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mart [117]
1 year 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:
lyudmila [28]1 year ago
8 0

<u>Answer:</u>

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

<u>Step-by-step explanation:</u>

We are given that the present value for the home is $120,000 and the rate of interest is 5.5% i.e. 0.055.

We will use the following formula:

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

where P is the present value, r is the rate of interest and x is the number of years.

Substituting the values in the above formula to get:

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

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

larisa86 [58]1 year ago
7 0

Answer:

C

F(x) = 120000(1.055)x

Step-by-step explanation:

Just took the test

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maxonik [38]

Given that:

Total number of fish = 140

Fish are green swordtails female = 44

Fish are green swordtails male = 36

Fish are orange swordtails female = 36

Fish are orange swordtails male = 24

Solution:

A. We have to find the probability that the selected fish is a green swordtail.

\text{P(green swordtail)}=\dfrac{\text{Total green swordtail fish}}{\text{Total fish}}

\text{P(green swordtail)}=\dfrac{80}{140}

\text{P(green swordtail)}=\dfrac{4}{7}

Therefore, the probability that the selected fish is a green swordtail is \dfrac{4}{7}.

B.  We have to find the probability that the selected fish is male.

\text{P(Male fish)}=\dfrac{\text{Total male fish}}{\text{Total fish}}

\text{P(Male fish)}=\dfrac{36+24}{140}

\text{P(Male fish)}=\dfrac{60}{140}

\text{P(Male fish)}=\dfrac{3}{7}

Therefore, the probability that the selected fish is a male, is \dfrac{3}{7}.

C. We have to find the probability that the selected fish is a male green swordtail.

\text{P(Male green swordtail)}=\dfrac{\text{Total male green swordtail fish}}{\text{Total fish}}

\text{P(Male green swordtail)}=\dfrac{36}{140}

\text{P(Male green swordtail)}=\dfrac{9}{35}

Therefore, probability that the selected fish is a male green swordtail is \dfrac{9}{35}.

D.

We have to find the probability that the selected fish is either a male or a green swordtail.

\text{P(Male or green swordtail)}=\dfrac{\text{Total male or green swordtail fish}}{\text{Total fish}}

\text{P(Male or green swordtail)}=\dfrac{44+36+24}{140}

\text{P(Male or green swordtail)}=\dfrac{96}{140}

\text{P(Male or green swordtail)}=\dfrac{24}{35}

Therefore, the probability the selected fish is either a male or a green swordtail is \dfrac{24}{35}.

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<em><u>The intervals included in solution are:</u></em>

\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0

<em><u>Solution:</u></em>

Given that,

A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip

On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph

The group needs to travel an average of at least 24 mph

<em><u>Given inequality is:</u></em>

\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}

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\frac{1}{x} + \frac{1}{x} - 10\geq \frac{2}{24}\\\\\frac{2}{x}  - 10\geq \frac{2}{24}

\mathrm{Subtract\:}\frac{2}{24}\mathrm{\:from\:both\:sides}\\\\\frac{2}{x}-10-\frac{2}{24}\ge \frac{2}{24}-\frac{2}{24}\\\\Simplify\\\\\frac{2}{x}-10-\frac{2}{24}\ge \:0

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\mathrm{Multiply\:both\:sides\:by\:}24\\\\\frac{24\left(48-242x\right)}{24x}\ge \:0\cdot \:24\\\\Simplify\\\\\frac{48-242x}{x}\ge \:0\\\\Factor\ common\ terms\\\\\frac{-2\left(121x-24\right)}{x}\ge \:0\\\\\mathrm{Multiply\:both\:sides\:by\:}-1\mathrm{\:\left(reverse\:the\:inequality\right)}

When we multiply or divide both sides by negative number, then we must flip the inequality sign

\frac{\left(-2\left(121x-24\right)\right)\left(-1\right)}{x}\le \:0\cdot \left(-1\right)\\\\\frac{2\left(121x-24\right)}{x}\le \:0\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{\frac{2\left(121x-24\right)}{x}}{2}\le \frac{0}{2}\\\\Simplify\\\\\frac{121x-24}{x}\le \:0

\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\frac{121x-24}{x}\\

This is attached as figure below

From the attached table,

\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:\le \:\:0\\\\0

<em><u>Therefore, solution set is given as</u></em>:

\frac{1}{x} + \frac{1}{x}-10\ge \frac{2}{24}\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:0

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