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3 years ago

Use complete sentences to describe why Set A = {x|x is an even whole number between 0 and 2} = ∅.

Mathematics

1 answer:

dolphi86 [110]3 years ago

5 0

Answer:

*1 month later*

Step-by-step explanation:

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A submarine dives 750 feet every 5 minutes and 4,500 feet every 30 minutes. Find the constant rate at which the submarine dives.

Anna35 [415]

Answer:

150 feet per minute

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3 years ago

According to the National Education Association (NEA), teachers generally spend more than 40 hours each week working on instruct

abruzzese [7]

Answer:

The median number of hours worked per week for the sample of 13 high school science teachers is 52.

Step-by-step explanation:

Median of a data set:

The median of a data set is the element that separates the lower 50% of the set from the upper 50%.

If the cardinality n of the set is odd, the median is the element at the position (n+1)/2 of the sorted sed.

If the cardinality n of the set is even, the median is the mean between the elements at the position n/2 and (n/2)+1 of the sorted sed.

In this question:

Hours worked for the sample of 13 high school science teachers:

55, 58, 52, 52, 56, 59, 48, 63, 52, 52, 50, 52, 56

Sorting in an ascending way:

48, 50, 52, 52, 52, 52, 52, 55, 56, 56, 58, 59, 63

Cardinality of 13, so odd, the median is the element at the 13+1/2 = 7th position of the sorted set, which is 52.

The median number of hours worked per week for the sample of 13 high school science teachers is 52.

8 0

3 years ago

HELP CONGRUENT ANGLES

Gemiola [76]

$\dfrac{RP}{RQ}=\dfrac{LJ}{LK}\\
\dfrac{RP}{1.6}=\dfrac{5.4}{3.2}\\
3.2RP=8.64\\
RP=2.7$

6 0

4 years ago

If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

6 0

3 years ago

TVs are described by the length of their diagonals. The diagonal of a TV is

elena55 [62]

Answer:

Step-by-step explanation:

4 0

3 years ago