PLEASE HELPPP MEEE PLEASEE!!!

Mathematics

1 answer:

vaieri [72.5K]2 years ago

3 0

Step-by-step explanation:

17)

sec(x) = 1/cos(x)

cot(x) = cos(x)/sin(x)

so,

cos(x)/sin(x) × 1/cos(x) = 1/sin(x) = csc(x)

18)

2×sin(x) + 1 = 0

2×sin(x) = -1

sin(x) = -1/2 = -0.5

x = 210° or x = 330°

why ? sin(30°) = 0.5

so, sin(x) = -0.5 means the angles in the 3rd and 4th quadrant (where sine points "down" and is therefore negative). and x is then either 30° more than 180° (210°) or 30° less than 360° (330°).

draw a circle with the coordinate axis through the center. and then try and see.

19)

again the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

where the sides (a, b, c) are always opposite to the correlated angles (A, B, C).

so, in our case we have

8/sin(A) = 10/sin(58)

sin(A) = 8×sin(58)/10 = 0.678438477...

A = 42.7217403...° ≈ 43°

20)

so, we have 2 sides and the enclosed angle.

the area of the triangle in this case is

1/2 × a×c×sin(B) = 1/2 × 12×8×sin(60) = 48×sin(60) =

= 41.56921938... ≈ 42

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Answer:

A.The probability that exactly six of Nate's dates are women who prefer surgeons is 0.183.

B. The probability that at least 10 of Nate's dates are women who prefer surgeons is 0.0713.

C. The expected value of X is 6.75, and the standard deviation of X is 2.17.

Step-by-step explanation:

The appropiate distribution to us in this model is the binomial distribution, as there is a sample size of n=25 "trials" with probability p=0.25 of success.

With these parameters, the probability that exactly k dates are women who prefer surgeons can be calculated as:

$P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{25}{k} 0.25^{k} 0.75^{25-k}\\\\\\$

A. P(x=6)

$P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.00024*0.00423=0.183\\\\\\$

B. P(x≥10)

$P(x\geq10)=1-P(x$

$P(x=0) = \dbinom{25}{0} p^{0}(1-p)^{25}=1*1*0.0008=0.0008\\\\\\P(x=1) = \dbinom{25}{1} p^{1}(1-p)^{24}=25*0.25*0.001=0.0063\\\\\\P(x=2) = \dbinom{25}{2} p^{2}(1-p)^{23}=300*0.0625*0.0013=0.0251\\\\\\P(x=3) = \dbinom{25}{3} p^{3}(1-p)^{22}=2300*0.0156*0.0018=0.0641\\\\\\P(x=4) = \dbinom{25}{4} p^{4}(1-p)^{21}=12650*0.0039*0.0024=0.1175\\\\\\P(x=5) = \dbinom{25}{5} p^{5}(1-p)^{20}=53130*0.001*0.0032=0.1645\\\\\\P(x=6) = \dbinom{25}{6} p^{6}(1-p)^{19}=177100*0.0002*0.0042=0.1828\\\\\\$

$P(x=7) = \dbinom{25}{7} p^{7}(1-p)^{18}=480700*0.000061*0.005638=0.1654\\\\\\P(x=8) = \dbinom{25}{8} p^{8}(1-p)^{17}=1081575*0.000015*0.007517=0.1241\\\\\\P(x=9) = \dbinom{25}{9} p^{9}(1-p)^{16}=2042975*0.000004*0.010023=0.0781\\\\\\$