Write an explicit formula for an, the n^th term of the sequence
2,−8,32,....

Answer:

The irrational numbers are:

368.5468432...

14.19274128...

√.156

The values for the cosine and cotangent functions for the angle x is

O cos0 = -√2/2, cot0 =-1

Let the angle be x

given that the point [ -√2/2, √2/2] is on the terminal ray of angle x

the x-coordinate of the point is -√2/2 and this is the cos hence

cos x = -√2/2.

To find the cotangent

the y coordinate is the sin therefore sin x = √2/2

tan x = sin x / cosx = (√2/2) / (-√2/2) = -1

and cotangent is the reciprocal of the tangent

cot x = 1 / tan x = -1/1 = -1.

cos x = -√2/2 and cot x = -1.

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The required posterior mean prevalence is closest to 0.47.

We can use Bayes' theorem to find the posterior distribution of the prevalence parameter, given the data and the Beta prior:

posterior ∝ likelihood x prior

where the likelihood is given by the binomial distribution:

likelihood = P(observing 4 cases out of 10 | prevalence)

and the prior is a Beta distribution with parameters α = β = 10:

prior = Beta(α=10, β=10)

We can calculate the posterior distribution by multiplying the likelihood and prior, and then normalizing:

posterior = Beta(α=14, β=16)

where the posterior Beta distribution has parameters α=14 (10 + 4) and β=16 (10 + 10 - 4).

The posterior mean of a Beta distribution with parameters α and β is:

posterior mean = α / (α + β)

Plugging in the values of α and β from the posterior distribution, we get:

posterior mean = 14 / (14 + 16) = 0.467

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Answer:

The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:

3(1), 3(2), 3(3), 3(4), 3(5), 3(6)

which simplify to:

3, 6, 9, 12, 15, 18

The sum of these terms is:

∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63

Therefore, S6, the sum of the first 6 terms of the series, is 63.

Answer:

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

Given system:

Add up the two equations to get same coefficient on both variables:

As we see none of the choices match the answer. It means either question or answer choices are inaccurate.

Answer:

7/25

Step-by-step explanation:

0.28 = 28/100 = 7/25

The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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The percentage of the sodas that was served which were regular would be = 18%

The quantity of regular sodas served = 18

The quantity of diet soda served = 82

The total number of soda served = 18+82 = 100

Therefore the percentage of soda that were regular would be;

= 18/100 × 100/1

= 18%

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Answer:

Step-by-step explanation: bot

Answer:

a

Step-by-step explanation:

If a₁ = 9 and sequence aₙ = -3aₙ₋₁ , then the value of a₅ is approximately equal to 729.

To find the value of a₅, we need to use the recursive formula provided, which relates each term in the sequence to the previous one. The formula given is a bit unusual, as it defines each term in terms of the negative three times the previous term. However, we can use this information to work out the value of a₅.

Starting with a₁ = 9, we can use the recursive formula to find the next few terms of the sequence:

a₂ = -3a₁ = -3(9) = -27

a₃ = -3a₂ = -3(-27) = 81

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

Therefore, the value of a₅ is 729. We can check that this is correct by verifying that it satisfies the given recursive formula:

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

This confirms that our solution is correct.

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The simplification of the fractions given above through multiplication would be;

1.) 9 11/12

2.) 11 19/40

For question 1.)

2 5/6 × 3 2/4

Change the mixed fraction to single fraction;

= 17/6 × 14/4

= 17/6 × 7/2

= 119/12

= 9 11/12

For question 2.)

5 2/5 × 2 1/8

= 27/5 × 17/8

= 459/40

= 11 19/40

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Answer:

69

Step-by-step explanation:

(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)

x - 28 = 41

x = 69

The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' is given as follows:

A rotation followed by a translation.

Examples of transformations are given as follows:

For this problem, we have that the inclination of the figure changed, and the figure moved from the second quadrant to the first/fourth, hence the figure underwent a rotation of 90º counterclockwise about the origin.

The figure also had the vertices changed from the rotation, hence a translation was also applied.

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The displacement of the particle at time t is 11t - t², and the total distance traveled by the particle in 2 seconds is 9 meters.

The displacement of a particle moving along a straight line can be calculated by finding the area under the velocity-time graph. In this case, the velocity function is v(t) = 11 - 2t for 0 ≤ t ≤ 2.

To find the displacement at time t, we need to find the area under the velocity-time from t = 0 to t = t. The formula for displacement is the integral of the velocity function with respect to time:

s(t) = ∫v(t) dt = ∫(11 - 2t) dt = 11t - t²

Therefore, the displacement of the particle at time t is given by s(t) = 11t - t².

To find the total distance traveled by the particle in 2 seconds, we need to consider both the forward and backward motion. Since the velocity is decreasing at a constant rate of 2 m/s², the particle will come to rest at t = 11/2 seconds.

The total distance traveled by the particle in 2 seconds is given by:

d(2) = ∫|v(t)| dt =  [tex]\int\limits^{11/2}_0[/tex] v(t) dt + [tex]\int\limits^2_{11/2}[/tex]|v(t)| dt from 11/2 to 2

= [[tex]\int\limits^{11/2}_0[/tex](11t - t²) ] + [[tex]\int\limits^2_{11/2}[/tex](-11t + t²) ]

= (121/2 - 121/4) + (4 - 121/2) = 9 meters

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If Group of students conducted an investigation to learn about "pea-plants", then the "independent-variable" is  "Water-per-day (mL)".

The "Independent-Variable" is defined as a variable which is controlled by the researcher.

In the investigation of the "pea-plants", the amount of water per day (mL) given to the plants is the independent variable because it is the variable that is intentionally varied by the students.

The students are manipulating the amount of water given to each plant to observe the effect it has on the height of the plant after two weeks.

By controlling the amount of water given to each plant, the students can determine whether there is a relationship between water intake and plant growth.

Therefore, water given to plants per-day will be the "independent-variable".

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The given question is incomplete, the complete question is

Group of students conduct an investigation to learn more about pea plants. Their data are summarized below.

Plant      Water per day (mL)        Height after 2 weeks (cm)

  1                     20                                          11

 2                     50                                          18

 3                    100                                         24

 4                     20                                          16

Which is the independent variable in the investigation?

Part(A),

The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and right endpoints is approximately 0.231 square units.

Part(B),

The estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.

To estimate the area under the graph of f(x) = 1/(x²+1) over the interval [3, 5] using four rectangles and right endpoints, we can use the following formula:

[tex]R_n = \dfrac{(b-a)}{n} \times [f(x_1) + f(x_2) + ... + f(x_n)],[/tex]

where a = 3, b = 5, n = 4, and xi = a + i(b-a)/n for i = 0, 1, 2, ..., n.

Using this formula with the right endpoints, we get:

[tex]R_4 = \dfrac{(5-3)}{4 }\times [f(3.5) + f(4) + f(4.5) + f(5)][/tex]

R₄ = (1/2) x [0.361 + 0.250 + 0.178 + 0.132]

R₄ = 0.231

Hence, the estimated area under the f(x) graph utilizing four rectangles and the right endpoints over the range [3, 5] is about 0.231 square units.

To repeat the approximation using left endpoints, we can use the following formula:

[tex]L_n = \dfrac{(b-a)}{n} \times [f(x_0) + f(x_1) + ... + f(x_{n-1)],[/tex]

where [tex]x_i = a + i\dfrac{(b-a)}{n}[/tex] for i = 0, 1, 2, ..., n-1.

Using this formula with left endpoints, we get:

[tex]L_4 = \dfrac{(5-3)}{4} \times [f(3) + f(3.5) + f(4) + f(4.5)][/tex]

L₄ = (1/2) x [0.250 + 0.361 + 0.250 + 0.178]

L₄ = 0.2405

Therefore, the estimated area under the graph of f(x) over the interval [3, 5] using four rectangles and left endpoints is approximately 0.2405 square units.

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Answer:

The artist used 1680 colored squares of glass.

Answer:

The correct answer is 98°.

Answer: 82

Step-by-step explanation: all the angles of the triangle have to add up to 180 you all up the other angles and you get 98. 98= angle A your trying to find the outside angle we know that a line equals 180 degrees therefore we subtract that angle from 180 and get 82 which is your answer

The length of cable in the coil that weighs 5 1/2 kilograms is 1/2 meter.

Let x be the length of cable in meters that weighs 5 1/2 kilograms.

Then, we can write:

1 meter / (75/1000) kilograms = x meters / 5.5 kilograms

Simplifying the left side, we get:

1 meter / (75/1000) kilograms = 1000 / 75 meters/kilogram

= 40/3 meters/kilogram

Substituting this into our proportion, we get:

40/3 meters/kilogram * x meters = 5.5 kilograms

Multiplying both sides by 3/40, we get:

x meters = (5.5 kilograms) * (3/40) * (40/3 meters/kilogram)

               = 1/2 meter

The length is 1/2 meter

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Answer:

Pre-algebra is a fundamental branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division, and introduces concepts like variables, equations, and inequalities. Here are some general steps to solve pre-algebra problems:

1. Identify the problem: Read the problem carefully and identify what it is asking you to do. Identify the key information and any variables that are given.

2. Translate the problem: Translate the problem into an equation or inequality, using variables to represent unknown quantities.

3. Solve the equation or inequality: Use algebraic manipulation to solve for the variable. Follow the order of operations and simplify the expression as much as possible.

4. Check your answer: Verify that your solution is correct by plugging it back into the original equation or inequality and making sure that it satisfies the conditions of the problem.

It's important to practice pre-algebra problems regularly to develop your problem-solving skills. You can find practice problems and tutorials online or in textbooks, and you can work with a tutor or teacher to get additional help. Remember to stay patient, focused, and positive, and don't be afraid to ask for help if you need it.

The value of x is 5.48 units

Let us assume that the left right triangle be ABC and the right triangle on the right side be ABD.

So, the larger right triangle would be DAC.

Consider thr outer right triangle DAC.

The length of the hypotenuse DC would be,

DC = CB + BD

DC  = 3 + 7

DC = 10 units

Also right triangle ABC and DAC are similar triangles.

We know that the sides of the smilar triangles are in proportion.

Using the definition of similar triangles for DAC and ABC,

DA/AB = AC/BC = DC/AC

Consider, AC/BC = DC/AC

x/3 = 10/x

this is the required proportion.

x² = 3 × 10

x² = 30

x = 5.48 units

Thus the value of x = 5.48 units

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The area of each square would be 36 square inch.

We have,

Area of sheet = 12 square inches

So, the area of square to be cut

= 12in × 12in

= 144 square in

Now, number of squares=4

So, area of each square =144÷4

                                        =36 square inches

Thus, the side of each square is

= 36/4

= 6 inch

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Answer:

To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:

miles per gallon = distance traveled / amount of gas used

distance traveled = 456 miles

amount of gas used = 12 gallons

miles per gallon = 456 miles / 12 gallons

miles per gallon = 38 miles/gallon

Therefore, Jodi's car traveled 38 miles per gallon of gas.

Answer:

38 miles

Step-by-step explanation:

Set up your division: 456 / 12

456 divided by 12 is 38

So, Jodi's car travels at 38 miles per gallon of gas.

Answer:

AB = (20/√2)(√2/√2) = 10√2

The diameter of the circle is 16.04 cm.

The circumference is 50.39 cm

A = πr²

where A is the area of the circle and r is its radius.

square both sides

r = √(A/π) = √(201.06/π) = 8.02 cm

The diameter of the circle is twice the radius, so we can find it by multiplying the radius by 2:

d = 2r = 2(8.02) = 16.04 cm

Therefore, the diameter of the circle is 16.04 cm.

To find the circumference of the circle, we can use the formula:

C = 2πr

where C is the circumference and r is the radius. We already know the value of the radius, so we can substitute it into the formula:

C = 2π(8.02) = 50.39 cm

Therefore, the circumference of the circle is 50.39 cm.

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The coordinates best represent the vertex of the graph is given by (1, -2).

Hence the correct option is (D).

Graph is a pictorial representation of a curve or a function or a relation.

From the given graph we can see that the curve is an upward parabola which has vertex at a point other than origin.

We can see that where the vertex is formed the value along X axis is 1 and the value along Y axis is -2 (towards down).

So the vertex of the given graph is at (1, -2).  

Hence the correct option will be (D).

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The solution of the triangle have been shown below.

To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.

Given that;

a/Sin A = b/SinB

Sin B = bSin A/a

B = Sin-1(bSin A/a)

B = Sin-1 (23Sin 40/17)

B = 60.4 degrees

Then we have that

C = 180 - (40 + 60.4)

= 79.4 degrees

Then;

a/sinA = c/Sin C

c= aSin C/Sin A

c = 17 * Sin 79.4/Sin 40

c =   16.71/0.643

c = 25.9

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