How many permutations exist of the letters a, b, c, d taken four at a time?
There are 24 permutations of the letters a, b, c, d taken four at a time, calculated using the formula 4!.
Explanation:The question revolves around finding the number of permutations of the letters a, b, c, d taken four at a time. To solve this, we need to understand that a permutation represents the arrangement of all members of a set in every possible order.
In the case of the letters a, b, c, d, we want to arrange them in all possible ways where order matters and taking all four at a time. The formula to calculate permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. However, since we are taking all four letters each time, we are essentially looking for 4!, which simplifies to 4*3*2*1.
Therefore, 4! equates to 24. This means there are 24 possible ways to arrange the letters a, b, c, d when taking all four at a time. It's an excellent exercise to manually write out all of these permutations to get practical experience with the concept.
How many combinations with 3 numbers 0-6?
In the united states, 20 ounces of a beverage that is 25% ethanol contains __________ ounces of alcohol
The central angle of a circle is equal in measure to one radian when the corresponding arc length is equal to which of the following? A) The radius of the circle B) Any chord of the circle C) The diameter of the circle D) One-half the circumference of the circle
If line segment ab is defined by the endpoints a(4,2) and b(8,6) , write an equation of a line that is the perpendicualr bisector line segment ab
An equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Given that, line segment AB is defined by the endpoints A(4,2) and B(8,6).
Midpoint of line AB is (x, y) =[(x₂+x₁)/2, (y₂+y₁)/2]
= [(8+4)/2, (6+2)/2]
= (6, 4)
Slope of line AB is (y₂-y₁)/(x₂-x₁)
= (6-2)/(8-4)
= 4/4
= 1
The slope of a line perpendicular to given line is m1=-1/m2
So, the slope of a line is -1
Now, substitute m=-1 and (x, y)=(6, 4) in y=mx+c, we get
4=-1(6)+c
c=10
Substitute m=-1 and c=10 in y=mx+c, we get
y=-x+10
Therefore, an equation of a line that is the perpendicular bisector line segment AB is y=-x+10.
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The total price of an article is $7.02, including tax. If the tax rate is 8%, what is the retail price of the article?
The solution is: The retail price is $6.50.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Here, we have,
given that,
The total price of an article is $7.02, including tax.
If the tax rate is 8%
Lets price of article = x
Tax is 8% of article = 0.08x
so, we get,
x+0.08x=7.02
1.08x=7.02
x=7.02/1.08
x=6.5
The retail price is $6.50.
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What is the interval for the number of people who are likely to want this restaurant in their city?
A hang glider is soaring over a 100-acre area that consists of thick forest and open fields. In the diagram below, the forested area is shaded in green and the open field is the white space. Upon landing, the hang glider realizes she has dropped her keys.
What is the probability that her keys have landed within the forest?
The blacked out middle section of the pyramid is 20 acres
A 0.2
B 0.6
C 0.8
D 1.0
The probability that her keys have landed within the forest will be C. 0.8.
How to calculate probability?From the information given, the blacked out middle section of the pyramid is 20 acres. Therefore, the probability will be:
= 20/100 = 0.2
Now, the probability that her keys have landed within the forest will be:
= 1 - 0.2
= 0.8
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Which measure is of an angle that is coterminal with a 425 degree angle
A. 425 degree-(1,000n)degree, for any integer n
B.425 degree-(840n)degree, for any integer n
C. 425 degree+(960n)degree, for any integer n
D. 425 degree+(1,440n)degree, for any integer n
We know that co terminal angles are those angles which have a difference equal to a multiple of 360 degrees. For example co terminal angle of 45 degrees is 76 degrees because their difference is equal to 720 degrees, which is a multiple of 360.
We have been given an angle 425 degrees.
From the given choices, we need to check if angles being added or subtracted to 425 degrees are multiples of 360 or not.
Let us check each of the options one by one.
(A) The angle being subtracted is [tex]1000n[/tex]. Therefore, we have [tex]\frac{1000n}{360}=2.77n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(B)
The angle being subtracted is [tex]840n[/tex]. Therefore, we have [tex]\frac{840n}{360}=2.33n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(C)
The angle being added is [tex]960n[/tex]. Therefore, we have [tex]\frac{960n}{360}=2.67n[/tex], which is not an integer for all values of n. Therefore, angle given in this option is not a co terminate angle to 425 degrees.
(D)
The angle being added is [tex]1440n[/tex]. Therefore, we have [tex]\frac{1440n}{360}=4n[/tex], which is an integer for all values of n. Therefore, angle given in this option is indeed a co terminate angle to 425 degrees.
Hence, correct answer is option (D).
The mathematics department of a college has 1414 male professors, 99 female professors, 99 male teaching assistants, and 1111 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male.
I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723
In how many different ways can someone arrange 6 books on a shelf
Leo has 100 coins in his piggy bank. All coins are either nickels, or dimes, or quarters. There are as many nickels as dimes and quarters together. How much money are nickels in Leo's piggy bank worth?
Answer:
33
Step-by-step explanation:
A ball is thrown into the air with an upward velocity of 32 ft/s. Its height h in feet after t seconds is given by the function h = −16t2 + 32t + 6. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?
The ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
To find the time at which the ball reaches its maximum height, we can first determine the vertex of the quadratic function [tex]\( h(t) = -16t^2 + 32t + 6 \),[/tex] where t represents time in seconds and h represents height in feet.
The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] is given by the formula:
[tex]\[ t_{\text{max}} = \frac{-b}{2a} \][/tex]
For the function [tex]\( h(t) = -16t^2 + 32t + 6 \)[/tex], we have a = -16 and b = 32 . Plugging these values into the formula:
[tex]\[ t_{\text{max}} = \frac{-32}{2(-16)} \]\[ t_{\text{max}} = \frac{-32}{-32} = 1 \][/tex]
So, the ball reaches its maximum height at t = 1 second.
To find the maximum height, we substitute t = 1 into the function h(t) :
[tex]\[ h(1) = -16(1)^2 + 32(1) + 6 \]\[ h(1) = -16 + 32 + 6 \]\[ h(1) = 22 \][/tex]
Therefore, the ball's maximum height is [tex]\( \boxed{22} \)[/tex] feet.
In ∆ABC, ∠BAC= 80°, ∠ABC=60°, a = 7, b = x.
Find x. (accurate to 3 significant figures)
The value of x = .
Rearrange the formula to calculate the diameter of a circle.
What is the least common multiple (LCM) of 8 and 10?
Answer:
LCM (8,10) = 2 × 2 × 2 × 5 = 40
Step-by-step explanation:
Least common multiple is the smallest number that is multiple of both the given numbers.
Example: LCM of 2 and 3 is 6 .
6 is a multiple of both 2 and 3 .
Given numbers are 8 and 10
First write both in factor form,
⇒ 8 = 2 × 2 × 2
⇒ 10 = 2 × 5
We find LCM by writing common terms one times and multiplying all terms together,
Here, 2 is common to both 8 and 10 so we write it once only.
Thus, LCM (8,10) = 2 × 2 × 2 × 5 = 40.
Suppose that on a particular computer, it takes the merge sort algorithm a total of 60 seconds to sort an array with 60,000 values. approximately how long will it take the algorithm to sort an array with 120,000 values? round to the nearest second.
How many zeros does the function f(x) = 4x^11 − 20x^7 + 2x^3 − 15x + 14 have?
I'm between 3 & 11.
Given:
CDKM is a parallelogram,
DA
⊥
CK
, DK – CD = 7
CA = 6, AK = 15
Find: CD and DK
In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.
The difference of the side DK and CD is,
[tex]DK - CD = 7\\DK=7+CD[/tex]
The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,
[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex] ....1
Again by using the Pythagoras theorem
[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]
Put the value of (AD)², from equation 1 in the above equation as,
[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]
Put the value of DK in the above equation as,
[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]
Hence, the value of DK is,
[tex]DK=7+10DK=17[/tex]
Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
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Easy math problem, please help.
O is the center of the circle. Assume that lines that appear to tangent are tangent. What is the value of x?
A. 56
B. 62
C. 248
D. 304
Answer:
Option A is correct that is x° = 56°
Step-by-step explanation:
Let Given Lines are tangents.
So we use a result which states that Tangents are perpendicular with radius at point of contacts.
⇒ ∠ B = ∠ D = 90°
Angle sum property of Quadrilateral = 360°
⇒ ∠A + ∠B + ∠O + ∠D = 360
x + 90 + 124 + 90 = 360
x + 304 = 360
x = 360 - 304
x = 56
Therefore, Option A is correct that is x° = 56°
how do we find the volume ?
The volume of figure is 877.876 yd³
1. Volume of Cone
= 1/3πr²h
= 1/3 x 3.14 x 2 x 2 x 4
= 16.746
2. Volume of cylinder
= 3.14 x 2 x 2 x 8
= 100.48
3. Volume of Hemisphere
= 2/3πr³
= 7.065
4. Volume of cylinder
= 3.14 x 1.5 x 1.5 x 9
= 63.585
5. Volume of prism
= 1/2 x ( 6 x 6) x 12
= 216
6. Volume of Cuboidal prism
= l w h
= 6 x 6 x 12
= 432
7. Volume of pyramid
= 1/3 x 3 x 2
= 2
8. Volume of cuboidal prism
= 10 x 2 x 2
= 40
So, the volume of figure is
= 16.746 + 100.48 + 7.065 + 63.585 + 216 + 432 + 2 + 40
= 877.876 yd³
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Can anybody help me with this question(#6)? It’s over systems word problems. ASAP!
10PTS!!!!!! UGRENT WILL MARK BRAINLYEST, THANK AND 5 STARS!!
Find the volume of the tank below.
could't inbed the image but it a cylindar 5m tall and has a radius of 2m
96 m3
78 m3
54 m3
63 m3
The combined cost of one advance ticket and one same-day ticket to a show was $50. it is known that 17 advance tickets were sold and 48 same-day tickets were sold, for total receipts of $1842. what was the price of each kind of ticket?
Need help please ASAP!!
(5.4+3)×(6−2) help plzzz
Express each product in the simplest form. 3wx\6x * 3wx\9w
Conor buys 75 tokens for games at the arcade. the price to play each game is 3 tokens. if conor has already played x games, which expression is equivalent to the number of tokens that remain?
Answer:
y = 75 - 3x
Step-by-step explanation:
Let the number of token left = y
total number of token bought = 75
Number of games played by Conor = x
It is given for playing one game, the price = 3 token
Therefore for playing x games, the price is = 3x
Therefore, the number of tokens left with Conor is given by
y = 75 - 3x
Thus, the expression that is equivalent to the number of remaining tokens is
y = 75 - 3x
Anyone know the answer?
HELPPPPPPPPPPPP and explain