A company purchased $11,100 of merchandise on June 15 with terms of 2/10, n/45, and FOB shipping point. The freight charge was $
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Answer:
52/3
Step-by-step explanation:
Use basic Thales therom,
Cross multiply,
3*(5x-8)=4*(3x+7)
3*5x - 3*8 = 4*3x + 4*7
15x - 24 = 12x +28
Add 24 to both sides
15x = 12x + 28 + 24
15x = 12x + 52
Subtract 12x from both sides
15x-12x =52
3x = 52
Divide both sides by 3
x = 52/3
Te x intercepts are where the graph crosses the x axis or wher y=0
the y intercept is where the graph crosses the y axis or where x=0
to find vertex, here is a hack
the x coordinate of the vertex for an equation in form ax^b+bx+c=y is -b/2a
so
y=3x^2+12x+7
-b/2a=-12/2(3)=-12/6=-2
sub that back
y=3(-2)^2+12(-2)+7
y=3(3)-24+7
y=9-17
y=-8
vertex is (-2,-8)
intercepts
x intercept is where y=0
0=3x^2+12x+7
using quadratic formula
x=(-6-√15)/3 and (-6+√15)/3
xints at ((-6-√15)/3,0) and ((-6+√15)/3,0)
yint is where x=0
set x=0
y=7
yint is at y=7 or (0,7)
vertex at (-2,-8)
xints at x=
and 
or at the points 
and 
yint at y=7 or at (7,0)
the y intercept is where the graph crosses the y axis or where x=0
to find vertex, here is a hack
the x coordinate of the vertex for an equation in form ax^b+bx+c=y is -b/2a
so
y=3x^2+12x+7
-b/2a=-12/2(3)=-12/6=-2
sub that back
y=3(-2)^2+12(-2)+7
y=3(3)-24+7
y=9-17
y=-8
vertex is (-2,-8)
intercepts
x intercept is where y=0
0=3x^2+12x+7
using quadratic formula
x=(-6-√15)/3 and (-6+√15)/3
xints at ((-6-√15)/3,0) and ((-6+√15)/3,0)
yint is where x=0
set x=0
y=7
yint is at y=7 or (0,7)
vertex at (-2,-8)
xints at x=
yint at y=7 or at (7,0)
Answer:
The P-value you would use to test the claim that the population mean of pencils produced in that factory have a mean length equal to 18.0 cm is 0.00736.
Step-by-step explanation:
We are given that a quality control specialist at a pencil manufacturer pulls a random sample of 45 pencils from the assembly line.
The pencils have a mean length of 17.9 cm. Given that the population standard deviation is 0.25 cm.
Let = <u><em>population mean length of pencils produced in that factory.</em></u>
So, Null Hypothesis, :
= 18.0 cm {means that the population mean of pencils produced in that factory have a mean length equal to 18.0 cm}
Alternate Hypothesis, :
18.0 cm {means that the population mean of pencils produced in that factory have a mean length different from 18.0 cm}
The test statistics that will be used here is <u>One-sample z-test</u> statistics because we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean length of pencils = 17.9 cm
= population standard deviation = 0.25 cm
n = sample of pencils = 45
So, <u><em>the test statistics</em></u> =
= -2.68
The value of z-test statistics is -2.68.
<u>Now, the P-value of the test statistics is given by;</u>
P-value = P(Z < -2.68) = 1 - P(Z 2.68)
= 1- 0.99632 = 0.00368
For the two-tailed test, the P-value is calculated as = 2 0.00368 = 0.00736.