Express in simplest radical form.
V9

Answer:

Limit=0

Converges

Absolutely converges

Step-by-step explanation:

If [tex]a_n=\frac{2^n n!}{(3n+4)!}[/tex]

then [tex]a_{n+1}=\frac{2^{n+1} (n+1)!}{(3(n+1)+4)!}[/tex].

Let's rewrite [tex]a__{n+1}[/tex] a little.

I'm going to hone in on (3(n+1)+4)! for a bit.

Distribute: (3n+3+4)!

Combine like terms (3n+7)!

I know when I have to find the limit of that ratio I'm going to have to rewrite this a little more so I'm going to do that here. Notice the factor (3n+4)! in [tex]a_n[/tex]. Some of the factors of this factor will cancel with some if the factors of (3n+7)!

(3n+7)! can be rewritten as (3n+7)×(3n+6)×(3n+5)×(3n+4)!

Let's go ahead and put our ratio together.

[tex]a_{n+1}×\frac{1}{a_n}[/tex]

The second factor in this just means reciprocal of [tex]{a_n}[/tex].

Insert substitutions:

[tex]\frac{2^{n+1} (n+1)!}{(3(n+1)+4)!}×\frac{(3n+4)!}{2^nn!}[/tex]

Use the rewrite for (3(n+1)+4)!:

[tex]\frac{2^{n+1} (n+1)!}{(3n+7)(3n+6)(3n+5)(3n+4)!}×\frac{(3n+4)!}{2^nn!}[/tex]

Let's go ahead and cancel the (3n+4)!:

[tex]\frac{2^{n+1} (n+1)!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{2^nn!}[/tex]

Use 2^(n+1)=2^n × 2 with goal to cancel the 2^n factor on top and bottom:

[tex]\frac{2^{n}2(n+1)!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{2^nn!}[/tex]

[tex]\frac{2(n+1)!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{n!}[/tex]

Use (n+1)!=(n+1)×n! with goal to cancel the n! factor on top and bottom:

[tex]\frac{2(n+1)×n!}{(3n+7)(3n+6)(3n+5)}×\frac{1}{n!}[/tex]

[tex]\frac{2(n+1)}{(3n+7)(3n+6)(3n+5)}×\frac{1}{1}[/tex]

Now since n approaches infinity and the degree of top=1 and the degree of bottom is 3 and 1<3, the limit approaches 0.

This means it absolutely converges and therefore converges.

9514 1404 393

Answer:

  45

Step-by-step explanation:

Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...

  5(x +y) = (10y +x) -9

The other relationship between the digits is given as ...

  4y = 1/2(10x)

A graphing calculator shows the solution to these equations is (x, y) = (4, 5).

The two-digit number is 45.

__

Additional comment

You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:

From the coefficients of these equations, differences of cross products are formed:

Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:

(x, y) = (4, 5)   ⇒   the number is 45.

__

This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.

Answer:

Step-by-step explanation:

In parallelogram adjacent angles are supplementary

∠U +∠V = 180

9x + 15 + 6x + 15 = 180

Combine like terms

9x + 6x + 15 + 15 = 180

          15x + 30 = 180

Subtract 30 from both sides

          15x = 180 - 30

         15x = 150

Divide both sides by 15

            x = 150/15

x = 10

∠U = 9x + 15

      = 9*10 + 15

      = 90 + 15

∠U = 105

∠V = 6x + 15

     = 6*10 + 15

     = 60 + 15

∠V = 75

Answer:

Equation: [tex]2(9x + 15 + 6x + 15) = 360[/tex]

x = 10°

∠U = 105°

∠V = 75°

Step-by-step explanation:

Hello!

The sum of angles in a parallelogram is 360°. The opposite angles of a parallelogram are congruent.

The value of x is 10°.

To find the measures of each angle, simply plug in 10° for x in each equation.

Angle U is 105°.

Angle V is 75°.

Answer:  First Number Line

Step-by-step explanation:

9514 1404 393

Answer:

  x ≈ 9.3

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(50°) = 6/x

Solving for x gives ...

  x = 6/cos(50°) ≈ 9.3343

  x ≈ 9.3

__

There is no 'c' to find the value of.

Answer:

x ≈ 9.3

Step-by-step explanation:

Since , this is right triangle, we can use trigonometry functions;

cos θ = Adjacent side / Hypotenuse

Where, θ = 50°

Solve for x

cos 50° = 6 / x

Multiply both side by x

cos 50° × x = 6 / x × x

cos 50° × x = 6

divide cos50° by both sides

cos 50° / cos 50° × x = 6 / cos 50°

x = 6 / cos 50°

x ≈ 9.33434296

Nearest tenth :- x ≈ 9.3

Answer:

p = 28.56

Step-by-step explanation:

Circumference of circle

c = 2πr

Since this is a semicircle the perimeter is half the circumference

p = πr

p = 3.14 * 4

p = 12.56

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

Triangle

the outer perineter is just the two outer sides

p = 6 + 10

p = 16

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

total outer perimeter

p = 12.56 + 16

p = 28.56

Answer:

Step-by-step explanation:

The position equation is given as

[tex]s(t)=-16t^2+21t+3[/tex] and we are looking for the times when the position of the ball is 9 feet. That means that we simply plug in a 9 for s(t) and factor to solve for t:

[tex]9=-16t^2+2t+3[/tex] and

[tex]0=-16t^2+21t-6[/tex] and this is what we factor to find t:

t = .42 sec and then again on its way back down at t = .89 sec

Answer:

You have 500 marbles.

The longest side of the biggest equalateral triangle that you can make with your marbles is 31

Step-by-step explanation:

28 + 4 = 32

So our equation is:

TR(32) - 28

Now find Triangular Number 32: (32 *33)/2=528

528 - 28 = 500

So, we have 500 marbles

Now we need to find the longest side of the biggest equalateral triangle that you can make make with your marbles

Let's go back to 28 + 4 = 32

One row above 32 is 31

So the longest side of the biggest equalateral triangle that you can make with your marbles is 31

Hope this helps!

Problem 22

a)

The face cards are Jack, Queen, King. We have four copies of each.

There are 3*4 = 12 face cards total.

12/52 represents the probability of picking a face card.

4/52 represents the probability of picking an ace, since we have 4 aces out of 52 cards. We don't drop to 51 since we put the first card back.

Multiplying the fractions gives (12/52)*(4/52) = 48/2704 = 3/169

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

b)

We do the same steps as before, but the 4/52 will be changed to 4/51. This is because the first card is not put back.

(12/52)*(4/51) = 48/2652 = 4/221

========================================================

Problem 23

a)

4/52 represents the probability of picking a '2', and it also represents the probability of picking a '10' if we put the first card back

(4/52)*(4/52) = 16/2704 = 1/169

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

b)

We'll change the second instance of 4/52 into 4/51 because that first card isn't put back

(4/52)*(4/51) = 16/2652 = 4/663

========================================================

Problem 24

a)

4/52 = probability of picking an ace

12/52 = probability of picking a face card

4/52 = probability of picking '7'

Each denominator is 52 because we are putting the cards back

(4/52)*(12/52)*(4/52) = 192/140608 = 3/2197

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

b)

We do the same thing as before, but we decrease the denominator by 1 each time we pull out another card

(4/52)*(12/51)*(4/50) = 192/132600 = 8/5525

========================================================

Problem 25

a)

The probability of picking a king is 4/52. This is the same whether we're on the first king, second or third. This is because we're putting the card back.

(4/52)*(4/52)*(4/52) = 64/140608 = 1/2197

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

b)

Now that the cards aren't put back, we'll have the denominators drop by 1 each time (52,51,50)

So the probability is

(4/52)*(4/51)*(4/50) = 64/132600 = 8/16575

Answer:

A = -1

B = -3

Step-by-step explanation:

you need to do all the multiplication on both sides and then simply compare the factors of the various powers of x.

so,

-9x² - 9×A×x + 2 = 3×B×x² + 6x -Bx - 2 + 4

-9x² - 9×A×x + 2 = 3×B×x² + (6-B)x + 2

the x-less constants 2 = 2 are correct. now we need to compare the factors for the other parts of x.

we have left and right only one expression of x²

-9x² on the left

3×B×x² on the right

therefore,

-9 = 3×B

=> B = -3

otherwise the equation would not be correct for all values of x.

the only other parts remaining are

-9×A×x = (6-B)x = (6 - -3)x = (6+3)x = 9x

=>

-9×A = 9

-A = 1

A = -1

remember, all parts of the left and of the right side must be equal for the equation to be true in all cases.

Answer:

946

Step-by-step explanation:

Let :

Amy's stamp = 2437

Maria's stamps = 1347

Let Number of stamps Amy gave to Maria = x

After Giving stamps to Maria ; we have the equation :

Amy's stamps = 2437 - x

Maria's stamps = 1347 + x

(1347 + x) = 3(2437 - x)

1347 + x = 7311 - 3x

x + 3x = 7311 - 1347

4x = 5964

x = 5964 / 4

x = 1491

Number of stamps Amy has in the end :

2437 - 1491 = 946

Answer:

<3=75°

Step-by-step explanation:

Angle 3 and angle 2x+95 are supplementary( supplementary angles add up to 180°)

So <3+2x+95=180

<3+2x=180-95

<3+2x=85( let's call this equation 1)

Next, angle 5 and angle 8x+71 are opposite angles (opposite angles are equal) therefore <5=8x+71

Now, <3 and <5 are co-interior angles(co-interior angles are supplementary)

So <3+8x+71=180

<3+8x=180-71=109

Thus, <3+8x=109(let's call this equation 2)

Now solving equation 1 and 2 simultaneously:

Make <3 the subject of equation 1

<3=85-2x

Put <3=85-2x into equation 2

85-2x+8x=109

6x=24

x=24/6=4

Now, remember that angle 2x+95 becomes

2(4)+95

8+95=103°

Therefore<3=180-105=75°

Answer:

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Step-by-step explanation:

sorry di ko po alam godbless po

Answer:

1/6 = 6

1/7 = 7

1/8 = 8

24/5 = -1/5 or 5

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

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Answer:

4

Step-by-step explanation:

Answer:

Survey Data Collection.

Step-by-step explanation:

This is a survey because there are survey questionnaires (wellness exam).

Answer:

Observational Study Is the Answer

Step-by-step explanation:

everything can be found in the picture

As per the given angle values, the value of sin θ = √19 / 10, cot θ = 9 / √19 and csc θ = 10 / √19.

Let's begin by labeling the sides of the right-angled triangle. The hypotenuse is the side opposite the right angle and has a length of 10 units. The adjacent side, which is the side adjacent to the angle θ, has a length of 9 units.

Using these side lengths, we can apply the trigonometric definitions to find the required values:

Sine (sin θ):

The sine of an angle θ in a right-angled triangle is defined as the ratio of the length of the side opposite the angle (opposite side) to the length of the hypotenuse. The formula for sine is: sin θ = opposite / hypotenuse.

In our case, the opposite side is the side we want to find, and the hypotenuse is 10 units. Therefore, sin θ = opposite / 10.

Using the Pythagorean theorem:

opposite² + 9² = 10²

opposite² + 81 = 100

opposite² = 100 - 81

opposite² = 19

opposite = √19 (taking the positive square root as the length cannot be negative)

Now, we can calculate sin θ:

sin θ = √19 / 10

Cotangent (cot θ):

The cotangent of an angle θ in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the opposite side. The formula for cotangent is: cot θ = adjacent / opposite.

In our case, the adjacent side is 9 units, and we have already found the length of the opposite side, which is √19. Therefore, cot θ = 9 / √19.

Cosecant (csc θ):

The cosecant of an angle θ in a right-angled triangle is defined as the ratio of the length of the hypotenuse to the length of the opposite side. The formula for cosecant is: csc θ = hypotenuse / opposite.

Again, the hypotenuse is 10 units, and the opposite side is √19. Thus, csc θ = 10 / √19.

To know more about angle here

https://brainly.com/question/4316040

#SPJ2

Answer:

7

Step-by-step explanation

v:numero de mi dios  vegetta

Answer:

5/7

Step-by-step explanation:

6=7k+1

-1        -1

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

5= 7k

Divide both sides by 7k

k= 5/7

[tex]\huge\color{purple}\boxed{\colorbox{black}{k=0.714}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]➺ \: 6 = 7k + 1[/tex]

[tex]➺ \: 7k = 6 - 1[/tex]

[tex]➺ \: 7k = 5[/tex]

[tex]➺ \: k = \frac{5}{7}\\ [/tex]

[tex]➺ \: k = 0.714[/tex]

Therefore, the value of [tex]k[/tex] is [tex]0.714[/tex].

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]➺ \: 6 = 7k + 1[/tex]

[tex]➺ \: 6 = 7 \times 0.714 + 1[/tex]

[tex]➺ \: 6 = 5 + 1[/tex]

[tex]➺ \: 6 = 6[/tex]

➺ L. H S. = R. H. S.

Hence verified.

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

If we define W as the width:

12m  ≤ W  ≤  22m

Step-by-step explanation:

We have a rectangle with length L and width W.

We know that:

"The length of a rectangle should be 9 meters longer than 7 times the width"

Then:

L = 9m + 7*W

We also know that the length must be between 93 and 163 meters long, so:

93m ≤ L ≤ 163m

Now we want to find the restrictions for the width W.

We start with:

93m ≤ L ≤ 163m

Now we know that L = 9m + 7*W, then we can replace that in the above inequality:

93m ≤  9m + 7*W ≤ 163m

Now we need to isolate W.

First, we can subtract 9m in the 3 sides of the inequality

93m - 9m  ≤  9m + 7*W  -9m ≤ 163m -9m

84m ≤ 7*W ≤ 154m

Now we can divide by 7 in the 3 sides, so we get:

84m/7 ≤ 7*W/7 ≤ 154m/7

12m  ≤ W  ≤  22m

Then we can conclude that the width is between 12 and 22 meters long.

Answer:

25 gfstuhfujjjjjgredeetuu

By the fundamental theorem of calculus,

f(x) = f (0) + ∫₀ˣ f '(t) dt

We're given that the plot of f(x) passes through the point (0, -7), so f (0) = -7, and

f(x) = -7 + ∫₀ˣ (9t ² + 4t - 4) dt

f(x) = -7 + (3t ³ + 2t ² - 4t )|₀ˣ

f(x) = -7 + (3x ³ + 2x ² - 4x)

f(x) = 3x ³ + 2x ² - 4x - 7

Answer:

Incomplete question, but the concepts of the uniform distribution needed to solve this question are given here.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

The probability of finding a value between c and d is:

[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]

The probability of finding a value above x is:

[tex]P(X > x) = \frac{b - x}{b - a}[/tex]

The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between a and b minutes.

From here, we get the values of a(smallest value) and b(highest value).

Question of the probabilities:

In the two probability questions, you will get the value of x, and will apply one of the three formulas given above, depending on the question, to find the desired probability.

Answer:

Step-by-step explanation:

2x − y = 4

2x − 4 = y

y = 2x - 4

negative inverse of slope is perpendicular

y = -1/2 x - 4

~~~~~~~~~~~~~~~~~~~~~~~

point slope form  of a line

(-5, 1) & m = -1/2

1 = -1/2 (-5) + b

1 = 5/2 + b

b = -3/2

Final answer:  y = -1/2 x - 3/2

or if you prefer: 2y + x = -3

Step-by-step explanation:

3.

1.4191919... = 1405/990

4.

√(2/5) and √(1/2)

Answer:

- 3/4

Step-by-step explanation:

-2 1/2 - (-1 3/4)

Subtracting a negative is like adding

-2 1/2 + (1 3/4)

Get a common denominator of 4

-2 2/4 + 1 3/4

The signs are different so we subtract and take the sign of the larger

2 2/4 - 1  3/4

Borrowing from the 2

1 4/4 + 2/4 - 1 3/4

1 6/4 - 1 3/4

3/4

2 2/4 was larger and it was negative so we add a negative sign

- 3/4

Answer:

b) f(x) = x + 6

Step-by-step explanation:

The coordinate (0, 6) makes the y-intercept = 6. Only one of these functions has that intercept: f(x) = x + 6. If you plug in each coordinate the outputted y-value matches up, making this the right answer.