Suppose that each child born is equally likely to be a boy or a girl. Consider a family with exactly three children. Let BBG indicate that the first two children born are boys and the third child is a girl, let GBG indicate that the first and third children born are girls and the second is a boy, and so forth.

a. List the eight elements in the sample space whose outcomes are all possible genders of the three children.

b. Write each of the events in the next column as a set and find its probability.

(i) The event that exactly one child is a girl.

(ii) The event that at least two children are girls.

(iii) The event that no child is a girl.

Answer:

pen = 2    book = 3

Step-by-step explanation:

p= pens

b=books

4p +3b =17

5p+2b=16

Multiply the first by 5

Multiply the second by -4

Add both (p variable will ce cancelled)

20p +15b = 85

-20p  -8b = -64

           7b = 21

              b=3        (book =3)

Lets plug this in one of the equations

4p + 3x3 = 17

4p +9 0 19

4p = 8

p= 2   (pencil = 2)

Answer:

Option 2

Step-by-step explanation:

For two angles to be adjacent they need to have a common side/ray and a common vertex!

Hope this helps!!!

Answer:

Step-by-step explanation:

In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.

->No, the two indicated angles do not share common vertex

Answer:

8p +56 +16q

Step-by-step explanation:

8 (p+7+2q)

If we distribute the 8 into everything in the parenthesis, we get:

8p +56 +16q

Answer:

Susanne will have about 130 heartbeats in one minute.

Step-by-step explanation:

You can look at this problem as 13 beats/6 seconds = x beats/60 seconds. This means that you can make the denominators equal by multiplying both numerator and denominator by 10. 6 x 10 = 60 and 13 x 10 = 130. This means that x would equal 130 so there are 130 beats in one minute.

Answer:

11+0.48+0.23=11.71.

On solving the provided question, we can say that by equation

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).

\(x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882\)

solution

\(x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35\)

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

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Answer:

D

Step-by-step explanation:

You have to use pythagorean theorem to solve this.

Answer:

D

Step-by-step explanation:

use pytherogream theory

sides, 5 and 12

pytherogream triple 5, 12, 13

Answer:

350

Step-by-step explanation:

Let \(s=\) total number of sixth-grade students.

It is given that 60% of sixth-grade students prefer pizza which is equivalent to 210 sixth-grade students. With this, the following can be written:

\(60\%s = 210\)

\(0.6s=210\) (\(60\%\) can be converted into the decimal form \(0.6\))

\(s = 210\div 0.6\)

\(=350\)

∴ There is a total of 350 sixth-grade students in the school.

Hope this helps :)

Answer:

∠ A = 42° , ∠ G = 85°

Step-by-step explanation:

the measure of an inscribed angle is half the measure of its intercepted arc.

(3)

∠ A is an inscribed angle , so

∠ A = \(\frac{1}{2}\) BC = \(\frac{1}{2}\) × 84° = 42°

(4)

∠ G is an inscribed angle but we require arc DF

the sum of the arcs in a circle = 360°

FG + GD + FD = 360°

70° + 120° + FD = 360°

190° + FD = 360° ( subtract 190° from both sides )

FD = 170°

Then

∠ G = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 170° = 85°

Drawing the situation, the top of Diego's ladder is 9 feet off the ground, the foot of the ladder is 4.5 away from the wall, and with an angle of 55 degrees the top is now 7.95feet off the ground.

a) Using the angle and hypotenuse of the ladder, we can calculate the height from the ground using the trigonometric function “SOHCAHTOA”:

Height = (Hypotenuse × sin(60°))/cos(60°)

Height = (9 feet × sin(60°))/cos(60°)

Height = 7.5 feet

b) Using the same trigonometric function, we can calculate the distance from the wall using the adjacent side and angle of the ladder:

Distance = (Adjacent × cos(60°))/sin(60°)

Distance = (9 feet × cos(60°))/sin(60°)

Distance = 4.5 feet

c) Using the same trigonometric function, we can calculate the new height from the ground using the hypotenuse and angle of the ladder:

Height = (Hypotenuse × sin(55°))/cos(55°)

Height = (9 feet × sin(55°))/cos(55°)

Height = 7.95 feet

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Answer:

The answer would be (17,-6). It's just add to the original coordinates.

Step-by-step explanation:

Answer:

√3 + 1

Step-by-step explanation:

Step below are self-explanatory

Answer:

I think it is 4 white and 3 blue

Step-by-step explanation:

Because they have 3 cups of white then 6 cups of white so i think they multiplied it. Then they have 4 cups of blue then 8 cups of blue. So if you multiply it, it will give you the answer. I hope this is right and it helped and can you mark me brainliest!!!!!!!!

The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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The statue is 2 meters taller than Kelly. Given that Kelly is 3 meters away from the statue and the distance between the top of the statue and Kelly's head is 5 meters, we can determine the height difference between them.

Since the distance from Kelly to the statue is 3 meters and the distance from the top of the statue to Kelly's head is 5 meters, we can subtract the distance from Kelly's head to the ground (which is assumed to be negligible) to find the height of the statue.

Therefore, the statue is 5 meters tall, while Kelly's height is 3 meters. The height difference between the statue and Kelly is 5 - 3 = 2 meters. Thus, the statue is 2 meters taller than Kelly.

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Answer:

2x^2+3x-13x-1

Step-by-step explanation:

Quadratic expressions are polynomial expressions in which the highest power of the variable is 2.

Looking at option A, the highest power of the variable in the polynomial is 4. Therefore, it is not a quadratic expression.

Looking at option B, the highest power of the variable in the polynomial is 3. Therefore, it is not a quadratic expression.

Looking at option C, the highest power of the variable in the polynomial is 2. Therefore, it is a quadratic expression.

Looking at option D, the highest power of the variable in the polynomial is 1. Therefore, it is not a quadratic expression.

Answer:

c

Step-by-step explanation:

its c bc i got it right on test

Answer:

(6.75,9.75)

Step-by-step explanation:

To find the x coordinate of the midpoint add the x coordinate of the endpoints and divide by 2

(4.5+9)/2 =13.5/2=6.75

To find the y coordinate of the midpoint add the y coordinate of the endpoints and divide by 2

(7.5+12)/2=19.5/2=9.75

(6.75,9.75)

Please find attached photograph for your answer

Answer:

\(f(x) = 2{x}^{2} - x + 5 \\ f( - 2) = 2 {( - 2)}^{2} - ( - 2) + 5 \\ f( - 2) = 2(4) + 2 + 5 \\ f( - 2) = 8 + 2 + 5 \\ \boxed{f( - 2) = 15}\)

Answer:

The cosine ratio of angle A is 28/197

Step-by-step explanation:

The cosine of the angle is the adjacent (to the angle) side and the hypotenuse

So, in this case, the side AC and the hypotenuse AB

Hence, cosine ratio of angle A is 28/197

(a) The linear density (mass/length) rho has SI units of kg/m. Since rho = a + bx, the SI units of a must be kg/m and the SI units of b must be kg/m^2.
(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod:
m = ∫₀ᴸ ρ(x) dx
Substituting in ρ(x) = a + bx:
m = ∫₀ᴸ (a + bx) dx
m = [ax + (1/2)bx²] from 0 to L
m = aL + (1/2)bL²
Therefore, the mass of the rod in terms of a, b, and L is m = aL + (1/2)bL².

(a) In this problem, rho (ρ) represents linear density, which has units of mass per length. In SI units, mass is measured in kilograms (kg) and length in meters (m). Therefore, the units of linear density are kg/m. Since ρ = a + bx, the units of a and b must be consistent with this equation. The units of a are the same as those of ρ, so a has units of kg/m. For b, since it is multiplied by x (which has units of meters), b must have units of kg/m² to maintain consistency in the equation.

(b) To find the mass of the rod, we need to integrate the linear density function over the length of the rod (from x=0 to x=L). Let's set up the integral:

Mass (M) = ∫(a + bx) dx, with limits from 0 to L

Now, we can integrate:

M = [a * x + (b/2) * x²] evaluated from 0 to L

Substitute the limits:

M = a * L + (b/2) * L²

So, the mass of the rod in terms of a, b, and L is:

M = aL + (bL²)/2

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The initial size of the bacteria culture was approximately 202.02.

To solve this problem, we can use the formula for exponential growth:

N(t) = N0 * e^(kt)

where N(t) is the size of the culture at time t, N0 is the initial size of the culture, k is the growth rate, and e is the natural logarithmic base.

We can use the given information to set up two equations:

300 = N0 * e^(k10)

1400 = N0 * e^(k40)

Dividing the second equation by the first equation gives:

1400/300 = e^(k40) / e^(k10)

Simplifying:

4.67 = e^(k*30)

Taking the natural logarithm of both sides:

ln(4.67) = k*30

Solving for k:

k = ln(4.67) / 30

Substituting back into the first equation:

300 = N0 * e^(ln(4.67)/3)

300 = N0 * 1.484

Solving for N0:

N0 = 300 / 1.484

N0 ≈ 202.02

Therefore, the initial size of the bacteria culture was approximately 202.02.

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Statement ii "at least one of the homes was sold for more than $130,000 and less than $150,000." must be true. Because Since the arithmetic mean sale price is $130,000, it means that half of the homes were sold for more than $130,000 and half were sold for less than $130,000. So, the correct option is Statement ii.

Since the arithmetic mean sale price is $150,000, it means that the total sale price of all 15 homes combined was $150,000 x 15 = $2,250,000. However, this does not necessarily mean that at least one of the homes was sold for more than $165,000, as some homes could have been sold for less than the mean to bring the average down. Therefore, statement i is not necessarily true.

On the other hand, statement iii is not necessarily true either, as we have no information about the sale price of the lowest-priced home or any other individual home. It is possible that all 15 homes were sold for more than $130,000, in which case statement iii would be false.

So, the correct answer is statement ii.

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Answer:

315

Step-by-step explanation:

You're welcome
Answer above is rounded btw

Full number is:315.24444

Answer:

Step-by-step explanation:

Number of people using more than one sport facility:

Since 16 is counted for all three, total number of those using more than one facility is therefore:

Number of people using exactly one facility is:

Probability of the person using exactly one facility is:

Answer:

  (a)  $810.45

Step-by-step explanation:

You want the value of an investment of $300 earning 5% interest compounded quarterly for 20 years.

The compound interest formula tells you the value is ...

  A = P(1 +r/n)^(nt)

where P = 300, r = 0.05, n = 4, t = 20.

Using the given parameters in the given equation, you find the account value to be ...

  A = $300(1 +0.05/4)^(4·20) ≈ $810.45

__

Additional comment

The "rule of 72" tells you the account value will approximately double in a number of years equal to 72 divided by the interest rate percentage: 72/5 = 14.4 years. After 20 years, it will be worth more than that doubled amount, $600. This only leaves one reasonable answer choice.

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In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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Answer: The answer is B

Step-by-step explanation:

-(5n-1\right)\left(25n^2+5n+1)

u gotta flip it and the answer is B on your screen!!!