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BabaBlast [244]
2 years ago
10

Alejandro will deposit $1,750 in an account that earns 6.5% simple interest every year. His sister Anallency will deposit $1,675

in an account that earns 7.5% interest compounded annually. The deposits will be made on the same day, and no additional money will be deposited or withdrawn from the accounts. Which sibling will have more money at the end of four years?
Mathematics
2 answers:
ivann1987 [24]2 years ago
6 0

Answer: Anallency

Step-by-step explanation:

First, lets make two equations for both siblings, using the base: SI = P(1 + rt) and CI = P(1 + r/n)^nt

Alejandro = 1750(1 + 0.065[4]) = 1750 + 455 = $2,205

Anallency = 1675(1 + 0.075/1)^4 = $2236.91

After 4 years, Alejandro will have $2,205, and Anallency will have $2236.91

Since $2236.91 > 2,205, Anallency will have more money after 4 years.

kogti [31]2 years ago
5 0

Answer:

Anallency will have mor money.

Step-by-step explanation:

Simple Interest:

I = Prt

I = $1750 × 0.065 × 4

I = $455

Total after 4 years: $1750 + $455 = $2205

Compound Interest:

F = P(1 + r/n)^(nt)

F = $1675(1 + 0.075)^(4)

F = $2236.91

Answer: Anallency will have mor money.

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50 per cup. If we plug this in to each equation, you'll see that 12 granola bars equals $12, and 7 cups of yogurt equals $3.50, for a total of $15.50.

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A zero in front of the x would make this a difference of two perfect squares. All of the other option would interfere by adding another term.
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Three times as many children as adults attended a concert on Saturday. An adult ticket cost $7 and a child’s ticket cost $3. The
Ierofanga [76]

For this case we propose a system of equations:

x: Let the variable representing the number of children in the concert

y: Let the variable representing the number of adults at the concert

According to the assistance we have:

x = 3y

According to the cost we have:

3x + 7y = 6000

Substituting the first in the second equation we have:

3 (3y) + 7y = 6000\\9y + 7y = 6000\\16y = 6000\\y = \frac {6000} {16}\\y = 375

Thus, the concert was 375 adults.

On the other hand we have:

x = 3 (375) = 1125

Thus, the concert was 1125 children.

In total they were:

375 + 1125 = 1500 people

ANswer:

The concert was 1500 people

3 0
3 years ago
John receives two credit card offers in the mail. Credit Card A: 1% introductory APR, 19.9% APR for purchases after the introduc
musickatia [10]

Answer:

(D) "...because he will not have to pay any interest on his purchases during the introductory APR period."

Step-by-step explanation:

There may be many reasons for John to choose one over the other depending on his future and planned usage patterns. However, answer the (D) is the only correct one in terms of stating a reason that is actually supported by the information in the question. Specifically, there is 0% APR for card B.

What's wrong with the other choices:

Choice A: incorrect statement re APR after intro period (is not 1%); B: incorrect statement re cash advance (is not 0%); C: statement is not supported by anything in the information given (it is an assumption, and is unlikely).

5 0
3 years ago
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A manufacturing process produces semiconductor chips with a known failure rate of . If a random sample of chips is selected, app
AleksandrR [38]

Answer:

The probability that at least 14 of the chips will be defective is 0.6664.

Step-by-step explanation:

The complete question is:

A manufacturing process produces semiconductor chips with a known failure rate of 5.4%. If a random sample of 300 chips is selected, approximate the probability that at least 14 will be defective. Use the normal approximation to the binomial with a correction for continuity .

Solution:

Let <em>X</em> = number of defective chips.

The probability that a chip is defective is, <em>p</em> = 0.054.

A random sample of <em>n</em> = 300 chips is selected.

A chip is defective or not is independent of the other chips.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 300 and <em>p</em> = 0.054.

But the sample selected is too large.

So a Normal approximation to binomial can be applied to approximate the distribution of X if the following conditions are satisfied:

  1. np ≥ 10
  2. n(1 - p) ≥ 10

Check the conditions as follows:

 np=300\times 0.054=16.2>10\\n(1-p)=300\times (1-0.054)=283.8>10

Thus, a Normal approximation to binomial can be applied.

So,  X\sim N(\mu =16.2,\ \sigma^{2}=15.3252).

Compute the probability that at least 14 of the 300 chips will be defective as follows:

Use continuity correction:

P (X ≥ 14) = P (X > 14 + 0.50)

               = P (X > 14.50)

               =P(\frac{X-\mu}{\sigma}>\frac{14.50-16.20}{\sqrt{15.3252}})

                =P(Z>-0.43)\\=P(Z

*Use a <em>z</em>-table for the probability.

Thus, the probability that at least 14 of the chips will be defective is 0.6664.

5 0
3 years ago
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