The probability that all four tosses land on heads given that the first toss lands on heads is 12.5%.
Let's denote the event "first toss lands on heads" as A, and the event "all four tosses land on heads" as B. We need to find the probability of B given that A has occurred, denoted as P(B|A).
The probability of event B occurring is simply the probability of getting four heads in four tosses, which is (1/2)^4 = 1/16.
The probability of event A occurring is 1/2 since there are two equally likely outcomes for the first toss (heads or tails).
To find the conditional probability P(B|A), we use the formula:
P(B|A) = P(A ∩ B) / P(A)
Since event B implies event A (if all four tosses land on heads, then the first toss must land on heads), we have P(A ∩ B) = P(B). Therefore:
P(B|A) = P(B) / P(A) = (1/16) / (1/2) = 1/8.
Converting the probability to a percentage, we have:
P(B|A) = (1/8) × 100 = 12.5%.
Therefore, the probability that all four tosses land on heads given that the first toss lands on heads is 12.5%.
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Given the following data: 46, 47, 110, 56, 71, 109, 63,91, 111,93, 125,78,85, 108,73, 118,70,89,99, 45,73.
Compute the five-number summary and draw the boxplot.
The five-number summary for the given data is as follows: Minimum = 45, First Quartile (Q1) = 71, Median (Q2) = 89, Third Quartile (Q3) = 108, Maximum = 125.
The five-number summary provides key descriptive statistics that summarize the distribution of the data. It consists of the minimum value, the first quartile (Q1), which represents the lower 25% of the data, the median (Q2), which represents the middle value or the 50th percentile, the third quartile (Q3), which represents the upper 25% of the data, and the maximum value.
To draw a boxplot based on this five-number summary, a box is drawn from Q1 to Q3, with a line indicating the median (Q2). Whiskers extend from the box to the minimum and maximum values. Outliers, if present, are represented as individual data points beyond the whiskers.
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Kim's fish is 10 inches long.
Sam's fish is 3 inches long.
How many inches shorter is Sam's fish?
Answer:
7
Step-by-step explanation:
Answer:
Sam's is 7in shorter
Step-by-step explanation:
[tex]10-3=7[/tex]
A university department installed a spam filter on its computer system. During a 21-day period, 6693 messages were tagged as spam. How much spam you get depends on what your online habits are. Here are the counts for some students and faculty in this department (with log-in IDs changed, of course): ID Count ID Count ID Count ID Count AA 1818 BB 1358 CC 442 DD 416 EE 399 FF 389 GG 304 HH 251 || 251 JJ 178 KK 158 LL 103 All other department members received fewer than 100 spam messages. How many did the others receive in total? Make a graph and comment on what you learn from these data. .
The number of people who received fewer than 100 spam messages in the university department is calculated below:
Total number of messages tagged as spam = 6693
Total number of people = 12
Total number of people who received more than 100 spam messages = 11
Number of people who received fewer than 100 spam messages = 1
The number of people who received fewer than 100 spam messages can be calculated by subtracting the total number of people who received more than 100 spam messages from the total number of people in the department.
Thus, the other 1 person received a total of: 6693 - (1818 + 1358 + 442 + 416 + 399 + 389 + 304 + 251 + 251 + 178 + 158 + 103) = 474
Graph illustrating the data collected from students and faculty in the department. it is clear that the majority of students and faculty members in the department received more than 100 spam messages. One person received fewer than 100 spam messages. The number of spam messages received seems to decrease with time, which may indicate that the spam filter is effective.
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A recent national report states the marital status distribution of the male population age 18 or older is as follows: Never Married (32.7%), Married (52.7%), Widowed (2.7%), Divorced (11.9%). The table below shows the results of a random sample of 1704 adult men from California. Test the claim that the distribution from California is as expected at the a-0.01 significance level. a. Complete the table by filling in the expected frequencies. Round to the nearest whole number: Frequencies of Marital Status Outcome Frequency Expected Frequency Never Married 545 Married 892 Widowed 27 Divorced 240 b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? c. What are the null and alternative hypotheses? H: Marital status and residency are dependent. The distribution of marital status in California is the same as it is nationally. The distribution of marital status in California is not the same as it is nationally. Marital status and residency are independent. H: The distribution of marital status in California is the same as it is nationally, The distribution of marital status in California is not the same as it is nationally. O Marital status and residency are independent. O Marital status and residency are dependent. d. The degrees of freedom e. The test-statistic for this data - (Please show your answer to three decimal places.) f. The p-value for this sample - (Please show your answer to four decimal places.) g. The p-value is Select an answer a h. Based on this, we should Select an answer 1. Thus, the final conclusion is... h. Based on this, we should Select an answer 1. Thus, the final conclusion is... There is insufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally. There is sufficient evidence to conclude that the distribution of marital status in California is the same as it is nationally. There is sufficient evidence to conclude that marital status and residency are dependent. There is sufficient evidence to conclude that the distribution of marital status in California is not the same as it is nationally. There is insufficient evidence to conclude that marital status and residency are dependent.
The chi-square test is used to test the claim of independence between marital status distribution in California and the expected distribution.
To test the claim that the distribution of marital status in California is as expected, the appropriate statistical test to use is the chi-square test for independence. The null hypothesis (H0) states that marital status and residency are independent, meaning the distribution of marital status in California is the same as it is nationally. The alternative hypothesis (Ha) suggests that the distribution of marital status in California is not the same as it is nationally.
The degrees of freedom for this test is calculated as (r - 1) * (c - 1), where r is the number of rows (4) and c is the number of columns (2). In this case, the degree of freedom is 3.
Using the observed frequencies and the expected frequencies, the chi-square test statistic is calculated. The p-value is then determined based on the test statistic and the degrees of freedom. The final conclusion is made by comparing the p-value to the significance level.
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You are creating a 4-digit pin code. How many choices are there in the following cases? a. With no restriction, b. No digit is repeated, c. No digit is repeated, 2 and 5 must be present.
the number of choices in each case is:
a. With no restriction: 10,000 choices.
b. No digit is repeated: 5,040 choices.
c. No digit is repeated, 2 and 5 must be present: 56 choices.
Let's calculate the number of choices in each case:
a. With no restriction:
For each digit in a 4-digit pin code, we have 10 choices (0-9). Since there are 4 digits in total, the number of choices is 10⁴ = 10,000.
b. No digit is repeated:
For the first digit, we have 10 choices (0-9).
For the second digit, we have 9 choices (any digit except the one chosen for the first digit).
For the third digit, we have 8 choices (any digit except the two chosen for the first and second digits).
For the fourth digit, we have 7 choices (any digit except the three chosen for the first, second, and third digits).
The total number of choices is 10 * 9 * 8 * 7 = 5,040.
c. No digit is repeated, and 2 and 5 must be present:
We have two fixed digits (2 and 5) that must be present in the pin code.
For the first fixed digit (2), we have only 1 choice.
For the second fixed digit (5), we have only 1 choice.
For the remaining two digits, we have 8 choices each (any digit except 2 and 5).
The total number of choices is 1 * 1 * 8 * 7 = 56
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does anyone know the answer
Answer:
I think it is A.
Step-by-step explanation:
I hope this helps.
6 1⁄6 - 3 5⁄12 =
plz help me with it
Answer:
33/12 or 2.75
Step-by-step explanation:
6 1⁄6 - 3 5⁄12
37/6 - 41/12
74/12 - 41/12
33/12 or 2.75
Can the following angle measures be the interior angles of a triangle: 29°, 29°, and 29° ? Justify your answer.
Answer:
No
Step-by-step explanation:
Angle measures of a triangle must add up to 180 and this only adds up to 87
The circle radius is 12 cm. Then the circle content is
PLEASE HEEEELP
Does anyone know how to do 3 & 4
Answer:
2.True
3. HGK
4. 17°
hope it helps
Find the total surface area of this triangular prism.
Answer:
28 i think
Step-by-step explanation:
Please help me.
Please simplify it and group it in like terms.
3a+6+2a-4+a-2=
Answer:
6a
Step-by-step explanation:
Answer:
6a
Step-by-step explanation:
3a+2a+a= 6a
6-4-2=0
6a+0=6a
Can someone help me with this. Will Mark brainliest.
Answer:
B ( -1, -8)
Step-by-step explanation:
A ( -7, -6)
midpt (-4, -7)
Equation:
(x + 3, y - 1)
Solve for B:
(-4, -7)
(x + 3, y - 1)
( -1, -8)
statistics are used to: a. ask questions b. make estimates of population parameters c. form a basis for analysis d. theoretically specify grouping of study elements
Statistics are used to make estimates of population parameters. Therefore, the correct option is B.
Statistics are used for various purposes in data analysis. One important application of statistics is to make estimates of population parameters. Population parameters are characteristics or measures that describe an entire population. However, it is often impractical or impossible to collect data from the entire population, so statistics provide methods for estimating these parameters based on a sample of the population.
By collecting and analyzing data from a sample, statisticians can make inferences and draw conclusions about the larger population. These estimates help researchers understand the characteristics, patterns, and relationships within the population.
Additionally, statistics form the basis for analysis in many fields, including scientific research, business, social sciences, and more. They provide tools and techniques to summarize, interpret, and draw meaningful insights from data, enabling researchers and decision-makers to make informed choices and draw valid conclusions from their observations and experiments.
Therefore, the correct choice is option b. Statistics play a crucial role in estimating population parameters and providing insights for analysis and decision-making.
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15% of $9.00 is $
I need help!!
Answer:
$ 1.35
Step-by-step explanation:
9 times 0.15 is 1.35
A student is required to solve the initial-value problem as follows:
y ' + 1x+3 y= x2 y-1 , y0= -4.
It is assumed here that x is positive. Then he/she has to find the numerical value of y 2.0, round it off to THREE figures and present the result. A student solved the problem and found that y 2.0 rounded-off to three figures was as follows :
Main Answer: The numerical value of y(2.0) rounded off to three figures is 1.279.
Supporting Explanation:
The student solved the initial-value problem and found that y(2.0) = 1.27977. The question asks to round off the value to three figures. Therefore, we have to keep only the first three digits after the decimal point, which are 279. The next digit after 9 is 7, which means we have to round up the last digit. Thus, the rounded off value of y(2.0) is 1.279.
The initial-value problem is a differential equation that has an initial condition given for a specific value of the independent variable. In this case, the initial condition is y(1) = 2. The solution of the initial-value problem gives the value of y for other values of x. Here, we are required to find the value of y for x = 2.0.
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find the value of each variable 13-17
Answer:
Step-by-step explanation:
Question 13.
By applying cosine rule,
cos(45°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{10}{y}[/tex]
y = 10√2
By applying sine rule,
sin(45°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{x}{y}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{x}{10\sqrt{2} }[/tex]
x = 10
Question 15.
By applying sine rule,
sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{y}{32}[/tex]
y = 16√3
By applying cosine rule,
cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{2}=\frac{x}{32}[/tex]
x = 16
Question 17.
By applying sine rule,
sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{11\sqrt{3} }{y}[/tex]
y = 22
By applying cosine rule,
cos(60°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{2}=\frac{x}{y}[/tex]
[tex]\frac{1}{2}=\frac{x}{22}[/tex]
x = 11
Approximately what percentage of hardcover books sold were nonfiction?
Answer:
B
Step-by-step explanation:
A rabbit is carrying a dominant allele for brown hair (B) and a recessive allele for white hair (b). What is the rabbit's phenotype?
Answer:
B
Step-by-step explanation:
Its dominant because its brown hair.
A dartboard has 20 equally divided wedges, and you are awarded the number of points in the section your dart lands in. If you are equally likely to land in any wedge, what is the probability you will score 10, 11, or 12 points?
Answer: 10 points
Step-by-step explanation:
PLEASE HELP FOR BRAINLIEST! The sum of two numbers is 4 and the difference of their squares is 64. Find the two numbers.
10 and -6
.....................................................
Joe, Josie and Bob has $35 when they put their money together. Joe has half as much as Josie. Bob has four times as much money as Joe. How much money does Josie have?
Answer: $10
Step-by-step explanation:
Let Josie's money be x
Since Joe has half as much as Josie. Joe's money will be: x/2 = 0.5x
Bob has four times as much money as Joe. Bob's money will be = (4 × 0.5x) = 2x
Therefore, we add all the amount together and equate to $35. This will be:
x + 0.5x + 2x = 35
3.5x = 35
x = 35/3.5
x = 10
Josie has $10
(a) Find ged(18675, 20112340) (b) Factor both numbers from (b) above. (c) Find the lem of the two numbers from (b) above.
The lem of 18675 and 20112340 is 2^2 * 3^2 * 5^2 * 7 * 83 * 143659.
(a) To find the greatest common divisor (GCD) of 18675 and 20112340, we can use the Euclidean algorithm. The algorithm involves repeatedly dividing the larger number by the smaller number until the remainder becomes zero.
Using the Euclidean algorithm:
20112340 = 1074 * 18675 + 12590
18675 = 1 * 12590 + 6095
12590 = 2 * 6095 + 4000
6095 = 1 * 4000 + 2095
4000 = 1 * 2095 + 1905
2095 = 1 * 1905 + 190
1905 = 10 * 190 + 15
190 = 12 * 15 + 10
15 = 1 * 10 + 5
10 = 2 * 5 + 0
Since the remainder is now zero, the GCD is the last non-zero remainder, which is 5.
Therefore, ged(18675, 20112340) = 5.
(b) To factor the numbers 18675 and 20112340, we can find their prime factorizations.
Prime factorization of 18675:
18675 = 3^2 * 5^2 * 83
Prime factorization of 20112340:
20112340 = 2^2 * 5 * 7 * 143659
(c) To find the least common multiple (LCM) of 18675 and 20112340, we can use the prime factorizations obtained in the previous step.
The LCM is the product of the highest powers of all the prime factors involved.
Prime factors in the LCM:
2^2 * 3^2 * 5^2 * 7 * 83 * 143659
Therefore, the lem of 18675 and 20112340 is 2^2 * 3^2 * 5^2 * 7 * 83 * 143659.
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HELP ASAP!! In the problem below there is an error in the math. Find the error and write what the error is in complete sentences. You will then work out the problem correctly.
Help help help! This is 40% of my grade and i am stuck.
FIND THE MEASURES OF THE INTERIOR ANGLES
Answer:
Angle A=68
Step-by-step explanation:
68+x+(x-24)=180
68+x+x-24=180
2x+44=180
2x=136
x=68
A. 5 cartoons/toy
B. 12 toys/ cartoon
C. 5 toys/ cartoon
Answer:
c
Step-by-step explanation:
What is the answer for these this question
The following data sets are the math and science test scores, out of 100, for a group of twelve seventh grade students
The interquartile range (IQR) of both the data sets is 8. Create a box plot for each data set Which statement correctly compares
the two data sets?
A. The majority of the math scores are greater than the median of the science scores
B. The majority of the science scores are greater than the median of the math scores
C. The medians of both data sets are equal
D. There is not enough information given to compare the data and medians of the math and science scores
Answer:
The answer and work are in the pdf
Step-by-step explanation:
Answer: A. The majority of the math scores are greater than the median of the science scores
Step-by-step explanation:
I took the test!
A local pet groomer accepts walk-in customers. From experience, the groomer has determined that the probability that a walk-in customer will get a full-service grooming, which includes a bath and nail trimming, is 0.71. The probability that a walk-in customer will get a haircut for their pet is 0.42. The probability that customers who get the full-service grooming will also ask for a haircut is 0.28. What is the probability that a walk-in customer will ask for both a full-service grooming and a haircut?
0.12
0.20
0.28
0.30
Answer:
0.28
Step-by-step explanation:
Answer:
0.20
Step-by-step explanation:
i got it right on edge 2022
Which is the cosine ratio of ∠A?
ACB is right angle triangle. The length of AC is 28, the length of CB is 195, and the length of AB is 197.
A. 195197
B. 28197
C. 28195
D. 19528
Answer:
d . 19528
Step-by-step explanation:
maaf jika salah