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3 years ago

10. FREEBIE

Mathematics

1 answer:

professor190 [17]3 years ago

8 0

Answer:

D. f(x) = 1.06x; $169.60

Step-by-step explanation:

x(1.06) = total after tax

160(1.06)= 169.6

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As part of quality-control program, 3 light bulbs from each bath of 100 are tested. In how many ways can this test batch be chos

hichkok12 [17]

Answer:

<h3>By 161700 ways this test batch can be chosen.</h3>

Step-by-step explanation:

We are given that total number of bulbs are = 100.

Number of bulbs are tested = 3.

Please note, when order it not important, we apply combination.

Choosing 3 bulbs out of 100 don't need any specific order.

Therefore, applying combination formula for choosing 3 bulbs out of 100 bulbs.

$^nCr = \frac{n!}{(n-r)!r!}$ read as r out of n.

Plugging n=100 and r=3 in above formula, we get

$^100C3 = \frac{100!}{(100-3)!3!}$

Expanding 100! upto 97!, we get

= $\frac{100\times 99\times 98\times 97!}{97!3!}$

Crossing out common 97! from top and bottom, we get

= $\frac{100\times 99\times 98}{3!}$

Expanding 3!, we get

= $\frac{100\times 99\times 98}{3\times 2\times 1}$

= 100 × 33 × 49

= 161700 ways.

<h3>Therefore, by 161700 ways this test batch can be chosen.</h3>

3 0

3 years ago

HELP PLEASE ASAP

Pie

$\bold{\huge{\underline{ Solution }}}$

We have, 

Line segment AB
The coordinates of the midpoint of line segment AB is ( -8 , 8 )
Coordinates of one of the end point of the line segment is (-2,20)

Let the coordinates of the end point of the line segment AB be ( x1 , y1 ) and (x2 , y2)

Also, 

Let the coordinates of midpoint of the line segment AB be ( x, y)

We know that,

For finding the midpoints of line segment we use formula :-

$\bold{\purple{ M( x, y) = }}{\bold{\purple{\dfrac{(x1 +x2)}{2}}}}{\bold{\purple{,}}}{\bold{\purple{\dfrac{(y1 + y2)}{2}}}}$

According to the question,

The coordinates of midpoint and one of the end point of line segment AB are ( -8,8) and (-2,-20) .

For x coordinates :-

$\sf{ -8 = }{\sf{\dfrac{(- 2 +x2)}{2}}}$

$\sf{2}{\sf{\times{ -8 = - 2 + x2 }}}$

$\sf{ - 16 = - 2 + x2 }$

$\sf{ x2 = -16 + 2 }$

$\bold{ x2 = -14 }$

For y coordinates :-

$\sf{ 8 = }{\sf{\dfrac{(- 20 +x2)}{2}}}$

$\sf{2}{\sf{\times{ 8 = - 20 + x2 }}}$

$\sf{ 16 = - 20 + x2 }$

$\sf{ y2 = 16 + 20 }$

$\bold{ y2 = 36 }$

Thus, The coordinates of another end points of line segment AB is ( -14 , 36)

Hence, Option A is correct answer

7 0

3 years ago

The half-life of Radium-224 is

Sholpan [36]

Answer:

10.98 days is 10.98/3.66 = 3 half life periods and half of the mass is lost at each half life. You can do this in your head. I have!!

Step-by-step explanation:

8 0

2 years ago

What is the total amount of 2/5+5/3+9/3 and the lowest common denominator?

gregori [183]

The lowest common denominator is lcm(5, 3), which is 15.

The sum of 2/5 + 5/3 + 9/3 is 6/15 + 25/15 + 45/15, which is 76/15 or $5\frac{1}{15}$ .

4 0

3 years ago

Sydney has 3 3/5 yards of ribbon to make bows. Each bow is made from a piece of ribbon that is 2/5. How many bows can Sydney mak

Zielflug [23.3K]

Answer:

Step-by-step explanation:

2/5 x 2 = 4/5

4/5 x 2, or 2/5 x 4 = 1 3/5

1 3/5 x 2, or 2/5 x 8 = 3 1/5

3 1/5 + 2/5, or 2/5 x 9 = 3 3/5

8 0

3 years ago