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Harlamova29_29 [7]
3 years ago
7

A bakery sells cakes for $23 and a dozen cupcakes for

Mathematics
1 answer:
lys-0071 [83]3 years ago
8 0

Answer:

23x + 18y = 1446

x + y = 72

Step-by-step explanation:

The bakery made $1446 total. We represent this as the cost of each cake ($23) times the number of cakes sold (x) plus the cost of each dozen cupcakes ($18) times the number of cupcakes sold (y).

Thus, 23x +18y = $1446.

The bakery sold 72 items total. We represent this as the number of cakes sold (x) plus the number of each dozen cupcakes sold (y).

Thus, x + y = 72.

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If the sum of the even integers between 1 and k, inclusive, is equal to 2k, what is the value of k?
Alisiya [41]
If k is odd, then

\displaystyle\sum_{n=1}^{\lfloor k/2\rfloor}2n=2\dfrac{\left\lfloor\frac k2\right\rfloor\left(\left\lfloor\frac k2\right\rfloor+1\right)}2=\left\lfloor\dfrac k2\right\rfloor^2+\left\lfloor\dfrac k2\right\rfloor

while if k is even, then the sum would be

\displaystyle\sum_{n=1}^{k/2}2n=2\dfrac{\frac k2\left(\frac k2+1\right)}2=\dfrac{k^2+2k}4

The latter case is easier to solve:

\dfrac{k^2+2k}4=2k\implies k^2-6k=k(k-6)=0

which means k=6.

In the odd case, instead of considering the above equation we can consider the partial sums. If k is odd, then the sum of the even integers between 1 and k would be

S=2+4+6+\cdots+(k-5)+(k-3)+(k-1)

Now consider the partial sum up to the second-to-last term,

S^*=2+4+6+\cdots+(k-5)+(k-3)

Subtracting this from the previous partial sum, we have

S-S^*=k-1

We're given that the sums must add to 2k, which means

S=2k
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But taking the differences now yields

S-S^*=2k-2(k-2)=4

and there is only one k for which k-1=4; namely, k=5. However, the sum of the even integers between 1 and 5 is 2+4=6, whereas 2k=10\neq6. So there are no solutions to this over the odd integers.
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What is the result when the number 82 is decreased by 8.6%? Round your answer to the nearest tenth.​
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Answer:

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Step-by-step explanation:

Have a nice day

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Answer:

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Step-by-step explanation:

Given:

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⇒ Rate of change = [(V2 - V1) / V1]100

⇒ Rate of change = [(7 - 4) / 4]100

⇒ Rate of change = [(3) / 4]100

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