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vampirchik [111]
2 years ago
9

Pls help

Mathematics
1 answer:
galina1969 [7]2 years ago
8 0

Answer:

  • van: 8
  • bus: 22

Step-by-step explanation:

If we let v and b represent the seating capacity of vans and buses, respectively, then the two trips can be described by ...

  8v +8b = 240

  4v +b = 54

Dividing the first equation by 8 gives ...

  v +b = 30

Subtracting that from the second equation gives ...

  3v = 24

  v = 8 . . . . . . . . . . . divide by 3

  b = 30 -8 = 22

The number of students in each van is 8; the number in each bus is 22.

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A real estate agent earned $7200 commission on a property sale of $240,000. What is her rate of commission?
cluponka [151]

The real estate agent has a commission rate of 33.3%

if youy divide 240000 by 7200 then you would get 33.33333333

which would mean she has a (1/3) commission rate. hope this helps you out!

8 0
3 years ago
Eva wants to make two pieces of pottery.She needs 3/5 pound of clay for one piece and 7/10 pound of clay for the other piece.She
marta [7]

Answer:

a) Eva will need 2 bags of clay to make both pieces of pottery.

b) She will have leftover \frac{11}{10} pounds of clay.

Step-by-step explanation:

Hi

a) We have to find the total amount of clay, as she needs \frac{3}{5}pound=P_{1} and \frac{7}{10}pound=P_{2}, so P_{1}+P_{2}= \frac{3}{5} +\frac{7}{10} =\frac{6+7}{10}=\frac{13}{10}pounds, is the total amount of clay. Then as we Know that one bag of clay has \frac{4}{5} =\frac{8}{10} pounds, It isn´t enough, but with two bags 2*\frac{8}{10}=\frac{16}{10}  pounds, It is enough clay.

b) She will have leftover \frac{16}{10} -\frac{13}{10} =\frac{3}{10}pounds of the second bag, then we add the third one, so \frac{3}{10} +\frac{8}{10} =\frac{11}{10}pounds are leftover.

6 0
2 years ago
2. If the present salary of an employee is $36,500 and they are to receive a 7% raise next year, what will be the new salary?
Natasha_Volkova [10]

Answer:

hello ! you multiply $36,500 by 7% and you get $25,550. add this amount to the original amount and you get $62,050.

6 0
2 years ago
3. Samantha earns $7.80 per hour. If her regular hours are 40
ddd [48]

Answer:

468

Step-by-step explanation:

312 for the regular 40 hours then overtime for 10 hours would be 7.80 doubled times 10

3 0
3 years ago
Find an equation of the tangent plane to the given parametric surface at the specified point.
Neko [114]

Answer:

Equation of tangent plane to given parametric equation is:

\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}

Step-by-step explanation:

Given equation

      r(u, v)=u cos (v)\hat{i}+u sin (v)\hat{j}+v\hat{k}---(1)

Normal vector  tangent to plane is:

\hat{n} = \hat{r_{u}} \times \hat{r_{v}}\\r_{u}=\frac{\partial r}{\partial u}\\r_{v}=\frac{\partial r}{\partial v}

\frac{\partial r}{\partial u} =cos(v)\hat{i}+sin(v)\hat{j}\\\frac{\partial r}{\partial v}=-usin(v)\hat{i}+u cos(v)\hat{j}+\hat{k}

Normal vector  tangent to plane is given by:

r_{u} \times r_{v} =det\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\cos(v)&sin(v)&0\\-usin(v)&ucos(v)&1\end{array}\right]

Expanding with first row

\hat{n} = \hat{i} \begin{vmatrix} sin(v)&0\\ucos(v) &1\end{vmatrix}- \hat{j} \begin{vmatrix} cos(v)&0\\-usin(v) &1\end{vmatrix}+\hat{k} \begin{vmatrix} cos(v)&sin(v)\\-usin(v) &ucos(v)\end{vmatrix}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u(cos^{2}v+sin^{2}v)\hat{k}\\\hat{n}=sin(v)\hat{i}-cos(v)\hat{j}+u\hat{k}\\

at u=5, v =π/3

                  =\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k} ---(2)

at u=5, v =π/3 (1) becomes,

                 r(5, \frac{\pi}{3})=5 cos (\frac{\pi}{3})\hat{i}+5sin (\frac{\pi}{3})\hat{j}+\frac{\pi}{3}\hat{k}

                r(5, \frac{\pi}{3})=5(\frac{1}{2})\hat{i}+5 (\frac{\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}

                r(5, \frac{\pi}{3})=\frac{5}{2}\hat{i}+(\frac{5\sqrt{3}}{2})\hat{j}+\frac{\pi}{3}\hat{k}

From above eq coordinates of r₀ can be found as:

            r_{o}=(\frac{5}{2},\frac{5\sqrt{3}}{2},\frac{\pi}{3})

From (2) coordinates of normal vector can be found as

            n=(\frac{\sqrt{3} }{2},-\frac{1}{2},1)  

Equation of tangent line can be found as:

  (\hat{r}-\hat{r_{o}}).\hat{n}=0\\((x-\frac{5}{2})\hat{i}+(y-\frac{5\sqrt{3}}{2})\hat{j}+(z-\frac{\pi}{3})\hat{k})(\frac{\sqrt{3} }{2}\hat{i}-\frac{1}{2}\hat{j}+\hat{k})=0\\\frac{\sqrt{3}}{2}x-\frac{5\sqrt{3}}{4}-\frac{1}{2}y+\frac{5\sqrt{3}}{4}+z-\frac{\pi}{3}=0\\\frac{\sqrt{3}}{2}x-\frac{1}{2}y+z=\frac{\pi}{3}

5 0
3 years ago
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