Answer:
y - 5 = (3/2)(x - 2)
Step-by-step explanation:
If two lines are perpendicular, their slopes are negative reciprocals of one another.
The slope of 2x + 3y = 5 is found by solving this equation for y:
3y = -2x + 5, or y = (-2/3)x + 5/3.
Thus, the slope of the new line is the negative reciprocal of -2/3, which in turn comes out to 3/2.
Use the point-slope formula y - k = m(x - h):
Substituting the givens, we get y - 5 = (3/2)(x - 2)
Answer:
Answer is C on edge
Step-by-step explanation:
Trust me
Answer:
5.971 cm
Step-by-step explanation:
Use formula
for the area of the circle. Since the area of the circle is
then
![\pi r^2=56\\ \\r^2=\dfrac{56}{\pi}\\ \\r=\sqrt{\dfrac{56}{\pi}}](https://tex.z-dn.net/?f=%5Cpi%20r%5E2%3D56%5C%5C%20%5C%5Cr%5E2%3D%5Cdfrac%7B56%7D%7B%5Cpi%7D%5C%5C%20%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B56%7D%7B%5Cpi%7D%7D)
A square is inscribed into the circle, then its diagonal is twice the radius. The diagonal of the circle is equal to
![d=2r=2\sqrt{\dfrac{56}{\pi}}\ cm](https://tex.z-dn.net/?f=d%3D2r%3D2%5Csqrt%7B%5Cdfrac%7B56%7D%7B%5Cpi%7D%7D%5C%20cm)
Let x cm be the length of the square side, then by Pythagorean theorem,
![x^2+x^2=d^2\\ \\2x^2=\left(2\sqrt{\dfrac{56}{\pi}}\right)^2\\ \\2x^2=4\cdot \dfrac{56}{\pi}\\ \\x^2=\dfrac{112}{\pi}\\ \\x=\sqrt{\dfrac{112}{\pi}}\approx 5.971\ cm](https://tex.z-dn.net/?f=x%5E2%2Bx%5E2%3Dd%5E2%5C%5C%20%5C%5C2x%5E2%3D%5Cleft%282%5Csqrt%7B%5Cdfrac%7B56%7D%7B%5Cpi%7D%7D%5Cright%29%5E2%5C%5C%20%5C%5C2x%5E2%3D4%5Ccdot%20%5Cdfrac%7B56%7D%7B%5Cpi%7D%5C%5C%20%5C%5Cx%5E2%3D%5Cdfrac%7B112%7D%7B%5Cpi%7D%5C%5C%20%5C%5Cx%3D%5Csqrt%7B%5Cdfrac%7B112%7D%7B%5Cpi%7D%7D%5Capprox%205.971%5C%20cm)
Answer:
The probability that a baby born with Down's syndrome is a boy is
.
Step-by-step explanation:
The probability of a baby born being a boy (B) or a girl (G) is same, i.e.
P (B) = P (G) = 0.50.
The probability of a boy is born with Down's syndrome is, P (D|B) = <em>p</em>.
The probability of a girl is born with Down's syndrome is, P (D|G) = <em>q</em>.
The law of total probability states that:
![P(X)=P(X|Y)P(Y)+P(X|Z)P(Z)](https://tex.z-dn.net/?f=P%28X%29%3DP%28X%7CY%29P%28Y%29%2BP%28X%7CZ%29P%28Z%29)
Use this law to compute the probability of a baby born with Down's syndrome as follows:
![P(D)=P(D|B)P(B)+P(D|G)P(G)\\=(p\times0.50)+(q\times0.50)\\=0.50(p+q)](https://tex.z-dn.net/?f=P%28D%29%3DP%28D%7CB%29P%28B%29%2BP%28D%7CG%29P%28G%29%5C%5C%3D%28p%5Ctimes0.50%29%2B%28q%5Ctimes0.50%29%5C%5C%3D0.50%28p%2Bq%29)
The conditional probability of an event <em>X</em> given that another event <em>Y</em> has already occurred is:
![P(X|Y)=\frac{P(Y|X)P(X)}{P(Y)}](https://tex.z-dn.net/?f=P%28X%7CY%29%3D%5Cfrac%7BP%28Y%7CX%29P%28X%29%7D%7BP%28Y%29%7D)
Compute the probability that a baby born with Down's syndrome is a boy as follows:
![P(B|D)=\frac{P(D|B)P(B)}{P(D)} =\frac{p\times0.50}{0.50(p+q)} =\frac{p}{p+q}](https://tex.z-dn.net/?f=P%28B%7CD%29%3D%5Cfrac%7BP%28D%7CB%29P%28B%29%7D%7BP%28D%29%7D%20%3D%5Cfrac%7Bp%5Ctimes0.50%7D%7B0.50%28p%2Bq%29%7D%20%3D%5Cfrac%7Bp%7D%7Bp%2Bq%7D)
Thus, the probability that a baby born with Down's syndrome is a boy is
.
Answer:
There is usually a word that represent the operation for example difference to subtract
Step-by-step explanation: