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stellarik [79]
3 years ago
10

Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6

inches, and Frame B has a length of 7 inches. 1. Without calculating, predict which frame has the shorter width. Explain your reasoning. 2. Find the width that you predicted to be shorter. Show your reasoning.​
Mathematics
1 answer:
Vilka [71]3 years ago
5 0

9514 1404 393

Answer:

  1. the longer frame (B) has the shorter width

  2. the shorter width is 6 3/7 inches, area divided by length

Step-by-step explanation:

The relation between area, length, and width is ...

  A = LW

Then the width is ...

  W = A/L . . . . .  inversely proportional to length

__

1. Since length and width are inversely proportional (when area is constant), the shorter width will be associated with the longer length. Frame B will have the shorter width.

__

2. The width of frame B is ...

  W = A/L = (45 in²)/(7 in) = 45/7 in = 6 3/7 in

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URGENT!! 100 POINTS, BRAINLIEST AS WELL
Olenka [21]

Answer:

C

Step-by-step explanation:

Notice that there is a little triangle formed by the lines on the right side of the diagram.

Let's find the angle measures of the triangle. One of them has a supplementary angle of 96 degrees, which means that the actual interior angle is 180 - 96 = 84 degrees.

Another angle has a supplementary angle of 137, which means that the actual interior angle of the triangle is 180 - 137 = 43 degrees.

Finally, we have the expression 2x - 23, which is an exterior angle. By definition, this exterior angle is equal to the sum of the interior angles of the triangle that do not include its supplementary angle. In other words:

2x - 23 = 84 + 43

Now we just solve for x:

2x - 23 = 84 + 43 = 127

2x = 127 + 23 = 150

x = 150/2 = 75 degrees

The answer is 75 degrees, or C.

8 0
3 years ago
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What is the equation of the graphed line written in standard form?
Dmitry_Shevchenko [17]

Answer:

A

Step-by-step explanation:

4 0
3 years ago
Kelly needs to order lunch for the 6 people at a business meeting. Her menu choices are chicken salad for acost of $5 per person
Lady bird [3.3K]
Hello There!! (: 
I'm Here to help!
If we say Kelly orders 1 chicken salad, then it means she ordered 5 egg salads. If she ordered x chicken salads, then she'll have to order the rest, which is <span>(6−x)</span> egg salads. For first equation, let's set y to be the meal's price. It consist of the price of all chicken salads ordered and the price of all egg salads ordered: <span>y=5x+4(6−x)</span> Again, x represents number of chicken salads ordered, and y represents the meal's price. A second equation would come to limit the price to the money Kelly has: <span>y≤28
</span> Notice there are more constraints to add on the values (x cannot be negative, no such thing negative number of salads or fractional number of salads) so just keep that in mind. Now, since we know the price based on the number of chicken salads, we can say for what number of salads it matches the second restriction: <span><span><span>5x+4(6−x)≤28</span><span>5x+24−4x≤28</span><span>x≤28−24</span><span>x≤4

Does this help you?
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6 0
3 years ago
Factor the expression 45b+40​
natali 33 [55]

Answer:

5(9b + 8)

Step-by-step explanation:

Rewrite 45 as 5 * 9

Rewrite 40 as 5 * 8

= 5 * 9b + 5 * 8

Factor out common term 5

=5 (9b + 8)

6 0
2 years ago
Read 2 more answers
A shipment of 50,000 transistors arrives at a manufacturing plant. The quality control engineer at the plant obtains a random sa
Aleks04 [339]

Step-by-step explanation:

remember, the number of possible combinations to pick m out of n elements is C(n, m) = n!/(m! × (n-m)!)

50,000 transistors.

4% are defective, that means 4/100 = 1/25 of the whole.

so, the probability for one picked transistor to be defective is 1/25.

and the probability for it to work properly is then 1-1/25 = 24/25.

now, 500 picks are done.

to accept the shipment, 9 or less of these 500 picks must be defective.

the probability is then the sum of the probabilities to get

0 defective = (24/25)⁵⁰⁰

1 defective = (24/25)⁴⁹⁹×1/25 × C(500, 1)

= 24⁴⁹⁹/25⁵⁰⁰ × 500

2 defective = (24/25)⁴⁹⁸×1/25² × C(500, 2)

= 24⁴⁹⁸/25⁵⁰⁰ × 250×499

3 defective = 24⁴⁹⁷/25⁵⁰⁰ × C(500, 3) =

= 24⁴⁹⁷/25⁵⁰⁰ × 250×499×166

...

9 defective = 24⁴⁹¹/25⁵⁰⁰ × C(500, 9) =

= 24⁴⁹¹/25⁵⁰⁰ × 500×499×498×497×496×495×494×493×492×491 /

9×8×7×6×5×4×3×2 =

= 24⁴⁹¹/25⁵⁰⁰ × 50×499×166×71×31×55×494×493×41×491

best to use Excel or another form of spreadsheet to calculate all this and add it all up :

the probability that the engineer will accept the shipment is

0.004376634...

which makes sense, when you think about it, because 10 defect units in the 500 is only 2%. and since the whole shipment contains 4% defect units, it is highly unlikely that the random sample of 500 will pick so overwhelmingly the good pieces.

is the acceptance policy good ?

that completely depends on the circumstances.

what was the requirement about max. faulty rate in the first place ? if it was 2%, then the engineer's approach is basically sound.

it then further depends what are the costs resulting from a faulty unit ? that depends again on when the defect is usually found (still in manufacturing, or already out there at the customer site, or somewhere in between) and how critical the product containing such transistors is. e.g. recalls for products are extremely costly, while simply sorting the bad transistors out during the manufacturing process can be rather cheap. if there is a reliable and quick process to do so.

so, depending on repair, outage and even penalty costs it might be even advisable to have a harder limit during the sample test.

in other words - it depends on experience and the found distribution/probability curve, standard deviation, costs involved and other factors to define the best criteria for the sample test.

3 0
2 years ago
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