Using the Induction hypothesis,
strong induction that every integer greater than 1 can be written as the product of primes
Induction Hypothesis:
This is the assumption that given a general element a[n], if something is true about the elements of an ordered set, we can show that it is also true for a[n+1]. is. This means it must be true for all elements. A classic example is the proof that the sum of the natural numbers is triangular.
Induction Has Strong and Weak Versions
This is a case where strong induction is needed because factoring n gives no information about the factorization of n+1.
For brevity, we say that even prime numbers are products of prime numbers. So the statement is: "Every number n≥2 is a product of primes". So the steps are:
base case, where we prove n=2.
If n>2 and every number m with 2≤m prove that n is also a product of primes. The
base case is because 2 is prime.
Let n>2. If n is prime, we are done. Otherwise, n=ab and 1 products of prime numbers.
Strong Induction: Base Case: n=2 and n has a factor of 1.2 n is prime:
Assume k is prime or can be expressed as the product of sets of prime factors for all k≤n To do.
We need to show that n+1 is prime or that n+1 can be expressed as the product of a set of prime factors.
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How do you compare a poem?.
Answer:Step 1: Summarise the main idea of each poem in 1-2 sentences. ...
Step 2: Find similarities – thematic, stylistic, structural and formal. ...
Step 3: Find differences from similarities. ...
Step 4: Identify 3 key ideas for comparison.
Step-by-step explanation:
How do you compare two poem structures?
These are some points to think about:
use the introduction to explain which poems you are writing about.
try to balance out the detail you include for each poem.
compare the poems throughout the essay.
comment on content, themes, ideas and attitudes as well as form, structure and language.
How do you compare poems in a level essay?
try to balance out the detail you include for each poem. compare the poems throughout the essay. comment on content, themes, ideas and attitudes as well as form, structure and language. sum up your thoughts on ways in which the poems are similar and different in your conclusion.
What is the constant variation of Y 8 when X 16?.
The constant variation of Y 8 when X 16 is 2.
What is Direct Proportion?
"When the relationship between two quantities is such that if we increase one, the other will also rise, and if we decrease one, the other quantity will also drop, then the two quantities are in a direct proportion," according to the definition of direct proportion. For instance, suppose there are two numbers, x and y, where x is the number of candies and y is the total amount of money spent. If we purchase more candy, we will be required to pay more, and if we purchase fewer candies, we will be required to pay less. This means that x and y are directly proportional to one another in this situation. The symbol for it is x y. Direct variation is another name for direct proportion.
So,
In the given question, we have:
y as 8 and x as 16;
So,
In order to find the proportional value, we have to divide the x quantity by the y quantity.
So, after dividing we get:
[tex]\frac{X}{Y} = \frac{16}{8}[/tex]
[tex]\frac{X}{Y} = 2[/tex]
So,
The constant proportion will be 2.
Hence,
The constant proportion will be 2.
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Wo familie viited an amuement park. The firt family bought 4 hot dog and 6 bottle of water, which totaled $22. The econd family bought 8 hot dog and 3 bottle of water, which totaled $35. How much did one hot dog cot?
The cost of one hot dog would be $4 and the cost of one water bottle would be $1.
What are the linear equations in two variables?
A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers and the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are two-variable linear equations.
Let the cost of one hot dog be 'x' dollars and the cost of one water bottle be 'y' dollars.
By using the given data, we can prepare the equations
4x + 6y = 22 ------(I)
8x + 3y = 35------(II)
Multiplying equation(I) and taking subtraction, we get
9y = 9
y = 9/9
y = 1
Put y = 1 in equation (I), and we get
4x + 6 = 22
4x = 22 - 6
4x = 16
x = 4
Hence, the cost of one hot dog would be $4 and the cost of one water bottle would be $1.
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match each expression to the correct point.
help please? :,)
The correct matching of a, b, and c with -6.283, -5.667, and -4.243, respectively.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The decimal number is the sum of a whole number and part of a fraction number. The fraction number is greater than zero but less than one.
The numbers are given below.
-17/3, -2π, and -√18
Convert each number into a decimal number. Then we have
-17/3, -2π, and -√18
-5.667, -6.283, and -4.243
Then the correct matching of a, b, and c with -6.283, -5.667, and -4.243, respectively.
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One day the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. How far did the water level drop during the week?
If the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. The water level drop during the week is 23 cm.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that one day the latter's water level was 35 cm above the mark. It was 12 cm below the mark one week later.
We have to apply the subtraction operation for the given operation,
In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
=35 - 12
=23 cm
Thus, if the level of the klater in the river klas 35cm above a mark. A week later it was 12cm below the mark. The water level drop during the week is 23 cm.
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An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, _____ the quantity demanded of the asset.
A) increases
B) decreases
C) has no effect on
D) erases
An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, (option a) increases the quantity demanded of the asset.
Given,
Asset's expected return;-
The weight of each asset is multiplied by its projected return to determine the expected return. The total predicted return for your portfolio may then be calculated by adding the figures for each investment. Hence, the equation Asset 1 Weight x Expected Return = Expected Portfolio Return Plus (Asset 2 Weight x Expected Return)
Hence,
An increase in an asset's expected return relative to that of an alternative asset, holding everything else constant, (option a) increases the quantity demanded of the asset.
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How many positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits? leading 0’s are also not allowed.
The number of 5 or fewer digits that are even or divisible by 5 and do not contain any repeated digits is 2500.
What are digits?In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.
A digit is a part of a set that, when combined, makes up a numeration system.
For example 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are digits.
The number of even digits 5 is 0,2,4,6,8.
Number of ways we can choose the first digit = 2,4,6,8 (0 cannot be taken in first)
Number of ways we can choose second, third, fourth, and fifth digits = 5
Number of ways or combinations,
4 × 5 × 5 × 5 × 5 = 2500
Hence "The number of 5 or fewer digits that are even or divisible by 5 and do not contain any repeated digits is 2500".
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Which statement describes 0.34? Select all that apply.
A It is a repeating decimal.
B It is a non-terminating decimal.
C It is a non-repeating decimal.
D It is a terminating decimal.
E It is a rational number.
F It is not a rational number.
The correct statements are A, B and E
SOLUTION:
Given, number is
We have to choose the statements that correctly describes the above number.
Now, we know that, a bar on a number represents it is repeating decimal. So let us check options now.
A. It is a repeating decimal.
As the number has it is repeating decimal. So this option is correct.
B. It is a non-terminating decimal.
As the number is repeating, it will not terminate, so this option is correct.
C. It is a non-repeating decimal.
No, it is repeating. So this is wrong statement.
D. It is a terminating decimal.
It is non – terminating, so this is wrong.
E. It is a rational number.
As it is repeating, we can represent it in fraction, so this is correct.
F. It is not a rational number.
It is rational number so, this is wrong option.
Answer:
The answers are
A.
B.
E.
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of. 5. How many subscribers must they sample to obtain this interval?.
The number of subscribers they must sample to obtain this interval is: b) 385.
How to find the sample?
95% confidence interval for z-score is 1.96
Using this formula to find the number of subscribers they must sample to obtain this interval
n≥ (zσ/2 ÷ 2ME)²
Where:
n= Sample
zσ = Z-score
ME = margin of error
Let plug in the formula
n≥ [1.96 / 2(0.05)]²
n≥ [1.96 / 0.1]²
= (19.6)²
= 384.16
=385 (Rounded)
Therefore the correct option is B.
The complete question is:
Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and TV shows. To do this, they plan to calculate a 95% confidence interval to estimate the proportion. They would like a margin of error of .05. How many subscribers must they sample to obtain this interval?
a) 1537
b) 385
c) 192
d) 10
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jessica does not notice when her father leaves the day care center and ignores him when he returns. jessica's behavior is characteristic of_______ attachment.
Jessica does not notice when her father leaves the day care center and ignores him when he returns. jessica's behavior is characteristic of Insecure-avoidant attachment.
Avoidant attachment:
Parents of children with avoidant attachments most often tend to be emotionally unavailable or unresponsive. These parents also discourage crying and encourage premature independence in their children, or learns early in life to suppress the natural urge to seek comfort from a parent when distressed.
Many people who avoid children have already become independent, precocious "little adults" as young children. As mentioned above, the primary defensive attachment strategy of children with avoidant attachment is to never outwardly demonstrate a desire for intimacy, warmth, affection, or love.
Insecure-Avoidant (aka Type A) is an attachment pattern identified by Ainsworth from an odd situation. This attachment type is ready for research but does not seek intimacy with their caregiver. They have low levels of fear of separation and fear of strangers and do not contact their mothers when reunited. Her 21% of children show this attachment pattern.
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a couple has three children. assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl? a. 1 b. .125 c. .5 d. .875
Answer:
d. 0.875
Step-by-step explanation:
Having at least 1 girl out of 3 children means that there can be 1, 2 or 3 girls out of the 3 children.
So having at lest 1 girl out of 3 children is the same as saying that all 3 children are not boys.
The probability that all 3 children are boys would be
chance that child 1 is a boy * chance that child 2 is a boy * chance that child 3 is a boy = 0.5 * 0.5 * 0.5 = 0.125
And the probability that NOT all 3 children are boys would be
100% - probability that all 3 children are boys = 1 - 0.125 = 0.875
What is the meaning of phenotype ratio?.
The alleles, or genes for a trait, are known as the genotype. A phenotypic ratio represents a relationship between the different physical characteristics and how often they occur. Ratios are typically done in relationship to a single trait among the individuals.
Phenotypic ratio pertains to the relative number of offspring manifesting a particular trait or combination of traits. It can be determined by doing a test cross and identifying the frequency of a trait or trait combinations that will be expressed based on the genotypes of the offspring.
For example: when a tall plant is crossed to a short plant, some of their offspring will be tall while others will be short. To determine the phenotypic ratio, the number of times the phenotypes (either tall or short) are expressed is counted. In this case, the phenotypic ratio shall indicate how many of the offspring will be tall and how many will be short based on the genotype.
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please answer asap (20 points)
only write down what I gotta put in the box and explanation
The value b is 8 if m=1 and the line is passing through the point P(-4,4).
What is a slope-intercept form?The line's equation is expressed in slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept. The slope of the line is 3 in our equation, y = 3 x + 5.
Consider the slope-intercept form equation y = 6 x + 9 y=6x+9 y=6x+9. We can find the x and y intercepts. The x-intercept occurs when y = 0, whereas the y-intercept happens when x equals 0. By setting the value of y to zero, we may find the x-intercept.
When an equation is not in the y = mx + b form, we can solve for the intercepts by substituting 0 and solving for the remaining variable.
Let, the slope-intercept form is,
y= mx +b
Given, m=1
And the line passes through the point P(-4,4)
Then,
4=1(-4)+b
b=4+4=8
b=8
Therefore, the value of b is 8
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the total probability rule is used when an analyst is interested in: a. all potential outcomes. b. a set of events. c. a single outcome.
The total probability rule is used when an an analyst is interested in a)all potential outcomes. So, correct option is a.
Probability is the branch of the mathematics concerning numerical descriptions of how likely an event is going to occur, or how likely it is that a proposition is true. The probability of an event is the number between 0 and 1, where, roughly speaking, 0 indicates that impossibility of the event and 1 indicates certainty. If probability of an event is higher then, the more likely it is that the event will occur.
Probability can be defined as the proportion of the number of favorable outcomes to the total number of outcomes of an event..
Hence, option a is correct.
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Which is true of the measures of the sides of the original square? each side of the original square is one-fourth the length of each side of the scale model. Each side of the original square is 4 times the length of each side of the scale model. Each side of the original square is the same length as each side of the scale model. Each side of the original square is 4 feet less than the scale model.
For the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.
It is known to us that -
The value of the scale factor = 4
We also know that -
Each side of the scale model = Scale factor * Side of the original square
=> Each side of the scale model = 4 * Side of the original square
=> Side of the original square = (1/4) * Each side of the scale model
Thus, for the measures of the sides of the original square, we can conclude that each side of the original square is one-fourth the length of each side of the scale model. Therefore, 1st option is correct.
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a poker hand consists of 5 cards dealth from a deck of 52 cards. let x and y be the number of aces and kings in a poker hand. find the joint distribution of x and uy
Joint Distribution of x and y is 25.
Joint Distribution is based on joint probability, which can be simply defined as the probability of two events happening together.
We know the formula for joint distribution
F(x,y) = P(X ≤ x and Y ≤ y) = ∑∑p(xi,yi)
Here x is the number of aces and y is the number of kings in a poker hand.
That means x can take values from 0 to 4 and y can take values from 0 to 4.
∴ F(x,y) = P(X ≤ 4 and Y ≤ 4)
⇒ F(x,y) = p(0,0) + p(0,1) + p(0,2) + p(0,3) + p(0,4) + p(1,0) + p(1,1) + p(1,2) + p(1,3) + p(1,4) + p(2,0) + p(2,1) + p(2,2) + p(2,3) + p(2,4) + p(3,0) + p(3,1) + p(3,2) + p(3,3) + p(3,4) + p(4,0) + p(4,1) + p(4,2) + p(4,3) + p(4,4).
To find all these values we will construct a table as follows;
P(x,y) Y=0 Y=1 Y=2 Y=3 Y=4
X=0 0 1/4 1/2 3/4 1
X=1 1/4 1/2 3/4 1 5/4
X=2 1/2 3/4 1 5/4 3/2
X=3 3/4 1 5/4 3/2 7/4
X=4 1 5/4 3/2 7/4 2
Now the joint distribution will become,
F(x,y) = 0 + 1/4 + 1/2 + 3/4 + 1 + 1/4 + 1/2 + 3/4 +1 + 5/4 + 1/2 + 3/4 + 1 + 5/4 + 3/2 + 3/4 + 1 + 5/4 + 3/2 + 7/4 + 1 + 5/4 + 3/2 + 7/4 + 2
F(x,y) = 25
Therefore the joint distribution of x and y is 25.
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How do you replace an equation with another?.
The algebraic approach to solving simultaneous linear equations is known as substitution method.
The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve. The steps shown below can be used to find the solution to the system of two equations with two unknown values. Here, the procedure for resolving the linear equation is listed. Those are Expand the parenthesis to simplify the given equation. Either x or y must be solved for in one of the equations. Replace the step 2 solution with the other equation, then use basic arithmetic operations to solve the newly obtained problem. Finally, obtain the second value by solving the equation.
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Which is the range of the function?.
The Range of the function f(x) = x² is [0,∞) .
Range of the function f(x) is defined as the set of all output values of the function.
In the question,
the function is given as f(x) = x² ,
we have to find the Range of it .
So , f(x) = x² ,
on substituting the x [tex]=[/tex] -1 , we get the value of f(-1) is = 1 ,
on substituting x = 0 , we get f(0) = 0 ,
on substituting x = 1 , we get f(1) = 1.
we see that Substituting positive values as well as negative values , the result is positive .
So , the Range of the function f(x) is [0,∞) .
Therefore , the Range of x² is [0,∞) .
The given question is incomplete , the complete question is
What is the range of the function f(x) = x² ?
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How do you know if a graph will cross or bounce?.
We know that the graph of a polynomial function will intersect the x-axis at its root values, and we know that if the multiplicity of that root is even, the graph will "bounce off"
If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero.
If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity.
If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity.
The sum of the multiplicities is n.
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What is the value of log 1 by 3?.
-0.477 is the value of log 1 by 3 .
A logarithm is defined simply?
The logarithm represents the power to which a number must be raised to obtain another number (see Section 3 of this Math Review for more about exponents).
For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.
log (1/3)
= log1 - log3
= 0 - 0.477
= -0.477
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Which ordered pair makes the inequality true?.
The ordered pairs (-2,3) and (5,1) make the inequality true.
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
(-2,3)
x= -2 , y= 3
-2+3(3) < 9
7< 9
true
(5,1)
x= 5 , y= 1
5+3(1) < 9
8< 9
true
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Question:
Which ordered pairs make the inequality true?
x + 3y < 9
Choose all answers that are correct.
(Points : 1)
(–2, 3)
(–1, 4)
(1, 3)
(5, 1)
You are a researcher working with the General Social Survey (GSS) on a project focusing on income and health service utilization among men. The first part of your project involves collecting random samples from men. You collect a random sample of men (N = 1500) and determine that the average income for this group is $31,607. Based on research, you know that the average income for males in the population is $33,405 with a standard deviation of $8,432. Before you do any additional analyses, you need to determine whether the mean earnings of men in the General Social Survey is representative of the earnings of the entire U.S. male population. In essence, You want to understand your sample’s value is really different from the population’s. Please reflect on how you would engage in statistical hypothesis testing and then provide the responses to the following items. This is a two-tailed test. Please consider alpha = .05. Fill in the blank:
Compute the standard error of the mean(two decimal places) =
The Standard Error of mean is 217.71 .
The critical value , Z꜀= 1.96 < Z , it is then concluded that the null hypothesis is rejected.
Hence, we can say that the the mean earnings of men in the General Social Survey is not representative of the earnings of the entire U.S. male population.
We have given that
A researcher working with the General Social Survey (GSS) on a project focusing on income and health.
Sample size, N = 1500
Sample mean , X-bar =$31,607
male population mean , μ = $33,405
Standard deviations, σ = $8,432
Std. error of mean , S.E = σ /√N
= 8432/√1500
= 217.71
Consider null and alternative hypothesis as
H₀ : μ = 33405
Hₐ : μ not equal to 33,405
Rejection region: Based on information provided the significance level,alpha = 0.05 and the critical value for two tailed test , Z꜀ = 1.96.
The rejection region for two tailed test R is
{ z : |z|> 1.96}.
Test Statistic:
Z- statistic test formula,
Z = (X-bar - u)/std. error
=> Z = ( 31,607 - 33,405)/217.71
=> Z = - 8.259
Decision: Since, it is observed that |z| = 8.259 > Z꜀ = 1.96 , it is concluded that Null hypothesis is rejected .
Conclusion: It is concluded that Null hypothesis H₀ is rejected. So there is sufficient evidence to support the claim that the population mean ,u is different from 33,405 at α = 0.05 significance level.
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.
[tex]2x + 3x=-3/4-1/5[/tex]
The value of variable x in the equation is as follows;
x = - 19 / 100
How to solve equations?An equation is a mathematical statement that shows that two mathematical expressions are equal.
In other words, equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Let's solve the equation for variable x.
Variables are numbers represented with letters in an equation.
Therefore,
[tex]2x+3x = -\frac{3}{4}-\frac{1}{5}[/tex]
[tex]5x = \frac{-15-4}{20}[/tex]
cross multiply
20(5x) = - 19
100x = -19
divide both sides by 100
Hence,
x = - 19 / 100
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Help me with this one?
Just write out the statements and reasons. thank u
Answer:
because these angles are equal to right angle triangle
Find the arc length of the partial circle.
The arc length of the partial circle is 12,56 units.
How to find the length of an arc?The arc of a circle is defined as the part or segment of the circumference of a circle.
Therefore,
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleHence,
∅ = 90 degrees
r = 8 units
length of an arc = 90 / 360 × 2 × 3.14 × 8
length of an arc = 4521.6 / 360
length of an arc = 12.56 units.
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the compounding periods and the payment periods are the same for an annuity and for an amortization. determine the present value of the annuity that will pay the given periodic payments. (round your final answer to two decimal places.) monthly payments of $430.80 for 6 years at 4.3% interest.
The present value of the annuity that will pay the given periodic payments is $ 332.99
since we are given a monthly payment of $430.80 for the period of 6 years with an interest of 4.3%, and it is said that the compounding periods and the payment periods are the same for an annuity and for an amortization.The formula for calculating the present value of the annuity is : FV= PV(1+i/12)¹²ⁿ, where F Vis the future value, PV is the present value, i is the interest and n is the period of time.So substituting the know values in the above formula, we get the present value to be: $ 332.99
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please help
It's really important
How to answer: You divide the first number by the second number
a) 85.50/7=12.21
b) 76.00/6=12.67 or 12.6 repeating
c) 120/10= 12
d) 30/0.5= 60
e) 6/2.40= 2.5
f) 399/3= 133
g) 3/2.25= 1.33 or 1.3 repeating
h) 400/5= 80
i) 43.80/5.5=7.7182 or 7.718 (the 18 repeating)
I hope this helped
the sum of two numbers is 30. when is the product of the first number multiplied by the square of the second number maximum
The two numbers required to solve the following problem are, 13.3 and 6.7
What is Derivative?
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives.
Solution:
Let the ture positive numbers be x,(x,y>0)
x + y = 20 -------- Given
We need to maximise [tex]xy^{2}[/tex]
x = 20 - y
f(y) = (20 - y)*[tex]y^{2}[/tex]
f(y) = 20[tex]y^{2}[/tex] - [tex]y^{3}[/tex]
f'(y) = 0
On differentiating:
f'(y) = 40y - 3[tex]y^{2}[/tex]
0 = 40 - 3y
y = 13.3
x = 6.7
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Present age of nick is 8 years and Jonas age is 14 years. What fraction of Jonas age represent the age of nick after 6 years?
Answer:
70%
Step-by-step explanation:
Nick now: 8
Jonas now: 14
Nick in 6 years: 8 + 6 = 14
Jonas in 6 years: 14 + 6 = 20
percent = part/whole × 100%
percent = 14/20 × 100%
percent = 0.7 × 100%
percent = 70%
Which function has no solution?.
Modulus function has no solution.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
Nothing can ever be 0 in an expression of an absolute value. That is a phrase for an absolute value that has been entirely lowered and must be larger than or equal to zero.
There are no solutions to an absolute value expression if, after simplifying it, the value on the opposite side is a negative number or has a negative sign.
Hence, the Modulus function has no solution.
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