Answer:
It is a combination answer
495 ways
Step-by-step explanation:
In this question, we are tasked with calculating the number of ways in which a manager can select 4 people out of 12 for the Sunday evening shift.
Firstly, the question talks about selecting a particular number from a mix, this is a combination question since the key word SELECT is mentioned.
Now, how do we go about it? To select a partial number from a mix , we use the combination formula as stated.
Mathematically, say we are selecting a number r from a total of numbers n, the number of ways we can do this is nCr = n!/(n-r)!r!
In this case however, we are simply selecting 4 out of 12
Our combinational equation thus becomes 12C4 = 12!/(12-4)!4! = 12!/8!4! = 495 ways
Final answer:
The manager can choose 4 from 12 employees in 495 different ways for the Sunday evening shift, using a combination rather than a permutation since the order of selection does not matter.
Explanation:
To determine the number of ways the manager can choose 4 out of 12 employees for the Sunday evening shift, we need to decide whether the order in which the employees are chosen matters. If the order does not matter, we will use a combination. If the order does matter, we would use a permutation. In this case, because the task is simply to choose 4 employees and the order in which they are chosen does not affect the outcome, we use a combination.
The formula for finding the number of combinations when choosing k objects out of a total of n objects without repetition is given by:
C(n, k) = n! / (k! * (n-k)!)
In this situation, we have n=12 and k=4, so we calculate:
C(12, 4) = 12! / (4! * (12-4)!) = 12! / (4! * 8!) = (12*11*10*9) / (4*3*2*1) = 495
Therefore, there are 495 different ways for the manager to choose 4 employees for the Sunday evening shift.
A cylindrical drinking glass can hold 56.52 cubic inches of
water. The diameter of the glass is 3 in. How tall is the glass?
Use 3.14 for T.
A. 4 inches
B. 6 inches
CC. 7 inches
D. 8 inches
Answer:
The answer is
D. 8 inches
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cylinder this time.
Given data
Volume of cylindrical shape v=
56.52 inch³
Diameter of cylindrical glass d= 3
inch
But raduis r =diameter/2=3/2= 1.5
inch
We know that the the expression for the volume of a cylinder is given as
v= πr²h
Substituting our given data to solve for the height h
56.52= 3.14*(1.5)²*h
56.52= 7.065h
h= 56.52/7.065
h= 8 inches
To calculate the height of the cylindrical glass, use the volume formula with the radius from the diameter, and solve for the height. The final calculation shows that the glass is 8 inches tall, corresponding to option D.
Explanation:To find the height of a cylindrical drinking glass given its volume and diameter, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, π (pi) is a constant approximated as 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
Since the diameter is given as 3 inches, the radius r is half of that, which is 1.5 inches. By substituting the values into the formula and solving for h, we get:
V = πr²h
56.52 = 3.14 × (1.5)² × h
56.52 = 3.14 × 2.25 × h
56.52 = 7.065 × h
h = 56.52 / 7.065
h = 8 inches
Therefore, the height of the drinking glass is 8 inches, which corresponds to choice D.
what is circumference of a circle with a radius of 25 feet?
Answer:
C≈157.08ft
Solution
C=2πr=2·π·25≈157.07963ft
Answer:
157.0796327 is my answer
Evaluate the following:
ln ex + 1
A) x-2
B) y+1
C) x+1
Pls help, I don't understand this :(
Answer:
I believe the answer is C, x+1 :)
What is the greatest common factor of 2e^2+12e+22
Answer:
2(e^2+6e+11) is the GCF
The common ratio in a geometric series is 4 and the first term is 3.
Find the sum of the first 8 terms in the series.
Show Calculator
Answer:
The sum of the first 8 terms in the series is 65535.
Step-by-step explanation:
We have,
The common ratio in a geometric series, r = 4
First term of GP is, a = 3
It is required to find the sum of the first 8 terms in the series. The sum of first n terms of a GP is given by :
[tex]S_n=\dfrac{a(r^n-1)}{r-1}, r>1[/tex]
Here, n = 8
[tex]S_8=\dfrac{3\times ((4)^8-1)}{4-1}\\\\S_8=65535[/tex]
So, the sum of the first 8 terms in the series is 65535.
In order to answer the following question, please use the following image down below:
Find the value of x.
X=(Blank)
What is the value of X? Please show all the work on how you got your answer.
(If you can't explain your work, then it's fine. The only thing that I'm asking for is for you to show the work alongside your answer)
Answer:
23
Step-by-step explanation:
(x-3)(9) = (10)(18)
9x - 27 = 180
9x = 207
x = 23
which expressions are equivalent to the one below? 21x/7x
Step-by-step explanation:
21x/7x = 21/7 (The x cancel out)
= 3
please help with this
Answer:
A = Quartile 1 = 74.725
B = Median (quartile 2) = 80.25
C = Quartile 3 = 82.125
D = Minimum = 74.1
E = Maximum = 82.7
Step-by-step explanation:
The values for the data for the average life expectancy are as follows;
North Carolina 79.6
Oregon 82
District of Columbia 77.9
Nevada 81.3
New York 82.5
Colorado 80.9
Alaska 74.9
Connecticut 82.7
Montana 74.1
Mississippi 74.2
Sorting the data we have;
74.1
74.2
74.9
77.9
79.6
80.9
81.3
82
82.5
82.7
The minimum value is 74.1
The maximum value is 82.7
The 1st quartile is the [tex]\frac{10 + 1}{4} th[/tex] term or 74.725
The median 2nd quartile is the [tex]\frac{10 + 1}{2} th[/tex] term and the value is 80.25
Third quartile value is the[tex]\frac{3\times (10 + 1)}{4} th[/tex] term or 82.125.
There are 16 baseball games per day at Lansing's annual baseball tournament, which lasts 10 days. Estimate the number of baseball games during the tournament by rounding the larger number to the nearest ten.
To estimate the total number of games during the baseball tournament, round the daily games (16) to the nearest ten (20) and multiply by the number of days (10), resulting in an estimated 200 games.
To estimate the number of baseball games during Lansing's annual baseball tournament, we can round the larger number to the nearest ten and then multiply it by the number of days in the tournament. The larger number, representing the number of games per day, is 16. Rounding 16 to the nearest ten gives us 20. As the tournament lasts 10 days, we calculate the total by multiplying these two numbers.
Estimated total number of games = Rounded number of games per day x Number of days in the tournament
Estimated total number of games = 20 x 10
Estimated total number of games = 200 games.
What is the area of a triangle whose sides measure 12 inches, 14 inches, and 18 inches?
Enter your answer, in simplified radical form, in the box.
Answer:
A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]
Step-by-step explanation:
In this question, we are tasked with calculating the area of a triangle given the length of its three sides
Mathematically, we can calculate this using the Heron's formula
For Heron's formula, A = [tex]\sqrt{S(S-A)(S-B)(S-C)}[/tex]
WHERE S = [tex]\frac{A+B+C}{2}[/tex]
we take the lengths of the triangle as A,B and C respectively as given
S = (12 + 14 + 18)/2 = 22
Plugging the values into the equation, we have;
A = [tex]\sqrt{22(22-12)(22-14)(22-18)}\\ \\\sqrt{22(10)(8)(4)} \\\\\sqrt{7040}[/tex]
A = [tex]8\sqrt{110}[/tex] [tex]inches^{2}[/tex]
Answer:
8*sqrt(110)
Step-by-step explanation:
Grace and her dad are planning to attend the state fair. An adult ticket is $15.00. The price of an adult ticket is one half the price of a student ticket plus $8.00. Write an equation to determine how much Grace will pay for a student ticket.
Answer:
(1/2)x + 8 = 15
Step-by-step explanation:
¿Cuántas personas encuestadas se comunican más de 77 minutos?
AYUDA POR FAVOR ES DE APRENDO EN CASA
Respuesta:
se comunican 27 personas 9 +14+4=27 personas
Explicación paso a paso:
para resolver vean los datos en la tabla de frecuencia que van a desarrollar
observamos el intervalo [77; 81[ a partir de el determinamos la cantidad de personas que se comunican 77 minutos o mas minutos
PLEASE HELPPP!!!!!!!!!!
A table has an area of 12 and a perimeter of 16 ft. What are the dimensions of the table?
A) 2 ft by 6 ft
B) 2 ft by 8 ft
C) 4 ft by 3 ft
D) 4 ft by 4 ft
Answer:
the answer is A
Step-by-step explanation:
if you are really stuck just go through each possible answer to see if its right
here is some help for solving:
area is equal to length times width or A = L x W
perimeter is equal to length plus width plus length plus width or L+W+L+W
perimeter is just adding up all the sides of the square or rectangle
so if you try with answer a you get:
2 x 6 = 12 and 2 + 6 + 2 + 6 = 16
the answer is A
What does V= If V/13 =14
Answer:
182
Step-by-step explanation:
Reverse the problem,
13 x 14 = ?
13 x 14 is 182
182/13=14
What is the slope of (2,4) and (6,7) ?
Answer:
(7-4)/(6-2)= 3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
Rise/ Run = (7-4)/(6-2) = 3/4
If you were to plot the point (4,-12) what would be the correct method?
Answer: it is the last one
Step-by-step explanation:
If you were to plot the point (4,-12), the correct method is to plot the point 4 units right, then 12 units down
Option D is correct
If a point is expressed in the form (x, y), the coordinate x represents the location of the point on the horizontal axis while the coordinate y represents the location of the point on the vertical axis
If x is positive, it means that the point is plotted on the right hand side of the horizontal axis. If x is negative, it means that the point is plotted on the left hand side of the horizontal axis
If y is positive, it means that the point is plotted on the top region of the vertical axis. If y is negative, it means that the point is plotted on the bottom region of the vertical axis
For the point (4, -12)
x = 4, and y = -12
Since x = 4 is positive, the graph is plotted 4 units to the right
Since y = -12 is negative, the graph is plotted 12 units down
Therefore, If you were to plot the point (4,-12), the correct method is to plot the point 4 units right, then 12 units down
Learn more here: https://brainly.com/question/17106183
Help asap please due tomorrow
Answer:
The first one is 15.75 lbs or 15 3/4. The second one is 28 years old. The third one is$9.90 each t-shirt
Step-by-step explanation:
For the first one you multiply 18 by 14 and you get 252. Then there is 16 ounces in a pound so you divide by 16. Then you get 15.75. So that is your answer. The 2nd one you take 84 and multiply it by 1/6 then since she is twice the age of her sister you multiply by 2. so it would look like: 84 times 1/6= 14
14 times 2 = 28. So she is 28 years old. The third one you take 32 and subtract it by 12.20. You will be left with 19.8. Then both t-shirts cost the same so you would divide 19.8 by 2. You are left with 9.9. So the answer is $9.90. Sorry this took 10 minutes.
Answer:
15.75lb of hotdogs
Amy is 28 years old
she paid $9.90 for each shirt.
Step-by-step explanation:
1) we multiply the number of packages by how much each package weighs. which gives us 252ounces we can then convert ounces to pounds by multiplying by 0.0625pounds/1ounce which gives us 15.75lb
2) amy's age is her fathers age devided by 6 which gives us fourteen. we know Hannah's age is twice Amy's age, so we multiply 14 by two, 14X2=28
3) we subtract the money Rose spent on the poster from the overall amount rose spent. $32.00-$12.20=$19.80. so we know Rose spent $19.80 on t-shirts, since we also know she bought two equaly priced t-shirts we can devide $19.80 by 2, $19.80/2=$9.90, therfore, she spent $9.90 on each shirt.
whats the slope of y=5x-1
Mars has m moons. The number of moons of Pluto is one more than twice the number of moons of Mars. The number of moons of Neptune is one less than 3 times the number of moons of Pluto. Write and interpret a simplified expression that represents the number of moons of Neptune
The simplified expression for the number of moons of Neptune, based on the variable for Mars' moons m, is 6m + 2, meaning Neptune has twice as many moons as Mars plus two more.
Explanation:The student has asked to write and interpret a simplified expression that represents the number of moons of Neptune, based on the information that Mars has m moons, Pluto has one more than twice the number of moons of Mars, and Neptune has one less than three times the number of moons of Pluto.
Let's denote the number of moons of Mars as m. According to the information, Pluto has 2m + 1 moons. Therefore, Neptune would have 3(2m + 1) - 1 moons. Simplifying this expression:
Neptune's moons = 3(2m + 1) - 1
= 6m + 3 - 1
= 6m + 2
The simplified expression 6m + 2 represents the number of moons of Neptune, which means that Neptune has twice as many moons as Mars plus an additional two moons.
Learn more about Moons of Neptune here:https://brainly.com/question/31374667
#SPJ2
Evaluate g(x)=x^3+9 when x=-2
Answer:
g(x) = 1
Step-by-step explanation:
A spinner travels around a circle. The radius is 3 inches. Mike spins the spinner and it travels completely around the circle 5 times. About how far did the tip of the spinner travel?
Answer:
The spinner travelled 94.2 inches.
Step-by-step explanation:
In order to solve this question we first need to calculate the length of the circle, that is given by the following formula:
length = 2*pi*r
length = 2*3.14*3 = 18.84 inches
Since the spinner revolved around the circle 5 times, the distance travelled by the tip is the length of the circle multiplied by 5, as shown below:
distance = length*5
distance = 18.84*5 = 94.2 inches
The spinner travelled 94.2 inches.
Answer:
94.2 inches.
Step-by-step explanation:
The length of the circle can be determined by
length 'l'= 2πr
l = 2 x 3.14 x 3 = 18.84 inches
As the spinner and it travels completely around the circle 5 times, therefore, we'll have the distance of
distance = l x 5
distance = 18.84 x 5 => 94.2 inches
Thus, the tip of the spinner traveled 94.2 inches.
Please help me solve just for the answer anything helps M varies inversely as the square of P. If M is 9 when P is 2, then find M when P is 3.
Answer:
4
Step-by-step explanation:
When M varies inversely P squared rhen this is represented as
[tex]M=\frac {k}{P^{2}}[/tex]
Here, k is a constant of proportionality
Now when M is 9 and P is 2, P squared will be 4. Now substituting the value of P squared and M into the equation we can find the xonstant of proportionality as
K=9*4=36
Now that we have k, when P is 3 then we substitute the value of P as 3 and k as 36 into the first equation hence
[tex]M=\frac {36}{3^{2}}=4[/tex]
Therefore, M=4
3. Given that (5,12, 13) is a Pythagorean triple, which of the following isn't a Pythagorcan
triple?
(1) (10, 24, 26)
(3) (50,120,130)
(2) (10, 17, 18)
(4) (15, 36, 39)
Answer:
(2) (10,17,18)
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Well, let’s use a cancelling technique.
We know that 10, 24, 26 is just 5, 12, 13 multiplied by 2. So that works! And 50, 120, 130 is just 5, 12, 13 multiplied by 10. So that also works! And 15, 36, 39 is just 5, 12, 14 multiplied by 3. Therefore 2 is our answer...
Use technology or a z-score table to answer the question.
The number of baby carrots in a bag is normally distributed with a mean of 94 carrots and a standard deviation of 8.2 carrots.
Approximately what percent of the bags of baby carrots have between 90 and 100 carrots?
Answer: 46%
Step-by-step explanation:
Since the number of baby carrots in a bag is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the number of baby carrots in the bag.
µ = mean
σ = standard deviation
From the information given,
µ = 94 carrots
σ = 8.2 carrots
The probability that a bag of baby carrots have between 90 and 100 carrots is expressed as
P(90 ≤ x ≤ 100)
For x = 90,
z = (90 - 94)/8.2 = - 0.49
Looking at the normal distribution table, the probability corresponding to the z score is 0.31
For x = 100,
z = (100 - 94)/8.2 = 0.73
Looking at the normal distribution table, the probability corresponding to the z score is 0.77
Therefore,
P(90 ≤ x ≤ 100) = 0.77 - 0.31 = 0.46
The percent of the bags of baby carrots that have between 90 and 100 carrots is
0.46 × 100 = 46%
PLEASE HELP
Select ALL of the expressions that correctly calculate the perimeter of the shape.
1. 40 + 20π
2. + 20π
3. 120 + 20π
4. 300 + 100π
5. 10 + 10 + 10π + 10 + 10 + 10π
Answer:
1 and 5
Step-by-step explanation:
The squares have a side length of 10 and 1 square side is the radius of the half-circles. Since there are two half-circles, find the circumference for one full circle:
[tex]C=2\pi r[/tex]
Insert the radius:
[tex]r=10\\C=2\pi *10[/tex]
Simplify pi:
[tex]C=2*3.14*10[/tex]
Simplify multiplication:
[tex]C=6.28*10\\C=62.8[/tex]
The circumference of the circles is 62.8. Now find the perimeter of the exposed squares with side length 10. There are 4 exposed sides, which equals one square. Find the perimeter:
[tex]P=10+10+10+10\\P=10+10+20\\P=10+30\\P=40[/tex]
Add the perimeter of the circle and the square together:
[tex]P=62.8+40=102.8[/tex]
Now see which of the options gives you the perimeter:
1. [tex]40+20\pi =102.8[/tex] ****
2. [tex]unavailable[/tex]
3. [tex]120+20\pi =182.8[/tex]
4. [tex]300+100\pi =614.2[/tex]
5. [tex]10+10+10\pi +10+10+10\pi =102.8[/tex] ****
Finito.
The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .
We have to determine, the perimeter of the given shape in the question.
According to the question,
The squares have a side length of 10 and 1 square side is the radius of the half-circles.
There are two half-circles,
To find the circumference for one full circle:
[tex]C = 2\pi r[/tex]
Where radius = 10
[tex]C = 2\times 3.14 \times 10\\\\C = 62.8[/tex]
The circumference of the circles is 62.8.
To find the perimeter of the exposed squares with side length 10.
There are 4 exposed sides, which equals one square.
Therefore, perimeter p is given as,
[tex]P = 10+10+10+10\\\\P = 40[/tex]
On adding the perimeter of the circle and the square together:
[tex]P = 62.8+ 40 = 102.8[/tex]
Check all the statement which give perimeter of the shape,
[tex]40+20\pi = 40+ 20\times3.14 = 102.8\\\\20\pi = 20 \times 3.14 = 62.8\\\\120+20\times \pi = 120+20\times3.14= 182.8\\\\300 + 100\times\pi = 300+100\times3.14 = 614\\ \\10+10+10\times\pi +10+10+10\times\pi = 40+ 20\times3.14 = 102.8[/tex]
Hence, The expression . 40 + 20π and 10 + 10 + 10π + 10 + 10 + 10π gives the correct value of the perimeter is 102.8 .
To know more about Perimeter click the link given below.
https://brainly.com/question/2589784
A _____________________________ has a constant change in the x values and a constant ratio in the y values.
A 'directly proportional' has a constant change in the x values and a constant ratio in the y values' is filled by the term .
A directly proportional relationship between two variables means that there is a constant change in the x values and a constant ratio in the y values. In mathematical terms, we say that y is directly proportional to x if y = kx, where k is known as the proportionality constant. This implies that for any constant increment in x, there will be a proportional constant change in y.
If we plot a graph of two variables that are directly proportional, the result is a straight line that passes through the origin (0, 0). This is because the ratio y/x remains constant at the value of k. The slope of this line represents the constant rate of change between y and x, and the slope is equal to the proportionality constant k.
At barlow school 4/9 of the 873 students are boys at willow school 2/3 of the 630 students are girls which school has the greater number of boys and by how many
Answer:
There are 178 more boys in Barlow school as compared to Willow school.
Step-by-step explanation:
We are given the following in the question:
Barlow school:
Total number of students = 873
Number of boys =
[tex]=\dfrac{4}{9}\times 873 = 388[/tex]
Willow school:
Total number of students = 630
Number of girls =
[tex]=\dfrac{2}{3}\times 630 = 420[/tex]
Number of boys =
Total number of students - total number of girls
[tex]=630-420 = 210[/tex]
Thus, Barlow school has greater number of boys than Willow school.
Difference between the number of boys =
[tex]=388-210\\=178[/tex]
Thus, there are 178 more boys in Barlow school as compared to Willow school.
Simplify -3xy 3 + 7xy 3 + (-xy 3) + (-3xy 3
(−3x)(y3)+7xy3+(−x)(y3)+(−3x)(y3) = 0
Which statements about square roots are true? Check all that apply.
The square root of a positive number cannot be negative.
All positive numbers have two square roots.
18 = 9 because 9(2) = 18.
149 = 7 because 7(7) = 49.
25 = 5 because 52= 25.
The square root of a positive number cannot be negative, all positive numbers have two square roots, and 25 = 5 because 52 = 25.
Explanation:The statements that are true about square roots are:
The square root of a positive number cannot be negative.All positive numbers have two square roots.25 = 5 because 52 = 25.These statements are correct because the square root of a positive number will always be positive, every positive number has two square roots (one positive and one negative), and the square root of 25 is 5 because 5 multiplied by itself is equal to 25.
Learn more about Square roots here:https://brainly.com/question/29286039
#SPJ12
Which function has an initial value of 0.2?
Group of answer choices
Function Three
Function Four
Function Two
Function One
PICTURE IS BELOW
Answer:
Function Four
Step-by-step explanation:
Put x=0 into each of the functions and see what you get.
1. 3
2. 2
3. 1
4. 0.2 . . . . function 4 is the one you want
5. 0
_____
Anything with an exponent of 0 has a value of 1. (except 0^0 is indeterminate)