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VashaNatasha [74]

3 years ago

9

You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of

those are kings. What is the probability that you will have at most three kings in your hand?

1 answer:

Gre4nikov [31]3 years ago

8 0

Answer:

((4 choose 3)·(48 choose 2) + (4 choose 4)·(48 choose 1)) / (52 choose 5) = 19/10829 = 0.0018

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On a number line, what is the distance between -0.6 to -0.4?

Mila [183]

Answer is B
-0.6- (-0.4)= -0.6+0.4= -0.2

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What is the minimum value for g(x)=x2−10x+16 ?

mr_godi [17]

G(x)=x^2-10x+16
g(x)=x^2-10x+25-25+16
g(x)= (x-5)^2-9
minimum value is -9

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Julie bought 3.5 pounds of cheese for $7.49. how much was the cheese per pound

snow_lady [41]

$2.14 per pound is the answer I found. Hope that helps.

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2 years ago

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Angle θ is in standard position. if sin(θ) = − 1 3 , and π < θ < 3π 2 , find cos(θ).

kramer

The value of the angle θ is 160.52° then the value of the cosine will be negative 0.9428.

<h3>What is trigonometry?</h3>

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Angle θ is in standard position.

If sin(θ) = − 1/3 , and π < θ < 3π/2

Then the angle will be

$\theta = \sin ^{-1}\dfrac{-1}{3}\\\\\theta = -19.47$

Then add 180 degrees, then we have

$\theta = -19.47 + 180\\\\\theta = 160.52$

Then the value of the cosine will be

$\cos 160.52^o=-0.9428$

More about the trigonometry link is given below.

brainly.com/question/22698523

7 0

2 years ago

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The E. coli bacteria has a volume of 6 µm3 . In optimal conditions, an E. coli bacteria will double about every 30 minutes. Unde

Zinaida [17]

Answer:

It is going to take around 19 hours and 15 minutes for a single bacteria to grow to fill a thimble with volume 1 cm3.

It will take 57.6 hours to for the volume to fill the entire earth

Step-by-step explanation:

We can say that the volume of the bacteria is a geometric sequence, and each time moment is an arithmetic sequence.

Each geometric sequence has the following format:

${a, ar, ar^{2}, ar^{3},...}$

In which:

a is the first term

r is the common ratio.

We can find any term of the sequence by the following equation:

$x_{n} = ar^{(n-1)}$

Each arithmetic sequence has the following format:

${a, a+d, a+2d,...}$

In which:

a is the first term

d is the difference between the terms.

We can find any term of the sequence by the following equation:

$x_{n} = a + d(n)$

How i am going to solve this problem.

We have the sequence that is the volume of the bacteria:

Obs: $1(um)^{3} = 10^{-18}m^{3}$

$V_{n} = {6*10^{-18}, 12*10^{-18},...}$

$a = 6*10^{-18}$

$r = 2$

And the following arithmetic sequence that are the time(in hours).

$T_{n} = {0,0.5,1,...}$

$a = 0$

$d = 0.5$

$T_{n} = 0.5n$

How long will it take for a single bacterium to grow to fill a thimble with volume 1 cm3 ?

I am going to find the value of n for which $V_{n} = 1cm^{3}$ , then i find the value at this position in the arithmetic sequence. So

$1cm^{3} = 10^{-6}m^{3}$

$V_{n} = 6*10^{-18}*(2^{(n-1)})$

$10^{-6} = 6*10^{-18}*(2^{(n-1)})$

$\frac{10^{-6}}{6*10^{-18}} = 2^{(n-1)})$

Obs: $a^{b-c} = \frac{a^{b}}{a^{c}}$

$\frac{10^{12}}{6} = \frac{2^{n}}{2}$

$2^{n} = \frac{10^{12}}{3}$

Now, we have to apply these following logarithim proprierties to find the value of n:

$log a^{n} = n log a$

$log(\frac{a}{b}) = log a - log b$

$log 10^{n} = n$

log 2 = 0.30

log 3 = 0.48

$log 2^{n} = log(\frac{10^{12}}{3})$

$n log 2 = log(10^{12}) - log 3$

$0.30n = 12 - 0.48$

$0.30n = 11.52$

$n = 38.4$

Lets find $T_{38}$ and $T_{39}$ in the arithmetic sequence.

$T_{n} = 0.5n$

$T_{38} = 0.5*38 = 19$

$T_{39} = 0.5*39 = 19.5$

It is going to take around 19 hours and 15 minutes for a single bacteria to grow to fill a thimble with volume 1 cm3.

How long will it take for the volume to fill the entire earth 1.08 × 108 km3 ?

$1 (km)^{3} = 10^{9}m^{3}$

So

$1.08*10^{8} km^{3} = 1.08*10^{17} m^{3} = 108*10^{15}m^{3}$

Lets solve the same way as the first question.

$V_{n} = 6*10^{-18}*(2^{(n-1)})$

$108*10^{15} = 6*10^{-18}*(2^{(n-1)})$

$\frac{108*10^{15}}{6*10^{-18}} = 2^{(n-1)})$

$18*10^{33} = \frac{2^{n}}{2}$

$2^{n} = 36 * 10^{33}$

Aside from the proprierties seen in the first exercise, we also have that

log a*b = log a + log b

$log (2^{n}) = log(36 * 10^{33})$

$n log 2 = log 36 + log 10^{33}$

$0.30n = 1.56 + 33$

$0.30n = 34.56$

$n = \frac{34.56}{0.30}$

$n = 115.2$

$T_{115} = 0.5*115.2 = 57.6$

It will take 57.6 hours to for the volume to fill the entire earth

4 0

3 years ago