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2 years ago

If c= 54$ when n is 9, what is the cost of the sandwich when n is 3

Mathematics

1 answer:

Katyanochek1 [597]2 years ago

5 0

That would be 18$, basically you're dividing n by three so you do the same with the outcome, so the cost is 18$

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Which of the following numbers is greatest, or furthest to the right on the number line? {56, 39, 74, 81, 62}

Dimas [21]

The greatest number is 81

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3 years ago

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90 hazelnuts have a mass of 125 g. Hazelnuts have 630 calories per 100 g. work out the number of calories per hazelnut

jenyasd209 [6]

90 hazelnuts = 125g

Therefore, the mass of one hazelnut is this...

90 / 90 = 125 / 90

1 hazelnut = 25/18 grams

630 calories = 100 grams

100 divided by 25/18 = 72

Therefore...

630 / 72 = 1 hazelnut

AND THE ANSWER IS

8.75 calories = 1 hazelnut

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3 years ago

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Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours dur

Gelneren [198K]

I am setting the week hourly rate to x, and the weekend to y. Here is how the equation is set up:

13x + 14y = $250.90
15x + 8y = $204.70

This is a system of equations, and we can solve it by multiplying the top equation by 4, and the bottom equation by -7. Now it equals:

52x + 56y = $1003.60
-105x - 56y = -$1432.90

Now we add these two equations together to get:

-53x = -$429.30 --> 53x = $429.30 --> (divide both sides by 53) x = 8.10. This is how much she makes per hour on a week day.

Now we can plug in our answer for x to find y. I am going to use the first equation, but you could use either.

$105.30 + 14y = $250.90. Subtract $105.30 from both sides --> 14y = $145.60 divide by 14 --> y = $10.40

Now we know that she makes $8.10 per hour on the week days, and $10.40 per hour on the weekends. Subtracting 8.1 from 10.4, we figure out that she makes $2.30 more per hour on the weekends than week days.

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2 years ago

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Find the volume of the solid.

dmitriy555 [2]

In Cartesian coordinates, the region (call it $R$ ) is the set

$R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}$

In the plane $z=2$ , we have

$2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2$

which is a circle with radius $\sqrt2$ . Then we can better describe the solid by

$R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx$

While doable, it's easier to compute the volume in cylindrical coordinates.

$\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}$

Then we can describe $R$ in cylindrical coordinates by

$R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}$

so that the volume is

$\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}$

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1 year ago

The owner of a bookstore asked her regular customers to rank 3 items from a list of products that she would like to bring to the

Mazyrski [523]

40 ways. 6!/3!(6-3)! =120. We are only trying to find 3 ways. 120 is the total, 120/30 =40. So 40 is the answer.

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2 years ago

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