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2 years ago

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A public interest group hires students to solicit donations by telephone. After a brief training period students make calls to p

otential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 80% of them give up their jobs in their first two weeks of employment. The group hires 7 students, which can be viewed as a random sample.

1 answer:

IceJOKER [234]2 years ago

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In the picture, the angle made by the goniometer is classified as a(n) ___ angle. ___ ° < θ < ___ .

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An obtuse angle which is greater than 90 degrees and less than 180 degrees.

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Manuel has $600 in a savings account at the beginning of the summer. He wants to have at least $300 in the account at the end of

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Four times the sum of a number and 15 is at least 120. Let x represent the number. Find all possible values for x.

lorasvet [3.4K]

Four times the sum of a number and 15 is at least 120
Let ‘x’ represent the number.
"The sum of a number and 15"
This can be written mathematically as x + 15
Given that 4 times this sum is at least 120,
This means that 4 times the sum is greater than or equal to 120
This can be written mathematically as 4(x + 15) >= 120
Solving for x
4(x + 15) >= 120
4x + 60 >= 120
4x >= 120 – 60
4x >= 60
x >= 60/4
x >= 15
x is greater than or equal to 15 <span>
</span>

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2 years ago

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Find the lengths of the median o

nexus9112 [7]

Answer:

$5/2units\\$ .

$\sqrt{47/2}units \\$ .

$\sqrt{41/2}units\\$ .

Step-by-step explanation:

The given points are A(1,2,3), B(-2,0,5) and C(4,1,5). The triangle is represented in the attach file where the three possible median are length AE, BF, and CD. We determine the coordinate of point D,E and F using the midpoint equation which is for any point A(x,y,z) and point B(a,b,c), the midpoint D is determine by

$D=(\frac{x+a}{2},\frac{y+b}{2},\frac{z+c}{2})\\$ .

Hence going by the above formula we determine the coordinate of point D,E and F

$D=(\frac{-2+1}{2},\frac{0+2}{2},\frac{5+3}{2})\\$ .

$D=(\frac{-1}{2},1,4)\\$ .

point E

$E=(\frac{4-2}{2},\frac{1+0}{2},\frac{5+5}{2})\\$ .

$E=(1,\frac{1}{2},5)\\$ .

Point F

$F=(\frac{4+1}{2},\frac{1+2}{2},\frac{5+3}{2})\\$ .

$F=(\frac{5}{2},\frac{3}{2},4)\\$ .

To determine the length of each median line we use the formula for distance between two points which is express as

$AB=\sqrt{(y_{2}-y_{1} )^{2} +(x_{2}-x_{1} )^{2}+(z_{2}-z_{1} )^{2}} \\$ .

Using the above formula we determine the length of line AE,BF and CD.

$AE=\sqrt{(1-1 )^{2} +(1/2-2)^{2}+(5-3 )^{2}} \\$ .

$AE=\sqrt{0 +9/4+4} \\$ .

$AE=\sqrt{25/4} \\$ .

$AE=5/2units\\$ .

For point BF

$BF=\sqrt{(5/2+2 )^{2} +(3/2-0)^{2}+(4-5 )^{2}}\\$ .

$BF=\sqrt{81/4 +9/4+1} \\$ .

$BF=\sqrt{47/2} \\$ .

$BF=\sqrt{47/2}units \\$ .

For point CD

$CD=\sqrt{(-1/2-4 )^{2} +(1-1)^{2}+(4-5 )^{2}}\\$ .

$BF=\sqrt{81/4 +0+1} \\$ .

$BF=\sqrt{41/2} \\$ .

$BF=\sqrt{41/2}units\\$ .

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The function expressed in the graph has a steeper slope than the function in the table.

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