If a man travels p hours at an average rate of q miles per hour, and then r hours at an average rate of s miles per hour, what is his overall average rate of speed?

Answers

Answer 1

Answer: Total miles traveled in p hours = p*q miles and
Total miles traveled in r hours = r*s miles
so, average rate of speed = total miles traveled / number of hours
=[{(p*q)+(r*s)} / (p+r)] miles per hour

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Simplify completely the quantity x squared plus x minus 12 over quantity x squared minus x minus 20 divided by the quantity 3 x squared minus 24 x plus 45 over quantity 12 x squared minus 48 x minus 60.
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Write the explicit rule.

-21, -51, -81, -111, -141

Answers

Answer:

aₙ = - 30n + 9

Step-by-step explanation:

You can tell this is an arithmetic sequence, as there is a difference of 30 between each value. Therefore the equation we will use here is aₙ = a₁ + (n - 1)d.

aₙ = a₁ + (n - 1)d

= - 21 + (n - 1) * - 30

= - 21 - 30n + 30

= - 30n + 9

Your solution would be option d. aₙ = - 30n + 9

There are 480 jellybeans in an 8-ounce jar. How many jellybeans are there per ounce in the jar?0.017
6
60
3,840

Answers

For this case, what we must do is divide the total amount of jellybeans by the total number of ounces.

For this, we use the following equation:

$r = \frac {amount\ of\ jellybeans} {number\ of\ ounces}$

Substituting values:

$r = \frac {480} {8}\nr = 60$

Answer:

There are 60 jellybeans per ounce in the jar.

Option 3

The answer would be 60. This is because 480/8=60.

A college freshman started the year with $4000 in spending money and after three months, she has $2800 left. Assume that she will continue to spend her money at this same rate.

Answers

To solve this question, you need to know the rate in which the money is being spent. First, you know the y-intercept, which is 4000, or the money she owned before spending it. Next, you know, how much she had spent in the duration of 3 months. So, if you substitute those numbers into y=ax+b, it would be 2800=-3a+4000 (or 2800=4000-3a either way it is equivalent) If you solve this, you know that the college freshman is spending her money at a rate of $400 per month. Hope this helps :)

4000-2800=1200

1200/3 equals 400 a moth

If she continues, she will have enough money for 7 more months

A ball is launched from a sling shot. Its height, h(x), can be represented by a quadratic function in terms of time, x, in seconds.After 1 second, the ball is 148 feet in the air; after 2 seconds, it is 272 feet in the air.

Find the height, in feet, of the ball after 6 seconds in the air.

I have no idea any help?

Answers

From the data given, generate first the quadratic equation which best describe the height of the ball. The quadratic function has a general form of
f(x) = Ax^2 + Bx

Substituting the known data,

(1) 148 = A(1^2) + B(1)
(2) 272 = A (2^2) + B (2)
solving for A and B simultaneously,

A = -12
B = 160

To answer this problem, substitute 6 to x. Thus, after 6 seconds, the height is 528 feet.

Dave has had a gym membership for 10 weeks. He goes to the gym 5 times a week. Each visit, he exercises for 1.75 hours. He spends 0.5 hours on the treadmill and the rest he spends on the stationary bicycle. How much time does Dave spend on the stationary bicycle in a week?

Answers

75 x 5 = 375 hour in a week

If 6.3% of your salary is deducted for a fund how much would be deducted from a $488.00 weekly salary

Answers

the issue is to find the 6.3% out of $488, that is easy, just multiply them both and remember that 6.3% is 6.3 out of 100, 6.3/100
deduction = 6.3%($488)
= (6.3/100)(488)
= 30.74
hence, will be deducted $30.74 which is 6.3% of $488

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