You deposit $200 in an account that earns simple interest at an annual rate of
6.5%. How much money is in the account after 3 years?

The recursive formula for our sequence is the one in the first option.

aₙ = aₙ₋₁ + 6

With a₁ = 7

Here we have the following sequence:

7, 13, 19, 25, ...

This one seems to be an arithmetic sequence, to check this, let's take the difference between consecutive terms:

13 - 7 = 6

19 - 13 = 6

25 - 19 = 6

This means that the recursive formula for our sequence is "add 6 to the previous term" or:

aₙ = aₙ₋₁ + 6

With a₁ = 7

so the correct option is the first one.

Laern more about sequences at:

https://brainly.com/question/6561461

#SPJ1

From the given results, we found that the relative frequency of rolling a 3 is 9/40.

What is the relative frequency?

The relative frequency is calculated as the ratio of the number of occurrences of a given value of the data in the set of all outcomes to the total number of outcomes. Frequency is a measure of how frequently an event happens. While not a theoretical concept, relative frequency is one that is currently being tested. The fact that it is experimental means that if we repeat the trials, we might get different relative frequencies. In order to compare the frequency of a specific event to all other occurrences, relative frequency is used.

The complete question is given below.

Number of times Danielle rolled a number cube = 40

We are asked to find the relative frequency of rolling a 3.

Relative frequency = frequency/ Total frequency

From the table,

Frequency of 3 = 9

Total frequency = 5 + 5+ 9 + 6 + 7 + 8 = 40

Then the relative frequency of 3 = 9/40

Therefore from the given results, we found that the relative frequency of rolling a 3 is 9/40.

To learn more about relative frequency, follow the link.

https://brainly.com/question/3857836

#SPJ1

The line passing through (24, 26, 1) and (22, 0, 23) is not parallel to the line passing through (10, 18, 4) and (5, 3, 14).

To find the direction vector of a line, we subtract the coordinates of one point from the coordinates of another point on the line. Let's label the first line as Line A and the second line as Line B.

For Line A: Direction vector = (22-24, 0-26, 23-1) = (-2, -26, 22)

For Line B: Direction vector = (5-10, 3-18, 14-4) = (-5, -15, 10)

To check if the direction vectors are parallel, we can compare their components. If the components of one vector are scalar multiples of the components of the other vector, the vectors are parallel.

In this case, the components of the direction vectors of Line A and Line B are not scalar multiples of each other. Therefore, the lines are not parallel.

Hence, the line passing through (24, 26, 1) and (22, 0, 23) is not parallel to the line passing through (10, 18, 4) and (5, 3, 14).

Learn more about direction vector here:

https://brainly.com/question/32090626

#SPJ11

To determine the maximum volume of a cone that can be carved from a foam cylinder, we need to compare the volumes of the two shapes. The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the cone's base and h is the height of the cone.

Answer :   28. 27 in³

Given that the foam cylinder has a diameter of 3 inches, we can find its radius by dividing the diameter by 2: r = 3/2 = 1.5 inches. The height of the cylinder is given as 4 inches.

Now, let's calculate the volume of the foam cylinder using the formula V = πr²h:

V_cylinder = π(1.5)²(4) = 9π in³ ≈ 28.27 in³ (rounded to the hundredths place)

The maximum volume of a cone that can be carved from the foam cylinder will be less than or equal to the volume of the foam cylinder.

Therefore, the correct answer is option 28. 27 in³, as it is the closest approximation to the volume of the foam cylinder rounded to the hundredths place.

Learn more about diameter  : brainly.com/question/4771207

#SPJ11

36

that is the answer

Answer:

36%

Step-by-step explanation:

"Percent'' or ''%'' means ''out of 100'' or '' per 100'',

Therefore x% can be written as x/100.

So we can write and solve for x;

27/75= x/100

100 X 27/75 = 100 X x/100

2700/75 = 100 X x/100

36=x

27/75= 36/100= 36%

Hope this helped

The decision and outcome that represents a Type I error in this scenario is if the prisoner is released and kills a family of five in cold blood within 48 hours. A Type I error occurs when the null hypothesis is rejected even though it is actually true. In this case, if the parole board releases the prisoner based on the hypothesis that they have been rehabilitated but in reality, they have not been rehabilitated, it would result in a Type I error. The prisoner's release would lead to a tragic outcome, which could have been avoided if the null hypothesis had not been rejected.

Learn more about Type I error here:

https://brainly.com/question/24320889

#SPJ11

Answer:

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

Answer:

1) 21.24cm

2)19.8ft

3)22.84mm [2.284cm]

Step-by-step explanation:

To calculate the perimeter of a triangle, add the length of its sides.

1) perimeter = 5.4+8.84+7

=>    5.4+8.84+7 = 21.24,

 21.24cm

2) perimeter = 6.6 + 6.6 + 6.6  i.e  6.6* 3

=>    6.6 x 3 = 19.8

 19.8ft

3) perimeter = 8.3 + 4.9 + 9.64

=>     8.3 + 4.9 + 9.64 =  22.84

22.84mm or 2.284cm

AREA

1) it's a right triangle,

 =>    Area of a right triangle = 1/2 × base × height.

 =>    here, base is a and height is b

 =>    a = 7, b = 5.4

 =>   now we multiply it,  

 => 7*5.4 = 37.8

 => now multiply it with 1/2,  

 => 1/2 x 37.8 =  37.8/2

 => 37.8/2  = 18.9

2) it's an equilateral triangle,

18.8620

the formula is  √3 a^2/ 4

=>    √3* 6.6^2/ 4  

=>    75.4481/4 = 18.8620

3)  20.335

    base = a = 8.3

    height = b = 4.9

=>    8.3 * 4.9 = 40.68

=>     40.68/2 = 20.335

hope this helps:)

Answer:

10

Step-by-step explanation:

C = 0.75 + L

For L = 3 ; Cost, C = 3.75

3.75 = 0.75 + 3L

3.75 - 0.75 = 3L

3 = 3L

L = 3/3

L = $1

C = 0.75 + 1L

If amount spent is $10.75; C = 10.75

10.75 = 0.75 + L

10.75 - 0.75 = L

10 = L

Number of letters = 10

Answer:

2:3

Step-by-step explanation:

Simply divide each by 10

20/10=2

30/10=3

and your ratio is 2:3

Answer:

a pod t.v. Ka ssh Mic yummy

The surface area of the new prism is 702 square inches.

Given that,

The area of triangular prism = 78 square inches

Use the fact that the surface area of a similar prism is proportional to the square of the scale factor.

Since,

The new prism is 3 times larger than the original, the scale factor is 3.

Therefore,

The surface area of the new prism will be 3 = 9 times larger than the original prism.

To find the surface area of the new prism, we can multiply the surface area of the original prism by 9,

78 in x 9 = 702 in²

Thus,

Surface area of new prism =  702 in².

To learn more about area of square visit:

https://brainly.com/question/1658516

#SPJ1

The value of ∠EFD is 107 ° as this angle is part of a linear pair .

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.

Given the two angles are ∠EFD and ∠DFG .

Now as they are on a straight line they form a linear pair .

As a part of a linear pair their sum add up to  180°.

Now substituting the given values :

11x - 3 + 6x + 13 = 180

or, 17 x + 10 =180

or, 17 x = 170

or, x = 10

Therefore the value of the ∠EFD is given as 11x - 3 = 110 - 3 = 107° .

To learn more about linear pair visit:

https://brainly.com/question/17525542

#SPJ1

To calculate the Mean Absolute Deviation (MAD) of a data set, you need to find the average of the absolute differences between each value and the mean of the data set. However, the table you provided only shows the distances between each value and the mean of 12, without the actual values of the data set. Without the actual values, it is not possible to calculate the MAD.

The Mean Absolute Deviation is a measure of the dispersion or spread of a data set. It quantifies the average distance between each data point and the mean. By finding the absolute difference between each value and the mean, summing up these differences, and then dividing by the number of data points, we can obtain the MAD.
If you can provide the actual values of the data set, I would be able to calculate the MAD for you.

Learn more about mean absolute deviation here
https://brainly.com/question/32035745



#SPJ11

It seems like you have a question related to a cone and its parametric equations. Based on the given information, the parametric equations for the cone are:

x = u * v * cos(v)
y = u * v * sin(v)
z = u

where u ranges from 0 to 1, and v ranges from 0 to 2π.

These equations describe the coordinates (x, y, z) of points on the surface of the cone as functions of the parameters u and v. The parameter u determines the height along the cone, while v represents the angle around the central axis of the cone.

To know more about cone please visit ,

https://brainly.com/question/1082469

#SPJ11

Answer:

7.A (5,1)

B(5,7)

8. D (0,6)

Step-by-step explanation:

7.  One vertex is at (5,4)

Move 3 units either direction in x

(5-3,4) = (2,4)

(5+3,4) = (8,4)

Or move 3 units in the y direction

(5,4+3) = (5,7)

(5,4-3) = (5,1)

If x is less than 2 or greater than 8 it is too far from the one vertex we are given

If y is less than 1 or greater than 7 it is too far away from the one vertex we are given

C cannot be a vertex since y =9

D is not a vertex since the point is (2,6) and not (2,4) which we know is 3 units away

E is not a vertex since the point is (2,1) and not (2,4) which we know is 3 units away

8.  The center is (0,0)

The points have to add to a radius of 6

r^2 = 36

The sum of the x^2 and y^2 = 36

3^2 +0^2 = 9

4^2 +2^2 = 16+4 = 20

5^2 +3^2 = 25+9 = 34

0^2+6^2 =36  yes  for D

4^2 +4^2 =16+16 = 32

1^2+5^2 = 26

Answer:

The scale factor from Figure A to Figure B is 1/2

Step-by-step explanation:

hope it helps!

Answer:

Its 8

Step-by-step explanation:because u add then divide and subtract

Answer:

18.2

Step-by-step explanation:

60 / 3.3 = 18.1818...

The length of the volleyball court in meters is 18.288 meters.

Given that, the standard length of a volleyball court is 60 feet.

We need to find the length of the volleyball court in meters.

Foot to meters formula is an important length conversion formula. And before going to know what is foot to meters formula, let us first recall what is a foot and what is a meter. Meter and foot are the units of length. Meter is a unit of length in the metric system.

The foot to meters formula is as follows. For the given n units of foot measurement, we need to multiply it by 0.3048 to obtain the value in meters. n feet  = n × 0.3048 meters

Now, 60 feet=60 × 0.3048

=18.288 meters

Therefore, the length of the volleyball court in meters is 18.288 meters.

To learn more about the foot-to-meter conversion vsit:

https://brainly.com/question/22500492.

#SPJ2

The coordinates of point P along the directed line segment AB is (10, 13).

The midpoint of a line segment is given as,

x = (a + c)/2

y = (b + d) / 2

Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.

We have,

The line AB.

P is the point between the line AB.

Now,

A = (4, 10) = (a, b) and B = (14, 15) = (c, d)

m : n = 3 : 2

So,

P = (x, y)

The coordinates is given by:

x = (mc + na) / (m + n)

y = (md + nb) / (m + n)

So,

x = (42 + 8) / 5

x = 10

y = (45 + 20) / 5

y = 13

Now,

P = (10, 13)

Thus,

The coordinates of point P is (10, 13).

Learn more about midpoints of line segments here:

https://brainly.com/question/13792156

#SPJ1

Answer:

(If compounded annually)

(first 5 years)

1 year = 48,000(1.031)¹ = £49,488.00

2 years = 48,000(1.031)² = £51,022.13

3 years = 48,000(1.031)³ = £52,603.81

4 years = 48,000(1.031)⁴ = £54,234.53

5 years = 48,000(1.031)⁵ = £55,915.80

Step-by-step explanation:

A = P(1 + r/n)^(nt)

money Kyle will have in his account in x years if compounded annually (once per year) per annum (every year) =

48,000(1 + 3.1%/1)^1x = 48,000(1.031)^x

Kyle can expect \(48000(1.031)^{n}\) in his account in n years after compounding.

The compound interest is the interest calculated on the aggregated interest and the principal amount. The formula to calculate the sum after compound interest is:

S=P\((1+r)^{n}\)

We have been given amount as 48000 pounds and the rate of compounding is 3.1%. We will apply the above formula to calculate the sum:

S=48000\((1+0.031)^{n}\)

Learn more about compound interest at https://brainly.com/question/24924853

#SPJ2

Answer:

The most quickly reveals the vertex is g(x) = -2(x + 4)² + 18 ⇒ b

The vertex = (-4, 18)

Step-by-step explanation:

The vertex form of the quadratic function f(x) is:

f(x) = a(x - h)² + k, where

The most quickly reveals to find the vertex is the vertex form above

Look at the answer and try to find a similar form to the vertex form above

∵ g(x) = -2(x + 4)² + 18

∴ a = -2

∴ h = -4

∴ k = 18

⇒ That means this form is similar to the form above

∴ The most quickly reveals the vertex is g(x) = -2(x + 4)² + 18

∴ The vertex = (-4, 18)

LCM of 8,9,12 is 72

HCF of 36 72 63 is 3

Answer:1/2 (1 over 2)

Step-by-step explanation:

Answer:

get it from some else pllease

Step-by-step explanation:

type this in

The graph shows a scuba diver's ascent over time. Use the graph to write an equation in slope-intercept form that represents the diver's depth over time.

The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

Learn more about probability:

brainly.com/question/30034780

#SPJ11

A continuum of consumers are uniformly distributed along the interval [0, 1]. Consumers have linear transportation costs and visit the shop that is closest to their location. Derive the locations a*, b*, and c* of the three shops that minimize aggregate transportation cost .

Let A, B, and C be the three shops’ locations on the line.[0, 1] Be ai and bi, Ci be the area of the line segments between Ai and Bi, Bi and Ci, and Ai and Ci, respectively.Observe that any consumer with a location in [ai, bi] will visit shop A, and similarly for shops B and C. For any pair of locations ai and bi, the aggregate transportation cost is the same as the sum of the lengths of the regions visited by the consumers.

Suppose, without loss of generality, that 0 ≤ a1 ≤ b1 ≤ a2 ≤ b2 ≤ a3 ≤ b3 ≤ 1, and let t = T(a, b, c) be the aggregate transportation cost. Then, t is a function of the five variables a1, b1, a2, b2, and a3, b3. Note that b1 ≤ a2 and b2 ≤ a3 and the bounds 0 ≤ a1 ≤ b1 ≤ a2 ≤ b2 ≤ a3 ≤ b3 ≤ 1.In particular, we can reduce the problem to the two-variable problem of minimizing the term b1−a1 + a2−b1 + b2−a2 + a3−b2 + b3−a3 with the additional constraints (i) and 0 ≤ b1 ≤ a2, b2 ≤ a3, and b3 ≤ 1.

To know more about consumers visit :

https://brainly.com/question/33474331

#SPJ11

Answer: A) 2.95 units

Step-by-step explanation:

The diameter of a circle is twice the radius.  Thus, simply do 5.9/2 to get that the radius is 2.95 units long.

Hope it helps <3

Answer:

your answer would be A-2.95

5.9/2=2.95

Step-by-step explanation:

The total price after applying the 10% discount of two $10 items and one $5 item is $40.50.

Let's calculate the original price of our items,

Two $20.00 items,

$20.00 x 2 = $40.00,

One $5.00 item, $5.00,

The total original price of our items is,

$40.00 + $5.00 = $45.00,

For finding the amount of the discount that we have to make, we just do the product of the percentage of the discount to total original amount of the items,

$45.00 x 10% = $4.50

So, the amount discounted is $4.50.

To find the amount after the discount, we subtract the discounted price from the original amount.

$45.00 - $4.50 = $40.50

Hence, the total price of the items will be $40.50.

To know more about discount, visit,

brainly.com/question/1548141

#SPJ4

Answer:

D

Step-by-step explanation:

từ O hạ đường vuông góc xuống các cạnh AB, AC, BC các đường vuông góc đó sẽ bằng nhau