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2 years ago

50 km/h to miles per hour

Mathematics

2 answers:

Gnoma [55]2 years ago

7 0

31.069 miles per hour

satela [25.4K]2 years ago

3 0

31.0686 miles per hours

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An elementary school is offering 3 language classes: one in Spanish, one in French,and one in German. The classes are open to an

Alona [7]

Answer:

A. 0.5

B. 0.32

C. 0.75

Step-by-step explanation:

There are

28 students in the Spanish class,
26 in the French class,
16 in the German class,
12 students that are in both Spanish and French,
4 that are in both Spanish and German,
6 that are in both French and German,
2 students taking all 3 classes.

So,

2 students taking all 3 classes,
6 - 2 = 4 students are in French and German, bu are not in Spanish,
4 - 2 = 2 students are in Spanish and German, but are not in French,
12 - 2 = 10 students are in Spanish and French but are not in German,
16 - 2 - 4 - 2 = 8 students are only in German,
26 - 2 - 4 - 10 = 10 students are only in French,
28 - 2 - 2 - 10 = 14 students are only in Spanish.

In total, there are

2 + 4 + 2 + 10 + 8 + 10 +14 = 50 students.

The classes are open to any of the 100 students in the school, so

100 - 50 = 50 students are not in any of the languages classes.

A. If a student is chosen randomly, the probability that he or she is not in any of the language classes is

$\dfrac{50}{100} =0.5$

B. If a student is chosen randomly, the probability that he or she is taking exactly one language class is

$\dfrac{8+10+14}{100}=0.32$

C. If 2 students are chosen randomly, the probability that both are not taking any language classes is

$0.5\cdot 0.5=0.25$

So, the probability that at least 1 is taking a language class is

$1-0.25=0.75$

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3 years ago

(a) Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 Correct

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Splitting up the interval of integration into $n$ subintervals gives the partition

$\left[0,\dfrac1n\right],\left[\dfrac1n,\dfrac2n\right],\ldots,\left[\dfrac{n-1}n,1\right]$

Each subinterval has length $\dfrac{1-0}n=\dfrac1n$ . The right endpoints of each subinterval follow the sequence

$r_i=\dfrac in$

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$\displaystyle\sum_{i=1}^n\frac{{r_i}^3}n$

and taking the limit as $n\to\infty$ gives the area exactly. We have

$\displaystyle\lim_{n\to\infty}\frac1n\sum_{i=1}^n\left(\frac in\right)^3=\lim_{n\to\infty}\frac{n^2(n+1)^2}{4n^3}=\boxed{\frac14}$

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Step-by-step explanation:

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