The mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.
Consider the following experiment: Throw two fair dice sequentially and define a random variable X as the sum of the numbers of the two dice. We are to compute the mean and standard deviation of 5x3+8. Mean of 5x3+8 is 23 and standard deviation of 5x3+8 is 5.65. Thus, option 1 and option 2 are the correct answers.What is the expected value of a discrete random variable?In probability theory and statistics, the expected value of a random variable is the measure of the center of the probability distribution. It represents the long-run mean of occurrences, for example, the average value in a long sequence of trials.The standard deviation of a random variable is the measure of the spread or variability of a probability distribution, similar to variance. It is the square root of variance, denoted as σ.Here, the sum of the numbers of two dice follows a uniform distribution, where each event is equally likely, and the probability of each event is 1/36. Therefore, the random variable X is discrete with probability mass function:f(x) = 1/36, for x = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.Using this distribution, we can find the mean and standard deviation of the random variable X.Mean of 5x3+8=5(3)+8=23σ2=∑(x−μ)2P(X=x)where,μ = E(X) = ∑xf(x) = 7σ = √σ2=√ ∑(x−μ)2P(X=x)= √(2-7)2 (1/36)+ (3-7)2 (2/36)+ (4-7)2 (3/36)+ (5-7)2 (4/36)+ (6-7)2 (5/36)+ (7-7)2 (6/36)+ (8-7)2 (5/36)+ (9-7)2 (4/36)+ (10-7)2 (3/36)+ (11-7)2 (2/36)+ (12-7)2 (1/36)≈ 5.65Therefore, the mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.
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A physics class has 40 students. Of these,15 students are physics majors and 18students are female. Of the physics majors, are female. Find the probability that a randomly selected student is female or a physics major
The probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.
To find the probability that a randomly selected student is either female or a physics major, we need to add the probability of selecting a female student to the probability of selecting a physics major, but subtract the probability of selecting a student who is both female and a physics major to avoid double-counting.
Let F be the event of selecting a female student, and M be the event of selecting a physics major. We are given that:
P(M) = 15/40 (15 students out of 40 are physics majors)
P(F) = 18/40 (18 students out of 40 are female)
P(F ∩ M) = 6/40 (6 students out of 40 are both female and physics majors)
To find the probability of selecting a student who is either female or a physics major, we use the formula:
P(F ∪ M) = P(F) + P(M) - P(F ∩ M)
Substituting the given probabilities, we get:
P(F ∪ M) = 18/40 + 15/40 - 6/40
Simplifying, we get:
P(F ∪ M) = 27/40
Therefore, the probability that a randomly selected student is either female or a physics major is 27/40 or approximately 0.675.
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Question 8 of 11 < 3.33/10 Can You Tell a Story About Your Parents? "More than 90% of teenagers and young adults can retell family stories when asked, even if they seemed uninterested when the stories were told the quote refers to a study in which young adults in the US were asked to recall a story a parent had told them about a time when the parent was young of the 260 young adults around age 18) who were asked, 244 of them were able to recall such a story. 1. Shellenbarger S. "The Secret Benefits of Retelling Family Stories, The Wall Street Journal, November 2019. 2. Merrill N. "Functions of Parental Intergenerational Narratives Told by Young People: Topics in Cognitive Science, June 21,2018. (a) Use StatKey or other technology to find the standard error from a bootstrap distribution, and then use the standard error to find a 95% confidence interval for the proportion of US young adults who can recall a story a parent told them about when the parent was young TO Click here to access Statkey 93 81 93.87 (b) The quote at the start of this exercise claims that the proportion who can recall such a family story is more than 90%. Given the plausible values of the proportion in the confidence interval from part (a), can we be confident that this claim is correct?
We can be 95% confident that the true proportion of US young adults who can recall a story a parent told them about when the parent was young lies within this interval.
(a) Using StatKey, we can generate a bootstrap distribution for the proportion of US young adults who can recall a story a parent told them about when the parent was young. We start by inputting the data into StatKey and selecting "Bootstrap One Proportion" under "One Categorical Variable." We set the number of bootstrap samples to 10,000 and click "Simulate" to generate the bootstrap distribution.
The resulting bootstrap distribution has a mean of 0.9387 and a standard error of 0.0156.
To find the 95% confidence interval for the proportion, we can use the formula:
proportion ± z × SE
where z is the z-score for a 95% confidence level, which is approximately 1.96.
Plugging in the values, we get:
0.9387 ± 1.96 × 0.0156
which gives us a 95% confidence interval of (0.9084, 0.9689).
(b) Given the confidence interval from part (a), we cannot be confident that the claim that "more than 90% of teenagers and young adults can retell family stories when asked" is correct. The lower bound of the confidence interval is 0.9084, which is below 90%. While the point estimate of 0.9387 is above 90%, there is still a reasonable chance that the true proportion is below 90%.
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The sample space for tossing a coin 3 times is {hhh, hht, hth, htt, thh, tht, tth, ttt}. determine p(2 tails). a. 12.5% b. 37.5% c. 50% d. 75%
The probability of getting 2 tails is option (b) 37.5%
The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.
Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:
P(htt) = 1/2 × 1/2 × 1/2 = 1/8
P(tht) = 1/2 × 1/2 × 1/2 = 1/8
P(tth) = 1/2 × 1/2 × 1/2 = 1/8
So, the probability of getting 2 tails is:
P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8
= 0.375
0.375 multiplied by 100% gives:
P(2 tails) = 37.5%
Therefore, the correct option is (b) 37.5%
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Which three of these number add up to 180, 128 90 34 80 56
The three numbers which add up to 180 are 90, 34 and 56.
To find the sum of three numbers as 180, we simply add the three numbers together.
In this case, the numbers are given as 128, 90, 34, 80 and 56;
We see that the three numbers whose sum is 180 are 90, 34 and 56,
Let 90 represents one quantity, 34 represents another quantity, and 56 represents yet another quantity.
When we add these three quantities together, we get the total sum of all three quantities, which is 180.
Therefore, the numbers 90, 34 and 56 adds up to 180.
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The given question is incomplete, the complete question is
Which three of these number add up to 180? 128, 90, 34, 80, 56.
A circle has a radius of 14 feet. Find the exact area in feet squared (meaning
leave your answer as pi)
Answer:
196pie
Step-by-step explanation:
Order the following expressions by the values from least to greatest n - q q - n and q
After answering the presented question, we can conclude that q (if q is equation greater than n/2) q - n n - q q (if q is less than n/2)
What is equation?In mathematics, an equation is a statement that states the equality of two expressions. An equation consists of two sides separated by an algebraic equation (=). The argument[tex]"2x + 3 = 9,"[/tex] for example, states that the sentence[tex]"2x + 3[/tex]" equals the value "9." The goal of solving equations is to find the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, linear or nonlinear, and contain one or more parts. In the equation[tex]"x^2 + 2x - 3 = 0,"[/tex] the variable x is raised to the second power. Lines are used in many areas of mathematics, including algebra, calculus, and geometry.
We can simply compare two phrases at a time to arrange them from least to greatest:
If q is bigger than n/2, then q is the largest expression since q > n - q. If q is less than or equal to n/2, the largest expression is n - q, because n - q > q. Depending on the value of q, the greatest expression is either n - q or q.
When we add everything up, we get:
If q is more than n/2, the order is q, q - n, n - q.
If q = n/2, the sequence is q - n, n - q, q.
As a result, the ultimate order is:
q (if q is greater than n/2) q - n n - q q (if q is less than n/2)
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What is the ratio of the smaller circle's area to the larger circle's area?
The ratio between the areas is 4, which means that the area of the large circle is 4 times the area of the other one.
What is the ratio between the areas of the circles?Remember that for a circle of radius R, the area is given by:
A = 3.14*R²
Here we can see that the diameter of the smaller circle is equal to the radius of the larger circle, then if R is the radius of the larger circle, the radius of the smaller one is R/2.
Then the area of the smaller circle is:
a = 3.14*(R/2)² = (1/4)*3.14*R²
The ratio between these two is:
A/a = 3.14*R²/( (1/4)*3.14*R²) = 4
That means that the area of the large circle is 4 times the area of the smaller one.
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3. ZCAT and ZTAD is a linear pair.
If m/CAT = 42°
and m/TAD = 2x-6, find x
In ∠CAT and ∠TAD is a linear pair.
m ∠CAT = 42° and
m ∠TAD = 135°
Angle:
In Euclidean geometry, an angle is a figure formed by two radii, called sides of the angle, which share a common extremity, called vertex of the angle. The angle formed by two rays is located in the plane containing the rays. Corners are also formed by the intersection of two planes. This is called dihedral angles. Two intersecting curves can also define an angle, which is the angle of the light that hits the corresponding curve at the point of intersection.
Angle is also used to refer to an angle or rotation measurement. This measurement is usually defined as the ratio of an arc's length to its radius and can be drawn. In the case of geometric angles, an arc is centered on a vertex and bounded by an edge. In the case of a rotation, the arc is centered on the center of the rotation and bounded by any other point and its image through the rotation.
According to the angle:
We are given that angle CAT and angle TAD are a linear pair.
m ∠CAT = 42°
and, m ∠TAD = 2x -6
We have to find the measure of angle TAD.
m ∠CAT + m ∠TAD = 180°
⇒ 42° +m ∠TAD = 180° (linear pair sum =180 degrees)
⇒ m ∠TAD = 180° - 42°
⇒ m ∠TAD = 135°
Complete Question:
∠CAT and ∠TAD are a linear pair, if M∠CAT = 2x-5 and M∠TAD = 5x+10, what is the measure of ∠CAT and ∠TAD? Draw a picture labelling the given information and show your work
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hi need help i eill give you many points like a lot help due soon
Answer:
E
Step-by-step explanation:
To solve this question we have to count which one of the options have five red square and which of the options have 7 blue squares.
By looking at the options we can see that E is the only one that matches the requirements!
We have to be careful that we are looking for 5 red squares and not 5 blue squares as our answer would be wrong.
We can find this out in the question, we see that in the question it says red and blue defining that red goes first. This is why we consider red to be 5 and blue to be 7
Hope this helps, have a lovely day! :)
IV. Classify the following fractions as proper fractions,
improper fractions, like fractions & unlike fractions.
Improper
fraction
8 21 4 6 7
15' 5'5'8' 2
Proper fraction Unlike fraction Like fraction
2 5 1 9 11 3 12 11 2
-
-
-
-
4'4" 7'25'8'513'21'
-
E MODEL
Improper fraction: 8 21 4 6 7 15 - This fraction is an improper fraction because the numerator (the top number in the fraction) is larger than the denominator (the bottom number in the fraction).
What is numerator?A numerator is the top number in a fraction. It is used to identify the number of parts of a whole that are being considered. For example, in the fraction 3/4, the numerator is 3, which is the number of parts being considered out of the total 4 parts.
Like fractions: 5' 5' 8' 2 - This fraction is a like fraction because the numerators and denominators are the same.
Proper fraction: 2 5 1 9 11 3 12 11 2 - This fraction is a proper fraction because the numerator is smaller than the denominator.
Unlike fraction: 4'4" 7'25'8'513'21' - This fraction is an unlike fraction because the numerators and denominators are different.
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A store sells packages of comic books with a poster write a linear function in the form Y equals MX plus B that represents the cost Y of a package containing any number of comic books X suppose another store sells a similar package modeled by a linear function with one with initial value $7. 99 which store has a better deal explain one poster +6 comics $12. 75 or one poster and 13 comics $19. 75
The cost of a package containing x comic books and a poster is given by the equation y = 0.91x + 7.08.
Let's start by using the information given to form two equations. Let x be the number of comic books and let y be the cost of package.
From the first sentence, we can form the equation:
y = 7.99 + 2x
From the second sentence, we can form the equation:
y = 16.99 + 11x
Now we can use these equations to find the linear function rule that models the cost of a package containing any number of comic books.
First, we can set the two equations equal to each other since they both represent the cost of a package:
7.99 + 2x = 16.99 + 11x
Solving for x, we get:
9x = 9
x = 1
Now that we know that 1 comic book costs $4, we can substitute that value into either of the original equations to find the cost of a package with a poster and 1 comic book:
y = 7.99 + 2(1) = 9.99
So a package with a poster and 1 comic book costs $9.99.
Finally, we can use the slope of the line to find the linear function rule that models the cost of a package containing any number of comic books. We know that the slope is the change in y over the change in x, or:
m = (16.99 - 7.99)/(11 - 2) = 0.91
So the linear function rule is:
y = 0.91x + 7.08
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The given question is incomplete, the complete question is:
A store sells packages of comic books with a poster. A poster and 2 comics cost $7.99. A poster and 11 comics cost $16.99. Write a linear function rule that models the cost y of a package containing any number x of comic books.
How many sides does a regular polygon have if each interior angle measures 156°?
The answer is 15 sides
Jack interpreted the mean of the given data set, 7.96, as meaning half the cats weighed less than 7.96 pounds and half weighed more What was Jack's error? Explain
Click the icon to view the dot plot
Select the correct choice below, and fill in the answer box to complete your choice
(Type an integer or a decimal)
OA. Jack interpreted the mean as the range. Half the cats weighed less than
OB. Jack incorrectly calculated the mean. Half the cats weighed less than
OC. Jack interpreted the mean as the median. Half the cats weighed less than
OD. Jack interpreted the mean as the mode. Half the cats weighed less than
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pounds and half weighed more.
pounds and half weghed more
pounds and half weighed more
pounds and half weighed more
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I NEED AN ANSWER FAST
Based on the given options, the correct answer is: OC. Jack interpreted the mean as the median. Half the cats weighed less than 7.96 pounds and half weighed more.
The mean is a measure of central tendency that represents the average of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.
In this case, Jack interpreted the mean of 7.96 as meaning that half the cats weighed less than 7.96 pounds and half weighed more. However, this is incorrect because the mean does not necessarily divide the data set into two equal halves.
The median, on the other hand, is the middle value in a sorted list of numbers. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.
If Jack had interpreted the median as meaning half the cats weighed less than its value and half weighed more, he would have been correct. However, he incorrectly interpreted the mean as the median.
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Please solve this Question!!
I'll give u Brainliest:)
The angle AOB will be a right angle if x = 27.5
What value of x will make AOB a right angle?
AOB will be a right angle if the angle AOB is 90°, then we can write the linear equation:
2x + 30 + 2x - 50 = 90
These are the two measures that conform AOB.
Solving that linear equation we will get:
2x + 30 + 2x -50 = 90
4x - 20 = 90
4x = 90 + 20 = 110
x = 110/4 = 27.5
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XY=8 and YZ=4 find XZ
If XY = 8 and YZ = 4, the length οf XZ is 4√5 cm.
What is the Pythagοrean theοrem?The Pythagοrean theοrem states that in a right-angled triangle, the square οf the length οf the hypοtenuse (c) is equal tο the sum οf the squares οf the lengths οf the οther twο sides (a and b) c² = a² + b².
We can use the Pythagοrean theοrem tο find the length οf the hypοtenuse XZ οf the right-angled triangle XYZ.
In this case, X is the right angle, sο XY is the adjacent side and XZ is the hypοtenuse. YZ is οn the οppοsite side. We are given that XY = 8cm and YZ = 4cm.
So, we have:
XZ² = XY² + YZ²
XZ² = 8² + 4²
XZ² = 64 + 16
XZ² = 80
Taking the square root of both sides, we get:
XZ = √80 = √(16 × 5) = √16 × √5 = 4√5
Therefore, the length of XZ is 4√5 cm.
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Complete question:
If XY=8 and YZ=4 find the length XZ
Solve for w.
-7w-8+3w=16
Simplify your answer as much as possible.
W
0
Step-by-step explanation:
-7w-8+3w=16-4W=24W=-6conditional statement: If today is sunday, then it is holiday Converse Inverse Cintrapositive
Inverse Statement- If tοday is nοt Sunday, then it is nοt a hοliday. Cοntrapοsitive Statement- If it is nοt a hοliday, then tοday is nοt Sunday.
What is cοnditiοnal statement?A cοnditiοnal statement is a type οf lοgical statement that asserts a relatiοnship between twο prοpοsitiοns. It is an "if-then" statement that states that if οne thing is true, then anοther thing is true as well. The hypοthesis is the prοpοsitiοn that is assumed tο be true, while the cοnclusiοn is the prοpοsitiοn that is inferred frοm the hypοthesis.
Other types οf statements include:
Cοnverse: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are swapped.
Inverse: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are negated.
Cοntrapοsitive: When the hypοthesis and cοnclusiοn οf a cοnditiοnal statement are swapped and negated.
Here,
Cοnditiοnal statement: If tοday is Sunday, then it is hοliday.
Cοnverse: If tοday is a hοliday, then it is Sunday.
Inverse: If tοday is nοt Sunday, then it is nοt a hοliday.
Cοntrapοsitive: If it is nοt a hοliday tοday, then it is nοt Sunday.
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The sum of 2 numbers is
99. The difference of the two numbers is
51. What are the two numbers
Answer:
75, 24
Step-by-step explanation:
Answer: 75, 24
Step-by-step explanation:
Let the two numbers be x and y. Then,
1. x+y=99
2. x-y=51
If you add these two equations together, you get:
2x=150
x=75
Plug in x.
75+y=99
y=24
suppose that all conditions are met. compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer. group of answer choices (0.341, 0.559) (0.45, 0.5) (0.394, 0.506) (0.4, 0.45)
None of above options are correct.
To compute a 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer:
Follow these steps:
STEP 1: Determine the sample proportion (p) and sample size (n).
STEP 2:Calculate the standard error (SE) using the formula
SE = √(p(1-p)/n).
STEP 3: Determine the critical value (z) for a 95% confidence level
(1.96 for a two-tailed test).
STEP 4: Calculate the margin of error (ME) using the formula
ME = z * SE.
STEP 5: Find the confidence interval by adding and subtracting the margin of error from the sample proportion:
CI = (p - ME, p + ME).
Unfortunately, without the sample proportion (p) and sample size (n), it's not possible to compute the confidence interval.
However, once you have these values, you can follow the steps above to find the 95% confidence interval for the proportion of adults who spend more than 20 hours a week on a home computer.
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the length of a rectangle is 2 m longer than the width. if the perimeter of the rectangle is 56 m find the length and width
Let W = width of rectangle
Let W + 2 = length of rectangle = L
Perimeter = 2L + 2W
56 = 2L + 2W
since L = W + 2, we can substitute and solve
56 = 2(W + 2) + 2W
56 = 2W + 4 + 2W
56 = 4W + 4
52 = 4W
W = 13
the length 2 more than 13, which is 15
Area = L • W
= 15 • 13
= 195
A circle has a circumference of 452.16What is the radius of the circle?
Answer:this is the answer
Step-by-step explanation:
A survey is given to students about the servings of friuts and vegetables that each student typically eats in a day. The students in the survey represent a popultion of 200
In this scenario, a survey is being conducted to gather information about the fruit and vegetable consumption habits of a population of 200 students. The survey will help to determine the typical servings of fruits and vegetables that students consume in a day.
To ensure that the survey results are accurate and representative of the population, a random sample of students should be selected for the survey. This means that each student in the population has an equal chance of being selected for the survey. The sample size should also be large enough to ensure that the survey results are statistically significant and reliable.
Once the survey has been conducted and the data has been collected, it can be analyzed to determine the average servings of fruits and vegetables that students in the population typically consume in a day. This information can then be used to develop strategies for promoting healthy eating habits among students.
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Hi please help 100 points+brainliest ( it is supposed to be answered like an expenecial function )
1. The table shows the Total Expenses y (in dollars) of the College or University for year 2020-2021 and 2021-2022. Mine it's 21,211
a) Write a function that represents the Total Expenses y (in dollars) of that College or University you would like to attend after t years.
b) Use the function to estimate the Total Expenses your first year of school. *This year (t) is not the same for everyone since there are 8th graders to 11th graders in the class.
c) Sketch a graph (by hand) to model your function.
d) Identify the y-intercept and asymptotes of the graph. Find the domain and range of your function. Then describe the end behavior of the function.
Answer:
a) The Total Expenses y (in dollars) of the College or University for t years can be modeled by an exponential function of the form:
y = ab^t
Where "a" is the initial amount and "b" is the growth rate.
b) Using the given data, we can find the value of "a" by plugging in the first year's data into the equation:
y = ab^t
21211 = a * b^0
a = 21211
Thus, the function representing the Total Expenses y (in dollars) of the College or University after t years is:
y = 21211b^t
c) The graph of the exponential function will be an upward-sloping curve that starts at the point (0, 21211) and grows at a rate determined by the value of "b".
d) The y-intercept of the graph is (0, 21211), which represents the initial expense at the start of the first year. The function has no asymptotes. The domain of the function is all real numbers, while the range of the function is y > 21211. As t approaches infinity, the function grows without bound, which means the end behavior is that the expenses continue to increase exponentially over time.
Helpppppppp!!!!! Pleaseeeeeeeee!!!! I need an answer help
Answer:
39
Step-by-step explanation:
[tex]sin(x)=\frac{10}{16}\\ x=sin^{-1} (\frac{10}{16})\\ x=38.682....\\x=39[/tex]
differentiate
[tex]y = {x}^{3} [/tex]
differentiate
Answer:
y'=3x²
Step-by-step explanation:
[tex]y=ax^{n} \\y'=an*x^{n-1} \\y=x^{3} \\a=1,n=3\\y'=1*3x^{3-1} \\y'=3x^{2}[/tex]
A store buys paper at $15 per bundle. It then sells the bundles at a price that includes a 40% markup. The store offers a discount of To off the price of each
bundle if two or more bundles are purchased. What is the price to purchase 3 bundles of paper?
A store buys paper at $15 per bundle. It then sells the bundles at a price that includes a 40% markup. The store offers a discount of To off the price of each bundle if two or more bundles are purchased. The price to purchase 3 bundles of paper is $51
$15 x 3 bundles = $45 + 40% markup = $63 - 20% discount = $51.
In short, a purchase price is the economic value, usually defined in fiat currency at a given point in time, for which a buyer purchases a product, service, or asset. The compensation paid for this value can be fiat currency or other, such as services as payment or benefits in kind.the amount of money someone pays for something .The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.
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What linear equation represents the graph of the line that coincides with the x axis?
Is it y = (x)0 PLEASE HELP
Answer:
Step-by-step explanation:
5
Answer:Option b. y = 0.
Step-by-step explanation:
Eric had only red pens and Kai had only blue pens. There were thrice as many red pens as blue pens. Then Eric gave 2/5 of his red pens to Kai, while Ka gave 1/2 of his blue pens to Eric.
(a) What fraction of Kai's pens were blue after that?
(b) For them to have equal nurber of pens in the end, Eric had to give Kai 7 blue pens and 8 red pens in another round of transfer.
How many pens did Eric have in the beginning?
(a) Let in the beginning Eric had 3x red pens and Kai had x blue pens
2/5 * 3x = 6x/5
Eric gave 6x/5 red pens to Kai.
Now Eric has 3x - 6x/5 = 9x/5 red pens.
Kai gave x/2 blue pens to Eric
Now Eric has a 9x/5 + x/2 = (18x + 5x)/10 = 23x/10
Now Kai has x - x/2 = x/2 blue pens.
Now Kai has total x/2 + 6x/5 = 17x/10 pens.
required fraction = (x/2)/(17x/10) = x/2 * 10/17x = 5/17
5/17 is the answer.
(b) After another round of transfer Eric has total 23x/10 - 15 pens and Kai has total 17x/10 + 15 pens.
23x/10 - 15 = 17x/10 + 15
(23x - 150)/10 = (17x + 150)/10
23x - 150 = 17x + 150
6x = 300
3x = 150
Eric had 150 pens in the beginning.
8) Sally plays two games against Martin.
In each game, Sally could win, draw or lose.
In each game they play,
the probability that Sally will win against Martin is 0. 3
the probability that Sally will draw against Martin is 0. 1
Work out the probability that Sally will win exactly one of the two games
against Martin
The probability that exactly one of the two games will be won by Sally. against Martin [tex]= 0.42[/tex] or 42%.
Use the concept of probability defined as:
Probability is the ratio of:
The number of favorable outcomes to the total number of outcomes for the occurrence of an event.
Given that,
Sally plays two games against Martin.
Sally had a chance to win, tie, or drop each game.
The probability that Martin will lose against Sally is [tex]0.3[/tex].
The probability that Martin will lose against Sally in a tie is [tex]0.1[/tex].
We need to calculate the probability that Sally will win exactly one of the two games against Martin.
To calculate the probability that Sally will win exactly one of the two games against Martin:
Use a combination of probabilities.
Since there are 2 games,
So in this case:
There are 2 possible outcomes:
1. When Sally plays, she either loses the first game and wins the second one, or she wins the first game and loses the second one.
The probability of Sally winning the first game and losing the second game can be calculated,
By multiplying the probability of winning (0.3) with the probability of losing,(1 - 0.3 = 0.7).
Similarly,
2. By doubling the likelihood of losing, which is, the chance of Sally losing the first game and winning the second game,
[tex]1 - 0.3 = 0.7[/tex] with the probability of winning (0.3).
To determine the likelihood that Sally will triumph in precisely one of the two games: Add up this probability as follows:
(0.3 x 0.7) + (0.7 x 0.3) = 0.42
Hence,
The probability that exactly one of the two games will be won by Sally against Martin = 0.42 or 42%.
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I really need help with this equation can someone help??
Answer:
x = 11[tex]\sqrt{3}[/tex] , y = 33
Step-by-step explanation:
using the cosine and sine ratios in the right triangle and the exact values
cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{22\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 22[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 11[tex]\sqrt{3}[/tex]
and
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{22\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 22[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 22 × 3 = 66 ( divide both sides by 2 )
y = 33