.1. The Fibonacci sequence is given recursively by Fo= 0, F₁ = 1, Fn = Fn-1 + Fn-2. a. Find the first 10 terms of the Fibonacci sequence. b. Find a recursive form for the sequence 2,4,6,10,16,26,42,... C. Find a recursive form for the sequence 5,6,11,17,28,45,73,... d. Find the initial terms of the recursive sequence ...,0,0,0,0,... where the recursive formula is ZnZn-1 + Zn-2. The moral of the story is that the initial values make a BIG difference to the sequence. Don't forget to give the initial values when defining a sequence recursively!

Answer: It should look something like this.

Step-by-step explanation:

The graph of f(x) = (x + 3)(x - 2) is a parabolic function that is the product of two linear factors, (x + 3) and (x - 2).

The graph is given below.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To understand the graph, we can begin by considering the x-intercepts, which are the points where the graph crosses the x-axis.

These occur where the value of f(x) is zero, which happens when either

x + 3 = 0 or x - 2 = 0.

So the x-intercepts are x = -3 and x = 2.

Next, we can consider the leading coefficient, which is 1 in this case.

Since the leading coefficient is positive, the parabola opens upward.

We can also find the vertex of the parabola by completing the square.

We have:

f(x) = x² + x(-2 + 3) - 2(-3)

f(x) = x² + x + 6

Now we can rewrite this in vertex form:

f(x) = (x + 1/2)² + 23/4

So the vertex is (-1/2, 23/4), which is a minimum point on the graph.

Thus,

We can sketch the graph of f(x) = (x + 3)(x - 2) as an upward-opening parabola that crosses the x-axis at -3 and 2 and has a minimum point at (-1/2, 23/4).

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The probability that both randomly selected voters are Democrats is approximately 0.123.

To find the probability that both randomly selected voters are Democrats, we can use the concept of independent events.

Given that 35% of all voters in the town are Democrats, the probability of selecting a Democrat for the first voter is 0.35. Since the events are independent, the probability of selecting another Democrat for the second voter is also 0.35.

To calculate the probability that both events occur, we multiply the probabilities together:

Probability of both voters being Democrats = 0.35 * 0.35 = 0.1225

Rounding to the nearest thousandth, the probability that both randomly selected voters are Democrats is approximately 0.123.

Therefore, the probability that both voters selected for the survey are Democrats is approximately 0.123 or 12.3% (rounded to the nearest thousandth).

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If the function be f(x) = 4x - 2 then the value of f(3) exists 10.

An expression, rule, or law that establishes a connection between an independent variable and a dependent variable.

In mathematics, a variable is referred to as the alphabetic symbol used to represent a number or numerical value. An unknown quantity is represented by a variable in algebraic equations.

In mathematics, a function is a relationship where the values of one or more independent variables determine the values of a single dependent variable. The term "function" denotes that the independent variable influences the dependent variable.

Let the function be f(x) = 4x - 2

substitute the value of x = 3, then

f(3) = 4 × 3 - 2

simplifying the above equation, we get

f(3) = 10

Therefore, the value of f(3) exists 10.

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Answer:

27

Step-by-step explanation:

Given that :

Dimension of poster board = 1 yd by 1 yd

Dimension of each poster sign = 1/3 yd by 1/9 yd

Number of poster signs that can be cut :

Area of poster sign = 1/3 * 1/9 = 1/27 yard²

Area of poster board = 1 yard²

Number of poster signs that can be cut :

Area of poster board / area of poster sign

1 yard² ÷ (1/27) yard²

1 ÷ 1/27

1 * 27/1

= 27 poster signs

Answer:7

Step-by-step explanation:

ball

Answer:

I believe it would be D, the smiley face that's on the bottom.

Step-by-step explanation:

Since the smiley face is first reflected on the y axis, (vertically,) it'd be upside down. Then, turning it 90 degrees clockwise is simply just turning it left once.

Answer:

Step-by-step explanation:

10x + 8x = 180 (angles on straight line)

x = 10

AFH = 10x = 100

AFE = 8x = 80

Answer:

19 duh

Step-by-step explanation:

Answer:

∡1 = 64°

Step-by-step explanation:

∡3 = 180-104 which is 76°

∡1 = 180 - (40 + 76) = 180-116 or 64°

Step-by-step explanation:

the graph should look something like this

45 students are not partticipating

Number of students that participated in school play = 30

% of students not participating = 60%

% of those participating = 100% - 60%

% of those participating = 40%

let the total number of students in 7th graders = y

Number of students that participated in school play = total number of students in 7th graders × % of those participating

30 = y × 40%

30 = y × 0.4

30 = 0.4y

divide both sides by 0.4:

Number of students not participating = total number of students in 7th graders - Number of students that participated in school play

Number of students not participating = 75 - 30

Number of students not participating = 45

Answer:

Statement (b) is equivalent to statement (c), but neither is equivalent to statement (a).

Step-by-step explanation:

Let \(F\) denote that "Fido is our fish's name" and let \(R\) denote that "Rex is our dog's name". The statements listed in this question would then become:

Apply de Morgan's Law \(\lnot (P \land Q) \iff (\lnot P) \lor (\lnot Q)\) to rewrite statement (b). Let \(P = (\lnot F)\) and \(Q = (\lnot R)\). By de Morgan's Law:

\(\begin{aligned} & \lnot ((\lnot F) \land (\lnot R)) \\ \iff \; & \lnot (P \land Q)\\ \iff \; & (\lnot P) \lor (\lnot Q) && (\text{by de Morgan's Law}) \\ \iff \; & (\lnot (\lnot F)) \lor (\lnot (\lnot R)) \\ \iff \; & F \lor R\end{aligned}\).

In other words, statement (b) \(\lnot ((\lnot F) \land (\lnot R))\) is equivalent to statement (c) \(F \lor R\).

Statement (a) \(F \implies R\) isn't equivalent to \(F \lor R\).

For example, when \(F = \texttt{True}\) and \(R = \texttt{False}\), \(F \implies R\) would be false since \(\texttt{True}\) does not imply \(\texttt{False}\). However, for the same \(F\) and \(R\), \(F \lor R\) would be true since \(F = \texttt{True}\!\).

Answer:

y = -2x + 7 is the equation if that's what you are asking for.

answer:

Linear equation :

y= -2x +7

Step-by-step explanation:

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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By using the property of exponential function, the results obtained are

Base of the function is 5.

Initial value of the function is close to zero.

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In \(2^4 = 2\times 2\times 2\times 2\)

Here, 2 is multiplied by itself 4 times.

If \(a^m = a \times a\times a....\times a\) (m times), a is the base and m is the index.

Here,

\(y = 5^w\) is an exponential function.

The base of the function is 5.

As \(x \rightarrow -\infty\), the function tends to 0

So the initial value of the function is close to zero.

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Answer:

275

Step-by-step explanation:

Answer:

I believe your answer is A.

Step-by-step explanation:

2x2x2

2x2=4

4x2=8

Therefore, x=2.

Answer: c

Step-by-step explanation:

The value of x in the expression (x³ - 10x² + 17x + 28) / 4 = 0 is -2, 2, or 6.

What is the value of x in the expression?

We can solve for x by multiplying both sides of the equation by 4, which gives:

x³ - 10x² + 17x + 28 = 0

Now, we can try to factor the polynomial by looking for integer roots using the Rational Root Theorem.

The possible integer roots of this polynomial are the divisors of the constant term, 28, divided by the divisors of the leading coefficient, 1. Therefore, the possible integer roots are ±1, ±2, ±4, ±7, ±14, and ±28.

By trying each of these possible roots, we find that x = -2 is a root of the polynomial, which means that (x + 2) is a factor of the polynomial.

We can use polynomial long division or synthetic division to find the other factor:

           x² - 8x + 14

          -----------------

x + 2  | x³ - 10x² + 17x + 28

          - x³ + 2x²

             -----------

              -8x² + 17x

              +8x² - 16x

                -----------

                 +x + 28

               -x - 2

                ------

                  26

Therefore, we have factored the polynomial as:

(x + 2)(x² - 8x + 14) = 0

To find the values of x that satisfy the equation, we set each factor equal to zero and solve for x:

x + 2 = 0 or x² - 8x + 14 = 0

The first equation gives us x = -2, which we already knew was a root.

The second equation can be solved using the quadratic formula:

x = [8 ± √(8² - 4(1)(14))] / (2)

x = [8 ± √(16)] / 2

x = 4 ± 2

Therefore, the values of x that satisfy the equation are:

x = -2, 2, or 6

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The complete question is below:

Find the value of x in the expression:

(x³ - 10x² + 17x + 28 ) / (4) = 0

Dr. Granger notices that 20 students in their longitudinal study of 100 college students dropped out of the experiment over time. when they look at the missing data, they discover that those 20 students had significantly lower pretest scores than the 80 with complete data. The type of threat we discover over here after careful analysis is attrition.

Okay, so as part of a longitudinal study, we track participants' replies over time. Additionally, he began with 100 students. Then 20 people left the group. So till now, just 80 students have completed and submitted all of their information. Consequently, you lose a number of participants over time in the longitudinal study. Therefore, you ended up with less than you had at the beginning. This is an illustration of the threat known as attrition in data research. When study participants drop out and you finish up with less data than you did at the beginning. There is attrition as a result.

In research investigations, attrition refers to participant dropout over time. Subject mortality is another name for it, However it doesn't always mean that participants are dead!

There will almost always be some dropout in longitudinal research, but the kind and degree of the dropout can be problematic. Attrition bias is the deliberate exclusion of some study participants who consistently vary from those who remain.

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The chance that each number will occur in a randomly generated list of numbers from 0 to 7, A. 1 / 8.

In a randomly generated list of numbers from 0 to 7, there are 8 possible numbers that can occur (0, 1, 2, 3, 4, 5, 6, and 7). If the list is generated randomly, each of these numbers has an equal chance of occurring.

Therefore, the chance that each number will occur is 1/8, or approximately 0.125. This means that if the list is generated many times, each number should occur approximately 1/8 of the time on average.

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Answer:

ok

Step-by-step explanation:

it's ammmmmmmmmmmmmmmmmmmmmost doen

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

Work Shown:

Let x be the measure of each of the two angles (which is valid because they both have the same measure). Since they are complementary, the angles add to 90

So,

x+x = 90

2x = 90

x = 90/2

x = 45

Each angle is 45 degrees

45+45 = 90

Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.

Side-Angle-Side (SAS) (SAS), The triangles are congruent if the included angles are also congruent and two sides of one triangle match two sides of another triangle.

The use of labels Triangle ABC is congruent to triangle DEF if the angles of triangles ABC and DEF are AB = DE, AC = DF, and A = D.

ABC=CDE: a) in accordance with the conditions BC=CD and AC=CE; b) BCA=m (DCE).

If ABC = CDE, then m(BAC) = m(DEC), and m(ABC) = m (CDE).

If m(BAC)=m(DEC), then AB || DE, or if m(ABC)=m(CDE), then AB || DE.

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1200 cards

All measurements should be taken in centimeters

Calculate the area of large rectangular card:

Calculate the area of each small cards:

Divide the area of large card by area of small card

Number of small cards: 1200 cards

For bigger rectangle:-

Area:-

For smaller rectangle

Area:-

Total cards:-

The probability that the defective memory chip came from Supplier B is approximately 0.8455 or 84.55%. This probability is calculated using Bayes' theorem, considering the probabilities of selecting a memory chip from each supplier and the probabilities of a memory chip being defective from each supplier.

To compute the probability that the defective memory chip came from Supplier B, we can use Bayes' theorem.

Let's define the events:

A: Memory chip came from Supplier A.

B: Memory chip came from Supplier B.

D: Memory chip is defective.

We have:

P(A) = 0.62 (probability of selecting a memory chip from Supplier A)

P(B) = 0.38 (probability of selecting a memory chip from Supplier B)

P(D|A) = 0.001 (probability of a memory chip being defective given it came from Supplier A)

P(D|B) = 0.009 (probability of a memory chip being defective given it came from Supplier B)

We need to find P(B|D), the probability that the defective memory chip came from Supplier B.

Using Bayes' theorem:

P(B|D) = (P(D|B) * P(B)) / (P(D|A) * P(A) + P(D|B) * P(B))

Plugging in the values:

P(B|D) = (0.009 * 0.38) / (0.001 * 0.62 + 0.009 * 0.38)

      ≈ 0.00342 / (0.00062 + 0.00342)

      ≈ 0.00342 / 0.00404

      ≈ 0.8455

Therefore, the probability that the defective memory chip came from Supplier B is approximately 0.8455 or 84.55%.

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Answer:

slope=3/4

Step-by-step explanation:

4-1

/      = 3/4

9-5

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The three sides of a triangle are consecutive if and only if they are represented by three consecutive natural numbers. The perimeter is the sum of the three side lengths, whose formula is presented below:

x + (x + 1) + (x + 2) = 141

3 · x + 3 = 141

3 · (x + 1) = 141

x + 1 = 47

x = 46

By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.

The statement is complete, the correct statement is the following:

The triangle has three consecutive sides and its perimeter is 141 centimeters. Work out the value of each side.

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Answer:

exact form: x=17/10

Decimal form: x=1.7

mixed number form: 1 7/10

Answer:

x = 17/10 (as a fraction) or x = 1.7(as a decimal) or x = 1 7/10(as a mixed number)

Step-by-step explanation:

3(5-x) = 7x - 2

3 * 5 - 3* x = 7x - 2 (brackets means multiply)

15 - 3x = 7x - 2 (when over equal sign negative changed to positive)

15 + 2 = 7x + 3x

17/10 = 10x/10 (cross-cancel cuz u tryna isolate the x)

17/10 = x

Answer:

subtract 5 , m=(-15)

Step-by-step explanation:

15-5

=10

n:

5-10

=(-5)

m:

(-5)-10

=(-15)

hope it help

Answer:

y = -24

Step-by-step explanation:

Solve for y:

y/8 + 38 = 35

Put each term in y/8 + 38 over the common denominator 8: y/8 + 38 = y/8 + 304/8:

(y/8 + 304/8) = 35

y/8 + 304/8 = (y + 304)/8:

((y + 304)/8) = 35

Multiply both sides of (y + 304)/8 = 35 by 8:

(8 (y + 304))/8 = 8×35

(8 (y + 304))/8 = 8/8×(y + 304) = y + 304:

y + 304 = 8×35

8×35 = 280:

y + 304 = 280

Subtract 304 from both sides:

y + (304 - 304) = 280 - 304

304 - 304 = 0:

y = 280 - 304

280 - 304 = -24:

Answer: y = -24