Find 9x + y when x = 7 and y=4 .

When a person places $48,800 in an investment account at an annual rate of 3.1% compounded continuously, using the formula, V = \(Pe^rt\), the amount of money (future value) after 13 years is $73,019.78.

Compounding refers to the process or interest system that computes periodic or continuous interest on both the principal and accumulated interest.

We can solve for the future value of an investment under continuous compounding using an online finance calculator as follows:

Using the formula V = \(Pe^rt\)

Principal (P) = $48,800.00

Annual Rate (R) = 3.1%

Compound (n) = Compounding Continuously

Time (t in years) = 13 years

Result:

V = $73,019.78

V = P + I where

P (principal) = $48,800.00

I (interest) = $24,219.78

Calculation Steps:

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

r = R/100

r = 3.1/100

r = 0.031 rate per year,

Solving the equation for V:

V = \(Pe^rt\)

V = \(48,800.00(2.71828)^(0.031)(13)\)

V = $73,019.78

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(A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

What is the explicit formula?

The explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geometric, or harmonic sequence.

A. The data provided is modeling a geometric sequence.

This is because the common ratio between consecutive terms is a constant value, specifically in this case is the ratio between consecutive terms is multiplied by 2.

B. To find the time Aurora will complete station 5 using a recursive formula,

we can use the formula T(n) = T(n-1) * r,

where T(n) is the time at the nth station, T(n-1) is the time at the (n-1)th station, and r is the common ratio.

In this case T(5) = T(4) * 2

and T(4) = 24 (from the data provided)

Therefore, T(5) = 24 * 2 = 48 minutes

C. To find the time Aurora will complete the 9th station using an explicit formula,

we can use the formula T(n) = T(1) * r^(n-1)

In this case, T(9) = T(1) * 2^(9-1)

and T(1) = 3 (from the data provided)

Therefore, T(9) = 3 * 2^8 = 3 * 256 = 768 minutes

The explicit formula assumes that the first term of the sequence is T(1) and the common ratio of the consecutive term is r.

Hence, (A) The data provided is modeling a geometric sequence, (B) the recursive formula is T(5) = T(4) * 2., and (C) the explicit formula T(n) = T(1) * r^(n-1).

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Step-by-step explanation:

1. 4^2 = 16

2. 32/16 = 2

3. 2*3 = 6

4. 17-6=11

5. 11 + 6 = 17

The answer is 17

When rotated 90 degrees, counterclockwise direction the new coordinates will result in the attached image.

The old coordinate where were rotated are:

A(-5,8)

B (-1, 7)

C(-3, 5)

D(-4, 2)

To rotate a point counterclockwise about the origin, we switch the x and y coordinates and change the sign of the new x  -coordinate.

The new coordinates are after 90 degrees, counterclockwise  are

A' = (-8, -5)

B' = (-7, -1)

C' = (-5, -3)

D' = (-2, -4)

See attached image.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Answer:

A normal good is a good that experiences an increase in its demand due to a rise in consumers' income. Normal goods has a positive correlation between income and demand. Examples of normal goods include food staples, clothing, and household appliances.

Step-by-step explanation:

Work Shown:

r = 6 = radius

h = 9 = height

\(V = \text{volume of cylinder}\\\\V = \pi*r^2*h\\\\V = \pi*6^2*9\\\\V = \pi*36*9\\\\V = \pi*324\\\\V = 324\pi\\\\\)

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

Answer:

3x+6

x+x+2+x+4

» You can group the like terms, in this case, the x's and the numbers.

x+x+x+2+4

3x+6

The other Washington DC landmark with coordinates (8,-10) is located in the fourth quadrant of the map.

To determine in which quadrant of the map a point with coordinates (8,-10) is located, we need to look at the signs of the x and y coordinates.

Since the x-coordinate (8) is positive and the y-coordinate (-10) is negative, this point is located in the fourth quadrant.

In general, the four quadrants of a Cartesian coordinate system are divided by the x and y-axes.

The first quadrant is located in the upper right-hand corner and contains points with positive x and y coordinates.

The second quadrant is located in the upper left-hand corner and contains points with negative x and positive y coordinates.

The third quadrant is located in the lower left-hand corner and contains points with negative x and y coordinates.

Finally, the fourth quadrant is located in the lower right-hand corner and contains points with positive x and negative y coordinates.

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Answer:

D

Step-by-step explanation:

sin  (  3pi / 4 )

 =  sin   (   pi   -   pi  /  4   )

 =  sin   (   pi / 4  )

 = 1/root(2)

  =  root(2) / 2

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Answer:

\(V=6912ft^3\)

Step-by-step explanation:

From the question we are told that:

Diameter  \(D=40ft\)

Radius \(r=d/2=>20ft\)

Depth at south \(d_s=3ft\)

Depth at north \(d_n=8ft\)

Average depth of the pool

 \(d_a=\frac{3+8}{2}\)

 \(d_a=5.5ft\)

Generally the equation for Volume is mathematically given by

 \(V=\pi r^2h\)

 \(V=3.142*(20)^25.5\)

 \(V=6912ft^3\)

The area of the cross section after the dilation has a value of  484 square units

When a square pyramid is dilated, all of its dimensions, including the base area and height, are multiplied by the same factor.

In this case, the base of the pyramid was dilated with a factor of k=0.55.

Therefore, the new area of the base can be calculated as:

New base area = k^2 * old base area

Plugging in the values given in the problem, we get:

New base area = (0.55)^2 * 1600

New base area = 484 square units

So, the new base area is 484 square units

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Answer:

24.3

Step-by-step explanation:

Answer:

The answer would be 24.3

Answer:

x = 5

Step-by-step explanation:

To find the value of x make sure to get it on one side

First subtract 3x from each side. This makes the equation now

3x + 2 = -8 + 25

Now see what 25 subtract by 8 is (17)

3x + 2 = 17

Next subtract 2 from both sides

3x = 15

Lastly, divide 15 by 3, making x equal 5

x = 5

Answer:

x = 80

Step-by-step explanation:

supplementary angles sum to 180°

sum the 2 angles and equate to 180

x + 40 + x - 20 = 180

2x + 20 = 180 ( subtract 20 from both sides )

2x = 160 ( divide both sides by 2 )

x = 80

Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

The angle measure explained in the solution.

Given that, a || b, we need to find the missing angles,

∠1 = 42° [vertically opposite angles]

∠3 = 62° [vertically opposite angles]

∠2 = 180°-(∠1+62°) [angle in a straight line]

∠2 = 76°

∠4 = ∠2 [vertically opposite angle]

∠4 = 76°

∠4 = ∠9 = 76° [alternate angles]

∠9 = ∠12 = 76° [vertically opposite angle]

∠3 = ∠ 6 = 62° [alternate angles]

∠ 6 = ∠7 = 62° [vertically opposite angle]

∠3 + ∠5 = 180° [consecutive angles]

∠5 = 118°

∠5 = ∠8 = 118° [vertically opposite angle]

∠4 + ∠10 = 180° [consecutive angles]

∠10 = 104°

∠10 = ∠11 [vertically opposite angle]

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Answer:

112.5

Step-by-step explanation:

450(45/220) = 450/4 = 112.5

Answer:

B

Step-by-step explanation:

pretty much just gave you the anwsers

The expression means "10 less than the sum of a and b" is 10 - (a + b). Then the correct option is C.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The sum of a and b is given as

→ a + b

Then the meaning of the less than is minus.

That means 10 minus a + b

This can be written as

→ 10 - (a + b)

Thus, the correct option is C.

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Answer:

Step-by-step explanation:

f(3)=-5(x+5)

     =5(3) +5

     =15+5

f(3)      =20

The median of the given data set is 26.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

Given the data set, we need to find the median.

So, let's arrange the numbers from smallest to largest in order to find the median.

\(\sf 15,20,22,26,28,35,36.\)

\(\text{Median}=\sf 26\)

Therefore, the median of the data set is 26.

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a) -32.06 (To the nearest hundredth)

b) -37.7 (To the nearest tenth)

c) 3.1 (To the nearest tenth)

d) 5.86  (To the nearest hundredth)

f) -4.33  (To the nearest hundredth)

g) 11.44  (To the nearest hundredth)

h) 62x + 45 = 38x + 79

i) 46y - 18 = -37y

An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equal sign (=), and shows the relationship between the variables present in the equation. Equations are used to model real-world problems and find solutions to various mathematical problems.

They can be solved for a specific variable by using various mathematical methods and techniques.

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Answer:

it may be 3

Step-by-step explanation:

it may be bcz am not much good but still just trying

Answer:

6 3/10 mph.

Step-by-step explanation:

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

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A rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

To determine how many square tiles can fit in a rectangular floor, we need to calculate the total number of tiles that can fit both horizontally and vertically.

Given:

Length of the rectangular floor = 14 ft

Width of the rectangular floor = 6 ft

Edge length of square tile = 3/4 ft

First, let's calculate the number of tiles that can fit horizontally:

Length of the rectangular floor / Edge length of square tile = 14 ft / (3/4 ft) = 14 ft × (4/3 ft) = 56/3 ft

Since we want a whole number of tiles, we need to round down or take the floor value:

Number of tiles horizontally = floor(56/3) = 18 tiles

Next, let's calculate the number of tiles that can fit vertically:

Width of the rectangular floor / Edge length of square tile = 6 ft / (3/4 ft) = 6 ft × (4/3 ft) = 24/3 ft

Again, we round down or take the floor value:

Number of tiles vertically = floor(24/3) = 8 tiles

To find the total number of tiles, we multiply the number of tiles horizontally by the number of tiles vertically:

Total number of tiles = Number of tiles horizontally × Number of tiles vertically = 18 tiles × 8 tiles = 144 tiles

Therefore, in a rectangular floor with a length of 14 ft and a width of 6 ft, square tiles with an edge length of 3/4 ft, a total of 144 tiles can fit.

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