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3 years ago

In a group of 28 students, 12 study both Art and Biology.

Mathematics

1 answer:

MAVERICK [17]3 years ago

3 0

Answer:

100%

Step-by-step explanation:

Use conditional probability:

P(B | A) = P(B and A) / P(A)

P(B | A) = (12/28) / P(A)

We need to find the probability that a student studies art.

P(A or B) = P(A) + P(B) − P(A and B)

24/28 = P(A) + (12+12)/28 − 12/28

P(A) = 12/28

P(B | A) = (12/28) / (12/28)

P(B | A) = 1

What this means is that all of the students who study art also study biology.

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The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the

gladu [14]

Answer:

Part 1) Australia $19,751,012\ people$

Part 2) China $1,319,645,764\ people$

Part 3) Mexico $109,712,539\ people$

Part 4) Zaire $60,534,681\ people$

Step-by-step explanation:

we know that

The equation of a exponential growth function is given by

$P(t)=a(1+r)^t$

where

P(t) is the population

t is the number of years since year 2000

a is he initial value

r is the rate of change

Part 1) Australia

we have

$a=19,169,000\\r=0.6\%=0.6\100=0.006$

substitute

$P(t)=19,169,000(1+0.006)^t$

$P(t)=19,169,000(1.006)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=19,169,000(1.006)^5=19,751,012\ people$

Part 2) China

we have

$a=1,261,832,000\\r=0.9\%=0.9\100=0.009$

substitute

$P(t)=1,261,832,000(1+0.009)^t$

$P(t)=1,261,832,000(1.009)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=1,261,832,000(1.009)^5=1,319,645,764\ people$

Part 3) Mexico

we have

$a=100,350,000\\r=1.8\%=1.8\100=0.018$

substitute

$P(t)=100,350,000(1+0.018)^t$

$P(t)=100,350,000(1.018)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=100,350,000(1.018)^5=109,712,539\ people$

Part 4) Zaire

we have

$a=51,965,000\\r=3.1\%=3.1\100=0.031$

substitute

$P(t)=51,965,000(1+0.031)^t$

$P(t)=51,965,000(1.031)^t$

Find the expected population in 2025,

Find the value of t

t=2005-2000=5 years

substitute the value of t in the equation

$P(5)=51,965,000(1.031)^5=60,534,681\ people$

8 0

3 years ago

Solve the inequality for w

kobusy [5.1K]

Answer:

w ≥ 23

Step-by-step explanation:

Add 3 to both sides of this inequality, obtaining:

w ≥ 23. In other words, w must be 23 or larger. Symbolically: [23, infinity)

3 0

3 years ago

Solve the following exponential equations. 10^(3x−5) = 7^x

zalisa [80]

Answer:

x = 2.3202

Step-by-step explanation:

Given equation:

$10^{(3x-5)} = 7^x$

on taking log both sides, we get

$\log(10^{(3x-5))} =\log(7^x)$

now,

using the property of log function

log(aᵇ) = b × log(a)

therefore,

we get

(3x-5)log(10) = xlog(7)

now,

log(10) = 1

and

log(7) = 0.84509

thus,

( 3x - 5 ) × 1 = 0.84509x

3x - 0.84509x - 5 = 0

2.15491x = 5

x = 2.3202

4 0

3 years ago

X and y vary inversely and x=50 when y=5 find y when x=10 what is k?

Kisachek [45]

Answer:

Part A)

1) $k=250$

2) $y=25$

Part B)

1) $k=7$

2) $y=84$

Step-by-step explanation:

Part 1) x and y vary inversely and x=50 when y=5 find y when x=10 what is k?

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form $y*x=k$ or $y=k/x$

step 1

Find the value of k

x=50 when y=5

substitute the values

$y*x=k$ ------> $5*50=k$ -----> $k=250$

The equation is equal to

$y*x=250$ or $y=250/x$

step 2

Find y when x=10

substitute the value of x in the equation and solve for y

$y*(10)=250$

$y=250/10=25$

Part B) x and y vary directly and x=6 when y=42 find k what is y when x=12

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

step 1

Find the value of k

x=6 when y=42

substitute the values

$y/x=k$ ------> $42/6=k$ -----> $k=7$

The equation is equal to

$y/x=7$ or $y=7x$

step 2

Find y when x=12

substitute the value of x in the equation and solve for y

$y=7(12)=84$

5 0

3 years ago

A restraint has one type of lemonade that is 12% sugar and another that is 7% sugar. How many gallons of each type does the rest

Xelga [282]

Answer:

Step-by-step explanation:

I have answers to whole packet:

1.D

2.A

3.C

4.D

5.C

6.D

7.A

8.C

9.A

10.B

11.A

12.A

13.A

14.B

15.A

16.B

17.A

18.A

19.B

20.C

21.A

22.A

23.D

24.B

7 0

3 years ago