a couple has four children. assuming independence and that the probability of a boy is 1 2, determine the probability that the two oldest children are girls and the two youngest children are boys.
Answers
The probability that the two oldest children are girls and the two youngest children are boys is 1/16.
Since the gender of each child is independent and the probability of a boy is 1/2, the probability of the two oldest children being girls is:
= (1/2)(1/2) = 1/4And the probability of the two youngest children being boys is also:
= (1/2)(1/2) = 1/4To find the probability of both events happening together, we multiply the probabilities:
= (1/4)*(1/4) = 1/16Therefore, the probability that the two oldest children are girls and the two youngest children are boys is 1/16.
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Related Questions
write the equation in spherical coordinates. (a) x2 + y2 + z2 = 25
Answers
The equation in spherical coordinates is ρ = 5. This equation represents a sphere centered at the origin with a radius of 5 units in the ρ direction.
To write the equation \(x^2 + y^2 + z^2 = 25\) in spherical coordinates, we need to express x, y, and z in terms of the spherical coordinates (ρ, θ, φ).
In spherical coordinates, ρ represents the distance from the origin to the point, θ represents the azimuthal angle measured from the positive x-axis in the xy-plane, and φ represents the polar angle measured from the positive z-axis.
To transform the Cartesian coordinates (x, y, z) to spherical coordinates, we can use the following equations:
x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)
Now let's substitute these equations into the given equation:
\((x^2) + (y^2) + (z^2) = 25\)
(ρ sin(φ) cos(θ))² + (ρ sin(φ) sin(θ))² + (ρ cos(φ))² = 25
ρ² (sin²(φ) cos²(θ) + sin²(φ) sin²(θ) + cos²(φ)) = 25
ρ² (sin²(φ) (cos²(θ) + sin²(θ)) + cos²(φ)) = 25
ρ²(sin²(φ) + cos²(φ)) = 25
ρ²= 25
This simplifies to:
ρ = 5
Therefore, the equation in spherical coordinates is ρ = 5. This equation represents a sphere centered at the origin with a radius of 5 units in the ρ direction.
In spherical coordinates, the equation ρ = 5 describes all points that are at a distance of 5 units from the origin, regardless of the values of θ and φ.
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What is the least common denominator for the fractions 5/6and3/8? A).14 B).18 C).24 D).48
Answers
Answer:
To find the least common denominator, or lcd, you have to find the least common multiple, or lcm. To do that you find the multiples of each number until they equal each other. I set up a chart like this,
6 -
8 -
and then I start listing multiples so,
6 - 6, 12, 18, 24,
8 - 8, 16, 24,
I stop after I find a number they are both equal to. So to get to that number I would multiply 8 by 3, and 6 by 4. This gives me 24 as the lcd. If you need the lcd to add the fractions together, then whatever you did to the bottom do to the top. So 5/6 would become 20/24 and 3/8 would become 9/24.
Answer: 24
Step-by-step explanation:
Solve the following equation.
5x = 60
x =
Group of answer choices
5
12
1
60
Answers
Answer:
x=12
Step-by-step explanation:
You have to do 60/5 which is 12
so x=12
Answer:
x=12
Step-by-step explanation:
5x=60
divide both sides by 5
x=12
answer: x=12
Help me pleas asap and pleas show your work
Answers
Answer:
y = 7 - 4x
Step-by-step explanation:
8x + 2y = 14
2y = 14 - 8x (since we're solving for "y", we want "y" by itself)
y = 14-8x / 2 (we want to separate "y" and 2, so we divide the other side of the equation by 2)
y = 7 - 4x (divide by 2)
Hope this helps :)
pls help on these and thku
Answers
Answer:
the second one
Step-by-step explanation:
If a*b=a^2+b, write the values of 4*(3*5)
Answers
Answer:
30
Step-by-step explanation:
Evaluate 3* 5 first , that is
3* 5 = 3² + 5 = 9 + 5 = 14 , then
4* 14
= 4² + 14
= 16 + 14
= 30
If p(x) = ax²-3x+10, for what value(s) of a is p(-2) = f(g(-2))? May you explain how you did this.
Answers
Answer:
If p(x) = ax²
-3x+10
p(-2) =
f(g(-2))
What is the domain of the function on the graph?
Answers
Answer:
Option 2
Step-by-step explanation:
y = 3/4x - 3/10 to standard form
Answers
Answer:
-3/4x+y=3/10
Step-by-step explanation:
standard form is Ax + By =C
In this case Ax is 3/4x , By is y and C is 3/10
Hope it helped
La suma de las probabilidades de todos los posibles resultados de un experimento aleatorio debe ser igual a
Answers
Respuesta: Uno
La suma de la probabilidad de todos los resultados posibles de un experimento aleatorio debe ser igual a uno.
Porque algunos resultados más ocurren en cada sendero y la suma de todas las probabilidades es 100% o uno.
Espero haber ayudado, buena suerte! :)
In a class of student 17 like volleyball like basketball and 10 like both games . show in venn-diagram and find the number student who do not like both games
Answers
The number of students who do not like both games is 3
What is a Venn Diagram?John Venn popularized the Venn diagram in the 1880s, which is a type of diagram that displays the logical relationship between sets. The illustrations are used in probability, logic, statistics, linguistics, and computer science to demonstrate basic set relationships and to teach rudimentary set theory.
How to solveStudents who like only volleyball=17-10=7
Students who like only basketball=15-10=5
Students who like both sports =10
Students who like one or more sports =7+5+10=22
Students who do not like any sport =25-22=3
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In a class of 25 students, 17 like volleyball, 15 like basketball and 10 like both games. Find the number of students who don't like any of the games.
8.2/3 of the students in a class are boys, 3/4 of the boys are right-handed There are 18 right-handed boys. How many students are there in the class?
Answers
Answer:
36
Step-by-step explanation:
3/4x = 18 multiply both sides by 4/3
(4/3)(3/4)x = (18/1) (4/3)
x = 24 There are 24 boys in the class.
2/3x = 24 Multiply both sides by 3/2
(3/2)(2/3)x = (24/1)(3/2)
x = 36
By solving a linear equation , we get the total number of students in the class are 36
What is a linear equation in one variable?An linear equation is a mathematical statement consists of expressions of only one variable that too with power 1 and constants and compares two such expressions by equating them.
Standard form of linear equation in one variable : ax +b = c
x = (c-b)/a
Let the total number of students in the class are x
Given that 2/3 of the students in a class are boys
∴ The number of boys = 2/3(x) =(2x)/3
Then given that 3/4 of the boys are right handed and there are 18 right-handed boys
∴ 3/4( no of boys ) =18
⇒3/4 *(2x/3) =18
⇒(3*2x)/(4*3) =18
⇒x/2 =18
Multiplying both sides by 2
⇒x = 2*18 = 36
Therefore, the total number of students in the class are 36
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Write the equation of the line parallel to
Y= 2x+ 3 that passes through the
point (6, -9).
Answers
The parallel line has an equation of y = 2x - 21
How to determine the line equation?The equation is given as
y = 2x + 3
The equation of a line can be represented as
y = mx + c
Where
slope = m
By comparing the equations, we have:
m = 2
The slopes of parallel lines are equal
This means that the slope of the other line is 2
i.e. m = 2
Recall that:
The equation of a line can be represented as
y = mx + c
Where
slope = m = 2
Also, we have
(x, y) = (6, -9)
So, we have
-9 = 2 * 6 + c
This gives
c = -9 - 12
Evaluate
c = -21
So, we have
y = 2x - 21
Hence, the equation of the parallel line is y = 2x - 21
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Jill's front door is 42 wide and 82 tall. She purchased a circular table that is 96 inches in diameter. Will the table fit through the front door???
Answers
Answer:
Step-by-step explanation:
Answer:
yes because 42+82 is greater than 96
it will just about fit through the door
hope this helps! :)
A snow globe is made out of regular right triangular prism that is inscribed in hemisphere with radius 12cm. help a designer to find the dimensions of maximum volume prison. state the exact answer.
Note: Find the dimensions of the prism for the case when the triangular base is on the grand circle of the hemisphere.
Answers
The maximum volume of the prism is 1728 cubic centimeters.
To find the dimensions of the prism with maximum volume, we need to consider the relationship between the volume of the prism and its dimensions.
Let's assume the base of the right triangular prism is an isosceles right triangle with legs of length 'a'. The height of the prism will be 'h'. The prism is inscribed in a hemisphere with a radius of 12 cm.
First, let's determine the relationship between 'a' and 'h'. Since the base of the prism is on the great circle of the hemisphere, the hypotenuse of the triangular base is equal to the diameter of the hemisphere, which is twice the radius. Therefore, the hypotenuse of the base is 2 * 12 = 24 cm.
By using the Pythagorean theorem, we can find 'a':
a^2 + a^2 = 24^2
2a^2 = 576
a^2 = 288
a = √288
Now, let's find the height 'h' of the prism. The height 'h' is equal to the radius of the hemisphere, which is 12 cm.
Therefore, the dimensions of the prism for maximum volume are:
Base length (a) = √288 cm
Height (h) = 12 cm
To find the maximum volume, we can use the formula for the volume of a right triangular prism:
Volume = (1/2) * a^2 * h
Substituting the values, we get:
Volume = (1/2) * (√288)^2 * 12
= (1/2) * 288 * 12
= 1728
Hence, the maximum volume of the prism is 1728 cubic centimeters.
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Does the table represent a proportional relationship?
O Proportional
O Not Proportional
Answers
Answer:
Not proportional
Step-by-step explanation:
1/5 = 0.2
2/8 = 0.25
6/18 = 0.33
etc...
Graph the following equation on the coordinate plane: y=2/3×+1
Answers
The correct graph of equation on the coordinate plane is shown in figure.
We know that;
The equation of line with slope m and y intercept at point b is given as;
y = mx + b
Here, The equation is,
y = 2/3x + 1
Hence, Slope of equation is, 2/3
And, Y - intercept of the equation is, 1
Thus, The correct graph of equation on the coordinate plane is shown in figure.
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The vertex of a quadratic function is (5,-6), what is the equation of the axis of symmetry in this function?
Answers
Answer:
x = 5
Step-by-step explanation:
A quadratic equation:
f(x) = y = a*x^2 + b*x + c
Has a vertex in a point:
(h, k) such that:
h = -b/2a
and:
k = f(-b/2a)
And the axis of symmetry (this is the line that cuts the graph in two halves) is:
x = h.
In this case, the vertex is (5, -6)
Then the axis of symmetry is:
x = 5.
IM GIVING OUT THE FIRST PERSON BRANLIEST WHO ANSWERS RIGHT FIRST: a floor that is 8 feet x 10 feet is covered by tiles that are 6 inch squares. How many fewer tiles would it take to cover the floor if the tiles were 12 inch squares? AND NO IT IS NOT 80!!
Answers
Therefore , the solution of the given problem of surface area comes out to be 240 tiles will cover the floor.
What is a surface area ,exactly?Calculating how much space would be needed to fully cover the outside will reveal its overall size. The surroundings are considered when determining the same surface with a rectangular form. The surface area of something determines its overall dimensions. The amount of edges present in the space between a cuboid's four trapezoidal corners determines how much water it can hold inside.
Here,
Let's first determine how many 6 inch squares are required to span the floor:
=> 80 square feet is the size of the floor (8 feet by 10 feet).
We require the following because each 6-inch square spans an area of => (1/2) ft x (1/2) ft = 1/4 square feet:
=> 80 square feet 1/4 square foot = 320 tiles in a row of 6 inch tiles.
Since a 12 inch square encompasses a space that is 1 foot by 1 foot, we require:
=> 80 square feet / 12 inch square tile,
which equals 80 tiles.
Using 12 inch squares rather than 6 inch squares allows us to save the following amount of tiles:
=> Number of 6 inch tiles - Number of 12 inch tiles = 320 - 80 = 240 tiles
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Part b)A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.
Answers
SOLUTION
The diagram below would help
So from the diagram, we can see that
\(\text{Volume of the foam = volume of cuboid - volume of cylinder }\)Volume of cuboid is given as
\(\begin{gathered} V=l\times w\times h \\ \text{where }l=\text{length = 1.8 m} \\ w=\text{width = 300}mm=\frac{300}{1000}m=0.3m \\ h=\text{height }=\text{ 300}mm=\frac{300}{1000}m=0.3m \end{gathered}\)So volume of the cuboid becomes
\(1.8\times0.3\times0.3=0.162m^3\)Volume of a cylinder is given as
\(\begin{gathered} \pi r^2h \\ \text{where r = radius = }\frac{diameter}{2}=\frac{150}{2}mm=75mm=\frac{75}{1000}=0.075m \\ r=0.075m \\ h=1.8m \end{gathered}\)So, the volume of the cylinder becomes
\(\begin{gathered} \pi r^2h \\ \frac{22}{7}\times0.075^2\times1.8 \\ =0.03182m^3 \end{gathered}\)Hence volume of the Foam becomes
\(\begin{gathered} 0.162-0.03182 \\ 0.13018 \\ 0.13m^3 \end{gathered}\)Hence the answer is 0.13 cubic meter to 2 decimal places
Could I please get assistance with this question. Create a mini cricket/rugby clinic explanation where you teach learners about cricket/rugby while incorporating Mathematics or English literacy. Your explanation should be informative and insightful.
Answers
Introduce the sport of cricket/rugby and explain its history and rules.
Use cricket/rugby as a context for teaching Mathematics or English literacy. For example:
Mathematics: You can use cricket/rugby statistics to teach learners about probability, percentages, and data analysis. For instance, you can ask learners to calculate the batting average of a cricket player or the conversion rate of a rugby team. You can also ask learners to solve word problems related to cricket/rugby, such as "If a cricket team scores 240 runs in 50 overs, what is their run rate per over?"
English literacy: You can use cricket/rugby as a context for teaching learners about reading comprehension, writing, and vocabulary. For instance, you can ask learners to read a cricket/rugby article and summarize it in their own words. You can also ask learners to write a persuasive essay on why cricket/rugby is the best sport. Additionally, you can teach learners cricket/rugby-specific vocabulary, such as "wicket," "boundary," "try," and "conversion."
Use cricket/rugby drills and exercises to reinforce the Mathematics or English literacy concepts you have taught. For example:
Mathematics: You can ask learners to measure the distance between the wickets or the length of the cricket pitch using a tape measure. You can also ask learners to count the number of runs scored in a cricket match or the number of tries scored in a rugby match.
English literacy: You can ask learners to write a cricket/rugby-themed story or poem using the vocabulary they have learned. You can also ask learners to read a cricket/rugby rulebook and explain the rules in their own words.
Overall, incorporating Mathematics or English literacy into a cricket/rugby clinic can make the learning experience more engaging and meaningful for learners. By using cricket/rugby as a context for teaching these subjects, learners can see the real-world applications of what they are learning and develop a deeper understanding of the concepts.
The sum of a number times 9 and 30 is at most 15 what is the answer?
Answers
Answer:
x ≤ - 5/3
Step-by-step explanation:
Let the number be x
The sum of a number times 9 and 30 is at most 15 translates algebraically to
9x + 30 ≤ 15
Subtracting 30 both sides:
9x ≤ -15
Dividing by 9 both sides:
x ≤ - 15/9
or
x ≤ - 5/3
Whats 5000+35548-455x4534+38534x233=?
Answers
Answer:
6,956,000
Do all the operations in order by following the PEMDAS method.
7) A stratified sample of 50 students is taken. How many year 7s are picked? Year 7 135
Year 8 150
Year 9 120
Year 10 154
Year 11 132
Answers
In a stratified sample of 50 students, approximately 10 Year 7 students are picked.
We have,
The total number of students in the population.
= 135 (Year 7) + 150 (Year 8) + 120 (Year 9) + 154 (Year 10) + 132 (Year 11)
= 691
The proportion of Year 7 students in the population.
= 135/691
= 0.1957
To calculate how many Year 7 students are picked in a sample of 50 students, we multiply the sample size by the proportion of Year 7 students in the population.
= 50 × 0.1957
= 9.785
Rounding to the nearest whole number.
= 10
Therefore,
In a stratified sample of 50 students, approximately 10 Year 7 students are picked.
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Jenna and Krista are accountants who both enjoy drinking coffee. Each accountant
recorded how many cups of coffee she drank each day for the 30 days in April, then
recorded that data in the box plots shown.
Jenna generally drank more coffee each day than Krista.
Jenna generally drank more coffee each day than Krista.
Krista generally drank more coffee each day than Jenna.
Krista generally drank more coffee each day than Jenna.
Both accountants drank at least 2 cups of coffee at least half the days in April.
Both accountants drank at least 2 cups of coffee at least half the days in April.
Both accountants drank at least 3 cups of coffee at least half the days in April.
Both accountants drank at least 3 cups of coffee at least half the days in April.
Both accountants drank at least 5 cups of coffee at least half the days in April.
Both accountants drank at least 5 cups of coffee at least half the days in April.
Both accountants drank at least 6 cups of coffee at least half the days in April.
Which of the following statements are true about the data? Select all that apply.
Answers
Answer: Krista's Maximum is the same as Jenna's upper quartile.
Step-by-step explanation:
1 2 2 4 3 9 4 16 what is the range of the function please help
Answers
Answer:
Step-by-step explanation:
x y
1 2
2 4
3 9
4 16
This sounds like a quadratic equation of f(x)=x^2, thus, the range is:
R(x): (-∞,+∞)If the function only has these points, then the range is:R(x): [2]∪[4]∪[9]∪[16]Please help. I don't understand this.
Answers
Answer:
radius=6
Step-by-step explanation:
arc ACB=6xPi
Pi=3.14159
arc ACB=18.85 (rounded to 2 places)
ACB is a half circle so a full circle would be 18.85x2 or 37.7
circumference (whole circle)=2 x Pi x radius
37.7=2 x 3.14159 x radius
radius= 37.7/(2 x 3.14159)
radius=6
Can someone explain how to answer this problem
Write an equation in point-slope form given the following: (1,2); m=7
thanks
Answers
Answer:
Step-by-step explanation:
Answer:
y-2 = 7(x-1)
Can somebody help pkease
Answers
4+6y=12x-2 helpp pleasee
Answers
Answer:
y=2x-1
Step-by-step explanation:
Explanation:
You will add ‘-4’ to each side of the equation so 4+ -4 +6y = -2+ -4 +12x
Then combine like terms 4 + -4 = 0
0+6y=-2+-4+12x -> 6y=-2+-4+12x
Again combine like terms -2+-4=-6
6y=-6+12x
Next divide each side by 6 to get answer
y=-1+2x