How much money will you have after 12 years if you deposit $1200 into an account that earns 6.5% annual interest compounded daily?

Answer:

"B".  Domain is all real numbers, and the Range is all positive real numbers

Step-by-step explanation:

It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form \(y=a*b^x\) where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.

Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).

The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.

The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.

Since "a" is positive, the Range is positive numbers only.

Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.

Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero".  There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0".  So, the Range is written as { y | y>0 }.

Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.

Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"

Answer:

-16/3 will be the answer for this question

Answer:

Robbie Glider

Step-by-step explanation:

Given

Melissa Glider

\(m(s) = 0.4(s^3 - 11s^2 + 31s - 1)\)

Robbie Glider

See attachment for function

Required

Which reaches the greater maximum within the first 6 seconds

Melissa Glider

First, we calculate the maximum of Melissa's glider

\(m(s) = 0.4(s^3 - 11s^2 + 31s - 1)\)

Differentiate:

\(m'(s) = 0.4(3s^2 - 22s + 31)\)

Equate to 0 to find the maximum

\(0.4(3s^2 - 22s + 31) = 0\)

Divide through by 0.4

\(3s^2 - 22s + 31 = 0\)

Solve for s using quadratic formula:

\(s = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}\)

Where

\(a = 3; b = -22; c = 31\)

So:

\(s = \frac{22 \± \sqrt{(-22)^2 - 4*3*31}}{2*3}\)

\(s = \frac{22 \± \sqrt{112}}{6}\)

\(s = \frac{22 \± 10.6}{6}\)

Split:

\(s = \frac{22 + 10.6}{6}\ or\ s = \frac{22 - 10.6}{6}\)

\(s = \frac{32.6}{6}\ or\ s = \frac{11.4}{6}\)

\(s = 5.4\ or\ s = 1.9\)

This implies that Melissa's glider reaches the maximum at 5.4 seconds or 1.9 seconds.

Both time are less than 6 seconds

Substitute 5.4 and 1.9 for s in \(m(s) = 0.4(s^3 - 11s^2 + 31s - 1)\) to get the maximum

\(m(5.4) = 0.4(5.4^3 - 11*5.4^2 + 31*5.4 - 1)\)

\(m(5.4) = 1.24ft\)

\(m(5.4) = 0.4(1.9^3 - 11*1.9^2 + 31*1.9- 1)\)

\(m(5.4) = 10.02ft\)

The maximum is 10.02ft for Melissa's glider

Robbie Glider

From the attached graph, within an interval less than 6 seconds, the maximum altitude is at 3 seconds

\(r(3) = 22ft\)

Compare both maximum altitudes, 22ft > 10.02ft. This implies that Robbie reached a greater altitude

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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Answer:

8 lions

Step-by-step explanation:

We need to subtract!!

14 - 6 = 8

Have an amazing day!!

Please rate and mark brainliest!!

Step-by-step explanation:

let the number of penguins be X and the number of lions be Y. then X=14 and since there are more penguins than lions the equation will be X=Y+6

Substitute 14 instead of X. 14=Y+6

and now shift 6 to the left 14-6=Y

then the answer should be 8lions

Answer:

Step-by-step explanation:

Its B my freind

Completing the frequency table, and using the percentage concept, it is found that 11% of students under age 15 travel to school by car.

\(P = \frac{a}{b} \times 100\%\)

In this problem:

Hence:

\(P = \frac{18}{165} \times 100\% = 11\%\)

Then, 11% of students under age 15 travel to school by car.

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The line's slope is \(\frac{1}{2}\) and the distance increases by 1 mile every 2 hours.

What is a good example of a line's slope?

The proportion of the increase in the y-value to the increase in the x-value may also be used to determine slope. For instance: We can get the slope of a line given two locations, P = (0, -1) & Q = (4,1) on the line.

A. Since the line's slope is 2, it follows that the y-variable, which is most likely distance, grows by 2 units for every increment in the x-variable, which is most likely time. The accurate statement is thus: speed is increased by Two miles per hour.

B. Since the line's slope is 2, it follows that the y-variable will drop by 2 units for every unit rise in the x-variable, which is most likely time. The accurate description is thus: speed drops by Two miles per hour.

C. If the line's slope is 1/2, the y-variable will rise by 1/2 unit for every increment in the x-variable, which is probably time. The precise description is that the distance grows by a mile every two hours.

D. If indeed the line's slope is 1/2, the y-variable will drop by 1/2 unit for every unit rise in the x-variable, which is probably time. The precise description is: distance shrinks by a mile every two hours.

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The value of x in the parallelogram is 112°.

In a parallelogram, adjacent angles are always supplementary. This means that the sum of two adjacent angles in a parallelogram is always 180 degrees.

To understand this concept, let's consider a parallelogram ABCD. The opposite sides of a parallelogram are parallel and equal in length, and the opposite angles are congruent. Adjacent angles are those that share a side. Let's say angle A and angle B are adjacent angles in the parallelogram.

Since opposite angles of a parallelogram are congruent, we have angle A is congruent to angle C, and angle B is congruent to angle D.

Now, let's consider angle A and angle B. The sum of angle A and angle B is equal to the sum of angle C and angle D because opposite angles are congruent.

Therefore, we can conclude that angle A + angle B = angle C + angle D = 180 degrees.

This property holds true for all parallelograms. So, in any parallelogram, the adjacent angles are always supplementary, meaning their sum is 180 degrees.

For the given question, we know x° + 68° = 180°.

Then x° = 180° - 68°

x° = 112°

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Answer:

y = 7

Step-by-step explanation:

3y + (y+1) + (4y-3) = 54

3y + y + 4y + 1 - 3 = 54

8y - 2 = 54

8y = 54 + 2

8y = 56

y = 56/8

y = 7

Check:

3*7 + (7+1) + ((4*7)-3) = 54

21 + 8 + 28-3 = 54

29 + 25 = 54

The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.

Given the function g(x) = f(x + 4) + 8, let's examine its features:

Domain:

The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f.  However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.

Range:

Similar to the domain, the range of the function g will depend on the range of the function f.

x-intercept:

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.

0 = f(x + 4) + 8

By subtracting 8 from both sides:

-8 = f(x + 4)

Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.

y-intercept:

The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:

g(0) = f(0 + 4) + 8

g(0) = f(4) + 8

Again, the specific value of f(4) will depend on the behavior of the function f.

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Answer:

C., D. (they are the same point)

Step-by-step explanation:

4x + 2y < 6

A. (5, 7)

4(5) + 2(7) = 20 + 14 = 34

34 > 6, so A. is not an answer.

B. (0, 4)

4(0) + 2(4) = 0 + 8 = 8

8 > 6, so B. is not an answer

C. (1, 0)

4(1) + 2(0) = 4 + 0 = 5

4 < 6 is true, so C. is an answer.

D. (1, 0)

Why is D. the same as C.?

Answer:

a = 8

Step-by-step explanation:

11a = 88

divide both sides by 11.

a = 8

Step-by-step explanation:

I think you are 100℅ clear.

The dimensions of the rectangular garden to maximize the area is length = width = 75 meters.

Let l be the length and w be the width of the rectangular garden.

We need to find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

The perimeter of the  rectangular garden = 300 meters

We know that the perimeter of the rectangle =2(length + width)

300 = 2(l + w)

l + w = 150               .......(1)

Now, the maximum area of a  rectangular garden is when Length  = width

So, for equation 1

l + l = 150

l = 75 meters

So, w = 75 meters

And the area of the rectangular garden = length * width

                                                               = 75 * 75

                                                               = 5625 m²

So the maximum area of the  rectangular garden is 5625 m²

Therefore, the dimensions of the garden to maximize the area is length = width = 75 meters and maximum area is  5625 m²

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The domain of the question is expressed as; 0 ≤ x ≤ 4

The range of the question is expressed as; 100 ≤ f(x) ≤ 207.36

The domain of a graph is defined as the set of all possible input values that makes the function possible while the range is defined as the set of all possible output values that can result from the possible input values.

Now, we are told that the insect population increases by 20% each month from May 1 to September 1.

The function that represents the insect population after x months is;

f(x) = 100(1.2)ˣ

Thus, the domain is from x = 0 to 4 months inclusive. 0 ≤ x ≤ 4

f(0) = 100(1.2)⁰

f(0) = 100

f(4) = 100(1.2)⁴

f(4) = 207.36

100 ≤ f(x) ≤ 207.36

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The y-intercept of the linear function means that her initial distance from the finish line is of 10 kilometers.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 10, hence the intercept b is given as follows:

b = 10.

The y-values represent the distance in the context of this problem, hence the initial distance is of 10 km.

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The fraction of the area of polygon H of polygon G's area would be: 1/16.

When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.

The scale factor = new dimension/original dimension

Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:

Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation

Area of polygon H/Area of polygon G = 1²/4² = 1/16

This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².

Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.

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Step-by-step explanation:

The equivalent formula that does not involve integrals is A(x) = 2x - 2x^2 + 4x - 4.

The First Fundamental Theorem of Calculus states that if f(x) is a continuous function on the interval [a, b], then the function F(x) = integral^x_a f(t) dt is an antiderivative of f(x), meaning that its derivative is equal to f(x). Therefore, if we have the antiderivative of a function, we can use the derivative to find an equivalent formula without an integral.

In this case, the derivative of the antiderivative of f(t) = 4 - 2t is f(t) = 4 - 2t, which is the original function. So, the equivalent formula for A(x) is A(x) = 2x - 2x^2 + 4x - 4, which does not involve integrals.

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Answer:

178 text messages sent

Step-by-step explanation:

$7.05 / 47 = $0.15 per text

$26.70/ $0.15 = 178 text messages

Answer:

178

Step-by-step explanation:

7.05 divided by 47 equals 0.15. so one text is 0.15. if you divide 26.60 by 0.15, you get 178.

Area = length x width

Area of square = 8 x 8 = 64 square inches

Area of rectangle = 24 x 20 = 480 square inches

Area of rectangle surrounding the square = 480 - 64 = 416 square inches

Answer: 416 square inches

4/3 is the value of k that makes the system of linear equations has no solutions .To determine the value(s) of k such that the system of linear equations has no solutions, we need to use the concept of consistency and consistency of a system of linear equations, which is the property that a system of equations has exactly one solution or no solution.

A system of linear equations is consistent if it has exactly one solution and inconsistent if it has no solution. We can use the concept of determinant of a matrix to check the consistency of the system of linear equations. The determinant of a matrix is a scalar value that can be calculated from the elements of a matrix and it tells us whether a matrix is invertible or not. An invertible matrix corresponds to a consistent system of linear equations and a non-invertible matrix corresponds to an inconsistent system of linear equations. To check the consistency of the system of linear equations, we can use Cramer's Rule, which states that the determinant of the coefficient matrix must be non-zero for the system to have a unique solution.

The coefficient matrix of the given system of equations is:

| 1 2 k |

| 3 6 8 |

The determinant of the coefficient matrix is:

|1 2 k|

|3 6 8| = (18) - (26) + (k*3) = 8 - 12 + 3k

If the determinant of the coefficient matrix is non-zero, the system of equations will have a unique solution, if the determinant of the coefficient matrix is zero, the system of equations will have no solution.

So for the system of linear equations to have no solution, the determinant of the coefficient matrix must be zero.

8 - 12 + 3k = 0

3k = 4

k = 4/3

So the value of k that makes the system of linear equations has no solutions is 4/3.

It is worth noting that if there are infinite solutions, the determinant of the matrix is zero but the rank of the matrix (the number of linearly independent rows or columns) is smaller than the number of variables

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Answer:

Step-by-step explanation:

45

Answer:

Step-by-step explanation:

5

Let the numbers are x and y

Given :

1) 5 times the larger + 3 times the smaller = 47

2) 4 times the larger - 2 times the smaller = 20

if the larger is x and the smaller is y

so, we have the following equations:

5x + 3y = 47 eq.(1)

4x - 2y = 20 eq.(2)

Multiply eq.(1) by 2 and eq.(2) by 3

So,

10x + 6y = 94

12x - 6y = 60

Add the last two equations:

10x + 12x = 94 + 60

22x = 154

divide both sides by 22

x= 154/22 = 7

Substitute at eq.(1) with x to find y

5 * 7 + 3y = 47

35 + 3y = 47

3y = 47 - 35

3y = 12

divide both sides by 3

y = 12/3 = 4

So, the numbers are 7 and 4

The required Comparison of the inequalities are

The range of values encompassing the region's junction is (-13, 15).

When comparing two numbers, an inequality indicates whether one is less than, larger than, or not equal to the other.

We take into account the various variables of the inequality

|x – 1| + 1 > 15

Therefore

|-x-1|+1-1<15-1

|-x-1|-1 <14

13<x<15

The required region lies between the inequality -13 <x< 15.

Simplify the inequality Ix-11+1 > 15 we get,

|x-1|+1 > 15

|x+1| +1-1 >15-1

|x-1| > 14

x> 15  

x<-13

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Answer:

Step-by-step explanation:

Your calculator or a spreadsheet can help you do this. The rules of exponents apply.

  (10^a)(10^b) = 10^(a+b)

__

(2×10^8)(2×10^-2) = 4×10^6

40×10^5 = 4×10^6

40^6 = 4.096×10^9

400,000 = 4×10^5

1.2×10^9/3×10^2 = 4×10^10   or  1.2×10^9/(3×10^2) = 4×10^6 (see note)

_____

Note: A multiplier that is a power of 10 is one factor of a product. A product does not go into the denominator of a fraction unless it has parentheses around it. a/bc = (a/b)c ≠ a/(bc) (This is a consequence of the Order of Operations.)

Answer:

B 49/3

Explanation:

I did the work, unlike your lazy ahh! :)

Answer:

a..x is what’s already in the bottle so 24-x= the number of ounces needed to fill the bottle

b.. 24-x= 12.....how many ounces is x

(don’t know if this question works)

Answer:

If a bottle holds 24 ounces of water, it has 24 ounces of water in it.

x=24

Step-by-step explanation:

Too complicated to explain.

Answer:

Step-by-step explanation:

  x + 6 I x³ + 2x²  - 10x + 84   I   x² - 4x + 14

              x³ + 6x²

            -     -      

                     -4x² - 10x

                    -4x²  - 24x

                    +       +    

                               14x + 84

                                14x + 84

                                -      -      

                                     0

P(x)  =(x +6)* ( x² - 4x + 14) + 0