 1 1/3kg

= 4 - 4/3

= (12-4)/3

= 8 /3

= 2 2/3 kg

He kept 2 2/3 kg of good tomatoes

The missing terms of the geometric sequence 1, 4 are 4 and 16.

To find the missing terms of a geometric sequence, we need to determine the common ratio. In this case, the common ratio can be found by dividing any term by its previous term. Let's calculate it:

4 ÷ 1 = 4

So, the common ratio is 4.

Now, we can find the missing terms.

To find the second term, we multiply the first term by the common ratio:

1 × 4 = 4

Therefore, the missing second term is 4.

To find the third term, we multiply the second term by the common ratio:

4 × 4 = 16

Therefore, the missing third term is 16.

In conclusion, the missing terms of the geometric sequence 1, 4 are 4 and 16.

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53,38

Step-by-step explanation:

x = √15² + 8²

x = √225 + 64

x = √289

x = 17

circle's circumference = π × d

3,14 × 17 = 53,38

Answer:

The constant value (often written k) relating amounts that rise or fall uniformly together.

It is the ratio of the amounts y and x:

k = y/x

Put another way: y = kx

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

tan A = 6/7.5 = 0.8

m < A = 38.7 degrees.

Answer:

320 sq in

Step-by-step explanation:

SA(rect prism) = 2(lw)+2(wh)+2(lh)

= 2(12·7)+2(7·4)+2(12·4)

= 2(84)+2(28)+2(48)

= 168+56+96

= 320

A Pythagorean triple consists of 3 integer numbers, say, a,b and c, such that

From the given information, we can see that

So, if these 3 numbers are a Pythagorean triple, then the following equality must be fulfilled:

which gives

so we have obtained that

which is an absurd result. This means that the given numbers do not form a Pythagorean triple

Part 1.

Since we have the equation

the equations which can be used to approximate the solutions are:

Part 2.

Let's make the graph of the 2 equations. The graph is

The approximate solution is given by the intersection point of the 2 graphs, which is the point ( 0.957 , 1.425). Then x-value corresponding to the solution is x= 0.957.

Answer:

B. 10x-13

Step-by-step explanation:

hope it helps!

\(-3(6x+7)+4(7x+2)\\\\=-18x - 21 + 28x +8\\\\=10x-13\)

(a) ∑n=1[infinity]8n7n is a geometric series and it diverges. Answer: DIV.

(b) ∑n=2[infinity]13n is a geometric series and it diverges. Answer: DIV.

(c) ∑n=0[infinity]3n92n+1 is a geometric series and it converges. Sum = 2.452.

(d) ∑n=5[infinity]7n8n is a geometric series and it converges. Sum = 0.0954.

(e) ∑n=1[infinity]7n7n+4 is a geometric series and it converges. Sum = 3.5

(f) ∑n=1[infinity] 7/8*\((7/8)^{(n-1)\) + \(3/8*(3/8)^{(n-1)\). Both of these are geometric series and the series converges. Sum= 1.6.

(a) This series can be rewritten as ∑n=1[infinity]\((8/7)^n\). This is a geometric series with ratio r=8/7 which is greater than 1. Hence, the series diverges. Answer: DIV.

(b) This is a geometric series with first term a=13 and common ratio r=13. Since |r|>1, the series diverges. Answer: DIV.

(c) This series can be written as ∑n=0[infinity] \(3^n/(9^2)^n\) * \(9^{(1/(2n+1))\). The first part of the series is a geometric series with a=1 and r=3/81<1. The second part of the series is also a geometric series with a=\(9^{(1/3)\) and r=\((9^{(1/3)})^2=9^{(2/3)\)<1. Therefore, the series converges. To find the sum, we use the formula for the sum of an infinite geometric series:

sum = a/(1-r) + b/(1-c)

where a and r are the first term and common ratio of the first geometric series, and b and c are the first term and common ratio of the second geometric series. Substituting the values, we get:

sum = 1/(1-3/81) + \(9^{(1/3)}/(1-9^{(2/3))\)

= 1.01 + 1.442

= 2.452

Answer: 2.452.

(d) This series can be written as ∑n=5[infinity] \((7/8)^n\). This is a geometric series with ratio r=7/8 which is less than 1. Hence, the series converges. To find the sum, we use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a and r are the first term and common ratio of the series. Substituting the values, we get:

sum = \((7/8)^5/(1-7/8)\)

= \(7/8^4\)

= 0.0954

Answer: 0.0954.

(e) This series can be rewritten as ∑n=1[infinity] \((7/7.4)^n\). This is a geometric series with ratio r=7/7.4<1. Hence, the series converges. To find the sum, we use the formula for the sum of an infinite geometric series:

sum = a/(1-r)

where a and r are the first term and common ratio of the series. Substituting the values, we get:

sum = 1/(1-7/7.4)

= 3.5

Answer: 3.5.

(f) This series can be rewritten as ∑n=1[infinity] \(7/8*(7/8)^{(n-1)\) + \(3/8*(3/8)^{(n-1)\). Both of these are geometric series with ratios less than 1, so the series converges. To find the sum, we add the sums of the two geometric series:

sum = 7/8/(1-7/8) + 3/8/(1-3/8)

= 1 + 3/5

= 1.6

Answer: 1.6.

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Answer:

X = 2

Have a safe and happy holiday :)

Answer:

2

Step-by-step explanation:

8=  7x  -6

+6         +6

14= 7x    0

7 divided by 7= 1

14 divided by 7= 2

Answer= X=2

Hope this helped! :))

MERRY CHRISTMAS!!

PEACE AND LOVE!

The work done by the force field F on the particle moving along the helix \(r(t) = 6 cos(t)i + 6 sin(t)j + 5tk\), \(0 \leq t \leq 2\pi\), is \(27\pi\).

The work done by the force field F on a particle moving along a curve C is given by the line integral:

\(W = \int\limit_C {F} \, dr\)

where \(dr\) is the differential displacement vector along the curve C.

In this problem, the force field \(F(x, y, z) = 3xi + 3yj + 6k\) and the curve C is given by \(r(t) = 6 cos(t)i + 6 sin(t)j + 5tk\), \(0 \leq t \leq 2\pi\).

To evaluate the line integral, we need to express the force field and the curve in terms of t:

\(F(x(t), y(t), z(t)) = 3x(t)i + 3y(t)j + 6k\)

\(= 3(6 cos(t))i + 3(6 sin(t))j + 6k\)

\(= 18 cos(t)i + 18 sin(t)j + 6k\)

\(r'(t) = (-6 sin(t))i + (6 cos(t))j + 5k\)

\(dr = r'(t) dt = (-6 sin(t))i + (6 cos(t))j + 5k dt\)

Substituting these expressions into the line integral, we get:

\(W = \int\limit_C {F} \, dr\)

\(= \int\limits^{(2\pi )}_0 {(18 cos(t)i + 18 sin(t)j + 6k) (-6 sin(t))i + (6 cos(t))j + 5k )} \, dt\)

\(= \int\limits^{2\pi }_0 {(-108 cos(t)sin(t) + 54 cos(t)sin(t) + 30)} \, dt\)

\(= \int\limits^{2\pi }_0 {(-54 cos(t)sin(t) + 30)} \, dt\)

We can use the trigonometric identity \(sin(2t) = 2sin(t)cos(t)\) to rewrite the integrand:

\(-54 cos(t)sin(t) + 30 = -27 sin(2t) + 30\)

Substituting this back into the integral, we get:

\(W = \int\limits^{2\pi} _0 {(-27 sin(2t) + 30)} \, dt\)

\(= [-13.5 cos(2t) + 30t]_{0}^{2\pi }\)

\(= (-13.5 cos(4\pi ) + 30(2\pi )) - (-13.5 cos(0) + 30(0))\)

\(= 27\pi\)

Therefore, the work done by the force field F on the particle moving along the helix \(r(t) = 6 cos(t)i + 6 sin(t)j + 5tk\), \(0 \leq t \leq 2\pi\), is \(27\pi\).

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Answer:

M2=65

Step-by-step explanation:

These two are congruent

congruent means- they are the same

so M1 is congruent to M2 and M3.....

Answer:

<m2 = 65°

Step-by-step explanation:

<m1 = <m2 (corresponding angles)

65° = <m2

a. What can you use to find the height of the pole?

solution: We can use Pythagoras theorem to find the height of the pole.

b. Write and solve a quadratic equation to find the height of the pole.

solution:

a² + b² = c²

\(\sf (x)^2 + (x-3)^2 = 15^2\)

\(\sf x^2 + x^2 - 6x + 9 = 15^2\)

\(\sf 2x^2 -6x + 9 = 225\)

\(\sf 2x^2 -6x -216=0\)

\(\sf 2x^2 -24x +18x -216 = 0\)

\(\sf 2x(x-12)+18(x-12) = 0\)

\(\sf (2x + 18)(x-12) = 0\)

\(\sf x = 12, -9\)

\(\sf x = 12\)

height of the pole: 12 ft

c. How far is the hook from the base of the pole?

solution: (x-3) → (12-3) → 9

Answer: 3

Step-by-step explanation:

I think…

Answer:

B

Step-by-step explanation

add all numbers then divide by the number of numbers and you get the means

Answer:

B

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

An integers are whole numbers and  their opposites.  ...-3,-2,-2,0,1,2,3...

I just played with the numbers and found that 14 + 14^2 (14 squared is 14 x 14).

14 + (14)(14) = 210

Answer:

refer to the attachment

Answer:

Step-by-step explanation:

If you simplify the second solution, you'll see it's equal to the first:

y=3x

2y=6x ; 2y/2 = 6x/2 ; y=3x

Knowing this, there are infinite solutions for this.

Answer:

Infinite solution

Step-by-step explanation: Simplify 2y=6x

This will equal y=3x, which is the same as y=3x.

It's the same line.

Inverse Linear= 1 solution

Parallel= No solution

Same Line= Infinite Solution

Just pick a point on the line and plug it in to see if it's a match.

For instance, (1,3) is a point on the line. Another point is (-1,-3).

3=3(1)

2(3)=6(1)

Answer:

Only child = 12 students

Step-by-step explanation:

Given information,

→ Total students = 32

→ Having siblings = 5/8

Fraction of only child,

→ 1 - (5/8)

→ (8 - 5)/8

→ 3/8

Now we have to,

→ Find number of only child.

Let's solve the problem,

→ 32 × (3/8)

→ (32 × 3)/8

→ 96/8

→ 12 students

Hence, the answer is 12.

The expected operational time of the machine is 6.75

For given x , y > 0 , the lifetime of the machine is max{x , y} because it stops when the two component will fail.

The life expectancy if therefore the expectancy of max{x, y}

t = E [ max{x,y} ]

So, the max{x , y} can be x or y

We have three integral

I₁ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} y \. dy\)

Solving the integration

=> I₁ =  729 / 162

=> 4.5

I₂ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{x}_{0} y \. dy\)

=> I₂ = 121.5/162

=> 0.75

=> I₃ = \(\frac{1}{162}\int\limits^9_0 \, dx \int\limits^{18-x}_{x} x \. dy\)

=> I₃ = 243 / 162

=>  1.5

So . the total is 4.5 + 0.75 + 1.5

=>  6.75 is expected operational time

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Answer:

How do you write out 8x in words? Um...eight times, I think.

Step-by-step explanation:

Answer:

Step-by-step explanation:

eight x

or eight times

(depends if it is a variable or multiplication sign)

To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Answer:

A, C, D

Step-by-step explanation:

I took the test lol :)

(A) The amount of change is different for the percent increase and the percent decrease.

(C) The ratio for the percent increase has a smaller denominator than the percent decrease.

(D) The ratio for the percent increase has a different numerator than the percent decrease.

Therefore, the correct options are as follows -

(A) The amount of change is different for the percent increase and the percent decrease.

(C) The ratio for the percent increase has a smaller denominator than the percent decrease.

(D) The ratio for the percent increase has a different numerator than the percent decrease.

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Answer:

See below for explanation.

Step-by-step explanation:

Each (x, y) point on the unit circle is equal to (cos θ, sin θ).

To find cot θ, where θ is the angle corresponding to the point (x, y) on the unit circle, we can use the formula:

\(\boxed{\cot \theta=\dfrac{\cos \theta}{\sin \theta}=\dfrac{x}{y}}\)

\(\hrulefill\)

If cot θ = 0, then x must be zero. (If y was zero, the value would be undefined). Therefore, we need to find the points on the unit circle where the x-coordinate (cos θ) is zero.

The points on the unit circle where x = 0 are:

The corresponding angles (in radians) at these points are:

    \(\bullet \quad \dfrac{\pi}{2}\;\;\textsf{and}\;\;\dfrac{3\pi}{2}\)

Therefore, the cotangent has the value of zero at π/2 and 3π/2.

\(\hrulefill\)

If we divide a number by the same (but negative) number, we get -1.

Similarly, if we divide a negative number by the same (but positive) number, we get -1.

Therefore, if cot θ = -1, then the x-coordinate and y-coordinate of the points must be the same, but opposite signs.

The points on the unit circle where -x = y and x = -y are:

    \(\bullet \quad \left(-\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)\;\; \textsf{and}\;\;\left(\dfrac{\sqrt{2}}{2},-\dfrac{\sqrt{2}}{2}\right)\)

The corresponding angles (in radians) at these points are:

    \(\bullet \quad \dfrac{3\pi}{4}\;\;\textsf{and}\;\;\dfrac{7\pi}{4}\)

Therefore, the cotangent has the value of -1 at 3π/4 and 7π/4.