Answer:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
On this case n =6 and x =6 we got:
[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]
Step-by-step explanation:
The utility for the combination formula is in order to find the number of ways to order a set of elements
For this case we want to find the following expression:
[tex] 6C6[/tex]
And the general formula for combination is given by:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
On this case n =6 and x =6 we got:
[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]
Which expression is equivalent to -80?
-415
-415
4.V5;
45
Answer:
It would be 4.v5
In how many ways you can put 20 books on 50 shelves so that there is not more than one book on a shelf?
9514 1404 393
Answer:
47129212243960 ≈ 4.713×10^13 if order doesn't matter114660755112113373922453094400000 ≈ 1.147×10^32 if it doesStep-by-step explanation:
If order doesn't matter, the number is the combinations of 50 things taken 20 at a time:
50C20 = 47129212243960 ≈ 4.713×10^13
If order does matter, then the number of ways is this value multiplied by 20!:
50P20 = 114660755112113373922453094400000 ≈ 1.147×10^32
_____
nCk = n!/(k!(n-k)!)
nPk = n!/(n-k)!
A pizza chain monitors the total weight of pepperoni that goes on its deluxe pepperoni pizzas to make sure customers are satisfied and product isn't being wasted. Suppose that for pizzas in this population, these weights are strongly skewed to the left with a mean of 250 g and a standard deviation of 8 g. Management takes a random sample of 64 of these pizzas and calculates the mean weight of the pepperoni on the pizzas. Assume that the pizzas in the sample are independent.
What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas LaTeX: \bar x is within 1 g of the true mean?
Answer:
68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 250, \sigma = 8, n = 64, s = \frac{8}{\sqrt{64}} = 1[/tex]
What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean?
This is the pvalue of Z when X = 64 + 1 = 65 subtracted by the pvalue of Z when X = 64 - 1 = 63. So
X = 65
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 64}{1}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413.
X = 63
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{63 - 64}{1}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
68.26% probability that the mean weight of the pepperoni from the sample of 64 pizzas is within 1 g of the true mean.
in a dog show there will be a gold and silver medal awarded. there are 3 finalists. in how many different ways can the 2 medals be awarded?
Answer: There can be 2 gold 1 silver, 2 silver one gold, 3 silver, or 3 gold.
I'm not really sure if this is correct but I hope this helps:)
What is six thousandths as a number?
Answer:
6000
Step-by-step explanation:
6 six
60 sixty
600 six hundred
6000 six thousand
//have a great day//
Can anyone help me with this question?
Answer:
x= 60°, y = 80°, z = 40°
Step-by-step explanation:
Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.
Hence z= 40° { corresponding angles of parallel lines}
Similarly;
Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.
60° = x° { corresponding angles of parallel lines}
Now looking at the angle between x and y; let's call the angle between them r
And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}
Note that x + r + y = 180°{ angle on a straight line}
y = 180° - ( x + r)
y = 180 - (60+40)
y = 180° - 100°
= 80°
Which calculation could not be used to find the percentage change
between 16 and 20?
look at the image attached and explain why
Answer:
Option (B).
Step-by-step explanation:
Percentage change between two numbers a and b can be calculated by the formula,
% change = [tex]\frac{|b-a|}{a}\times 100[/tex]
Where, (b - a) = Change in values
a = Initial value
If a = 16 and b = 20
Percentage change between 16 and 20 will be,
= [tex](\frac{20-16}{16})\times 100[/tex]
= [tex]\frac{4}{16}\times 100[/tex]
= 25%
If a = 20 and b = 16,
Percentage change = [tex]\frac{|16-20|}{20}\times 100[/tex]
= 20%
Therefore, %change between 16 and 24 may be 16% or 20%.
Option (A),
[tex]\frac{20-16}{16}\times 100[/tex] = 25%
Option (B),
[tex]\frac{20}{16}-1\times 100[/tex] = 1.25 - 1 × 100
= 1.25 - 100
= -98.75%
Option (C),
[tex]100\times \frac{1}{4}[/tex] = 25%
Option (D),
[tex]\frac{(20-16)}{20}\times 100[/tex] = 20%
Therefore, we can not use the calculation used in Option (B).
Find the value of x a)10 b)6 c)5
Please answer this correctly
Answer:
[tex]10\dfrac{5}{8}[/tex]
Step-by-step explanation:
The perimeter of a shape is the sum of the lengths of the sides.
[tex]2\dfrac{1}{8}+3\dfrac{3}{16}+2\dfrac{1}{8}+3\dfrac{3}{16}=10\dfrac{5}{8}[/tex] yards
Hope this helps!
Answer:
10 5/8
Step-by-step explanation:
The perimeter is the sum of all sides
2 1/8 + 3 3/16 + 2 1/8 + 3 3/16
Add the whole numbers
2 + 3 + 2 + 3 = 10
Add the fractions
1/8+ 1/8 + 3 3/16 + 3 3/16
2/8 + 6/16
1/4 + 3/8
2/8+3/8 = 5/8
Put them back together
10 5/8
BACTROBAN ointment contains 2% w/w mupirocin. How many grams of a polyethylene glycol ointment base must be mixed with the contents of a 22-g tube of the BACTROBAN ointment to prepare one having a concentration of 5 mg/g?
Answer:
66g of polyethylene ointment base!
Ying Zyiyu covered the first 300 miles of a trip going at 60 mph and the last hundred going at 40 mph. What was his average speed for the entire trip?
Answer:
53.33mph
Step-by-step explanation:
Let's calculated the total time spent on the journey first;
For the first 300miles the time spent is ;
From Distance = speed× time
time = Distance/ speed
= 300/60 = 5 hours
Similarly for the last 100mile the time taken is ;
100/40 = 2.5 hours
Total time spent = 5 +2.5 = 7.5 hours
Total distance covered 400miles
Therefore average speed = 400/7.5 =53.33mph
Answer:
53.33 mph
Step-by-step explanation:
I just wanted to say that the other guy's answer is correct, I checked :)
An experiment was done to look at whether there is an effect of the number of hours spent practising a musical instrument and gender on the level of musical ability. A sample of 30 (15 men and 15 women) participants who had never learnt to play a musical instrument before were recruited. Participants were randomly allocated to one of three groups that varied in the number of hours they would spend practising every day for 1 year (0 hours, 1 hours, 2 hours). Men and women were divided equally across groups. All participants had a one-hour lesson each week over the course of the year, after which their level of musical skill was measured on a 10-point scale ranging from 0 (you can’t play for toffee) to 10 (‘Are you Mozart reincarnated?’). An ANOVA was conducted on these data, and the results revealed significant main effects of gender and the number of hours spent practising. Which of the following contrasts could we use to break down the effect of gender?
A- Helmert contratst
B- Simple contrast
C- Repeated contrast
D- None
Answer: Repeated contrast
Step-by-step explanation:
In the two way ANOVA that was performed above, there were 3 groups of which 30 people (15 men and 15 women) participants who had never learnt to play a musical instrument before were recruited and divided equally.
The ANOVA is of repeated measures. There is within group effect, between group effect and interaction effect. The result also shows significant main effect for the gender and the hours used practicing. Hence, to breakdown the effect of gender, the repeated contrast method will be utilized. The repeated contrast method compares the mean of every level with the succeeding level except the last level.
Joanna went school supply shopping. She spent $33.33 on notebooks and pencils. Notebooks cost
$1.85 each and pencils cost $1.39 each. She bought a total of 21 notebooks and pencils. How many of
each did she buy?
Answer:
Joanna bought 21 items that come out to a total of $33.33. She bought 9 notebooks and 12 pencils.
Step-by-step explanation:
Notebooks (N) = $1.85 Pencils (P) = $1.39
9N+12P= $33.33
9*1.85=16.65
12*1.39=16.68
16.65+16.68=33.33
What is the circumference of the circle shown below (round your answer to nearest tenths)
Answer:
A. 38.3
Step-by-step explanation:
[tex]circumference \\ \: \: \: \: \: = 2 \times radius \times \pi \\ or =diameter \times \pi \\ thus \: the \: answer \: is \\ 12.2 \times 3.14 = 38.3 \\ ( \: a \: ) [/tex]
Find the value of x in the parallelogram below.
Answer:
x=106 degrees
Step-by-step explanation:
The two opposite angles in a parallelogram are always the same and we know 360 degrees in a parallelogram.
x+x+74+74=360.
2x+148=360
2x=212
x=106 degrees
Please answer this correctly without making mistakes
Area = 0.785
Area=0.79
I hope it helps
A truncated cube is a convex polyhedron with 36 edges and 24 vertices. A truncated tetrahedron is a convex polyhedron
with 18 edges and 12 vertices.
How do the number of faces of a truncated cube and a truncated tetrahedron compare?
The truncated cube has 6 more faces than the truncated tetrahedron.
The truncated cube has 8 more faces than the truncated tetrahedron.
The truncated cube has 12 more faces than the truncated tetrahedron.
The truncated cube has 18 more faces than the truncated tetrahedron.
Answer:
The truncated cube has 6 more faces than the truncated tetrahedron.
Step-by-step explanation:
==>Given:
truncated cube=>
edges (E) = 36
vertices (V) = 24
faces (F) = ? (unknown)
According to Euler's polyhedron formula, Vertices (V) - Edges (E) + Faces (F) = 2, let's find how many faces the truncated cube has
=> 24 - 36 + F = 2
- 12 + F = 2
F = 2 + 12
F = 14
truncated tetrahedron=>
edges (E) = 18
vertices (V) = 12
faces (F) = ? (unknown)
Using V - E + F = 2, find F
=>12 - 18 + F = 2
- 6 + F = 2
F = 2 + 6
F = 8
Comparing the faces of the truncated cube (14) and the truncated tetrahedron (8), the truncated cube has 6 more faces than the truncated tetrahedron (14 - 8 = 6)
Answer:
Answer A:The truncated cube has 6 more faces than the truncated tetrahedron.
Step-by-step explanation:
Which numbers are the extremes of the proportion shown below
Answer:
3 and 8 are the extremes of the given proportion (first listed answer option)
Step-by-step explanation:
In a proportion of the type:
[tex]\frac{A}{B} =\frac{C}{D}[/tex]
the values "A" and "D" are called "extremes of the proportion, while "B" and "C" are called the "means" of the proportion.
This comes from writing it as: A : B = C : D
where we observe that A and D are the more "extreme" values being further away from the equal sign than the quantities B and C which are more towards the middle (center of the proportion).
So in your case, the numbers 3 and 8 are the extremes
Answer:
3 and 8
Step-by-step explanation:
The total cost (in dollars) for a company to manufacture and sell x items per week is C = 40 x + 640 , whereas the revenue brought in by selling all x items is R = 66 x − 0.2 x 2 . How many items must be sold to obtain a weekly profit of $ 200 ?
Answer:
The company must sell 60 or 70 items to obtain a weekly profit of 200.
Step-by-step explanation:
The profit is the difference between the revenue and the cost of a given task, therefore:
[tex]\text{profit} = R - C\\\text{profit} = 66*x - 0.2*x^2 - (40*x + 640)\\\text{profit} = 66*x - 0.2*x^2 - 40*x - 640\\\text{profit} = - 0.2*x^2 + 26*x - 640[/tex]
To have a profit of 200, we need to sell:
[tex]-0.2*x^2 + 26*x - 640 = 200\\-0.2*x^2 + 26*x -840 = 0\text{ } *\frac{-1}{0.2}\\x^2 -130 + -4200 = 0\\x_{1,2} = \frac{-(-130) \pm \sqrt{(-130)^2 - 4*1*(-4200)}}{2*1}\\x_{1,2} = \frac{130 \pm \sqrt{16900 + 16800}}{2}\\x_{1,2} = \frac{130 \pm \sqrt{100}}{2}\\x_{1,2} = \frac{130 \pm 10}{2}\\x_{1} = \frac{130 + 10}{2} = \frac{140}{2} = 70\\ x_{2} = \frac{130 - 10}{2} = \frac{120}{2} = 60[/tex]
The company must sell 60 or 70 items to obtain a weekly profit of 200.
OMG THIS QUESTION IS SO HARD WILL RATE IF U GET IT
Answer:
252
Step-by-step explanation:
I have a question about this.
3 lines intersect. A horizontal line with points G, N, K intersects a vertical line with points J, N, M at point N and forms a right angle. The third line contains points H, N, L and intersects the other lines at N. It is diagonal and cuts through angles J N G and M N K. Which statements are true regarding the diagram? AngleGNH and AngleHNJ are complementary. AngleJNK and AngleKNL are supplementary. AngleKNL and AngleLNM are complementary. mAngleHNK + mAngleKNL = 180° mAngleMNG + mAngleGNH = 90°
Answer:
A, C, D
Step-by-step explanation:
Answer: A , C , D
Step-by-step explanation: edge2022
Miles draws three cards at random from a standard deck of 52 cards, without replacement.
(a) Find the probability that all three cards are red.
(b) Find the probability that all three cards have the same rank.
Answer:
P( red, red, red no replacement ) = 2/17
P( 3 cards with same rank, no replacement) = 1/425
Step-by-step explanation:
There are 52 cards, 26 are red
P( red) = red/total =26/ 52 = 1/2
Now draw the second card without replacement
There are 51 cards, 25 are red
P( red) = red/total =25/51
Now draw the third card without replacement
There are 50 cards, 24 are red
P( red) = red/total =24/50 = 12/25
P( red, red, red no replacement ) = 1/2 * 25/51 * 12/25 = 2/17
P ( all have the same rank)
There are 52 cards, 4 of each rank
We don't care what the first rank is, now the second and third draw have to have the same rank as the first
P( rank) = 1/1
Now draw the second card without replacement
There are 51 cards, 3 are left with the same rank
P( same rank) = cards with same rank/total = 3/51
Now draw the third card without replacement
There are 50 cards, 2 are left with the same rank
P( same rank) = cards with same rank/total = 2/50 = 1/25
P( 3 cards with same rank, no replacement) = 1 * 3/51*1/25 = 1/425
Multiply
4.2
x0.6
Type
Type an integer or a decir
Answer:
2.52
Step-by-step explanation:
4.2 × 0.6
Multiply the terms.
= 2.52
Answer:
2.52
hope it helps
Step-by-step explanation:
4.2 x 0.6
To solve this first, you simply multiply 42*06
(Exclude the decimal point)
42 x 6
= 252
Now since there are two numbers after the point (one is 4.2 and one is 0.6)
Move 252 two decimal places to left
= 2.52
Help is appreciated ❤
Simplify the radical expression -2 √250
Answer:
-10 sqrt(10)
Step-by-step explanation:
-2 sqrt(250)
We know that sqrt(ab) = sqrt(a) sqrt(b)
-2 sqrt(25*10)
-2 sqrt(25)*sqrt(10)
-2 *5*sqrt(10)
-10 sqrt(10)
The congressional committees on mathematics and computer science are made up of five representatives each, and a congressional rule is that the two committees must be disjoint. If there are 385 members of congress, how many ways could the committees be selected?
Answer:
The committes can be selected in [tex]1.752507297 \times 10^{19}[/tex] ways
Step-by-step explanation:
The order in which the members are chosen to the committee is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The two committees must be disjoint.
This means that a person cannot be part of both committes.
If there are 385 members of congress, how many ways could the committees be selected?
Since the committes are disjoint, 5(math) + 5(computer science) = 10 people will be chosen from the set of 385. So
[tex]C_{385,10} = \frac{385!}{10!(385-10)!} = 1.752507297 \times 10^{19}[/tex]
The committes can be selected in [tex]1.752507297 \times 10^{19}[/tex] ways
Can someone help me With This
Answer:
D
Step-by-step explanation:
Find out if they match in all of them
Hope this helps
Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of time, the first person standing at point A hears the burst. Six seconds later, the second person standing at point B hears the burst. If the person at point B is due west of the person at point A and if the display is known to occur due north of the person at point A, where did the fireworks display occur? Note that sound travels at 1100 feet per second.
Answer: approximately 5148 feet directly north of point A
This is equivalent to 0.975 miles
==============================================================
Explanation:
Check out figure 1 (attached image below) to see how the drawing is set up.
Points A and B are separated by 2 miles, or 10560 feet. Use the conversion factor 1 mile = 5280 feet.
Because sound travels at roughly 1100 feet per second (assuming all of the conditions are right), this means that after x seconds, the sound wave has traveled a total distance of 1100x feet. This is the distance from A to C. Point C is the firework location.
The distance from B to C is 1100(x+6) feet because it takes 6 more seconds for the soundwave to travel from C to B, compared from C to A.
Note that triangle ABC is a right triangle. The 90 degree angle is at point A.
We can use the pythagorean theorem to solve for x
See figure 2 in the attached images to see the steps on solving for x. The numbers get quite big, though in the end x is fairly small. We end up with x = 4.68, which is approximate due to the 1100 figure being approximate.
This means the sound wave takes about 4.68 seconds to go from point C to point A.
With this x value, we can compute the expression 1100x to get
1100*x = 1100*4.68 = 5,148 feet
To convert this to miles, divide by 5280
(5148)/(5280) = 0.975
Therefore,
5148 feet = 0.975 miles
Solve for x.
6(x - 1) = 9(x + 2)
x = -8
X = -3
X = 3
x = 8
Answer:
[tex]x=-8[/tex]
Step-by-step explanation:
[tex]6\left(x-1\right)=9\left(x+2\right)\\\mathrm{Expand\:}6\left(x-1\right):\quad 6x-6\\6\left(x-1\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=6,\:b=x,\:c=1\\=6x-6\cdot \:1\\\mathrm{Expand\:}9\left(x+2\right):\quad 9x+18\\9\left(x+2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=9,\:b=x,\:c=2\\=9x+9\cdot \:2\\\mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18\\=9x+18\\6x-6=9x+18\\\mathrm{Add\:}6\mathrm{\:to\:both\:sides}[/tex]
[tex]6x-6+6=9x+18+6\\Simplify\\6x=9x+24\\\mathrm{Subtract\:}9x\mathrm{\:from\:both\:sides}\\6x-9x=9x+24-9x\\Simplify\\-3x=24\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{24}{-3}\\Simplify\\\frac{-3x}{-3}=\frac{24}{-3}\\\mathrm{Simplify\:}\frac{-3x}{-3}:\quad x\\\frac{-3x}{-3}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{3x}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{3}{3}=1\\=x\\\mathrm{Simplify\:}\frac{24}{-3}:\quad -8\\\frac{24}{-3}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{24}{3}\\\mathrm{Divide\:the\:numbers:}\:\frac{24}{3}=8\\=-8\\[/tex]
Answer:
x=-8
Step-by-step explanation:
6(x-1)= 9(x+2)
6x-6= 9x+18
6x-9x= 18+6
-3x= 24
-3x÷-3= 24÷-3
x=-8
What is the value of x?
Answer:
Oioj[
Step-by-step explanation:
Step-by-step explanation:
Write the equation to solve it in order to know the exact value of X.