write an explicit formula for an the nth term of the sequence 6, 12, 18

Answer:

y = -5x + 29

Step-by-step explanation:

Slope-Intercept Form of the Line

Given a line of slope m and y-intercept b, the equation of the line can be written as:

y = mx + b

The slope can be calculated by using the formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Where (x1,y1) and (x2,y2) are the points through which the line passes.

We are given the points (5,4) and (6,-1), thus:

\(\displaystyle m=\frac{-1-4}{6-5}=\frac{-5}{1}=-5\)

Now we use one of the points to find the value of b, for example (5,4):

4 = -5(5) + b

b = 25+4 = 29

Thus, the equation of the line is:

y = -5x + 29

The vectors in R4 of length 5 that make an angle of 45◦ with the positive y-axis and 60◦ with the negative x-axis can be written as \($\vec{v} = \left(\frac{\sqrt{25}}{\sqrt{3+2w^2}}\sqrt{3}, \frac{\sqrt{25}}{\sqrt{3+2w^2}}, -\frac{\sqrt{25}}{\sqrt{3+2w^2}}, \pm \sqrt{\frac{25-3y^2}{2y^2}}\right)$\).

A vector in R4 making an angle of 45◦ with the positive y-axis and 60◦ with the negative x-axis can be written as:

\($\vec{v} = (v_1, v_2, v_3, v_4) = (x, y, -z, w)$\)

where \($x = y\tan60° = y\sqrt{3}$ and $z = y\tan45° = y$\)

The length of the vector is:

\($|\vec{v}| = \sqrt{x^2 + y^2 + z^2 + w^2} = \sqrt{y^2\left(\sqrt{3}^2 + 1^2 +1^2 + w^2\right)} = \sqrt{y^2\left(3 + 2w^2\right)} = 5$\)

Therefore, \($y^2\left(3 + 2w^2\right) = 25$\)

Solving for y and w,

\($y = \frac{\sqrt{25}}{\sqrt{3+2w^2}}$\\\\$w = \pm \sqrt{\frac{25-3y^2}{2y^2}}$\)

Therefore, the required vector is:

\($\vec{v} = \left(\frac{\sqrt{25}}{\sqrt{3+2w^2}}\sqrt{3}, \frac{\sqrt{25}}{\sqrt{3+2w^2}}, -\frac{\sqrt{25}}{\sqrt{3+2w^2}}, \pm \sqrt{\frac{25-3y^2}{2y^2}}\right)$\)

Thus, all the vectors in R4 of length 5 that make an angle of 45◦ with the positive y-axis and 60◦ with the negative x-axis can be written in the form of the vector \($\vec{v}$\) as given above.

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Since the triangle is a right triangle , We can apply the trigonometric function.

Sin θ = opposite side / hypotenuse

Where the hypotenuse is the longest side of the triangle (32) and the opposite side to θ is 23.

Replacing:

Sin θ = 23/32

Solve for θ

θ = arc sin 23/32

θ = 45.95°

Answer:

5/6 quarts of water

Step-by-step explanation:

2/3 same as 4/6. 4/6 + 1/6 = 5/6

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

The conclusion about angles B and C is that the angles are equal angles

How to determine the true statement?

The given parameters are:

Angle A and Angle B are supplements

Angle A and Angle C are supplements

Supplementary angles add up to 180 degrees.

This means that

A + B = 180

A + C = 180

Subtract the two equations

So, we have

A - A + B - C = 180- 180

Evaluate the like terms

So, we have

B - C = 0

Add C to both sides

B = C

Hence, both angles are congruent angles

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Answer:

16.2

Step-by-step explanation:

because 3x2=6

I AM SOOOO SORRY IF I GET IT WRONG

To find the exact value of (7π/6) using the unit circle, locate the angle (π/6) on the unit circle in the second quadrant, determine the coordinates, and adjust the y-coordinate to be negative. The final answer is (√3/2, -1/2). This answer is obtained by understanding the reference angle and using the coordinates of the point where the angle intersects the unit circle.

To find the exact value of (7π/6) using the unit circle, follow these steps:

1. Start by understanding the reference angle. The reference angle for (7π/6) is (π/6).

2. Locate the angle (π/6) on the unit circle. This angle lies in the second quadrant.

3. Determine the coordinates of the point where the angle intersects the unit circle. For (π/6), the x-coordinate is √3/2 and the y-coordinate is 1/2.

4. Since (7π/6) lies in the second quadrant, the x-coordinate will remain the same, but the y-coordinate will be negative. Therefore, the coordinates for (7π/6) are (√3/2, -1/2).

5. The exact value of (7π/6) is (√3/2, -1/2).

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

8

Step-by-step explanation:

bResponses

y = 8

y, = 8

y = 3

y, = 3

y=−3

Answer:

(d) 18 in.

Step-by-step explanation:

When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:

P = s1 + s2 + s3, where

P = 2 + 6 + 10

P = 8 + 10

P = 18

Thus, the perimeter of the triangle is 18 in.

Answer:

Step-by-step explanation:

add 12 for every hour  and to find the answer 12 times 7

it will be 4:00p.m when they have 84.

hope this helps

Answer:

mid point is 31

Step-by-step explanation : why? because if take what ae equals which is 31.

the correct answer is 31.

Answer: the correct answer is 31.

Step-by-step explanation:

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

A reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.

In the given image, one of the figures is a reflection image of the other.

Hence, the correct statement is:

One figure is a reflection image of the other

1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

We have,

To calculate the amount of barbed wire needed to fence the circular piece of land, we need to find the circumference of the circle.

Given:

Radius (r) = 25 cm

The formula for the circumference (C) of a circle is:

C = 2πr

Substituting the given radius into the formula, we have:

C = 2π x 25 cm

Now, we can calculate the circumference in centimeters.

C = 2 x 3.14 x 25 cm

C ≈ 157 cm

Now,

To convert centimeters to meters, we divide the circumference by 100.

C (in meters) = 157 cm / 100

C (in meters) ≈ 1.57 meters

Therefore,

Approximately 1.57 meters of barbed wire are needed to fence the circular piece of land with a radius of 25 cm.

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The complete question.

A circular piece of land with a radius of 25 cm is going to be fenced. How many meters of barbed wire are needed?

Step-by-step explanation:

I hope you are 100% clear.

Given:

Sol:.

Answer:

r = 6

Step-by-step explanation:

34 = 7r - 8

+8 .       +8  

42 = 7r

__ .  __

7 .     7

6 = r  

Answer: C,D

Step-by-step explanation

Answer:

C and F

Step-by-step explanation:

Answer:

3/85

Step-by-step explanation:

that's the answer above

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

144

Step-by-step explanation:

This means that 5% of the 10-1/2-month-old baby boys in the reference population weigh 16.7 pounds or less, and 95% of these baby boys weigh 16.7 pounds or more.

The determination is based on the definition of a percentile. A percentile is a value below which a certain percentage of the data falls. So, in this case, if a weight of 16.7 pounds is at the 5th percentile for 10-1/2-month-old baby boys, then 5% of the baby boys in the reference population have a weight of 16.7 pounds or less. This also means that the remaining 95% of the baby boys in the reference population have a weight of more than 16.7 pounds.

The calculation of percentiles is based on the ranking of the data set. The data is first sorted in ascending order and then divided into 100 equal parts, with each part representing a percentile. The value at each percentile is the value below which a certain percentage of the data falls.

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Answer:

(6 times n) - 5 = 8

Step-by-step explanation:

First we need to multiply 6 by a number and then subtract 5 from the total which will then equal to 8

Answer:

y = 1/405 x² + 25

101 feet

Step-by-step explanation:

The vertex of the parabola is (0, 25).

The equation of the parabola is:

y − 25 = a (x − 0)²

y = ax² + 25

Two points on the parabola are (-225, 150) and (225, 150).

Plugging in one of those points:

150 = a (225)² + 25

125 = 50625 a

a = 1/405

The equation is therefore:

y = 1/405 x² + 25

50 feet from a tower is 175 feet from the center.

y = 1/405 (175)² + 25

y ≈ 101

Answer:

Design 1: 151.19≤x≤160.37

Design 2: 152.46≤x≤155.88

Step-by-step explanation:

Confidence interval formula is expressed as;

CI = xbar ± Z×σ/√n

xbar is the mean of the sample

σ is the standard deviation

n is the sample size

z is the z score at 80% confidence level

For Design 1:

158.5 138.4 168.1 149.4 145.8 168.7 154.4 162.9

xbar = Sum of the samples/sample size

Sum of samples = 158.5+ 138.4+ 168.1+149.4+ 145.8+ 168.7+ 154.4+ 162.9

Sum of samples = 1246.2

Sample size = 8

xbar = 1246.2/8

xbar = 155.78

Standard deviation

σ = √\sum(x-xbar)²/N

σ = (158.5 - 155.775)² + ... + (162.9 - 155.775)²/8

= 821.075/8

= 102.634375

= √102.634375

= 10.13

σ = 10.13

CI = 155.78±(1.282×10.13/√8)

CI = 155.78±(1.282×3.5815)

CI = 155.78±(4.5915)

CI = {155.78-4.5915, 155.78+4.5915}

CI = {151.19, 160.37}

The range for the true mean is 151.19≤x≤160.37

For Design 2:

150.3 155.4 151.6 158.8 151.4 150.8 161.4 157.6 156.8 147.6

xbar = Sum of the samples/sample size

Sum of samples = 150.3+ 155.4+ 151.6+158.8 +151.4+ 150.8+ 161.4 +157.6+ 156.8 +147.6

Sum of samples = 1541.7

Sample size = 10

xbar = 1541.7/10

xbar = 154.17

Standard deviation

σ = (150.3 - 154.17)²+ ... + (147.6 - 154.17)²/10

σ = 177.681/10

σ = 17.7681

σ = √17.7681

σ = 4.22

CI = 154.17±(1.282×4.22/√10)

CI = 154.17±(1.282×1.3345)

CI = 154.17±(1.7108)

CI = {154.17-1.7108, 154.17+1.7108}

CI = {152.46, 155.88}

The range for the true mean is 152.46≤x≤155.88