Can someone help me with question 1 and 2?

Mildred bought 2-cent stamps, 4-cent stamps, and 5-cent stamps for $4.35. The number of 2-cent stamps exceeded the number of 5 c

vfiekz [6]

5 cent = 0.05x

2 cent = 0.02(x+50)

4 cent = 0.04(2x-10)

0.05x + 0.02(x+50) + 0.04(2x-10)

0.05x + 0.02x +1 + 0.08x -0.4 = 4.35

0.15x +0.6 = 4.35

0.15x = 3.75

X = 3.75 / 0.15 = 25

25 5 cent stamps ( 25*0.05 = 1.25)

25+50 = 75 2 cent stamps ( 75*0.02 = 1.50)

2*25 =50-10 = 40 4 cent stamps ( 40*0.04 =1.60)

1.25 + 1.50 +1.60 = 4.35

5 cent = 25

2 cent = 75

4 cent = 40

8 0

3 years ago

Park rangers tagged fish in a state park to track their population. The function f(x)=200(1.05)x can be used to find the populat

Sedbober [7]

The given exponential function can be used to determine the

population of the fish at different times.

Response:

1. 200

2. 0.05

3. Please find attached the graph of the exponential function and the table

$\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}$

4. Range; [0, ∞)

Domain: [200, ∞)

5. 346 fishes (approximate value)

<h3>How is the population of the fish obtained from the exponential function?</h3>

The given function is f(x) = 200·(1.05)ˣ

1. The initial population is given by the value of the function when x = 0,

which is given as follows;

At x = 0, f(0) = 200·(1.05)⁰ = 200

The initial population of the fish is 200

2. The rate of growth of the fish from the exponential function is given as follows;

The growth factor = 1.05

The growth rate = 0.05

3. Please find attached the graph of the exponential function created

with MS Excel.

The asymptote of the exponential function is the line, y = 0

The table of values is presented as follows;

$\begin{array}{|c|c|c}x&f(x)\\0&200 & y-intercept\\1&210\\3&231.525\\4&243.1\\5&255.26\end{array}$

4. The domain is the possible x-values which is; 0 ≤ x < ∞

The range is the possible y-values which is; 200 ≤ f(x) < ∞

Which gives;

Domain; [0, ∞)

Range: [200, ∞)

5. The population of the fish after 11 years is f(11) = 200·(1.05)¹¹

f(11) = 200 × (1.05)¹¹ ≈ 342

The population of the fish after 11 years is 346 (fishes)

Learn more about exponential function here:

brainly.com/question/15662160

3 0

2 years ago

Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

Alecsey [184]

Answer:

y^2 = 28x

Step-by-step explanation:

Since the directrix is horizontal, use the equation of a parabola that opens left or right.

(y−k)^2 = 4p(x−h)

Find the vertex.

(0,0)

Find the distance from the focus to the vertex.

p = 7

Substitute in the known values for the variables into the equation

(y−k)^2 = 4p(x−h).

(y−0)^2 = 4(7)(x−0)

Simplify.

y^2 = 28x

7 0

2 years ago

Read 2 more answers

Explain why each function is continuous or discontinuous. (a) The temperature at a specific location as a function of time (b) T

Mekhanik [1.2K]

Answer:

(a) The temperature at a specific location as a function of time.

This is a continuous function as the temperature cannot increase in an instant like time.

(b) The temperature at a specific time as a function of the distance due west from New York City.

This is a continuous function as the temperature in one location is affected by its neighboring places.

(c) The altitude above sea level as a function of the distance due west from New York City.

The altitude above sea level can be discontinuous at a cliff, or continuous at very deep hole.

(d) The cost of a taxi ride as a function of the distance traveled.

This is a discontinuous function as the cost still raises if you make a stop.

(e) The current in the circuit for the lights in a room as a function of time.

This is a discontinuous function as the function takes the value of 0 when the switch is off and 1 when the switch is on.

The electron traveling speed makes this discontinuous.

3 0

2 years ago

The ratios of measures of the angles in Triangle ABC is 4:13:19. Find the measures of each of the angles. Show all of your work/

Grace [21]

Answer:

20

65

95

Step-by-step explanation:

Remark

You have to use a constant to get the ratio so that it will produce angles that will add up to 180. Let that constant = x

Equation

4x + 13x + 19x = 180

Solution

Add the like terms on the left.

36x = 180

Divide both sides by 36

36x/36 = 180 /36

Combine

x = 5

Answer

4x = 20

13x = 65

19x = 95

Total = 180

5 0

3 years ago