Find a recurrence relation for the number of strictly increasing sequences of positive integers that have 1 as their first term and n as their last term, where n is a positive integer. that is, sequences a1, a2,...,ak, where a1 = 1, ak = n, and aj < aj+1 for j = 1, 2,...,k − 1.

b.what are the initial conditions?

c.how many sequences of the type described in (a) are there when n is an integer with n ≥ 2?

Answer:x=18

Step-by-step explanation:2x-9=x+9

The number generator is fair. it picked the approximate percentage of red most of the time.

Answer:

The number generator is fair, It picked the approximate percentage of red s*ckers most of the time.

Step-by-step explanation:

7*3+9*3+8*4 = 80

80 divided by 10 gives you an average of 8 red s*ckers each time which is exactly 80% of the amount of s*ckers picked

(s*ckers is banned for some reason)

Answer:

25%

Step-by-step explanation:

Assuming the catching of a fish is a random process and that the probability of catching any of the listed kinds of fish is proportional to their population, then the probability of catching a sturgeon is 50%. The probability of catching another one is also 50% (assuming the events are independent). So, the joint probability is the product of these:

0.50 × 0.50 = 0.25 = 25% . . . . . probability of catching 2 sturgeon in a row.

The probability of both fish being white sturgeon is 0.25.

To calculate the probability, we need to multiply the probabilities of catching a white sturgeon each time. Since 50% of the fish are white sturgeon, the probability of catching one is 0.5. Therefore, 0.5 multiplied by 0.5 equals 0.25.

im pretty sure it's the first option.

Answer:

#1) is right

Step-by-step explanation:

Answer:

sec Ф = 13/12

Step-by-step explanation:

If tan Ф = 5 / 12, we can find the third side of this triangle (that is, the hypotenuse) by applying the Pythagorean Theorem:  

hyp² = 5² + 12² = 169.  Thus, the hyp is 13.

Thus, cos Ф = adj / hyp = 12/13.

The secant function is the reciprocal of the cosine function, so

sec Ф = 13/12.

Answer:

[tex]\boxed{320}[/tex]

Step-by-step explanation:

    Let x = calories in chocolate bar

       ¼x = ¼ of the calories

¼x – 10 = 10 calories less than half the calories

¼x – 10 = 70

       ¼x = 80

          x = 320

There are [tex]\boxed{320}[/tex] calories in the chocolate bar.

Answer: d) 2.5

Step-by-step explanation:

The mean is 16 so it has a z-score is 0

The standard deviation is 4 so:

Notice that 26 is between the z-scores of 2 and 3 = 2.5

Algebraically: [tex]\dfrac{26-16}{4}=\dfrac{10}{4}=2.5[/tex]

Answer:

  D)  168 ft^3

Step-by-step explanation:

The volume of a cone is given by the formula ...

  V = (1/3)πr^2·h

Putting your numbers in, we have ...

  V = (1/3)π(4 ft)^2·(10 ft) = (160π/3) ft^3 ≈ 168 ft^3

The answer is d 168ft3

Explanation:

(1/3)*(4^2)*10*pi

[tex]\boxed{W=2ft}[/tex]

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. On the other hand, a rectangular prism is a solid whose base is a rectangle.  Multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

[tex]V=L\times W\times H[/tex]

From the statement of the problem we know:

[tex]V=24ft^3 \\ \\ H=3ft \\ \\ W=W \\ \\ L=W+2[/tex]

So:

[tex]24=(W+2)(W)(3) \\ \\ 3W(W+2)=24 \\ \\ 3W^2+6W-24=0 \\ \\ From \ the \ Quadratic \ Formula: \\ \\ W_{12}=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ W_{12}=\frac{-6 \pm \sqrt{6^2-4(3)(-24)}}{2(3)} \\ \\ W_{1}=2 \\ \\ W_{2}=-4[/tex]

Since we can't have negative distance, the only valid option is [tex]\boxed{W=2ft}[/tex]

the answer would be 3 I believe

1-7=

-6

4-(-2)=

6

-6/6=

-1

The slope is -1

Conditional probability means that an event happening only happened because another even had already occurred , Mean while independent probabilitty is like if two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring.

The addition is a Conditional probability.

The Addition Rule, used for calculating the probability of either event A or B occurring, applies to both independent and dependent events, requiring adjustment for overlapping probabilities.

The difference between independent and conditional probability is that independent events do not affect each other's occurrence, whereas conditional probability is the likelihood of one event given that another has occurred. The Addition Rule of probability is used with either independent or dependent events when you are calculating the probability of either event A or event B occurring (denoted as P(A OR B)). However, the rule requires an adjustment in the case of dependent events. The Addition Rule is P(A OR B) = P(A) + P(B) - P(A AND B). It is used to make sure that the probability of the intersection of A and B (which is counted in both P(A) and P(B)) is not counted twice.

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Answer:

1st prize

Step-by-step explanation:

Not all people use a car. Some people walk, take a bike, etc. So, if you won free gas for life, you might not be able to use it.

1st prize. To decide between $250,000 in cash or free gas for life, one must analyze projected gas consumption, inflation, and investment opportunities. The cash offers immediate value and investment potential, whereas the value of free gas depends on driving habits and future fuel prices.

The answer is:

The first option,

[tex]y=3.5[/tex]

To solve the problem, we need to follow the next steps:

- Set your calculator in degree mode to calculate Cos(64°)

- Isolate Y by multiplying each side of the equation by 8.

Solving we have:

[tex]Cos(64\°)=\frac{y}{8}\\\\0.44=\frac{y}{8}[/tex]

Multiplying each side of the equation by 8, we have:

[tex](0.44)*8=\frac{y}{8}*8\\3.52=y[/tex]

[tex]y=3.52[/tex]

Rounding to the nearest tenth, we have:

[tex]y=3.5[/tex]

Hence, the answer is the first option,

[tex]y=3.5[/tex]

Have a nice day!

Answer:  $4080

Step-by-step explanation:  25 x 11 = 275,  4355-275 = 4080

The Haugh family will need to pay $4,080 in the 12th month if they make only the minimum payment for 11 months. The monthly payment they should pay is $362.92 (rounded to the nearest cent).

A) To find out how much the Haugh family will need to pay in the 12th month if they make only the minimum payment for 11 months, we need to calculate the remaining balance after 11 months. The total cost of the hot tub is $4,355. The minimum monthly payment is $25, so the remaining balance after 11 months is $4,355 - 11 * $25 = $4,080. Therefore, the Haugh family will need to pay $4,080 in the 12th month.

B) To calculate the monthly payment, we divide the total cost of the hot tub by the number of months (12). So, the monthly payment is $4,355 / 12 = $362.92. However, since there is a minimum payment requirement of $25, the Haugh family should pay $362.92 each month (rounded to the nearest cent).

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Answer:

The area of the circle is [tex]78.5\ units^{2}[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=31.4\ units[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values

[tex]31.4=2(3.14)r[/tex]

[tex]r=31.4/[2(3.14)]=5\ units[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

substitute the values

[tex]A=(3.14)(5)^{2}[/tex]

[tex]A=78.5\ units^{2}[/tex]

Answer:

78.5

Step-by-step explanation:

Answer:

xy = 1

k = 79

Step-by-step explanation:

Question One

The first and third frames look to me to be the same. I'll treat them that way.

y = x^2                        Equate y = x^2 to the result of 2y + 6 = 2x + 6

2y + 6 = 2(x + 3)         Remove the brackets

2y + 6 = 2x + 6           Subtract 6 from both sides

2y = 2x                       Divide by 2

y = x

Now solve these two equations.

so x^2 = x                  

x > 0

1 solution is x = 0 from which y = 0. This won't work. x must be greater than 0. So the other is

x(x) = x                           Divide both sides by x            

x = 1                            

y = x^2                           Put x = 1 into x^2

y = 1^2                           Solve

y = 1                      

The second solution is

(1,1)

xy = 1*1

xy = 1

Answer: A

Question Two

square root(k + 2) - x = 0

Subtract x from both sides

sqrt(k + 2) = x                Square both sides

k + 2 = x^2                    Let x = 9

k + 2 = 9^2                    Square 9

k + 2 = 81

k = 81 - 2

k = 79

Answer:

84.463°

Step-by-step explanation:

Determine the x- and y-components of these two vectors.  Sum up the x-comps and the y-comps separately, and then find the magnitude and direction of the vector sum:

x-comps:

5 cos 30° + 7 cos 120° = 5(0.866) + 7(-0.5) = 0.83

y-comps:

5 sin 30° + 7 sin 120° = 5(0.5) + 7(0.866) = 2.5 + 6.062 = 8.562

Both components are in Quadrant I, so the direction angle ∅ is between 0° and 90°:  ∅ = arcctan 8.562/0.83 = arctan 10.316 = 1.474 radian, or

1.474 rad       180°

-------------- * -----------  =  84.463°

       1                π

Answer:

  D(4, 1)

Step-by-step explanation:

The two diagonals have the same midpoint, so ...

  (A+C)/2 = (B+D)/2

  A+C = B+D . . . . multiply by 2

  A+C-B = D . . . . . subtract B

  D = (1, 1) + (5, 3) - (2, 3) = (1+5-2, 1+3-3)

 D = (4, 1)

Answer:

D(4 ; 1)

Step-by-step explanation:

vector(AB)=(2-1 ; 3-1) = (1 ; 2)

vector(DC)=(5-x ; 3-y)  and D(x ; y )

ABCD  parallelogram :vector(AB)=vector(DC)

you have the system : 5-x =1

                                       3-y =2

so : x=4 and y=1

D(4 ; 1)

Answer:

  D.  7 +11i

Step-by-step explanation:

In many situations, you can treat "i" as though it were a variable. Collect terms in the usual way.

  (2 +8i) -(-5-3i) = 2 +8i +5 +3i = (2+5) +(8+3)i

  = 7 +11i

Answer:

 The direction angle of vector v is equal to  [tex]9.5\°[/tex]

Step-by-step explanation:

Let

[tex]A(-5,0),B(7,2)[/tex]

The vector v is given by

[tex]v=B-A[/tex]

[tex]v=(7, 2) - (-5, 0)[/tex]

[tex]v=((7 - (- 5)), (2-0))[/tex]

[tex]v=(12, 2)[/tex]

 Remember that

The direction angle of the vector is equal to

 [tex]tan (\theta) =\frac{y}{x}[/tex]

substitute the values

 [tex]tan (\theta) =\frac{2}{12}[/tex]

 [tex]\theta=arctan(\frac{2}{12})=9.5\°[/tex]

Answer:

The direction angle of vector v is equal to  9.5\°

Step-by-step explanation:

Let

A(-5,0),B(7,2)

The vector v is given by

v=B-A

v=(7, 2) - (-5, 0)

v=((7 - (- 5)), (2-0))

v=(12, 2)

Remember that

The direction angle of the vector is equal to

tan (\theta) =\frac{y}{x}

substitute the values

tan (\theta) =\frac{2}{12}

\theta=arctan(\frac{2}{12})=9.5\°

Step-by-step explanation:

put that in a computer calc and  it shoud give u the awnser

Answer:  b) -0.625

Step-by-step explanation:

The formula for the z-score is:

[tex]z=\dfrac{x-\mu}{\sigma}\\\\\bullet z \text{ is the z-score}\\\bullet x \text{ is the value}\\\bullet \mu \text{ is the mean}\\\bullet \sigma \text{ is the standard deviation}\\\\z=\dfrac{6-8}{3.2}\\\\\\.\ =\dfrac{-2}{3.2}\\\\\\.\ =\large\boxed{-.0625}[/tex]

Answer:

(x + 5)² + (y + 7)² = 288

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

The radius is the distance from the centre (- 5, - 7) to the point on the circle (7, 5)

Use the distance formula to calculate r

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (7, 5)

r = [tex]\sqrt{(7+5)^2+(5+7)^2}[/tex] = [tex]\sqrt{12^2+12^2}[/tex] = [tex]\sqrt{288}[/tex]

Hence

(x - (- 5))² + (y - (- 7))² = ([tex]\sqrt{288}[/tex])², that is

(x + 5)² + (y + 7)² = 288

the expanded form of (3x + 4)(2x − 5) is 6x² - 7x - 20. The third option is the correct option.

The simplified form of (3x + 2y) - (x + 2y) is 2x. The correct option is the third option.

3x + 4y equals 36. The third option is the correct option.

To evaluate f(x) = 4x + 3x² - 5, f(x) evaluates to -1. The last option is the correct option.

The Breakdown

To expand the expression (3x + 4)(2x − 5), you can use the distributive property:

(3x + 4)(2x − 5) = 3x(2x) + 3x(-5) + 4(2x) + 4(-5)

Now, simplify each term:

= 6x² - 15x + 8x - 20

Combine like terms:

= 6x² - 7x - 20

So, the expanded form is 6x² - 7x - 20.

To simplify the expression (3x + 2y) - (x + 2y), we can remove the parentheses and combine like terms:

(3x + 2y) - (x + 2y) = 3x + 2y - x - 2y

The terms "2y" and "-2y" cancel each other out:

= 3x - x

Simplifying further:

= 2x

Therefore, the simplified form of (3x + 2y) - (x + 2y) is 2x.

To find the value of 3x + 4y, we need to solve the given equation and then substitute the values into the expression.

Given: 1/2x + 2/3y = 6

To eliminate the fractions, we can multiply the entire equation by the least common multiple (LCM) of the denominators, which is 6:

6 × (1/2x + 2/3y) = 6 × 6

This simplifies to:

3x + 4y = 36

Therefore, 3x + 4y equals 36.

To evaluate f(x) = 4x + 3x² - 5 when x = -2, we substitute -2 for x in the expression:

f(-2) = 4(-2) + 3(-2)² - 5

Simplifying:

f(-2) = -8 + 3(4) - 5

f(-2) = -8 + 12 - 5

f(-2) = -1

Therefore, when x = -2, f(x) evaluates to -1.

Answer:

It is easy it is a 2 step equation if you know the 2 four boxes

Step-by-step explanation:

is the variable alone?

No

what is it attached to?

you always do adding or subtracting first so it is attached to 3

How is it attached?

by subtraction

what is the inverse operation?

it is addition

then all you do is the same thing but with multiplication or division

Answer:

Use Substitution.

Plug in 2x-3 in place of y in the second equation.

4x - 3(2x-3) = 31

4x - 6x + 9 =31

            -9     -9

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

-2x=22 so x=-11

Then, y=2(-11)-3, so y=-25

So the solution would be (-11,-25).

Answer:

She will owe $16987.35 when she begins making payments

Step-by-step explanation:

* Lets explain how to solve the problem

- The loan is $16,000

- The loan at a 4.8% APR compounded monthly

- She will begin paying off the loan in 15 months

- The rule of the future money is [tex]A=P(1 + \frac{r}{n})^{nt}[/tex], where

# A is the future value of the loan

# P is the principal value of the loan

# r is the rate in decimal

# n is the number of times that interest is compounded per unit t

# t = the time in years the money is borrowed for

∵ P = $16,000

∵ r = 4.8/100 = 0.048

∵ n = 12 ⇒ compounded monthly

∵ t = 15/12 = 1.25 years

∴ [tex]A=16000(1+\frac{0.048}{12})^{12(1.25)}=16987.35[/tex]

* She will owe $16987.35 when she begins making payments

Answer:

Step-by-step explanation:

X=15

Answer:

Step-by-step explanation:

[tex]log_6 6^{(x-8)} = log_6 730\\x-8 = log_6 730\\x= 8+log_6 730[/tex]

Answer:

C. 6 feet

Step-by-step explanation:

The answer is:

The correct option is B. the string is 3.9 feet long.

To solve the problem, we need to use the given formula, substituting "T" equal to 2.2 seconds, and then, isolating "L".

Also, we need to remember the formula to calculate a simple pendulum:

[tex]T=2\pi \sqrt{\frac{L}{g} }[/tex]

Where,

T, is the period in seconds

L, is the longitud in meters or feet

g, is the acceleration of the gravity wich is equal to:

[tex]g=9.81\frac{m}{s^{2} }[/tex]

or

[tex]g=32\frac{feet}{s^{2} }[/tex]

We are given the formula:

[tex]T=2\pi \sqrt{\frac{L}{32} }[/tex]

Where,

T, is the period of the pendulum (in seconds).

L, is the length of the string.

32, is the acceleration of the gravity in feet.

So, substituting "T" and isolating "L", we have:

[tex]2.2seconds=2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}} }}\\\\2\pi \sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=2.2seconds\\\\\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}}=\frac{2.2seconds}{2\pi }[/tex]

Then, squaring both sides of the equation, to cancel the square root, we have:

[tex]\sqrt{\frac{L}{32\frac{feet}{seconds^{2} }}}=\frac{2.2seconds}{2\pi}\\\\(\sqrt{\frac{L}{32\frac{feet}{seconds^{2}}}})^{2}=(\frac{2.2seconds}{2\pi})^{2}=(0.35seconds)^{2} }\\\\\frac{L}{32\frac{feet}{seconds^{2}}}}=0.123seconds^{2}\\\\L=32\frac{feet}{seconds^{2}}*0.123seconds^{2}\\\\L=3.94feet=3.9feet[/tex]

Hence, we have that the answer is:

B. the string is 3.9 feet long.

Have a nice day!

Check the picture below.

Answer:

Step-by-step explanation:

55

Tan(angle) = opposite leg / adjacent leg.

Tan(64) = x /30

x = 30 * tan(64)

x = 61.51

Answer:

the answer is d 61.51

Step-by-step explanation:

Answer:

it's false

Step-by-step explanation:

If you have the equation of a parabola in vertex form y=a(x−h)^2+k, then the vertex is at (h,k) and the focus is (h,k+14a).

In this case, h = 0,k = 0 and a = 1/4

Then the focus is at (h, k +14a) = (0, 0 + 14*1/4) = ( 0, 1)

So, it's false.

Answer:

false

Step-by-step explanation: