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3 years ago

7

Sales tax in Pennsylvania is 6%. Carlos bought a mountain bike that costs $125.50 before tax. What was the cost of the new bike

including sales tax?

2 answers:

hoa [83]3 years ago

7 0

I’m pretty sure the answer is 113.03

muminat3 years ago

7 0

Answer:

$878.50

Step-by-step explanation:

it's asking about new bike cost including sales tax.

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Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

Answer:

a) $\sqrt{144-288t+208t^2}$ b.) -12knots, 8 knots c) No e) $4\sqrt{13}$

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved $12\dot t (n.m)$ and ship B has moved $8\dot t (n.m)$ . We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

b)

We want to find $\frac{ds}{dt}$ for t=0 and t=1

$\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots$

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = $s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0$

Since function $f(x)=199-288x+208x^2$ is quadratic, concave up and has no real roots, we know that $199-288x+208x^2>0$ for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

$\lim_{t \to \infty} \frac{ds}{dt}$

So, lets check this limit:

$\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}$

Notice that:

$4\sqrt{13}=\sqrt{12^2+5^2}$ =√(speed of ship A² + speed of ship B²)

5 0

3 years ago

Find the solution to the system:

Sliva [168]

Answer:

u = 12, v= 15

Step-by-step explanation:

Given the system of simultaneous equation:

1/6 u− 1/3 v=−3... (1)

0.2u+0.1v=3.9...(2)

Rewriting both equation as fraction

1/6 u− 1/3 v=−3

1/5 u + 1/10 v = 39/10

Multiplying equation (1) by 6 and (2) by 10 we have:

u - 2v = -18... (3)

2u + v = 39...(4)

Using elimination method, we will first multiply equation (3) by 2 and (2) by 1 to have:

2u-4v = -36 ...(5)

2u+v = 39...(6)

Subtracting (5) from (6);

-4v-v = -36-39

-5v = -75

v = -75/-5

v = 15

Substituting v = 15 into equation (3) to get u we have:

u - 2(15) = -18

u - 30 = -18

u = -18+30

u = 12

The solution to the system of simultaneous equation are u = 12 and v = 15

7 0

3 years ago

The binomial (a + 5) is a factor of a2 + 7a + 10. What is the other factor?

malfutka [58]

(a+5)(a+2) = a^2 + 7a + 10
look at what adds to make 7 and multiplies to make 10
as you know one is 5, the other is 2 and 5 + 2 = 7 so both positive
(a+2)

7 0

3 years ago

Read 2 more answers

Maria, age 28, wants to pay no more than $300 a year in life insurance. what is the face value of the largest 20-year term polic

shusha [124]

The face value of the largest 20-year term policy which Maria can buy without spending more than $300 annually is $158,000.

<h3>What is face value?</h3>

Face is the term used in finance, is used for the amount which has to be paid to the policyholder at the time of maturity.

Maria, age 28, wants to pay no more than $300 a year in life insurance.

The period for this policy is 20-year term.

Annual life insurance premium (per 1,000 dollars of face value) for age 28.

A 10-year term for female is 1.28,
A 15 year term for female is 1.54,
A 20 year term for female is 1.89,
A whole life for female is 9.46.

For the 20 year term for female is 1.89 and annular premium is $300. Thus, the face value is,

$\rm Face \; Value=\dfrac{300}{1.89}\times1000\\\rm Face \; Value\approx158000$

Thus, the face value of the largest 20-year term policy which Maria can buy without spending more than $300 annually is $158,000.

Learn more about the face value here;

brainly.com/question/25596583

8 0

2 years ago

In a box of marbles, the ratio of red marbles to total marbles is 2:5. the ratio of green marbles to total marbles is 3:10. if t

STALIN [3.7K]

Ratio:

Red : Total
2 : 5
(x2) (x2)
4 : 10

Green : Total
3 : 10

Total of red and green marbles = 4 + 3 = 7

Blue marbles = 10 - 7 = 3

10 parts = 40 marbles
1 part = 40 ÷ 10 = 4
3 parts = 4 x 3 = 12

Answer: There are 12 blue marbles.

7 0

3 years ago