Answer:
125,970
Step-by-step explanation:
Even if jury are assigned numbers, the order in which they are picked has no importance. That means that it's a combination, not a permutation.
The formula to calculate possible combinations is:
[tex]C(n,r) = \frac{n!}{(r! (n-r)!)}[/tex]
Where n is the global population, and r is the number of selected items.
In our case, n = 20 and r = 12, so...
[tex]C(20,12) = \frac{20!}{(12! (20-12)!)} = 125970[/tex]
There are 125970 different ways to select 12 jury members out of 20 people.
there are 125970 different 12 person juries that can be chosen from a pool of 20 people.
The question is asking how to determine the number of different ways to choose a 12-person jury from a pool of 20 potential jurors. This type of problem is solved using the concept of combinations in mathematics, specifically the binomial coefficient formula which is given by the following:
C(n, k) = n! / (k!(n - k)!)
where:
n represents the total number of items (in this case, jurors).
k represents the number of items to choose (jurors to be selected for the jury).
n! means factorial of n, which is the product of all positive integers up to n.
In this scenario, n = 20 and k = 12. Therefore, the number of different 12 person juries that can be chosen is calculated as:
C(20, 12) = 20! / (12!(20 - 12)!)
Further calculation yields:
C(20, 12) = 20! / (12!8!) = 125970
Therefore, there are 125970 different 12 person juries that can be chosen from a pool of 20 people.
-1/5(x-4) =-2 what is the answer for x
Answer: x=14
Step-by-step explanation:
1. Simplify 1/5(x−4) to (x−4)/5.
(−x−4)/5=−2
2. Multiply both sides by 5.
−x+4=−2×5
3. Simplify 2×5 to 10.
−x+4=−10
4. Regroup terms.
4−x=−10
5. Subtract 4 from both sides.
−x=−10−4
6. Simplify −10−4 to −14.
−x=−14
7. Multiply both sides by −1.
x=14
Use the ratio table to solve the percent problem what percent is 8 out of 40
Answer:
20%
Step-by-step explanation:
So, 40 is the dependent and 8 is the independent
40% divided by 8% equals 5%
100% divided by 20% equals 5%
Using paper folding to construct a line perpendicular to a given line through a point
Answer: upon itself
Step-by-step explanation: apex
The wholesale cost of a sofa is $520. Based on selling price, the original markup was 69%. Find the final sale price after the following series of price changes occurred: a markdown of 13%, a markup of 30%, and a second markdown of 36%. Round each intermediate selling price to the nearest cent.
Answer:
$1214.19
Step-by-step explanation:
Let c and p represent the cost of the sofa and the original selling price, respectively. The original markup was 0.69·p, so we have ...
c + 0.69p = p . . . . . based on selling price, the original markup was 69%
c = p(1 -0.69) = 0.31p . . . . subtract the markup
p = c/0.31 . . . . . . . . . . . . . divide by the coefficient of c
So, the original selling price was ...
520/0.31 ≈ 1677.42
The first markdown decreased the selling price to ...
1677.42 - 0.13·1677.42 = 0.87·1677.42 ≈ 1459.36
The markup increased the selling price to ...
1459.36 +0.30·1459.36 ≈ 1897.17
And the final markdown decreased the selling price to ...
1897.17 -0.36·1897.17 ≈ 1214.19
The final sale price was $1214.19.
Which expression can you substitute in the indicated equation to solve the system below?
x + y = 6
12x + y = 5
1. 6 - y for x in 12x + y = 5
2. 5 + 12x for y in x + y = 6
3. 6 + y for x in 12x + y = 5
4. 5 - x for y in x + y = 6
Final answer:
To solve the system of equations x + y = 6 and 12x + y = 5, substitute 6 - y for x in 12x + y = 5 and solve for y.
Explanation:
To solve the given system of equations x + y = 6 and 12x + y = 5, we need to substitute the value of x or y into the second equation. In this case, substituting 6 - y for x in 12x + y = 5 will allow us to solve for y.
Let's substitute 6 - y for x:
12(6 - y) + y = 5
After simplifying, we get:
72 - 12y + y = 5
Combining like terms:
-11y = -67
Dividing both sides by -11, we find that y = 67/11 or approximately 6.09.
So, option 1: 6 - y for x in 12x + y = 5 is the correct expression to substitute.
Please help me!!!!!!!
Answer:
B(5,2)
Explanation:
AC=8 units
AB must equal 2 units.
If line AC is y=x-3, and x values are -1<x<7 in AC, then B is located in x= 5. Plug x in equation.
y=5-3
y=2
B(5,2)
ind the volume of the pyramid, if the base is a square with the side 3.5 cm and height of the pyramid is 1.5 cm
Answer:
The volume of the pyramid is [tex]6.125\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of the pyramid
h is the height of the pyramid
Find the area of the base B
[tex]B=3.5^{2}= 12.25\ cm^{2}[/tex]
we have
[tex]h=1.5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(12.25)(1.5)[/tex]
[tex]V=6.125\ cm^{3}[/tex]
write the equation of the line
Answer:
y = 1/2x -8
Step-by-step explanation:
The two marked points are 1 unit apart vertically and 2 units apart horizontally. The vertical rise is positive for a positive horizontal run, so the slope is ...
rise/run = 1/2
The y-intercept is the leftmost marked point, at y=-8. Then the slope-intercept form of the equation of the line is ...
y = slope·x + y-intercept
y = 1/2x -8
y intercept,slope,and linear equation=
ANSWER
Y-intercept: 3000
Slope:-275
Linear equation:y=-275x+3000
EXPLANATION
The straight line touches the y-axis at
(0,3000).
The y-intercept is b=3000
The line also passes through (2,2450).
The slope is calculated using the formula,
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex] = \frac{3000 - 2450}{0 - 2} [/tex]
[tex] = \frac{550}{ - 2} = - 275[/tex]
The slope is -275.
The linear equation is given by:
[tex]y = mx + b[/tex]
[tex]y = - 275x + 3000[/tex]
For which values of P and Q does the following equation have infinitely many solutions ?
Px+57=-75x+Q
Answer:
(P, Q) = (-75, 57)
Step-by-step explanation:
The equation will have infinitely many solutions when it is a tautology.
Subtract the right side from the equation:
Px +57 -(-75x +Q) = 0
x(P+75) +(57 -Q) = 0
This will be a tautology (0=0) when ...
P+75 = 0
P = -75
and
57-Q = 0
57 = Q
_____
These values in the original equation make it ...
-75x +57 = -75x +57 . . . . . a tautology, always true
please help
Find the x-intercepts for the parabola defined by the equation below.
y = 2x2 + 2x - 4
A.
(-4, 0) and (2, 0)
B.
(-2, 0) and (1, 0)
C.
(0, -2) and (0, 1)
D.
(0, -4) and (0, 2)
Answer:
B. (-2, 0) and (1, 0)
Step-by-step explanation:
The equation can be factored as ...
y = 2(x^2 +x -2) = 2(x +2)(x -1)
The x-intercepts are the values of x where y=0, so will be the values of x that make one or the other of the binomial factors zero:
x = -2
x = 1
Then the intercept points are (-2, 0) and (1, 0). . . . . . . . . matches choice B
How many 4-digit multiples of 2 are there?
there are 4,500 of 4 digit multiples of 2
Answer:
4500
Step-by-step explanation:
By United States cultural standards, it has been determined that 6 people live comfortably in 1500 square feet of living space. Based on this standard, how many square feet would be needed to comfortably house 200 people? Enter the number only.
Answer:
50,000
Step-by-step explanation:
Set up a proportion:
6/1500 = 200/x
Cross multiply and solve for x:
200x1500 = 6x
300000 = 6x
50000 = x
Answer:
50000
Step-by-step explanation:
Find the "unit rate" for occupancy:
1500 ft²
------------- = 250 ft²/person
6 people
Now multiply this unit rate by 200 people. "people" drops out, and you are left with
250 ft²
--------------- * 200 people = 50,000 ft²
1 person
Enter 50000. 200 people will need 50000 ft² of housing.
A bag contains cars numbered from 1 to 14. Find the Probability of:
a) selecting a prime number or multiple of 4
b) selecting a multiple of 2 or 3
c) selecting 3 or 4
d) selecting 8 or a number less than 8
A)
Prime numbers and numbers with a multiple of four that are between 1 and 14 include: 1, 2, 3, 4, 5, 7, 8, 12, 13.
There are 9 numbers listed.
9/14 = ~0.64285... or roghly 65.3%
B) Numbers between 1 and 14 with the multiples of 2 or 3 include: 2, 4, 6, 8, 9, 10, 12, 14.
There are 8 numbers listed.
8/14 = ~0.5714... or, about 57.14%
C) 3 and 4 is a list of two numbers.
2/14 = 1/7 = ~0.1429, or about 14.9%
D) There is a total of numbers equal to or less than 8 in a list of 1 and 14.
8/14 = ~0.5714... or, about 57.14%
Please help question about currency exchange rate....
If 55LRD=1USD and 100LRD=1CHD
how much does ?CHD=1USD?
Answer:
Step-by-step explanation:
55 LRD = 1 USD
100 LRD = 1 CHD
[tex]1 LRD = \frac{1}{55} USD\\\\100 LRD = \frac{100}{55} USD = 1\frac{45}{55} USD=1\frac{9}{11} USD\\1 CHD = \frac{100}{55} USD\\1 USD = \frac{55}{100} CHD = 0.55CHD[/tex]
What is the simplified form of 4z^2-16z+15/ 2z^2-11z+15
[tex]\frac{4z^2-16z+15}{2z^2-11z+15}[/tex] Factor the numerator and the denominator
[ax² + bx + c]
4z² - 16z + 15 Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.
(a·c) --> (4 · 15) = 60
Factors of 60:
1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10
[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z
4z² - 6z - 10z + 15 Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15
2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:
(2z - 3)(2z - 5)
Do the same for the denominator, and you should get (z - 3)(2z - 5)
Now you have:
[tex]\frac{(2z - 3)(2z-5)}{(z-3)(2z - 5)}[/tex] You can cancel out (2z - 5)
[tex]\frac{2z - 3}{z-3}[/tex]
ANSWER
[tex]\frac{(2z-3)}{(z-3)} [/tex]
EXPLANATION
The given expression is:
[tex] \frac{4z^2-16z+15}{2z^2-11z+15} [/tex]
Let us split the middle terms to get,
[tex]\frac{4z^2-6z - 10z+15}{2z^2-6z - 5z+15} [/tex]
Factor by grouping:
[tex]\frac{2z(2z-3) - 5(2z - 3)}{2z(z-3) - 5(z - 3)} [/tex]
Factor further:
[tex]\frac{(2z - 5)(2z-3)}{(2z - 5)(z-3)} [/tex]
We cancel the common factors,
[tex]\frac{(2z-3)}{(z-3)} [/tex]
where
[tex]z \ne \frac{5}{2} \: or \: z \ne3[/tex]
If the second term of an arithmic progression is -3 and the fourth term is 5, find the ninth term
Answer:
25
Step-by-step explanation:
You can get that the common difference for all of the terms if four by finding the difference between -3 and 5, which gives us four. Using this, we can calculate the last term by doing 5+4*5 which is 25.
Find m∠1 if m∠2=73°, m∠3=107°, m∠4=92°. Justify your response!
Answer:
m∠1 = 92°
Step-by-step explanation:
∠2 corresponds to the supplement of ∠3 if (and only if) lines a and b are parallel. We find that
m∠2 + m∠3 = 73° +107° = 180°
so, the angles are supplementary and lines a and b are parallel.
Angles 4 and 1 are corresponding angles where the line d crosses the parallel lines a and b, so are congruent.
m∠1 = m∠4 = 92°
What is the product of 5/6 and 2/3?
Answer:
The product of [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{3}[/tex] is [tex]\frac{5}{9}[/tex] .
Step-by-step explanation:
Multiply both numerators and denominators.
[tex]\frac{5*2}{6*3}[/tex]
[tex]\frac{10}{18}[/tex]
Simplify this by dividing both the numerator and denominator by 2.
[tex]\frac{10/2}{18/2}[/tex]
[tex]\frac{5}{9}[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{The word product means multiply}[/tex]
[tex]\dfrac{5}{6}\times\dfrac{2}{3}=\ ?\\\\\\\dfrac{5(2)}{6(3)}=\dfrac{5\times2}{6\times3}\\\\\bf{5\times2=10}\\\\\bf{6\times3=18}\\\\\\=\dfrac{10}{18}\\\\\\\text{Both numbers foes into two so we can DIIVIDE it by two}\\\\\\\dfrac{10\div2}{18\div2}=?[/tex]
[tex]10\div2=5\\\\\18\div2= 9\\\\\\\boxed{\boxed{\bf{Answer:\dfrac{5}{9}}}}\checkmark[/tex]
[tex]\text{Good luck on your asignment and enjoy your day!}\\\\\\\frak{LoveYourselfFirst:)}[/tex]
You buy a quart of ice cream that comes in a cylindrical tub. A quart has a volume of about 58 cubic inches. The tub has a height of 5 inches. What is the radius of the ice-cream tub? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
Givens
V = 58 in^3
h = 5 inches
pi = 3.14
Formula
V = pi * r^2 * h
Solution
58 = 3.14 * r^2 * 5
58 = 15.7 * r^2
58/15.7 = r^2
3.6942 = r^2
sqrt(r^2) = sqrt(3.6942)
r = 1.922 which when rounded is
r = 1.92
Answer: r=1.92
given what we know about the equation i can determine what steps are needed to solve this :)
volume
1) V = 58 in^3
we know that h=5inches
2) h = 5 inches
heres what pi equals
3) pi = 3.14
then we use pi in the equation
4)= pi * r^2 * h
heres the solution steps
1)58 = 3.14 * r^2 * 5
2)58 = 15.7 * r^2
3)58/15.7 = r^2
4)3.6942 = r^2
5)sqrt(r^2) = sqrt(3.6942)
6)r = 1.922 then we round and get r = 1.92
so final solution is r = 1.92
×║hope this helps║×
PLZ HELP I BEG YOU 20 POINTS!!!!
Answer:
[tex]b=\frac{g}{x} + \frac{5}{x^{3} } +\frac{1}{x^{2} }[/tex]
Step-by-step explanation:
[tex]10=\frac{5}{-2}-b(-2)^{2} +1\\\\\\9=\frac{5}{-2} -b(4)\\\\-18=5-b(4)\\\\-23=-b(4)\\\\\frac{-23}{4} =-b\\\\\frac{23}{4}=b\\\\\\b=\frac{23}{4}[/tex]
Show the Standard form of this problem
the answer is C. move the decimal place to the left 4 times since it is positive to the 4th power
why does the function k(f(x)) provide a better model for the scatter plot when 4
Answer:
It reduces the distance from the plotted points to the function curve.
Step-by-step explanation:
The goodness of fit of a model is measured by the "residuals", the differences between the given points and the modeled points. The smaller the residuals, the better the model. Any change to the model that will put it closer to the plotted points makes it a better model. The change proposed in your problem statement does that.
Hey help me on this??
Answer:
C
Step-by-step explanation:
Use such properties of logarithms:
[tex]\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa[/tex]
Thus,
[tex]\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).[/tex]
Answer:
The answer is C
Step-by-step explanation:
Use such properties of logarithms:
\log_w\dfrac{a}{b}=\log_wa-\log_wb,\\ \\\log_wa^b=b\log_wa
Thus,
\log_w\dfrac{(x^2-6)^4}{\sqrt[3]{x^2+8} }=\text{use the first property}=\\ \\=\log_w(x^2-6)^4-\log_w\sqrt[3]{x^2+8}=\\ \\=\log_w(x^2-6)^4-\log_w(x^2+8)^{\frac{1}{3}}=\text{use the second property}=\\ \\=4\log(x^2-6)-\dfrac{1}{3}\log_w(x^2+8).
Enter the missing numbers in the boxes to complete the table of equivalent ratios please help me
Answer:
3 : 36 10: 120 6:72
Step-by-step explanation:
60 divided by 5 is 12
3 x 12 = 36
10 x 12 = 120
72/12= 6
3-36
5-60
6-72
10-120
One month equals 12$ saved
Please help on this question
Answer:
26 terms
Step-by-step explanation:
The n-th term of this sequence with a common difference of 5 and a first term of -2 is ...
an = -2 +5(n -1)
The sum of the first n terms is ...
(a1 +an)/2·n = (-2 -2 +5(n -1))/2 ·n = 1573
n(5n -9) = 3146
5n^2 -9n -3146 = 0 . . . . . quadratic in standard form
Using the quadratic formula, we can find the positive solution for n to be ...
n = (9+√((-9)^2-4(5)(-3146)))/(2·5) = (9+√63001)/10 = 260/10 = 26
26 terms must be added to give the desired sum.
_____
Relevant formulas are ...
Sn = n(2a1 +d(n-1))/2 . . . . sum of n terms of arithmetic sequence with first term a1 and common difference d
x = (-b±√(b^2 -4ac))/(2a) . . . . . solutions to ax^2 +bx +c = 0
PLEASE! Someone help me answer this and explain it
Answer:
12.5
Step-by-step explanation:i did that problem before
Which statements are true about the median of a data set?
Check all that apply.
The median isn’t affected much by one outlier.
The median is always affected by one outlier.
The median is the number in the middle on an ordered set of data.
To find the median, find the difference between the highest and lowest numbers.
To find the median of an even data set, find the average of the two middle numbers.
Answer: Third and fifth option
3) The median is the number in the middle on an ordered set of data.
5) To find the middle of an even data set, find the average of the two middle numbers.
Step-by-step explanation:
Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.
For example, for the following set of 7 data:
2, 3, [5], 8, 13
the median is 5.
If the data number is even, for example 10 data:
3, 5, 9, 12, [19, 21], 33, 35, 40, 69
The median is the average between the two data that are in the middle
[tex]\frac{19 +21}{2} = \frac{40}{2} = 20[/tex]
Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example
2, 4, 4.5, 4.8, 5 Median = 4.5
2, 4, 4.5, 67, 1506 Median = 4.5
The median does not represent the difference between the highest and the lowest data.
Therefore the correct affirmations are:
3) The median is the number in the middle on an ordered set of data.
5) To find the middle of an even data set, find the average of the two middle numbers.
If possible, could someone assist me by showing me how to get the plausible answer as I was absent while my professer went over this topic.
Answer:
[tex]7.5m^2[/tex]
Step-by-step explanation:
Divide the composite shape into two shapes, a rectangle and a triangle.
We can see that the rectangle has dimensions of 3 x 2.
We can use the area formula.
[tex]A=b*h[/tex]
[tex]A=3*2[/tex]
[tex]A=6[/tex]
We can also see that the triangle has a height of 3 and a base of 1 (3 - 2).
We can use the area formula.
[tex]A=\frac{1}{2}(b*h)[/tex]
[tex]A=\frac{1}{2}(3)[/tex]
[tex]A=1.5[/tex]
Now we can add these areas together.
[tex]1.5 +6=7.5[/tex]
A bookcase has a mass of 30 kilograms. A book in the bookcase has a mass of 400 grams. How many books of the same mass would it take to equal the mass of the bookcase? A. 75 books B. 120 books C. 750 books D. 1,200 books
Answer: OPTION A
Step-by-step explanation:
You can convert 30 kilograms to grams ([tex]1\ kilogram= 1,000\ grams[/tex]), then:
[tex](30\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=30,000\ grams[/tex]
Then, if a book in the bookcase has a mass of 400 grams and you need to find the number of books of the same mass that would take to equal the mass of the bookcase, you can divide the weight of the bookcase (in grams) by the weigth of one of these books.
Therefore:
[tex]books=\frac{30,000\ grams}{400\ grams}\\\\books=75[/tex]