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aev [14]
2 years ago
5

Mr. Rodriguez is assembling supply kits for his students. He has 24 pencils and 32 erasers. All the kits must have the same numb

er of each item, and all items must be used.
1.
What is the largest number of kits Mr. Rodriguez can make?
2.
How many pencils and erasers will be in each kit?
Mathematics
1 answer:
lbvjy [14]2 years ago
4 0

Answer:

1. 8 kits

2. 3 pencils and 4 erasers

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Can a local maximum also be a point of inflection? Explain.
myrzilka [38]
<span>Inflection points are where the function changes concavity. Since concave up corresponds to a positive second derivative and concave down corresponds to a negative second derivative, then when the function changes from concave up to concave down (or vise versa) the second derivative must equal zero at that point. So the second derivative must equal zero to be an inflection point. But don't get excited yet. You have to make sure that the concavity actually changes at that point.</span>
7 0
3 years ago
A cash box contains $74 made up of quarters, half-dollars, and one-dollar
Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

0.25q+0.50h+1.00d=74

\displaystyle{h=\frac{3}{5}d+1}

q=4(d+h)

Then, substitute <em>q</em> in the first equation with the expression from the third equation:

0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74

Next, substitute <em>h</em> in that equation with the expression from the second equation:

\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}

2d+0.9d+1.5=74\\2.9d+1.5=74

Solve for <em>d</em>, the number of one-dollar coins:

2.9d+1.5=74\\2.9d=72.5\\d=25

Substitute 25 for <em>d</em> in the second equation to find <em>h</em>, the number of half-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{h=\frac{3}{5}(25)+1}

h=15+1\\h=16

Substitute 25 for <em>d</em> and 16 for <em>h</em> in the third equation to find <em>q</em>, the number of quarters:

q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164

Then, verify that the coins total $74:

0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

\displaystyle{h=\frac{3}{5}d+1}

\displaystyle{16=\frac{3}{5}(25)+1}

16 = 15 + 1\\16 = 16\\\text{Check.}

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}

6 0
3 years ago
In the sequence below, a, = 9. Which of the following would be the correct way to label the 3 in the
zysi [14]

Answer:

Step-by-step explanation:3,9,27,81 because this is multiplication

8 0
3 years ago
Prove that ΔADB∼ΔADE by writing a proportion which solves for the Pythagorean Theorem.
Cloud [144]

Answer:

B) AD/DE = BD/AD

Step-by-step explanation:

6 0
3 years ago
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Your car averages 380 miles on a 14-gallon tank of gas. You run out of gas on a deserted highway, but have 1/2 gallon of lawn mo
spin [16.1K]

Hey!

Hope this helps...

~~~~~~~~~~~~~~~~~~~~~~~~~~~

So to solve this, we want to know how many miles can we do in every 1 gallon of gas.

To solve this, we do: 380 / 14 = 27.14 miles for every 1 gallon

Okay, so if we have 1/2 a gallon stashed away, how far can we get on every 1/2 gallon...

To solve this, we do: 27.14 / 2 = 13.57 miles for every 1/2 gallon


So...

The answer is: We will NOT be able to get to the Gas Station that is 15miles away, because we can only go about 13.5 miles with every 1/2 gallon.

6 0
3 years ago
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