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ella [17]
3 years ago
14

A scientist will be measuring the total amount of leaf litter in a random sample (n = 5) of forest sites selected without replac

ement from a population of 45 sites. The sites are labeled 01, 02, . . . , 45 and she starts at the beginning of the line of random digits and takes consecutive pairs of digits. Which of the following is correct?
Mathematics
1 answer:
yulyashka [42]3 years ago
6 0
Eighty five and one twin
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How do you calculate the midpoint of question e)? I am very desperate. please help
andrey2020 [161]

Answer:

(-1,-1)

Step-by-step explanation:

Midpoint equation: (\frac{x_2+x_1}{2}, \frac{y_2+y_1}{2})

= (\frac{-5/2+1/2}{2},\frac{-1/2-3/2}{2} )

= (\frac{-2}{2},\frac{-2}{2})

=(-1,-1)

Use the formula and plug it in :)

7 0
2 years ago
Which property is shown? –7 + 24 = 24 + (–7) A. associative property B. distributive property C. opposite of a sum property D. c
erastova [34]
B Commutative Property
4 0
3 years ago
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Fitta spends 25 minutes on his rowing machine everyday, except for the weekends. How long will Fitta spend on his rowing machine
andrezito [222]

Answer:

25×20×60 =30000

30000/60=500 hours

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2 years ago
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Diagram 5 shows a right cylinder with a diameter of 2xcm. Given that the total surface area of the cylinder is 96cm³.Find the ma
Paraphin [41]

Given:

The diameter of the right cylinder is 2x cm.

The total surface area is 96 cm cube.

The radius is calculated as,

\begin{gathered} r=\frac{d}{2} \\ r=\frac{2x}{2} \\ r=x\text{ cm} \end{gathered}

The total surface area is,

\begin{gathered} S=2\pi rh+2\pi(r)^2 \\ 96=2\pi xh+2\pi(x^2) \\ h=\frac{96-2\pi(x^2)}{2\pi x} \end{gathered}

Volume is,

\begin{gathered} V=\pi(r)^2h \\ =\pi(x^2)\frac{96-2\pi(x^2)}{2\pi x} \\ =\frac{x(96-2\pi(x^2)}{2} \end{gathered}

Now, differentiate with respect to x,

\begin{gathered} \frac{dV}{dx}^{}=\frac{d}{dx}(\frac{x(96-2\pi(x^2)}{2}) \\ =\frac{d}{dx}\mleft(x\mleft(-\pi x^2+48\mright)\mright) \\ =\frac{d}{dx}\mleft(x\mright)\mleft(-\pi x^2+48\mright)+\frac{d}{dx}\mleft(-\pi x^2+48\mright)x \\ =1\cdot\mleft(-\pi x^2+48\mright)+\mleft(-2\pi x\mright)x \\ =84-3\pi(x^2)\ldots\ldots\ldots\ldots\text{.}(1) \end{gathered}

Now,

\begin{gathered} \frac{dV}{dx}=0 \\ 84-3\pi(x^2)=0 \\ x^2=\frac{16}{\pi} \\ x=\sqrt[]{\frac{16}{\pi}} \end{gathered}

Now, differentiate (1) with respect to x again,

\begin{gathered} \frac{d^2V}{dx^2}=\frac{d}{dx}(84-3\pi(x^2)) \\ =-6\pi x \\ At\text{ x=}\sqrt[]{\frac{16}{\pi}} \\ \frac{d^2V}{dx^2}=-6\pi\sqrt[]{\frac{16}{\pi}}

Since, the double derivative is negative.

So,\text{ the volume is maximum at }\sqrt[]{\frac{16}{\pi}}

So, the volume becomes,

\begin{gathered} V=\pi(x^2)h \\ V=\pi(\sqrt[]{\frac{16}{\pi}})^2h \\ V=\frac{16h}{\pi} \end{gathered}

Answer: maximum volume of the cylinder is,

6 0
1 year ago
Solve for x<br> 5x + 6 &lt; 3x + 7
Illusion [34]

Answer:

5x + 6 < 3x + 7 \\ 5x - 3x < 7 - 6 \\ 2x < 1 \\ x <  \frac{1}{2}

8 0
3 years ago
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