The volume of the rectangular prism:
![60x^3 + 145x^2 + 70x=5x(12x^2+29x+14)\\\\=5x(12x^2+21x+8x+14)=5x[3x(4x+7)+2(4x+7)]\\\\=5x(4x+7)(3x+2)\\\\Answer:\\length=5x\\width=4x+7\\height=3x+2](https://tex.z-dn.net/?f=60x%5E3%20%2B%20145x%5E2%20%2B%2070x%3D5x%2812x%5E2%2B29x%2B14%29%5C%5C%5C%5C%3D5x%2812x%5E2%2B21x%2B8x%2B14%29%3D5x%5B3x%284x%2B7%29%2B2%284x%2B7%29%5D%5C%5C%5C%5C%3D5x%284x%2B7%29%283x%2B2%29%5C%5C%5C%5CAnswer%3A%5C%5Clength%3D5x%5C%5Cwidth%3D4x%2B7%5C%5Cheight%3D3x%2B2)
In a study of 250 adults, the mean heart rate was 70 beats per minute. Assume the population of heart rates is known to be appro
ximately normal with a standard deviation of 12 beats per minute. What is the 99% confidence interval for the mean beats per minute?
68.9 − 76.3
70 − 72
61.2 − 72.8
68 − 72
68.9 − 76.3
70 − 72
61.2 − 72.8
68 − 72
1 answer:
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Answer:
, or x-2y=14
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (2, -6) and is parallel to the line x-2y=8
First, we need to find the slope of x-2y=8, since parallel lines have the same slopes
We can convert the equation from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept), in order to help us find the slope of the line
Start by subtracting x from both sides
-2y=-x+8
Divide both sides by -2
y=-4
The slope of the line x-2y=8 is 1/2
It's also the slope of the line parallel to it.
Since we know the slope of the line, we can plug it into the equation for slope intercept form:
Now we need to find b.
As the equation of the line passes through (2, -6), we can use it to help solve for b
Substitute -6 as y and 2 as x:
Multiply
-6=1+b
Subtract 1 from both sides
-7=b
Substitute -7 as b into the equation:
The equation can be left as that, or you can convert it into standard form if you wish.
In that case, you will need to move 1/2x to the other side:
A rule about the coefficients a, b, and c in standard form is that a (coefficient in front of x) CANNOT be negative, and every coefficient must be an integer (a whole number, not a fraction or decimal).
So multiply both sides by -2 in order to clear the fraction, as well as change the sign of a
x-2y=14
Hope this helps!
Answer:
The 75th percentile of this distribution is 11 .25 minutes.
Step-by-step explanation:
The random variable <em>X</em> is defined as the waiting time in line at an ice cream shop.
The random variable <em>X </em>follows a Uniform distribution with parameters <em>a</em> = 3 minutes and <em>b</em> = 14 minutes.
The probability density function of <em>X</em> is:
The <em>p</em>th percentile is a data value such that at least p% of the data-set is less than or equal to this data value and at least (100-p)% of the data-set are more than or equal to this data value.
Then the 75th percentile of this distribution is:
Thus, the 75th percentile of this distribution is 11 .25 minutes.