With geometric sequences, if you divide a term by the term before it you'll get the common ratio. That's how they are all constructed, and in this problem:
So -1/4 is our common ratio.
Answer:
$111
Step-by-step explanation:
First we need to take a look at the bank account of Hakim. Hakim initially invested $700 in the bank with a 5% simple interest annually. Since Hakim waited for an entire year before buying the computer, he will then have the extra 5% interest from the bank.
Let's first compute for how much Hakim will have in total in the bank.
A = P(1 + rt)
P = 700 Initial Investment
r = 5% or 0.05 Interest
t = 1 Year
A = 700(1 + (0.05 x 1))
A = 700(1 + 0.05)
A = 700(1.05)
A = 735
So now we know that Hakim has a total of $735 in his bank account.
Now let's move on to calculating the total cost of the computer. We know that the sales tax is always computed after the discounted price.
So first we find the discounted price.
x = 750
d = 20% or 0.20
Discount = 750 x 0.20
Discount = 150
Now that we have the discount of the computer, we then simply subtract the discount to the initial price.
750 - 150 = 600.
The computer will then cost $600 with the discounted price.
Now we have to find the sales tax.
Sales Tax = 4% or 0.04
Total Discounted Price = 600
600 x 0.04 = $24
Now that we have the sales tax, we simply add the sales tax to the discounted price.
600 + 24 = 624.
Now that we know how much the total cost of the computer is with the discount and sales tax, we simply subtract the total cost of the computer to Hakim's current account balance.
735 - 624 = 111
Hakim will have a total of $111 in his bank account after purchasing the computer.
X×2=10
X=10÷2
X=5
Proof: 5×2=10
Answer:
0.8 or 80%
Step-by-step explanation:
Let A and B be the events
<em>A: “The concert goer went to Orlampa Skydome”
</em>
<em>B: “The concert goer went to the Bithlo Megaplax”
</em>
<em>
</em>Then the probability P(A) that a concert goer went to Orlampa Skydome is
<em>P(A) = 120/200 = 0.6
</em>
Similarly,
<em>
P(B) = 100/200 = 0.5
</em>
<em>
</em>We are looking for P(A∪B), the probability that a concert goer went to Orlampa Skydome OR the Bithlo Megaplax.
We know that
P(A∪B) = P(A) + P(B) - P(A∩B)
but P(A∩B) is the likelihood that a concert goer went to Orlampa Skydome AND the Bithlo Megaplax.
Since the events are independent,
<em>
P(A∩B) = P(A)P(B) = 0.6*0.5 = 0.3
</em>
and
P(A∪B) = 0.6 +0.5 - 0.3 = 0.8 or 80%
Answer:
B
Step-by-step explanation:
The orthocenter of a triangle is the point of intersection of the three altitudes of the triangle.
In an obtuse triangle, two altitudes are completely outside the triangle; therefore, the three altitudes cannot possibly intersect inside the triangle.
Answer: B
