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topjm [15]
2 years ago
10

A pharmacist is filling small empty bottles with cough syrup from a larger bottle. He can solve the inequality to find the numbe

r of small bottles, x, that can be filled from the larger bottle and still have 250 milliliters left in the larger bottle. Which statement describes the number of small bottles the pharmacist can fill?
Mathematics
1 answer:
andrey2020 [161]2 years ago
7 0

Let us assume capacity of large bottle = 1000 ml.

And capacity of each small bottle = 25 ml.

Reaming milliliters in large bottle = 250 milliliters.

Number of bottles = x bottles.

Total capacity of large bottle - capacity of a small bottle × number of bottles > Reamining milliliters in large bottle.

Therefore, we can setup an inequality.

1000 - 25 × x > 250.

1000 -25x >250.


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Find an equation of the plane that contains the points p(5,−1,1),q(9,1,5),and r(8,−6,0)p(5,−1,1),q(9,1,5),and r(8,−6,0).
topjm [15]
Given plane passes through:
p(5,-1,1), q(9,1,5), r(8,-6,0)

We need to find a plane that is parallel to the plane through all three points, we form the vectors of any two sides of the triangle pqr:
pq=p-q=<5-9,-1-1,1-5>=<-4,-2,-4>
pr=p-r=<5-8,-1-6,1-0>=<-3,5,1>

The vector product pq x pr gives a vector perpendicular to both pq and pr.  This vector is the normal vector of a plane passing through all three points
pq x pr
=
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-4 -2 -4
-3  5  1
=<-2+20,12+4,-20-6>
=<18,16,-26>

Since the length of the normal vector does not change the direction, we simplify the normal vector as
N = <9,8,-13>

The required plane must pass through all three points.
We know that the normal vector is perpendicular to the plane through the three points, so we just need to make sure the plane passes through one of the three points, say q(9,1,5).

The equation of the required plane is therefore
Π :  9(x-9)+8(y-1)-13(z-5)=0
expand and simplify, we get the equation
Π  :  9x+8y-13z=24

Check to see that the plane passes through all three points:
at p: 9(5)+8(-1)-13(1)=45-8-13=24
at q: 9(9)+8(1)-13(5)=81+9-65=24
at r: 9(8)+8(-6)-13(0)=72-48-0=24
So plane passes through all three points, as required.

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The mean number of hours of study time per week for a sample of 562 students is 23. If the margin of error for the population me
Vadim26 [7]

Answer:

The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).

Step-by-step explanation:

Confidence interval:

Sample mean plus/minus the margin of error.

In this question:

Mean of 23.

Margin of error 2.1.

Then

23 - 2.1 = 20.9

23 + 2.1 = 25.1

The 98% confidence interval for the mean number of hours of study time per week for all students is (20.9, 25.1).

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