Consider the sequence shown.

436, 218, 109, 54.5, 27.25,...



Select the correct explicit formula for the sequence.

a
g_n=0.5·436^{(n-1)}

b
g_n=436·2^{(n-1)}

c
g_n=436·0.5^{(n-1)}

d
g_n=2·436^{(n-1)}

The angular displacement of each vehicle is θ = 693.4rad.

The angle at which a point revolves around a particular axis or center defines the angular displacement of a body.

Because a body rotates about its axis, its motion cannot simply be analyzed as a particle because it is constantly altering its speed and acceleration.

So, the angular displacement can be calculated as follows:
\(\begin{aligned}& \theta=\omega_0 t+\frac{1}{2} \alpha t^2 \\& \omega_0=\frac{v_0}{R}=\frac{20.0 \mathrm{~m}^{\mathrm{s}}}{0.300 \mathrm{~m}}=66.67 \mathrm{rad} / \mathrm{s} \\& \alpha=\frac{a_T}{R}=\frac{1.50 \mathrm{~m} / \mathrm{s}^2}{0.300 \mathrm{~m}}=5.00 \mathrm{rad} / \mathrm{s}^2\end{aligned}\),

Calculate further as follows:
\(\begin{aligned}& \theta=\omega_0 t+\frac{1}{2} \alpha t^2=(66.67 \mathrm{rad} / \mathrm{s})(8.00 \mathrm{~s})+\frac{1}{2}\left(5.00 \mathrm{rad} / \mathrm{s}^2\right)(8.00 \mathrm{~s})^2 \\& \theta=(66.67 \mathrm{rad} / \mathrm{s})(8.00 \mathrm{~s})+\frac{1}{2}\left(5.00 \mathrm{rad} / \mathrm{s}^2\right)(8.00 \mathrm{~s})^2=693.4 \mathrm{rad}\end{aligned}\)

Therefore, the angular displacement of each vehicle is θ = 693.4rad.

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Correct question:
A car is traveling with a speed of 20.0 m/s along a straight horizontal road. The wheels have a radius of 0.300 m. If the car speeds up with a linear acceleration of 1.50 m/s2 for 8.00 s, find the angular displacement of each wheel during this period.

Answer:

334 in^2.

Step-by-step explanation:

The surface area = area of the top prism + area of the bottom - 2 * area of the base of the  top smaller prism

= 2(5*3 + 5*3 + 3*3) + 2(9*7 + 9*5 + 7*5) -  2* 3*5

= 2* 39 + 2*143 - 30

= 334

Answer:

Step-by-step explanation:

7x - 44 = 4x + 4

3x - 44 = 4

3x = 48

x = 16

7(16) - 44 = 112 - 44 = 68

4(16) + 4 = 64 + 4 = 68

8y - 43 + 39 = 180

8y - 4 = 180

8y = 184

y = 23

8(23) - 43 = 184 - 43 = 141

The missing term in the equation (x + 9)² = x² + 18x + is 81. The simplified form of the (x + 9 )² = x² + 18x + 81. The correct option is C.

Given

(x + 9)² =  x² + 18x +----

Required to find the missing term =?

It is given the form of ( a + b)² = a² + 2ab + b²

Putting the given values in the above form we get the value of the missing term from the equation

(x + 9 )² = x² + 2 × x ×9 + 9 × 9

              = x² + 18x + 81  

A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.

Thus, we get the value of the missing term as 81.

Thus, the ideal selection is option C.

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Answer:

y=1/2x-4

Step-by-step explanation:

subtract 4x from the left side and the right side. It becomes:

-8y=-4x+32

divide -8 from both sides and it becomes:

y=1/2x-4

Answer

2890

Step-by-step explanation:

2,890 meters^2 is grass

Step-by-step explanation:

First find the area of the garden

Area of a rectangle can be found using:

a=lw

a=85*50

a=4,250 meters^2

We know that 32% of the area is flowers, so we can multiply 32% and 4250

32%*4250

Convert 32% to a decimal by dividing by 100

32%/100=0.32

0.32*4250=1360

So, 1360 meters^2 is flowers.

The rest must be grass, so we can find the difference between the total area and the flowers

4250-1360=2890

The answer is closest to option 4 \(1,260 mm^3\)is not a close approximation of the actual volume of the figure.

Volume is a measure of the amount of space occupied by an object or a substance. It is a three-dimensional quantity that is usually expressed in cubic units, such as cubic meters (m^3), cubic centimeters (cm^3), or cubic feet (ft^3).

This figure appears to be a cylinder with a cone on top of it. To find the volume of this figure, we need to find the volumes of the cylinder and the cone separately, and then add them together.

First, let's find the volume of the cylinder. We can use the formula for the volume of a cylinder:

\(V_{cylinder }= \pi r^2h\)

where r is the radius of the base of the cylinder and h is the height of the cylinder.

From the image, we can see that the height of the cylinder is 6 mm, and the radius of the base is half of the diameter, which is 4 mm. So, we have:

\(V_{cylinder} = \pi (4 mm)^2(6 mm)\\V_{cylinder } = 301.44 mm^3\)

Next, let's find the volume of the cone. We can use the formula for the volume of a cone:

\(V_{cone} = (1/3)\pi r^2h\)

where r is the radius of the base of the cone and h is the height of the cone.

From the image, we can see that the height of the cone is 4 mm, and the radius of the base is also 4 mm. So, we have:

\(V_{cone} = (1/3)\pi (4 mm)^2(4 mm)\\V_{cone} = 67.02 mm^3\)

Finally, we can find the total volume of the figure by adding the volume of the cylinder and the volume of the cone:

\(V_{total} = V_{cylinder} + V_{cone}\\V_{total} = 368.46 mm^3\)

Rounding this answer to the nearest whole number, we get:

\(V_{total} = 368 mm^3\)

Therefore, the answer is closest to option 4: \(1,260 mm^3\) is not a close approximation of the actual volume of the figure.

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Answer: 12500 gallons

Step-by-step explanation:

Number of mobile homes in a trailer park = 50

Gallons of water used by each mobile home = 250 gallons

The amount of water used by the trailer park uses in one day will be:

= Number of mobile homes in the trailer park × Gallons of water used by each mobile home

= 50 × 250

= 12500 gallons

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

The answer is D, or the bottom one.

\(\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.\)  is equivalent to \(\left \{ {{35x^2+42y^2 = 350} \atop {-35x^2-10y^2=-50}} \right.\).

An equivalent relation of \(\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.\)  is to determine.

Relation between two values is defined as the how the value associate with others.

Here,
⇒  \(\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.\)  
⇒ multiply by 7 in first equation and by -5 in second equation.

⇒ \(\left \{ {{35x^2+42y^2 = 350} \atop {-35x^2-10y^2=-50}} \right.\)

Thus, \(\left \{ {{5x^2+6y^2=50} \atop {7x^+2y^2=10}} \right.\)  is equivalent to \(\left \{ {{35x^2+42y^2 = 350} \atop {-35x^2-10y^2=-50}} \right.\).

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Answer:

$18

Step-by-step explanation:

If she starts with $50 and has $32 left when she's done then. 50-32= 18

So she spent $18 on clothing.

Answer:

y=−2x−15

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

3(5+12) (taking the common between the two numbers)

3(17)

51

brainliest please

Hence the average rate of change, in simplest form is -10 .

What is average rate of change?

Using the coordinate points from the table  ( 4,53) ( 8, 13 )

Substitute the coordinate into the expression

Average rate of change  = y₂ - y₁/x₂ - x₁

                                         = 13 - 53/8 - 4                    

                                         = -  4 0/4 ⇒ -10

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Given:

The polynomial is:

\(3x^4-5x+7\)

To find:

The degrees and determine whether it is a monomial, binomial, or trinomial.

Solution:

We have,

\(3x^4-5x+7\)

The highest power of the variable x in the given polynomial is 4. So, the degree of the polynomial is 4.

Monomial: Polynomial with one term.

Binomial: Polynomial with two terms.

Trinomial: Polynomial with three terms.

In the given polynomial, we have three terms \(3x^4,-5x,7\). So, the given polynomial is trinomial.

Therefore, the degree of the polynomial is 4 and it is a trinomial.

The new coordinate of the points after the dilation will be (3, 5).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The point is (6, 10). And the scale factor is 1/2. Then the new coordinate of the points after the dilation is given as,

⇒ (1/2)(6, 10)

⇒ (1/2 x 6, 1/2 x 10)

⇒ (3, 5)

The new coordinate of the points after the dilation will be (3, 5).

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Answer:

the larger one is 105º

the smaller one is 75º

x=11

Step-by-step explanation:

9x+6+6x+9=180

15x+15=180

15x=165

x=11

9(11)+6=106

6(11)+9=75

Answer:

x = 11

Step-by-step explanation:

the larger one is 105º

the smaller one is 75º

x = 11

Answer:

The area of the black portion = 219.752280681013 cm²

Step-by-step explanation:

the canvas has the shape of a square

with sides of length 8×4 = 32 cm

Then

• The area of the canvas

= 32²

= 1024 cm²

•• The area of the four circles

= 4×(π×8^2)

= 804.247719318987 cm²

••• The area of the black portion

= 1 024 - 804.247719318987

= 219.752280681013 cm²

The statement "secondary data should be gathered first because this type of information is less expensive to obtain" is actually false because it has already been collected, there are some important factors to consider.

Primary data is data that is collected specifically for the purpose of the research project at hand. This type of data can include surveys, interviews, experiments, and observations. On the other hand, secondary data is data that has already been collected by someone else for a different purpose.

Firstly, it's important to consider the quality of the data. Secondary data may not always be reliable or up-to-date, which could impact the accuracy of your research findings. In some cases, you may need to spend time and resources verifying the accuracy of the secondary data, which could end up being more expensive in the long run.

Additionally, it's important to consider the specific needs of your research project. Depending on your research question, primary data may be necessary to obtain the specific information you need. In other cases, secondary data may be sufficient.

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Answer:d

Step-by-step explanation:

The answer is d. None of the above is true.

To calculate velocity, we need to use the equation:

Velocity = M * P / Y

Given:

M = 1,000

P = 2.25

Y = 2,000

Plugging in the values:

Velocity = 1,000 * 2.25 / 2,000

Simplifying:

Velocity = 2.25 / 2

The result is:

Velocity = 1.125

Therefore, the correct answer is: d. None of the above is true.

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Answer:

It is 25

Step-by-step explanation:

If the equation is 4/5 x n = 20, you will find the answer by dividing because its the opposite of multiplication.

\(20/\frac{4}{5} = 20x5/4=\\24\)

The answer is 25

I hope this helps :3

For Mrs. Robinson to use the prism to fill the pyramid, she needs to fill the prism 3 times.

Volume is the amount of space occupied by a three dimensional shape or object.

For a pyramid and prism with the same height and base, the volume of the pyramid is one third the volume of the prism.

Hence, for Mrs. Robinson to use the prism to fill the pyramid, she needs to fill the prism 3 times.

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14 ft to 21 ft = 2 ft to 3 ft

Answer:

  A). (0, ∞)

Step-by-step explanation:

The function value is negative where the red line is below the x-axis. That is the case for all values of x that are greater than 0. In interval notation, this is ...

  (0, ∞)

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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On solving the provided question, we can say that, 16 square units make up the area of a circle with a radius of 4 units.

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. Through the center of the circle, a straight line defines the diameter. Half of the diameter is the radius. End in the circle's center after beginning at one of its points.

Pi times the radius squared equals the area of a circle (A = π r²). Learn how to apply this equation to determine a circle's area given its diameter.

16 square units make up the area of a circle with a radius of 4 units.

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The inverse of matrix B is:

     25   -560

     -1     23

To find the inverse of matrix B, we need to perform a series of operations. First, we calculate the determinant of B, denoted as |B|. In this case, |B| = (23 * 0) - (1 * 560) = -560.

Next, we need to find the adjugate of B, denoted as adj(B). The adjugate of a matrix is obtained by taking the transpose of the cofactor matrix. In this case, the cofactor matrix of B is:

      0     560

     -1     23

Taking the transpose of the cofactor matrix gives us the adjugate:

      0    -1

    560    23

Finally, we can find the inverse of B by dividing the adjugate by the determinant:

     0    -1

    -560/(-560)    23/(-560)

Simplifying the fractions, we get:

     0     -1

     1    -23/560

Therefore, the inverse of matrix B is:

     25   -560

     -1     23

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