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zlopas [31]
3 years ago
13

In the year 2000, the population of Mexico was about 100 million, and it's was growing by 1.53% per year. at this rate, the func

tion f(x)=100(1.0153)^x gives the population, in millions, X years after 2000. Using this model, in what year would the population reach 109 million? Round your answer to the nearest year.
A.2007
B.523
C.2006
D.2004
Mathematics
1 answer:
My name is Ann [436]3 years ago
7 0

109 = 100(1.0153)^x  

x = 5.68  

thus  

6 years after 2000  

so  

2006

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For what values of the variable, do the following fractions exist: y^2-1/y+y/y-3
ale4655 [162]

Answer:

Remember that the division by zero is not defined, this is the criteria that we will use in this case.

1) \frac{y^2 - 1}{y}  + \frac{y}{y - 3}

So the fractions are defined such that the denominator is never zero.

For the first fraction, the denominator is zero when y = 0

and for the second fraction, the denominator is zero when y = 3

Then the fractions exist for all real values except for y = 0 or y = 3

we can write this as:

R / {0} U { 3}

(the set of all real numbers except the elements 0 and 3)

2) \frac{b + 4}{b^2 + 7}

Let's see the values of b such that the denominator is zero:

b^2 + 7 = 0

b^2 = -7

b = √-7

This is a complex value, assuming that b can only be a real number, there is no value of b such that the denominator is zero, then the fraction is defined for every real number.

The allowed values are R, the set of all real numbers.

3) \frac{a}{a*(a - 1) - 1}

Again, we need to find the value of a such that the denominator is zero.

a*(a - 1) - 1 = a^2 - a - 1

So we need to solve:

a^2 - a - 1 = 0

We can use the Bhaskara's formula, the two values of a are given by:

a = \frac{-(-1) \pm \sqrt{(-1)^2 + 4*1*(-1)}  }{2*1}  = \frac{1 \pm \sqrt{5} }{2}

Then the two values of a that are not allowed are:

a = (1 + √5)/2

a = (1 - √5)/2

Then the allowed values of a are:

R / {(1 + √5)/2} U {(1 - √5)/2}

7 0
2 years ago
-10,20,-40 what are the next two terms
dybincka [34]

Answer:

80

Step-by-step explanation:

10+10= 20

20+20=40

40+40=80

4 0
2 years ago
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Evaluate this problem<br> 8²+18-2(6+2)÷4
ale4655 [162]

I hope this helps. Good Luck!

4 0
3 years ago
Read 2 more answers
4. Determine all unknown sides and angles to 1 decimal place.
Ksju [112]

Answer:

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees

Step-by-step explanation:

4a) Given the following

Opposite side = 38cm (side facing the given angle)

Required

Adjacent and hypotenuse side

According to SOH CAH TOA

tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp=  60.81cm

Next is to get the adjacent

Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm

Next is to get the missing

Since sum of angle in the triangle is 180degrees

32 + 90 + x = 180

122 + x = 180

x = 180 - 122

x = 58degrees

7 0
3 years ago
Sally has 3 /4 of a yard of ribbon. she uses 1/8 yard of ribbon to make each bow. does she have enough ribbon to make 7 bows?
tekilochka [14]

Answer:

No

Step-by-step explanation:

3/4 of a yard is equal to 6/8 of a yard. If Sally wants 7 ribbons, she needs at least 7/8 yards of ribbon.

3 0
2 years ago
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