The Probability that no person is next to their partner is 104/105.
Probability of an event E represented by P(E) can be defined as (The number of favorable outcomes )/(Total number of outcomes).
Permutations is defined as arrangement of elements/objects in a particular way.
According to the question ,
8 people can be arranged in 8! ways = 40320ways
First let us find the probability that person is next to their partner.
4 couples can be arranged in 4! ways
and the couple itself can be arranged in 2! ways
Since there are 4 couples ,
Number of arrangement = [tex]4!(2!)^{4}[/tex]
=24x16
=384 ways
Probability that person is next to their partner = [tex]\frac{384}{40320} =\frac{1}{105}[/tex]
and the probability that no person is next to their partner is [tex]1-\frac{1}{105} =\frac{104}{105}[/tex].
Therefore , the probability that no person is next to their partner is [tex]\frac{104}{105}[/tex].
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What is the appropriate measure of variation (spread) for these data points? 47234213985132324365 what are q1 and q3 for these data?
The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.
The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.
Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.
For the given data points, Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.
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The Interquartile Range (IQR) is the appropriate measure of variation for the given data points. Q1 and Q3 are 2 and 5 respectively.
The IQR is a method that gives the value of data at the 25th and 75th percentile. Alternatively, it gives the average of the two values which are nearest to these two percentiles, in case a single value does not exist. These values are called Q1 and Q3.
Because these values are less impacted by outliers than the standard deviation, it is best to use them with skewed data.
For the given data points, Q1 and Q3 are 2 and 5 respectively. Q1 is the average of 5th and 6th values. Q3 is the average of 15th and 16th values.
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The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x)= 10(0.5)". What
is the multiplicative rate of change of the
function?
0.5
2.5
5
Mark this and retum
/ContentViewers/AssessmentViewer/Activit...
The multiplicative rate of a change of the function is 0.5
To solve this question, look at the y coordinates. To get from 10 to 5, and from 5 to 2.5, you divide them by 2. In other words, you multiply them by 0.5. So, the multiplicative rate will be 0 .5.
if we want to find the multiplication. The rate of change of a function, that just means we need to divide one item by the one that comes before it .
An exponential function is a nonlinear function that has the form of. y=abx,wherea≠0,b>0. An exponential function with a > 0 and b > 1, like the one above, represents an exponential growth and the graph of an exponential growth function rises from left to right,this is the multiplicative rate in exponential function.
You can also calculate exponential growth using the formula f(x) = a(1 + r)x, where:
The f(x) term represents the function.
The a variable stands for the beginning value of your data.
The r variable represents the growth rate.
The x variable is the time interval.
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Solve
each of the following equations. Show its solution set on a number line. Check a
your answers.
|5x |=3
Lashonda is participating in a 4 day cross-country biking challenge. she biked for 50,51,63 and miles on the first three days. how many miles does she need to bike on the last day so that her average (mean) is 54 miles per day?
Lashonda biked for 50,51, and 63 miles on the first three days, to make average 54 miles per she needs to bike 52 miles on the last day.
As given,
Lashonda biked for first three days = 50, 51, 63 miles
Let x miles she bike last day
Average = 54 miles per day
Average = (50 + 51 + 63 + x) /4
⇒ 54 = (164 + x) /4
⇒ x = 216-164
⇒ x= 52 miles
Therefore, Lashonda needs to bike 52miles last day to make average 54miles per day.
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During a cake-eating contest, Dave ate three and a half pizza and Daisy
ate two-thirds of a pizza. How many pizzas did they eat altogether?
HELP EXPLAIN STEP BY STEP!
Answer:
4 1/6
Step-by-step explanation:
Dave eats 3 3/6
Daisy eats 4/6
Together they eat 3 1/6
First you have to make it to a common denominator for Dave and Daisy. then you add the fractions.
4 full pizzas plus 1/6 of a pizza
i.e. 4 full pizzas plus one extra slice
======================================================
Explanation:
1/2 = 3/6
2/3 = 4/6
The fractions add to 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 & 1/6
That first "1" is the carry and it adds to the 3 whole pizzas Dave ate. So we have 3+1 = 4 full pizzas consumed, plus an additional 1/6 of a pizza.
This gives the mixed number 4 & 1/6
Check out the diagram below. I show Dave's slices in blue, and Daisy's slices in pink for the first two rows. The third row is the combination of those slices to get 4 full pizzas and 1 extra slice (to represent that extra 1/6). Let me know if you have questions about the diagram, or the steps in general.
4a + 2b - 12ax + 15b = -40x - 52. What is a and b
Answer:
a = 10/3 and b = -196/51.
Step-by-step explanation:
4a + 2b - 12ax + 15b = -40x - 52
Equating coefficients of x:
-12ax = -40x
-12a = -40
a = 40/12
= 10/3.
Equating constants:
4a + 2b + 15b = -52
4a + 17b = -52
Substituting a = 10/3:
40/3 + 17b = -52
17b = -52 - 40/3
b = (-52 - 40/3) / 17
= (-156/ 3 - 40/3) / 17
= -196 / 51
Express this number in scientific notation.
621,000
621,000=
(Use scientific notation. Use the multiplication symbol in the math palette as needed.)
Answer:
6.21 × 10⁵
Step-by-step explanation:
move thee decimal from .21000 thats how you get 5
Ken alone takes x days to finish a project
Anson alone takes 3 days more than Ken
alone to finish the project. If they together
take 2 days to finish the project, find the
value of x.
Are -345° and 2185° co-terminal?
Answer:
No
Step-by-step explanation:
You want to know if angles -345° and 2185° are coterminal.
Coterminal anglesAngles are co-terminal when their terminal sides are coincident. Each angle will have the same measure modulo 360°.
-345° / 360° = -1 remainder 15°
2185° / 360° = 6 remainder 25°
These angles have different values, modulo 360°, so are not co-terminal.
Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards
long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
11 inches : ? yards
The scale used by Wyatt is; 11 inches : 4 yards.
What is defined by the term scale factor?The Scale Factor is utilised to scale forms in various dimensions. The scale factor is a measurement for figures with similar appearances but distinct scales or measures. Assume two circles appear similar but have different radii.The scale factor specifies how much larger or smaller a figure is than the earlier figure.Now, for the given values in question.
For the area of picnic is 84 yards.= long.
The length in the drawing is 31 inches.
Let the scale for yards is 'x'.
Then;
231 inches: 84 yards = 11 inches: x yards
Write in the fraction form,
231/84= 11/x
Cross multiplying;
x = (11×84)/231
x = 4
Thus, scale becomes; 11 inches : 4 yards.
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Rewrite the expression with rational exponents as a radical expression. 7 times x to the two thirds power 9 times the cube root of x to the power of 2 7 times the square root of x to the power of 3 cube root of the quantity 9 times x to the power of 2 square root of the quantity 9 times x to the power of 3
According to the given statement:
Equation one:
(7x)[tex]\frac{2}{3}[/tex]
Equation two:
√(9x)²
Equation three:
√(7x)³
Equation four:
∛(9x)²
Equation five
√(7x)³
What radical expression would that be?Square-root-containing expressions are known as radical expressions. The radical symbol's "radicand" is a number or expression. A radical equation is one that uses radical expressions as the radicands for variables.
According to the given data:The expression's root is represented by the symbol known as the radical. n√x.
The following radical expression can be used to write the given statement:
Equation one:
(7x)[tex]\frac{2}{3}[/tex]
Equation two:
√(9x)²
Equation Three:
√(7x)³
Equation four:
∛(9x)²
Equation Five:
√(7x)³
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I understand that the question you are looking for is:
Rewrite the expression with rational exponents as a radical expression.
7 times x to the two thirds power9 times the cube root of x to the power of 2 7 times the square root of x to the power of 3cube root of the quantity 9 times x to the power of 2square root of the quantity 9 times x to the power of 3-10+l 6+-17l - - 14 show how you got the answer
The solution to the expression -10 + |6 + -17| -- 14 is 15
How to evaluate the expression?The expression is given as:
-10+l 6+-17l - - 14
Rewrite properly as
-10 + |6 + -17| -- 14
Evaluate the sum and the difference
So, we have:
-10 + |6 + -17| -- 14 = -10 + |-11| + 14
Remove the absolute bracket
-10 + |6 + -17| -- 14 = -10 + 11 + 14
Evaluate the sum
-10 + |6 + -17| -- 14 = 15
Hence, the solution to the expression -10 + |6 + -17| -- 14 is 15
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What values of b satisfy 3(26 + 3)² = 36?
The numeric value of the b is 0.23 which satisfy the given equation.
According to the statement
We have to find that the value of the b.
So, For this purpose, we know that the
The numeric value refers to the worth of each digit depending on where it lies in the number.
From the given information:
The equation is a
3(2b + 3)² = 36
then to find the value of b rearrange the terms then
(2b + 3)² = 12
(2b + 3) = \sqrt{12}
(2b) = \sqrt{12} -3
then
b = \sqrt{12} -3/ 2
b = 3.46 - 3/2
b = 0.46/2
b = 0.23.
So, The numeric value of the b is 0.23 which satisfy the given equation.
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An elementary school is offering 3 language classes one in spanish one in french, if 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
The probability that atleast one students is taking a language class is 0.7
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Let :
Spanish = S ; French = F ; German = G
SnFnG = 3
(SnF) only = 9 - 3 = 6
(SnG) only = 5 - 3 = 2
(FnG) only = 5 - 3 = 2
S only = 28 - (6+3+2) = 17
F only = 21 - (2+3+2) = 14
G only = 12 - (6+3+2) = 1
Student not taking any of the classes are;
(100 - (17+14+1+2+2+6+3))
100 - 45 = 55
Atleast 1 is taking a language class out of 2 selected
The probability that atleast one students is taking a language class :
(45/100 * 55/99) + (55/100 * 45/99) + (45/100 * 44/99)
= 0.7
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(MGSE9-12.N.RN.2) Multiply radical expression and write your answer in the simplest radical form. 2√5 (√6 +2). A) 30√2+4√5 B) 2√30+4√5 C) 2√11+4√5 D) 60+4√5
The simplest radical form. 2√5 (√6 +2).
The Simplification form of 2√5 (√6 +2) is B) 2√(30) + 4√5Given that
2√5 (√6 +2)To find
Simplest radical form of 2√5 (√6 +2) = ........?We know that
Simplest radical form is the expression in radical form that, after rationalizing the denominator, leaves no more square roots, cube roots, fourth roots, or other roots to find
So, according to the question
We have
2√5 (√6 +2)To find the simplest radical form of the given problem, we must first solve those brackets, then multiply under root numbers in root and without root numbers with without root numbers.
So now, let's follow that process
We will get,
2√5 (√6 +2) = 2√5 ×√6 +2√5 ×2
= 2√(5×6) + 2×2×√5
= 2√(30) + 4√5
So the radical form of that given problem is B) 2√(30) + 4√5
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Which graph represents the equation y=34x−3?
Answer:
The graph in the top right hand corner.
Hope this helps :)
Step-by-step explanation:
The formula y = mx + b
shows that m is the slope and b is the y-intercept.
m = 34
b = - 3
So to find the equation of the graph I looked at the y-intercept which is -3 and the graph in the right hand corner has a y-inyercept of -3 so that graph represents the equation y = 34x - 3
Reason:
The equation is y = (3/4)x - 3 which is in y = mx+b form
m = slope = 3/4
b = -3 = y intercept
The y intercept of -3 means the point (0,-3) is on the line. Start at this point and go up 3, then to the right 4 to arrive at (4,0) which is the x intercept. The motion "up 3, right 4" is directly from the slope 3/4
slope = rise/run = 3/4
rise = 3 = go up 3
run = 4 = go right 4
mina's explanation: i counted up from 15.75 to 176.3 to find the difference. i underlined each number i added on each line.
160.55 is the difference. i underlined each number i added on each line.
What is an linear equation in math?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
The two numbers are 15.75 and 176.3
First we will compare the numbers.
1. A=176.3
2. B=15.75
one's place of A is greater than once place of B.
tens place of A is greater than tens place of B.
Hundred place of A is greater than hundred place of B.
So, A>B
So we will subtract 15.75 from 176.3.
176.30 -15.75=
176.30 ----A
- 1 5.75 ----B
Hundreths place of A - Hundreths place of B = 0-5=10-5=5
Tenth place of A - Tenth place of B =12-7=5
ones place of A - ones place of B=5-5=0
Tens place of A - Tens place of B =7-1=6
So the solution is 160.55
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the international shark attack file recorded the number of shark attacks between 1837 and 2016 for 8 different u.s. states.
what is the mean number of shark attacks over these states?
4,8, 5, 13,3,4, 1, 10
The mean of the data given 4, 8,5, 13, 3, 4, 1, 10 shows number of shark attacks over 8 different states is 6.
As given,
Number of different states 'n'= 8
Number of sharks attacks for 8 different states
[tex]x_{i}[/tex] = 4, 8,5, 13, 3, 4, 1, 10
Mean = [tex]\frac{\sum x_{i} }{n}[/tex]
= (4+ 8+ 5 + 13 + 3 + 4 + 1 + 10) /8
=48 /8
=6
Therefore, the mean of the data given 4, 8,5, 13, 3, 4, 1, 10 shows number of shark attacks over 8 different states is 6.
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Answer: 16.0 is the correct answer
Step-by-step explanation:
What is the answer ?
Answer:
xy + z = 16
5(2) = 10 + 6 = 16
Fice card are dealt fom a deck. what is the probability of getting any two distinct face values occuring axactly twice?
The likelihood of any two different face values occurring exactly twice is 0.0475.
Describe probability using an example?
The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.An event's probability grows with its likelihood of happening. Tossing a fair (impartial) coin provides a simple illustration.Two pairs
two pairs = 13C2 *4C2 * 4C2 * 11C1 * 4C1 = 123552
P( two pairs) = 123552/2598960 = 0.0475
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The complete question is -
In a poker game, five cards are dealt at random from an ordinary deck of 52 playing cards. Find the probability of gettingtwo pairs (any two distinct face values occurring exactly twice)
Write an expression that represents the total owed for 4 months of cable at a price of c dollars for each month, plus a one-time equipment fee of $35?
Answer:
4c + 35
Step-by-step explanation:
What every the monthly amount is (c) you would multiply that by 4 to find the cost for 4 months and then you have to add in the one time cost of 35
If f(x) = 24x + 24, find the instantaneous rate of change of f(x) at x = 6
Answer:
168
Step-by-step explanation:
You'd plug 6 in for x
f(x) = 24x + 24
f(6) = 24(6) + 24
f(6) = 144 + 24
f(6) = 168
Segment AC has a length of 60. Find the following values.
DG = 60
Therefore,[tex]4x - 3 + 2x + 21 = 60[/tex]
→[tex]6x+18 = 60 \\ 6x = 60 - 18[/tex]
→[tex]6x = 42[/tex]
Divide both sides by 6
→[tex]x = 7[/tex]
DO =[tex]4x - 3 [/tex]
→[tex]4(7) - 3 \\ 28 - 3[/tex]
DO [tex]= 25[/tex]
OG [tex]= 2x + 21[/tex]
→[tex]2(7) + 21 \\ 14 +21[/tex]
OG [tex]= 35[/tex]
Therefore:
[tex]x = 7[/tex]
[tex]DO = 25 ft[/tex]
[tex]OG = 35 ft[/tex]
I hope this helpsPls help i will give brainly
Answer:
B. y = -1/4x + 2
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So slope is -1/4
Using m = -1/4, y =4, x = -8
y = mx + b
4 = -1/4(-8) + b
4 = 2 + b
b = 2
so y = -1/4x + 2
A polynomial function g(x) has a negative leading coefficient. Certain values of g(x) are given in the following table. x –4 –1 0 1 5 8 12 g(x) 0 –3 –1 –2 0 3 0 If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
By factor theorem and limits, it is found that the end behavior of g(x) is that it goes to negative infinity.
The values of x and g(x) are
x –4 –1 0 1 5 8 12
g(x) 0 –3 –1 –2 0 3 0
We need to find the end behavior of g(x).
What is Factor theorem?The Factor Theorem states that a function with leading coefficient a and zeros x1,x2,x3...xn is defined by:
g(x)=(x-x1)(x-x2)(x-x3)..(x-xn)
By definition of factor theorem,
g(x)=a(x-(-4))(x-12)
g(x)=a(x+4)(x-12)
g(x)=a(x2-8x-48)
The end behavior is the limit of g(x) as x goes to infinity, thus:
lim[tex]lim \lim_{x \to \infty} g(x)= \lim_{x \to \infty} ax^{2} =a*\infty[/tex]
Since the leading coefficient a is negative:
a*infinity= - infinity
Thus the end behaviour of g(x) it goes to negative infinity.
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Create a Box and Whisker Plot using the following data: 13, 16,
17, 19, 23, 24, 25, 27, 30, 32, 35. What is the median of the set
of data?
24 is the median number because it is found to be at the Middle of all digits
What should be added to -7/12 to get 9/16
Answer:
1/48 should be added.
Step-by-step explanation:
If you add 9/16 to -7/12 you will get -1/48. Then do -7/12 + 1/48 and it will give you 9/16.
A loaf of bread 9 in. long is cut into slices 3/8 in. thick.
Answer:
32
Step-by-step explanation:
There is nothing this but the answer is 32.
someone pls help asap thank u so much
Answer: $16.67
Step-by-step explanation:
8% of $48 = 16.67
The first one would be $ 3.59
Explanation- 15% of 23.95 = 3.5925
Rounded off to max. 2 decimal places:
Percentage of
15% of 23.95 ≈ 3.59
The formula for the area of a trapezoid is given. Solve this equation for h, height. a=H(B1+B2)/2
The solution of the equation for h is H = 2a/(B1 + B2)
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to solve the equation for h?The equation is given as
a=H(B1 + B2)/2
The above means that the variable h is represented by the variable H
Multiply both sides of the equation by 2
So, we have
2a = H(B1 + B2)
Divide both sides of the equation by (B1 + B2)
H = 2a/(B1 + B2)
Hence, the solution of the equation for h is H = 2a/(B1 + B2)
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