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3 years ago

What is the slope of a line that is perpendicular to the line whose equation is 2y = 3x - 1?

Mathematics

1 answer:

alexandr1967 [171]3 years ago

4 0

Answer:

The slope of the line is $-\frac{2}{3}$

Step-by-step explanation:

For any line $y=mx+b$ , a line that is perpendicular to it is $y_\perp =-\frac{1}{m} x+b$ .

Therefore the slope of the perpendicular line is $-\frac{1}{m}$ .

For our case $y=\frac{3}{2}x-\frac{1}{2}$ therefore the slope of the prependicular is the reciprocal of $\frac{3}{2}$ multiplied by $-1.$

$\therefore\:slope=-\frac{2}{3}.$

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assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. find the

drek231 [11]

Answer:

65.3658 inches

Step-by-step explanation:

Let X be the height of a woman randomly choosen. We know tha X have a mean of 63.6 inches and a standard deviation of 2.5 inches. For an x value, the related z-score is given by z = (x-63.6)/2.5. We are looking for a value $x_{0}$ such that $P(X < x_{0}) = 0.76$ , but, $0.76 = P(X < x_{0}) = P((X-63.6)/2.5 < (x_{0}-63.6)/2.5) = P(Z < (x_{0}-63.6)/2.5)$ , i.e., $(x_{0}-63.6)/2.5$ is the 76th percentile of the standard normal distribution. So, $(x_{0}-63.6)/2.5 = 0.7063$ , $x_{0} =63.6+(2.5)(0.7063) = 65.3658$ . Therefore, the height of a woman who is at the 76th percentile is 65.3658 inches.

7 0

3 years ago

I need 7-12 please!!!

sergiy2304 [10]

Answer:

number 7 is y= $\frac{-ax+c}{b}$

Step-by-step explanation:

6 0

3 years ago

John took all his money from his savings account. He spent $110 on a radio and 4/11 of what was left on presents for his friend

svp [43]

Answer:

$1210

Step-by-step explanation:

Let x be total amount

First John spent $110 on a radio and 4/11 of what was left on presents for his friends so he was left with

$\frac{7}{11}(x-110)=\frac{7}{11}x-70$

Then he put 2/5 of his remaining money into a checking account

$\frac{3}{5}\left(\frac{7}{11}x-70\right)$

Rest he donated to charity

$420=\frac{3}{5}\left(\frac{7}{11}x-70\right)\\\Rightarrow \left(\frac{7}{11}x-70\right)=\frac{2100}{3}\\\Rightarrow \frac{7}{11}x-70=700\\\Rightarrow \frac{7}{11}x=770\\\Rightarrow x=1210$