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3 years ago

Suppose we want to choose 5 objects,without replacement from 16 distinct objects

Mathematics

1 answer:

lesya692 [45]3 years ago

4 0

Answer:

4368 ways

Step-by-step explanation:

We want to choose 5 objects,without replacement from 16 distinct objects.

We can use combination in this case. The formula for the combination is given by :

$_{n}C_r=\dfrac{n!}{r!(n-r)!}$

We have, n = 16 and r = 5

So,

$_{16}C_5=\dfrac{16!}{5!(16-5)!}\\\\_{16}C_5=\dfrac{16!}{5!11!}\\\\=4368$

So, there are 4368 ways in which we want to choose 5 objects,without replacement from 16 distinct objects.

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(02.02)Angle A measures 50 degrees. If angle A is rotated 45 degrees, what is the measure of angle A'? 45 degrees 50 degrees 95

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95 degrees
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4 years ago

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SOVA2 [1]

Answer:

Hi how are you doing?. Is that nice enough

Step-by-step explanation:

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4 years ago

4.) Complete the equations of the system in slope-intercept form. Use a decimal for the slope if necessary.

marissa [1.9K]

The slope is found by $y_{2} -y_{1} / x_{2} - x_{1}$
Line 1: y2 is 6, y1 is 4, x2 is 2, x1 is -2
6-4/2- -2= 2/4=1/2

Slope intercept is written as y= mx+b. m is the slope, and b is the intercept (the intercept is the value of y when x is 0). To find out the intercept, we plug in values of y, m and x
4= 1/2(-2) +b
4=-1+b
5=b
The equation for line 1 is y= 1/2x +5
Using the same formulas as above, the equation for line 2 is y= 3x+4
The solution to the system is a point where both lines would meet in the graph, or a set of x and y values that satisfies both equations.
y= 3x+4
y= 1/2x+5
3x+4 = 1/2x+5
3x= 1/2x +5 -4
3x= 1/2x +1
3x-1/2x= 1
2.5x=1
2.5x/2.5=1/2.5
x=0.4
Plug 0.4 into the slope intercept equation
y= 3(0.4) +4
y= 1.2 +4
y=5.2

y= 1/2(0.4) +5
y= 0.2 +5
y= 5.2
The solution is 0.4, 5.2

The other set of lines
Line 1: y= 3x+2
Line 2: y= -2x +7
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4 0

4 years ago

We saw two distributions for triathlon times: N(Âµ = 4313, Ï = 583) for Men, Aged 30 - 34 and N(Âµ = 5261, Ï = 807) for the Wome

zzz [600]

Answer:

a) 3354 seconds

b) 6294 seconds

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) The cutoff time for the fastest 5% of athletes in the men's group, i.e. those who took the shortest 5% of time to finish.

$\mu = 4313, \sigma = 583$

The cutoff for the shortest 5% is the 5th percentile, which is X when Z has a pvalue of 0.05. So X when Z = -1.645.

$Z = \frac{X - \mu}{\sigma}$

$-1.645 = \frac{X - 4313}{583}$

$X - 4313 = -1.645*583$

$X = 3354$

Cutoff of 3354 seconds.

(b) The cutoff time for the slowest 10% of athletes in the women's group.

$\mu = 5261, \sigma = 807$

The slowest 10% is the 10% that takes more time, so the cutoff is the 100 - 10 = 90th percentile, which is X when Z has a pvalue of 0.9. So X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 5261}{807}$