Sebastian writes the recursive formula f(x+1) = 4f(x) to represent a geometric sequence whose second term is 12.

Which explicit formula can be used to model the same sequence?

f(x) = 12(4)x
f(x) = 3(4)x − 1
f(x) = 4(12)x
f(x) = 4(3)x − 1

Answer:

x+14=21 Add 14 to both sides of the equation. Subtract 14 from the left side of the equation. Add 14 to the left side and subtract 14 from the right side of the equation.

Step-by-step explanation:

Answer: x = 7

Step-by-step explanation:

U first subtract 14 from both sides

x + 14 - 14 = 21 - 14

And then u simplify

and get 7

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Chelsea is sewing handmade scarves she has 7 1/2 yards of material and needs 2 1/4 yards of material for each scarf, so the number of scarves can she make with the existing material = 3. This can be solved using the concept of fractions.

In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.

Total material = \(7\frac{1}{2}\) yards

\(= 7\frac{1}{2} = 7 + \frac{1}{2} = \frac{15}{2}\) yards

Materials required for each scarf = \(2\frac{1}{4}\) yards

Number of scarfs she make with the existing material

= Total Material ÷ Material required for each scarf

= \(\frac{15}{2}\) ÷ \(\frac{9}{4}\)

= \(\frac{15}{2}\) × \(\frac{4}{9}\)

= \(\frac{10}{3}\)

= \(3\frac{1}{3}\) ≈ 3

Hence, the number of scarves can she make with the existing material = 3.

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1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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a) The inequality for the expression 2z + 9 is 2z + 9 > 13.

b) The inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The inequality for the expression 4 + 2z is 4 + 2z > 8.

d) The inequality for the expression 5(3z - 2) is 15z - 10 > 20.

a) To write an inequality for the expression 2z + 9, we can multiply the given inequality z > 2 by 2 and then add 9 to both sides of the inequality:

2z > 2 * 2

2z > 4

Adding 9 to both sides:

2z + 9 > 4 + 9

2z + 9 > 13

Therefore, the inequality for the expression 2z + 9 is 2z + 9 > 13.

b) For the expression 3(z - 4), we can distribute the 3 inside the parentheses:

3z - 3 * 4

3z - 12

Since we are given that z > 2, we can substitute z > 2 into the expression:

3z - 12 > 3 * 2 - 12

3z - 12 > 6 - 12

3z - 12 > -6

Therefore, the inequality for the expression 3(z - 4) is 3z - 12 > -6.

c) The expression 4 + 2z does not change with the given inequality z > 2. We can simply rewrite the expression:

4 + 2z > 4 + 2 * 2

4 + 2z > 4 + 4

4 + 2z > 8

Therefore, the inequality for the expression 4 + 2z is 4 + 2z > 8.

d) Similar to the previous expressions, we can distribute the 5 in the expression 5(3z - 2):

5 * 3z - 5 * 2

15z - 10

Considering the given inequality z > 2, we can substitute z > 2 into the expression:

15z - 10 > 15 * 2 - 10

15z - 10 > 30 - 10

15z - 10 > 20

Therefore, the inequality for the expression 5(3z - 2) is 15z - 10 > 20.

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Answer:

C

Step-by-step explanation:

The equation of the ellipse is \((x - 3)^2 / 16 + (y - 3)^2 / 64 = 1.\)

To determine the equation of the ellipse, we need to find its major and minor axes, as well as the distance from each focus to the center.

Given that the foci of the ellipse are located at (3, 1) and (3, 5), we can determine that the center of the ellipse is at the midpoint between these two foci, which is (3, 3).

The endpoints of the minor axis are (7, -2) and (-1, -2), which tells us that the length of the minor axis is 7 - (-1) = 8 units.

Now, let's calculate the distance from the center to one of the foci. Using the distance formula, we have:

sqrt((3 - 3)^2 + (3 - 1)^2) = sqrt(0 + 4) = 2.

Since the foci are vertically aligned, the major axis is vertical. Therefore, the length of the major axis is twice the distance from the center to one of the foci, which gives us 2 \(\times\) 2 = 4 units.

Using the standard form of the equation for an ellipse centered at (h, k), with a horizontal major axis of length 2a and a vertical minor axis of length 2b, the equation is:

\((x - 3)^2 / 4^2 + (y - 3)^2 / 8^2 = 1.\)

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Answer:

36.9°

Step-by-step explanation:

→ Identify the triangle required by seeing which side is not given

Hypotenuse is not given so we need to use Tan⁻¹ = Opposite / Adjacent

→ Substitute values in

Tan⁻¹ =  ( 3 ÷ 4 )

→ Simplify

36.9°

Answer:

Angle A is 82

Angle B is 8

Step-by-step explanation:

Complementary means they add to 90 degrees

3x+46+x-4=90

4x+42=90

4x=48

x=12

Angle A is 3(12)+46= 82

Angle B is 12-4=8

82+8=90

Midpoint formula =

Endpoint 1 = (x1,y1 ) = (6,-2)

midpoint = (mx,my) = (-2,3)

mx = x1+x2 /2

-2 = 6+x / 2

-2(2) = 6+x

-4 =6+x

-4-6 = x

x= -10

3 = -2+y/2

3(2)= -2+y

6 = -2+y

6+2 = y

8 =y

y= 8

Endpoint = ( -10,8)

The two figures show equivalent graphs because:

A. The graphs have several edges that match the number of vertices.

B. The graphs have the same number of edges.

C. The vertices are connected in the same way.

D. The graphs have the same number of vertices.

The third equivalent graph is at option D.

The graphs that have the same number of vertices connected in the same way are called equivalent graphs. If they are connected in the same way then their count of edges will be the same for both graphs. They are also said to be isomorphic graphs.

The given graphs have
Graph1: vertices BCJK

Graph2: vertices BCJK

So, there is the same number of vertices for both graphs.

The connection between the vertices:

Graph1: J - B - C - K - B

Graph2: J - B - C - K - B

So, they are connected in the same way.

The edges formed by these vertices:

Graph1: JB; BC; CK; KB

Graph2: JB; BC; CK; KB

So, there is the same number of edges for both graphs.

Here the number of edges = the number of vertices i.e., (4 = 4)

From all these comparisons, the given graphs are equivalent.

The third equivalent graph made from these graphs is at option D in the diagram attached below.

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Disclaimer: The given question is incomplete. There is no image attached in the given question. Here the image is attached.

The statement that is true about the points shown below is: "The distance between them is zero because they have the same y-coordinate."

The distance between two points is typically calculated using the distance formula, which involves the difference between their x-coordinates and y-coordinates. However, in this case, the statement specifies that the points have the same y-coordinate.

The y-coordinate represents the vertical position on a graph, while the x-coordinate represents the horizontal position. When two points have the same y-coordinate, it means they lie on the same horizontal line.

Since distance is measured in a straight line, and these points are already on the same horizontal line, their distance from each other is zero. This is because they are effectively occupying the same position along the horizontal axis.

In summary, when two points have the same y-coordinate, their distance from each other is zero. This is because they lie on the same horizontal line and are already as close to each other as possible in the horizontal direction.

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Answer:

Step-by-step explanation:

The three angles in a triangle add up to 180 :

If angle 1 is 90 because it is a right angle triangle then :

Angle 2 + Angle 3 = 180 -90

Angle 2 + Angle 3 = 90

The ratio of Angle 2:Angle 3 is 1:2

There are 3 shares in total (1+2=3)

1 share = 90 ÷ 3 = 30

So Angle 2 is 30 and angle 3 is 60

Hope this helped and have a good day

Answer: 34,650 permutations

While one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

In a race between two runners, one of them had a personal best time, while the other runner neither trained nor had a personal best time.

The runner who had a personal best time implies that they had trained and put in effort to improve their performance. A personal best time suggests that they have achieved their highest level of performance in a race. This indicates that the runner has dedicated time and effort to their training regimen, focusing on improving their speed and endurance.

On the other hand, the runner who neither trained nor had a personal best time implies that they did not invest effort in training or actively seek to improve their performance. They may have participated in the race casually or without specific training goals in mind. As a result, they did not achieve a personal best time, indicating that they did not put in the necessary effort to reach their full potential.

In summary, while one runner demonstrated dedication and improvement through a personal best time, the other runner's lack of training and absence of a personal best time suggest a more casual or unprepared approach to the race.

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Answer:

1) a)  accepting the new drug is better based on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) Accepting and using the current drug in use when it is not as effective as the new drug

c) Type 1 error

2) a) rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) Increase the significance level  ( A )

Step-by-step explanation:

1)

a) To make a type 1 error in this situation is accepting the new drug is better and prescribing it to the millions of people based only on its effectiveness when in reality the drug ain't better than the drug in current use because of its side effects

b) A type II error in context is :Accepting and using the current drug in use when it is not as effective as the new drug

c)  Type I error

2)

a) Type 1 error is rejecting the vitamin supplement based on not knowing the harmful side effects

b) Accepting the Vitamin supplement based on just health benefits it portrays without comparison with other supplement.

c) Type II error

3) If committing a type 1 error is much worse

Increase the significance level

The volume of the solid obtained by rotating the specified region about the x-axis is 12.

Here we have to find the volume of the solid.

Data given:

f(x) = x² + 3

Limit of x is -1≤x≤2

Volume = \(\int\limits^2_-1 {(x^{2} + 3}) \, dx\)

             = ( x³/3 + 3x\()^{2} _{-1}\)

             = [( 8/3 + 6) - ( -1/3 - 3)]

             = 26/3 +10/3

             = 36/3

             = 12

Therefore the volume is 12.

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Kiet will make his another observation at every multiples of 6 until it reaches at 60 which is at 2 : 00 pm.

Given that,

Kiet needs to observe a science experiment every 6 minutes for one hour.

He makes his first observation at 1:00 p.m.

Now he needs to make the observation every 6 minutes.

This means that his second observation will be at 1:06 pm.

Third observation will be at 1:12 pm.

Fourth will be at 1:18 pm.

It goes on like this for every multiples of 6.

His last observation will be at 2:00 pm which is at the 60th minute after 1.

Hence Kiet will make his observations at every multiples of 6 until it reaches 60.

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The current weight of the truck is given as follows:

3496 kg.

The current weight of the truck is obtained applying the proportions in the context of the problem.

The initial weight of the truck is given as follows:

3796 kg.

The weight removed from the truck is given as follows:

6 x 50 = 300 kg.

Hence the current weight of the truck is given as follows:

3796 - 300 = 3496 kg.

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Answer:

Prime number - 3/6 = 1/2

Head - 1/2

Step-by-step explanation:

prime numbers are 2, 3 and 5 on a die

The period of the oscillating mass is π/5 seconds.

To determine the period of the oscillating mass, we need to identify the coefficient of the 't' term in the given equation.

In the equation x(t) = (1.6 cm) cos(10t), we can see that the coefficient of 't' is 10.

The period (T) of an oscillating function can be found using the formula T = 2π/ω,

where ω represents the angular frequency.

In this case, the angular frequency (ω) is equal to the coefficient of 't', which is 10.

Therefore, we can calculate the period as follows:

T = 2π/10

= π/5.

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Answer:

70%

Step-by-step explanation:

you do it

Answer:

remember

1h=60min

1min=60 sec

now come to the question

1h=60min

1min=60 sec

60min=60×60=3600sec in 1hour

25min=60×25=1500sec in 25 min

total all sec=3600+1500+29=5129sec

Step-by-step explanation:

Answer:

5129

Step-by-step explanation:

So first we know we have 29 seconds then we know there is 60 seconds in a minute so I'm going to take 60 times 25 which equals 1500 so right now I have 1529 seconds I also know that there is 60 minutes in 1 hour so I'm going to do 60 times 60 which is 3600 so now I'm going to add all my seconds together 1500 + 3600 = 5100

The type of sytudy that we have here is the observational study.

In an observational study, the researcher observes and analyzes data from individuals without actively intervening or manipulating any variables.

In this case, the researcher is observing and comparing the health outcomes of two groups of individuals: those who have eaten a vegan diet for the past five years and those who have not.

The participants are not randomly assigned to the groups, and the researcher does not actively control or manipulate the diet of the individuals.

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The ratio which is equivalent to 30:20 is option C, 3:2.

Suppose the  real measurements were "a" and "b"

Then their ratio will be formed as

\(\dfrac{a}{b} = \dfrac{p \times x}{q \times x} = \dfrac{p}{q}\)

where is a common factor (not 1)? This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly canceled from both the numerator and the denominator.

Thus, a = px, b = qx

We have given that a 2-column table has 2 rows. Column 1 is labeled

The Total with entries 30, and 15. Column 2 is labeled Red with entries 20, and 10.

Given ratio is 30:20

Or

3:2

Therefore, we can conclude that the ratio which is equivalent to 30:20 is option C, 3:2.

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5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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Answer:

m<B = 93°

Step-by-step explanation:

Based on the inscribed quadrilateral theorem, the opposite angles of a cyclic quadrilateral are supplementary.

Thus:

m<B + m<D = 180°

Substitute

m<B + 87° = 180°

m<B = 180° - 87°

m<B = 93°

The height of the stand is 15 inches

The formula for determining the volume of a right triangular pyramid is expressed as;

V = 1/3 BA × h

Given that the parameters are;

To determine the base area, we have;

Base area = 1/2  × 81

Base area = 40. 5 in²

Substitute the values

202. 5 = 1/3 × 40. 5 × h

Divide  the values

202. 5 = 13. 5h

Make 'h' the subject of the formula, we have;

h = 15 inches

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Answer:

it should be the 5th one because it shows defencicy

Step-by-step explanation:

from what i know