Answer:
the answer is
The answer is
The answer is
The answer is 73
Step-by-step explanation:
Suppose that X ∼ Geom(p) and Y ∼ Geom(r) are independent. Find the probability P (X < Y )
The value of P(X<Y) could be p(1−q) / p+q−pq if X ∼ Geom(p) and Y ∼ Geom(r) are independent
What is probability ?
Probability could be defined as the ratio of number of favourable outcomes and total number of outcomes.
Given ,
X ∼ Geom(p) and Y ∼ Geom(r) are independent.
P(X<Y)=P(⋃1≤k<n,n∈N{X=k,Y=n})
=∑1≤k<n,n∈NP(X=k,Y=n)
=∑n=1∞∑k=1n−1P(X=k)P(Y=n)
=∑n=1∞∑k=1n−1p(1−p)k−1q(1−q)n−1
=pq∑n=1∞(1−q)n−11−(1−p)n−1p
=q∑n=1∞(1−q)n−1(1−(1−p)n−1)
=1−q / ∑n=1∞[(1−q)(1−p)]n−1
=1−q / 1−(1−p)(1−q)
=1−(1−p)(1−q)−q / 1−(1−p)(1−q)
=p(1−q) / p+q−pq.
Hence, The value of P(X<Y) could be p(1−q) / p+q−pq if X ∼ Geom(p) and Y ∼ Geom(r) are independent.
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What is the sum of the greatest common factor of $3$ and $6$ and the least common multiple of $3$ and $6$?
The sum of the greatest common factor (HCF) and least common multiple (LCM) of 3 and 6 is 9.
Highest common factor (HCF) and Least common multiple(LCM)The H.C.F. defines the highest common factor present in between given two or more numbers, while L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers.
factors of 3 are 1 and 3
factors of 6 are 1, 2, 3, and 6
3 = 1 × 3
6 = 2 × 3
LCM = 2 × 3
LCM = 6
HCF = 3
sum of HCF and LCM of 3 and 6 = 3 + 6
sum of HCF and LCM of 3 and 6 = 9
Therefore, 9 is the sum of the greatest common factor HCF least common multiple LCM of 3 and 6.
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54 is 72% of what number?
When the inverse of a function is itself a function it is called?
When the inverse of a function is itself a function it is called self-inverse.
A mathematical phrase, rule, or law establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
This relationship is commonly symbolized as y = f(x)—which is said “f of x”—and y and x are related such that for every x, there is a unique value of y.
A self-inverse function ‘reverses itself’ to produce the original input.
A function f is self-inverse if it has the property that f(f(x))=x for every x in the domain of f. In other words, f(x)=f−1(x).
For example, 1x and 3−x are self-inverse.
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PLEASE HELP PICTURE ATTACHED
Answer:
11. ∠5 and ∠7 are corresponding angles
12. ∠1 and ∠8 are alternate exterior angles
13. ∠3 and ∠6 are alternate interior angles
14. ∠6 and ∠7 are consecutive interior angles.
15. ∠1 = 58
∠2 = 122
∠3 = 58
∠5 = 122
∠6 = 58
∠7 = 122
∠8 = 58
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4x² - 20x = -21????????
Answer:
x=7/2
x=3/2
Step-by-step explanation:
Answer: ax^2+bx+c=0
(4x^2+20x+20=0)
Step-by-step explanation:
It may not make sense but...
Add -20 to both sides of the equation.
4x-20x=-20
Add -20 to both sides of the equation.
4x^2-20x+20=-20+20
Simplify the expression.
4x^2+20x+20=0
I hope this was what you were looking for. :) If not I'm still glad to help.
use a table to organize your guesses
A jar is filled with 100 coins, all of which are nickels and dimes. The change in the jar is worth $6.75. How many coins are nickels, and how many are dimes?
Answer:
35 dimes and 65 nickels
Step-by-step explanation:
We will need use a system of equations to find the total number of nickels and dimes.
Because there are 100 dimes and there are only nickels and dimes, one equation is N + D = 100, where N is the total number of nickels and D is the total number of dimes.
Because a dime is worth $0.10, a nickel is worth $0.05, and the total change in the jar is worth $6.75, the second equation is 0.05N + 0.1D = 6.75
Substitution will be the easiest method to solve:
[tex]0.05N+0.1D=6.75\\N+D=100\\\\N=-D+100\\\\0.05(-D+100)+0.1D=6.75\\-0.05D+5+0.1D=6.75\\0.05D+5=6.75\\0.05D=1.75\\D=35\\\\N+35=100\\N=65[/tex]
dividing decimals up to 2 decimal places
1.0.2÷6.11
Answer:
its 6.11
6.11 ÷ 1 = 6.11
Calculated to 2 decimal places.
6. 1 1
1 6. 1 1
− 6
0 1
− 1
0 1
− 1
0
The figure below is a scale drawing of a playhouse. In the drawing, the side of each house represents two and a half feet. Find the actual length of each segment.
5. The width of the house. = 30 feet
6. The height of the house. = 22.5 feet
7. The height of the first floor. = 12.5 feet
8. The height of the roof. = 10 feet
9. The width of the door. = 5 feet
10. The height of the door. = 7.5 feet
How to find the actual length of each segmentThe actual length of each segment is calculated by counting the units in the scale drawing and multiplying by the scale factor
In the problem, the scale factor is two and a half feet = 2.5 feet
5. The width of the house
number of units from the drawing = 12 units
actual length = number of units from the drawing * scale factor
actual length = 12 * 2.5 = 30 feet
6. The height of the house
number of units from the drawing = 9 units
actual length = 9 * 2.5 = 22.5 feet
7. The height of the first floor
number of units from the drawing = 5 units
actual length = 5 * 2.5 = 12.5 feet
8. The height of the roof
number of units from the drawing = 4 units
actual length = 4 * 2.5 = 10 feet
9. The width of the door.
number of units from the drawing = 2 units
actual length = 2 * 2.5 = 5 feet
10. The height of the door.
number of units from the drawing = 3 units
actual length = 3 * 2.5 = 7.5 feet
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A glass fish tank in the shape of a rectangular prism has a bace that measures 22 inches by 12 inches. Find the surface area if the height = 15 inches
Answer:
Surface Area = 2(22 x 15) + 2(12 x 15) + 2(22 x 12)
Surface Area = 660 + 360 + 528
Surface Area = 1,548 inches²
Step-by-step explanation:
Given: AAED ≈ ABEC and
AC BD.
Prove: AABD≈ ABAC.
Note: quadrilateral properties are not permitted in this
proof.
The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.
What are the four traits of triangles that are similar?The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.
According to given information:Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.
Given that ΔAED ≈ΔBEC & AC = BD.
as ΔAED ≈ΔBEC, AD = BC .................(1)
Now in ΔABD and ΔBAC,
AD = BC
(corresponding sides of similar triangles) [from (1)]
AB = AB
(common side)
AC = BD
(given)
∴ ΔABD ≈ΔBAC (By SSS criteria)
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Sophia buys 11 bottles of pineapple juice at the corner store for a total cost of $9.90. Assume each bottle of juice is the same price. If c represents the total cost in dollars and cents of the juice for any number, j, of bottles of juice, write a proportional equation for c in terms of j that matches the context. How do I do that
The proportion equation for c in terms of j is written as c = 0.9j
How to write the equationIn order to find the proportional equation for c in terms of j that matches the context, what you would have to do would be to divide 9.90 dollars by 11 bottles of pineapple juice.
This would tell us the price that one of the bottles of juice is been sold for.
Hence we would have
9.90 / 11
= 0.9
Hence the equation would be: c = 0.9j
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Reasoning Which of these is the best estimate for 225% of 50? greater than O but less than 1. 50 greater than 1-50 but less than 2. 50 greater than 2. 50 but less than 3. 50 greater than 3. 50
The best estimate for 225% of 50 is (a) greater than O but less than 1. 50
What is another term for estimate?The maximum likelihood method will be used to calculate the point estimate as follows:
T, note the total number of trials.
List the number of accomplishments, S.
MLE = S / T should be used. Your point estimate is the outcome. Prior to explaining a "formal" method of approximation by rounding each number in the calculation to one significant figure, students must first estimate the result of a computation, use a calculator to determine the precise result, then compare the two results. The most accurate estimate is a definite estimate, as it is created by estimating the individual expenses for the various aspects of the project and then combining them into one estimate. Typically, bottom-up estimates are classified under this heading.
The best estimate for 225% of 50 is
= (225*50)/100
= 11250/100
= 112.5
So that, The best estimate for 225% of 50 is (a) greater than O but less than 1. 50
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Word Problems
1) Sandy has 22 books in her library. She bought several books at a yard
over the weekend. She now has 61 books in her library. How many be
did she buy at the yard sale?
) How many ink cartridges can you buy with 143 dollars if
one cartridge costs 11 dollars ?
) Melanie is baking a cake. The recipe calls for 6 cups of flour. She alre
4 cups. How many more cups does she need to add ?
Answer:
1) 39
2) 13
3) 2
Step-by-step explanation:
1) She had 22 books, she now has 61 books, so she bought 61-22 = 39 books at the yard sale.
2) 143/11 = 13
3) 6-4 = 2
Brady tosses a coin three times. Each toss could be heads or tails. Which
outcome would be included in the compound event "at least two tails"?
The outcome for the event "at least two tails" is HTT. Option B
A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
HHH → All heads
HHT → Two heads + one tail
HTH → Two heads + one tail
HTT → Two tails + one head
THH → One tail + two heads
THT → Two tails + one head
TTH → Two tails + one head
TTT → All tails
Therefore, At least two tails means → Sample space outcome with two tails Or all tails
Therefore, from the given options HTT is having two tails. Option B is the correct option.
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A population of bacteria grows according to function p (t) = p. 1. 42', where t is measured in hours. If the initial population size was 1,000 cells, approximately
how long will it take the population to exceed 10,000 cells? Round your answer to the nearest tenth
The time duration for the population to exceed 10,000 is approximately 6.6 hours
What is time ?
In mathematics, time is described as a continuing and continuous series of events that take place in chronological order from the past through the present and into the future. The duration of events, the gaps between them, or even the sequencing of occurrences can all be quantified, measured, or compared using time.
the time frame that an activity, process, or state lasts or continues to exist: duration is a non-spatial continuum that is measured in terms of subsequent occurrences from the past, present, and future.
The mathematical symbol used to represent the multiplication process and its subsequent product is the multiplication sign, sometimes referred to as the times sign or the dimension sign.
t = The time duration in hours
The initial population of the cells = 1,000
Therefore, at t = 0, P(0) = 1,000 = P₀ × 1.42^0
∴ P(0) = 1,000 = P₀ × 1 = P₀
P₀ = 1,000
When the population is 10,000, we have;
P(t) = 10,000 = 1,000 × 1.42^t
∴ 1.42^t = 10,000/1,000 = 10
㏒(1.42^t) = ㏒(10) = 1
∴ t × ㏒(1.42) = 1
t = 1/㏒(1.42) = 6.56649071898
∴ The time duration for the population to exceed 10,000, t ≈ 6.6 hours.
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A performance score on the normally distributed WAIS Test that is higher than all but 2 percent of all scores earns an intelligence score of:
Scores earns an intelligence score of 130
What percentage of WAIS scores fall into this range?According to the 68-95-99.7 rule, 68% of persons have WAIS scores ranging from 100-15 to 100+15. WAIS scores between 85 and 115 are obtained by 99.7% of the population. As a result, 32% of adults have WAIS scores of 85 or above. Factor Analysis is a statistical process used to discover clusters of similar questions (called factors) on a test; it is used to identify multiple levels of performance that underpin one’s overall score.
The WAIS categories are shown below and are based on a mean of 100: Scores of 130 and higher are deemed talented. Scores between 120 and 129 are regarded extremely intelligent. Normal intellect is defined as a score between 110 and 119.
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Complete question is: A performance score on the WAIS that is higher than all but 2 percent of all scores earns an intelligence score of:
115.120.130.145.what is k if 1 1/3k=1/3
Answer: k = 11
Step-by-step explanation:
[tex]\frac{11}{3k} = \frac{1}{3} \\\\[/tex]
Cross multiply:
[tex]11 * 3 = 1*3k[/tex]
[tex]33 = 3k[/tex]
[tex]k = 11[/tex]
What is (f + g)(x)?
f(x) = -3x² + 3
g(x) = −3x
Answer:
Step-by-step explanation:
(f.g)(x)=[tex]-3*(-3x)^{2}+3=-27x^{2}+3[/tex]
The solutions to this problem
Answer: x<-2 or -2>x<1 or x>1
(-infinity,-2) U (-2,1) U (1,infinity)
Step-by-step explanation:
n 2010, the population of a small town in Alabama was 8,250 people. By 2015, the population had decreased by 10%. From 2015, to 2020, the population then increased by 15%. What was the population of the town in 2020
The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.
What is population?A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex] people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]
From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]
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PLEASE HELPPP
Given the diagram below, which statement is true?
∠1 and ∠3 are vertical angles and congruent.
What is congruence?
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
What are vertical angles?
The opposing angles form when two lines cross. They are constantly on par. In this illustration, the angles a° and b° are vertical. The term "vertical" refers to the vertex, not up or down, where they cross.
Here,
we have given a diagram and we have to determine which statement is true that satisfies the true conditions.
By applying congruent property. we get
∠1 = ∠3 are vertivally opposite angle.
This is the only condition that satisfy the true condition from given statement.
Hence, ∠1 and ∠3 are vertical angles and congruent.
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how would you read absolute value -5
Answer:
-5 = |5|
Step-by-step explanation:
Absolute value is the number of distance from zero. Therefore, it doesn't matter if the number is positive or negative in absolute value it is always positive.
show a²-4= (a+ 2)(a-2) in diagram
The equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
What is Factorization?Factorization refers to the process of breaking down a mathematical expression into simpler parts that can be multiplied together to give the original expression. For example, factorizing the expression x² + 4x - 12 would give (x - 3)(x + 4) as the factors.
In algebra, factorization is used to simplify expressions and to find the solutions of equations. For example, in the quadratic equation ax² + bx + c = 0, the first step in solving the equation is to factorize the quadratic expression ax² + bx + c. Once this is done, it becomes easier to find the solutions of the equation by setting each factor equal to zero and solving for x.
Factorization can also be used to simplify expressions in other branches of mathematics, such as number theory. For example, the prime factorization of a composite number is the representation of that number as a product of prime numbers.
Given:
The equation a²-4= (a+ 2)(a-2) is a factorization of a quadratic expression. It states that the expression a²-4 can be represented as the product of two binomials, (a+ 2) and (a-2).
This can be visualized as the graph of a parabola, where the x-intercepts of the parabola are -2 and 2. These are the solutions of the equation a²-4=0, which corresponds to the factorization of a²-4= (a+ 2)(a-2)
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slope intercept form of y + 6 = (x - 4)
look at picture please
The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ
What are trigonometric identities?Trigonometric identities are equations which contain the trigonometric ratios.
How to show the equivalent identity of cot²θ + 1?Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.
So, we proceed as follows
Since cot²θ + 1 = 1/tan²θ + 1 (since cot²θ = 1/tan²θ)
Now taking the L.C.M, we have that
1/tan²θ + 1 = (1 + tan²θ)/tan²θ
We know that the trigonometric identity 1 + tan²θ = sec²θ
So, substituting this into the equation, we have that
(1 + tan²θ)/tan²θ = sec²θ/tan²θ
Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that
sec²θ/tan²θ = cot²θsec²θ
So, cot²θ + 1 = cot²θsec²θ
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How do I find parameter?
Answer:
Depending of the figure that you are trying to find perimeter on, you just add up all the sides of that figure.
Answer:
The perimeter is the distance around a figure.
Step-by-step explanation:
For example, if I have a square where each side is 5 inches. The perimeter would be 20 inches. 5 + 5+ 5 + 5, a square has four sides and each side length is 5 inches.
help i really don’t understand this
Answer:
45 degree
Step-by-step explanation:
45+45 90 +90 180
All triangles will have 180 degrees angle
Rewrite 21/3 as a whole number
Answer:
7
Step-by-step explanation:
As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
21/3 = 7
A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number
On solving the provided question, we can say that number 12 is the smallest natural number is abundant
What is natural number?Natural numbers are those employed in mathematics for counting and ranking. Cardinal numbers are the ones used for counting, and ordinal numbers are the ones used for organizing. The natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11... are the ones to use while counting or sorting them. Integer a sum that consists of integers and zero. not using decimals or fractions. Integers are not fractions or decimals. Although all integers are integers (as are all natural numbers), not all integers are also integers or natural numbers. For instance, the integer -5 is both an integer and a natural number, but it is neither.
number 12 is the smallest natural number is abundant
factor of 12 = 1,2,3,4,6,12,
1~1
2>1
3>1
4>2+1
.............
10> 1+2+5
11>1
therefore, number 12 is the smallest natural number is abundant
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Complete question: A natural number is abundant if it is less than the sum of its proper divisors. What is the smallest abundant number?