Answer: ![\dfrac{1}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B6%7D)
Step-by-step explanation:
The given event : A randomly drawn marble is blue.
The number of blue marbles in the bag = 2
The total number of marbles in the bag = ![2+7+3=12](https://tex.z-dn.net/?f=2%2B7%2B3%3D12)
Now, the probability of drawing a blue marble is given by :-
![\text{P(Blue)}=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}\\\\\Rightarrow\text{P(Blue)}=\dfrac{2}{12}=\dfrac{1}{6}](https://tex.z-dn.net/?f=%5Ctext%7BP%28Blue%29%7D%3D%5Cdfrac%7B%5Ctext%7BNumber%20of%20blue%20marbles%7D%7D%7B%5Ctext%7BTotal%20number%20of%20marbles%7D%7D%5C%5C%5C%5C%5CRightarrow%5Ctext%7BP%28Blue%29%7D%3D%5Cdfrac%7B2%7D%7B12%7D%3D%5Cdfrac%7B1%7D%7B6%7D)
Hence, the probability of the given event event = ![\dfrac{1}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B6%7D)
Answer:
Option A - 0.9938
Step-by-step explanation:
Given : Assume that blood pressure readings are normally distributed with a mean of 118 and a standard deviation of 6.4. If 64 people are randomly selected.
To find : The probability that their mean blood pressure will be less than 120?
Solution :
The formula to find the probability is
![P(Z=X)=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=P%28Z%3DX%29%3D%5Cfrac%7BX-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
Where, X is the sample mean
is the population mean
is the standard deviation
n=64 is the number of sample
The probability that their mean blood pressure will be less than 120 is given by,
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C120%29%3D%5Cfrac%7B120-118%7D%7B%5Cfrac%7B6.4%7D%7B%5Csqrt%7B64%7D%7D%7D)
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C120%29%3D%5Cfrac%7B2%7D%7B%5Cfrac%7B6.4%7D%7B8%7D%7D)
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C120%29%3D%5Cfrac%7B2%7D%7B0.8%7D)
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C120%29%3D2.5)
From the z-table the value of z at 2.5 is
![P(Z](https://tex.z-dn.net/?f=P%28Z%3C120%29%3D0.9938)
Therefore, Option A is correct.
The probability that their mean blood pressure will be less than 120 is 0.9938.
We are asked to simplify the expression
![\frac{-7x}{5y} \cdot \frac{5x}{-7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-7x%7D%7B5y%7D%20%5Ccdot%20%20%5Cfrac%7B5x%7D%7B-7%7D%20%20)
,
what we do is, we form a single fraction where the numerator is the product of the numerators, and the denominator is the product of the denominators, that is:
![\frac{-7x}{5y} \cdot \frac{5x}{-7}= \frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-7x%7D%7B5y%7D%20%5Ccdot%20%5Cfrac%7B5x%7D%7B-7%7D%3D%20%5Cfrac%7B-7%5Ccdot5%20%5Ccdot%20x%20%5Ccdot%20x%7D%7B5%20%5Ccdot%28-7%29%20%5Ccdot%20y%7D%20)
simplify the common numbers and terms in the numerator and denominator:
![\frac{-7\cdot5 \cdot x \cdot x}{5 \cdot(-7) \cdot y}=\frac{5 \cdot x \cdot x}{5 \cdot y}=\frac{x \cdot x}{y}= \frac{ x^{2} }{y}](https://tex.z-dn.net/?f=%5Cfrac%7B-7%5Ccdot5%20%5Ccdot%20x%20%5Ccdot%20x%7D%7B5%20%5Ccdot%28-7%29%20%5Ccdot%20y%7D%3D%5Cfrac%7B5%20%5Ccdot%20x%20%5Ccdot%20x%7D%7B5%20%20%5Ccdot%20y%7D%3D%5Cfrac%7Bx%20%5Ccdot%20x%7D%7By%7D%3D%20%5Cfrac%7B%20x%5E%7B2%7D%20%7D%7By%7D%20)
Answer:
Parallel lines have the same a slope.
The slope-intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
We have y = -2x - 6 → the slope m = -2. Therefore we have the equation of a line:
![y = -2x + b](https://tex.z-dn.net/?f=y%20%3D%20-2x%20%2B%20b)
Put the coordinates of the point (-4, 1) to the equation:
![1=-2(-4)+b](https://tex.z-dn.net/?f=1%3D-2%28-4%29%2Bb)
<em>subtract 8 from both sides</em>
![-7=b\to b=-7](https://tex.z-dn.net/?f=-7%3Db%5Cto%20b%3D-7)
<h3>Answer: y = -2x - 7</h3>
Answer:
5
Step-by-step explanation:
the height 5
the base 2
5*2*1/2 = 5