what is the probalityof rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll
Answers
The probability of rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll is \(\frac{1}{9}\).
There are two main steps involved in solving this problem.
The first step is to figure out the probability of rolling an even number on the first roll of a standard die, which is \(\frac{1}{2}\) since there are three even numbers (2, 4, and 6) and three odd numbers (1, 3, and 5) on a standard die.
The second step is to figure out the probability of rolling a total of 7 in two rolls of the die given that an even number was rolled on the first roll.
This probability can be calculated using conditional probability.
Conditional probability is the probability of an event occurring given that another event has occurred.
In this case, the event we are interested in is rolling a total of 7 in two rolls of a standard die, and the other event is rolling an even number on the first roll of the die.
We can use the following formula to calculate the conditional probability of rolling a total of 7 given that an even number was rolled on the first roll:
\(P(total of 7 | even on first roll) = \frac{P(total of 7 and even on first roll)}{P(even on first roll)}\)
To calculate the numerator of this equation, we need to figure out the probability of rolling a total of 7 and an even number on the first roll of the die.
There are two ways this can happen: either a 2 is rolled on the first roll and a 5 is rolled on the second roll, or a 4 is rolled on the first roll and a 3 is rolled on the second roll.
The probability of each of these events is
\(\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}\)
since there is only one way to roll a 2 or a 4 and one way to roll a 5 or a 3 on a standard die.
Therefore, the numerator of the equation is
\(\frac{1}{36} + \frac{1}{36} =\frac{2}{36} =\frac{1}{18}.\)
To calculate the denominator of the equation, we simply need to use the probability of rolling an even number on the first roll that we calculated earlier, which is \(\frac{1}{2}.\)
Therefore, the conditional probability of rolling a total of 7 given that an even number was rolled on the first roll of a standard die is:
\(P(total of 7 | even on first roll) = \frac{(\frac{1}{18}) }{\frac{1}{2}} =\frac{1}{9}\).
In other words, the probability of rolling a total of 7 in two rolls of a standard die if you get an even number on the first roll is \(\frac{1}{9} .\)
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Related Questions
Consider the sets A and B, where A={3,|B|}A={3,|B|} and B={1,|A|,|B|}.B={1,|A|,|B|}. What are the sets?
Answers
The sets are A= {3} and B= {1,3}.
Solution:
To find the sets of A and B, we need to evaluate |B| and |A|.
|B| is the cardinality of set B which gives the number of elements in set B.
Let us calculate |B|, We have B1, |A|, |B|}. Here |B| is one of the elements in set B.
So, we have |B|=3.Therefore, B= {1,3}. Similarly,
we can calculate the value of |A| as shown below. A={3, |B|} is given. Here |B| is one of the elements of set A.
We have |B|=3.
Therefore, A= {3,3= {3}. The sets are A= {3} and B= {1,3}.
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Use inductive reasoning to predict the next number in the pattern: 832, 208, 52...
A.) 13
B.) -228
C.) -26
D.) 26
Answers
Answer:
A) 13 i think
Step-by-step explanation:
832 , 208 , 52
The difference between 832 and 208 is 624 and then the difference between 208 and 52 is 156. If we check the relation between 624 and 156 which is 624/4 = 156 so then if we divide 156 by 4 we get 39 and then subtract 39 from 52 we get 13.
Answer:
13
Step-by-step explanation:
Inductive reasoning is collecting data to make a conjecture.
The current date - June 12, 2009. what date is atleast 10 years, 3 months, and 17 days after this date? A. September 18, 2021 B. September 29, 2019 C. September 18, 2019 D. September 29, 2021 E. September 18, 2009
Answers
Answer:
B
Step-by-step explanation:
What is the correlation coefficient of these six data points? express your answer as a decimal, fraction, or simple mathematical expression. your fraction does not need to be reduced. x y 0 8 1 11 3 10 4 13 7 10 10 6
Answers
The correlation coefficient is -0.29.
Correlation refers to a process for establishing whether or not relationships exist between two given variables.
In statistics, correlation coefficients are used to quantify the strength of the association between two variables. Like Pearson's correlation, which is frequently employed in linear regression, there are other varieties of correlation coefficients. It is widely used in statistics and is highly well-liked.
X Y X² Y² XY
0 8 0 64 8
1 11 1 121 11
3 10 9 100 30
4 13 16 169 52
7 10 49 100 70
10 6 100 36 60
∑X = 25
∑Y = 58
∑X² = 175
∑Y²= 590
∑XY= 231
r = N×∑XY−(∑X∑Y) / √[N∑x2−(∑x)2][N∑y2−(∑y)2]
Putting all the values,
r = 6*231 - (25*58) / √(6*175-625)(6*590-3364)
r = 1368 - 1450 / √(425)(176)
r = -82/ √ 74800
r = -82/ 273.49
r= -0.29
Therefore, the correlation coefficient is -0.29.
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A certain paint is sold and bought 1 gallon cans in 1 quart cans. The gallon can cost $12 and the carton cost $5. How much do you save per gallon buying the larger can?
Answers
If the paint gallon cost $12 and carton cost is $5 , then the amount saved per gallon buying the larger can is $8 .
We know that 1 gallon is = 4 quarts. So , a one-gallon can is equal to four one-quart cans.
To buy one gallon of paint, we need to buy 4 one-quart cans.
Each one-quart can costs $5, so 4 one-quart cans will cost:
⇒ 4 × $5 = $20 ,
Now, the cost of one gallon of paint if it is bought in one one-gallon can.
⇒ One one-gallon can costs $12.
So , if we buy the larger one-gallon can, we will save:
⇒ $20 - $12 = $8
Therefore, We will save $8 per gallon buying the larger can.
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Identify the true statements about the correlation coefficient, ????. if two variables are negatively correlated, when one variable increases, the other variable also increases. the correlation coefficient is not affected by outliers. a correlation coefficient of zero means that no relationship exists between the two variables. the sign of ???? describes the direction of the association between two variables. when the data points in a scatter plot are randomly scattered, the correlation between the two variables is weak. the value of ???? ranges from negative one to positive one.
Answers
a. Since both a strong-positive and weak-positive correlation are formally considered to be "growing," this is ambiguous (positive slope). In the same way, negative correlation. Speaking strictly in terms of truth or untrue, I would classify this as false
b. This is once more a little tricky. When "r" is zero, there isn't any evidence of a linear link. It doesn't necessarily follow that the variables don't correlate with one another. The answer is probably True if this is a course on statistics for beginners. If not, False.
c. This is simple to understand. Inverse relationships are indicated by negative coefficients. One grows while the other shrinks (or vice versa). False.
d. The range of the coefficient r is [0, 1] (inclusive), not (0,1). In this case, True if the text suggests [0,1].
e. Simple and accurate
f. Plain and simple, FALSE. Quite a high correlation coefficient
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A systematic sampling procedure will be used. The first store will be selected and then every third store. Which stores will be in the sample
Answers
Systematic sampling is a probability sampling technique used in statistical analysis where the elements of a dataset are selected at fixed intervals in the dataset.
It is mostly used in cases where a simple random sample is too costly to perform, for instance, time-wise or financially. When a systematic sampling procedure is used, the first store is selected randomly, then every nth item is picked for the sample until the necessary number of stores is achieved.
The question proposes that a systematic sampling procedure will be used, with the first store picked at random and every third store afterwards to be included in the sample. Let's say that there are 100 stores in total.
If we use this method to select a sample of 20 stores, the first store selected could be the 21st store (a random number between 1 and 3), then every third store would be selected, i.e., the 24th, 27th, 30th, and so on up to the 60th store. It's worth noting that it's possible that the number of stores in the sample will be less than three or more than three.
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I If the game with 3 hits is considered to be recorded in error, it might be removed from the data set. If that happens a. What happens to the mean of the data set? b. What happens to the median of the data set? plot data- 2(0) 3(1) 4(0) 5(0) 6(0) 7(2) 8(4) 9(5) 10(4) 11(4) 12(0) 13(0) .please help
Answers
Answer:
If the game with 3 hits is ignored the data becomes:
7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11a) The mean will increase.
With 3:
(3 + 7*2 + 8*4 + 9*5 + 10*4 + 11*4)/20 = 8.9Without 3:
(7*2 + 8*4 + 9*5 + 10*4 + 11*4)/19 = 9.21b) The median will remain as is.
With 3 and without the median is same = 9A circle has a central angle measuring startfraction 7 pi over 6 endfraction radians that intersects an arc of length 18 cm. what is the length of the radius of the circle? round your answer to the nearest tenth. use 3.14 for pi. 3.7 cm 4.9 cm 14.3 cm 15.4 cm
Answers
The length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm
How to calculate the length of aan arc?The formula for calculating the legnth of an arc is expressed as:
L = rtheta
r is the radius
Theta is the subtended angle
Given the following
18 = r(7pi/6)
7pi r = 18 * 6
7pi r = 108
r = 108/7pi
r = 4.9cm
Hence the length of the radius of the circle with a central angle measuring 7pi/6 is 4.9cm
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Answer:
B or 4.9cm
Step-by-step explanation:
When data is positively skewed the mean will be?
Answers
Dr.Osborne has scheduled Anita Blanchette for a spirometry test and wants you to telephone her the day before the test to prepare her so that optimal results are obtained.
1.) What information do you give Anita before her spirometry so that the best test results can be obtained?
2.) How would you explain the rationale for the performance of this procedure?
Answers
To ensure the best test results, Anita should be provided with the following information before her spirometry:
1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.
2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.
3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.
4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.
The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.
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a poll showed that 60.4% of americans say they believe that some people see the future in their dreams. what is the probability of randomly selecting someone who does not believe that some people see the future in their dreams.
Answers
The probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
Probability is an area of mathematics that deals with the study of chance events.
We have, A poll showed that 60.4% of Americans say they believe that some people see the future in their dreams.
Therefore, the probability of randomly selecting someone who does not believe that some people see the future in their dreams can be calculated as follows:
P(A) = 1 - P(B)
Where,
P(A) = Probability of selecting someone who does not believe that some people see the future in their dreams.
P(B) = Probability of selecting someone who believes that some people see the future in their dreams.
P(A) = 1 - P(B)
⇒ 1 - 60.4/100
⇒39.6/100
⇒ 0.396 or 39.6%
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is 39.6%.
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R language
Create a 4 by 4 matrix
Compute the mean and the variance for each row
Compute the mean and the variance for each column
Answers
Print the results to the console using the `print()` function
In R programming language, a 4x4 matrix can be created using the following command:
matrix(1:16, nrow=4, ncol=4)
The above code creates a 4x4 matrix with elements from 1 to 16.
Now, to compute the mean and variance for each row of the matrix, we can use the following command:apply(matrix, 1, function(x) c(mean(x), var(x)))
Here, we are applying the `apply()` function to the matrix and specifying 1 to indicate row-wise calculations. The `function(x) c(mean(x), var(x))` computes the mean and variance of each row and returns the result as a vector.
To compute the mean and variance for each column of the matrix, we can use the same command but with 2 as the second argument to the `apply()` function:
apply(matrix, 2, function(x) c(mean(x), var(x)))
This will compute the mean and variance for each column and return the result as a vector.
Finally, we need to print the results to the console using the `print()` function:
print(apply(matrix, 1, function(x) c(mean(x), var(x))))
print(apply(matrix, 2, function(x) c(mean(x), var(x))))
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The distance a body falls from rest varies as the square of the time the body is falling. If a body falls 64 ft. in two seconds, how far will it fall in seven seconds?
Answers
Answer:
224
Step-by-step explanation:
Answer:
224 feet
Step-by-step explanation:
So because the body falls from rest at 64 feet in two seconds, we can divide that by two so that the body falls from rest at 32 feet in one second. Since we are talking about in seven seconds, multiply 32 by 7 which equals 224 feet which is your answer.
What is the domain of this relation?
Answers
Answer:
The answer is {-8, -2, 3, 4, 8}
Domain is basically the x,
while range OR image is the y,
while codomain is y values that do not have ties to any x value
Solve.
24 + d = 30 fastt
Answers
To get the answer subtract but 6 is your answer
Solve for x:
4(1 - x) + 2 x=-3( x + 1)
Answers
Answer:
x= -7
Step-by-step explanation:
Simplify both sides of the equation.
4(1−x)+2x=−3(x+1)
(4)(1)+(4)(−x)+2x=(−3)(x)+(−3)(1)(Distribute)
4+−4x+2x=−3x+−3
(−4x+2x)+(4)=−3x−3(Combine Like terms)
Add 3x to both sides.
−2x+4+3x=−3x−3+3x
x+4=−3
Subtract 4 from both sides.
x+4−4=−3−4
x=−7
2x + kx = m solve for x
Answers
Answer:
x=m/2+k , k≠-2
Step-by-step explanation:
2x+kx=m
Factor out x from the expression:
(2+k)x=m
Assume 2+k≠0 and divide both sides of the equation by 2+k:
x=m/2k , 2+k≠0
Rewrite the restriction:
x=m/2+k≠-2
Solution:
x=m/2+k , k≠-2
The value of x in the given expression is x = m / (k+2)
What is an expression?An expression is a mathematical statement containing variables, numerical, and they are related by at least one mathematical operation.
Given an expression, 2x + kx = m
We are asked to rearrange the values and find the value of x.
Therefore,
2x + kx = m
Since, two terms have same variable, therefore, taking x common from both,
x(2+k) = m
x(k+2) = m
Now, transpose (k+2) to right side, we get,
x = m / (k+2)
Hence, we get the value of x as, x = m / (k+2)
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Find the solutions to the equation −16t2+40t+5=10 using the quadratic formula.
Answers
Answer:
x1= \(\frac{5-2\sqrt{5} }{4} \\\) x2=\(\frac{5+2\sqrt{5} }{4}\)
Which side lengths form a right triangle?
Answers
Answer:
c
Step-by-step explanation:
the surface area of a cylinder is 936pi squares meters. the radius is 13m use the formula sa=2b=ph. to find the height of cylinder.
Answers
Answer: The formula for the surface area of a cylinder is:
SA = 2πr^2 + 2πrh
where SA is the surface area, r is the radius, and h is the height.
In this case, we know that the surface area is 936π square meters and the radius is 13 meters. So we can plug those values into the formula and solve for h:
936π = 2π(13^2) + 2π(13)(h)
Simplifying:
936π = 338π + 26πh
936π - 338π = 26πh
598π = 26πh
h = 598/26 = 23
Therefore, the height of the cylinder is 23 meters.
Step-by-step explanation:
Step-by-step explanation:
you made some mistakes with the formula.
the surface area of a cylinder is
the outside mantle area
+
the 2 circle areas on top and bottom.
the outside mantle area is
2×pi×radius×height
the 2 circle areas are
2 × pi×radius²
in total that is
2×pi×radius×height + 2×pi×radius² =
2×pi×radius×(height + radius) = 936pi
2×pi×13×(height + 13) = 936pi
pi×(height + 13) = 36pi
height + 13 = 36
height = 36 - 13 = 23 m
Which table represents a function?
Answers
The answer choice which represents a function among the given answer choices is; Choice B.
Which answer choice represents a function among the given answer choices?According to the given task content; the table which represents a function among the given answer choice is to be identified.
Recall that a function can be defined as a relation in which case; each input value is assigned not more than one value.
By observation, only the answer choice B has a combination of input and output values in which case; each input value is assigned only one output value.
Hence, since a function is a relation which is characterized by assigning only one output value to each input value; the correct answer choice is; Choice B.
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ravelocity would like to test if the average roundtrip airfare between new york and london differs from $1,400. the correct hypothesis statement for this test would be
Answers
The "hypothesis of no change," "status quo," and "conventional wisdom" are all alternative names for the null hypothesis. Unless there is overwhelming evidence to the contrary, the null hypothesis is assumed to be correct.
H0: u = 1: u ≠ 1,400
When testing hypotheses with the P value, the null hypothesis is rejected if?
The evidence against the null hypothesis is stronger when the p-value is smaller (closer to 0).If the p-esteem is not exactly or equivalent to the predetermined importance level α, the invalid speculation is dismissed;The null hypothesis is not rejected otherwise.
A statement of expectation or prediction that will be tested by research is called a research hypothesis. Read up on the subject that interests you before coming up with your research hypothesis.
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Write an equation in slope-intercept form that passes through the point (3,7) and has a y-intercept of 4.
Answers
Answer:
y = x + 4
Step-by-step explanation:
Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)
Slope-Intercept Form: y = mx + b
Step 1: Define variables and points
b = 4
Random point (3, 7)
Step 2: Find slope
m = (7 - 4)/(3 - 0)
m = 3/3
m = 1
y = x + b
Step 3: Rewrite linear equation
y = x + 4
(›)
Which is more, 1 tablespoon or 2 teaspoons?
Answers
Answer: 1 tablespoon
Step-by-step explanation:
Given the equation y+2=5(x-3), identify the point and slope being used in the problem.
A. Point (2, -3), slope 5
B. Point (-2,5), slope3
C. Point (3,-2), slope 5
D. Point (-3, 2), slope 5
Answers
Answer:
Point (3,-2) and Slope = 5
Option C is correct option.
Step-by-step explanation:
Given the equation \(y+2=5(x-3)\), identify the point and slope being used in the problem.
The equation is given in point-slope form
The general equation of point-slope form is: \(y-y_1=m(x-x_1)\)
Where m is slope and (x₁,y₁) is the point
Comparing the given equation \(y+2=5(x-3)\) with general equation we get
m=5,
x₁=3
y₁=-2
So, Point (3,-2) and Slope = 5
Option C is correct option.
Pleasseeee help me It's for a test Mars is extremely far from the Earth. Scientists estimate that it could take astronoauts 245 days to travel from Earth to Mars. This is more than half of a year! Suppose astronauts travel to Mars when the distance between Earth and Mars is 108 million miles. If the trip takes 245 days, on average, how many miles would be traveled each day? In your calculator, write the large number as a multiple of a power of 10 to compute the answer. Round to the nearest mile.
Answers
Answer:
440,816 miles per day
Step-by-step explanation:
PLEASE ANSWER I WILL GIVE CORRECT ANSWER BRAINIEST!!!!!!!!!!!!!!!!!
Answers
Answer:
C- table A and graph B
Step-by-step explanation:
BRAINIEST me pls
Have a nice day!
Answer:
B
Step-by-step explanation:
I hope this helps you out!
PLEASE HURRY IM TIMED!!!!!
Ari decides to run 8.5 kilometers this weekend. He jogs 8.9 laps around the running track on Saturday. How many more kilometers does he need to jog on Sunday?
Venue
Kilometers
Pool
0.05
Running Track
0.4
Which equation shows the first step in solving this problem?
y=8.9x0.4
y=8.5x0.4
y=8.5 divided by 0.4
y=8.9 divided by 0.4
Answers
Answer:
0.4 kmffffffffffffffffffffffffffffffffff
Answer
v=8.5x0.4
Step-by-step explanation:
If point B is reflected across the y axis, what are the coordinates of the new point?
(-3,2)
(-2,-3)
(-2,3)
(3,-2)
Answers
Answer: (3,-2)
Step-by-step explanation: We're reflecting to the y-axis, thus, we're going to reflect to the right.
(-x,-y) ⇒ (x,-y)
Our current coordinate is (-3,-2)...let's convert it now...
(3,-2)
I hope this helps!
Answer:
(3, -2).
Step-by-step explanation:
When you reflect across the y axis the y coordinate stays the same and the x axis changes sign : (x, y) --> (-x, y).
So B (-3, -2) --> (3, -2).