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3 years ago

A school custodian waxed a gymnasium floor that measured 20feet by 20 feet. How many square feet did she have to wax

1 answer:

8 0

Here the dimension of the waxed gymnasium floor is given which is 20 feet by 20 feet. It means the floor is of square shape . And we need to find how many square feet she have to wax. Here square feet is given, which means we have to find the area. SO we need to find the area of the gymansium floor . And area of square is side square. So area of gymnasium floor = 20 ft times 20 ft = 400 square feet .

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in 2012, the population of a city was 63,000. by 2017, the population was reduced to approximately 54,100. identify any equation

Akimi4 [234]

Answer:

$f(x) = 63000(0.97)^x$

Step-by-step explanation:

Given

$f(0) = 63000$ ---x = 0, in 2012

$f(5) = 54100$ -- x = 5, in 2017

Required

Select all possible equations

Because there is a reduction in the population, as time increases; the rate must be less than 1.

An exponential function is represented as:

$f(x) = ab^x$

Where

$b = rate$

rate > 1 in options (a) and (b) i.e. 1.03

This implies that (a) and (b) cannot be true

For option (c), we have:

$f(x) = 63000(0.97)^x$

Set x = 0

$f(0) = 63000(0.97)^0 = 63000*1=63000\\$

Set x = 5

$f(5) = 63000(0.97)^5 = 63000*0.8587=54098.1 \approx 54100$

This is true because the calculated values of f(0) and f(5) correspond to the given values

For option (d), we have:

$f(x) = 52477(0.97)^x$

Set x = 0

$f(0) = 52477(0.97)^0 - 52477* 1 = 52477$

This is false because the calculated value of f(0) does not correspond to the given value

For option (e), we have:

$f(x) = 63000(0.97)^\frac{1}{5x}$

Set x = 0

$f(0) = 63000(0.97)^\frac{1}{5*0} = 63000(0.97)^\frac{1}{0} =$ undefined

This is false because the f(x) is not undefined at x = 0

For option (f), we have:

$f(x) = 52477(0.97)^{5x$

Set x = 0

$f(0) = 52477(0.97)^{5*0} = 52477(0.97)^0 =52477*1= 52477$

This is false because the calculated value of f(0) does not correspond to the given value

From the computations above, only (c) $f(x) = 63000(0.97)^x$ is true

4 0

3 years ago

Write 3 addition facts that have the same sum as 5 + 9

Dovator [93]

Answer:

10+4=14

8+6=14

13+1=14

5 0

3 years ago

Read 2 more answers

Jace's average gross pay is $1,630.00 bi-weekly. Determine how many years it will take Jace to earn his first million dollars.

vesna_86 [32]

The number of years it will take to earn his first million is 24 years

Average bi-weekly gross pay = $1,630

Bi-weekly = 2 weeks

Number of 2 weeks(bi-weeks) in a year = 26 bi-weeks

The least million he can earn is $1,000,000

Let the number of years = n

We could use the equation :

Least million = gross pay × (Number of bi-weeks × number of years)

1000000 = 1630 × (26n)

1000000 = 42380

Divide both sides by 34230

1000000 / 42380 = n

n = 23.59

The least number of years is 24.

Learn more : brainly.com/question/18796573

6 0

3 years ago

One year, the population of a city was 333,000. Several years later it was

Sunny_sXe [5.5K]

Answer:12%

Step-by-step explanation:

(333000-293040)×100/333000

7 0

3 years ago

We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measure

STALIN [3.7K]

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be $h(t) = -16\cdot t^{2} + 128\cdot t + 320$ , the first and second derivatives are, respectively:

First Derivative

$h'(t) = -32\cdot t +128$

Second Derivative

$h''(t) = -32$

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

$-32\cdot t +128 = 0$

$t = \frac{128}{32}\,s$

$t = 4\,s$ (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

$h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320$

$h(4\,s) = 576\,ft$

The highest altitude that the object reaches is 576 feet.

6 0

3 years ago