Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match each sequence to its appropriate recursively defined function.

f(1) = -18

f(n) = 6 · f(n - 1) for n = 2, 3, 4, ...

f(1) = -18

f(n) = f(n - 1) + 21 for n = 2, 3, 4, ...

f(1) = 11

f(n) = f(n - 1) + 22 for n = 2, 3, 4, ...

f(1) = 11

f(n) = 3 · f(n - 1) for n = 2, 3, 4, ...

f(1) = -18

f(n) = f(n - 1) + 22 for n = 2, 3, 4, ...

f(1) = -18

f(n) = 2 · f(n - 1) for n = 2, 3, 4, ...

Sequence

Recursively Defined Function

11, 33, 55, 77, ...

arrowBoth

-18, -108, -648, -3,888, ...

arrowBoth

-18, 3, 24, 45, ...

arrowBoth

Step-by-step explanation:

After taking the square root:

x + 2 = ±2

Notice that x + 2 can also equal -2, because (-2)² = 4.

Answer:   [tex]32\pi[/tex] cubic units.

Step-by-step explanation:

You can use this formula for calculate the volume of a cone:

[tex]V_{cone}=\frac{1}{3}\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the diameter of the base of the cone measures 8 units, then, the radius can be found by dividing the diameter by 2:

[tex]r=\frac{8units}{2}\\\\r=4units[/tex]

Since you already know that height and  the radius, you can substitute them into the formula. Then, the volume of this cone is:

[tex]V_{cone}=\frac{1}{3}\pi (4units)^2(6units)[/tex]

[tex]V_{cone}=32\pi \ units^3[/tex]

Answer: 48

Step-by-step explanation:

Answer:

25 feet

Step-by-step explanation:

Basically that non-regulation tennis court is a rectangle. You want to know the length of the diagonal. If you draw it on paper, you'll see that this then become 2 triangles... of which you have 2 sides, and are seeking the hypotenuse.  So....

H² = A² + B²

H² = 20² + 15² = 400 + 225 = 625

H = 25 feet.

Answer:

The diagonal of a non-regulation tennis court = 25 feet

Step-by-step explanation:

Pythagorean theorem

Hypotenuse² = Base² + Height²

The  tennis court  is like a rectangle.

We can consider the court as made of two right angled triangle

To find the length of diagonal of court

Here base = 15 feet and height = 20 feet

Diagonal or hypotenuse can be written as,

Diagonal ² = Base² + Height²

 = 15² + 20²

 = 225 + 400

 = 625

Diagonal = √625 = 25 feet

Therefore  the diagonal of a non-regulation tennis court = 25 feet

Answer:

see explanation

Step-by-step explanation:

A

If the sequence is arithmetic then the common difference d is

d = t - 4 = 9 -t, that is

t - 4 = 9 - t ( add t to both sides )

2t - 4 = 9 ( add 4 to both sides )

2t = 13 ( divide both sides by 2 )

t = [tex]\frac{13}{2}[/tex] = 6 [tex]\frac{1}{2}[/tex]

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

B

If the sequence is geometric then the common ratio r is

r = [tex]\frac{t}{4}[/tex] = [tex]\frac{9}{t}[/tex] ( cross- multiply )

t² = 36 ( take the square root of both sides )

t = [tex]\sqrt{36}[/tex] = 6

A: If the sequence is arithmetic, what is the value of t is 6.5.

B: If the sequence is geometric, what is the value of t is 6.

If the sequence is arithmetic then the common difference d is,

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms are the same.

d = t - 4

d= 9 -t,

that is,

t - 4 = 9 - t ( add t to both sides )

2t - 4 = 9 ( add 4 to both sides )

2t = 13 ( divide both sides by 2 )

t =[tex]\frac{13}{2}[/tex]  = 6.5

If the sequence is geometric then the common ratio r is

r = [tex]\frac{t}{4} =\frac{9}{t}[/tex] =  ( cross- multiply )

t² = 36 ( take the square root of both sides )

t =  [tex]\sqrt{36}[/tex]= 6

Therefore we get,

A: If the sequence is arithmetic, what is the value of t is 6.5.

B: If the sequence is geometric, what is the value of t is 6

To learn more about the sequence visit:

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Answer:

What school you go to

Step-by-step explanation:

step by step go catch friend and step by step friends

Intersecting Chord Theorem:

X = 1/2(78 + 76)

X = 1/2(154)

x = 77

Answer:

22 quarters

Hope this helps! Correct me if im wrong.

To find x you can use cosine since you know the adjacent side and the hypotenuse. Remember that for cosine it is adjacent over hypotenuse

cos(x) = [tex]\frac{28}{72}[/tex]

cos(x) = [tex]\frac{7}{18}[/tex]

To find the x we must take the inverse of cosine:

[tex]cos^{-1}[/tex]([tex]\frac{7}{18}[/tex] = x

x = 67.1146...

x ≈ 67.1 degrees

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

67.1

Step-by-step explanation:

i took the test

Answer:

78.9  degrees to the nearest tenth.

Step-by-step explanation:

This equals the angle whose tangent is 320/62.5 ( opposite side / adjacent side).

The angle of elevation from the coin to the top of the tower

The angle formed by the line of sight and the horizontal plane for an object above the horizontal.

Given that:

The coin  lands 62.5m away from the center of the base of the 320m- high structure.

Height= 320 m

Base= 62.5 m

Now, tan [tex]\theta[/tex] = [tex]\frac{P}{B}[/tex]

                  =[tex]\frac{320}{62.5}[/tex]

                  = 5.12

               [tex]\theta[/tex]= [tex]tan^{-1} (5.12)[/tex]

               [tex]\theta[/tex]= [tex]78.94^{0}[/tex]

The angle of elevation is: 78.94 degrees.

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Answer:

[tex]\frac{8}{81}[/tex]

Step-by-step explanation:

Since the sequence is geometric there is a common ratio r between consecutive terms.

r = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex]

  = [tex]\frac{1}{3}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{3}[/tex]

Multiplying [tex]\frac{4}{27}[/tex] by r gives the next term in the sequence

[tex]\frac{4}{27}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{81}[/tex]

Answer:

131 m³

Step-by-step explanation:

The volume (V) of a cone is

V = [tex]\frac{1}{3}[/tex] area of base × height

  = [tex]\frac{1}{3}[/tex] × π × 5² × 5

  = [tex]\frac{1}{3}[/tex] π × 125 ≈ 131

Answer:

12x - 15 dollars

Step-by-step explanation:

Sunny earns $12 per hour for delivering cakes.

She worked for x hours this week.

Unfortunately, she was charged $15 for a late delivery on Tuesday

She was supposed to earn $12 × x = $12x this week

But she was charged $15 for late delivery on Tuesday

So her net earning this week is; $12x - $15

Answer:

12x-15

Step-by-step explanation:

it can be concluded that [tex]\( \angle BAD = \angle CBD \) and \( \angle ABD = \angle BCD \).[/tex] So, all three angles are equal.

From the given information:

[tex]\( \angle BAD + \angle ABD = 90^\circ \)[/tex]

[tex]\( \angle CBD + \angle BCD = 90^\circ \)[/tex]

[tex]\( \angle ABD + \angle DBC = 90^\circ \)[/tex]

[tex]\( \angle BAD + \angle BCD = 90^\circ \)[/tex]

We can see that:

[tex]\( \angle BAD + \angle ABD = \angle CBD + \angle BCD \)[/tex]

[tex]\( \angle BAD + \angle BCD = \angle ABD + \angle DBC \)[/tex]

[tex]\( \angle BAD + \angle BCD = \angle BAD + \angle BCD \)[/tex]

From equations (1) and (2), we can conclude that:

[tex]\[ \angle BAD + \angle ABD = \angle CBD + \angle BCD = \angle ABD + \angle DBC \][/tex]

This implies that [tex]\( \angle ABD = \angle CBD \) and \( \angle BCD = \angle DBC \).[/tex]

Therefore, it can be concluded that [tex]\( \angle BAD = \angle CBD \) and \( \angle ABD = \angle BCD \).[/tex] So, all three angles are equal.

The complete question is:

According to the diagram below, which similarity statements are true? Check all that apply.

A. △ ABDsim △ BCD

B. △ ABCsim △ BDC

C. △ ABCsim △ ADB

D. △ ABDsim △ ADC

The similarity statements that are true are:

[tex]\(\triangle ABD \sim \triangle BCD\):[/tex]

  - Since D lies on AC and [tex]\( \angle ADB = \angle BDC = 90^\circ \),[/tex] both [tex]\(\triangle ABD\)[/tex]and \[tex](\triangle BCD\)[/tex]share [tex]\( \angle ADB = \angle BDC \).[/tex]

  - They both share the common angle [tex]\( \angle B \).[/tex]

  - Therefore, [tex]\(\triangle ABD \sim \triangle BCD\).[/tex]

[tex]\(\triangle ABC \sim \triangle ADB\):[/tex]

  - Both triangles share the angle [tex]\( \angle A \).[/tex]

  - They both have right angles at [tex]\( \angle ABC = \angle ADB = 90^\circ \).[/tex]

  - Therefore, [tex]\(\triangle ABC \sim \triangle ADB\).[/tex]

[tex]\(\triangle ABC \sim \triangle BDC\):[/tex]

  - Both triangles share the angle [tex]\( \angle C \).[/tex]

  - They both have right angles at [tex]\( \angle ABC = \angle BDC = 90^\circ \).[/tex]

  - Therefore, [tex]\(\triangle ABC \sim \triangle BDC\).[/tex]

Answer:

  320 cubic units

Step-by-step explanation:

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

  V = (1/3)Bh

where B is the area of the base, and h is the height.

Your pyramid has a rectangular base with edge lengths 8 units and 10 units. Hence the area of the base is ...

  8×10 = 80 . . . . square units

The height is 12 units, so the volume formula gives the volume as ...

  V = (1/3)(80)(12) = 320 . . . . cubic units

There are 6 letters: (4 consonants, 2 vowels)

The probability that Allen will not select a consonant is: (2/6 which simplifies to 1/3) because there are only 2 letters out of the 6 that are not consonants

Fraction: 1/3

Decimal: 0.3333

Percentage: 33.33%

The probability that Allen does not select a consonant is 1/3 as a fraction, 0.3333 as a decimal, and 33.33% as a percentage.

You've asked what the probability is that Allen will not select a consonant when drawing one letter from the mix of letters 's, c, h, o, o, l'. First, let's determine how many vowels and consonants there are in the selection. We have two vowels ('o', 'o') and four consonants ('s', 'c', 'h', 'l'). This gives us a total of six letters.

To find the probability of not selecting a consonant, we look at the likelihood of selecting a vowel instead, since those are the only two types of letters available. There are 2 vowels out of a total of 6 letters. The probability as a fraction is thus 2/6, which simplifies to 1/3.

To express this probability as a decimal, divide the numerator by the denominator: 1 divided by 3 equals approximately 0.3333. Finally, to express this as a percentage, multiply the decimal by 100 to get 33.33%.

In summary:

Answer:

Part 1) The exponential function is equal to [tex]y=1,350(0.95)^{x}[/tex]

Part 2) The population in 2010 was  [tex]992\ fish[/tex]

Step-by-step explanation:

Part 1) Write an exponential decay function that models this situation

we know that

In this problem we have a exponential function of the form

[tex]y=a(b)^{x}[/tex]

where

y ----> the fish population of Lake Collins since 2004

x ----> the time in years

a is the initial value

b is the base

we have

[tex]a=1,350\ fish[/tex]

[tex]b=(100\%-5\%)=95\%=0.95[/tex]

substitute

[tex]y=1,350(0.95)^{x}[/tex] ----> exponential function that represent this scenario

Part 2) Find the population in 2010

we have

[tex]y=1,350(0.95)^{x}[/tex]

so

For [tex]x=(2010-2004)=6\ years[/tex]

substitute

[tex]y=1,350(0.95)^{6}=992\ fish[/tex]

Final answer:

The exponential decay function for the fish population in Lake Collins is P(t) = 1350 * e^(-0.05t). Using this, the estimated fish population in 2010 is about 1,000.

Explanation:

We need to write an exponential decay function to model the decreasing fish population in Lake Collins and then use it to find the population in 2010.

To create an exponential decay function, we can use the formula P(t) = P0 * e^(rt), where:

P(t) is the population at time t,

P0 is the initial population,

r is the rate of decay (as a negative value), and

t is the time in years since the initial count.

Given the initial population of 1,350 fish in 2004 and a decay rate of 5% per year, we can write the function as:

P(t) = 1350 * e^(-0.05t)

To find the population in 2010, we first calculate the time passed since 2004, which is 6 years. Thus, t = 6:

P(6) = 1350 * e^(-0.05*6)

Calculating this gives us:

P(6) ≈ 1350 * e^(-0.3) ≈ 1350 * 0.740818 ≈ 1000 (rounded to the nearest whole number)

Therefore, the fish population in 2010 was approximately 1,000 individuals.

Answer:

a^2b(7 + 10b + 14b^2)

Use wolframalpha for math questions, or photomath!

To solve this, factor out a^2b from the expression.

For this case we must indicate an expression equivalent to:

[tex]7a ^ 2b + 10a ^ 2b ^ 2 + 14a ^ 2b ^ 3[/tex]

We must draw the common term of the three terms, we have:

[tex]a ^ 2b (7 + 10b + 14b ^ 2)[/tex]

So:

[tex]7a ^ 2b + 10a ^ 2b ^ 2 + 14a ^ 2b ^ 3 = a ^ 2b (7 + 10b + 14b ^ 2)[/tex]

Answer:

[tex]a ^ 2b (7 + 10b + 14b ^ 2)[/tex]

Option B

Answer:

Step-by-step explanation:

<EAF is a central angle. Its measure is 12o

Arc EF has angular measure of 12 degrees as well.

The formula for the arc length in cm is

Arc length = (given arc angle/360) * 2 * pi * r

r = 30 cm which is given

Given arc angle = 12 degrees.

Arc length = (12/360) * 2* pi * r

Arc length = 1/30 * 2*pi * 30

Arc length = 6.28

Answer:

Step-by-step explanation:

I'll show you with an example.  I'll make a table and then show you how to find the exponential equation, ok?

 x                 y

 0                 3

 1                  12

 2                 48

 3                192

The standard form of an exponential equation is

[tex]y=a(b)^x[/tex]

We will take 2 (x,y) coordinates from our table and fit them into the equations to solve for a and b.  Using the point (0, 3):

[tex]3=a(b)^0[/tex]

b to the 0 power is equal to 1, so the equation then becomes a(1) = 3 so a = 3.  We will use the other x, y coordinate along with that a value to now solve for b:

[tex]12=3(b)^1[/tex]

b to the first is b, so now that equation becomes 3b = 12 and b = 4.  Filling that info back into the standard form:

[tex]y=3(4)^x[/tex]

There you go!

Answer:

circle should be the answer

The answer is A. Circle

Answer:

Step-by-step explanation:

the answer is 27%.

Answer:

27 %

Step-by-step explanation:

To find the percentage of which her net income is her rent payment you do

[tex]\frac{200}{740}[/tex] × 100 = 27.027027027

Answer:

maximum value y = 30

Step-by-step explanation:

Given

- x² + 10x + 5

To complete the square the coefficient of the x² term must be 1

factor out - 1

= - (x² - 10x) + 5

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 10x

= - (x² + 2(- 5)x + 25 - 25) + 5

= - (x - 5)² + 25 + 5

= - (x - 5)² + 30 ← in vertex form

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Hence vertex = (5, 30)

The max/ min occurs at the vertex

Since a < 0 then vertex is a maximum

Hence maximum value is y = 30

bart has a choice of twelve different movies at 5 different times each so you just multiply twelve and five to get 60 choices

Answer:

Step-by-step explanation:

Givens

To find the total number of choices of movies and showtime that Bart have, we just need to multiply. Because, if each movie is shown at five different times, and there are 12 movies, then the total number of choices are

[tex]12 \times 5 = 60[/tex]

Therefore, Bart has 60 choices to watch a movie.

Answer:

12

Step-by-step explanation:

If square 1's area is 25, that must mean its side is 5

If square 2's area is 16, that must mean its side is 4

Since it looks like its going in order, square 3's side is 3, and since there's 4 sides to a square, the perimeter is 12.

Answer:

12 units²

Step-by-step explanation:

4^2+b^2=5^2

b=25-16

b^2=9

b=√9

b=3

there are 4 sides in a square so 3•4=12

Answer:

a)

The total number of students who participated in the survey is 97

b)

P(male) = 0.5361

c)

P(A) = 0.2474

d)

The events male and TV show B are not mutually exclusive since 5 males prefer TV show B.

e)

The events female and TV show C are mutually exclusive since no female participant prefers TV show C

Step-by-step explanation:

a)

The total number of students who participated in the survey is obtained as;

Number of male participants + number of female participants

52 + 45 = 97

b)

P(male)

This is the probability that a randomly selected individual would be a male;

P(male) = ( number of male participants) / ( total participants)

             = 52/97 = 0.5361

c)

P(A)

This is the probability that a randomly selected participant would prefer TV show A;

P(A) = ( participants who prefer TV show A) / (total participants)

       = 24/97 = 0.2474

d)

Two events are said to be mutually exclusive if they cannot happen at the same time. Another word that means mutually exclusive is disjoint. If two events A and B are disjoint, then the probability of them both occurring at the same time is 0.

The events male and TV show B are not mutually exclusive since 5 males prefer TV show B. The probability is thus not 0.

e)

Two events are said to be mutually exclusive if they cannot happen at the same time. Another word that means mutually exclusive is disjoint. If two events A and B are disjoint, then the probability of them both occurring at the same time is 0.

The events female and TV show C are mutually exclusive since no female participant prefers TV show C. The probability is thus 0.

Answer:

  see below

Step-by-step explanation:

If you haven't memorized it so you know it already, it takes about 10 seconds with your calculator to discover that ...

  arccos((√3)/2) = β = 30°

This fact matches only one answer choice.

Answer:

90.51 (rounded to the nearest hundredth)

Step-by-step explanation:

We can use trigonometry to figure this out

sin = opposite side / hypothenuse

The 45° angle's opposite side is a leg of the triangle

sin 45 = leg / 128

sin 45 * 128 = (leg / 128 ) * 128

0.7071 * 128 =  leg

90.51 = leg

Answer:

b

Step-by-step explanation:

Answer:

  B. 40/61

Step-by-step explanation:

There are 40 spots out of the 61 in the lot with numbers greater than or equal to 22. The probability of choosing one of them at random is 40/61.

_____

About the answer choices

61/21 and 61/40 are both numbers that are greater than 1. A probability is always a number between 0 and 1 (inclusive), so these answers can be rejected immediately.

There are 21 spots with numbers less than 22, so 21/61 is the probability of choosing one of those. That is not what the question is asking for.

Answer:

25% = 1/4

Step-by-step explanation:

It is 25% because there are 4 outcomes that you can get which are

HT, TH, HH, TT

H = Head

T = Tail

and out of the four outcomes, there is one that will be Head first and Tails on the second flip. So 1 out of 4 = 25%

Answer:

Jackie's total contribution the school would be $18.00

Step-by-step explanation:

Jackie's contribution to the school bazaar = a batch of baklava

No. of pieces in a batch = 12 pieces

Price of one piece = $1.50

CASE: All baklava is sold

No. of pieces of Baklava sold = 12 pieces

Price of 12 pieces of Baklava = no. of pieces * Price of one piece

= 12 * $1.50

= $18.00