Answer:
The likelihood that the professor's socks matched his pants on both days is 0.5625
Step-by-step explanation:
Total no. of pair of socks = 24
No. of black pairs = 18
We are given that he selects one pair of socks on Monday and one on Tuesday. Since he has lots of clean socks in the drawer he does not do laundry.
So, It is a case of replacement
He always wears black pants.
We are supposed to find he likelihood that the professor's socks matched his pants on both days i.e. Black socks both days.
So ,Probability of wearing black socks on Monday = [tex]\frac{18}{24}[/tex]
So ,Probability of wearing black socks on Tuesday =[tex]\frac{18}{24}[/tex]
So,the likelihood that the professor's socks matched his pants on both days = [tex]\frac{18}{24} \times \frac{18}{24}=0.5625[/tex]
Hence the likelihood that the professor's socks matched his pants on both days is 0.5625
Final answer:
The probability that the professor picks black socks on both Monday and Tuesday is 9/16.
Explanation:
The question asks about the probability that a professor will pick black socks on two consecutive days without doing laundry in between. With 24 pairs of socks, of which 18 pairs are black and 6 pairs are brown, we will calculate the likelihood of the professor picking black socks on both Monday and Tuesday.
First, the probability of picking black socks on Monday (first pick) is 18 black pairs divided by 24 total pairs, which simplifies to:
Probability of black socks on the first pick = 18/24 = 3/4Since the socks are not washed between Monday and Tuesday, the number of socks available remains the same. Therefore, the probability of picking black socks again on Tuesday (second pick) is also 3/4.
To find the overall probability that the professor picks black socks on both days, we must multiply the probability of the first event by the probability of the second event. In this case:
Overall probability = Probability on Monday × Probability on TuesdayOverall probability = 3/4 × 3/4 = 9/16The probability that the professor's socks matched his pants (picked black socks) on both days is 9/16.
30 percent of 120 is the same as 80 percent of what number?
Answer:
45
Step-by-step explanation:
Taking into account the definition of equation and percentage, 30 percent of 120 is the same as 80 percent of 45.
An equation is defined as an established equality between two expressions, in which there may be one or more unknowns or variables.
So solving an equation consists of finding the value or values of the variables so that they fulfill the equality represented in the equation. That is, when changing the variable for the solution found, the equality must be true.
On the other side, the percentage is a value that represents the proportionality between two established quantities. That is, the percentage tells what part of a total represents a quantity.
Mathematically, the percentage is the division between an initial quantity and the total quantity, all multiplied by one hundred.
And to calculate the percentage of a quantity, the quantity is multiplied by the percentage and divided by 100. Then, 30 percent of 120 can be expressed as: (30×120)÷100
On the other hand, 80 percent of a number can be expressed as: (80×number)÷100
Since 30 percent of 120 must be the same as 80 percent of an unknown number, the following equation can be expressed:
(30×120)÷100= (80×number)÷100
Solving:
3600 ÷100= (80×number)÷100
36= (80×number)÷100
36×100= 80×number
3600= 80× number
3600÷ 80= number
45= number
The, 30 percent of 120 is the same as 80 percent of 45.
Learn more about percentage with this examples:
https://brainly.com/question/19295956?referrer=searchResultshttps://brainly.com/question/1301322?referrer=searchResultsFind the area of the shaded sector in circle P. Please!
Answer:
the answer is c
Step-by-step explanation:
Answer: C. 25π/3 cm²
Step-by-step explanation:
The sector is an area of a circle bounded by two radii. The formula for determining the area of a sector is expressed as
Area of sector = θ/360 × πr²
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 10 cm
θ = 30 degrees
Therefore,
Area of sector = 30/360 × π × 10²
= 3000π/360 = 25π/3 cm²
There are three children in the McComb family. Which sample space represents the gender order, M (Male) or F(Female), in which the children could have been born?
Answer:
d
Step-by-step explanation:
{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}
Use a tree diagram to list the possibilities.
Answer:
The answer is D
Step-by-step explanation:
A child who is 58 inches tall is standing next to the woman who is 5 feet and 4 inches tall casts a shadow that is 40 inches long. How long is the child’s shadow?
Final answer:
To find the length of the child's shadow, set up a proportion comparing the woman's height and shadow length to the child's height and unknown shadow length. Solving the proportion 64/40 = 58/Child's shadow, we find that the child's shadow is approximately 36.25 inches long.
Explanation:
The question involves using proportions to calculate the length of the child’s shadow. Since the child is shorter than the woman, we can expect that the child’s shadow will also be shorter in proportion to her height. The woman is 5 feet and 4 inches tall, which converts to 64 inches. The shadow to height ratio is the same for both individuals because they are standing under the same lighting conditions.
We can set up a proportion using the woman’s height and shadow length to find the child’s shadow length:
Woman’s height / Woman’s shadow = Child’s height / Child’s shadow
64 inches / 40 inches = 58 inches / Child’s shadow
To solve for the child’s shadow, we cross-multiply:
64 * Child’s shadow = 58 * 40
Child’s shadow = (58 * 40) / 64
Child’s shadow = 2320 / 64
Child’s shadow = 36.25 inches
Therefore, the child’s shadow is roughly 36.25 inches long.
Can someone help me answer this question please.
Answer:
55 and 7.5 for number 3
Step-by-step explanation:
A jar lid has a diameter of 32
millimeters. What is the
circumference of the lid to the
nearest tenth?
Answer:
32pi cm or 100.530964915 mm
Step-by-step explanation:
To find this answer you will need to use the equation 2*pi*r or pi*d.
Your value 32 can be plugged in as your value of d which can then be substituted to make 32 pi or if you use a calculator you get 100.530964915.
hope this helps!
Answer: 100.5 mm
Step-by-step explanation: The formula to find the circumference of a circle is 2(pi)r
Since we know the diameter is 32, divide 32 by 2 to get the radius: 16
2(pi)(16) = 100.5309
To the nearest tenth, that would be 100.5
Which ordered pair is a solution of the equation ? y + 1 = 3(x - 4) Choose 1 answer: Only * (4, - 1) ) Only (5, 2) Both (4, - 1) ) and (5, 2) ) Neither
Replacing the ordered pairs into the equation, we find that the correct option is:
Both (4, - 1) and (5, 2)
The equation is:
[tex]y + 1 = 3(x - 4)[/tex]
Ordered pair:An ordered pair (x,y) is a solution to the equation if we replace (x,y) in the equation and get an identity.
Test if (4,-1) is a solution:
[tex]-1 + 1 = 3(4 - 4)[/tex]
[tex]0 = 0[/tex]
Identity, so it is.
Test if (5,2) is a solution:
[tex]2 + 1 = 3(5 - 4)[/tex]
[tex]3 = 3[/tex]
Identity, so it is.
Hence, both is the correct option.
You can learn more about ordered pairs at https://brainly.com/question/10585472
Which of the following graphs are identical?
y= square root of x
y= ^3 square root of x
y= square root of negative x
y= ^3 square root of negative x
y= negative square root of x
y= negative ^3 square root of x
Answer:
1. D & F
2. A, C, D
Step-by-step explanation:
DID ON EDGE
None of the given graphs are identical. Their differences arise from the distinct characteristics of their specific square root or cube root functions, as well as the range of x-values they apply to.
Explanation:None of the aforementioned graphs are identical. The syntax y=√x corresponds to the graph of the square root function, which is always positive and only defined for x≥0. On the other hand, the syntax y=-√x describes the graph that's a reflection of y=√x in the x-axis. However, y=∛x and y=-∛x both entail the cube root function, which is distinguishable from the square root function by its shape and the fact it includes values for negative x. Lastly, y=√-x and y=∛-x are not properly defined real functions, since taking square or cube roots of negative x values leads to complex numbers.
Learn more about Functions, Graphs and Roots here:https://brainly.com/question/35883921
#SPJ2
Please Help!!!!! 17 Points!!!!!!! I don't know if I have the right answer.
Answer:
SAS
Step-by-step explanation:
The sides have the same ratio and the angle between them is congruent, so it's SAS
A bungee jumper is jumping off the New River Gorge Bridge in West Virginia, which has a height of 876 feet. The cord stretches 850 feet and the jumper rebounds 75 of the distance fallen.
(a) After jumping and rebounding 10 times, how far has the jumper traveled downward? How far has
the jumper traveled upward? What is the total distance traveled downward and upward?
(b) Approximate the total distance, both downward and upward, that the jumper travels before coming to rest.
In this scenario, a bungee jumper's total distance traveled can be calculated using a geometric series. The initial drop is the bridge's total height, and each following jump is 75% of the previous one. Summing this series gives the total downward and upward travel.
Explanation:This problem is a classic example of a geometric series used in mathematics. The first downward travel is the entire height of the bridge, 876 feet. Each consecutive downward travel will be 75% of the previous downward travel, as the question specifies that the jumper rebounds 75% of the distance fallen.
For the downward distance after 10 jumps, you sum the geometric series with first term (a) of 876 feet, common ratio (r) of 0.75, and n terms (n) being 10. The sum S of such a series can be calculated as: S = a * (1 - r^n) / (1 - r). The upward travel distance will be 75% of the total downward distance.
To find out the total distance before the jumper comes to rest, we look at the situation when the sum of the geometric series tends to infinity (i.e., as the number of terms n approaches infinity) which can be calculated as S = a / (1 - r).
Learn more about Geometric Series here:https://brainly.com/question/30264021
#SPJ12
If the point ( x , √3/2) is on the unit circle, what is x?
A. √3/2
B. 1/2
C. - √3/2
D. 2/√3
Answer:
B. 1/2
Step-by-step explanation:
This problem involves the use of the Pythagorean theorem. In the unit circle, the hypotenuse of any right triangle formed is 1 while the coordinates of the point are then the two legs that make up the triangle.
a = 1 (given)
b = √3/2 (given)
a² = b² + c² (Pythagorean Theorem)
1² = (√3/2)² + c² (Substitute information)
Now, we need to solve for c
1 = (3/4) + c² (square the hypotenuse and one of the legs)
1 - (3/4) = (3/4) + c² - (3/4) (subtract 3/4 on both sides)
1/4 = c² (combine like terms)
√(1/4) = √(c²) (square root both sides)
√1 / √4 = c (square root both sides)
1/2 = c (final answer)
Therefore the other leg of the right triangle is 1/2, this also means that the other coordinate, or x, is 1/2, so the answer is B. 1/2.
Final answer:
The x-coordinate for the point (x, √3/2) on the unit circle is determined using the Pythagorean theorem for a unit circle. After substituting √3/2 for y and solving for x, the x-coordinate can be ±1/2. The correct option from the given choices is B. 1/2.
Explanation:
If the point (x, √3/2) is on the unit circle, we must use the Pythagorean theorem that applies to the unit circle, which states that x² + y² = 1, where x and y are the coordinates of a point on the circle. For a unit circle, the radius is 1. Since the y-coordinate is given as √3/2, we can substitute this value into the equation and solve for x:
x² + (√3/2)² = 1
x² + (3/4) = 1
x² = 1 - 3/4
x² = 1/4
x = ±√(1/4)
x = ±(1/2)
Therefore, x could be either 1/2 or -1/2. Since the question doesn't specify which quadrant the point is in, both answers are correct. However, within the given options, the correct answer is B. 1/2.
She Elle has 100 meters of fencing to build a rectangular garden. The garden's area (in square meters) as a function of the garden's width "w" (in meters) is modeled by: A(w) = -(w-25)^2+625 What is the maximum area possible in square meters?
Answer:
[tex]625 m^2[/tex]
Step-by-step explanation:
In this problem, we are told that the area of the garden is given by the expression
[tex]A(w)=-(w-25)^2+625[/tex]
where
w is the width of the garden (in meters)
Here we want to find the maximum possible area.
The maximum of a function f(x) can be found by requiring that its first derivative is zero:
[tex]f'(x)=0[/tex]
Therefore, here we have to calculate the derivative of [tex]A(w)=0[/tex] and find the value of w for which it is equal to zero.
Let's start by rewriting the area function as
[tex]A(w)=-(w^2-50w+625)+625=-w^2+50w[/tex]
Now we calculate the derivative with respect to w:
[tex]A'(w)=-2w+50[/tex]
Now we require this derivative to be zero, so
[tex]-2w+50=0\\w=-\frac{50}{-2}=25 m[/tex]
So now we can substitute this value of w into the expression of A(w) to find the maximum possible area:
[tex]A(25)=-(25-25)^2+625 = 625 m^2[/tex]
This value is allowed because we know that the maximum length of the perimeter of the fence is 100 meters; If the garden has a square shape, the length of each side is [tex]L=\frac{100}{4}=25 m[/tex], and the area of the squared garden is
[tex]A=L^2=(25)^2=625 m^2[/tex]
Which is equal to what we found earlier: this means that the maximum area is achieved if the garden has a squared shape.
Answer:
Step-by-step explanation:
To find the surface area of the figure shown Mia found the surface area and the rectangular prism and the rectangular prism from this Mia subtracted 6ft did mia make an error
Answer:
The answer is b
Step-by-step explanation:
Because i just did it and got it right
Answer:
B
Step-by-step explanation:
just got it right
10) Stephanie spent half of her weekly
allowance buying pizza. To earn more
money her parents let her weed the garden
for $4. What is her weekly allowance if
she ended with $8?
Answer:
$16
Step-by-step explanation:
-Given that her balance after buying one pizza is half her weekly allowance.
#We multiply her balance times 2 to determine her total weekly allowance:
[tex]Total \ Allowance=Balance \times 2\\\\=8\times 2\\\\=\$16[/tex]
Hence, her total weekly allowance is $16
Dwayne buys ingredients to make a cake. He buys 1/1/2 pounds of flour, 12 ounces of coconut, and 1/1/4 pounds of sugar. What is the total weight of the ingredients Dwayne bought?
Answer:
3 1/2 pounds or 3.5 pounds
Step-by-step explanation:
Two ingredients are measured in pounds while one is measured in ounces. Recall that 1 pound = 16 ounces. Thus, 12 ounces of cocoanut comes out to
(12/16) pound. Next, we sum up 1 1/2 pounds of flour, 12/16 pound of cocoanut and 1 1/4 pounds of sugar, after rewriting these mixed numbers with the same denominator (4):
1 1/2 pounds stays 1 2/4 pounds;
12 ounces becomes 3/4 pound; and
1 1/4 pounds stays 1 1/4 pounds
Summing up the fractions results in 6/4 pounds, or 1 1/2 pounds; and summing up the integers results in 2 pounds.
The final sum is 1 1/2 pounds + 2 pounds, or 3 1/2 pounds.
Dwayne buys 3 1/2 pounds of ingredients.
Alternatively, we could convert all of these measurements to decimal fractions and then add up those fractions:
1.5 pounds + 0.75 pounds + 1.25 pounds = 3.5 pounds (same as before).
A circle with area 36 pi has a sector with a central angle of
48°
What is the area of the sector?
Either enter an exact answer in terms of # or use 3.14 for
a and enter your answer as a decimal rounded to the
nearest hundredth.
Answer: 36 pi over 7.5
Step-by-step explanation:
The clocks radius is 10m. What is the circumference of the clock
Answer:
20π or 62.8 roughly
Step-by-step explanation:
Hello!
The formula for finding the circumference of a circle is 2rπ:
In that case, all we have to do is substitute 10m for our r.
2 × 10 = 20.
So circumference will be 20π.
Using 3.14 for π:
We get that 62.8 is a rough estimate for the circumference.
Really, it's 62.831..... going on forever since π is irrational.
Thus, the answer exactly is [tex]\boxed{20\:\pi}}[/tex].
Hope this helps!
Final answer:
The circumference of a clock with a radius of 10m is calculated using the formula C = 2πr, resulting in a circumference of 20π m or approximately 62.83185 m when using the approximate value of π (3.14159).
Explanation:
The circumference of a clock can be calculated using the formula for the circumference of a circle which is C = 2πr, where C is the circumference and r is the radius of the clock. Given that the radius of the clock is 10m, we substitute the value into the formula to get the circumference.
So, the circumference of the clock is C = 2π(10m) = 20π m.
The exact value of π (π is approximately 3.14159) would allow us to find the numerical value for the circumference, which would be approximately C ≈ 62.83185 m.
Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = √x 2 + y 2 and bounded above by the sphere x 2 + y 2 + z 2 = 8. Evaluate the integral to find the volume.
Answer:
Evaluate The Integral To Find The Volume. This problem has been solved! See the answer. Sketch the solid and set up the triple integral in Cartesian coordinates that gives the volume of the solid bounded below by the cone z = \sqrt{x^2+y^2} and bounded above by the sphere x2 + y2 + z2 = 8. Evaluate the integral to find .
Step-by-step explanation:
took it
Your college fund has $56,000. It is currently in an account which pays 3.4% compounded quarterly. How much money will you have in 11 years
Answer:
$81,269.53
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 3.4% into a decimal:
3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034
Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:
[tex]A=56,000(1+\frac{0.034}{4})^{4(11)}[/tex]
[tex]A=81,269.53[/tex]
After 11 years, you will have $81,269.53
a bag of pretzels contains approximately 17 1/2 ounces. one serving of pretzels is 1 1/4 ounces. how many servings of pretzels are in the bag?
Answer:
14
Step-by-step explanation:
Answer: The answer is: 14
Step-by-step explanation: I just took that test!
Have a great day!
-Sunny
What is the volume of the smallest square-based prism that would hold this cylinder?
Answer:
The answer to your question is Volume = 80000 cm³
Step-by-step explanation:
Data
height = 50 cm
radius = 20 cm
Process
1.- The smallest dimensions of the prism must have the same dimensions that the cylinder.
Radius = 20 cm then the length of a side = 2 x radius = 40 cm
2.- Calculate the area of the base
Area = 40 x 40
= 1600 cm²
3.- Calculate the volume of the prism
Volume = Area x height
= 1600 x 50
= 80000 cm²
Which of the following statements is NOT true about the graph of a system of
equations with infinitely many solutions?
The lines will have the same slope.
The lines will have one positive y-intercept and one negative
y-intercept.
The lines will have the same y-intercept.
The lines will share all of the same points.
Answer:
The lines will have one positive y-intercept and one negative y-intercept is NOT true.
Step-by-step explanation:
If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.
The lines will have one positive y-intercept and one negative y-intercept that is not true.
What is the graph?The graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.
Determining:The lines will have one positive y-intercept and one negative y-intercept is NOT true.
If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, and y-intercept, and will share all of the same points. Answer b is the only choice left.
Learn more about the Graph:
https://brainly.com/question/4291574
#SPJ2
Please Help!!!!! 25 Points!!!!!!
Answer: 7 yards will be your answer.
Step-by-step explanation: I tried. Sorry if the answer is wrong!
Answer:
8 yards
Step-by-step explanation:
The small triangle is inside the big triangle and shares two of it's legs which means it is similar to the big triangle.
12:15
x:10
4:5
x must be 8
Marian can weed a garden in 3 hrs. Robin can weed the same garden in 4 hrs. If they work together, how long will the weeding take them?
Marian and Robin, by combining their efforts, can weed a garden together in approximately 1 hour and 43 minutes by adding their individual work rates and calculating the time taken to complete one whole task at this combined rate.
Explanation:The question involves discovering the collective work rate of Marian and Robin when weeding a garden. To solve, we first identify the individual rates: Marian can weed a garden in 3 hours, which means her rate is 1/3 of the garden per hour. Robin's rate is 1/4 of the garden per hour, as he can complete it in 4 hours. To find the rate at which they can weed the garden together, we add their individual rates: (1/3) + (1/4) = 4/12 + 3/12 = 7/12.
Thus, their combined rate is 7/12 of the garden per hour. To find the total time taken, we divide the whole task (1 garden) by their collective rate (7/12). Hence, the time taken for them to complete the weeding together is 12/7 hours, which can be simplified to approximately 1 hour and 43 minutes.
Can anyone help??????
Answer:
C) 109.5
Step-by-step explanation:
Use cosine of 64°
cos 64° = 48/x
Put x on one side
x = 48/ cos 64°
x = 109.4962576
Answer:
The answer is C or 109.5 units
Step-by-step explanation:
We have to use the trig function cosine to find the answer.
cosine = [tex]\frac{adjacent}{hypotenuse}[/tex]
cosine of 64 = 0.438371147
the equation is: cos 64 = [tex]\frac{48}{hypotenuse}[/tex]
So using this equation,
we must divide 48 by the cosine of 64 to get the hypotenuse
this equals 109.5
The hypotenuse is our length that we need to find so the question is solved.
Hope This helps
Branliest is appreciated!
What is the sum of -20 and 4?
Answer:
-16
Step-by-step explanation:
-20 + 4 Equals -16. Try it on a number line.
Answer:-16
Step-by-step explanation:
-20+4=-16
UN NADADOR 50 METROS POR MINUTO EN LA COPETENCIA DE NADO LIBRE CUANTO ES POR 33.3 MINUTOS POR FAVOR AYUDENME
Answer:
99000 meters.
Step-by-step explanation:
We have the swimmer going at 50 m / s, and we want to know where he is going in 33.3 minutes.
The first thing is to pass the time from minutes to seconds, we know that 1 minutes is 60 seconds, therefore:
33.3 min * 60 s / 1 min = 1998 seconds
Now to know the distance is to multiply this time by the speed they give us, like this:
1998s * 50m / s = 99900 m
Which means that in that time and at the speed of the swimmer, he has traveled 99000 meters.
Which is the solution set for (z+4)>15
Answer:
Sol set = {12, 13, 14, 15, 16, 17,....... ".}
Step-by-step explanation:
[tex](z + 4) > 15 \\ z + 4 > 15 \\ z > 15 - 4 \\ z > 11 \\ z = \{12, \: 13, \: 14, \: 15, \: 16, \: 17, ........... \}[/tex]
if A=(3,9] and B= [6,9) then find A u B
U means "Union" or all the numbers from one set and all the numbers from the other set combined. So your answer is any of the numbers included in one set or the other or both.
John invests 18000 at a rate of 4.5% compounded annually. What will his new balance be after 6 years
Final answer:
John's new balance after 6 years with an original investment of $18,000 at a 4.5% annual compound interest rate will be approximately $23,362.65.
Explanation:
To calculate John's new balance after 6 years with a principal investment of $18,000 at an annual compound interest rate of 4.5%, we use the formula for compound interest:
A = P[tex](1+r/n)^{(nt)}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
In this case, P = $18,000, r = 0.045 (4.5%), n = 1 (since it's compounded annually), and t = 6 years.
Now we plug the values into the formula:
A = 18000(1 + 0.045/1)⁶
A = 18000(1 + 0.045)⁶
A = 18000(1.045)⁶
Calculating this, we get:
A ≈ 18000(1.297925)
A ≈ $23,362.65
Therefore, after 6 years, John will have approximately $23,362.65 in his account.