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3 years ago

Stephanie goes shopping on Sunday. She

1 answer:

4 0

Started with: $60
left with: $10
items bought: 20

60 - 10 = 50 < amount spent

50/20 = amount spent/items bought
= $ 2.50 < each chocolate

you can check this by multiplying the items bought and the amount each item cost to get how much you spent

20 × 2.5 = 50

Stephanie started off with 60 dollars and ended with 10 dollars

60 - 50 = 10

hope this helps :)

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A rectangular storage container with an open top is to have a volume of 10 m3 . then length of its base is twice the width. mate

katrin [286]

Answer:

The cost of materials for the cheapest such container is $163.54.

Step-by-step explanation:

A rectangular storage container with an open top is to have a volume of 10 m³.

The volume of the rectangle is

$\text{Volume} =\text{Length} \times \text{Width} \times \text{Height}$

Length of its base is twice the width.

Let Width be 'w'.

Length is l=2w.

Height be 'h'.

$10 =2w\times w\times h$

$10=2w^2h$

The height in terms of width is represented as,

$h=\frac{10}{2w^2}$

$h=\frac{5}{w^2}$

According to question,

The cost is 10 times the area of the base and 6 times the total area of the sides.

i.e. Cost is given by,

$C=10(L\times W)+6(2\times L\times H+2\times W\times H)$

$C=10(2w\times w)+6(2\times 2w\times \frac{5}{w^2}+2\times w\times \frac{5}{w^2})$

$C=20w^2+\frac{120}{w}+\frac{60}{w}$

$C(w)=20w^2+\frac{180}{w}$

To get the minimum value,

Differentiate the cost w.r.t 'w',

$C'(w)=20\frac{d(w^2)}{dw}+180\frac{d(w^{-1})}{dw}$

$C'(w)=20\times 2w-180 w^{-2}$

$C'(w)=40w-\frac{180}{w^2}$

To find critical points put derivate =0,

$40w-\frac{180}{w^2}=0$

$40w=\frac{180}{w^2}$

$w^3=\frac{180}{40}$

$w=\sqrt[3]{4.5}$

$w=1.65$

We find the second derivative to minimize,

$C''(w)=40\frac{d(w)}{dw}-180\frac{d(w^{-2})}{dw}$

$C''(w)=40+360(w^{-3})$

$C''(w)>0$

As $C''(w)>0$ it is the minimum cost.

The cost is minimum at w=1.65.

Substitute the values in the cost function,

$C(1.65)=20(1.65)^2+\frac{180}{1.65}$

$C(1.65)=54.45+109.09$

$C(1.65)=163.54$

Therefore, the cost of materials for the cheapest such container is $163.54.

7 0

4 years ago

What percent of 90 is 54?

Helga [31]

Answer should be 60! hope this helps :)

5 0

4 years ago

Read 2 more answers

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almana

pochemuha

A. P(492 < x-bar < 512)

z = (492-502)/100/√90 

z = -0.95 is 0.1711 

z = (512-502)/100/√90 

z = 0.95 is 0.8289 

b. P(505 < x-bar < 525) 

z = (505-515)/100/ √90 

z = -0.95 

z = (525-515)/100/ √90 

z = 0.95 

P(-0.95< z < 0.95) = 0.6578 

P(-0.95< z < 0.95) = 0.6578 

c. P(484 < x-bar < 504) 

z = (484-494)/100/√100 

z = -1 is 0.1587 

z = (504-494)/100/√100 

z = 1 is 0.8413 

P(-1< z <1) = 0.6826

6 0

3 years ago

S=2×πrh, solve for r. I got S/2xh=r is that right?

olga nikolaevna [1]

$given \: that \: s = 2 \times \pi \times r \times h$

by making r the subject, you need to divide the whole equation by 2πh

s/2πh = 2πhr/2πh

cancel out

r = s/2πh

5 0

4 years ago

I need help asap questions 12-17 please.

user100 [1]

Answer:

12. -5 and 4

13. -2 and -1

14. -5 and 6

15. -4 and -3

16. -2 and 8

17. -3 and 8

Step-by-step explanation:

4 0

4 years ago