It is proved that, for every positive integer n, there are n consecutive composite integers.
Given statement,
For every positive integer n, there are n consecutive composite integers.
Proof:
Assume that m is less than n and that both m and n are positive integers. When m is less than n,
n! = 1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n,
which is to say that m is a factor of n!
So,
m + n! = m + ( 1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n )
= m ((1 ⋅ 2 ⋅ 3 ⋅ ⋅ ⋅ m ⋅ ⋅ ⋅ n) / m + 1)
Since m is a multiple of n!, n!/m is still an integer. Since the integer m is bounded between 1 and n, it follows that any number you choose up to n can divide m + n!, making it composite until the nth integer.
However, since n! contains the nth integer, the nth integer is also composite, meaning you can choose any integer between 1 and n inclusively and it will be composite.
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Find the missing length. (the ?)
In the given triangle, the length of missing side is 15.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given triangle,
Side BD = 5, CE = 3 and AE = 9
Let the side AD is x,
Since, line BC and DE and parallel to each other,
Therefore, by side splitter theorem,
A line that is parallel to one side of a triangle and crosses the other two sides equally divides the side in proportional ratio.
Implies that,
AD/BD = AE/EC
x/5 = 9/3
x/5 = 3
x = 15
The value of side AD is 15.
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Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?
A 0.09
B 0.19
C 0.28
D 0.72
E 0.91
The correct option C 0.28; for the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed.
Explain the term binomial probability distribution?A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials whenever the trial has an equal chance of producing a particular result.This problem involves a binomial probability distribution.
Now that five thumbtacks have been thrown, we want to determine the likelihood that at least two of them will land pointing up. As it is written;
P(X ≥ 2) = P(2) + P(3) + P(4) + P(5)
Based on the histogram
P(5) = 0.02
P(4) = 0.02
P(3) = 0.05
P(2) = 0.19
So,
P(X ≥ 2) = 0.19 + 0.05 + 0.02 + 0.02
P(X ≥ 2) = 0.28
Thus, the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed is 0.28.
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A thumbtack that is tossed can land point up or point down. The probability of a tack landing point up is 0.2. A simulation was conducted in which a trial consisted of tossing 5 thumbtacks and recording the number of thumbtacks that land point up. Many trials of the simulation were conducted and the results are shown in the histogram.
Based on the results of the simulation, which of the following is closest to the probability that at least 2 thumbtacks land pointing up when 5 thumbtacks are tossed?
A 0.09
B 0.19
C 0.28
D 0.72
E 0.91
Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 40 expectant mothers have mean weight increase of 16 pounds in the second trimester, with a standard deviation of 6 pounds. At the 5% significance level, we can conduct a one-sided T-test to see if the mean weight increase in 2015 is greater than 14 pounds. Statistical software tells us that the p-value = 0.021.Which of the following is the most appropriate conclusion?There is a 2.1% chance that a random sample of 40 expectant mothers will have a mean weight increase of 16 pounds or greater if the mean second trimester weight gain for all expectant mothers is 14 pounds.There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 14 pounds in 2015.There is a 2.1% chance that mean second trimester weight gain for all expectant mothers is 16 pounds in 2015.There is 2.1% chance that the population of expectant mothers will have a mean weight increase of 16 pounds or greater in 2015 if the mean second trimester weight gain for all expectant mothers was 14 pounds in 1959.Find the p-value for the hypothesis test. A random sample of size 50 is taken. The sample has a mean of 420 and a standard deviation of 81.H0: µ = 400Ha: µ > 400The p-value for the hypothesis test is
We accert H1 alternative that is result is population mean greater than 400.
There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.
What is standard deviation?
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
We have given: μ = 14, x bar = 16, n = 40, s = 6, α = 5%, = 0.05
To test μ0 : μ = 14 Vs H1: μ > 14
Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081
So, P value = 0.021
Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.
P value for the hypothesis test
n = 50, x bar = 420, sx = 81, μ = 400,
To test: H0: μ 400 Vs H1: μ > 400
It is right tail test
Test statistics = (X bar - μx)√n / sx = (420 - 400) √50 / 81 =
z = 1.7459
P value = 0.04093
Declsion: We reject H0 is p value < α
Here α = 0.05
Hence P value < α
Conclusion: We accert H1 alternative that is result is population mean greater than 400.
Hence, we accert H1 alternative that is result is population mean greater than 400.
There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.
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-5-4-3
Mark this and return
y
5
4+
3+
2+
14
T
-2-
-3-
4
-5
1 2 3 4 5
X
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
Save and Exit
Next
Submit
The answer is all real numbers greater than or equal to -3, as domain and range.
What is the domain and range of function?
A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.
The domain of a relation or a function is the set of all possible values for an input in that relation/function.
The range of a relation or function is the set of all possible values that can be the result of a relation or function.
From the graph, nothing can be seen on the left side of x = - 3 and the graph is continuous and going in the direction of infinity on the right side of the x axis.
Hence all real numbers greater than or equal to -3
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What are the 3 linear functions?.
There are three major forms of linear equations:
point-slope form, standard form, and slope-intercept form.Point slope form:
The point-slope form, as its name suggests, identifies a point on a line and its slope. Not frequently is this form provided to assist with line graphing. To get from a verbal or visual representation of a line to its slope-intercept or standard form, however, is where it is more frequently utilized.
Slope intercept form:
A line's slope and y-intercept are communicated using the slope-intercept form. Technically speaking, it is an exception to the point-slope form.
Standard form:
An equation's conventional form is as follows:
Ax+By=C
Where A is not a negative number and B, C, and all three are whole numbers.
Hence we get the required answer.
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A set of 1000 cards numbered 1 through 1000 is randomly distributed among 1000 people with each receiving one card. Compute the expected number of cards that are given to people whose age matches the number on the card.
One of people expected to receive a card with a number that matches its age.
What is expected value?
The anticipated value is an extension of the weighted average in probability theory. Informally, the anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
Let, a set of 1000 cards numbered 1 through 1000 is randomly distributed among 1000 people with each receiving one card.
[tex]x_i=\left \{ {1, if the i^t^h person card numbermatches his/her age } \atop {0 , Otherwise}} \right.[/tex]
[tex]X_i[/tex] is a new variable.
Expected one of 1,000 people to receive the card which matches its age is,
[tex]E(X_i) = \frac{1}{1000}[/tex]
Expected number of card is,
X= (i=1 to 1000)∑ Xi
E(X) = (i = 1 to 1000) ∑ E(Xi)
= (i = 1 to 1000) ∑ (1 / 1000)
= 1000 x (1 / 1000)
= 1
E(X) = 1
Hence, One of people expected to receive a card with a number that matches its age.
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Prove the following statement by strong mathematical induction:
The sequence a0, a1,... recursively defined by a0 = 0, a1 = 1 and an = 2an−1 − an−2 +2 for n = 2, 3, ..
satisfies an = n2 for all non-negative integers n.
By using the principal of mathematical induction, it can be proved that
[tex]a_n = a_{n-1} - 2a_{n-2}+2[/tex] for [tex]a_n = n^2[/tex]
What is Principle of Mathematical Induction?
Suppose a statement P(n) is given. At first P(n) is proved to be true for
n = 1. Then P(n) is assumed to be true for n = m. If it can be proved that P(n) is true for n = m + 1, then by principle of Mathematical Induction, it can be proved that P(n) is true for all natural numbers
Here
[tex]a_n = n^2\\P(n) = 2a_{n-1} - a_{n-2} + 2\\P(0) = 0^2 = 0\\P( 1)= 1^2 = 1\\P(2) = 2a_1-a_0 + 2\\P(2) = 2(1)^2 - 0^2+2 =4[/tex]
Let us assume P(0), P(1),... P(k) is true
[tex]a_{k+1} = 2a_k - a_{k-1} + 2\\a_{k+1} = 2k^2 - (k-1)^2 + 2\\a_{k+1} = 2k^2 - k^2 +2k -1 + 2\\a_{k+1} = k^2+2k + 1\\a_{k+1} = (k+1)^2[/tex]
P(k+1) is true
By Principle of Mathematical Induction,
P(n) is true for all natural numbers
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Can a triangle be possible with the sides 3cm 4cm 5cm?.
Answer:
Yes, the measurements 3cm, 4cm and 5cm are possible to create a triangle!
Step-by-step explanation:
Determine which set of side measurements could be used to form a triangle. 9, 13, 21 8, 9, 18 3, 18, 21 2, 5, 9
The set of side measurements that could be used to form a triangle is 9, 13, 21.
A triangle is a polygon with three sides and three vertices.
To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.
9, 13, 21 : 9 + 13 > 21 ; 13 + 21 > 9 ; 9 + 21 > 13
8, 9, 18 : 8 + 9 < 18
3, 18, 21 : 3 + 18 = 21
2, 5, 9 : 2 + 5 < 9
Hence, the side measurements 9, 13, 21 is the only set that can be used to form a triangle.
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Two players, A and B alternatively toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The sequence of heads and tails is recorded. If there is a head followed by a tail (HT sub-sequence), the game ends and the person who tosses the tail wins. What is the expected length of this game? Let T number of coin tosses until the game ends. Find E(T). Round answer to 3 decimals
The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).
Given that,
A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on). The heads and tails are recorded in order. The game is over and the winner is the person who throws the tail if there is a head followed by a tail (HT sub-sequence).
We have to find what is the anticipated game length. Let the game continue for T number of coin tosses. Find E (T).
We know that,
Here,
E(T )=first time sequence HT occurs
E(T) = P(first H)× P(expected number till 1st T |first H)+ P(first T)× P(expected number till 1st HT |first T)
E(T) =0.5×(1+2)+0.5×(1+E(T))
0.5×E(T)=0.5×4
E(T) =4
Therefore, The E(T) is 4 when A and B, two players, alternately toss a fair coin (A tosses the coin first, then B tosses the coin, then A, then B and so on).
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5x+6y=6 Put the following equation of a line into slope-intercept form, simplifying all fractions.
The slope intercept form of the given line equation is y=-5/6 x+1.
The given equation of a line is 5x+6y=6.
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Here, the equation can be written in slope intercept form as
5x+6y=6
6y=6-5x
y=-5/6 x+1
Therefore, the slope intercept form of the given line equation is y=-5/6 x+1.
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After analyzing this data set, francine calculates a value of 20. 73 g. Which of these characteristics has been calculated? mean median mode range.
The correct answer is mean.
The characteristic which is being calculated here is the mean or the average of the data set.
(20.73 + 20.76 + 20.68 + 20.75)/4
when we divide it by 4 because there are four data sets
= 82.92 / 4
= 20.73
The complete question is 'Francine makes several measurements of the mass of a metal block and the data set is shown in the table below. The measurement mass of metal blocks(g) are a) 20.73 b) 20.76 c) 20.68 d) 20.75 . After analyzing the given data set, Francine calculates a value of 20.73 g so which of these characteristics has been calculated?'
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14. the height of a rectangular box is a constant 10 inches. its length increases at the rate of 2 in/sec, its width decreases at the rate of 4 in/sec. when the length is 8 inches and the width is 6 inches, find the rate at which the volume is changing in cubic inches per second.
The rate at which the volume of the box of height 10 inches is changing when the width is 8 inches and the length is 6 inches is 440 cubic inches per second
What is the volume of a rectangular box?The volume of a rectangular box is the product of the length, the width and the height of the box.
The height of the rectangular box, h = 10 inches
The rate of change of the length of the box is; [tex]\frac{dl}{dt}[/tex] = 2 in/sec
The rate at which the width is decreasing is; [tex]\frac{dw}{dt}[/tex] = 4 in/sec
When the length is 8 inches and the width is 6 inches, we get;
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt} \left(l\cdot w \cdot h\right)[/tex]
[tex]\dfrac{dV}{dt} =h\times \left(l\cdot \dfrac{dw}{dt} + w \cdot \dfrac{dl}{dt} \right)[/tex]
When l = 8, and w = 6, we get;
[tex]\dfrac{dV}{dt} =10\times \left(8\times 4 + 6 \times 2 \right)=440[/tex]
The rate at which the volume of the rectangular box is changing in cubic inches per second is therefore;
[tex]\dfrac{dV}{dt} =440 \ in^3/sec[/tex]
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What are the 4 types of functions?.
The four types of function are One One Function , Many to One Function , Onto Function and Into Function .
The four types of functions are :
A one-to-one function is defined as f: A B, where each element in set A is connected to a specific element in set B. The one-to-one function is also known as an injective function. Each domain element in this case has a distinct image or co-domain element for the given function.A many-to-one function is defined by the function f: A B, which links various elements of set A to a single element of set B. In a many to one function, multiple elements share the same co-domain or image.In an onto function, the domain element and each codomain element are connected. For a function described by f: A B, every element in set B has a pre-image in set A. The onto function is also known as a subjective function.The characteristics of an onto function and an into function are identical. In this instance, some co-domain components are missing pre-images. Set B contains an excessive number of components in its range, and none of them are related to anything in set A.To learn more about functions visit:
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What is the y-intercept of the function FX 4 5x 5 4 4 5?.
y-intercept of the function = 4
What in mathematics is a y-intercept?
A point on the y-axis at which the slope of a line passes is referred to as an intercept in mathematics.
It is a place on the y-axis where a straight line or a curve crosses. This is shown by writing the equation for a line as y = mx+c, where m denotes the slope and c the y-intercept.
Here the given function is
f(x) = 4 – 5x
Which can be rewritten as
f(x) = – 5x + 4
Which is of the form f(x) = mx + c
Where m = - 5 , c = 4
Hence y-intercept of the function = 4
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The complete question is -
What is the y-intercept of the function f(x)=4 – 5x?
–5
–4
4
5
primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.
Maintenance primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.
Preventive maintenance schedules can be regular or periodic (time-based). When an issue is discovered, corrective maintenance is performed. Maintenance is predetermined and follows a factory schedule. Condition-based maintenance occurs when a situation or condition indicates the need for maintenance.
What is modifying a program?
A program modification is defined as a programmatic change that does not clearly qualify as a new program or a nonsubstantive change, such as a new program composed primarily of course work from a previously approved program; an approved program to be offered at an off-campus location; a change in the.
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Full Question:_____ primarily involves modifying programs to meet new business needs, but also debugging of errors that were not detected when testing the developed code.
After 3 day, what i the balance in an account that ha a $1,000 balance and earn 6% compounded daily?
After 3 days the balance will be $1050.130
What does "compound daily rate" mean?
Daily compounded interest is higher than interest compounded on a monthly or quarterly basis due to the high frequency of compounding, which means interest is accrued daily and calculated by charging interest on principal plus interest earned daily.
How is compounded daily determined?
How Compounding Works
For the purpose of calculating compound interest:
Investment total: Start amount multiplied by interest rate plus one, then daily interest rate
The interest rate will be divided by 365 and the number of years (n) will be multiplied by 365 to determine daily compound interest.
Added Up Monthly: CI = P(1 + (r/12) ) 12t – P
P represents the principal sum.
r is the time and t is the decimal form of the interest rate.
Given that:
t: the amount of time. Assume that the $1,000 in the savings account from the preceding illustration earned daily compound interest at a rate of 6%. This results in an interest rate of 0.0164384% each day: 6% multiplied by 365.
[tex]At = $1,000 * (1 + 0.0164384)^3[/tex]
At = $1,000 × 1.050130
At = $1,050.130
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Which equation shows the point-slope form of the line that passes through 3 2 and has a slope of 1 3?.
The point-slope form of the line is y - 2 = 1/3(x - 3).
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
The equation of the line into point slope-form is equal to
y - y1 = m(x - x1)
slope(m) = 1/3
(3,2)....x1 = 3 and y1 = 2
now we sub
y - 2 = 1/3(x - 3)
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This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why
The conclusion of step 4 and step 5 are not valid . Therefore, this is an invalid proof that all isosceles triangles.
Each step is valid, but the conclusion is not. At the end of step 4, there are a series of isometric maps that lead A to D and C to F, as claimed.. After the final rotation in Step 5, the sequence of isometries takes B to E and C to F —but here’s the hitch—there is no reason why it should still take A to D, in fact it can’t take A to D unless the rotation angle is zero.
If the rotation angle in Step 5 is zero, then the isometries take [A,B,C] to [D,E,F] and the two triangles are indeed similar. But this requires the dilation in Step 2 to have made A′B′ congruent to DE , in other words, it requires assuming the triangles are similar before performing any of of the transformations.
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Complete Question:
This is an invalid proof that all isosceles triangles are similar. Explain which step is invalid and why. 1. Draw 2 isosceles triangles ABC and DEF where AC = BC and DF = EF. 2. Dilate triangle ABC to a new triangle A'B'C' using center C and scale factor DF/AC so that A'C= BC - DF = EF. 3. Translate by directed line segment CF to take A'B'C' to a new triangle A" B" F. Since translation preserves distance, A"F = A'C=DF and B" F = BC = EF. 4. Since A"F=DF, we can rotate using center F to take A" to D. 5. Since B" F = EF, we can rotate using center F to take B" to E. 6. We have now established a sequence of dilations, translations, and rotations that takes A to D, B to E, and C to F, so the triangles are similar.
if we standardize both variables what would the regression equation be that predicts standardized mortgage amounts
If we standardize both variables what would the regression equation the mortgage amount will be 220.88 and the interest amount will be 7.768.
[tex]b_1[/tex] = r*[tex]S_{xy}/S_{xx}[/tex]
= -0.84
[tex]b_0 = y - b_1x[/tex]
Regression model is used to identify the relation between two variables.In the relation between two variables.
From the given question the regression model fits best to identify the mortgage amount from interest rates.
The interest rate and mortgage both are quantitative values so the regression model is most suitable for this given condition.
Therefore If we standardize both variables what would the regression equation the mortgage amount will be 220.88 and the interest amount will be 7.768.
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A dressmaker needs to cut 18-inch pieces of ribbon from rolls of ribbon that are 6 feet in length. How many 18-inch pieces can the dressmaker cut from 15 of these rolls of ribbon?.
Using simple Units Measurement System,
Dressmaker cut total 40 pieces of length 18 inch from 15 of given rolls of ribbon.
We have given that,
total length of roll of ribbon = 6 feet
the length of ribbon cut by dressmaker = 18 inch
As we know , 1 inch = 2.5 cm --(1)
then 1 feet = 30cm --(2)
from (1) and (2) , we get
1 feet = 12 inch
total length of roll ribbon in inch = 6×12
= 72 inches
we have total number of ribbons = 5
so, total number of inches = 5 ×72 = 360 inches
As per question given that dressmaker need to cut 18 inch piece for making dress .
So, total number of 18 inch pieces Dressmaker has is equal to ratio of total length of ribbon / length of ribbon dressmaker needed
= 720/18
= 40
Hence, total 40 pieces of length 18 inch dressmaker have.
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x-2.
2x + 4
25
2x - 2
24
Solve for x.
48
36
Answer: x-2
and 2x+4
Step-by-step explanation:
How do you show that a function is a linear function?.
The approach to identify linear functions is whether the change in y will always have the same value for any given change in x.
Possibly the most significant mathematical function is the linear function. One of the simplest functions to comprehend, it frequently appears when you least expect it. We frequently turn more complex functions into linear functions for understanding purposes since it is so convenient to do so. The linear function is incredibly straightforward for one variable. A linear function is one with the formula f(x)=ax, where an is a real number of any value. The parameter an is the slope of the line through the origin that makes up the graph of the function f.
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How do you describe the transformation of Y x2?.
The transformation of y = x² can be described as, Right and left one and down one-half, right and left two and down two, and right and left three and down four and one-half are the points plotted from the vertex.
Define transformation.A transformation is a technique for moving or repositioning a shape. Every point in the shape is moved in the same direction and by the same amount. When a shape is rotated, a point is turned into the center. When a shape appears in a mirror line, it is said to be reflecting. When a shape is shifted a predetermined amount from its initial position, this is known as translation.
Given,
The transformation of y = x² can be described as,
A vertical stretch is the name for this change. Transformation of y = x² can be described as. Right and left one and down one-half, right and left two and down two, and right and left three and down four and one-half are the points plotted from the vertex.
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how many integers fall between the square root of 7 and the square root of 77 on a number line
Answer:
There are 6 integers between sqrt7 and sqrt77.
Step-by-step explanation:
Sqrt9, sqrt16, sqrt25, sqrt36, sqrt49, sqrt64 are all between sqrt7 and sqrt77. Since these are all perfect squares, they simplify to integers.
sqrt9 = 3
sqrt16 = 4
sqrt25 = 5
sqrt36 = 6
sqrt49 = 7
sqrt 64 = 8
There are 6 integers between sqrt7 and sqrt77.
I really need help to get this done, please.
Answer:
The area of the base of the cylinder (the circle face) is the same as the area of the base of the prism (the triangle face).
Step-by-step explanation:
The volume of a prism is the area of the base of the prism multiplied by its height.
The volume of a cylinder is the area of the base of the cylinder multiplied by its height.
So because the volumes are both equal, and the heights are both equal
Then the area of the bases should also be equal.
say whether the given pair of events is independent, mutually exclusive, or neither. a: your first coin flip results in heads. b: your second coin flip results in heads.
independent
mutually exclusive
neither
The given pair of events are independent when your first coin flip results in heads. and your second coin flip results in heads.
Events that occur independently of any other events are referred to as independent events. if we flip a coin in the air and get the head, we will then flip the coin again, but this time we will get the tail. The occurrence of both events is unrelated in either instance. Tossing the coin the first time does not affect the outcome of the second toss.
Note that the events are not mutually exclusive as it is possible that both the first and the second toss are headed.
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After analyzing several months of sales data, the owner of an appliance store produced the following joint probability distribution of the number of refrigerators and stoves sold hourly
0 1 2 Stoves
0 0.08 0.14 0.12 0.34
1 0.09 0.17 0.13 0.39
2 0.05 0.18 0.04 0.27
REF 0.22 0.49 0.29 1
b. What are the laws for a discrete probability density function?
c. If a customer purchases 2 stoves, what is the probability they will also purchase two refrigerators?
d. What is the average number of refrigerators purchased?
e. What is the variance in the number of refrigerators purchased?
f. Are the sale of stores and refrigerators independent?
g. What is the conditional probability distribution for sales in refrigerators if the customer did not purchase a stove?
h. What is the expected value and variance for sales in refrigerators, if the customer did not purchase a stove?
Each probability lies between 0 to 1, If a customer purchases 2 stoves, the probability is 0.1379 they will also purchase two refrigerators, the average number of refrigerators purchased is 0.93, and the variance in the number of refrigerators purchased is 0.6051.
A) 0 1 2 stoves
0 0.08 0.14 0.12 0.34
1 0.09 0.17 0.13 0.39
2 0.05 0.18 0.04 0.27
RF 0.22 0.49 0.29 1
B) Each probability lies between 0 to 1
All the probabilities sum up to 1
C) P(2 Ref/ 2 stoves) = P(2 Ref and 2 stoves) / 2 stoves)
= 0.04/0.29 = 4/29 = 0.1379
D) Average number of Ref purchased E(x) = ∑xi pi
X 0 1 2
Prob. 0.34 0.39 0.27
= 0.39 + 0.54
= 0.93
E) Var(x) = ∈(x)² - (∈{x})²
= (0.39 + 1.08) - (0.93 * 0.93)
= 1.47 - 0.8649
= 0.6051
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the diagrams below show the application of a force f on a block of mass m. which diagram(s) produces the largest acceleration on the block in the horizontal direction?
The diagram 1 and 3 produces the largest acceleration on the block in the horizontal direction
The diagram below show the application of a force f on a block of mass m
The force is defined as the product of mass and acceleration
The first picture represents the force pulling to right in the horizontal direction here the angle is zero therefore it will produce the largest acceleration on the block in horizontal direction. Because it depends on the angle which F cosθ
Similarly in the third figure the force is pushing on the block to the right. The angle is zero, therefore it will produce largest acceleration in horizontal direction
In other figures the angle is greater than zero therefore the acceleration in the horizontal direction will be small
Hence, the diagram 1 and 3 produces the largest acceleration on the block in the horizontal direction
The complete question is:
The diagrams below show the application of a force f on a block of mass m. which diagram(s) produces the largest acceleration on the block in the horizontal direction?
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Solve using method of elimination
3x - y= 5
4x + y= 9
Answer:
Step-by-step explanation:
solving by elimination means to get rid of one of the variables, pick either one, X or Y and use the other equation to make it zero.
3x - y = 5
4x + y = 9
+______ add the two equations, column for column,
7x + 0y = 14
now solve for x, that is, get x by itself
7x / 7 = 14/7
x = 2
Now that you've solved for x, plug that x into either equation.
3(2) - y = 5
6-y = 5
6-5 = y +5-5
1 = y
Now you have both :)
