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Brilliant_brown [7]
3 years ago
8

One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196

legs. How many humans and horses were there?
A. 37 humans and 98 horses
B.24 horses and 50 humans
C. 31 horses and 74 humans
D. 24 humans and 50 horses
Mathematics
2 answers:
saw5 [17]3 years ago
7 0

Answer:C

Step-by-step explanation:

Alexus [3.1K]3 years ago
3 0
Answer: B: The person counts 24 horses and 50 humans.
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Tacoma's population in 2000 was about 200 thousand, and had been growing by about 9% each year. a. Write a recursive formula for
KIM [24]

Answer:

a) The recurrence formula is P_n = \frac{109}{100}P_{n-1}.

b) The general formula for the population of Tacoma is

P_n = \left(\frac{109}{100}\right)^nP_{0}.

c) In 2016 the approximate population of Tacoma will be 794062 people.

d) The population of Tacoma should exceed the 400000 people by the year 2009.

Step-by-step explanation:

a) We have the population in the year 2000, which is 200 000 people. Let us write P_0 = 200 000. For the population in 2001 we will use P_1, for the population in 2002 we will use P_2, and so on.

In the following year, 2001, the population grow 9% with respect to the previous year. This means that P_0 is equal to P_1 plus 9% of the population of 2000. Notice that this can be written as

P_1 = P_0 + (9/100)*P_0 = \left(1-\frac{9}{100}\right)P_0 = \frac{109}{100}P_0.

In 2002, we will have the population of 2001, P_1, plus the 9% of P_1. This is

P_2 = P_1 + (9/100)*P_1 = \left(1-\frac{9}{100}\right)P_1 = \frac{109}{100}P_1.

So, it is not difficult to notice that the general recurrence is

P_n = \frac{109}{100}P_{n-1}.

b) In the previous formula we only need to substitute the expression for P_{n-1}:

P_{n-1} = \frac{109}{100}P_{n-2}.

Then,

P_n = \left(\frac{109}{100}\right)^2P_{n-2}.

Repeating the procedure for P_{n-3} we get

P_n = \left(\frac{109}{100}\right)^3P_{n-3}.

But we can do the same operation n times, so

P_n = \left(\frac{109}{100}\right)^nP_{0}.

c) Recall the notation we have used:

P_{0} for 2000, P_{1} for 2001, P_{2} for 2002, and so on. Then, 2016 is P_{16}. So, in order to obtain the approximate population of Tacoma in 2016 is

P_{16} = \left(\frac{109}{100}\right)^{16}P_{0} = (1.09)^{16}P_0 = 3.97\cdot 200000 \approx 794062

d) In this case we want to know when P_n>400000, which is equivalent to

(1.09)^{n}P_0>400000.

Substituting the value of P_0, we get

(1.09)^{n}200000>400000.

Simplifying the expression:

(1.09)^{n}>2.

So, we need to find the value of n such that the above inequality holds.

The easiest way to do this is take logarithm in both hands. Then,

n\ln(1.09)>\ln 2.

So, n>\frac{\ln 2}{\ln(1.09)} = 8.04323172693.

So, the population of Tacoma should exceed the 400 000 by the year 2009.

8 0
3 years ago
Read 2 more answers
a jug for a baseball team holds 20 gallons of water to make an energy drink one cup of mix is used for every 2 gallons of water
Solnce55 [7]
Assuming that the mix disolves into the 20 gallons and doesn't take up space

1:2
x:20
1/2=x/20
multiply btoh sides by 20
10=x

answer is 10 cups of mixture
5 0
3 years ago
Dimitri wrote the equations y = 3x and y = x + 3.
sweet-ann [11.9K]

Answer: y = 3x (3,6)

Step-by-step explanation:

8 0
3 years ago
What is the probability of rolling a number greater than 4 on a number cube and then spinning an
oee [108]

Answer:

1/6

Step-by-step explanation:

There are 2 numbers greater than 4 on a die (5 and 6).

A spinner divided into 12 equal sectors numbered 1 through 12 has 6 even numbered sectors.

Therefore, the probability is:

P = (2/6) (6/12)

P = 1/6

5 0
2 years ago
Question content area top
Mumz [18]

Answer:

(-6,-4)

Step-by-step explanation:

So there actually is really easy way to solve this problem(that many people will never teach you for some weird reason).

Find difference between two points first in x and y direction.

X difference = (-3 - (-8)) = 5

Y difference = (-1 - (-6))  = 5

Multiply 2/5 to each difference

X difference 5 * 2/5 = 2

y difference 5* 2/5 = 2

just add the two number to First point(point A)

-8 + 2 = -6

-6 + 2 = -4

(-6,-4)

7 0
2 years ago
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