6. Round 456,872 to the nearest thousand.

Seth’s father is thinking of buying his son a six-month movie pass for $40. With the pass, matinees cost $1.00. If matinees are

Ymorist [56]

Answer:

In order for it to benefit his father to buy the pass Seth have to attend the movies for 11 times.

Step-by-step explanation:

Given:

Cost of movie pass = $40

Cost per matinees with pass = $1.00

Cost per matinees without pass = $3.50

To Find:

Number of times must Seth attend in order for it to benefit his father to buy the pass = ?

Solution:

Let x be the number of times he wants to visit

To profit his father

The number of visits without pass = the number of visits with passin the cost of $3.50

Then, without pass if he visits for x times then the cost will be = 3.50x

Also with pass, the number of times he can visit the pass = $\frac{40}{3.50}$

then

$\frac{350 x}{3.50} = \frac{40}{3.50}$

$3.50x = 40$

$x = \frac{40}{3.50}$

x = 11.42

x = 11 (approx)

3 0

4 years ago

The ratio of the perimeters of two rectangles is 4 to 7. The perimeter of the larger rectangle is 42 inches. What is the perimet

Lelu [443]

P = 42(4/7)

p = (42)(4)/(1)(7)

p= 168/7

p= 24 inches

Answer : D , 24 inches

I hope that's help !

6 0

4 years ago

A yo-yo is moving up and down a string so that its velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. The initial pos

jeka57 [31]

Part A - The average value of v(t) over the interval (0, π/2) is 6/π

Part B - The displacement of the yo-yo from time t = 0 to time t = π is 0 m

Part C - The total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

<h3>Part A: Find the average value of v(t) on the interval (0, π/2)</h3>

The average value of a function f(t) over the interval (a,b) is

$f(t)_{avg} = \frac{1}{b - a} \int\limits^b_a {f(t)} \, dx$

So, since velocity at time t is given by v(t) = 3cos(t) for time t ≥ 0. Its average value over the interval (0, π/2) is given by

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {v(t)} \, dt$

Since v(t) = 3cost, we have

$v(t)_{avg} = \frac{1}{\frac{\pi }{2} - 0} \int\limits^{\frac{\pi }{2} }_0 {3cos(t)} \, dt\\= \frac{3}{\frac{\pi }{2}} \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= \frac{6}{{\pi}} [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= \frac{6}{{\pi}} [{sin(\frac{\pi }{2})} - sin0]\\ = \frac{6}{{\pi}} [1 - 0]\\ = \frac{6}{{\pi}} [1]\\ = \frac{6}{{\pi}}$

So, the average value of v(t) over the interval (0, π/2) is 6/π

<h3>Part B: What is the displacement of the yo-yo from time t = 0 to time t = π?</h3>

To find the displacement of the yo-yo, we need to find its position.

So, its position x = ∫v(t)dt

= ∫3cos(t)dt

= 3∫cos(t)dt

= 3sint + C

Given that at t = 0, x = 3. so

x = 3sint + C

3 = 3sin0 + C

3 = 0 + C

C = 3

So, x(t) = 3sint + 3

So, its displacement from time t = 0 to time t = π is

Δx = x(π) - x(0)

= 3sinπ + 3 - (3sin0 + 3)

= 3 × 0 + 3 - 0 - 3

= 0 + 3 - 3

= 0 + 0

= 0 m

So, the displacement of the yo-yo from time t = 0 to time t = π is 0 m

<h3>Part C: Find the total distance the yo-yo travels from time t = 0 to time t = π. (10 points)</h3>

The total distance the yo-yo travels from time t = 0 to time t = π is given by

$x(t) = \int\limits^{\pi}_0 {v(t)} \, dt\\= \int\limits^{\pi }_0 {3cos(t)} \, dt\\= 3 \int\limits^{\pi }_0 {cos(t)} \, dt\\ = 3 \int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt + 3\int\limits^{\pi }_{\frac{\pi }{2}} {cos(t)} \, dt\\= 3 \times 2\int\limits^{\frac{\pi }{2} }_0 {cos(t)} \, dt\\= 6 [{sin(t)}]^{\frac{\pi }{2} }_{0} \\= 6[{sin\frac{\pi }{2} - sin0]\\\\= 6[1 - 0]\\= 6(1)\\= 6$

So, the total distance the yo-yo travels from time t = 0 to time t = π is 6 m.

Learn more about average value of a function here:

brainly.com/question/15870615

#SPJ1

4 0

1 year ago

In a bag of marbles 12% were red, 14% were blue , and the rest where white. If the bag has 250 marbles, how many were red or blu

Svetach [21]

Answer:

Ok so, im sure if this is the right answer, but Im thinking there were 224% of red (or) blue marbles. If this is right, There you go, but if it's not, Im so sorry

Step-by-step explanation:

7 0

3 years ago

Can someone help me? Its Measurement. Attached a photo! Thank you!

kykrilka [37]

Answer:

24lb 11oz , 4lb 4oz

Step-by-step explanation:

<u>The first question:</u>

14lb + 9lb, or 14 + 9, = 23lb

15oz + 12oz, or 15 + 12, = 27oz

This means the answer is 23lb 27oz.

If it is asking for a simplified answer:

There are 16oz in 1lb.

27oz - 16oz = 11oz

So, the simplified answer would be 24lb 11oz.

<u>The second question:</u>

This is done the same way, just subtraction instead of addition.

14lb - 10lb = 4lb

10oz - 6oz = 4oz

This means the answer is 4lb 4oz.

This is the most simplified this answer can get.

4 0

4 years ago