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2 years ago

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Massimo spent $90 riding the bus. Each bus ride cost $2.50. Write and solve an equation to determine how many times Massimo rode

the bus.

2 answers:

Studentka2010 [4]2 years ago

7 0

Answer:36 times

Step-by-step explanation: 2.50r if r = rides taken 2.50 × 36 = 90

vagabundo [1.1K]2 years ago

7 0

Answer:

2.50x=90

Explanation:
2.50 is the cost for each ride, x represents how many times he rode the bus, and 90 is the total

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Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for

KIM [24]

Answer:

a) The recurrence formula is $P_n = \frac{109}{100}P_{n-1}$ .

b) The general formula for the population of Tacoma is

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write $P_0 = 200 000$ . For the population in 2001 we will use $P_1$ , for the population in 2002 we will use $P_2$ , and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that $P_0$ is equal to $P_1$ plus 9% of the population of 2000. Notice that this can be written as

$P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0$ .

In 2002, we will have the population of 2001, $P_1$ , plus the 9% of $P_1$ . This is

$P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1$ .

So, it is not difficult to notice that the general recurrence is

$P_n = \frac{109}{100}P_{n-1}$ .

b) In the previous formula we only need to substitute the expression for $P_{n-1}$ :

$P_{n-1} = \frac{109}{100}P_{n-2}$ .

Then,

$P_n = \left(\frac{109}{100}\right)^2P_{n-2}$ .

Repeating the procedure for $P_{n-3}$ we get

$P_n = \left(\frac{109}{100}\right)^3P_{n-3}$ .

But we can do the same operation n times, so

$P_n = \left(\frac{109}{100}\right)^nP_{0}$ .

c) Recall the notation we have used:

$P_{0}$ for 2000, $P_{1}$ for 2001, $P_{2}$ for 2002, and so on. Then, 2016 is $P_{16}$ . So, in order to obtain the approximate population of Tacoma in 2016 is

$P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062$

d) In this case we want to know when $P_n>400000$ , which is equivalent to

$(1.09)^{n}P_0>400000$ .

Substituting the value of $P_0$ , we get

$(1.09)^{n}200000>400000$ .

Simplifying the expression:

$(1.09)^{n}>2$ .

So, we need to find the value of $n$ such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

$n\ln(1.09)>\ln 2$ .

So, $n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693$ .

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0

2 years ago

Read 2 more answers

Plz plz helpppppppppppppp i really need it

tatuchka [14]

Answer:

3

Step-by-step explanation:

8*3=24

8 0

2 years ago

What would the answer to this question be? show work please

AURORKA [14]

Answer:

B

Step-by-step explanation:

The volume of a rectangular prism is the length times width times height.

V = LWH

V = (4√3)(3√6)W

V = 12√18 W

V = 36√2 W

If the volume is irrational, then W cannot have a radical that is half of a perfect square, because when multiplied by √2, that would yield a rational volume. For example, √18 × √2 = √36 = 6.

Therefore, the answer must be B, because 12 is not half of a perfect square.

V = 36√2 (4√12)

V = 144√24

V = 288√6

5 0

2 years ago

Solve. −35x+15>720 Drag and drop a number or symbol into each box to show the solution.

vampirchik [111]

Answer:

The solution of the inequality - 35x + 15 > 720 is $x$

Step-by-step explanation:

Consider the given inequality

- 35x + 15 > 720

Subtract both side by 15 , we get

- 35x + 15 - 15 > 720 - 15

- 35x > 705

Multiply both sides by -1 (Reverse the inequality )

(-35x)(-1) < 705 (-1)

35x < -705

Now, divide both side by 35

$\frac{35x}{35}=\frac{-705}{35}$

$\Rightarrow x=\frac{-141}{7}$

Thus, the solution of the inequality - 35x + 15 > 720 is $x$

6 0

3 years ago

For the given line segment, write the equation of the perpendicular bisector.

Jlenok [28]

Answer:

D) y = -4/5x – 47/10

Step-by-step explanation:

Step 1. Find the <em>midpoint of the segmen</em>t.

The two end points are (-6, -4) and (-2, 1).

The midpoint is at the average of the coordinates.

(xₚ, yₚ) = ((x₁ + x₂)/2, (y₁ + y₂)/2)

(xₚ, yₚ) = ((-6 - 2)/2, (-4 + 1)/2)

(xₚ, yₚ) = (-8/2, -3/2)

(xₚ, yₚ) = (-4, -3/2)

===============

Step 2. Find the <em>slope (m₁) of the segment</em>

m₁ = (y₂ - y₁)/(x₂ - x₁)

m₁ = (1 - (-4))/(-2 - (-6))

m₁ = (1 + 4)/(-2 + 6)

m₁ = 5/4

===============

Step 3. Find the <em>slope (m₂) of the perpendicular bisector </em>

m₂ = -1/m₁

m₂ = -4/5

====================

Step 4. Find the <em>intercept of the perpendicular bisector</em>

y = mx + b

y = -(4/5)x + b

The line passes through (-4, -3/2).

-3/2 = -(4/5)(-4) + b

-3/2 = 16/5 + b Multiply each side by 10

-15 = 32 + 10 b Subtract 32 from each side

-47 = 10b Divide each side by 10

b = -47/10

===============

Step 5. Write the <em>equation for the perpendicular bisector</em>

y = -4/5x – 47/10

The graph shows the midpoint of your segment at (-4, -3/2) and the perpendicular bisector passing through the midpoint and (0, -47/10).

4 0

3 years ago