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3 years ago

S and T are mutually exclusive events. Find p(s or t) p(s)=10/13, p(t)=1/3

Mathematics

1 answer:

Arturiano [62]3 years ago

7 0

p(s) + p(t) = p(s or t)

just add the fraction together. remember denominators must be the same

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In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

3 0

3 years ago

Pls answer i need answer fast

puteri [66]

Answer:

-24

Step-by-step explanation:

Given expression:

3z (2y - 4)²

z = -2 and y = 3

To solve this problem, simply substitute:

3z (2y - 4)² = 3(-2){2(3) - 4}²

= -6(6-4)²

= -6 (2)²

= -6 x 4

= -24

3 0

3 years ago

Read 2 more answers

Please help I'll give brainiest

Irina18 [472]

What do you need help on exactly?

6 0

3 years ago

Read 2 more answers

Suppose triangle ABC has vertices at A(1, 0), B(10, 0), and C(2, 6). After a 60° counterclockwise rotation about the origin, ver

Artemon [7]

Check the picture attached.

Let OB be the radius of circle with center O.

Let B' be the image of B after the described rotation

OB and OB' are sides of the equilateral triangle OBB'.

The x coordinate of B' is the midpoint of OB, that is 5.

In the right triangle B', point (5, 0) and B:

Distance point (5, 0) to B is 5
|B'B|=|OB|=10

so by the pythagorean theorem:

$a= \sqrt{ 10^{2} - 5^{2} } = \sqrt{ 2^{2} *5^{2} - 5^{2} }= \sqrt{5^{2}(4-1)}=5 \sqrt{3}$ units

Answer: $5 \sqrt{3}$

3 0

3 years ago

Can anyone simplify 24q2/8q-3

Morgarella [4.7K]

24q^2 / 8q^-3

lets break this down...
24/8 = 3

q^2 / q^-3....when dividing exponents with the same base, keep the base and subtract the exponents. q^2 / q^-3 = q^(2 -(-3) = q^(2 + 3) = q^5

put them together and u get : 3q^5

4 0

3 years ago

S and T are mutually exclusive events. Find p(s or t) p(s)=10/13, p(t)=1/3​

S and T are mutually exclusive events. Find p(s or t) p(s)=10/13, p(t)=1/3