MATHEMATICS HIGH SCHOOL

If there is an 80% chance of rain and a 50% chance of wind and rain, what is the probability that it is windy, given that it is rainy? Round your answer to the nearest percent.

Answers

Answer 1

Answer:

Answer:

The probability that it is windy, given that it is rainy is:

62.5%≈63%

Step-by-step explanation:

Let A denote the event that it will rain.

B denote the event that it is windy.

A∩B denote the event that it is rainy and windy.

Let P denote the probability of an event.

i.e. we have:

P(A)=0.80

( Since there are 80% chance of rain)

P(A∩B)=0.50

(Since there are 50% chance of wind and rain)

We are asked to find:

P(B|A)

We know that:

$P(B|A)=(P(A\bigcap B))/(P(A))\n\n\nP(B|A)=(0.50)/(0.80)\n\n\nP(B|A)=0.625$

Hence, the probability in percent is:

62.5%≈63%

Answer 2

Answer: The total probability when given it is rainy is 80%. Among them, the windy probability among 80% is 50%. So the total probability is 50%/80%=62.5%≈63%.

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A nest of ants initially contains 500 individuals. The population is increasing by 12% each week.a) How many ants will be there after :
i. 10 weeks
ii. 20 weeks

b)How many weeks will it take for the ant population to reach 2000.

Answers

Answer:

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Step-by-step explanation:

Given,

The initial number of ants, P = 500,

Also, the rate of increasing per week, r = 12% = 0.12,

So, the number of ants after x weeks,

$A=P(1+r)^x$

$\implies A=500(1+0.12)^x=500(1.12)^x$

a) (i) If x = 10 weeks,

The number of ants would be,

$A=500(1.12)^(10)=1552.92\approx 1553$

(ii) If x = 20 weeks,

The number of ants would be,

$A=500(1.12)^(20)=4823.15\approx 4823$

b) If A = 2000

$\implies 2000 = 500(1.12)^x$

$4=(1.12)^x$

Taking log both sides,

log(4) = xlog(1.12)

⇒ x = 12.23 ≈ 12 weeks

A)4, 823
B)13 Weeks

A: 500 (1 + .12)^x (which is 500 (1 + .12)^20 now)
= 4823. 15 which is ≈ 4823.

B: 2000/ y1 = 500 (1 + .12)^x / y2

12.23 so 13 weeks

The sum of three integers is 270. The sum of the first and second integers exceeds the third by
98.
The third integer is
47 less than the first.

Answers

The answer is 223 its easy subtractions hope it helps.:)

If f(x)=|3x-4|+2, find f (-10)

Answers

$f(x)=|3x-4|+2\n\n\nf(-10)=|3\cdot(-10)-4|+2=|-30-4|+2\n\n=|-34|+2=34+2=36$

$f(x)=|3x-4|+2\n \n f (-10)=|3\cdot(-10)-4|+2=|-30-4|+2=|-34|+2=36$

A cylinder has a radius of 30 ft and a height of 19 ft. What is the exact surface area of the cylinder?

Answers

$A=2\pi r(r+h)\n A=2\pi\cdot30\cdot(30+19)\n A=60\pi\cdot49\n A=2940\pi\hbox{ ft}^2$

$SA=2(pi)rh+2(pi)r^2$

$SA=2(pi)(30)(19)+2(pi)(30^2)$

$SA=2(pi)(30)(19)+2(pi)(900)$

$SA=3581.3+5654.7$

$SA=9236$

9236 square feet

What is the x-intercept for 6x-y=30

Answers

$the x-intercept: \n \n 6x-y=30 \n \n \n \n6x=y+30 \ \ / : 6\n \nx=(1)/(6)y+(30)/(6) \n \nx=(1)/(6)y+5\n \ny=0\n \n x=(1)/(6)\cdot 0 +5\n \nx= 5 \n \n(5,0)$

The x intercept is when the y value is 0. To find it, we just set y = 0 in the equation

6x - y = 30
6x - 0 = 30
x = 30 / 6
x = 5

So the x intercept is (5, 0)

Write a word phrase for 49+m

Answers

The sum of 49 and m.

Answer:

Step-by-step explanation:

Mathematical expressions are expressions which are combinations of constants, variables and mathematical operations . A constant is a symbol in maths which has fixed numerical value for example 2 , 3, -6, $(2)/(3)$ are constants .A variable is a symbol in algebra which takes various numerical values and has no fixed value . Mathematical operations include $+,-,/ ,*$ .

By term word phase, we mean mathematical expression using constants and variables.

Given: 49 + m

Word Phase:

Sum of 49 and m

Here, 49 is a constant

m is a variable

+ is a mathematical operation.

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