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Anton [14]
3 years ago
6

Mr.Lee wants to survey 20 of the 210 students in seventh grade about the hours they slerp each night. He finds 2 of the 20 stude

nts surveyed sleep for 9 hours each night. About how many of the 210 seventh graders sleeo for 9 hours each night?​
Mathematics
1 answer:
allsm [11]3 years ago
6 0

21 students sleep for 9 hours each night

<em><u>Solution:</u></em>

Given that, Mr.Lee wants to survey 20 of the 210 students in seventh grade about the hours they sleep each night

He finds 2 of the 20 students surveyed sleep for 9 hours each night

Therefore, 2 out of 20 students sleep for 9 hours each night

Find out the percentage of 2 out of 20

\rightarrow \frac{2}{20} \times 100 = 10 \%

Thus 10 % of 210 students sleep for 9 hours each night

Find out 10 % of 210

\rightarrow 10\% \text{ of } 210\\\\\rightarrow 10 \% \times 210\\\\\rightarrow \frac{10}{100} \times 210\\\\\rightarrow 21

Thus 21 students sleep for 9 hours each night

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A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid
Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = 2 \times width

Base area = lb

= 2x^2

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}

Now, cost is

= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}

now we have to minimize C(x)

So, we need to compute the C'(x)

= 52x - \frac{648}{x^2}

C"(x)  = 52x - \frac{1,296}{x^3}

now for the critical points, we will solve the equation C'(x) = 0

= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}

C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0

So, x is a point of minima that is

= (\frac{648}{52} )^\frac{1}{3}

Now, Base material cost is

= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}

= 139.75

Side material cost is

= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3}  }

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

4 0
3 years ago
Which equation is the inverse of y = 16x2 + 1?
Llana [10]

Answer:

y=\frac{\sqrt{x-1} }{4}

Step-by-step explanation:

The given equation is

y=16x^2+1

For this function to have an inverse, we must restrict the domain, say x\ge0

We interchange x and y to get,

x=16y^2+1


We now make y the subject to get;


x-1=16y^2


x-1=16y^2

We divide through by 16 to get;


\frac{x-1}{16}=y^2


We now take the square root of both sides to get;

\pm \sqrt{\frac{x-1}{16}}=y


y=\pm \frac{\sqrt{x-1} }{4}


Since  x\ge 0, the inverse function is


y=\frac{\sqrt{x-1} }{4}


6 0
3 years ago
Please help 30 points
leva [86]
Wow this question is very difficult,hold up
8 0
3 years ago
Val is going to plant n vegetables seeds in one garden and 2n+5 vegetables seeds in another. How many seeds is Val going to plan
mezya [45]
Val will plant:
2n+5+n
seeds. 

This is equal to:
3n+5

So, in total, Val will plant 3n + 5 seeds.
8 0
3 years ago
1.) The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approxi
const2013 [10]

Answer:

c .3.3

Step-by-step explanation:

pH is the negative log of the molar hydrogen ion concentration.The equation to calculate pH is;

pH = -log10[H+]

pH = -log10(5.0 x 10-4)

pH = 3.30

6 0
3 years ago
Read 2 more answers
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