There are five boys and five girls in a class. The teacher randomly selects three different students to answer questions. The first student is a girl, the second student is a boy, and the third student is a girl. Find the probability of this occuring.

Answers

Answer 1

Final answer:

The probability of selecting a girl, then a boy, and then another girl from a class with 5 girls and 5 boys is 10.42%.

Explanation:

The probability of a specific sequence of students being selected in a random draw can be calculated by multiplying the probabilities of each event occurring in succession. Since there are five boys and five girls in the class, the probability of drawing a girl first is 5/10, or 1/2. After drawing one girl, there are now four girls and five boys left, so the probability of drawing a boy second is 5/9. Finally, with one girl and one boy already picked, there are three girls and four boys left, making the probability of drawing a girl third 3/8.

To find the overall probability, we multiply these individual probabilities:

Probability = (First girl drawn) × (Second boy drawn) × (Third girl drawn)
Probability = (1/2) × (5/9) × (3/8)
Probability = (1 × 5 × 3) / (2 × 9 × 8)
Probability = 15 / 144
Probability = 0.1042 or about 10.42%

Answer 2

Final answer:

The probability of the teacher randomly selecting a girl, a boy, and another girl from a class of 5 boys and 5 girls is 5/6.

Explanation:

To find the probability of the teacher randomly selecting three different students, we need to consider the number of possible outcomes and the number of favorable outcomes. In this case, there are 10 students to choose from and the teacher needs to select one girl, one boy, and another girl. To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes.

The number of favorable outcomes is 5 for the first girl, 5 for the boy, and 4 for the second girl (since the first girl has already been selected). So the total number of favorable outcomes is 5 x 5 x 4 = 100.

The number of possible outcomes is the total number of ways to choose 3 students from the 10 available. This can be calculated using the combination formula: C(10, 3) = 10! / (3!(10-3)!) = 120.

Therefore, the probability of selecting a girl, a boy, and another girl is 100/120 = 5/6.

Related Questions

If 300 cm^2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.

Answers

Hello,
Assume a the side of the base, b the height.

[tex]V=a^2*b\\ a^2+4ab=300==\ \textgreater \ b= \dfrac{300-a^2}{4a} \\ V=a^2*\dfrac{300-a^2}{4a}= \frac{1}{4} *(300a-a^3)\\ \dfrac{dV}{da} = \frac{1}{4} *(300-3*a^2)=0\\ ==\ \textgreater \ a=10 \ and\ b=5\\ V=10^2*5=500\\ [/tex]

The formula used to calculate simple interest is modeled by I=prt, where I=simple interest, p=principle, r=interest rate, and t=time, measured in years. Which of the following options represent(s) an alternative equivalent version of the simple interest formula? select all that apply....TY
I = trp
I = p + rt
I - rt = p
t= l/rp
p= l/rt

Answers

An alternative equivalent versions are:

I = trp
t= l/rp
p= l/rt

Step-by-step explanation:

The formula for simple interest is as follows.

I = prt

where, I = simple interest

p = principle

r = rate

t = time

This formula can be alternatively written by shifting I, r, t, and p either on the right or left side of equals sign.

Therefore, the formula can be rewritten as follows.

I = trp[tex]t = \frac{I}{rp}[/tex] [tex]p = \frac{I}{rt}[/tex]

If k pencils cost c cents what is the cost in cents of p pencils

Answers

the cost in cents of 1 pencil = c/k

the cost in cents of p pencils = (c/k) * p

If k pencils cost c cents. Then the cost in cents of p pencils will be cp / k.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

If k pencils cost c cents. Then the cost of each pencil is given as,

⇒ c / k

Then the cost in cents of p pencils is given as,

⇒ (c / k) x p

⇒ (cp) / k

If k pencils cost c cents. Then the cost in cents of p pencils will be cp / k.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ5

A local carpet company has been hired to carpet a planetarium which is in the shape of a circle. If the radius of the planetarium is six yards, and the cost of the carpet is $14 per square yard, find the total cost to carpet the planetarium. (use 3.14 for π )

Answers

This is the concept of application of geometry and financial mathematics; To calculate for the total cost of the carpet we proceed as follows;
Total cost=[area of the carpet]*[price per square yard]
area of carpet is given by:
Area=πr^2
where;
radius,r=6 yeards
=π*6^2
=113.1 square yards
therefore the price of the carpet will be:
113.1*14
=$1,583.4

There were n balloons at the beginning of the party. By the end of the party, 5 of them had popped. Using n, write an expression for the number of balloons that were left

Answers

Answer:

The expression for the number of balloons that were left is [tex]n-5[/tex].

Step-by-step explanation:

There were n balloons at the beginning of the party.

By the end of the party, 5 of them had popped.

Let the remaining balloons be represented by x

So, x = total balloons minus 5

This gives: [tex]x=n-5[/tex]

Therefore, the expression for the number of balloons that were left is [tex]n-5[/tex].

Find cos θ if sin θ = negative twelve divided by thirteen and tan θ > 0. negative five divided by twelve negative five divided by thirteen twelve divided by five negative thirteen divided by twelve

Answers

1.
Sin∅=opposite side / hypotenuse, in a right triangle, as shown in the figure.

In this triangle, the length of the hypotenuse is 13, the length of one side 12, and the other side can be found by the Pythagorean theorem to be:

[tex] \sqrt{13^{2} - 12^{2} }= \sqrt{169-144}= \sqrt{25}=5 [/tex]

2.
The value of the cosine is (adjacent side)/(hypotenuse)=5/13.

3.
The tangent is positive in the first and third quadrants.

Since Tan=Sine/Cosine, and Sine is negative, then cosine must be negative as well

Answer: -5/13

To raise money for charity,Polly climbs the 1,776 steps in the CN Tower in Toronto,Canada.If it takes her 40 minutes to complete the climb,what is Polly's average rate per minute?

Answers

The Average Is 44.4 Steps

A girl scout troop sold cookies. If the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?

Answers

week1 = x

week2 = x+5

week3 = 2(x+5)

x + (x+5) + 2(x+5) = 431

x + x + 5 + 2x + 10 = 431

4x + 15 = 431

4x = 431 - 15

4x = 416

x = 104

week1 = x = 104 boxes

week2 = x+5 = 104+5 = 109 boxes

week3 = 2(x+5) = 2(104+5) = 2*109 = 218 boxes

You decide to put $150 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2.5% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
10.1101 years
119.954 years
121.321 years
134.34 years

Answers

The formula is
A=p (1+r/k)^kt
3000=150 (1+0.025/12)^12t
Solve for t
3000/150=(1+0.025/12)^12t
Take the log
Log (3000/150)=12t×log (1+0.025/12)
12t=Log (3000/150)÷log (1+0.025/12)
T=[Log (3000/150)÷log (1+0.025/12)]÷12
T=(log(3,000÷150)÷log(1+0.025÷12))÷12
T=119.954 years

I need help with geometry.

Answers

1.

In any trapezoid, the length of the midsegment is [tex] \frac{|base_1|+|base_2|}{2} [/tex]

substituting the known values:

[tex] \frac{24+|base_2|}{2}=19 [/tex]

[tex]24+|base_2|=38[/tex]

[tex]|base_2|=38-24=14[/tex]

2.

Notice that since D and have the same y-coordinate, then DE is horizontal, and since F and D have the same x-coordinate, FD is vertical.

Thus FD and DE are perpendicular, so the triangle FED is a right triangle.

The median drawn from the right angle, is equal to half the hypotenuse.

That is, |DO|=1/2 |FE|, thus |OE|=|OF|=|OD|, are all radii of the circle centered at O.

O is the midpoint of EF, and is found by the Midpoint formula:

[tex]O=( \frac{1+7}{2} , \frac{5+1}{2} )=(4, 3)[/tex]

Answer:

1. 14

2. (4, 3)

What is the 32nd term of the arithmetic sequence where a1 = 4 and a6 = 34 ?

Answers

hello :
the nth term of an arithmetic sequence is :
An =Ap+(n-p)d ....a common difference is : d
in thie exercice : p=1 and n=6
A6 = A1 + (6-1)d
34 = 4 +5d
5d= 30
d= 6
A32 = A1+(32-1)(6) =4 + 31(6) = 190

Which of the following points is in the solution set of y>-x^2+5?

A. (0,5)

B. (1,3)

C. (2,4)

Answers

The only point which is a solution is C

A hair-styling salon charges $11.00 for a haircut, and an average of 75 people stop in for haircuts each day. The owner is thinking of increasing the price, and he estimates that every time he raises the price of a haircut by $1.00, the number of people coming in for haircuts will decrease by 3 per day. Which of these functions represents the estimated revenue per day from haircuts as a function of the number of dollars the price of a haircut is raised?

Answers

Final answer:

The estimated daily revenue function, given the described price increase and corresponding customer decrease, can be represented as R(x) = (11 + x)(75 - 3x), where x is the number of dollars by which the price is raised.

Explanation:

The question asks us to find a function that represents the estimated revenue per day from haircuts as a function of the number of dollars the price of a haircut is raised. Initially, the salon charges $11.00 for a haircut with an average of 75 people per day. When the price increases by $1, the number of customers decreases by 3.

Let x represent the number of dollars by which the haircut price is raised. The new price will be $11.00 + x. The number of customers is initially 75, and for each $1 increase, we lose 3 customers, so the new number of customers will be 75 - 3x. The daily revenue, R(x), can be found by multiplying the new price by the new number of customers:

R(x) = (11 + x)(75 - 3x)

This function will give us the estimated daily revenue after increasing the haircut price by x dollars.

An expression is shown below:

square root of 32 plus square root of 2

Which statement is true about the expression?

please help 25 points

A. It is rational and equal to 4

B. It is rational and equal to 5

C. It is rational and equal to 5√2

D. It is rational and equal to 4√2

Answers

C) sqrt(32) = sqrt(2^5)=4sqrt(2), then + sqrt(2) = 5 * sqrt(2)

√(2^5)+√2

4√2+√2

(4+1)√2

5√2

There is a problem however...5√2 is IRRATIONAL because √2 is irrational, ie, it cannot be expressed as a ration of two integers...

So the problems simplified is certainly 5√2, but it is irrational.

Maybe there is a typo and should read:

C. It is IRrational and equal to 5√2

The scale on a map indicates that 1 in = 2.5mi. How far apart are two cities that measure 2.5 ft apart on the map? A. 60 miles B. 6.25 miles C. 75 miles D. 90 miles

Answers

The answer is C. 75 miles

What is the probability of flipping a penny and a nickel and obtaining one head and one tail?

Answers

Final answer:

The probability of flipping a penny and a nickel and obtaining one head and one tail is 0.25, or 25%.

Explanation:

The probability of flipping a penny and a nickel and obtaining one head and one tail can be calculated by multiplying the probabilities of getting a head on one coin and a tail on the other coin. Since the chance of getting a head on a fair coin is 0.5 and the chance of getting a tail is also 0.5, the probability of getting one head and one tail is:

Probability = (Probability of getting a head on the penny) × (Probability of getting a tail on the nickel)

Probability = 0.5 × 0.5 = 0.25, or 25%.

How do you solve all of these ?

Answers

5)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ -3}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-3)=-1(x-5) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+3=-x+5\implies y=-x+2[/tex]

6)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 2}}\quad ,&{{ 1}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 3 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=3(x-2) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-1=3x-6\implies y=3x-5[/tex]

7)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ 5}}\quad ,&{{ 2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 0 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=0(x-5) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-2=0\implies y=2[/tex]

8)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]

9)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{5}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-0=\cfrac{5}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y=\cfrac{5}{2}(x+2)\implies y=\cfrac{5}{2}x+5[/tex]

10)

[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{-2}}\quad ,&{{ -2}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{3}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-(-2)=\cfrac{3}{2}(x-(-2)) \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y+2=\cfrac{3}{2}(x+2)\implies y+2=\cfrac{3}{2}x+3\implies y=\cfrac{3}{2}x+1[/tex]

The surface areas of two similar solids are 289 ft2 and 900 ft2. The volume of the larger solid is 1,755 ft3. What is the volume of the smaller solid?

Answers

The volume of the smaller solid is 319 ft^3.

The base of a triangle measures (3x − 6) units and the height measures (2x + 4) units. Part A: What is the expression that represents the area of the triangle? Show your work to receive full credit. (4 points) Hint: Area = 0.5bh Part B: What are the degree and classification of the expression obtained in Part A? (3 points) Part C: How does Part A demonstrate the closure property for polynomials? (3 points)

Answers

To answer this item, we use the equation given for the calculation of the area of the triangle.

A = 0.5bh

Substituting the known expressions,

A = (0.5)(3x – 6)(2x + 4)

Part A: Use distribution method to simplify the expression for the calculation of area.

A = 0.5(6x^2 + 12x – 12x – 24)

A = 0.5(6x^2 – 24)

A = 3x^2 – 12

Part B: The equation for area of has a degree of two because the highest exponent is 2.

Part C: The closure property of polynomials is always closed for multiplication.

Answer With Step-by-step explanation:

Part A:

.5[ (3x – 6) (2x + 4) ]

.5(6x^2 - 24)

3x^2 - 12

Part B:

Second Degree Binomial

Part C:

For Part A, a polynomial was multiplied by another polynomial. The resulting product was a polynomial. This is a demonstration of the closure property for multiplying polynomials.

Select the inequality that corresponds to the given graph. graph of an inequality with a solid line through the points negative 8 comma 0 and 0 comma negative 4 and shading above the line A 4x − 3y > − 12 B x + 4y > 4 C 4x − 2y < − 8 D 2x + 4y ≥ − 16

Answers

well by looking at the graph I can see that the equation for the line is y=-0.5x-4
rearranging I can get the answer.
y>=-0.5x-4
y+0.5x>=-4
2y+x>=-8

the answer is
2x+4y>=-16

Answer: 2x+4y ≥ -16

Step-by-step explanation: In the given graph x-intercept is -8 and y-intercept is -4.

Also the graph is shaded up of the line for greater values of y's.

On the option 2x+4y ≥ -16 has x-intercept at -8 and y-intercept at -4.

Also all other inequalities has only less than or greater than sign.

In the given graph we have a solid line.

So, there should be greater than or equal to inequality sign for the inequality.

Only option 4 has greater than with equal to sign.

Therefore, correct option is 2x+4y ≥ -16

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -5 - 5 cos θ

Answers

y-axis symmetry=(r, theta)=(-r,theta)
-5-5cos(theta)=r
-r=5+5cos(theta)
no y-axis symmetry
x-axis symmetry=(r,theta)=(r,-theta)
cosine is an even function, so yes it is symmetric around x-axis
origin symmetry=(r,theta)=(-r,theta) or (r, theta+pi)
no, as there is no y-axis symmetry

Answer:

x-axis symmetry

Step-by-step explanation:

You have a total of 21 coins, all nickles and dimes. The total value is $1.70 Which of the following is the system of linear equations that represent this scenario? Let n= the number of nickles and let d= the number of dimes.

Answers

You need one equation for the physical nickels and dimes, which total to 21:

n+d=21

Secondly, you need one equation for the numerical value of those nickels and dimes. We know nickels are worth $0.05 and dime are worth $0.10:

.05n+.1d=1.70

Harmony can spend up to $100 on a shopping trip. She needs to buy socks and shoes. Each pair of socks costs $5.00 and each pair of shoes costs $20.00. Which graph shows all of the ways she can purchase shoes and socks, spending up to $100?

Answers

20y+5x≤100 divide all terms by 5

4y+x≤20 subtract x from both sides

4y≤-x+20 divide both side by 4

y≤-0.25x+5

So just in simplest terms, the slope is slightly negative and it should be shaded under the line since y is less than the line...so it is the second graph.

What are the solutions of 2x^2+3x=-8

Answers

The equation given above is written here below with all the terms transposed to only one side of the equation.
2x² + 3x + 8 = 0
The quadratic formula used for the determination of the roots is,
x = (-b +/- sqrt (b² - 4ac)) / 2a

In the quadratic equation above, we have the numerical coefficients.
a = 2
b = 3
c = 8

Substituting the known values,
x = (-3 +/- sqrt (3² - 4(2)(8))/ (2)(2)
x = -0.75 + 1.854i and x = -0.75 - 1.854i

By the calculated roots above, it is known that the roots are imaginary.

The sum of 3 consecutive even numbers is 78

Answers

x+(x+2)+(x+4)=78
3x+6=78
3x=72
x=24

Final answer: 24, 26, 28

The table below shows the surface area y, in square inches, of a shrinking puddle in x hours: Time (x) (hours) 1 4 7 10 Surface area (y) (square inches) 100 85 70 55 Part A: What is the most likely value of the correlation coefficient of the data in the table? Based on the correlation coefficient, describe the relationship between time and surface area of the puddle. [Choose the value of the correlation coefficient from −1, −0.99, −0.5, −0.02.] (4 points) Part B: What is the value of the slope of the graph of surface area versus time between 1 and 4 hours, and what does the slope represent? (3 points) Part C: Does the data in the table represent correlation or causation? Explain your answer. (3 points)

Answers

The picture of how the graph looks like is shown in the picture.

Part A. The correlation coefficient, R², is the quantitative evaluation of how the data points are well-fitted to a model. The closer it is to 1, the better. But a R²=1 is very ideal and rare. This can be only true if the points coincides exactly with the given model. Since we can see in the graph that the points are exaclty passed through by the linear model, the correlation coefficient is 1.

Part B. The slope of the graph is measured between two points as Δy/Δx. So, between 1 to 4 hours, the slope is: (85-100)/(4-1) = -5. The slope represents the instantaneous rate of change of surface area with time. It is called instantaneous because the change was only between than interval, not the whole set of data. Also, the negative sign signifies that the trend is decreasing.

Part C. The data represents causation if the time was the cause of the change of the pond's surface area. However, this is not technically true because there might be other factors to be considered like environmental conditions. But, definitely, these data are in correlation because together they show an observable trend.

Work out problem in picture

Answers

for x multiply 6 by sin(45) = 3sqrt(2) = 4.2426

for y since it is a right triangle with 45 degree angle both legs are equal

so y = x

A scientist begins an experiment with a petri dish containing a culture of bacteria cells and records the cell growth every hour. At 1 hour, the bacteria had grown to 880 cells, and at 2 hours, had grown to 3,520 cells. Which function can be used to represent the relationship between the number of bacteria cells, y, and the time in hours, x?

y = 4 x
y = 220(4) x
y = 880(4) x
y = 880(0.25) x

Answers

880 = 220(4)^1
3520 = 220(4)2

B is correct choice.

Answer:

Step-by-step explanation:

What are the solutions of the equation 2x2=2 use a graph of the related function

Answers

The equation given is
2x² = 2
x² = 1
x = √1
x = 1

The solution is both -1 and 1 and the graph is shown below

Answer:

[tex]x=-1\text{ or }x=1[/tex]

Step-by-step explanation:

We have been given an equation [tex]2x^2=2[/tex]. We are asked to find the solutions of our given equation.

First of all, let us divide both sides of our equation by 2.

[tex]\frac{2x^2}{2}=\frac{2}{2}[/tex]

[tex]x^2=1[/tex]

Upon taking square root of both sides of our equation we will get,

[tex]x=\sqrt{1}[/tex]

[tex]x=\pm 1[/tex]

[tex]x=-1\text{ or }x=1[/tex]

Therefore, [tex]x=-1\text{ or }x=1[/tex] are two solutions for our given function.

Calvin and hobbes are making snowballs to throw at suzi calvin made 3/7 of the snowballs and hobbes made 8/14 of the snowballs who mae more snowballs in fractions

Answers

recalculate 3/7 to have the same denominator as 8/14 ( 14)

so multiply both top and bottom by 2. 3/7 becomes 6/14

8/14 - 6/14 = 2/14 reduces to 1/7

Hobbes made more snowballs by 1/7

recalculate 3/7 to have the same denominator as 8/14 ( 14)

so multiply both top and bottom by 2. 3/7 becomes 6/14

8/14 - 6/14 = 2/14 reduces to 1/7

Hobbes made more snowballs by 1/7

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