What's the next ones?

Cate and Elena were playing a card game. The stack of cards in the middle had 24 cards in it to begin with. Cate added 8 cards t

gregori [183]

Starting out with 24.

Cate added 8.

24 + 8 = 32

Elena took 12.

32 - 12 = 20

Cate took 9.

20 - 9 = 11

11 are left.

8 0

3 years ago

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Question

Zielflug [23.3K]

Convert the 6 seconds to hours:

5 seconds x x 1/60 ( minutes per seconds) x 1/60 (Hours per minute) = 6/3600 = 1/600 hours.

Distance = speed x time

Distance = 585 x 1/600 = 585/600 = 0.975 miles

Convert miles to feet:

0.975 x 5280 = 5,148 feet

The plane traveled 5,148 feet in 6 seconds.

4 0

3 years ago

Danny is thinking of buying a gym membership. He has two gums available to choose from. Gym A has a $35 initial fee and costs $4

Ivanshal [37]

For this, all you have to do is create equations where all you have to do is change the x value. The equation for gym A would be 35 + 42x, where x is the number of months he has the membership, and the first number is the initial fee. The equation for gym B would be 65 + 36x, following the same rules. Now all you have to do is set both of these equations equal to each other:
65+36x=35+42x
Solving this equation results in x=5, which means that he has to have the memberships for 5 months for them to be equal. Now just plug that in to one side of the equation to get the amount he has to spend:
65+36(5) = $245

6 0

2 years ago

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

5 0

3 years ago

Which of the following statements are equivalent to the statement "price decreased by one third"?

N76 [4]

75% of what it before

4 0

2 years ago