Using the arrangements formula, the number of ways that they can be seated for each case is given as follows:
a) No restrictions: 362,880.
b) Sam next to Sarah: 80,640.
c) Boy-girl-boy-girl: 2,880.
What is the arrangements formula?The number of possible arrangements of a set containing n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
For item a, we consider that 9 people will be seated with no restrictions, hence the number of ways is given as follows:
9! = 362,880
For item b, there is the restriction that Sam has to be seated next to Sarah, hence:
There are 8 pairs of seats in which they can be seat, each in 2 ways(Sam-Sarah or Sarah-Sam).The other 7 people can be seated in 7! ways, as there are no restrictions for them.Hence the number of ways is:
2 x 8 x 7! = 80,640.
For item c, we can treat the boys and the girls places as independent, hence:
There are 5! ways for the boys to sit, as there are five boys in the group.There are 4! ways for the girls to sit, as there are four girls in the group.Hence the number of ways is:
5! x 4! = 2,880.
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The height of a trapezoid can be expressed as x - 4, while the bases can be expressed as x + 4 and x + 9. If the area of the trapezoid is 99 cm², find the length of the larger base.
Answer: 19 cm
Step-by-step explanation:
Substituting into the formula for the area of a trapezoid,
[tex]\frac{1}{2}(x-4)(x+4+x+9)=99\\\\\frac{1}{2}(x-4)(2x+13)=99\\\\(x-4)(2x+13)=198\\\\2x^2 +5x-250=0\\\\(2x+25)(x-10)=0\\\\x=-12.5, 10[/tex]
However, as x must be positive (since length must be positive), x=10. This means the length of the longer base is 19 cm.
5. Follow the rule to find the next three numbers in the pattern. Describe
the pattern using the terms even and odd.
Add 5: 1, 6, 11,
Any integer that cannot be divided into twos is considered an odd number. Five computers, for instance, cannot be arranged in pairs only. 5 is therefore an odd number.
The next three numbers in the pattern is 16,21,26. The pattern is odd.
What is odd and even numbers?Any integer that cannot be divided into twos is considered an odd number. Five computers, for instance, cannot be arranged in pairs only. 5 is therefore an odd number.
An even number is one that can be divided by two and leaves residue of zero. The even numbers include 2, 4, 6, 8, 10, and so on. Let's say, for instance, that you have ten chocolates. There are two groups of these chocolates that each include five chocolates. Ten is therefore an even number.
An even number is produced by adding two even numbers. In this case, 12 + 8 equals 20.
Odd numbers are created by adding odd numbers to even numbers. For example, 6 + 7 equals 13.
The outcome of adding two odd numbers is an even number. For an instance, 15 + 11 = 26.
Now for the above question,
The next three numbers: 16, 21, 26.
Number pattern is odd, because 5 is odd number.
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Does coordinates s or coordinate t represent a greater number in the following
parallelogram?
(-2,3)
(s, -1)
(0, -1)
(t, 3)
Thus, t has a greater value than s for the co-ordinates (s, -1) and (t, 3).
How to analyze points of an axis for a two dimensional entity?
We can use the fact that both points on the x-axis to compare the values of s and t for the provided parallelogram. As a result, each point that is closest to the x coordinate reflects a higher value than its equivalent counterparts.
Given, the co-ordinates of the parallelogram are: (-2, 3), (s, -1), (0, -1),
(t, 3).
Also, the co-ordinates of the parallelogram are also shown in the figure below.
To compare for the values of s and t for the given parallelogram,
we can analyze that both s and t represent points on the x-axis, therefore any point that stands rightmost with the x co-ordinate represents a higher value than the corresponding counterparts.
Therefore, t has a greater value than s for the co-ordinates (s, -1) and (t, 3), since t is on the right side from s.
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I need help solving for x assume that lines which appear tangent are tangent
SOLUTION:
Case: Secant secant theorem
Secant-Secant Power Theorem: If two secants are drawn from an external point to a circle, then the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant
Method:
[tex]\begin{gathered} 7(7+x+6)=8(8+x+2) \\ 7(x+13)=8(x+10) \\ 7x+91=8x+80 \\ 91-80=8x-7x \\ x=11 \end{gathered}[/tex]Final answer:
x = 11
(5)(3) - (2-7) divided by 4?
Answer:
Step-by-step explanation:
Answer:
[tex]{ \tt{(5)(3) - (2 - 7) \div 4}}[/tex]
- We are going to simplify the expression using BODMAS
B stands for BracketsO stands for OfD stands for DivisionM stands for MultiplicationA stands for AdditionS stands for Subtraction- From our expression, relating it to BODMAS, Brackets come first, so let's first operate the brackets
[tex] = { \tt{(5 \times 3) - ( \frac{2 - 7}{4}) }} \\ \\ = { \tt{15 - ( - \frac{5}{4} )}} \\ \\ = { \tt{15 + 5 \div 4}}[/tex]
- Then in our last expression, Division comes next
[tex] = { \tt{15 + \frac{5}{4} }} \\ [/tex]
- Then addition comes last
[tex] = { \tt{ \frac{65}{4} }} \\ [/tex]
- Simplifying our answer into mixed fraction and decimal format;
[tex] = { \tt{16 \frac{1}{4} \: \: or \: \: 16.25}}[/tex]
[tex]{ \boxed{ \delta}}{ \underline{ \mathfrak{ \: \: beicker}}}[/tex]
An object is dropped from 34 feet below the trip of the pinnacle atop a 710 fr tall building. The height h if the object after t seconds is given the equation h=-16t to the power of 2 +676 find how many seconds pass baffle the object reaches the ground
Setting h=0 and solving for t we get:
[tex]\begin{gathered} 0=-16t^2+676, \\ 16t^2=676, \\ t^2=\frac{676}{16}, \\ t^2=42.25 \\ t=\pm\sqrt[]{42.25}. \end{gathered}[/tex]Since t<0 does not have real meaning, we get that:
[tex]t=6.5.[/tex]Answer: 6.5 seconds.
The graph to the right is the uniform probability density function for a friend who is x minutes late.
(a) Find the probability that the friend is between 10 and 20 minutes late.
(b) It is 10 A.M. There is a % probability the friend will arrive within how many minutes?
Using the uniform distribution, it is found that:
a) The probability that the friend is between 10 and 20 minutes late is of 1/3.
b) There is a 30% probability that the friend will arrive within 9 minutes.
Uniform distributionThe uniform has two bounds, a and b, and each outcome of the distribution is equally as likely.
From the image given at the end of the answer, the bounds are given as follow:
a = 0, b = 30.
The probability of finding a value between c and d in the distribution is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence, the probability that the friend is between 10 and 20 minutes late is given as follows:
P(10 <= X <= 20) = (20 - 10)/(30 - 0) = 1/3.
The 30th percentile of the distribution, which is what item b is asking, is given as follows:
0.3 x (30 - 0) = 0.3 x 30 = 9 minutes.
Missing informationThe complete problem is given by the image at the end of the answer.
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need help!! algebra 1
Answer:
Step-by-step explanation:
6a) f(1)=-3
b) x=-5 x=-1 x=1
:]
Find and simplify each of the following for f(x) = 4x2 - 5x + 7.(A) f(x + h)(B) f(x +h)-f(x)f(x+h) – f(x)(C)h
(A) f(x+h)
[tex]\begin{gathered} f(x+h)=4(x+h)^2\text{ - 5(x + h) + 7} \\ =\text{ 4(x + h)(x + h) - 5x - 5h + 7} \\ =4(x^2+2xh+h^2)\text{ - 5x - 5h + 7} \\ =4x^2+8xh+4h^2\text{ - 5x - 5h + 7} \end{gathered}[/tex](B) f(x + h) - f(x)
[tex]\begin{gathered} =4x^2+8xh+4h^2\text{ - 5x - 5h + 7 - }(4x^2\text{ - 5x + 7)} \\ =4x^2+8xh+4h^2-5x-5h+7-4x^2\text{ + 5x - 7} \\ =4x^2-4x^2-5x+5x+7-7+8xh+4h^2\text{ - 5h} \\ \text{ = 0 + 0 + 0 + 8xh + 4h}^2\text{ - 5h} \\ =8xh+4h^2\text{ - 5h} \end{gathered}[/tex](C)
[tex]\begin{gathered} =\text{ }\frac{f(x+h)\text{ - f(h)}}{h} \\ =\text{ }\frac{8xh+4h^2\text{ - 5h}}{h} \\ =\text{ }\frac{8xh}{h}\text{ + }\frac{4h^2}{h}\text{ - }\frac{5h}{h} \\ =\text{ 8x + 4h - 5} \end{gathered}[/tex]you have 27 teaspoons of peppercorns you need 0.25 teaspoons make one serving of beef brisket how many servings can you make
Given:
Total Number of teaspoons of peppercorns = 27
Amount of teaspoons you need for one serving of brief brisket = 0.25
Let's find the amount of servings can be made.
To find the amount of servings that can be made, apply the formula:
[tex]\text{Number of servings = }\frac{TotalNumber\text{ of teaspoons}}{Teaspooons\text{ for one brisket}}\text{ }[/tex]Thus, we have:
[tex]\begin{gathered} \text{Number of servings = }\frac{27}{0.25} \\ \\ \text{Number of servings = }\frac{27}{\frac{25}{100}} \\ \\ \text{Number of servings = }\frac{27}{25}\ast100=1.08\ast100=108 \end{gathered}[/tex]Therefore, 108 servings can be made.
ANSWER:
108
If f(x) = -x-11, find -3f(5) x f(2)
Given the function :
[tex]f(x)=-x-11[/tex]we need to find the value of 3f(5) x f(2)
so, to find the value of f(5), substitute with x = 5 at the given function
And to find the value of f(2) , substitute with x = 2 at the given function
so,
[tex]\begin{gathered} f(5)=-5-11=-16 \\ \\ f(2)=-2-11=-13 \\ \\ 3f(5)\cdot f(2)=3\cdot-16\cdot-13=624 \end{gathered}[/tex]2) At a party, Karen notices the amount songs being played. The chart shows wh she figured out. Number of hours 50 Number of songs VSJ 3 4 5 6 60 80 A. 85 C. 100 After five hours, how many songs were played? 120 B. 90 D. 110
Answer:
C. 100
Step-by-step explanation:
If 60 songs are played in 3 hours, 80 songs in 4 hours, and 120 songs in 6 hours, you want to know the number played in 5 hours.
Linear functionConsidering the rate of change of songs per hour, we find ...
hours 3-4: 80-60 = 20 songs, over the 1-hour period
hours 4-6: 120 -80 = 40 songs, over the 2-hour period
It appears that the number of songs being played is steady at 20 songs per hour. Then 5×20 = 100 songs were played in 5 hours.
1.) You are one of five people who have been hired to mow the lawn at the local college. Each week, the dimensions of the plot you are responsible to mow changes. The college conducts a lottery, and whichever number is drawn, represents the x value. Your plot has a length which is five more than two times x and the width is three less than three times x. a.) What are the dimensions of your mowing plot? (2 points) Length: ______________________________________ Width: ______________________________________ x=13 meters
The dimensions of your mowing plot if x = 13 meters is;
Length = 31 meters
Width = 36 meters
How to solve Algebra Word Problems?We are told that Your plot has a length which is five more than two times x and the width is three less than three times x
This means that, the length given as words is "5 more than 2 times x" and the width given as words is "3 times x minus 3"
The expression for length would be 2x + 5
The expression for width would be 3x - 3
Now, if x = 13 meters, then we see that;
Length = 2(13) + 5 = 31 meters
Width = 3(13) - 3 = 36 meters
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A 90% confidence interval is found to be (72, 78). What is the margin of error?
In order to find the margin of error, we need to know that the width of the confidence interval is equal to 2 times the margin of error.
The width of this confidence interval is given by:
[tex]\begin{gathered} width=upper\text{ }limit-lower\text{ }limit\\ \\ width=78-72\\ \\ width=6 \end{gathered}[/tex]If the width is 2 times the margin of error, we have:
[tex]\begin{gathered} width=2\cdot E\\ \\ 6=2\cdot E\\ \\ E=\frac{6}{2}\\ \\ E=3 \end{gathered}[/tex]The margin of error is equal to 3, therefore the correct option is D.
SOMEONE HELP ME ASAP PLEASE!!!!
Find all values of n for which the equation has two complex (non-real) solutions.
3z² - 9z = (n − 3)
-
Write your answer starting with n, followed by an equals sign or inequality symbol (for
example, n < 5). Reduce all fractions.
For a quadratic [tex]ax^2+bx+c[/tex], the sign of its determinant, given by
[tex]\Delta = b^2 - 4ac[/tex]
"determines" the nature of its roots. In particular, if [tex]\Delta<0[/tex], then the quadratic has two distinct non-real roots.
Now, we have
[tex]3z^2 - 9z = n-3 \implies 3z^2 - 9z - (n-3) = 0[/tex]
with determinant
[tex]\Delta = (-9)^2 - 4\cdot3(n-3) = 117 - 12n[/tex]
Solve for [tex]n[/tex] such that [tex]\Delta<0[/tex].
[tex]\Delta = 117 - 12n < 0 \implies 12n > 117 \implies n > \dfrac{117}{12} \\\\ ~~~~ \implies \boxed{n > \dfrac{39}4}[/tex].
of estion Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. 60° X y 93 2 y
The 30-60-90 ratio is a special right triangle that always has angles with measures: 30º, 60º, and 90º. Its side lengths have also the same relationship one with another.
For any 30-60-90 the ratio is as follows:
The side opposite to the 30º angle has length: z
The side opposite to the 60º angle has a length z√3
The side opposite to the 90º angle has a length: 2z
Following these ratios, you can determine the side lengths of the triangle.
The measure opposite to the 60º angle is z√3 = 9√3 → From this we can determine the value of z, which is z=9
Once we know the value of z, we can calculate the values of the sides opposite to the other angles.
The side opposite to the 30º angle is y= z= 9
The side opposite to the 90º angle is x= 2z= 2*9 = 18
How can you write the expression (28 + 70) as a multiple of a sum of whole numbers with no common factor?
The expression (28 + 70) as a multiple of a sum of whole numbers with no common factor is given as
7x(4+10). This is further explained below.
What is an expression?Generally, An express is a finite combination of symbols that have been formed according to principles that rely on the context in which it is used. In mathematics, an expression is also known as a mathematical expression.
In conclusion, When expressed as a multiple of a total of whole numbers that do not have a common component, the equation (28 + 70) is written as 7 times (4 + 10).
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Finding Slope From Two Points
Find the slope of the line through each pair of points.
1) (19,-16), (-7, -15)
The slope of a line from given points (19,-16), (-7, -15) is - 1/26
Slope :
In Mathematics, Slope of a line defined as the direction of the line and the change in y-coordinate with respect to x - coordinate. Slope of a line is denoted by 'm'
The formula for slope of a line which passes through the points (x₁, y₁) and (x₂, y₂) is given by Slope (m) = (y₂– y₁)/(x₂ – x₁)
Here, we have pair of points (19,-16), (-7, -15)
Take (x₁, y₁) = (19,-16) and (x₂, y₂) = (-7, -15)
Slope (m) = [-15 -(-16) ] / [ -7 -19 ]
= [ - 15+16] / [ -26 ]
= [ 1 ] / [ -26 ]
= - 1/26
Therefore,
The slope of line from given points (19,-16), (-7, -15) is - 1/26
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7. Are the lines represented by the equations below parallel, perpendicular, or neither?
Justify your answer with words and numbers. (3 points)
- 3x + 6y = 12
y =
3x + 10
The two lines are neither parallel nor perpendicular.
What is condition for perpendicular, parallel?
if two given lines are parallel, perpendicular, or neither, we need to compare their slopes. For this, we need to make sure that their equations are in the form y = mx + b. This represents the equation of a straight line in the slope-intercept form, where m is the slope and b is the y-intercept.
If the given lines have the same slope, they’re parallel to one another. On the other hand, if they have slopes that are opposite reciprocals, i.e., the slopes have opposite signs and are flipped fractions of one another, they are perpendicular to each other. Else, they are neither.
The given lines are
- 3x + 6y = 12 or, y = (1/2)x + 2 ... (1)
y = - 3x + 10 ... (2)
The gradient of the lines (1) and (2) are 1/2 and (- 3) respectively.
Since the gradients are not equal, the lines are not parallel and also since (1/2) × (- 3) ≠ - 1, the lines are not perpendicular to each other.
Hence we can conclude that the given two lines are neither parallel nor perpendicular.
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Hello what is ALL of the answers to this question
Answer
The function that describes the height of the rocket in terms of the is
[tex]h(t)=-16t^2+224t+68[/tex]
Find the total cost of 12 boxes of cookies if each box costs $3.
each box costs $3 : The cost of one box = $3
12 boxes of cookies : The total number of boxes = $12
For the total cost of 12 boxes : Multiply the cost of one box by the number of boxes
The total cost of 12 boxes = 12 x $3
The cost of 12 boxes = $36
The cost of 12 boxes of cookies ia $36
Answer : $36
For which value of x is therelation not a function?{(3, 1), (x, 0),(9,5),(12, 6)}A) 1. B)3C) 8. D)6
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
Here the domain of the relation is {3,x,9,5}.
The given relation is a function only if x not takes any of the value 3, 9 or 5.
So, option B is correct.
Rectangle ABCD is shown. What is the length of diagonal BD? Round to the nearest tenth if needed
THe diagonal, BD divides the rectangle into two right angle triangles.
BD represents the hypotenuse
BC represents the opposite side
DC represents the adjacent side
We would determine BD by applying the pythagorean theorem which is expressed as
[tex]\begin{gathered} \text{hypotenuse}^2=oppositeside^2+adjacentside^2 \\ BD^2=7^2+12^2=49\text{ + 144 = 193} \\ BD\text{ = }\sqrt[]{193} \\ BD\text{ = 13.9 } \end{gathered}[/tex]The length of the diagonal, BD is 13.9m to the nearest tenth
The table below gives the material of each item in Maria’s jewelry box. These are the only items in Maria’s jewelry box. Give the contra positive
The contra positive of the conditional statement is given as follows:
If an item is not made from copper, then it is not a pendant.
How to find the contra positive of a conditional statement?A conditional statement is modeled as follows:
p -> q.
In which:
p is the hypothesis.q is the conclusion.Hence the statement is read as:
If p then q.
The contra positive of the statement is given by:
~q -> ~p.
Hence it is read as:
If not q, then not p.
In the context of this statement, the hypotheses and the conclusion are given, respectively, by:
p: Item is a pendant.q: Item is made from copper.Hence the contra positive of the statement is:
If an item is not made from copper, then it is not a pendant.
What is the missing information?The statement is missing and is given as follows:
"If an item is a pendant, then the item is made from copper".
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show each quadratic equation by factoring (show your solution)
7x^2+25x+12
PLEASE HELP
Answer:or a polynomial of the form
a
x
2
+
b
x
+
c
, rewrite the middle term as a sum of two terms whose product is
a
⋅
c
=
7
⋅
−
12
=
−
84
and whose sum is
b
=
25
.
7
x
2
−
3
x
+
28
x
−
12
Factor out the greatest common factor from each group.
Tap for more steps...
x
(
7
x
−
3
)
+
4
(
7
x
−
3
)
Factor the polynomial by factoring out the greatest common factor,
7
x
−
3
.
(
7
x
−
3
)
(
x
+
4
)
Step-by-step explanation:
Find the perimeter of the figure shown. Round your answer to the nearest centimeter. This is for problem number 9
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Hello!
For a line with slope '0':
⇒ the equation is 'y = y-coordinate of point that the line passes through'
Since the line passes through (-1, -4) and has the slope of '0'
⇒ y = -4
Hope that helps!
Evaluate (10 – 41) ÷ (5 + 1).
Step-by-step explanation:
option B is correct answer
circumference =33.5, find radius, diameter, area
(CIRCLE)
Answer: Radius = 5.33
Diameter = 10.66
Area = 89.3
Step-by-step explanation:
Circumference = 2πr
33.5 = 2πr
r = 33.5 / 2π
Diameter = 2r
Area = r²π
Area = 5.33²π
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the graphs with the absolute value relations they represent
Given
Answer
The graph is given by y = -3/2|x|
The graph of |y| = x/2
The graph of y = |x|
The graph of -1/2 |y| = x