Hence, in response to the provided question, we can say that As a result, function the discus takes approximately 0.03125 seconds to strike the ground.
what is function?Mathematicians research numbers and their variants, equation and related structures, objects and their locations, and prospective locations for these things. The term "module" is used to describe the connection that exists in between set of inputs, each of which has a corresponding output. A function is an input-output connection in which each inputs results in something like a single, distinct return. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On capabilities, one-to-one capabilities, multiple prowess, in capabilities, and on capabilities are the four major types of accessible functions.
The supplied function for discus height is as follows:
[tex]h(t) = -16t^2 + 38t + 5\\h(0) = -16(0)^2 + 38(0) + 5 = 5[/tex]
As a result, the discus's starting height is 5 feet.
[tex]-16t^2 + 38t + 5 = 0\\[/tex]
To find t, we can apply the quadratic formula:
t = (-b \sqrt(b2 - 4ac)) (2a)
where a=-16, b=38, and c=5.
[tex]t = (-38 + \sqrt(38^2 - 4(-16)(5))) / (2(-16))\\t = (-38 + \sqrt(1524)) / (-32) (-32)\\t = (-38 + 39) / (-32) (-32)\\[/tex]
As a result, [tex]t = (-38 + 39) / (32) or t = (-38 - 39) / (32) (-32)[/tex]
t = 1/32 or t = 77/32
As the negative value doesn't make sense in this situation, we chose the positive value:
t = 1/32
As a result, the discus takes approximately 0.03125 seconds to strike the ground.
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Next year, Frank plans to complete a triathlon. It will consist of a 2. 25-km swim, a 65-km bike ride, and a 20-km run. With which set of rates could Frank complete each event to finish the triathlon within 7. 5 hours?
The set o rates that Frank could use to finish the events within 7.5 hours is (0.75 km/h, 25 km/h, 12.5 km/h).
What is the rates needed by Frank to complete the events?
To determine the rates at which Frank must complete each event to finish the triathlon within 7.5 hours, we can use the formula:
time = distance / rate
where;
time is the amount of time it takes to complete the event, distance is the distance of the event, and rate is the speed at which Frank completes the event.Let x be the rate at which Frank completes the swim,
y be the rate at which he completes the bike ride, and
z be the rate at which he completes the run.
Then, we have the following three equations:
2.25 / x + 65 / y + 20 / z = 7.5
x > 0, y > 0, z > 0
We want to find the set of rates (x, y, z) that satisfy these equations and inequalities.
Here is one possible set of rates that would allow Frank to complete the triathlon within 7.5 hours:
x = 0.5 km/hour
y = 20 km/hour
z = 10 km/hour
Using these rates, we can calculate the time it would take Frank to complete each event:
Swim: 2.25 km / 0.5 km/hour = 4.5 hours
Bike ride: 65 km / 20 km/hour = 3.25 hours
Run: 20 km / 10 km/hour = 2 hours
The total time would be:
4.5 + 3.25 + 2 = 9.75 hours
This is greater than 7.5 hours, so Frank would need to increase his rates to finish within the time limit.
Here are some possible sets of rates that would allow him to do so:
x = 0.75 km/hour, y = 25 km/hour, z = 12.5 km/hour
x = 1 km/hour, y = 30 km/hour, z = 15 km/hour
x = 1.25 km/hour, y = 35 km/hour, z = 17.5 km/hour
Using any of these sets of rates, Frank would be able to complete the triathlon within 7.5 hours.
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Show that there is no finite triangle in hyperbolic geometry that achieves the maximum area bound.
As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) equation exceeds the size of T, which contradicts the premise that T has the greatest area.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
The area of a triangle in hyperbolic geometry is determined by the formula:
Area = K ∙ (α + β + γ - π)
where K is a constant that depends on the curvature of the space and,, and are the triangle's angles.
we want to emphasise the expression + + -.
Consider the following two situations:
Case 1: T has angles that add up to be less than.
Moreover, the total of the areas of triangles PTA, PTB, and PTC is larger than the area of T since their angles add up to more than T's angles. As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) exceeds the size of T, which contradicts the premise that T has the greatest area.
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factorise 4px-3my-2pm-6xy
Answer:
E
Step-by-step explanation:
NO
Instructions: Rewrite the equation in Standard Form. y+3=−(x−5)
what percent of 1225 is 147?
Answer:
12%
Step-by-step explanation:
147/ 1225 x 100/ 1
0.12 x 100 = 12%
Answer:
Therefore, 147 is 12% of 1225.
a. Solve - 11y -13>42. Graph the solution on a number line.
The solution to the inequality - 11y -13>42 is y < -5.
What is inequality?An inequality is a mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥ to indicate whether one is less than, greater than, less than or equal to, or greater or equal to the other.
To solve the inequality -11y - 13 > 42, we need to isolate y on one side of the inequality.
-11y - 13 > 42
First, we can add 13 to both sides:
-11y > 55
Next, we can divide both sides by -11, remembering to reverse the direction of the inequality because we are dividing by a negative number:
y < -5
To graph this on a number line,
Here is a rough sketch of the number line:
<=====(●)------------------------
-5
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i need help on this question
Solving a system of equations we can see that the correct option is A.
How many snacks are in each pack?Here we can define the variables:
g = snacks in one pack of granola bars.
f = snacks in one pack of fruit rolls.
And we can write a system of equations like:
10g + 6f = 152
7g + 12f = 200
If we take the difference between two times the first equation and the second, we will get:
2*(10g + 6f) - (7g + 12f) = 2*152 - 200
13g = 104
g = 104/13 = 8
There are 8 snacks in a pack of granola, and with that value we can find f.
10g + 6f = 152
6f = 152 -10g
f = (152 - 10*8)/6 = 12
We conclude that the correct option is A.
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A: What was the percent markup on this item?
B: What was your total profit (in dollars)?
let's move like the crab, backwards.
B)
profit is simply the surplus amount or 3.75 - 2.50 = 1.25.
A)
since the item was bought for $2.50, that's our origin amount, and thus that's our 100%, what's 1.25 off of it in percentage?
[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 2.50 & 100\\ 1.25& x \end{array} \implies \cfrac{2.50}{1.25}~~=~~\cfrac{100}{x} \\\\\\ 2.5x=125\implies x=\cfrac{125}{2.5}\implies x=50[/tex]
In ∆ABC, AB//QR and AP:PB =BR: RC. With reasons, prove that PQ// BC
In triangle ABC, if AB is parallel to QR and if AP:PB=BR:RC, then PQ is parallel to BC.
Since AB is parallel to QR, we can use the alternate interior angles theorem to conclude that ∠PAB = ∠QBR and ∠PBA = ∠QRB.
Also, since AP:PB=BR:RC, we can let AP=x and PB=y, so that BR=z and RC=w. Then we have:
x/y = z/wCross-multiplying, we get:
xw = yzNow consider triangles ABP and QBR. By the angle-angle similarity theorem, we have that these triangles are similar. So:
AB/PB = QB/BRSubstituting our values for PB and BR, we get:
AB/y = QB/zCross-multiplying, we get:
ABz = QBySimilarly, considering triangles APC and RCB, we can use the angle-angle similarity theorem to conclude that these triangles are also similar. So:
AC/RC = RB/CBSubstituting our values for RC and RB, we get:
AC/w = RB/zCross-multiplying, we get:
ACz = RBwNow, let's consider the ratio of the lengths of PQ and BC. We have:
PQ/BC = (QB + BP)/(RB + BC)Substituting in the values we found earlier for ABz, QBy, ACz, and RBw, we get:
PQ/BC = [(ABz + QBy)/(RBw + ACz)]Using the fact that ABz = QBy and ACz = RBw (which we found earlier), we can simplify this expression to:
PQ/BC = 1This means that PQ and BC are parallel, which is what we wanted to prove.
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Triangle a b c. side a c is 9 units, c b is 9 units, a b is 7 units. dilate triangle abc about point a by a scale factor of 1/3. what is the length of ac'? what is the length of ab'?
After dilating the triangle abc about point a by a scale factor of 1/3, the length of new side length of ac' is equals to the 3 units.
Dilation is a transformation used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image of the same shape as the original. For a scale factor k, the algebraic representation of inflation is (x, y) → (kx, ky). Here we have a triangle abc with side length, ac = 9 units
side length, cb = 9 units
side length, ab = 7 units
remove triangle abc around point a, and
factor dilation scale = 1/3
We need to determine the length of the new side ac'. Dimensions of original shape, ac × scale factor = Dimensions of new shape, ac'
=> length of ac' = 9 units × 1/3
=> length of ac' = 3 units
Hence, required length is 3 units.
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A tamily has 4 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 4 girls if it is known the family has at least one giri. Answer
Therefore , the solution of the given problem of probability comes out to be the likelihood that they have four girls is 1/15.
What precisely is probability?The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.
Here,
Given that the family has at least one girl, we can use Bayes' theorem to determine the likelihood that they have four girls:
=> P(4 girls | at least one girl) = P(4 girls)
=> Times P(at least one girl | 4 girls) / P. (at least one girl)
Additionally, we are aware that the probability of having at least one female is
=> P(at least one girl = 1 - P(no girls) = 1 - (1/2)4 = 15/16.
The likelihood of not having any females is equal to the likelihood of having four boys,
which is
=> (1/2)4 = 1/16.
Given that all four of the children are female, the likelihood of producing girls is one.
Combining everything, we have:
=> P(4 females | a girl)
=> 1 * (1/16) / (15/16) = 1/15
Given that the household has at least one girl, the likelihood that they have four girls is 1/15.
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Lupita deposited $5,000 into a savings account that earns 2% interest compounded annually. Rounded to the nearest cent, how much interest will Lupita have earned after 48 months?
The difference between the total and the initial contribution, which is: Interest [tex]= $5,409.09 - $5,000, I[/tex] nterest $409.09, is the amount of interest earned. Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.
We can use the compound interest calculation to determine how much money Lupita will receive after 48 months:
Where: [tex]A = P(1 + r/n)(nt)[/tex] A represents the whole sum after t years.
P represents the primary sum.
The yearly interest rate is r.
Given that interest is compounded yearly, [tex]P = $5,000, r = 0.02, n = 1,[/tex]and[tex]t = 48/12 = 4[/tex] (since the time is given in months, we need to convert to years by dividing by 12).
Hence, the equation is: [tex]A = $5,000(1 + 0.02/1)^(1*4)[/tex]
[tex]A = $5,000(1.02)^4\sA ≈ $5,409.09[/tex]
The amount that differs between the total and the original deposit that represents interest earned is: Interest equals [tex]$5,000 - $5,409.09$409.09[/tex] in interest
Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.
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A rectangle has side lengths of x cm and (x + y) cm, where x and y are
both positive.
The rectangle has an area of 57 cm² and a perimeter of 44 cm.
Work out the values of x and y.
The values of x and y are 7 and 6 respectively
What is area and perimeter of a rectangle?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.
The area of a rectangle = l× w
The perimeter of rectangle = 2(l+b)
length = x
breadth = x+y
57 = x(x+y)
44 = 2( x+(x+y)
therefore ;
57 = x²+y. equation 1
44 = 4x + 2y equation 2
from equation 2, y = 22-2x
substitute 22-2x for y in equation 1
57 = x²+22-2x
57 -22= x²-2x
x²-2x -35 = 0
(x²-7x)(+5x -35 )= 0
x( x-7) 5( x-7) = 0
x+5 = 0
x-7 = 0
therefore x = -5 or 7
but we are going to take the positive answer for x
57 = 7²+y
y = 55-49
y = 6
therefore the value of x and y are 7 and 6 respectively
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If the company orders 27 boxed lunches from a deli for $245. 70 and each boxed lunch costs the same amount then the unit cost of each boxed lunched is $9. 1. What is the unit cost of each boxed lunch?
Given that;
27 boxed lunches from a deli cost $245. 70
Cost of 1 box = ?
To determine the unit cost of each
If the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1.
This example belongs to a word problem.
What is the unit cost of each boxed lunch?
Given that;
27 boxed lunches from a deli cost $245.70
Cost of 1 box =?
To determine the unit cost of each boxed lunch, we say;
Cost of each box = $245.70 ÷ 27
Cost of each box = $9.1
Hence, if the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1
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HELP ME!!!! THIS IS DUE TODAY
Answer:
No, it is not reasonable. The scaled drawing would be 12 inches wide by 30 inches tall.
Step-by-step explanation:
First, scale down the sides. 48in divided by 4 is 12in , and 120 in divided by 4 is 30 in. So no, it would not fit on her paper.
If the sum of the 2nd and 7th term of an arithmetic progression is 25 and the fifth term is 15 find the common difference
Answer: Let's call the first term of the arithmetic progression "a" and the common difference "d". Then we can use the following formulas to find the second, fifth, and seventh terms:
- The second term is a + d.
- The fifth term is a + 4d.
- The seventh term is a + 6d.
We are given that the sum of the second and seventh terms is 25:
(a + d) + (a + 6d) = 25
Simplifying this equation, we get:
2a + 7d = 25 ...(1)
We are also given that the fifth term is 15:
a + 4d = 15 ...(2)
Now we can solve for the common difference "d" by using equations (1) and (2) to form a system of two equations in two variables. One way to do this is to solve equation (2) for "a" in terms of "d", and then substitute that expression for "a" into equation (1):
a = 15 - 4d ...(3)
Substituting equation (3) into equation (1), we get:
2(15 - 4d) + 7d = 25
Simplifying this equation, we get:
30 - 8d + 7d = 25
Solving for "d", we get:
d = -5
Therefore, the common difference is -5.
Step-by-step explanation:
The purpose of this assignment is to apply hypothesis tests to the case of Bayview University. 1. Open the dataset of Bayview University (attached) and read the case in its entirety at the end of Chapter 9
2. Use descriptive statistic to summarize the data and comment on your finding
The strengths and weaknesses of the data will help to identify the areas that need to be improved.
The steps that are to be taken to apply hypothesis tests to the case of Bayview University are given below:Open the dataset of Bayview University and read the case in its entirety at the end of Chapter 9. After opening the dataset of Bayview University, read the case in its entirety at the end of Chapter 9. It is important to read the case carefully in order to understand it properly. This is the first step that is to be taken in order to apply hypothesis tests to the case of Bayview University.
Use descriptive statistics to summarize the data and comment on your findings. Once the case has been read carefully, descriptive statistics are to be used to summarize the data. Descriptive statistics are statistical techniques that are used to describe and summarize the data. They are used to summarize the data in a way that is meaningful and easy to understand. The descriptive statistics will help to identify the central tendency and the variability of the data. After summarizing the data, comments are to be made on the findings. These comments will help to identify the strengths and weaknesses of the data. The strengths and weaknesses of the data will help to identify the areas that need to be improved.
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sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions. a. random b. snowball c. stratified d. convenience
Random sampling is the correct answer. Which is option (A).
Sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is referred to as Random sampling.
What is sampling?
In statistics, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Sampling is frequently employed in social science research. The method employed to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is known as random sampling.
Content-loaded sampling refers to a form of sampling that is more sophisticated than simple random sampling.
In order to form a sample, it involves first determining which variables (or characteristics) are essential to the study, and then choosing people based on those variables, hence the name "content-loaded."On the other hand, in Stratified sampling, the population is divided into subgroups (strata) based on one or more characteristics that are expected to impact the study's outcomes. The proportion of people chosen from each group should reflect the group's percentage of the overall population.
Snowball sampling is a method for selecting a sample of individuals by locating others who share the characteristics being studied and asking them to suggest additional individuals who might participate in the study. Among the given options, (A) random sampling is the correct answer.
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PLEASE HELP ME OUT GUYS
Answer:
Given as steps.
Step-by-step explanation:
Step 2: Opposite angles of a parallelogram are Equal
Step 4 ( After " Definition of a parallelogram"): Given
Step 5: ASA congruency Property / Therom
Step 6: CPCTC
P.S: It is ASA congruency Therom as both angles are adjacent to the side they are trying to prove.
Hope It Helps!
need help with part a part b part c
Answer:
Part A 4 Part B 20 Part C C
there are total 28 balls. 1 / 7 = 4 balls.
Explain how you can use this product to determine that (15)(5)=75
The product shown below in simplest form (x+5) (x-5) and we can use this product to determine that (15) (5)= 75.
First, we need to find the product shown below in simplest form:
we have = (x+5) (x-5)
we need to explain how you can use this product to determine that,
(15) (5) = 75
for us to get the solution we will let x = 10
Then (x + 5) (x - 6) will be:
(10 + 5) (10 - 5), or we can also say that: (15)(5) = 75
Also, this could be calculated as:
10(10 - 5) + 5(10 - 5) = 100 - 50 + 50 - 25 = 75
Therefore we can say that the product shown below in simplest form (x+5) (x-5) and we can use this product to determine that (15) (5)= 75
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Full question: Find the product shown below in simplest form: (x+5) (x-5) explain how you can use this product to determine that (15) (5) = 75
What is one example of math in mr. Maxs life outside the classroom
Here some examples of math by using Mr. Maxs life outside the classroom.
Define the examples of math?One example of math in Mr. Max's life outside the classroom could be calculating the amount of gas needed to fill up his car's tank before a road trip. This involves using basic arithmetic operations such as addition, subtraction, multiplication, and division to calculate the total distance he intends to travel, the fuel efficiency of his car, and the capacity of the fuel tank. By doing so, he can estimate the amount of gas needed for the trip and plan accordingly. Additionally, he may also use math to calculate the cost of the gas based on the current price per gallon or liter, and decide on the most cost-effective way to fill up his tank.
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complete question is:
What is one example of math in Mr. Max's life outside the classroom? 10. Is math everywhere, as Bobby believes? Support your answer with evidence.
can someone pls help me
Answer:b
Step-by-step explanation:
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x values containing values negative 3, negative 1, 1, 3, and 5 and another circle labeled y values containing values 0, 2, and 5 and arrows from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5. Is the relation a function? Explain. No, because for each input there is not exactly one output No, because for each output there is not exactly one input Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input
The relatiοnship in the given diagram is nοt a functiοn, because fοr each input there is nοt exactly οne οutput. Sο Optiοn A is cοrrect
What are functiοns?Functiοn is a relatiοn between a set οf inputs and a set οf οutputs which are permissible. In a functiοn, fοr particular values οf x we will get οnly a single image in y. It is denοted by f(x).
Vertical line test:-
Whenever we want tο check whether a given expressiοn is a functiοn οr nοt we can apply a vertical line test, in this test we check fοr a single image οf x , we are getting a single image οr mοre.
If we get mοre images then it will nοt be a functiοn.
Fοr example, let us take, y² = 4ax
y = ±√4ax
Fοr single value οf x we get twο values οf y
Hence, it will nοt be a functiοn.
Given that,
Values οf x and values οf y
In given diagram,
fοr x = 0,
there are twο values οf y, -4 and -2
but accοrding tο definitiοn οf y, it shοuld give οnly οne value
Hence, it is nοt a functiοn
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Raven usually does 5 out of every 7 math problems correctly. Which table accurately shows how many math problems she will do correctly out of 14, 21, or 28 total problems?
Answer:
B.
Step-by-step explanation:
The proportions should be exactly the same for each set of questions and correct questions.
Based on Raven's history, she get 5 of 7.
Choice B. shows exactly that with a scalar of 2, 3, and 4. For Row 2, the set is twice as large, so Raven gets exactly twice as many questions correct and exactly twice as many incorrect.
For Option B., the [tex]\frac{correct}{total}[/tex] always simplifies to [tex]\frac{5}{7}[/tex] for every row.
The Martinez family picked 3 1/2 lb of apples. Ana picked 1/4 of those apples.
How many pounds of apples did Ana pick?
As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.
what is unitary method ?Finding a value of a single unit or the ratio of two values, then using this value to determine the value of a bigger or smaller number, is the unitary method, a problem-solving strategy used in mathematics. The unit method, single unit method, and percentage method are additional names for the unitary approach. The unitary method, which can be used to address issues in a number of disciplines including mathematics, algebra, geometry, and physics, entails using a ratio, proportion, or factor. The approach is founded on the proportionality concept, according to which two ratios or quantities are proportional if they have the same ratio or proportion.
given
Three and a half pounds of apples, which can be expressed as a mixed amount or an incorrect fraction, were harvested by the Martinez family:
3 1/2 = 7/2
Ana selected one-fourth of those apples, so the quantity she selected can be calculated by dividing by the total number of apples selected by the Martinez family:
1/4 × 7/2 = (1 × 7)/(4 × 2) = 7/8
As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.
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Please help and show work thank youuu
Based on the information provided, the total Diane will need to pay is $11.6.
How much does Diane need to pay?Let's start by calculating the total from the items she ordered, the process is shown below:
Garden salad: $2.95Monte Cristo: $7.85Soda: $1.25Total: 2.95 + 7.85 + 1.25 = $12.05Now, let´s apply the coupon by using the 10% as a reference:
12.05 x 0.9 (she will paid only 90%) = $10.845
Finally, let's calculate the tax by using its percentage and let's add it:
$10.845 x 0.0775 = $0.84
$10.845 + $0.84 = $11.6
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The Blacktop Speedway is a supplier of automotive parts. Included in stock are 12 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable z represent the number that are not correctly calibrated Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.) P(x) N 3 3 Find the mean of this probability distribution. (Appropriate rounding rules apply.) mean = Submit Question
The mean of the given probability distribution is 0.2007.
The probability distribution table for the given scenario can be completed as follows:
| x | P(x) |
|---|------|
| 0 | 0.8036 |
| 1 | 0.1929 |
| 2 | 0.0036 |
| 3 | 0.0000 |
The probabilities are calculated using the hypergeometric distribution formula:
P(x) = (C(N-K, n-x) * C(K, x)) / C(N, n)
Where N is the total number of items (14), K is the number of items that are not correctly calibrated (2), n is the number of items selected (3), and x is the number of items that are not correctly calibrated in the selection.
For x = 0:
P(x) = (C(14-2, 3-0) * C(2, 0)) / C(14, 3) = (C(12, 3) * C(2, 0)) / C(14, 3) = (220 * 1) / 364 = 0.8036
For x = 1:
P(x) = (C(14-2, 3-1) * C(2, 1)) / C(14, 3) = (C(12, 2) * C(2, 1)) / C(14, 3) = (66 * 2) / 364 = 0.1929
For x = 2:
P(x) = (C(14-2, 3-2) * C(2, 2)) / C(14, 3) = (C(12, 1) * C(2, 2)) / C(14, 3) = (12 * 1) / 364 = 0.0036
For x = 3:
P(x) = (C(14-2, 3-3) * C(2, 3)) / C(14, 3) = (C(12, 0) * C(2, 3)) / C(14, 3) = (1 * 0) / 364 = 0.0000
The mean of this probability distribution can be calculated by multiplying each value of x by its corresponding probability and summing the results:
mean = (0 * 0.8036) + (1 * 0.1929) + (2 * 0.0036) + (3 * 0.0000) = 0.2007
Therefore, the mean of this probability distribution is 0.2007.
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two triangle are similar. rye length of one side of one triangle is 4 times that of the corresponding side of the other determine the ratio of the perimeter the ratio of the areas of the polygon
The ratios for the similar triangles are given as follows:
The ratio of the perimeter is of 4.The ratio of the area is of 16.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The length of one side of one triangle is 4 times that of the corresponding side of the other, hence the constant of the proportional relationship for the side lengths is given as follows:
k = 4.
The perimeter is measured in units, just like the side lengths, while the area is measured in units squared, hence the ratios are given as follows:
The ratio of the perimeter is of 4.The ratio of the area is of 4² = 16.More can be learned about similar triangles at brainly.com/question/14285697
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Q.2) A jar contains three balls numbered 1,2, and 3. If two balls are drawn: a) Write the probability space? b) what is the probability that the sum of the numbers is 4 ? c) what is the probability that the sum of the numbers is at least 4 ?
a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).
b) The probability that the sum of the numbers drawn is 4 is 2/9.
c) The probability that the sum of the numbers is at least 4 is 2/3.
a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:
P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)
Hence, the probability space can be written as a set, S = {1,2,3}.
b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:
P = 2/9
c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:
(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)
Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3
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