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3 years ago

10

Kevin has $24 to buy a gift for his cousin. He found a gift for $22. With 5% sales tax added on, will Kevin have enough money to

buy the gift? If so, how much will he pay?

1 answer:

mojhsa [17]3 years ago

8 0

Answer:

Yes; $23.10

Step-by-step explanation:

5% of 22 is 1.10 and if you add the tax to the give price it is less than $24

You might be interested in

Aunt Jane weighs 45 newtons. What is her mass in kilograms?

zimovet [89]

Answer:

45 newtons = 10.1164024 pounds/force

Step-by-step explanation:

Hope this helps!!!

5 0

3 years ago

Harper has $15 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 and one box of crackers that coa

kolezko [41]

Box of crackers-1 15.00-3.50= 11.50

bags of fruit- 2 4.75*2= 9.50

Remainder- $2.00

6 0

3 years ago

Please help meeeeeeeeeeeeeeeee please

Harman [31]

9514 1404 393

Answer:

2.1 ft³

Step-by-step explanation:

Put the given radius and height into the volume formula and do the arithmetic.

V = 1/3πr²h

V = 1/3(3.14159)(1 ft)²(2 ft) ≈ 2.094 ft³

Rounded to tenths, this is 2.1 cubic feet.

__

The picture cuts off your rounding requirements. If it is hundredths, you need to use 2.09 ft³. If it is thousandths, your answer will depend on the value of pi you are asked to use.

4 0

3 years ago

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

kifflom [539]

Looks like we have

$\vec F(x,y,z)=z^2x\,\vec\imath+\left(\dfrac{y^3}3+\sin z\right)\,\vec\jmath+(x^2z+y^2)\,\vec k$

which has divergence

$\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(z^2x)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial z}=z^2+y^2+x^2$

By the divergence theorem, the integral of $\vec F$ across $S$ is equal to the integral of $\nabla\cdot\vec F$ over $R$ , where $R$ is the region enclosed by $S$ . Of course, $S$ is not a closed surface, but we can make it so by closing off the hemisphere $S$ by attaching it to the disk $x^2+y^2\le1$ (call it $D$ ) so that $R$ has boundary $S\cup D$ .

Then by the divergence theorem,

$\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(x^2+y^2+z^2)\,\mathrm dV$

Compute the integral in spherical coordinates, setting

$\begin{cases}x=\rho\cos\theta\sin\varphi\\y=\rho\sin\theta\sin\varphi\\z=\rho\cos\varphi\end{cases}\implies\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

so that the integral is

$\displaystyle\iiint_R(x^2+y^2+z^2)\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^1\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{2\pi}5$

The integral of $\vec F$ across $S\cup D$ is equal to the integral of $\vec F$ across $S$ plus the integral across $D$ (without outward orientation, so that

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\iint_D\vec F\cdot\mathrm d\vec S$

Parameterize $D$ by

$\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

with $0\le u\le1$ and $0\le v\le2\pi$ . Take the normal vector to $D$ to be

$\dfrac{\partial\vec s}{\partial v}\times\dfrac{\partial\vec s}{\partial u}=-u\,\vec k$

Then we have

$\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^1\left(\frac{u^3}3\sin^3v\,\vec\jmath+u^2\sin^2v\,\vec k\right)\times(-u\,\vec k)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{2\pi}\int_0^1u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac\pi4$

Finally,

$\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\frac{2\pi}5-\left(-\frac\pi4\right)=\boxed{\frac{13\pi}{20}}$

6 0

4 years ago

Use I = PRT to solve. (time is in years) Find R. [?]% (Give your answer as a percent.) P = $1,200 1 = $99 T = .75 years Enter

KatRina [158]

Answer:

Rate = 0.11%

Step-by-step explanation:

Using I = PRT

Where,

P = Principal = $1200
R = Rate = ✘
T = Time in years = 0.75 years
I = Interest = $99

⟼ I = PRT

Substitute values

⟼ 99 = 1200 × 0.75 × ✘

Multiply

⟼ 99 = 900✘

Divide both sides by the coefficient of ✘

⟼ 99/900 = ✘

⟼ ✘ = 0.11

Therefore, Rate is 0.11%

7 0

2 years ago