PLEASE HELP URGENT!!!!

The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady.

Given:

For two events X and Y,

[tex]P(X)=\dfrac{2}{3}[/tex]

[tex]P(Y)=\dfrac{2}{5}[/tex]

[tex]P(X|Y)=\dfrac{1}{5}[/tex]

To find:

The probabilities [tex]P(Y\cap X), P(Y)\cdot P(X)[/tex].

Solution:

Using the conditional probability:

[tex]P(X|Y)=\dfrac{P(Y\cap X)}{P(Y)}[/tex]

[tex]P(X|Y)\times P(Y)=P(Y\cap X)[/tex]

Substituting the given values, we get

[tex]\dfrac{1}{5}\times \dfrac{2}{5}=P(Y\cap X)[/tex]

[tex]\dfrac{2}{25}=P(Y\cap X)[/tex]

And,

[tex]P(Y)\times P(X)=\dfrac{2}{5}\times \dfrac{2}{3}[/tex]

[tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex]

Therefore, the required probabilities are [tex]P(Y\cap X)=\dfrac{2}{25}[/tex] and [tex]P(Y)\times P(X)=\dfrac{4}{15}[/tex].

Answer:

2/5√2

Step-by-step explanation:

2/√ 25 * 2

further:

ans (1/5)(√2)

Hi,

[tex]2\sqrt{50}\\\\=2\sqrt25*2}\\\\=2*5\sqrt{2}\\\\=10\sqrt{2}[/tex]

Answer:

Angle 1 is 58. Angle 2 is 32.

Step-by-step explanation:

The measure of Angle ACB is 90 because C is on the circle and A and B connect to form a diameter of the circle. So, Angle 1 and Angle 2 add up to 90 (total degrees in triangle - 90). Now you can add the expressions the question gave for Angle 1 and Angle 2, and you get 7x + 6. So you have the equation 7x + 6 = 90. Solve the equation and you get x = 12. Now you can plug in that value for x into the expressions for Angles 1 and 2 to find their measures.

Answer:

5(x-2) = 5x -7

- no solution

-3(x-4) = 3x + 12

- infinitely many solution

4(x+1) = 3x + 4

- Only one solution

-2(x-3) = 2x -6

- Only one solution

6(x+5) = 6x + 11

- no solution

Answer: the correct answer is A. Between 0 and 90

If an angle is between 0 and 90 it is acute

If an angle is EXACTLY 90 it is a right angle

If an angle is between 90 and 180 it is obtuse angle

If it's 360 then it is a full circle

Answer:

8

Step-by-step explanation:

Find 1/3 of 24, which is 8.

Answer:

Sam gave 8 balls to Rita.

Step-by-step explanation:

24 / 3 = 8

1/3 of 24 is 8, therefore Sam gave 8 balls to Rita.

Answer:

see explanation

Step-by-step explanation:

cosM = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{MN}{LM}[/tex] = [tex]\frac{8}{17}[/tex]

sinM = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{LN}{LM}[/tex] = [tex]\frac{15}{17}[/tex]

tanM = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{LN}{MN}[/tex] = [tex]\frac{15}{8}[/tex]

Answer:

65/264 or 0.2462

Step-by-step explanation:

The given series is

(1/1.2.3) + (1/2.3.4) + (1/3.4.5) + ………………

If we denote the series by

u(1) + u(2) + u(3) + u(4) +……………..u(n),

where u(n) is the nth term, then

u(n) = 1/[n(n+1)(n+2)] , n = 1,2,3,4,………n.

which can be written as

u(n) = (1/2) [1/n(n+1) - 1/(n+1)(n+2)] ………………………(1)

In the question, the number of terms n =10, thereby restricting us only to first 10 terms of the series and we have to find the sum for this truncated series. Let S(10) denote the required sum. We have then from (1),

u(1) = (1/2) (1/1.2 - 1/2.3)

u(2) = (1/2) (1/2.3 - 1/3.4)

u(3) = (1/2) (1/3.4 - 1/4.5)

u(4) = (1/2) (1/4.5 - 1/5.6)

u(5) = (1/2) (1/5.6 - 1/6.7)

u(6) = (1/2) (1/6.7 - 1/7.8)

u(7) = (1/2) (1/7.8 - 1/8.9)

u(8) = (1/2) (1/8.9 - 1/9.10)

u(9) = (1/2) (1/9.10 - 1/10.11)

u(10) = (1/2) (1/10.11 - 1/11.12)

Let us now add the terms on LHS and the terms on RHS independently. The sum of LHS is nothing but the sum S(10) of the series up to 10 terms. On the RHS, alternate terms cancel and we are left with only the first and the last term. Therefore,

S(10) = (1/2) (1/1.2 - 1/11.12) = (1/2) (66–1)/132 = [65/(132.2)]

= 65/264

= 0.2462 (correct to four decimal places)

#carryonlearnig

1. f(-6)=8

2.-2

3. 4

Hope this helps you...

Answer:

[tex]2x + 6 = 4x + -2[/tex]

[tex]\Longrightarrow2x+6-6=4x-2-6[/tex]

[tex]\Longrightarrow 2x=4x-8[/tex]

[tex]\Longrightarrow 2x-4x=4x-8-4x[/tex]

[tex]\Longrightarrow -2x=-8[/tex]

[tex]\Longrightarrow \frac{-2x}{-2}=\frac{-8}{-2}[/tex]

[tex]\hookrightarrow \underline{ANSWER: x=4}[/tex]

-------------------------

hope it helps...

have a great day!!

Answer:

1/4

Step-by-step explanation:

Answer:

the families who use both radio and television is 44.

Step-by-step explanation:

yes they are because they have the same variables which are X& Y

Answer:

5yx-7xy

they are like terms, it's all multiplication just a different arrangement

5xy-7xy=-2xy

Step-by-step explanation:

hope this is helpful

Let the height of the rectangle = h

2b + 2h = 100

2(38) + 2h = 100

2h = 100 - 76

h = 12mm

area of rectangle = base x height

= 38 x 12

= 456mm²

Answer:

456mm²

Step-by-step explanation:

using formula;

b/2( P - 2b) = A

substitute values

Answer:

67,200 (please note you did not specify the currency this is figured in so that is important to include in your answer. If this answer is in dollars, then make sure you add a dollars sign and specify "dollars" in your answer. If it is in another currency then put that in).

Step-by-step explanation:

First, we need to figure out how much the doctor makes per hour. Since there are 4, 15 minute billing periods per hour, we multiple to find the hourly billing charges:

4[tex]4*1200=4800[/tex] (this is the amount the doctor makes per hour)

Next, we have to take that hourly charge and multiply it by 2 because we know the doctor works two hours per day:

[tex]4800*2=9600[/tex] (this is the amount the doctor makes per day working two hours)

Finally, we know the doctor attends to the clinic two hours per day and seven days per week. We have to multiply the amount of money earned in two hours (9600) by 7 days:

[tex]9600*7=67,200[/tex] (this is the amount the doctor makes in seven days, billing two hours per day)

Answer:

y + 3 = -1/2(x - 2)

General Formulas and Concepts:

Algebra I

Coordinates (x, y)

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

Point (2, -3)

Slope m = -1/2

Step 2: Find Equation

Answer:

c = 4

See explanation

Step-by-step explanation:

Given:

4c = 3c - 4

Your calculation:

4c = 3c + 4

4c = 4 - 3c

4c = 1c

c = 4/1

c= 4

Correct calculation:

4c = 3c + 4

Collect like terms by subtracting 3c from both sides

4c - 3c = 3c + 4 - 3c

c = 4

Check:

4c = 3c + 4

4(4) = 3(4) + 4

16 = 12 + 4

16 = 16

Therefore,

Your final answer is correct but your method of calculation is not correct

Answer:

Option D, 140 sq. units

Step-by-step explanation:

Area of the rectangle part, 11*5 = 55 sq. units

Area of the pentagon part (3.4*5)*5/2 = 42.5 sq. units

Total area,

55+2*42.5 sq. units (since there are two pentagons)

= 55+85 sq. units

= 140 sq. units

Answer:

18 liters

Step-by-step explanation:

Blue : red : White = 5 : 3 : 2

Quantity of Blue paint = 5x

Quantity of Red paint = 3x

Quantity of White paint = 2x

Total paint = 5x + 3x + 2x = 10x

10x = 60 liters

x = 60/10

x = 6

Quantity of red paint = 3x = 3*6 = 18

Answer:

Arc XY = 180- 43

= 137º

answer is C

Step-by-step explanation:

Answer: [tex]317.2\ ft[/tex]

Step-by-step explanation:

Given

Angle of elevation [tex]\theta=65^{\circ}[/tex]

Length of string [tex]L=350\ ft[/tex]

Suppose the height of kite from the ground level is h

from the figure, we can write

[tex]\Rightarrow \sin \theta=\dfrac{h}{L}\\\\\Rightarrow \sin 65^{\circ}=\dfrac{h}{350}\\\\\Rightarrow h=350\sin 65^{\circ}\\\Rightarrow h=317.2\ ft[/tex]

Answer;

x² = 42 - 2

3

Step-by-step explanation:

#carryonlearning

Answer:

Step-by-step explanation:

y² - 3x² = 6

Subtract y² from both sides

-3x² = 6 - y²

Divide by -3

[tex]\frac{-3x^{2}}{-3}=\frac{6-y^{2}}{-3}\\\\x^{2}=\frac{y^{2}-6}{3}[/tex]

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Here you have to use the Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

STEP 1: Define your variables

a and b are the legs of the triangle, and c is the hypotenuse

a = 7

b = x

c = 9

STEP 2: Plug the variable into the equation

7^2 + x^2 = 9^2

STEP 3: Solve

7^2 + x^2 = 9^2

49 + x^2 = 81

49 - 49 + x^2 = 81 - 49

[tex]\sqrt{x}[/tex]^2 = [tex]\sqrt{32}[/tex]

x = [tex]\sqrt{32}[/tex]

STEP 4: Simplify

Since the questions asks you to put it in simplified radical form, you do not have to approximate the answer, but you do have to simplify the radical.

x = [tex]\sqrt{32}[/tex]

x = [tex]\sqrt{16}[/tex] * [tex]\sqrt{2}[/tex]

x = 4[tex]\sqrt{2}[/tex]

Hope this helps

Answer:

The answer is below

Step-by-step explanation:

a) The patio is in the form of a rectangle. The patio has a width of (x - 10) ft. Therefore given that the area of the patio is x² + 10x - 200, hence:

[tex]Area=length*breadth\\\\x^2+10x-200=length*(x -10)\\\\x^2+20x-10x-200=length*(x -10)\\\\x(x+20)-10(x+20)=length*(x -10)\\\\(x-10)(x+20)=length*(x -10)\\\\length=x +20[/tex]

b) Area of original house = length of house * breadth of house

The length of house = length of patio = x + 20; breadth of house = x + 10; therefore:

Area of original house = (x + 20)(x + 10) = x² + 10x + 20x + 200

Area of original house = x² + 30x + 200

c) If the width is extended, hence:

[tex]Area=length*breadth\\\\x^2+12x-160=(x+20)*width\\\\x^2+20x-8x-160=(x+20)*width\\\\x(x+20)-8(x+20)=(x+20)*width\\\\(x-8)(x+20)=(x+20)*width\\\\width=x-8\\\\Extended \ width=(x-8)-(x-10)\\\\Extended \ width=2\ feet[/tex]

Answer:

there you go

Step-by-step explanation:

angle DOB is 60 degree.

Answer:

see explanation

Step-by-step explanation:

Given ∠ DOC = 90° then

∠ DOB = 90 - p and

Since AOB is a straight angle , then

4p + 90 - p = 180

3p + 90 = 180 ( subtract 90 from both sides )

3p = 90 ( divide both sides by 3 )

p = 30

4p = 4 × 30 = 120

Then

∠ DOB = 180° - 4p = 180° - 120° = 60°

Answer:

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = [tex]\frac{2x}{x-5}[/tex] ( multiply both sides by x - 5 )

y(x - 5) = 2x ← distribute left side

xy - 5y = 2x ( subtract 2x from both sides )

xy - 2x - 5y = 0 ( add 5y to both sides )

xy - 2x = 5y ← factor out x from each term on the left side )

x(y - 2) - 5y ← divide both sides by y - 2

x = [tex]\frac{5y}{y-2}[/tex]

Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then

[tex]f^{-1}[/tex] (x) = [tex]\frac{5x}{x-2}[/tex]

Look into the image. I hope it helps❤

Answer:

2nd option

{(-8, -2), (-4, 1), (0, -2), (2, 3), (4, -4)}

Step-by-step explanation:

For a function to exist, every value of input must have exactly one value of output.

The rest of the relations(1, 3, and 4) have 2 outputs for 1 input so they dont make a function.

Answer:

(B)

Step-by-step explanation:

If you noticed, all the other input values have one input value that has two output values. This doesn't represent a function. Only (B) has one output for each input.

Hope that helps (●'◡'●)

Answer:

x = 10

Step-by-step explanation:

Mathematically, the sum of the interior angles of a triangle is 180

Thus, we have it that;

55 + 45 + (5x + 30) = 180

100 + 5x + 30 = 180

5x = 180-30-100

5x = 50

x = 50/5

x = 10