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1 year ago

1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually.

Mathematics

1 answer:

DaniilM [7]1 year ago

6 0

Answer:

Step-by-step explanation:

a) We would use the formula for exponential growth model which is expressed as

y = b(1 + r)^t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 5655

r = 1.4% = 1.4/100 = 0.014

Therefore, the equation would be

y = 5655(1 + 0.014)^t

y = 5655(1.014)^t

b) in 2022, t = 2022 - 2010 = 12 years

y = 5655(1.014)^12

y = 6682

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Solve the equation or inequality 3/2t-16=4/3t-6

Tamiku [17]

Answer:

Step-by-step explanation:

3/2t-16=4/3t-6

(subtract 4/3t from both sides)

3/2t-16-4/3t=-6

(add 16 to both sides)

3/2t-4/3t=-6+16

(simplify)

1/6t=10

(divide by 1/6 (or multiply by 6 on both sides)

t=60

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1 year ago

On a recent road trip, Mr. Yost drove 210 miles in 3 1/2 hours. Find both the miles driven per hour and the hours driven per mil

amid [387]

Miles driven per hour is 60 miles per hour

Hours driven per mile is 0.01667 hours per mile

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

Given that,

On a recent road trip, Mr. Yost drove 210 miles in 3 1/2 hours

Therefore,

Miles driven = 210 miles

$Time\ taken = 3\frac{1}{2}\ hour = \frac{7}{2} = 3.5\ hour$

To find: miles driven per hour and the hours driven per mile

<h3><u>Miles driven per hour</u></h3>

$\frac{miles}{hour} = \frac{210}{3.5}\\\\\frac{miles}{hour} = 60\ miles\ per\ hour$

<h3><u>Hours driven per mile</u></h3>

$\frac{hours}{miles} = \frac{3.5}{210}\\\\\frac{hours}{miles} = 0.01667\ hours\ per\ miles$

Thus both the miles driven per hour and the hours driven per mile are found

7 0

1 year ago

What is 1.532 rounded to the nearest hundredth

Anni [7]

Answer:

1.53 would be the answer

Step-by-step explanation:

If you are rounding to the nearest hundredth you are rounding to the 2nd decimal place. Since the next number is under 5, we would just drop it.

8 0

1 year ago

What are the coordinates of the circumcenter of this triangle? Enter your answer in the boxes.

Juliette [100K]

Answer:

(2,1)

Step-by-step explanation:

We can see that the given triangle.

The coordinates of A are (-1,5) .

The coordinates of B are (-1,-3).

The coordinates of C are (5,-3).

Distance formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB= $\sqrt{(-3-5)^2+(-1+1)^2}=8$ units

BC= $\sqrt{(5+1)^2+(-3+3)^2}=6$ units

AC= $\sqrt{(5+1)^2+(-3-5)^2}=10$ units

Pythagoras theorem: $(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2}$

$AB^2+BC^2=8^2+6^2=100$

$AC^2=(10)^2=100$

Therefore, $AC^2=AB^2+BC^2$

When a triangle satisfied the Pythagoras theorem then, the triangle is right triangle.

Hence, the given triangle is a right triangle.

We know that circum-center of right triangle is the mid point of hypotenuse.

Mid-point formula: $x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}$

Using this formula then, we get

Mid-point of hypotenuse AC is given by

$x=\frac{-1+5}{2}=2,y=\frac{5-3}{2}=1$

Hence, the circum-center of triangle is (2,1).

7 0

1 year ago

You plan to accumulate 100,000 at the end of 42 years by making the follow-

Mariana [72]

Answer:

Y = 479.17

Step-by-step explanation:

At the end of year 14, the balance from the deposits of X can be found using the annuity due formula:

A = P(1+r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the periodic payment, n is the number of payments and compoundings per year, t is the number of years, and r is the annual interest rate.

A = X(1.07)(1.07^14 -1)/0.07 ≈ 24.129022X

This accumulated amount continues to earn interest for the next 28 years, so will further be multiplied by 1.07^28. Then the final balance due to deposits of X will be ...

Ax = (24.129022X)(1.07^28) = 160.429967X

The same annuity due formula can be used for the deposits of Y for the last 10 years of the interval:

Ay = Y(1.07)(1.07^10 -1)/.07 = 14.783599Y

Now we can write the two equations in the two unknowns:

Ax +Ay = 100,000

X - Y = 100

From the latter, we have ...

X = Y +100

So the first equation becomes ...

160.429967(Y +100) +14.783599Y = 100000

175.213566Y +16,043.00 = 100,000

Y = (100,000 -16,043)/175.213566 ≈ 479.17

Y is 479.17

7 0

1 year ago