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3 years ago

HELP!!! Lucas deposits $250,000 into two investment accounts. Over a year, the first account

1 answer:

6 0

The amount deposited in the account that earns 3.6% interest is $57,600 and the amount deposited in the account that earns 2.1% interest is $192,400

The first step is to determine the amount of interest he earned in total over a year

Interest = Amount in the account - amount deposited

$256,114 - $250,000 = $6,114

The second step is to formulate two set of equations and use simultaneous equation to solve the question

a + b = $250,000 equation 1

0.036a + 0.021b = $6,114 equation 2

Where a represent amount deposited in the account that earns 3.6% interest

b represent amount deposited in the account that earns 2,1% interest

Multiply equation 1 by 0.036

0.036a + 0.036b = 9000 equation 3

Subtract equation 2 from 3

2886 = 0.015b

divide both sides of the equation by 0.015

b = $192,400

Substitute for b in equation 1

a + 192,400 = 250,000

a = 250,000 - 192400

a = $57,600

To learn more about simultaneous equations, please check: brainly.com/question/23589883?referrer=searchResults

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If you take half my age and add 7, you get my age 13 years ago. How old am I?

mestny [16]

Answer:

You are currently 40 years old

Step-by-step explanation:

Let's say the current age is represented by the variable x.

x = current age

The question says that "if you take half my age and add 7, you get my age 13 years ago"

This can be represented like this:

1/2(x) + 7 = x - 13

Now we solve for x using basic algebra:

1/2(x) = x - 20

-1/2(x) = -20

x = 40

To check if this is correct, plug it back into the equation and see if both sides equal each other:

1/2(40) + 7 = (40) - 13

20 + 7 = 27

27 = 27

Hope this helps (●'◡'●)

3 0

2 years ago

Find the length of YZ

emmainna [20.7K]

Larger triangle’s base length

a^2 + b^2 = c^2
a^2 + 3^2 = 8^2
a^2 = 8^2 - (3^2)
sqrt(a^2) = sqrt(55)
a = sqrt(55)
__________________

Smaller triangle’s base length:

The same formula applies.
a^2 + 3^2 = 5^2
a^2 = 5^2 - (3^2)
sqrt(a^2) = sqrt(16)
a = 4
____________

The finale!

Add the two side lengths of a, which is sqrt(55) + 4 (exact answer)
or... 11.416 (unrounded to thousandths place)

Good luck to you!

5 0

3 years ago

Begin a one-day journal, where you record every math process (no matter how small or trivial) you used during the day. You may w

saw5 [17]

Nnddnbdjsjsjjdjdjdjdjdhbcbxbjsjsiaisjbdd

4 0

3 years ago

Aidan uses 1/4 of the water in a bucket to water one potted plant. How many potted plants can aiden water with 3 full buckets of

Ahat [919]

If Aidan can fill 1 potted plant from a full bucket but still have enough left for 3 more, this means Aidan can water 4 plants per full bucket. And if you multiply that 4 by 3 full buckets, it gives you 12, which is the amount of plants 3 full buckets can water.

8 0

3 years ago

There is a 70 percent chance that an airline passenger will check bags. In the next 16 passengers that check in for their flight

GenaCL600 [577]

Answer:

a) $P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.00332$

b) $P(X$

And we can find the individual probabilities like this:

$P(X=10)=(16C10)(0.7)^{10} (1-0.7)^{16-10}=0.1649$

$P(X=11)=(16C11)(0.7)^{11} (1-0.7)^{16-11}=0.2099$

$P(X=12)=(16C12)(0.7)^{12} (1-0.7)^{16-12}=0.2040$

$P(X=13)=(16C13)(0.7)^{13} (1-0.7)^{16-13}=0.1465$

$P(X=14)=(16C14)(0.7)^{14} (1-0.7)^{16-14}=0.0732$

$P(X=15)=(16C15)(0.7)^{15} (1-0.7)^{16-15}=0.0228$

$P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.0033$

And replacing we got:

$P(X$

c) $P(x \geq 10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)$

And replacing we got 0.825

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=17, p=0.7)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

And we want to find this probability:

$P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.00332$

Part b fewer than 10 will check bags

We want this probability:

$P(X$

We can use the complement rule and we have:

$P(X$

And we can find the individual probabilities like this:

$P(X=10)=(16C10)(0.7)^{10} (1-0.7)^{16-10}=0.1649$

$P(X=11)=(16C11)(0.7)^{11} (1-0.7)^{16-11}=0.2099$

$P(X=12)=(16C12)(0.7)^{12} (1-0.7)^{16-12}=0.2040$

$P(X=13)=(16C13)(0.7)^{13} (1-0.7)^{16-13}=0.1465$

$P(X=14)=(16C14)(0.7)^{14} (1-0.7)^{16-14}=0.0732$

$P(X=15)=(16C15)(0.7)^{15} (1-0.7)^{16-15}=0.0228$

$P(X=16)=(16C16)(0.7)^{16} (1-0.7)^{16-16}=0.0033$

And replacing we got:

$P(X$

Part c at least 10 bags

We can find this probability like this:

$P(x \geq 10) = P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)$

And replacing we got 0.825

4 0

3 years ago