In a group of 700 people, must there be 2 who have matching first and last initials? Why? (Assume each person has a first and last name.) Correct: Your answer is correct. . Let A be the set of 700 distinct people and let B be the 52 Incorrect: Your answer is incorrect. different unique combinations of first and last initials. If we construct a function from A to B, then by the Correct: Your answer is correct. principle, the function must be Correct: Your answer is correct. . Therefore, in a group of 700 people, it is Correct: Your answer is correct. that no two people have matching first and last initials.
Answer:
Yes, there are only 676 different possibilities, which is less than the number of people in the group.
Step-by-step explanation:
Assuming that the English alphabet has 26 different letters, the number of possible combinations of first and last name initials is:
[tex]n = 26*26\\n=676[/tex]
If we try to assign a different combination to each person in the group, it would only be possible to do it for the first 676 people, while the remaining 24 would have a repeated first and last initial. Therefore, the answer is yes, there must be 2 people who have matching first and last initials.
The Pigeonhole Principle in mathematics implies in a group of 700 people, there must be at least two people who have matching first and last initials.
Explanation:The concept of this problem involves understanding the Pigeonhole Principle in mathematics. Considering the English alphabet has 26 letters, we can have 26 possible first initials and 26 possible last initials. Therefore, there are 26x26=676 unique combinations of first and last initials. However, we have a group of 700 people which is more than 676. The Pigeonhole Principle states that if you try to distribute more items than there are containers, then at least one container must hold more than one item. Therefore, applying this principle, there must be at least two people among the group of 700 who have matching first and last initials because the number of people (700) is greater than the possible unique combinations of first and last initials (676).
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Can someone please help me solve this
Answer:
30
Step-by-step explanation:
Everything has to add up to 90.
Add EVERYTHING together.
3x + 33
3x + 33 = 90
90 - 33 = 57
57 / 3 = 19
19 = x
19 x 2 = 38
38 - 8 = 30
Answer:
The answer for ∠CDF is 30°.
Step-by-step explanation:
It ia given that complemetary angle is 90° so we can make an expression in terms of x :
It ia given that complemetary angle is 90° so we can make an expression in terms of x :∠AFB + ∠BFC + ∠CFD = 90°
32° + (x+9)° + (2x-8)° = 90°
In order to find ∠CFD, we have to find the value of x first so we have to move all the like-terms to one side :
32° + x + 9° + 2x - 8° = 90°
2x + x = 90° - 32° - 9° + 8°
3x = 57°
Then divide both sides by 3 :
3x ÷ 3 = 57° ÷ 3
x = 19°
We have already found the value of x. Now, the question ask us to find ∠CDF, (2x-8)°. We just have to substitute x value into the expression :
Let x = 19,
∠CDF = 2x - 8
= 2(19) - 8
= 30°
write 0.1 as a fraction in simpliest form
Answer:
1/1000
Step-by-step explanation:
A manufacturer of hard safety hats for construction workers is concerned about the mean and the variation of the forces its helmets transmit to wearers when subjected to a standard external force. The manufacturer desires the mean force transmitted by helmets to be 800 pounds (or less), well under the legal 1000-pound limit, and desires σ to be less than 40. Tests were run on a random sample of n = 40 helmets, and the sample mean and variance were found to be equal to 825 pounds and 2350 pounds2 , respectively.Construct a 95% confidence interval for the population variance.
Answer:
Step-by-step explanation:
Hello!
You need to construct a 95% CI for the population variance of the forces the safety helmets transmit to wearers.
The variable of interest is X: Force a helmet transmits its wearer when an external force is applied (pounds)
Assuming this variable has a normal distribution, the manufacturer expects it to have a mean of μ= 800 pounds and a standard deviation of σ= 40 pounds
A test sample of n=40 was taken and the resulting mean and variance are:
X[bar]= 825 pounds
S²= 2350 pounds²
To estimate the population variance per confidence interval you have to use the following statistic:
[tex]X^2= \frac{(n-1)S^2}{Sigma^2} ~~X^2_{n-1}[/tex]
And the CI is calculated as:
[[tex]\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}}[/tex];[tex]\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}}[/tex]]
[tex]X^2_{n-1;1-\alpha /2}= X^2_{39;0.975}= 58.1[/tex]
[tex]X^2_{n-1;\alpha /2}= X^2_{39;0.025}= 23.7[/tex]
[[tex]\frac{39*2350}{58.1}[/tex];[tex]\frac{39*2350}{23.7}[/tex]]
[1577.45; 3867.09] pounds²
Using a confidence level of 95% you'd expect that the interval [1577.45; 3867.09] pounds² contains the value of the population variance of the force the safety helmets transmit to their wearers when an external force is applied.
I hope this helps!
Consider the following time series data: Month 1 2 3 4 5 6 7 Value 23 14 20 11 19 24 15 (a) Compute MSE using the most recent value as the forecast for the next period. If required, round your answer to one decimal place. What is the forecast for month 8? If required, round your answer to one decimal place. Do not round intermediate calculation. (b) Compute MSE using the average of all the data available as the forecast for the next period. If required, round your answer to one decimal place. Do not round intermediate calculation. What is the forecast for month 8? If required, round your answer to one decimal place. (c) Which method appears to provide the better forecast?
Answer:
a) MSE = 61.33
Forecast for 8th month = 15
b) MSE = 34.51
Forecast for 8th month = 18
c) The average method provides a better forecast because of its low MSE
Explanation:
Check the attached file for the solvings.
To answer this two-part question, you'll need to calculate the mean square errors (MSE) using two different forecasting methods: using the most recent value as a forecast and using the average of all data for a forecast. The one with lower MSE is the correct prediction. The forecast for the next month is always based on the previous value or average value depending on the method.
Explanation:To answer this question, you need to understand how mean square error (MSE) and forecasting work. For (a), we use the last value as the forecast for the next value and compute MSE. For (b), we use the average of all data as the forecast for the next value and calculate the MSE. Finally, we compare which method gives a lower MSE, therefore better forecasting.
For (a), the forecast values would be the previous month's data, i.e., forecast for month 2 is 23, month 3 is 14 and so on. To calculate MSE, you subtract each monthly value from its forecast, square the result and find the average of these squares. The forecast for month 8 would be the value of month 7 which is 15.
For (b), you calculate the average of all the data available and use it as a forecast for all the next periods. The MSE and forecast for month 8 can be calculated in a similar manner as in (a).
In step (c), compare the MSE calculated in step (a) and step (b). A lower MSE indicates a better forecast and consequently represents an accurate choice for a predictive model.
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Can someone please answer this question I am confused
Answer:
Step-by-step explanation:
Maryam showed the location of each vertex of a polygon on the grid below. On a coordinate plane, points are at (1, 3), (4, 1), (3, negative 3), (negative 1, negative 3), and (negative 2, 1). If the points are connected, which statements about the polygon are true? Check all that apply. The polygon has six sides. The polygon is a pentagon. The vertices of the polygon are (–2, 1), (1, 3), (4, 1), (3, –3), and (–1, –3). The polygon has five vertices. The polygon is a heptagon.
Answer:
bcd
Step-by-step explanation:
Answer:
B C D
Step-by-step explanation:
Solve the inequality.
x/3-x-1/2≥1 a. x≤-3 b. x≥-3 c. x≤3 d. x≥3
Answer:
x ≤-9/4
Step-by-step explanation:
x/3-x-1/2≥1
Multiply each side by 6 to get rid of the fractions
6(x/3-x-1/2)≥1*6
2x -6x -3≥6
Combine like terms
-4x-3≥6
Add 3 to each side
-4x-3+3≥6+3
-4x ≥9
Divide each side by -4, remembering to flip the inequality
-4x/-4 ≤9/-4
x ≤-9/4
On solving the inequality x/3 - x - 1/2 ≥ 1, we get x ≤ -3. Hence the correct option is A.
Solve the inequality: x/3 - x - 1/2 ≥ 1
Combine like terms: x/3 - (2x + 1)/2 ≥ 1
Get a common denominator: 2x/6 - 3(2x + 1)/6 ≥ 6/6
Simplify the equation: -4x - 3 ≥ 0
Solve for x: x ≤ -3
what should 2.33 be multiplied by to make a whole number
Answer:
You dont multiply anything, you just round
Step-by-step explanation:
basically, you round the 2.3 to the nearest whole number which is most likely 2 because 3 is under five so it doesnt round up
The number of passengers on coaches travelling along 12 popular scenic routes are 29 42 45 39 36 41 38,37.43,35 and 40 find the mean numbres of passengers on coaches
Dan rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total that is a factor of 15
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
The factors of 15 are numbers that can divide even through 15 without any remainders.
These numbers are 1, 3, 5 and 15;
When we roll two fair dice once, there are about 36 possible out comes and this is the sample space of rolling this fair dice.
1 2 3 4 5 6
1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
2 (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
3 (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
4 (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
5 (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
6 (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The total that will give a factor of 15;
(1, 2) (2, 3) (1, 4) (2, 1) (3, 2) (4, 1)
Out of the 36 possible outcomes, we have 6 whose sum will give a factor of 15;
Probability of this = [tex]\frac{6}{36}[/tex] = [tex]\frac{1}{6}[/tex]
You see that country B can make 60 units of X and no Y at point j, or it can make no X and 30 Y at point f. So, if country B decides to produce point j instead of point f (if can do any point f through j) where it gives up units of Y it gets back X, how many units of X does it gain for each unit of Y given up
Answer:
Country B gaines 2 units of good X , per unit of Good Y sacrifised.
Step-by-step explanation:
Country B's production possibilities in form of goods (X,Y) are :
Point J [Only good X] = (60,0) Pont F [Only good Y] = (0,30)The country can produce 60 units of good X or 30 units of good Y, by complete specialisation in either good & not producing the other good.
The country has more (twice) advantage in producing good X. As, it can produce 2 times more good X, than good Y, from the same available resources.
If it decides to produce at point J, production specialising in Good X: It will produce only good X, no units of Y. This implies that - it gains 2 units of good X per unit of good Y sacrifised, as per their production potential ratio (60:30)
A copy machine makes 36 copies per minute. How many copies does it make in four minutes and 45 seconds?
Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.
Step-by-step explanation:
Let's dissect the question. The copy machine makes 36 copies per minute.
36 per min.
To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.
[tex]36 * 4.75=171[/tex]
It makes 171 copies in 4 minutes and 45 seconds.
HELP PLEASE
Find the are of the circle.Leave your answer in terms of pie
A.9pi ft
B.324pi ft
C.18pi ft
D.81 pi ft
Answer:
A = 81 pi ft^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
The radius is 9
A = pi 9^2
A = 81 pi ft^2
covert the units of weight 32IB 12oz = blank IB ? Help please as fast as you can
Answer:
32¾
Step-by-step explanation:
1 pound (lb) = 16 ounces
12 oz = 12/16 = 3/4 lb
32 pounds 12 oz
32 ¾ lb
Cual es la diferencia entre circulo y circunferencia
A firework rocket is shot upward at a rate of 640ft/sec. Use the projectile formula h= -16t^2 +v0t to determine the times when the height of the firework will be 1,200 feet. Round your answer to the nearest whole number.
Answer:
2 seconds and 38 seconds
Step-by-step explanation:
h=-16t²-vot
1,200=-16t²-640t
turn this into standard form
16t²-640t+1200=0
now plug thes numbers into the quadratice formula
a 16 b -640 c 1200
solve with quadratic formula to get ≅2 and ≅38 seconds
Answer:
t≈2 seconds,t≈38 seconds
Step-by-step explanation:
h=−16t2+ v0t
Step 1. Solve the equation.
1,200= −16t^2+ 640t
We know the velocity, v0, is 640 feet per second.
The height is 1,200 feet. Substitute the values.
This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.
ax^2 + bx + c . = 0
16t^2 −640t + 1,200 = 0
Identify the values of a, b, and c.
a=16, b=−640, c=1,200
Write the quadratic formula.
t=−b± √b2−4ac‾‾‾‾‾‾‾‾
2a
640+ √332,800‾‾‾‾‾‾‾‾ t= √640− √332,800‾‾‾‾‾‾‾
32 32
Rewrite to show two solutions.
t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32
Approximate the answer with a calculator.
t≈2 seconds,t≈38 seconds
Step 2. Check the answer. The check is left to you.
Step 3. Answer the question.
The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.
What is .54444 as a fraction?
Answer:
.54444 = .54444/1 = 5.4444/10 = 54.444/100 = 544.44/1000 = 5444.4/10000 = 54444/100000, any one of those works
Answer:
54/99
Step-by-step explanation:
Casey has a total of 18 pens. Twelve of these pens are blue, and the rest are red.
What is the ratio of blue pens to red pens?
Answer: For every 12 blue pens, she has 6 red pens 12:6
Simplifying this would be: 2:1
Answer:
3 : 1
Step-by-step explanation:
18 : 6
simplified ratio is
3 : 1
Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a two, or the 3rd a three, or . . . , or the 13th a king, or the 14th an ace, or the 15th a two, and so on, we say that a match occurs. Compute the expected number of matches that occur.
Answer:
Expected number of matches that occur = 4 matches
Step-by-step explanation:
First of all, let X_i be the event that when we turn over card i if it matches the required cards face.
Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.
The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;
The expected number of matches when cards are drawn from a standard 52-card deck is 4.
We define a match for each card position as X_i = 1 if a match occurs, and X_i = 0 otherwise. The expectation E(X_i) for each card is 1/13 because the probability of the ith card being an i-matched card (Ace in the 1st position, Two in the 2nd position, and so on up to King in the 13th, then repeat with Ace) is 1/13.
Given there are 52 cards, each having the same pattern of matching, the expected number of matches is computed as:
E(X) = E(X_1 + X_2 + ... + X_52) = E(X_1) + E(X_2) + ... + E(X_52)
Since E(X_i) = 1/13 for all i:
E(X) = 52 * (1/13) = 4
Therefore, the expected number of matches is 4.
estimate 1.3 - (-2.5)
Answer:
3.8
Step-by-step explanation:
Based on the list, how many different-color pants does Megan have to choose from?
Answer:
Whats on the list?????
Step-by-step explanation:
A quality inspector inspect random box of 50 tablets. He discovers 2 are defective. In an order of 2,000 tablets,how many are likely to be defective
Answer:
80
Step-by-step explanation:
So if 50 tablets are made and 2 are defective then it’s 50:2. That means for every 50 tablets are made 2 are defective. And since 50 goes into 2000 40 times, you would multiply 40 x 2 to get 80, the number defective tablets
Suppose a company that makes fitness watches samples 15 watches. They know the probability one of their watches fails, within 1 year of purchase, is 0.12. The chance one watch fails is independent of other watches. What type of distribution will best model the number of watches out of the 15 sampled that fail within 1 year
Answer:
Binomial probability distribution.
Step-by-step explanation:
For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows:
Disk: 269.0 249.3 255.2 252.7 247.0 261.6
Oval: 268.8 260.0 273.5 253.9 278.5 289.4 261.6 280.2
Can you conclude that the mean dissolve times differ between the two shapes?
Answer:
[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]
[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]
So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups
Step-by-step explanation:
Data given and notation
Disk:[269.0 249.3 255.2 252.7 247.0 261.6]
Oval:[ 268.8 260.0 273.5 253.9 278.5 289.4 261.6 280.2]
[tex]\bar X_{D}=255.8[/tex] represent the mean for the sample Disk
[tex]\bar X_{O}=270.74[/tex] represent the mean for the sample Oval
[tex]s_{D}=8.215[/tex] represent the sample standard deviation for the sample Disk
[tex]s_{O}=11.903[/tex] represent the sample standard deviation for the sample Oval
[tex]n_{D}=6[/tex] sample size for the group Disk
[tex]n_{O}=8[/tex] sample size for the group Oval
t would represent the statistic (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the means are different, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{D} = \mu_{O}[/tex]
Alternative hypothesis:[tex]\mu_{D} \neq \mu_{O}[/tex]
If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{D}-\bar X_{O}}{\sqrt{\frac{s^2_{D}}{n_{D}}+\frac{s^2_{O}}{n_{O}}}}[/tex] (1)
t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Calculate the statistic
We can replace in formula (1) the results obtained like this:
[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]
Statistical decision
For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:
[tex]df=n_{D}+n_{O}-2=6+8-2=12[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]
So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups
{71.NS.6b and 18.NS.6c} The three points (4,0), (-6,0), and (-6,-4) form three corners of a rectangle. Determine the coordinates of the fourth point.
Answer:
(4,-4)
Step-by-step explanation:
Diagonals of a rectangle share a common midpoint
(4-6)/2 , (0-4)/2 = (-6+x)/2, (0+y)/2
-2 = -6 + x
x = 4
-4 = y
We determined the fourth point of a rectangle by ensuring that the sides of the rectangle are parallel to the axes and the sides are equal in length. The fourth point of the rectangle formed by the points (4,0), (-6,0), and (-6,-4) is (4,-4).
Explanation:The fourth point of the rectangle should have the same x-coordinate as the point (4,0) and the same y-coordinate as the point (-6,-4). Therefore, the fourth point is (4,-4)
To better understand the reasoning, let's consider the points on a plane. We recall that rectangles have sides of equal length and parallel to the axes. Therefore, since the line connecting (4,0) and (-6,0) is parallel to the x-axis, the fourth point's x-coordinate has to be the same as the point on the opposite side of the rectangle, which is 4. Similarly, as the line connecting (-6,0) and (-6,-4) is parallel to the y-axis, the fourth point's y-coordinate has to equal the y-coordinate of the point on the opposite side (-6,-4), which is -4. Hence, the fourth point is (4,-4).
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Multiply 2 and 1 half by 3 and 1 third
Answer:
8 1/3
Step-by-step explanation:
2 1/2 * 3 1/3
Change each to an improper fraction
2 1/2 = (2*2 +1)/2 = 5/2
3 1/3 = (3*3+1)/3 = 10/3
5/2 *10/3 = 50/6
Divide the top and bottom by 2
25/3
Change to a mixed number
3 goes into 25 8 times with 1 left over
8 1/3
Which of the following are like radicals? Check all of the boxes that apply.
Answer:
3x√x²y, –12x√x²y, x√yx², 2√x²y. or on Edge is A,B,D,F
Step-by-step explanation:
Got 100% on edge...
A die is rolled twice.
What is the probability that the first roll was a 6 and the second roll was an odd number?
Answer:
1/12
Step-by-step explanation:
1/6 * 3/6 (First roll has a one in 6 chance, second 3 in 6)
1*3 / 36 =
3 / 36 =
1/12
What is the probability of picking A-day that begins with the letter s
Answer:
28 or 29%
Step-by-step explanation:
There are 7 days total, 2 of which start with “S”, divide the 2 by 7 to get your percentage of 28-29%
The probability of picking a day that begins with the letter s is 2/7.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
There are seven days in a week, and two of them start with the letter s: Sunday and Saturday.
Now,
The probability of picking a day that begins with the letter s.
= 2/7
Or,
= 0.2857
Or,
= 0.2857 x 100%
= 28.57%.
Thus,
The probability of picking a day that begins with the letter s is 2/7.
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