A bag contains five red socks and eight blue socks. Lucky reaches into the bag and randomly selects two socks without replacement. What is the probability that Lucky will get different colored socks? Express your answer as a common fraction. I will give brainliest if you give a full explanation, I have the answer but I need to know HOW to solve the problem!!!
Answers
The probability that Lucky will get different colored socks is 1/6 or 1 out of 6.
To solve this problem, we can use the concept of probability and combinations.
Step 1: Determine the total number of possible outcomes.
When Lucky selects two socks without replacement, there are a total of 13 socks in the bag (5 red + 8 blue). So, the total number of possible outcomes is given by selecting 2 socks out of 13, which is represented as C(13, 2) or 13 choose 2.
C(13, 2) = (13!)/(2!(13-2)!) = (13 * 12)/(2 * 1) = 78
Step 2: Determine the number of favorable outcomes.
For Lucky to get different colored socks, there are two cases to consider: selecting a red sock first and a blue sock second, or selecting a blue sock first and a red sock second.
Case 1: Red sock first, then blue sock:
The number of ways to select one red sock out of five is C(5, 1) = 5. After selecting one red sock, there are eight blue socks remaining, and Lucky needs to select one blue sock out of eight, which is C(8, 1) = 8.
Case 2: Blue sock first, then red sock:
The number of ways to select one blue sock out of eight is C(8, 1) = 8. After selecting one blue sock, there are five red socks remaining, and Lucky needs to select one red sock out of five, which is C(5, 1) = 5.
So, the total number of favorable outcomes is 5 + 8 = 13.
Step 3: Calculate the probability.
The probability of getting different colored socks is the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(Different Colored Socks) = Number of Favorable Outcomes / Total Number of Possible Outcomes
= 13 / 78
= 1/6
Therefore, the probability that Lucky will get different colored socks is 1/6 or 1 out of 6.
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Related Questions
In a triangle ABC,AB=5.8 cm BC=4.2cm and CA=3.6cm,name the greatest and smallest angles of the triangle.
Answers
Step-by-step explanation:
c is greatest angle
where as b is smallest
A jet airplane reaches ( )/(h) on a certain flight. What distance does it cover in 10.0min ?
Answers
The distance covered by the jet airplane in 10.0 minutes is ( )/(h) * 1/6 hours.
We need to find the distance covered by the jet airplane in 10.0 minutes. To do this, we can use the formula:
Distance = Speed * Time
Given that the airplane reaches ( )/(h) speed, we can substitute the given speed and time into the formula:
Distance = ( )/(h) * 10.0 minutes
Since the unit of speed is ( )/(h) and the unit of time is minutes, we need to make sure the units are consistent. We can convert the time to hours:
10.0 minutes = 10.0/60 hours
Now we can calculate the distance:
Distance = ( )/(h) * 10.0/60 hours
Simplifying the expression, we get:
Distance = ( )/(h) * 1/6 hours
Therefore, the distance covered by the jet airplane in 10.0 minutes is ( )/(h) * 1/6 hours.
The distance covered by the jet airplane in 10.0 minutes is ( )/(h) * 1/6 hours.
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Which statements are true for this function and graph? Select three options.
The initial value of the function is One-third.
The base of the function is One-third.
The function shows exponential decay.
The function is a stretch of the function f(x) = (one-third) Superscript x.
The function is a shrink of the function f(x) = 3x.
Answers
The statements that are true for this function and graph include the following:
B. The base of the function is One-third.
C. The function shows exponential decay.
D. The function is a stretch of the function f(x) = (one-third) Superscript x \(f(x) = (\frac{1}{3} )^x\).
What is an exponential function?In Mathematics, an exponential function can be modeled by using this mathematical equation:
\(f(x) = ab^x\)
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, base, or constant.By comparison, we have the following:
Initial value or y-intercept, a = 1.
Base, b = 1/3.
In conclusion, we can logically deduce that the function represents an exponential decay with a vertical stretch by a scale factor of 1/3.
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Complete Question:
Consider the exponential function f(x) = 3(1/3)^x and its graph
Which statements are true for this function and graph? Check all that apply.
The initial value of the function is 1/3.
The growth value of the function is 1/3.
The function shows exponential decay.
The function is a stretch of the function f(x) = (1/3)^x
The function is a shrink of the function f(x) = 3^x
One point on the graph is (3, 0).
A person weighing 150 pounds burns about 320 calories per hour walking at a moderate rate. Suppose the same person burns about 1500 calories per day through basic activities. The total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking. What is the slope and y- intercept
Answers
The slope of the equation and y- intercept is 320 and 1500 respectively.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
Given that the total calories y burned by that person can be represented by the equation y=320x+1500, where x represents the number of hours spent walking.
To find the slope and y- intercept.
y=320x+1500
Therefore, the slope of the line is;
m =320
Then the y- intercept is 1500
Hence, The slope of the equation and y- intercept is 320 and 1500 respectively.
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II NEED HELP!!!!!!!! Are the graphs of the lines in the pair parallel? Explain. y = 2/3x– 17 4x – 6y = –6 4x-6y=-6 Yes, since the slopes are the same and the y-intercepts are the same. A )No, since the y-intercepts are different. B)No, since the slopes are different. C)Yes, since the slopes are the same and the y-intercepts are different.
Answers
Answer:
C) Yes, since the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
You need to have both equations in slope-intercept form.
4x - 6y = -6
-6y = -4x - 6
y = 2/3x + 1
The two equations are
y = 2/3x + 1
y = 2/3x - 17
For lines to be parallel, the slopes must be equal. The y-intercepts don't matter.
Since the lines have the same slopes but different y-intercepts the answer is C.
What are the answers?
Answers
Answer:
Hi! answer: 28.3
answer: 38.5
answer: 105
answer: 64
answer: 192
solve for x. Enter your answer in interval notation using grouping symbols. x^2+9x<-20
Answers
Step-by-step explanation:
x^2+9x<-20
x^2+9x+20<0
( x+5)(x+4)<0
x+5<0,x+4<0
x<-4 (because x<-5 is extraneous solution)
Which of the following is not a theorem taught from this lesson?
If two angles of a triangle are equal, then the sides opposite those angles are equal.
The altitude to the base of an isosceles triangle bisects the vertex angle of the triangle.
The base angles of an isosceles triangle are equal.
Corresponding Parts of Congruent Triangles are Congruent.
Answers
Answer: Corresponding Parts of Congruent Triangles are Congruent.
Step-by-step explanation:
I had this question & this was the correct answer.
? Write 126 as a product of primes. Use index notation when giving your answer.
Answers
Answer:
2 x 7 x 3²
Step-by-step explanation:
When finding primes, you use the method I attatched as a picture. Start with the large number at the top, slowly dividing it by factors of it.
The picture shows that the primes 126 is a product of is:
2, 7, 3, 3
Or:
2 x 7 x 3 x 3
This can be simplified into:
2 x 7 x 3²
Hope this helps!
Answer:
Write 126 as a product of primes.
Use index notation when giving your answer.
Step-by-step explanation:
Find the value of ∫71ln(x)dx using three rectangles of equal with, with each right end-point used to find the height of each rectangle.
a) 0.5(ln3+ln5+ln7)
b) 0.5(ln1+ln3+ln5)
c) 2(ln3+ln5+ln7)
d) ln2+2ln3+2ln5
Answers
The value of ∫71ln(x)dx using three rectangles of equal width, with each right end-point used to find the height of each rectangle, is (c) 2(ln3+ln5+ln7).
To evaluate the integral, we can approximate it using the right-endpoint Riemann sum. Since we have three rectangles of equal width, we divide the interval [1, 7] into three subintervals: [1, 3], [3, 5], and [5, 7]. The width of each rectangle is (7 - 1) / 3 = 2.
For the first rectangle, we use the right endpoint x = 3 to find its height: ln(3).
For the second rectangle, we use the right endpoint x = 5 to find its height: ln(5).
For the third rectangle, we use the right endpoint x = 7 to find its height: ln(7).
The area of each rectangle is given by the product of its width and height. Therefore, the area of the first rectangle is 2× ln(3), the area of the second rectangle is 2× ln(5), and the area of the third rectangle is
2 × ln(7).
To find the total area, we sum the areas of the three rectangles:
2 ×ln(3) + 2× ln(5) + 2 × ln(7) = 2(ln(3) + ln(5) + ln(7)).
Hence, the value of the integral is 2(ln(3) + ln(5) + ln(7)), which corresponds to option (c).
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Determine the equation of a cubic polynomial function with roots at (3,0), (2,0) and (-4,0) that also passes through the point (1,30).
Answers
Step-by-step explanation:
Step 1: Setting Up the Factors
Our roots are 3, 2, and -4 so
our factors are
\((x - 3)(x - 2)(x + 4)\)
Step 2: Initial Test to see if the result equal 30
Let a be a constant, such we have
\(a(x - 3)(x - 2)(x + 4) = 30\)
Plug in. 1 for x.
\(a(1 - 3)(1 - 2)(1 + 4) = 30\)
\(a( - 2)( - 1)(5) = 30\)
\(a(10) = 30\)
\(a = 3\)
So our equation is
\(3(x - 3)(x - 2)(x + 4)\)
Or if you want it simplifed
\(3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72\)
Answer:
\(f(x)=3(x-3)(x-2)(x+4)\)
Step-by-step explanation:
General form of a cubic polynomial function with 3 roots:
\(f(x)=a(x-b)(x-c)(x-d)\)
where:
a is some constant to be foundb, c and d are the roots of the functionGiven roots:
(3, 0)(2, 0)(-4, 0)Substitute the given roots into the general form of the function:
\(\implies f(x)=a(x-3)(x-2)(x-(-4))\)
\(\implies f(x)=a(x-3)(x-2)(x+4)\)
To find the value of a, substitute the given point (1, 30) into the equation:
\(\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}\)
Therefore, the equation of the cubic polynomial function is:
\(f(x)=3(x-3)(x-2)(x+4)\)
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If 34+5= 36
56 +2 = 39
27 +6 = 45
47 +5 = 48
28 +1 = 33
then 41 + 5=
please help
Answers
Answer:
I'm guessing 46 if its actually adding
PLEASE HELP WILL MARK BRAINLIEST
What is the location of A on the decimal number line below?
Write your answer as a decimal.
Answers
Answer:
2.6
Step-by-step explanation:
A is after the 6th of 10 spaces between 2 and 3. It has the value 2 +6/10 = 2.6.
Joyce and Donald Conner's new car cost $7,362. After 5 years the car will have a change in value of -$3,600. What will be the average change in value of the car each year?
Answers
The current average lifespan of a car now is 11.8 years, the highest it has ever been. Cars average 150,000 to 300,000 miles, many higher. Let’s take a look at some impressive statistics on Ford car longevity.
A Well-Maintained Car Lives a Long Life
With vehicle owners keeping their cars longer than ever, and the vehicles designed to last 250,000 miles or more, routine car maintenance is important. The key factor in lengthening your car’s life is to follow the maintenance schedule outlined in your Ford Owner’s Manual.
Regular maintenance is more than periodic oil changes. It includes having all fluids checked and filled as needed, plus regular tire rotations. The Ford dealership where you purchased your vehicle is the perfect location for all service needs.
Whether you use the service center at your Ford dealership or an outside mechanic, it must be someone who is familiar with Ford vehicles and runs a trustworthy service. They should know when your car is due for service and be familiar with your vehicle’s recommended service schedule. A Ford dealership service department can handle all your vehicle’s needs
Answer: the average change in value of the car each year would be 720$
Step-by-step explanation: the over-all change in those 5 years was 3,600$ so we divide 3600$ into 5 to see how much the average change in value would be each year to get our final answer.
Hopefully this helped!
-Joshua
Studious athletes A university is concerned about the academic standing of its intercollegiate athletes. A study committee chooses an SRS of 50 of the 316 athletes to interview in detail. Suppose that $40 \%$ of the athletes have been told by coaches to neglect their studies on at least one occasion. What is the probability that at least 15 in the sample are among this group?
Answers
The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.
Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.
To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:
$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$
We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:
$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$
Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.
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Find the value or values of c that satisfy the equation f(b)-f(a) b-a f(x)= 3x³+4x²2. [-2.21 0-0 (Use a comma to separate answers as needed. Round to three decimal places as needed.) =f(c) in the conclusion of the Mean Value Theorem for the following function and interval.
Answers
The value of c that satisfies the conclusion of the Mean Value Theorem for the given function and interval is approximately -0.431.
The Mean Value Theorem states that if a function f(x) is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a value c in the open interval (a, b) such that the average rate of change of f(x) over [a, b] is equal to the instantaneous rate of change of f(x) at c.
In this case, we are given the function f(x) = 3x³ + 4x² + 2 and the interval [-2, 1]. To find the value of c that satisfies the conclusion of the Mean Value Theorem, we need to calculate the average rate of change of f(x) over [-2, 1].
The average rate of change is given by (f(b) - f(a))/(b - a). Plugging in the values a = -2 and b = 1, we have:
(f(1) - f(-2))/(1 - (-2)) = (3(1)³ + 4(1)² + 2 - (3(-2)³ + 4(-2)² + 2))/(1 + 2)
= (3 + 4 + 2 - (-24 + 16 + 2))/3
= (9 + 18)/3
= 27/3
= 9
Therefore, the average rate of change of f(x) over [-2, 1] is 9. According to the Mean Value Theorem, there exists a value c in the interval (-2, 1) such that f'(c) = 9.
To find the value of c, we need to find the derivative of f(x). Taking the derivative of f(x) = 3x³ + 4x² + 2, we get:
f'(x) = 9x² + 8x
Setting f'(c) = 9 and solving for c, we have:
9c² + 8c = 9
9c² + 8c - 9 = 0
Solving this quadratic equation, we find that c is approximately -0.431 or c ≈ -0.431.
The value of c that satisfies the conclusion of the Mean Value Theorem for the given function and interval is approximately -0.431. This means that there exists a point c in the interval (-2, 1) where the instantaneous rate of change of the function f(x) = 3x³ + 4x² + 2 is equal to 9, which is the average rate of change of f(x) over the interval [-2, 1].
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Order the following expressions by their values from least to greatest.
b-a
a -0.5
a
Answers
Answer:
a
a -0.5
b -a
i believe that is the order but i could be wrong
Answer:
hi there !!
the correct answer should be: a - 0.5, a, b - a
Step-by-step explanation:
first let's show -0.5 on the number line.
now let's show b - a on the number line.
the given expressions are ordered by their values below.
Which of the following are true statements about angle parking. Angle parking spots have a larger blind spaces than perpendicular spaces. Angle parking spots have a larger blind spaces than perpendicular spaces. Angle parking spots have half the blind spot as compared to perpendicular parking spaces. Angle parking spots have half the blind spot as compared to perpendicular parking spaces. Parking lots that have angle parking spaces can fit fewer cars than perpendicular parking. Parking lots that have angle parking spaces can fit fewer cars than perpendicular parking. Angle parking is more common than perpendicular parking. Angle parking is more common than perpendicular parking. All are true statements.
Answers
Answer:
Angle parking is more common than perpendicular parking.
Angle parking spots have half the blind spot as compared to perpendicular parking spaces
Step-by-step explanation:
Considering the available options, the true statement about angle parking is that" Angle parking is more common than perpendicular parking." Angle parking is mostly constructed and used for public parking. It is mostly used where the parking lots are quite busy such as motels or public garages.
Therefore, in this case, the answer is that "Angle parking is more common than perpendicular parking."
Also, "Angle parking spots have half the blind spot as compared to perpendicular parking spaces."
A right circular cylinder has the dimensions shown below.
r = 17.2 yd
h = 45.3 yd
What is the volume of the cylinder? Use 3.14 for π.
Round to the nearest tenth and include correct units.
Show all your work.
Answers
The volume of the cylinder is 42080.87 cubic yd
What is a Cylinder?Cylinder is a 3-dimensional solid shape that consists of two identical and parallel bases linked by a curved surface.It has two curved edges, one curved surface, and two flat faces.
Volume of a cylinder = π * r^2 * h
Where π = 3.14
r = 17.2 td
h = 45.3 yd
Volume of a cylinder = 3.14 * (17.2)^2 * 45.3
Volume = 3.14 * 295.84 * 45.3
Volume = 42080.87 cubic yard
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I need to fill in the blanks for this equation and I cant figure it out
Answers
Answer:
1. +12x and 15
2. 14x
3. 2
Step-by-step explanation:
Step 1: Distribute -3
To distribute -3, you would multiply both -4x and -5 by -3, changing them to 12x and 15
Step 2: Combine 12x and 2x
Then you would combine like terms, meaning that you would add 12x and 2x, creating 14x.
Step 3: Combine 15 and -13
You would finish combining like terms by adding 15 to -13, creating 2
if quiz grades are normally distributed with a mean of 85 and a standard deviation of 8.0, what is the probability that a student will have a quiz grade of 95 or greater?
Answers
There is a 0.022 percent chance that a student may receive a quiz grade of 95 or above.
The z-score formula is as follows:
z = (95-85)/8.0
= 1.25
Using the z-score table, calculate the probability:
P(z >= 1.25)
= 0.022
The z-score formula can be used to determine the likelihood that a student would receive a quiz grade of 95 or higher. The data set's mean and standard deviation are considered in the formula. The mean score on the quiz in this instance is 85, and the standard deviation is 8.0. By deducting the mean from the desired score (95), the z-score can be computed by dividing the result by the standard deviation (8.0). The z-score in this instance is 1.25. The likelihood that a student will receive a quiz grade of 95 or higher can be determined using the z-score table. The likelihood of a z-score of 1.25 or higher is 0.022, according to the table. This indicates that there is a 0.022 percent chance that a student will receive a quiz grade of 95 or above.
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The perimeter of the hexagon is 24 m.
What is the value of x?
Answers
Answer:
3.5
Step-by-step explanation:
add the two 5 and then subtract the perimeter which is 24 , so 24-10 is 14 then divide it by 4 for the missing sides and u get 3.5
The value of x in the given hexagon is 3.5 m.
What is the Perimeter of Hexagon?
Perimeter of Hexagon is equal to sum of all sides.
Here, Two sides are 5 m long
and remains 4 sides have length x m.
Perimeter = Sum of all sides
24 = 2 X 5 + 4x
24 = 10 + 4x
4x = 24 -10
4x = 14
x = 14/4
x = 3.5 m
Thus, the value of x in the given hexagon is 3.5 m.
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Mr. Darling went shopping for some new school clothes and wanted to use his credit card to earn points for his purchases. At the start of the day he owed $35.74 on his card and then bought two items that total $99.78. What is the new balance on Mr. Darling’s credit card?
Answers
Answer:
$135.52
Step-by-step explanation:
He already had a balance of 35.74 then he bought two items so
35.74+99.78=$135.52
The company Eve works for is seeing a 25% growth in profits every year. If the company
makes $363,200 this year, what will the annual profits be in 3 years?
If necessary, round your answer to the nearest cent.
Answers
The annual profits of the company Eve works for will increase by 25% every year. The annual profits in 3 years will be approximately $709,555.52.
The annual profits of the company Eve works for will increase by 25% every year. If the company makes $363,200 this year, we can calculate the annual profits in 3 years by applying the 25% growth rate.
To find the annual profits in 3 years, we need to multiply the current year's profits by \((1 + \text{growth rate})^{\text {number of years}\).
In this case, the growth rate is 25% or 0.25, and the number of years is 3.
So, the calculation would be:
Annual profits in 3 years = $363,200 * (1 + 0.25)³
To simplify the calculation, let's break it down step by step:
Step 1: Calculate the growth rate by adding 1 to the percentage growth rate: 1 + 0.25 = 1.25
Step 2: Raise the growth rate to the power of the number of years: 1.25³ ≈ 1.9531
Step 3: Multiply the current year's profits by the result of step 2: $363,200 * 1.9531 ≈ $709,555.52
Therefore, the annual profits in 3 years will be approximately $709,555.52.
Please note that rounding the answer to the nearest cent gives $709,555.52.
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Find the distance between the two given points: (5, 9) and (13, -5). Round to the hundredths place.
Answers
Answer:
AB=
\( \sqrt{260} \)
Step-by-step explanation:
plz mark as brainliest if it helps
Myles deposited $5000 for 4 years at a rate of 5.5%. What will his balance be at the end of that time
Answers
Rs. $6,100 will be his balance at the end of that time.
Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more. When you pay back a loan, the monthly interest is deducted first, and any remaining funds are applied to the principle.The Simple Interest (S.I.) formula is a way to figure out how much interest will accrue on a given principal sum of money. However, borrowing money is not unrestricted in the actual world. You frequently need to take out a loan from a bank to borrow money. In addition to the loan amount, you must pay back additional funds based on the loan amount and the length of time you borrowed the money. We refer to this as simple interest. This phrase is frequently used in banking.Here, according to the given information, we are given that,
Principal \(\text{(P) = Rs}\). 5000,
Time period \(\text{(t)}\) = 4 years,
Rate of interest \(\text{(r)}\) = 5.5%
Then, the simple interest obtained = \(\dfrac{\text{Prt}}{100} =\dfrac{5000\times(4)\times(5.5)}{100} =1100\)
Then, the final amount at the end of that time is,
\(\text{Rs}. \ (5000 + 1100) = \text{Rs}. \ 6100.\)
Hence, Rs. $6,100 will be his balance at the end of that time.
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The balance at the end of 4 years with deposit of $5000 for 4 years at a rate of 5.5%. is $6100.
The interest earned on Myles's deposit will be $5000 * 5.5% * 4 = $1100.
So, his balance at the end of 4 years will be $5000 + $1100 = $6100.
Here is the formula for calculating the interest earned:
Interest = Principal * Interest Rate * Time
In this case, the principal is $5000, the interest rate is 5.5%, and the time is 4 years.
Plugging these values into the formula, we get:
Interest = 5000 * 0.055 * 4 = $1100
The balance at the end of 4 years is simply the principal plus the interest earned, so it is $5000 + $1100 = $6100.
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Can someone please help me with this
Answers
Answer:
Equation 1
Step-by-step explanation:
What is the y intercept for the 3rd graph.
Answers
7. Copy and complete to factorise the expression.
3x2+5x-2=(3x___)(x___)
Answers
Answer:
(3x - 1)(x + 2).
Step-by-step explanation:
3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x(x + 2) - 1(x + 2)
= (3x - 1)(x + 2).
Each model represents one whole. In which model does the shaded section represent the product of 5/8 and 3/8? Please show me the steps on how you got your answer! (Nevermind! I found out the answer)
Answers
Answer:
Step-by-step explanation:
