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frutty
1 month ago
6

A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find

the value of the home after x years? f(x) = 120,000(1.055x) f(x) = 120,000(0.055)x f(x) = 120,000(1.055)x f(x) = [(120,000)(1.055)]x
Mathematics
2 answers:
Svet_ta [12.7K]1 month ago
8 0

Answer:

f(x)=120000 \times (1.055)^{x}

Step-by-step explanation:

The present value of the house is $120,000 and the interest rate is 5.5%, or 0.055.

We will utilize the following equation:

f(x)=P \times (1+r)^{x}

where P represents the present value, r symbolizes the interest rate, and x refers to the number of years.

By inputting the values into the above equation, we can obtain:

f(x)=120000 \times (1+0.055)^{x}

f ( x ) = 120000 \times ( 1.055 ) ^ { x }

Leona [12.6K]1 month ago
7 0

Answer:

C

F(x) = 120000(1.055)x

Step-by-step explanation:

Just took the test

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Jacob's lunch account will deplete in 16 days while Samantha's will run out in just 2 days. Step-by-step explanation:
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1 month ago
Biologists stocked a lake with 240 fish and estimated the carrying capacity (the maximal population for the fish of that species
Inessa [12570]

Answer:

2.30 years

Step-by-step explanation:

The fish population increased threefold in the first year, resulting in 240 * 3 = 720 fish.

(a) The logistic equation can be represented as follows

P = P_0e^{kt}

where P0 = 240 denotes the initial fish count; substituting P = 720 and t = 1 allows us to determine the constant k

720 = 240e^{1k}

e^k = 3

k = ln3 = 1.1

b) By applying the formula below

P = P_0e^{kt}

with P set to 3000, P0 as 240, and k equal to 1.1, we can compute the duration needed for the population to reach 3000 fish

3000 = 240e^{1.1t}

12.5 = e^{1.1t}

1.1t = ln12.5 = 2.53

t = 2.30 years

6 0
1 month ago
Toby goes on holiday to Geneva, Switzerland. In Geneva, Toby sees a watch costing 193.75 CHF (Swiss Francs). In Manchester, An i
zzz [12365]
1.55 CHF =?1 The price of the watch in Geneva is 1.55 CHF =?1 while 193 CHF =??1, which can be designated as x. Setting up a proportion, we cross-multiply, resulting in 1.55x = 193. Dividing by 1.55, we find x = 124.52 in x units. However, Manchester merchants are pricing it at 143 x units, so the difference is 143 - 124.52 = 18.48 units more expensive in Manchester.
6 0
1 month ago
Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his sc
AnnZ [12381]

1) 4.55

2) Short hit

Step-by-step explanation:

1)

The score and corresponding probabilities are shown in the following table:

Score 3 4 5 6 7

Probability 0.15 0.40 0.25 0.15 0.05

Let us define

X = Miguel's score on the Water Hole

The expected value of the variable X can be represented as:

E(X)=\sum x_i p_i

where

x_i represents the different possible outcomes of X

p_i denotes the associated probabilities

Accordingly, the expected value of Miguel's score is calculated as follows:

E(X)=3\cdot 0.15 + 4\cdot 0.40 + 5\cdot 0.25 + 6\cdot 0.15 + 7\cdot 0.05=4.55

2)

Here, we will again consider:

X = Miguel's score on the Water Hole

In this case:

- For a successful long hit, the expected value of X is

E(X)=4.2

- Conversely, if the long hit isn't successful, the expected value of X becomes

E(X)=5.4

We also know that the likelihood of succeeding with a long hit is

p(L)=0.4

Consequently, the chance of failure in a long hit is

p(L^c)=1-p(L)=1-0.4=0.6

Thus, the expected value of X when opting for the long hit strategy is:

E(X)=p(L)\cdot 4.2 + p(L^C)\cdot 5.4 = 0.4\cdot 4.2 + 0.6\cdot 5.4 =4.92

In the first part of this question, we calculated the expected value using the short hit strategy, yielding:

E(X)=4.55

Given that the expected value for X is smaller (which is better) when utilizing the short hit option, we can conclude that this approach is superior.

8 0
2 months ago
Noah drew a scaled copy of Polygon P and labeled it Polygon Q. If the area of Polygon P is 5 square units, what scale factor did
babunello [11817]

Answer:

The scale factor equates to 3.

Detailed explanation:

Please refer to the provided image for clarity regarding this issue.

We know that

If two shapes are similar, then the ratio of their areas corresponds to the square of the scale factor.

Let

z -----> scale factor

x -----> area of polygon Q

y ----> area of polygon P

Thus, we have

z^{2}=\frac{x}{y}

so, we proceed with

y=5\ units^2

Determining the area of polygon Q

The polygon Q can be divided into five distinct squares.

Refer to the additional figure N 2.

The area of polygon Q, which represents the total area of the five squares, is

x=5(3^2)=45\ units^2

Calculating the scale factor

z^{2}=\frac{x}{y}

Thus, we derive

x=45\ units^2

y=5\ units^2

By substituting the values, we find

z^{2}=\frac{45}{5}

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Taking the square root of both sides results in

z=3

Thus,

The scale factor resolves to 3.

8 0
2 months ago
Read 2 more answers
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