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8 months ago

A box of stuffing costs $1.99 for 16 oz. Find the unit cost, round to the nearest hundredth.

Mathematics

1 answer:

Misha Larkins [42]8 months ago

7 0

The given ratio is:

$\frac{\text{ \$1.99}}{16oz}$

To find the unit cost per ounce, we can use proportions as follows:

$\frac{\text{ \$1.99}}{16oz}=\frac{x}{1oz}$

Now, solve for x:

$\begin{gathered} x=\frac{1oz\cdot\text{ \$1.99}}{16oz} \\ x=0.12 \end{gathered}$

The cost per ounce (unit cost) is then $0.12/oz

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Linear system word problem

soldi70 [24.7K]

Good job, you got the equations! XD

I'll just help you solve

Multiply the 2nd row by 9
9x+9y=117
9x+27y=207

Subtract the 2nd row from the 1st row
−18y=−90
Divide both sides by −18
y=−90/−18
Two negatives make a positive
y=90/18
y = 5

Substitute 5 into an equation
9x+9(5)=117
9x+45=117
Subtract 45 from both sides
9x=117−45

9x=72
Divide both sides by 9
x = ___

Hope this will help

3 0

3 years ago

A small rocket is fired from a launch pad 10 m above the ground with an initial velocity left angle 250 comma 450 comma 500 righ

jonny [76]

Let $\vec r(t),\vec v(t),\vec a(t)$ denote the rocket's position, velocity, and acceleration vectors at time $t$ .

We're given its initial position

$\vec r(0)=\langle0,0,10\rangle\,\mathrm m$

and velocity

$\vec v(0)=\langle250,450,500\rangle\dfrac{\rm m}{\rm s}$

Immediately after launch, the rocket is subject to gravity, so its acceleration is

$\vec a(t)=\langle0,2.5,-g\rangle\dfrac{\rm m}{\mathrm s^2}$

where $g=9.8\frac{\rm m}{\mathrm s^2}$ .

a. We can obtain the velocity and position vectors by respectively integrating the acceleration and velocity functions. By the fundamental theorem of calculus,

$\vec v(t)=\left(\vec v(0)+\displaystyle\int_0^t\vec a(u)\,\mathrm du\right)\dfrac{\rm m}{\rm s}$

$\vec v(t)=\left(\langle250,450,500\rangle+\langle0,2.5u,-gu\rangle\bigg|_0^t\right)\dfrac{\rm m}{\rm s}$

(the integral of 0 is a constant, but it ultimately doesn't matter in this case)

$\boxed{\vec v(t)=\langle250,450+2.5t,500-gt\rangle\dfrac{\rm m}{\rm s}}$

and

$\vec r(t)=\left(\vec r(0)+\displaystyle\int_0^t\vec v(u)\,\mathrm du\right)\,\rm m$

$\vec r(t)=\left(\langle0,0,10\rangle+\left\langle250u,450u+1.25u^2,500u-\dfrac g2u^2\right\rangle\bigg|_0^t\right)\,\rm m$

$\boxed{\vec r(t)=\left\langle250t,450t+1.25t^2,10+500t-\dfrac g2t^2\right\rangle\,\rm m}$

b. The rocket stays in the air for as long as it takes until $z=0$ , where $z$ is the $z$ -component of the position vector.

$10+500t-\dfrac g2t^2=0\implies t\approx102\,\rm s$

The range of the rocket is the distance between the rocket's final position and the origin (0, 0, 0):

$\boxed{\|\vec r(102\,\mathrm s)\|\approx64,233\,\rm m}$

c. The rocket reaches its maximum height when its vertical velocity (the $z$ -component) is 0, at which point we have

$-\left(500\dfrac{\rm m}{\rm s}\right)^2=-2g(z_{\rm max}-10\,\mathrm m)$

$\implies\boxed{z_{\rm max}=125,010\,\rm m}$

7 0

2 years ago

All of the following are rational numbers: .5, 7, V16 O True O False

wel

Answer:

Your answer is: A) True

( I say true because 1) .5 2) 7 are rational) ( I dont know about v16, if that is what it is supposed to say, then I cant quite tell)

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Step-by-step explanation:

Hope this helped : )

4 0

2 years ago

HELP!!!!!!!!!!!!!!!!!! What is the perimeter of the figure shown on the coordinate plane?

densk [106]

You can look at those dots, for example, you see (2,8) and (2,2) then look at y and the difference is 6. so if you see it like that, (2,8) and (5,8) is 3, (5,8) and (5,4) would be 4, (5,4) and (8,4) would be 3, (8,4) and (8,2) would be 2, and lastly (2,2) and (8,2) is 6
Now you add all of them up which will be 6+3+4+3+2+6 = 24
so the perimeter of this figure is 24

7 0

3 years ago

Find the area of a square with sides 17 centimeters long.

pickupchik [31]

Answer:

289 cm²

Step-by-step explanation:

Length (L) = 17 cm

Area of a square

= L²

= (17cm)²

= 289 cm²

7 0

2 years ago

Read 2 more answers