In how many ways can we seat 6 people around a round table if Fred and Gwen insist on sitting opposite each other? (Two seatings are considered equivalent if one is a rotation of the other.)
Answers
Fred and Gwen are seated opposite each other, and we name the 4 remaining seats 1, 2, 3, 4, starting from the right of Fred.
There are 4 options for seat 1,
then 3 for the seat 2, after one is seated in the 1.st seat
2 options for the seat 3,
and 1 for the seat 4.
That is, the 4 friends can sit in 4*3*2*1=24 different ways.
Answer: 24
Answer:
24
Step-by-step explanation:
Related Questions
Find the product of 543.1187 and 100
Answers
Joshua is 25 years old and has a high risk job making $72,000 a year. The insurance company charges him an extra 20% on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, what is the annual premium for the cheapest policy?
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Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.
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Aiden should have calculated
area = (1.1 * 5.4) / 2
because triangle area = half the base times the altitude.
Answer: The correct option is
(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.
We are to select the correct option which states the error made by Aiden.
The AREA of a triangle is given by
[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]
where the altitude is perpendicular to the base.
In ΔQRS, the length of the base is given by
b = QS = 0.9 + 4.5 = 5.4 units
and
the length of the altitude is given by
h = 1.1 units.
So, the area of the triangle QRS will be
[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]
Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.
So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.
Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.
Option (B) is correct.
solve for b, then find the value of b when a = 3.
4a=2b-7
a. -9/2
b. 5/2
c. 19/2
d. 17
Answers
4(3) = 2b - 7
12 = 2b - 7
2b = 12 + 7
2b = 19
b = 19/2
answer
c. 19/2
What can you say about the function that generated the following table of values
Answers
best answer is b = it has exactly 1 x intercept
Answer:
B.
Step-by-step explanation:
We know that for x-intercept the graph crosses x-axis i.e the value of y = 0.
As in the table, the value of y is changing from negative to positive, so it will obtain the value y = 0 for some vale of x.
Therefore, this function will have only one x-intercept.
Hence, option A, C, D are discarded and option B is correct.
Simplify 5(6x - (6 - 7y + 7x) + 6y)
-80x + 87y - 91
-5x + 65y - 30
-82x + 73y - 54
-60x + 9y - 17
None of the above
Answers
= 5(6x - 6 + 7y - 7x + 6y)
= 5(-x + 13y -6)
= -5x +65y -30
Hence, the answer is B.
Write an equation for each translation of y=lxl
7 units up
Answers
[tex]\bf % template detailing \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind.. .let's see
[tex]\bf y=|x|\implies \begin{array}{lllcll} y=&1|&1x&+0|+&0\\ &\uparrow&\uparrow &\uparrow &\uparrow \\ &A&B&C&D \end{array}[/tex]
7 units up, meaning D = 7
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the formula A= Pe^rt, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.
Answers
okay, what you want to do is plug in the numbers you already have, to get the number you don't have(r).
First, you plug in the numbers.
1. P= $2000
A=$2543
t= 4(years)
r=?
2543=2000^r(4)
Secondly, you want to solve the equation.
Answer:
Rate of interest = 6%
Step-by-step explanation:
Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account.
Use the formula,
[tex]A=Pe^{rt}[/tex]
[tex]P\rightarrow \$2000[/tex]
[tex]r\rightarrow ?[/tex]
[tex]A\rightarrow \$2543[/tex]
[tex]t\rightarrow 4\text{ years}[/tex]
Substitute the value into formula and solve r
[tex]2543=2000e^{4r}[/tex]
[tex]e^{4r}=1.2715[/tex]
Apply ln both sides
[tex]4r\ln(e)=\ln(1.2715)[/tex]
[tex]r=0.06[/tex]
Rate of interest = 6%
Hence, The rate of interest is 6%
A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?
Answers
the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $4? use formula P(t)=1.1*e^0.047t A.)2007 B.)2005 C.)2003 D.)2009
Answers
40/11=e^(0.047t) take the natural log of both sides
ln(40/11)=0.047t divide both sides by 0.047
t=ln(40/11)/0.047
t≈24.5
1980+24.5
2007.5
So during 2007 the price will reach $4.
Answer:
The option A.) 2007 is correct
Step-by-step explanation:
The formula which is to be used is given :
[tex]P(t) = 1.1\cdot e^{0.047t}[/tex]
where P(t) is the function of time t and t is the time in years after January 1 , 1980
Now, we need to find the year when the price will reach $4
So, substituting P(t) = 4 and finding the value of t from the given equation.
[tex]\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49[/tex]
So, t = 27.49 which is approximately equals to 27.5 years
So, 27.5 years after January 1, 1980 is the year 2007
Hence, The price will reach $4 in the year 2007
Therefore, The option A.) 2007 is correct
One ordered pair $(a,b)$ satisfies the two equations $ab^4 = 12$ and $a^5 b^5 = 7776$. what is the value of $a$ in this ordered pair?
Answers
To find the value of a in the ordered pair (a,b), we can solve the given equations. Substituting ab^4 with 12 in the second equation, we get a^5 (12)^5 = 7776. Solving for a gives a = 0.03125^(1/5) = 0.5.
Explanation:To find the value of a in the ordered pair (a,b), we can solve the given equations.
From the first equation, ab^4 = 12, we can substitute ab^4 with 12 in the second equation:
a^5 b^5 = 7776
This gives us:
a^5 (12)^5 = 7776
12^5 = 12 * 12 * 12 * 12 * 12 = 248,832
Dividing both sides of the equation by (12^5) gives:
a^5 = 7776 / (12^5) = 7776 / 248,832 = 0.03125
Taking the fifth root of both sides gives:
a = 0.03125^(1/5) = 0.5
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What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280?
Answers
a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.
Here we are give the initial term so we have to solve to solve for the common ratio...
a(5)=-1280 and a(1)=-5 so
-1280=-5r^(5-1)
-1280=-5r^4
256=r^4
256^(1/4)=r
4=r, so our sequence is:
a(n)=-5(4^(n-1)), so the 7th term is:
a(7)=-5(4^6)
a(7)= -20480
Simplify the expression 3^5*6^-6/3^3*6^-4
A. 180
B. 5/2
C. 1/4
D. 3/20
Answers
= 3^(5-3) 6^(-6+4)
=3^2 6^-2
= 9/36
= 1/4
answer
C. 1/4
A stick 42 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two pieces ?
Answers
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
The answer is 14 inches and 28 inches:
Total length of stick = 42 inches.
Let the shorter piece be x inches.
Thus, the longer piece is 2x.
2x + x = 42
3x = 42
x = 14
Therefore, the length of the two pieces are 14 inches and 28 inches.
What is the slope of the line on the graph below?
A. -1/2
B. 1/2
C. 1
D. 2
Answers
---------------------------------------------------------------------
---------------------------------------------------------------------
Work Shown:
Pick any two points on the line. I'm going to pick (0,1) and (1,3)
Label these two points as (x1,y1) and (x2,y2).
So,
(x1,y1) = (0,1) meaning that x1 = 0 and y1 = 1
(x2,y2) = (1,3) meaning that x2 = 1 and y2 = 3
Now use the slope formula
m = (y2 - y1)/(x2 - x1)
m = (3-1)/(1-0)
m = 2/1
m = 2
Going from (0,1) to (1,3) we move 2 units up and 1 unit to the right.
The "2 units up" is the "rise"
The "1 unit to the right" is the "run"
Slope = rise/run = (change in y)/(change in x)
Answer:
d on edge
Step-by-step explanation:
How to convert decimal to binary by hand?
Answers
10 : 2 = 5 | 0
5 : 2 = 2 | 1
2 : 2 = 1 | 0
1 : 2 = 0 | 1
↑
Finally: 10 ( decimal ) = 1010 ( binary )
Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.
Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.
Answers
Answer:
Number One / Letter A
Step-by-step explanation:
Add 2, subtract 2x, then divide by 2.
Hope This Helps!
Find the equation of the perpendicular line passing through the midpoint of the line segment connecting (−1, 7) and (2, 3). incorrect: your answer is incorrect.
Answers
Slope (12,-18),(11,12)
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x2-x1. You will get the fraction -30/1 or -30 which is your slope. Hope that made sense!
The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.
Explanation:The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.
To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:
Slope (m) = (12 - (-18)) / (11 - 12).
This simplifies to Slope (m) = 30 / -1 = -30.
So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.
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What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\
Answers
Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Explanation:-
Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]
To simplify, rewrite the numbers inside the root in the product of primes, we get
[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]
Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.
Am I doing this right?
Answers
What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?
Answers
A=p(1/r/100)^n
A=10000
r=5.9/12=0.5%
10000=p(1+0.5/100)^(4*12)
10000=p(1.005)^48
p=10000/(1.005)^48
p=7,871
the monthly payment will be:
7871/12
=$655.92
Answer:
$234.39
Step-by-step explanation:
The sum of two consecutive integers is 111. find the largest of these integers
Answers
divide 111 in half
111/2 = 55.5
take the whole number above and below 55.5
so you get 55 and 56
55 + 56 = 111
56 is the larger one
Braces are used in interval or roster notation?
Answers
While parenthesis is used in interval notation.
Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Benny start with?
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Solve each proportion. Show your work
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2x/7 = 12/14
x=6
I don't know b i am sorry
cross multiply
(2x)(14) = (7)(12)
28x = 84
x = 84/28
x = 3
3 / (x - 1) = 5/7
cross multiply
5(x-1) = (7)(3)
5x - 5 = 21
5x = 21 + 5
5x = 26
x = 26/5 or 5.2
-x+3+5(2x-6)+9(3x+11) will you answer with work shown and answer
Answers
[tex]#-x + 3 + 5(2x - 6) + 9(3x + 11)# #-x + 3 + 10x - 30 + 27x + 99# Put the common terms together #-x + 10x + 27x + 3 + 99# #36x + 72#[/tex]
Given the point (5, 6) and the slope of 5, find y when x = 21.
Answers
6=5(5)+b
6=25+b
-19=b
y=5x-19
y=5(21)-19
y=105-19
y=86
Final answer: y=86
The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.
Answers
y - 3x = 5...y = 3x + 5
x + (3x + 5) = 61
4x + 5 = 61
4x = 61 - 5
4x = 56
x = 56/4
x = 14
y - 3x = 5
y - 3(14) = 5
y - 42 = 5
y = 42 + 5
y = 47
ur 2 numbers are 14 and 47
Which of the relations given by the following sets of ordered pairs is a function?
Select one:
a. {
(2,4),(2,6),(2,8),(2,10),(2,12)
(2,4),(2,6),(2,8),(2,10),(2,12)
}
b. {
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
(−5,−4),(−4,−3),(−3,−2),(−4,−5),(−2,−1)
}
c. {
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
(0,3),(−6,8),(−3,5),(0,−3),(7,11)
}
d. {
(8,1),(−4,1),(3,5),(0,4),(−1,2)
(8,1),(−4,1),(3,5),(0,4),(−1,2)
}
Answers
ur answer would be D....because ur x values (8,-4,3,0,-1) are all different
Since no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The relation might be put up as a table of ordered pairs. The next step is to determine if each element in the domain matches precisely one element in the range.
A function is a collection of ordered pairs where no two ordered pairs are the same in terms of x-coordinate. A function is defined by an equation that yields such a collection of paired objects.
The relations given by the following sets of ordered pairs is a function is,
d. {(8,1),(−4,1),(3,5),(0,4),(−1,2)(8,1),(−4,1),(3,5),(0,4),(−1,2)}
Thus, no two different ordered pairs have the same x -coordinate, relations D given by the following sets of ordered pairs is a function.
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