Hence, The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is 2/21.
What is the probability?The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
What is the event in probability?In probability theory, an event is a set of outcomes of an experiment to which a probability is assigned. A single outcome may be an element of many different events, and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes.
The word "ORLANDO" consists of 7 letters,
in this word "ORLANDO" the O letter is 2 times and A is one times
probability of "O" letters is 2/7 before there are two "O"s in total out of the seven letters because we are putting the first letter back before drawing the second.
After that, there are still 2 "O"s and 1 "A" in the bag for the second draw because we placed the first "O" back. Because there is only one "A" out of a possible three letters, the probability of drawing one on the second draw is one in three.
We multiply the probabilities of each occurrence to determine the probability that both will occur:
P("O" on the first draw)* P("A" on the second draw) = (2/7) * (1/3) = 2/21
The theoretical probability of selecting a "O", returning it to the bag, and then selecting a "A" from the collection is therefore 2/21, or roughly 0.095, or 9.5%.
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5 × (10 + 7) = (5 × 10) + (5 ×7)
Answer:
Same equation just using the assocaitive property
Step-by-step explanation:
For example, 8 + (2 + 3) = (8 + 2) + 3 = 13
Hope this helps! =D
a professor at the university of florida wanted to determine if offering video tutorials for the course software would increase student engagement. the engagement ratings are below for a random sample of 5 students before and after implementing the course change. ratings were on a scale between 0 and 50. the higher scores translated to higher student engagement score. student before after 1 30 40 2 20 40 3 32 37 4 43 46 5 48 44 what is the test statistic for the wilcoxon signed rank test? group of answer choices 1
According to the information, he test statistic for this sample is 5.
How to calculate the test statistic for the Wilcoxon signed-rank test?To calculate the test statistic for the Wilcoxon signed-rank test, we need to calculate the differences between the "before" and "after" engagement ratings and rank them in order of their absolute values.
Student Before After Difference Absolute Difference Rank
1 30 40 10 10 1
2 20 40 20 20 2
3 32 37 5 5 3
4 43 46 3 3 4
5 48 44 -4 4 5
The sum of the ranks for the positive differences is 1 + 2 + 3 + 4 = 10, and the sum of the ranks for the negative differences is 5.
The smaller of the two sums (in this case, the sum of the ranks for the negative differences) is the test statistic for the Wilcoxon signed-rank test.
Therefore, the test statistic for this sample is 5.
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When adding or subtracting mixed numbers with like denominators, the numerators ___ , but the denominators ______ .
A. Stay the same
B. change
Answer:
Yo, when you adding or subtracting mixed numbers with the same denominators, the numerators stay chill, they don't change, bro.
But the denominators, they also stay the same, man. It's like keeping things consistent, ya feel me? So the answer is A, dude. Numerators stay put, denominators stay put. It's all good vibes, bro! ✌️
Find the distance, d, of AB.
The distance between A and B is approximately 8.06 units.
In order to find the distance, d, of AB, we need to use the distance formula. The distance formula gives us the distance between two points in a coordinate plane. It is given as:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where (x1, y1) and (x2, y2) are the coordinates of the two points in question.
In this case, A and B are the two points for which we need to find the distance. Let's assume that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2).
Then the distance formula becomes:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
$$d = \sqrt{((8 + 4) - 2)^2 + ((5 - 1) - 3)^2}$$
$$d = \sqrt{(10 - 2)^2 + (4 - 3)^2}$$
$$d = \sqrt{(8)^2 + (1)^2}$$
$$d = \sqrt{64 + 1}$$
$$d \approx \sqrt{65}$$
$$d \approx 8.06$$
Therefore, the distance between A and B is approximately 8.06 units.
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Maggie spent $18. 00 Of $30. 00 In her wallet which decimal represents the fraction of the $30. 00 Maggie spent
The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.
Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.
So, we can write this as a fraction:
$18.00 / $30.00
To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.
$18.00 / $30.00 = 0.6
Another way to say this is that Maggie spent 60% of the money she had in her wallet.
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Three machines are used to produce nails. The table displays the total number of nails produced by the 3 machines
over different lengths of time.
Nail Production with 3 Machines
Time (minutes)
Number of Nails
(thousands)
15
16
45
48
55
593
ON
If each machine produces nails at the same rate, how many nails can 1 machine produce in 1 hour?
nails
One machine can produce 600,000 nails in one hour.
Finding the total number of nails produced by the three machines in a minute and dividing that number by three to obtain the number of nails produced by a single machine in a minute are the first two steps in the solution to this problem.
The number of nails produced by a single machine in an hour can then be calculated by multiplying that number by 60.
Now, we add up the total number of nails produced during :
(15 + 16 + 45 + 48 + 55 + 59 + 3) / 7 = 30
To find the number of nails produced by one machine in one hour, we multiply by 60: 10,000 x 60 = 600,000
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given: weight a: 140 pounds at 17 inches aft of datum weight b: 120 pounds at 110 inches aft of datum weight c: 85 pounds at 210 inches aft of datum based on this information, the cg would be located how far aft of datum?
The center of gravity is located 96.7 inches aft of the datum.
To determine the location of the center of gravity (CG) of the system, we need to calculate the moment of each weight about the datum, and then divide the sum of the moments by the total weight of the system.
The moment of each weight is equal to its weight multiplied by its distance from the datum. In this case:
Moment of weight a = 140 pounds x 17 inches = 2,380 inch-pounds
Moment of weight b = 120 pounds x 110 inches = 13,200 inch-pounds
Moment of weight c = 85 pounds x 210 inches = 17,850 inch-pounds
The total weight of the system is:
Total weight = weight a + weight b + weight c = 140 + 120 + 85 = 345 pounds
Therefore, the location of the CG can be calculated as follows:
CG location = (Moment of weight a + Moment of weight b + Moment of weight c) / Total weight
CG location = (2,380 + 13,200 + 17,850) / 345
CG location = 33,430 / 345
CG location = 96.7 inches aft of datum
As a result, the center of gravity is 96.7 inches aft of the datum.
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Number 7. I don’t understand, what’s the fraction? How do you get fraction and the + a number.
Answer:
A
Step-by-step explanation:
Equation of a line is: y = mx + b where m = slope b = y axis intercept
To find the slope between any two of the given points :
say 18, 100 and 27, 85
m = slope = (y1-y2) / (x1-x2) = (85-100) / ( 27-18) = -15/12 = -5/3
so now you have
y = - 5/3 x + b we still need to find the value of b
use any point to calculate b
say 15, 106
106 = - 5/3 (15) + b
b = ~ 131
the equation is then y = - 5/3 x + 131 closest to answer 'A'
Find the measures of angle a and B. Round to the
nearest degree.
The measure of angle A and B is 29° and 61° respectively
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
The opposite is 6 and the adjascent = 11
Therefore tan (tetha) = 11/6 = 1.833
tetha = tan^-1( 1.833)
= 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore,
angle A = 180-( 61+90)
= 180-151
= 29°
therefore the measure of angle A and B is 29° and 61° respectively.
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21st term: 3,8,13,18 What is the indicated term
The 21st term of the sequence 3, 8, 13, 18, .. is 103
To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as
a(n) = a(1) + (n-1)d
where a(1) is the first term of the sequence, d is the common difference, and n is the term number.
In this case, we have:
a(1) = 3 (the first term)
d = 5 (the common difference)
To find the 21st term, we substitute n = 21 in the formula:
a(21) = a(1) + (21-1)d
a(21) = 3 + 20(5)
a(21) = 103
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find the smallest which 108 must be multiplied to get a perfect square
Answer:
The answer is 3
Step-by-step explanation:
x×108=y
x×2²×3³=y
3×108=324
justin developed the below hypothesis. h1: younger adults (18-28 years old) spend more time on social media than the middle-aged (29-65 years old) group and older adults (older than 65 years old). what statistical test should he use to test his hypothesis?
To verify if older adults and middles ages people spend less time on social media, Justin can use the Analysis of variance (ANOVA) test.
ANOVA is used to compare means across two or more groups. Justin can use this test on the different category of younger adults, middle-aged and older adult. This test is done when there is statistically significant difference between the group of samples.
Justin can utilize post-hoc tests (such as Tukey's HSD and Bonferroni) to identify whether particular groups are statistically different from one another if an ANOVA shows a significant difference.
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Here is a bank statement.
=
$
Responsible Bank
210 2nd Street
Anytown, MH 06930
Andre Person
1729 Euclid Ave
Anytown, MH 06930
Date
2017-10-03 Previous Balance
2017-10-05 Check Number 256
2017-10-06 ATM Deposit - Cash
2017-10-10 Wire Transfer
2017-10-17 Point of Sale - Grocery Store
2017-10-25 Funds Transfer from Savings
2017-10-28 Check Number 257
2017-10-29 Online Payment - Phone Services
Description
Checking Account Statement
Page: 1 of 1
Statement Period
2017-10-01 to 2017-11-01
Withdrawals Deposits
28.50
37.91
16.43
42.00
72.50
45.00
50.00
1. If we put withdrawals and deposits in the same column, how can they be represented?
2. Andre withdraws $40 to buy a music player. What is his new balance?
3. If Andre deposits $100 in this account, will he still be in debt? How do you know?
Account No.
1120635978
Balance
39.87
11.37
56.37
18.46
2.03
52.03
10.03
-62.47
The analysis of the bank statement thus, given below. Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.
What is bank statement analysis?1. If we put withdrawals and deposits in the same column, they can be represented as positive and negative values in a single column. Deposits would be represented with positive values, and withdrawals would be represented with negative values.
2. Andre's new balance would be $16.37. We can calculate this by subtracting $40 (the withdrawal) from his previous balance of $56.37:
$56.37 - $40 = $16.37
3. If Andre deposits $100 in this account, he will no longer be in debt. We can calculate his new balance by adding his previous balance and the deposit, and then subtracting any withdrawals:
$56.37 + $100 = $156.37 (balance after the deposit)
$156.37 - $28.50 - $37.91 - $16.43 - $42.00 - $72.50 - $45.00 - $50.00 - $10.03 - $62.47 = -$49.47
Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.
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Quadrilateral ABCD has vertices A = (2, 5), B = (2, 2), C = (4, 3) and D = (4, 6). Quadrilateral A'B'C'D' is formed when Quadrilateral ABCD is dilated by a scale factor of 2. Which statement is true? Select all that apply
Choose all that apply:
A) None of the answers apply
B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.
C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same.
The statement which is true for the quadrilateral is B.
How to determine which statements are true for the quadrilateral?To dilate a figure by a scale factor of 2, each point of the original figure is multiplied by 2.
So the coordinates of each vertex of A'B'C'D' are twice the coordinates of the corresponding vertex of ABCD.
The coordinates of A' are (4,10), B' are (4,4), C' are (8,6), and D' are (8,12).
To determine which statements are true, we can compare the angles and side lengths of the two quadrilaterals:
A) None of the answers apply. This may be a valid answer, but we should check the other options before concluding that none of them apply.
B) The angles of Quadrilateral ABCD and Quadrilateral A'B'C'D' are the same. This is true because dilation does not change angles. The corresponding angles of the two quadrilaterals are congruent.
C) The side lengths of Quadrilateral ABCD and Quadrilateral A'B'C'D' are not the same. We can see this by calculating the length of each side of both quadrilaterals.
Therefore, the correct answer is B.
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A rock of radioactive material has 500 atoms in it. The number of atoms decreases at a rate of 11% a day. Write an exponential function that models this situation. f(x) type your answer... (1 choose your answer... choose your answer... ✓)^x
Answer:
[tex]f(x) = 500( {.89}^{x} )[/tex]
the anova procedure is a statistical approach for determining whether the means of . a. more than two samples are equal b. two or more populations are equal c. two samples are equal d. two or more samples are equal
The means of two or more populations being equal is determined by a statistical approach for the ANOVA procedure. Option B is correct.
The ANOVA (Analysis of Variance) procedure is a statistical method used to determine whether there is a significant difference between the means of two or more groups. To statistically test the equality of means ANOVA uses F-tests.
The repeated-measures ANOVA is a two-stage process that is described as an analysis of dependencies. This test is used to prove an assumed cause-effect relationship between variables. The conditions that must be met for the results of an ANOVA are Independence, Random Sampling, Large Sample Size, and Normality.
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it is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. an experienced travel agent believes this is wrong. of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. we want to test the travel agent's theory with a hypothesis test. if you used a significance level of 0.05, what is your decision?
Based on the given information, we can set up the following hypotheses for the hypothesis test:
Null Hypothesis (H0): The actual proportion of people taking the cruise within 1 year is equal to the believed proportion of 5%.
Alternative Hypothesis (H1): The actual proportion of people taking the cruise within 1 year is not equal to the believed proportion of 5%.
Let p be the proportion of people taking the cruise within 1 year. We can use the sample proportion, denoted as p-hat, which is calculated as the ratio of the number of people who took the cruise within 1 year (3 in this case) to the total number of people who requested the brochures (100 in this case).
Given that the significance level is 0.05, we can use a z-test to compare the sample proportion with the believed proportion of 5%. The z-test statistic is calculated as:
z = (p-hat - p) / sqrt(p * (1 - p) / n)
where n is the sample size, which is 100 in this case.
Now we can calculate the z-test statistic and compare it with the critical value for a two-tailed test at a significance level of 0.05. If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis; otherwise, we would fail to reject the null hypothesis.
Since the sample proportion p-hat is 3/100 = 0.03, and the believed proportion p is 0.05, we can substitute these values into the z-test formula:
z = (0.03 - 0.05) / sqrt(0.05 * (1 - 0.05) / 100)
Calculating the above expression, we get the value of z. We can then compare this value with the critical value for a two-tailed test at a significance level of 0.05 from a standard normal distribution table or using a statistical calculator.
If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis and conclude that the actual proportion of people taking the cruise within 1 year is different from the believed proportion of 5%. If the calculated z-test statistic falls within the critical value, we would fail to reject the null hypothesis and not conclude that the actual proportion is different from the believed proportion.
Without the actual values of the calculated z-test statistic and the critical value, we cannot provide a specific decision for this hypothesis test. Please note that hypothesis testing requires careful consideration of the sample size, significance level, and other relevant factors, and should be conducted with caution and in consultation with a qualified statistician or expert in statistical analysis.
Walking tours at a park begin every 25 minutes and bus tours begin every 45 minutes. Both tours start at 8:00 a.m. when the park opens. When is the next time the tours will start at the same time?
The next time the walking and bus tours will start at the same time is 11:45 a.m.
What is the lcm?
The LCM is multiple which is useful if fractions need to be expressed in the same name, when the other number is multiple, LCM will have the larger number:
To find out when the walking and bus tours will start at the same time, we need to find the least common multiple (LCM) of 25 and 45, which is the smallest time interval that is a multiple of both 25 minutes and 45 minutes.
The prime factorization of 25 is 5 * 5, and the prime factorization of 45 is 3 * 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in either factorization, so:
LCM = 3 * 3 * 5 * 5 = 225
Therefore, the walking and bus tours will start at the same time every 225 minutes, or 3 hours and 45 minutes. To find the next time they will start at the same time, we need to add 225 minutes to the starting time of 8:00 a.m.
8:00 a.m. + 3 hours and 45 minutes = 11:45 a.m.
Hence, the next time the walking and bus tours will start at the same time is 11:45 a.m.
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We need to simplify it. How would I do this
The simplified expression is 4(x - 3y).
What is logarithmic means ?logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.
Using the following logarithmic identities:
log a (bc) = log a (b) + log a (c)
log a (b/c) = log a (b) - log a (c)
We can simplify the expression as follows:
2㏒4 x - 6 log4 y = 2(㏒4) x - 6(㏒4) y
= 2(㏒4) x - 2(㏒4)3 y
= 2(㏒4)(x - 3y)
Now, we can simplify further by using the fact that ㏒4 = 2:
2(㏒4)(x - 3y) = 2(2)(x - 3y) = 4(x - 3y)
Therefore, the simplified expression is 4(x - 3y).
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2. Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his house t minutes after 7:00 a.m. a. Explain what d(5) = 0.25 means in this context. b. On snowy days, Tyler's school has a 2 hour delayed start time (120 minutes). The function is gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s? c. Write an expression for s in terms of d. A new function, n, is defined as n(t) = d(t +60) explain what this means in terms of Tyler's distance from school.
Answer: a. In this context, d(5) = 0.25 means that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. This is because the function d(t) gives the distance of Tyler from his house t minutes after 7:00 a.m.
b. If d(5) = 0.25, then we know that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. If there is a 120-minute delayed start time, then Tyler will walk for 20 + 120 = 140 minutes to reach his school. We want to find the corresponding point on the function s, which gives Tyler's distance from home t minutes after 7:00 a.m. with a 120-minute delayed start time. Since Tyler walks the same distance regardless of the delayed start time, we can use the same function for s as we did for d. Therefore, s(145) = 1.25, since Tyler is 1 mile away from his house after walking for 140 minutes and then an additional 5 minutes to account for the delayed start time.
c. Since Tyler walks the same distance regardless of the delayed start time, we can express s(t) in terms of d(t) by adding 120 minutes to the time t. Therefore, s(t) = d(t + 120).
d. The function n(t) = d(t + 60) gives Tyler's distance from his house t minutes after 8:00 a.m. This is because adding 60 minutes to t corresponds to adding one hour to the time, which means that Tyler leaves his house at 8:00 a.m. instead of 7:00 a.m. Therefore, n(t) gives Tyler's distance from school one hour after he leaves his house.
Step-by-step explanation:
the quality control manager at a computer manufacturing company believes that the mean life of a computer is 80 months, with a variance of 64 . if he is correct, what is the probability that the mean of a sample of 77 computers would be greater than 82.59 months? round your answer to four decimal places.
The probability that the mean of a sample of 77 computers would be greater than 82.59 months, assuming the population mean is 80 months and the variance is 64, is approximately 0.0606
The situation described can be modeled using a normal distribution, with a mean of 80 months and a standard deviation of the square root of the variance, which is 8 months (since variance = standard deviation squared).
To find the probability that the mean of a sample of 77 computers would be greater than 82.59 months, we need to standardize the sample mean using the formula
z = (x - μ) / (σ / √n)
where
x is the sample mean
μ is the population mean (believed to be 80 months)
σ is the population standard deviation (8 months)
n is the sample size (77)
Plugging in the values, we get
z = (82.59 - 80) / (8 / √77) ≈ 1.55
To find the probability of a z-score being greater than 1.55, we can use a standard normal distribution table or calculator. From the table, we find that the probability of z being greater than 1.55 is approximately 0.0606.
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Any help? Please. Whoever answer it first gets brainliest!
Answer:
[tex]c + 15 > 24[/tex]
[tex]c > 9[/tex]
The additional amount will be more than $9.
Charlie made the following table to record the height of each person in his family.
If Cheyenne and Hannah lay end to end, how far will they reach?
A. 9
B. 9, 1/2
C. 10
D. 8
If f(x) = 5x - 6, which of these is the inverse of f(x)?
A. f^-¹(x) = x/5 +6
B. f^-¹(x) = x/5 -6
C. f^-¹(x) = x+6/5
D. F^-¹(x) = x-6/5
To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.
So, let's start by swapping x and y in the function f(x) = 5x - 6:x = 5y - 6
Next, we'll solve this equation for y:
x + 6 = 5y
y = (x + 6)/5
Therefore, the inverse of f(x) is f^-1(x) = (x + 6)/5, which is option C.A survey found that the ratio of students who play intruments to those who do not was 7/20 of the students do not play an instrument 440 surveyd how many students surveyd play an instument
The number of students surveyed who plays an instrument is 114 students.
The ratio of students who play instruments to those who do not is 7/20, which means that out of every 7+20=27 students, 7 of them play an instrument and 20 of them do not.
If we know that 440 students were surveyed, we can set up a proportion to find the number of students who play an instrument:
7/27 = x/440
To solve for x, we can cross-multiply:
7 * 440 = 27 * x
3080 = 27x
x = 114.07
Since we can't have a fraction of a student, we should round up to the nearest whole number, which means that approximately 114 students surveyed play an instrument.
Therefore, the required answer is 114.
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how many 6 card hands are there (from a standard deck) with at least 3 kings? (enter an integer without commas)
There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.
To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:
Case 1:
Exactly 3 Kings
There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:
4 * (48 choose 3) = 4 * 17,296 = 69,184
Case 2:
Exactly 4 Kings
There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:
4 * (48 choose 2) = 4 * 1.128 = 4.512
Case 3:
Exactly 5 kings
There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:
4*1=4
Case 4:
6 cards are king
There is only one way to choose all 6 cards as king.
Therefore, the total number of 6-card hands with at least 3 kings is:
69,184 + 4,512 + 4 + 1 = 73.701
So there are 73,701 different 6-card hands with at least 3 kings.
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Solve Triangle
Because I Need Answer My Assignment:-)
Good Perfect Complete=Brainlist
Copy Wrong Incomplete=Report
Good Luck Answer Brainly Users:-)
Answer:
x = 4√5 ≈ 8.94 (2 d.p.)
y = 8√5 ≈ 17.89 (2 d.p.)
Step-by-step explanation:
To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).
Geometric Mean Theorem (Leg Rule)The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.
[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]
From inspection of the given right triangle RST:
Altitude = SVHypotenuse = RT = 20Leg 1 = RS = ySegment 1 = RV = 16Leg 2 = ST = xSegment 2 = VT = 4Substitute the values into the formulas:
[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]
Solve the equation for x:
[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]
[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]
[tex]\implies 80=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]
[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]
[tex]\implies x=4\sqrt{5}[/tex]
Solve the equation for y:
[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]
[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]
[tex]\implies 320=y^2[/tex]
[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]
[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]
[tex]\implies y=8\sqrt{5}[/tex]
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches. Which lengths, in inches, could be the length of the third side?
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
Triangle Inequality Theorem:In a triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
We can apply this rule to find the possible lengths of the third side of the triangle, given that the lengths of the two sides are 5.2 inches and 3.1 inches.
Here we have
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches
Let's denote the length of the third side as x. Then, we have:
3.1 + 5.2 > x > 5.2 - 3.1
8.3 > x > 2.1
Therefore, the length of the third side x must be greater than 2.1 inches and less than 8.3 inches.
We can write this as an inequality:
2.1 < x < 8.3
Therefore,
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
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If anyone is reading this, rn i would be so flipping happy if u got this for me ive been waiting for so long and got nothing please answer correctly please
Answer: The answer is A.
Step-by-step explanation: Because I am smart don't underestimate me.
Answer:
C
Step-by-step explanation: (look at attachment)
3x + 4 = -2x -2
By looking at the y-intercepts, you automatically know the answer is C.
The y-intercept of the pink line is 4 because of 3x + 4.
The y-intercept of the blue line is -2, because of -2x - 2.
which combination of factors would definitely cause the confidence interval to become wider? group of answer choices none of these will definitely reduce the width of a confidence interval. use a smaller sample and decrease the level of confidence use a larger sample and increase the level of confidence use a larger sample and decrease the level of confidence use a smaller sample and increase the level of confidence
To reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.
What are the factors?
what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder.
The combination of factors that would definitely cause the confidence interval to become wider is to use a larger sample and increase the level of confidence or to use a smaller sample and increase the level of confidence.
When using a larger sample size, the standard error of the mean decreases, and the interval will become narrower. Conversely, when using a smaller sample size, the standard error of the mean increases, and the interval will become wider. However, increasing the level of confidence will also increase the width of the interval as a wider interval is required to capture the true population parameter with a higher level of confidence.
Therefore, to reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.
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