f(n)=5*(-2)^n-1. Complete the recursive formula for f(n).

Answer:

To perform the matrix operations, we need to ensure that the dimensions of the matrices match. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.

A is a row matrix with 1 row and 3 columns, while B is a matrix with 2 rows and 2 columns. Since the number of columns in A does not match the number of rows in B, we cannot calculate AB.

However, we can perform CA since C has 3 rows and 2 columns, which matches the dimensions for left multiplication by A (a 1x3 matrix).

C = 2 2 0

2 3 3

4 0 1

A = 3 2 1

CA = (3)(2) + (2)(2) + (1)(4) (3)(2) + (2)(3) + (1)(0)

(3)(2) + (2)(3) + (1)(0) (3)(2) + (2)(0) + (1)(1)

(3)(0) + (2)(3) + (1)(1) (3)(0) + (2)(3) + (1)(1)

CA = 14 12

12 7

7 9

Therefore, CA = 14 12

12 7

7 9

For simplicity, let's use common denominators.

1/2 = 3/6

So, let's first figure out the fractional value of the water added. We can accomplish this by taking the resulting amount and subtracting the initial amount of water.

3/6 - 1/6 = 2/6

2 gallons = 2/6 of the tank

Next, let's figure out how many gallons will fill 1/6 of the tank.

2 gallons = 2/6 of the tank

1 gallon = 1/6 of the tank

Now that we know how many gallons 1/6 of the tank is, we can figure out how many gallons 6/6 of the tank is.

1 gallon = 1/6 of the tank

6 gallons = 6/6 of the tank

Answer: The total capacity of the aquarium tank is 6 gallons.

Hope this helps!

Between each of the integers, 0, 1, 2, 3, etc., the space is divided into 6 units. We can use this to our advantage.

Since 1/2 = 2/4 = 5/10 = 3/6 = ....., thus:

2 1/2 = 2 3/6. Now we can easily plot points on the number line.

2 3/6 = 2 units and 3 sub units.

1 5/6 = 1 unit and 5 sub units

Check the attached image to see the graphical solution of the question!

Hope that helps!

Answer:

Step-by-step explanation:

Range is largest value - smallest value. 12-3=9! EZ

Rounding to the nearest hundredth, the debt of Country G after 15 years would be approximately $14.89 billion dollars.

How to solve the question?

The given equation for the debt of Country G is A = 18.5(0.995), where A represents the debt after one year, and the factor of 0.995 represents the decay factor. To estimate the debt after 15 years, we can use this equation iteratively.

After the first year, the debt would be A = 18.5(0.995) = 18.4 billion dollars. To find the debt after the second year, we can use the same equation, but replace the initial debt of 18.5 billion dollars with the debt after one year, which is 18.4 billion dollars. Therefore, the debt after two years would be A = 18.4(0.995) = 18.3 billion dollars.

We can repeat this process for each subsequent year, using the previous year's debt to calculate the next year's debt. After 15 years, the debt would be:

A = 18.5(0.995)¹⁵

A = 18.5(0.80424)

A = 14.8866 billion dollars

Rounding to the nearest hundredth, the debt of Country G after 15 years would be approximately $14.89 billion dollars.

It's important to note that this estimate assumes that the decay factor remains constant over the 15-year period. In reality, economic and political factors could impact the decay rate and the actual debt of Country G.

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Answer:

Please help me by marking me brainliest

Step-by-step explanation:

To determine which bus is the most consistent, we need to compare the measures of variability for each data set.

The range is the simplest measure of variability, and it is calculated by subtracting the minimum value from the maximum value in the data set. From the given line plots, we can see that Bus 18 has a range of 16 (from 6 to 22), while Bus 47 has a range of 24 (from 4 to 28). Therefore, Bus 18 has a smaller range, which might suggest that it is more consistent.

However, the interquartile range (IQR) is a better measure of variability, as it is less sensitive to extreme values. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) of the data set.

From the given line plots, we can see that Bus 18 has an IQR of 16 (from Q1=10 to Q3=26), while Bus 47 has an IQR of 24 (from Q1=6 to Q3=30). Therefore, Bus 18 has a smaller IQR, which indicates that it is more consistent than Bus 47.

In conclusion, we can determine that Bus 18 is the most consistent based on its smaller IQR. This means that the travel times for Bus 18 students are more tightly clustered around the median than the travel times for Bus 47 students.

Using the measures of variability, it can be concluded that Bus 18 is the most consistent because it has a lower Interquartile Range (IQR) and a lower range in its times.

The most consistent bus can be found by using measures of variability, specifically the range and the interquartile range (IQR). The range is the difference between the highest and lowest values, while the IQR represents the middle 50% of data. In this case, the range of Bus 47 is 24 (28-4) and that of Bus 18 is 16 (22-6). Similarly, the IQR of Bus 47 is 12 (22-10) and 8 for Bus 18 (16-8).

A lower IQR and range indicate more consistency, as the data points are closer together. Therefore, Bus 18 is the most consistent in terms of travel times as it has both a lower range and a lower IQR.

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The length of the rectangular prism will be 13.5 cm.

Given that:

Volume, V = 324 cubic cm

Height, H = 4 cm

Width, W = 6 cm

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as,

V = L x W x H

Then the length of the rectangular prism is calculated as,

324 = L x 6 x 4

324 = 24L

L = 13.5 cm

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The unknown measurements for the triangle are given as follows:

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Considering that the sum of the measures of the angles is of 180º, the missing angle is given as follows:

m < B = 180 - (130 + 12)

m < B = 38º.

Then the relation is given as follows:

sin(130º)/12 = sin(38º)/b = sin(12º)/c

Then the length b is given as follows:

sin(130º)/12 = sin(38º)/b

b = 12 x sine of 38 degrees/sine of 130 degrees

b = 9.6.

The length c is then given as follows:

sin(130º)/12 = sin(12º)/c

c = 12 x sine of 12 degrees/sine of 130 degrees

c = 3.3.

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Answer:

[tex](x+4)^2+(y-4)^2=16[/tex]

Step-by-step explanation:

A tangent is a straight line that touches a circle at only one point.

Since the circle is tangent to both axes, and the center of the circle is in the second quadrant, the center of the circle lies on the line y = -x.

As the circle is tangent to the x-axis, the distance between the center of the circle and the x-axis is equal to the radius of the circle.

Similarly, as the circle is tangent to the y-axis, the distance between the center of the circle and the y-axis is also equal to the radius of the circle.

Therefore, the center of the circle will be 4 units to the left of the y-axis and 4 units up from the x-axis. Therefore, the coordinates of the center are (-4, 4).

[tex]\boxed{\begin{minipage}{5 cm}\underline{Equation of a circle}\\\\$(x-h)^2+(y-k)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(h, k)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Substitute the center (-4, 4) and the radius, r = 4, into the standard equation of a circle:

[tex]\implies (x - (-4))^2+(y-4)^2=4^2[/tex]

[tex]\implies (x+4)^2+(y-4)^2=16[/tex]

Therefore, the equation of the circle that satisfies the given conditions is:

[tex]\boxed{(x+4)^2+(y-4)^2=16}[/tex]

The volume of this sphere is 10976 feet³

It is crucial that we know that the formula that used in calculating the volume of a sphere is expressed with the equation;

V = 4/3 πr3

Given that the parameters in the formula are;

From the given information,

we have that;

Radius = 14 feet

Substitute the values, we have;

Volume = 4/3 × 3.4×14³

Find the cube values, we get;

Volume = 4/3 × 3 × 2744

Multiply the values

Volume = 10976 feet³

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Answer:

To find the critical t-value for a confidence level of 80% with a sample size of 11, we need to consult a t-distribution table or use a statistical software.

Using a t-distribution table with 10 degrees of freedom (sample size - 1), we can find the critical t-value for a two-tailed test at a confidence level of 80%.

From the table, we find that the critical t-value is approximately 1.363.

Therefore, the critical t-value for a confidence level of 80% with a sample size of 11 is approximately 1.363.

Step-by-step explanation:

jew

(a) The amount of square feet of laminate flooring Samantha need to purchase for her kitchen is 268 ft².

(b) The amount of linear trim of feet Samantha need to purchase for her kitchen 80 ft.

Perimeter is the total distance around an plane figure.

(a) To calculate the amount of square feet for laminate flooring, she needed to purchase for her kitchen, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

(b) To calculate the amount of the linear trim of feet needed, we find the Perimeter of the shape

Hence, The amount of linear trim of feet is 80 ft.

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If the average wingspan of monarch butterflies at a butterfly preserve is 8.5. the probability, to t nearest hundredth, that monarch butterflies have a wingspan longer than 8.8 centimeters is : 0.23.

First step is to standardize the value of 8.8 centimeters using the z- score  formula:

z = (x - mu) / sigma

where:

x  = wingspan

mu = mean wingspan

sigma= standard deviation

z  standardized score

Substituting the given values

z = (8.8 - 8.5) / 0.4

z = 0.75

So,

P(z > 0.75) = 1 - P(z <= 0.75)

Using a standard normal distribution table  P(z <= 0.75) = 0.7734

P(z > 0.75) = 1 - P(z <= 0.75)

= 1 - 0.7734

= 0.2266

= 0.23 (  Approximately)

Therefore the probability is 0.23.

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Answer:

[tex]P= 49.2m[/tex], [tex]A=140.4m^2[/tex]

Step-by-step explanation:

The diagonal splits the rectangle into two right triangles so we can use Pythagorean theorem to find the length of the missing side.

Pythagorean theorem states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the other two sides

So we can label our unknown side as x

x^2 + 9^2 = 18^2

x^2 + 81 = 324

Subtract 81 from both sides to isolate the x

x^2 = 243

Find the square root of both sides

√x^2 = √243

x ≈ 15.6

(The instruction said round to the nearest 10th).

So now we know

l = 15.6m and w = 9m

P= 2l + 2w

A= lw

P= 2(15.6) + 2(9)

P= 31.2 + 18

P= 49.2m

A=15.6(9)

A=140.4m^2

The amount that Floyd will be paid each month from this annuity is $6,374.83 each month.

To calculate the monthly payments from a 20-year annuity with an initial investment of $1,000,000 at an APR of 4.6% compounded monthly, we can use the formula for calculating the monthly payment of an ordinary annuity: Monthly Payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Data

P = $1,000,000)

r = 4.6% / 12 / 100 = 0.00383

n = = 20 * 12 = 240

Plugging in the values. The monthly payment will be:

= $1,000,000 * 0.00383 * (1 + 0.00383)^240 / ((1 + 0.00383)^240 - 1)

= $1,000,000 * 0.00383 * 1.66538674279

= $6,378.43122

= $6,378.43

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Answer: To place √31 on the number line, we first need to find its approximate value.

√31 is between 5 and 6 since 5²=25 and 6²=36. To find a more precise value, we can use a calculator or estimate using long division.

Using a calculator, we get:

√31 ≈ 5.56776436

Rounding to tenths, we get:

√31 ≈ 5.6

To place 5.6 on the number line, we can mark the point between 5.5 and 5.7.

Here's a rough sketch of what it might look like:

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         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

         |         |         |         |         |         |         |         |         |         |

Step-by-step explanation:

A. Mean: This measure of central tendency signifies the average value in a dataset, derived by summing each data point and dividing by total quantity.

B. Median: An indicator of central tendency is utilized to discern the middle value for a given set. Primarily, the tabulated elements must be listed from least to greatest before arriving at the average between two centermost figures if the number of components is even.

C. Mode: As an analysis concerning where centrality lies, this technique seeks out the most regularly occurring element in a gathered dataset.

D. Range: The range serves as an assessment of variability measured via the differences between the upper and lower bounds registered within the collection. To calculate, subtract the minimum value from the maximum quota.

E. Interquartile range: Better known as IQR, this method measuring disparity quantifies dissimilarities between the 75th percentile (Q3) and 25th percentile (Q1). To ascertain, subtract Q1 from Q3. Such information is often used to pinpoint irregularities and evaluate the discrepancies among separate datasets.

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The value of standard deviation 's' is 2.08700, as indicated in the display.

Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the average of the squared deviations from the mean, it is the square root of the variance.

The value of s is 2.08700, as indicated in the display.

The symbol "Sx" represents the sample standard deviation, which is commonly denoted as "s". The other values in the display are:

So, the correct answer is 2.08700.

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Answer:

Step-by-step explanation:

Rounding to the nearest tenth, the area of the regular octagon is approximately 282.8

128

With the help of Apollonius theorem, we know that

3(sum of square of sides)=4(sum of square of medians)

3(sum of square of sides)=4×96

sum of square of sides= 4×96/3= 128

Max and Pam will be able to spend $676.1 on their trip.

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Principal P = $600.00

Compounded quarterly n = 4

Time t = 3  years

Interest rate r = 4%

Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year.

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = $600( 1 + 0.04/4 )^( 4 × 3 )

A = $600( 1 + 0.01 )^( 12 )

A = $600( 1.01 )^( 12 )

A = $676.1

Therefore, the accrued amount after 3 years is $676.1.

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Area of the triangle is 56 cm².

What is the area of triangle?

The formula for the area of a triangle is:

[tex]A = \frac{ (base \times height) }{ 2}[/tex]

where A is the area of the triangle and the base is the length of one of its sides and the height is the perpendicular distance between the base and the opposite vertex.

Alternatively for the triangle we can use Heron's formula to calculate the area of a triangle if we know the lengths of all three sides,[tex]A = \sqrt{ (s(s-a)(s-b)(s-c))}[/tex] where A is the area of the triangle, a, b and c are the lengths of the sides and s is the semi-perimeter of the triangle which is half the sum of the lengths of the sides,

[tex]s = \frac{(a + b + c)}{2}[/tex]

Here, it is clear that base of the triangle is 14 cm and height is 8 cm.

Now area of the tria is[tex] \frac{1}{2} \times 14 \times 8 = 14 \times 4 = 56 \: {cm}^{2} [/tex]

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Answer:

integrates by parts:

             U = x   dV = f''

            dU  = dx   V = f'

The integral becomes:

     x f'  - integral f' dx

 =   x  f'  -  f

limit as x->4 :   4 * f'(4) - f(4) = 4 * -3 -  7

                                  = -12-7 = -19

limit as x->1 : 1 * f'(1) - f(1) = 1 * 9 - 8 = 1

subtracting: -19-1 = -20

Step-by-step explanation:

Answer:

Step-by-step explanation:

The correct measurement of the paper clip to the nearest inch is 1 inch.

The graph of the function below y = 9x² - 12x + 4 intersect the x-axis at exactly one point (0.667, 0).

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

In this exercise, we would use an online graphing calculator to plot the quadratic equation in order to determine the x-intercepts as shown in the graph attached below.

Therefore, the x-intercept of the graph of the given quadratic equation y = 9x² - 12x + 4 include the following:

x = (0.667, 0).

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71*8=568

568+379=947

Step-by-step explanation:

The angular velocity of the wheel is 11.74 radians per second and the distance travelled is 2.81 km/min.

The angular velocity is given by the formula rpm×2π/60

Angular velocity = 2 × 3.14 × 112/60

Multiply the numerator followed by division by denominator

Angular velocity = 703.36/60

Angular velocity = 11.72 radians per second

The distance travelled will be given by the formula -

Distance = circumference × revolutions per minute

Distance = 2 × 40 × 3.14 × 112

Multiply the values on Right Hand Side

Distance = 281,227 cm/min

As, 100 cm is 1 m and 1000 m is 1 km, the distance will be 2.81 km/min.

Thus, the angular velocity is 11.72 radians per second and distance is 2.81 km/min.

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The table which most accurately reflects the relationship between the distance traveled and the total cost is table D.

Given that,

A bakery charges $4.50 per delivery, plus $0.40 per mile.

The relationship is between the distance traveled and the total cost.

This is a linear relationship.

Slope = 0.4

Since delivery charge is fixed, we can write the equation as,

y = 0.4x + 4.5, where y is the total cost and x is the distance travelled.

When x = 2, y = (0.4 × 2) + 4.5 = 5.3

When x = 3, y = (0.4 × 3) + 4.5 = 5.7

When x = 7, y = (0.4 × 7) + 4.5 = 7.3

When x = 8, y = (0.4 × 8) + 4.5 = 7.7

Hence the correct option is D.

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