find the mean absolute deviation {3,4,5,6,7}
Answer:
it's 1.2
Step-by-step explanation:
there's also a calculator online for mad
A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen? Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 28 balloons that can be chosen is . (b) If the store has only 12 red balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question. If the store has only 12 red balloons, then the number of different selections of 28 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let T be the set of all possible selections, assuming that there are at least 28 balloons of each type, let R≤12 be the set of selections in T that contain 12 or fewer red balloons, and let R≥13 be the set of selections from T that contain 13 or more red balloons. Use the relationships among R≤12, R≥13, and T to find that the number of different combinations of 28 balloons that can be chosen is . (c) If the store has only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? (d) If the store has only 12 red balloons and only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
Answer:
(a) [tex]Selection = 6724520[/tex]
(b) [tex]At\ most\ 12 = 6553976[/tex]
(c) [tex]At\ most\ 8 = 6066720[/tex]
(d) [tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638[/tex]
Step-by-step explanation:
Given
[tex]Colors = 8[/tex]
[tex]Balloons = 28[/tex] --- at least
Solving (a): 28 combinations
From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
[tex]n => 28 + 8-1[/tex][tex]= 35[/tex]
[tex]r = 28[/tex]
[tex]Selection = ^{35}^C_{28[/tex]
[tex]Selection = \frac{35!}{(35 - 28)!28!}[/tex]
[tex]Selection = \frac{35!}{7!28!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29}{7!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}[/tex]
[tex]Selection = \frac{33891580800}{5040}[/tex]
[tex]Selection = 6724520[/tex]
Solving (b): At most 12 red balloons
First, we calculate the ways of selecting at least 13 balloons
Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)
So:
[tex]n => 15 + 8 -1 = 22[/tex]
[tex]r = 15[/tex]
Selection of at least 13 =
[tex]At\ least\ 13 = ^{22}C_{15}[/tex]
[tex]At\ least\ 13 = \frac{22!}{(22-15)!15!}[/tex]
[tex]At\ least\ 13 = \frac{22!}{7!15!}[/tex]
[tex]At\ least\ 13 = 170544[/tex]
Ways of selecting at most 12 =
[tex]At\ most\ 12 = Total - At\ least\ 13[/tex] --- Complement rule
[tex]At\ most\ 12 = 6724520- 170544[/tex]
[tex]At\ most\ 12 = 6553976[/tex]
Solving (c): At most 8 blue balloons
First, we calculate the ways of selecting at least 9 balloons
Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)
So:
[tex]n => 19+ 8 -1 = 26[/tex]
[tex]r = 19[/tex]
Selection of at least 9 =
[tex]At\ least\ 9 = ^{26}C_{19}[/tex]
[tex]At\ least\ 9 = \frac{26!}{(26-19)!19!}[/tex]
[tex]At\ least\ 9 = \frac{26!}{7!19!}[/tex]
[tex]At\ least\ 9 = 657800[/tex]
Ways of selecting at most 8 =
[tex]At\ most\ 8 = Total - At\ least\ 9[/tex] --- Complement rule
[tex]At\ most\ 8 = 6724520- 657800[/tex]
[tex]At\ most\ 8 = 6066720[/tex]
Solving (d): 12 red and 8 blue balloons
First, we calculate the ways for selecting 13 red balloons and 9 blue balloons
Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)
So:
[tex]n =6+6-1 = 11[/tex]
[tex]r = 6[/tex]
Selection =
[tex]^{11}C_6 = \frac{11!}{(11-6)!6!}[/tex]
[tex]^{11}C_6 = \frac{11!}{5!6!}[/tex]
[tex]^{11}C_6 = 462[/tex]
Using inclusion/exclusion rule of two sets:
[tex]Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)[/tex]
[tex]Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462[/tex]
[tex]Only\ 12\ red\ and\ only\ 8\ blue\ = 827882[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638[/tex]
Find the exact value under the given conditions.
NEED HELP ON THIS ASAP
Answer:
34
Step-by-step explanation:
6/10 of the class has a pet dog. 27/100 of the class has a pet cat. The rest of the class has a pet fish. What fraction of the class has a pet fish?
Answer:
13/100 have pet fish
Step-by-step explanation:
6/10 = 60/100
60/100 + 27/100 = 87/100 have cats and dogs
that leaves 13/100 have pet fish
please help guys asap
Answer:
28 i think
Step-by-step explanation:
If I have 10 apples, 3 oranges and 7 pears how may oranges do i have?
Answer:
20 oranges.
Step-by-step explanation:
If you add 10 and 3 that gives you 13,
now add the 7 and that should give you 20.
#9 Order of Operations
Evaluate the expression below.
4 x {3 x (2 + 1}} + 3 =
a. 22
b. 28
C. 39
d. 40
Answer:
c=39
Step-by-step explanation:
If C is the incenter of ∆AMD, m∠A M C = 3 x + 6 and m∠ DMC= 8 x − 49.
find ∠ M A D (just numbers, no degrees signs).
Hope this will help you lot.
Answer:
<MAD=66
Step-by-step explanation:
to find x:
8x-49=3x+6
x=11
to find DMC:
8(11)-49
<DMC=39
<ADM=36
to find ADC:
36/2
<ADC=18
Then determine whether the relation is discrete or continuous?
Answer:
Can you please include the complete question?
Step-by-step explanation:
A. one solution
B. infinitely many solutions
C. no solution
solve for x:x - 14 < - 23
Answer:
Step-by-step explanation:
x - 14 < -23
x < -9
With a measurement question built on a multiple rating list scale, ____. participants rate multiple items on a three-point scale the participant is restricted to circling their rating. the data generated are always ordinal None of the above is correct. it is possible to visualize the results better than with other numerical scales.
Answer:
it is possible to visualize the results better than with other numerical scales
Step-by-step explanation:
A rating scale is been set up extract information concerning quantitative as well qualitative attribute.
A rating scale can be regarded as
method of data collection devices in collection of comparative information about as regards a specific research subject. It do comes in form of a multiple-choice question so that values could be assigned to a product by survey respondents. multiple rating list scale gives a better and broad results and give better chance in visualizing the gotten result compare with numerical scales( numerical scale are scales that gives quantitative symbolization as regards attribute).
It should be noted that With a measurement question built on a multiple rating list scale it is possible to visualize the results better than with other numerical scales
All whole numbers greater than 0 are also called the ____________ integers.
Answer: positive integers
Step-by-step explanation:
All whole numbers greater than 0 are also called the positive integers.
Answer:
[tex]\Large \boxed{\sf positive}[/tex]
Step-by-step explanation:
Whole numbers greater than zero on the number line are always positive integersAll whole numbers are integersZero is neither positive or negativePls, help solve this asap..
Answer:
the answer is 8
Step-by-step explanation:
3(8^2) + 1
8^2 = 64
64 x 3 = 192
192 +1 =193
Can someone help having trouble solving this question
Answer:
114
Step-by-step explanation:
to get the degrees of hexagon u should know first the greatest degree so you can subtract the others from it and how to get that
by this formula (no of sides-2)*180
(6-2)*180=720
so 138+128+120+160+90=606
and the remaining angle should be 720-606
which is 114
Each of 200 subjects were shown a proposed commercial and asked to identify the marketed product 5 minutes after the viewing. A 95% confidence interval was calculated, but the client indicated that the resultant margin of error is too large and must be one-fourth its current size. How large does the new sample need to be?
Answer:
Step-by-step explanation:
first off we need to know the original sample size and if it is in there then im just cant see it
Blake is going to invest $79,000 and leave it in an account for 9 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Blake to end up with $96,000?
Answer:
r =2.2%
Step-by-step explanation:
Emma is choosing a weekly meeting time. She hopes to have two different
managers attend on a regular basis. The table shows the probabilities that
the managers can attend on the days she is proposing.
Assuming that manager A's availability is independent of manager B's
availability, which day should Emma choose to maximize the probability that
both managers will be available?
A. Monday. The probability that both managers will be available is
0.94.
B. Monday. The probability that both managers will be available is
0.67.
C. Wednesday. The probability that both managers will be available is
0.91.
D. Wednesday. The probability that both managers will be available is
0.71.
Answer:
Probability that both managers can attend:
Monday- 0.73x0.94 = 0.69
Tuesday- 0.78 x 0.91 = 0.71
So, d is correct.
Let me know if this helps!
The day Wednesday choose to maximize the probability that both managers will be available. The probability that both managers will be available is 0.71.
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.
The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Probability that both managers can attend, consider that manager A's availability is independent of manager B's availability,
Monday;
0.73x0.94 = 0.69
Tuesday;
0.78 x 0.91 = 0.71
So, the option d is correct.
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ7
PLEASE ANSWER ASAP FOR BRAINESLT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which values are solutions to × > 7? A. × = 11 and × = 1 B. × = 0 and × = 8 C. × = 8 and × = 11 D. × = -8 and × = 0
Answer:
C
Step-by-step explanation:
Guess how old I am. hints: I'm not really in college, I'm in Middle School. When you find out my age you are in for a shock for I, I am the youngest in my dock. less than 13, higher than 8 once you get it right, it's time to celebrate. P.S (The reason that the category is "Math" is because I am a Mathmagician So don't make this a compotion!)
Which graph represents a function?
Answer:
the bottom graph in the first photo
Step-by-step explanation:
it is a function, unlike the others, because that graph is the only one where the x values dont repeat. in order for it to be a function, the x values cannot repeat
Omar’s tank is 3/10 full. After he buys 11 gallons of gas, it is 4/5 full. How many gallons can Omar’s tank hold?
Answer:
22 gallons.
Step-by-step explanation:
11 gallons took you from 3/10 to 4/5 (same as 8/10).
so the 11 gallons was 5/10- or 1/2 the tank.
if 11 gallons =half a tank, then a full tank is 22 gallons
How many 1/5s are in 1?
Answer:
5!
Step-by-step explanation:
Find the volume........
Answer:
765
Step-by-step explanation:
1/4 xbxaxh
0.5 x 17 x5 x 18
Which equals to 765
Answer:
18X17X5X.5=765
i think
Step-by-step explanation:
all you do is X all the sides and then add a *.5
A manufacturer orders lots of steel rods from a supplier (each lot consists of thousands of rods). Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter. The quality manager accepts a lot if the mean length of the randomly selected sample of 64 rods from that lot is at least 4.005 meters, otherwise the lot is returned to the supplier. a) What percentage of the lots received by the manufacturer will be returned to the supplier
Answer:
84.13% of the lots received by the manufacturer will be returned to the supplier
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 normal distributions can be 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.
Assume that the mean length of the rods in each lot is 4 meters and standard deviation is 0.04 meter.
This means that [tex]\mu = 4, \sigma = 0.04[/tex]
Sample of 64:
This means that [tex]n = 64, s = \frac{0.04}{\sqrt{64}} = 0.005[/tex]
a) What percentage of the lots received by the manufacturer will be returned to the supplier
The proportion is the pvalue of Z when X = 4.005. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{4.005 - 4}{0.005}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413*100% = 84.13%
84.13% of the lots received by the manufacturer will be returned to the supplier
Solve for t. t + -24 = -29 -8
what is t value?
Hope this helps
Step-by-step explanation:
t-24= -37
t= -34+24
t= -13
Answer:
t = -13
Step-by-step explanation:
Add or subtract the numbers
t- 24 = - 37t−24=−37
Separate the constants and variables
t = - 37 + 24t=−37+24
Add or subtract the numbers
t = - 13t
Please help:( I’m stuck on this problem
Answer:
x=33
Step-by-step explanation:
If you didn't know all of the angles in a triangle add up to equal 180
We are given to angles, 90 (the square indicates that its a right angle which is equal to 90) and 57
So to find the missing anlge we subtract the given angles from 180
180-90=90
90-57=33
therefore x=33
Evaluate the following expression.
3 to power of 1
Answer:
3
Step-by-step explanation:
it is 3 3x1 is 3