The proof of divisibility is correct in this question.
DivisibilityThe capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.
According to the question
It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.
The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes 75^30 = 31 * 52^30 = 3^30 * 5^60. Similar to how 45 may be expressed as 3^2 * 5^1, 3^90 * 5^45 is equal to 45^45 = (3^2 * 5^1)^45. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.
75 = 3^1 * 5^2,
∴ 75^30 = (3^1 * 5^2)^30 = 3^30 * 5^60.
It follows that 75^30, or 3^30 * 5^60, divides 45^45 * 15^15, or 3^90 * 5^45 * 3^15 * 5^15, as 3^30 divides 3^90 and 5^60 divides 5^45.
45 = 3^2 * 5^1,
∴ 45^45 = (3^2 * 5^1)^45 = 3^90 * 5^45.
15 = 3^1 * 5^1,
∴ 15^15 = (3^1 * 5^1)^15 = 3^15 * 5^15.
In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.
To know more about divisibility on brainly : brainly.com/question/21416852
#SPJ4
The proof of divisibility is correct in this question.
Divisibility
The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.
According to the question,
It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.
The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes [tex]75^{30}=(31*52^{30})=(3^{30}*5^{60})[/tex]. Similar to how 45 may be expressed as [tex](3^2*5^1)[/tex]. [tex](3^{90}*5^{45})[/tex] is equal to [tex]45^{45}=(3^2*5^1)^{45}[/tex]. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.
[tex]75=3^1*5^2[/tex],
∴ [tex]75^{30}=(3^1*5^2)^{30}=3^{30}*5^{60}[/tex].
It follows that [tex]75^{30}[/tex], or [tex](3^{30}*5^{60})[/tex], divides [tex](45^{45}*15^{15})[/tex] or [tex](3^{90}*5^{45}*3^{15}*5^{15})[/tex], as [tex]3^{30}[/tex] divides [tex]3^{90}[/tex] and [tex]5^{60}[/tex] divides [tex]5^{45}[/tex].
[tex]45=3^2*5^1[/tex]
∴ [tex]45^{45}=(3^*5^1)^{45}=3^{90}*5^{45}[/tex]
[tex]15=3^1*5^1[/tex]
∴ [tex]15^{15}=(3^1*5^1)^{15}=3^{15}*5^{15}[/tex]
In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.
To know more about divisibility
brainly.com/question/21416852
#SPJ4
Sara's past year at work pushed her to the limit, and she needs to recharge. She wants to splurge by spending 13 of his savings on a monster vacation. Her financial planner suggests that she spend less than $2500 on the vacation. Let x be the amount of money Sara has in savings. a) Write an inequality that best represents this situation. b) Solve the inequality for x. c) What does the value of x in part b represent in this situation.
An inequality that best represents this situation is: x - 1300 > 2500.
How to solve for the inequality?a) Let x be the amount of money Sara has in savings. We know that the amount she wants to spend on vacation is $1300, so we have x - 1300 > 2500.
b) To solve for x, we can add 1300 to both sides: x > 3800.
c) The value of x in this situation represents the amount of money Sara has in savings.
The inequality x > 3800 means that Sara must have more than $3800 in savings in order to spend $1300 on a vacation while following the financial planner's suggestion to spend less than $2500.
Read more about inequalities here:
https://brainly.com/question/24372553
#SPJ1
Bowler World charges $5. 00 to rent shoes and $1. 10 per game. Lucky Spares charges $3. 00 for shoes and $1. 50 per game.
Part A
Drag numbers to complete a system of equations to represent the situation, using g for number of games and c for cost. Numbers may be used once, more than once, or not at all.
Bowler World: c = ?g + ?
Lucky Spares: c = ?g + ?
(Numbers: 1, 1. 1, 1. 5, 2. 6, 3, 5, 8)
The number of games that would make the cost equal in both locations is 5. The total cost is $10.50.
The equation that can be used to determine the total cost of renting shoes at both locations is:
total cost = fixed cost + variable cost
Total cost of renting at Bowler World = $5 + $1.1x
Total cost of renting at Lucky Spares = $3 + $1.50x
Where
x = number of games played
In order to determine the number of games that would make the cost
equal in both locations, the following steps would be taken:
$5 + $1.1x = $3 + $1.50x
Combine similar terms
$5 - $3 = $1.50x - $1.1x
$2 = $0.40x
Divide both sides of the equation by $0.4
x = 2 / 0.4
x = 5 games
Total cost = $5 + $1.1(5) = $5 + $5.5 = $10.50
Learn more about the cost estimation here :
https://brainly.com/question/2611396
#SPJ4
Please help me I have no idea how to do this it’s about Multiples
Answer:
Step-by-step explanation:
Can anyone help me solve this problem step by step?
Step-by-step explanation:
to solve an equation with a variable we want to transform the equation, so that in the end we have the variable alone on one side of the equation, and everything else on the other side.
so, when we look at
(n + 8)/2 - 4 = 16
what blocks us from reading the value of n ?
several things on the left side.
I would start with the "- 4".
to get rid of that from the side of the variable we need to add 4. and to keep the equality true, we need to add this on both sides :
(n + 8)/2 - 4 + 4 = 16 + 4
and we get
(n + 8)/2 = 20
what blocks us now ?
I would say the fraction, this division by 2.
how do we get rid of that ?
by multiplying everything by 2 :
2×(n + 8)/2 = 2×20
and we get
n + 8 = 40
still, something is blocking us from reading the value of n : the "+ 8".
how do we get rid of that ?
by subtracting 8 from both sides :
n + 8 - 8 = 40 - 8
and we get
n = 32
that's it. we are finished. goal achieved.
Which ordered pair a solution of the equation? -x-4y=-10
Answer:
-10+4=-x
-x_=-6_
x=6
if you don't understand
negative x over negative x and negative x over 6 the negative will cancle the negative you will get x to be 6
problem 3: compute the general solution for: d^2y/dt2 − 2 dy/dt − 15y = e^4t
The general solution for d^2y/dt^2 - 2dy/dt - 15y = e^4t is a sum of a homogeneous solution (c1e^(r1t) + c2e^(r2t)) and a particular solution (Ate^4t).
What is differentiation ?
Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.
The general solution for the second-order homogeneous linear ordinary differential equation d^2y/dt^2 - 2dy/dt - 15y = 0 can be found using the characteristic equation:
r^2 - 2r - 15 = 0
The characteristic equation has two roots, which are the eigenvalues of the corresponding homogeneous linear system. Let r1 and r2 be the roots of the characteristic equation, then the general solution for the homogeneous equation is:
y(t) = c1e^(r1t) + c2e^(r2t)
where c1 and c2 are arbitrary constants.
y(t) = c1e^(r1t) + c2e^(r2t) + Ate^4t
The general solution for d^2y/dt^2 - 2dy/dt - 15y = e^4t is a sum of a homogeneous solution (c1e^(r1t) + c2e^(r2t)) and a particular solution (Ate^4t).
To learn more about differentiation visit : brainly.com/question/24898810
#SPJ4
PLEASE ANSWER WILL GIVE BRAINLIEST!!!
The box plot shows the times for sprinters on a track team. A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds. Which value does 50% of the data lie above, and what is it called? 54, the upper quartile 44, the lower quartile 50, the median 42, the median
The value that 50% of the data, is 50 the median.
What is the Box Plot?An illustration of variation in a set of data is called a box and whisker plot. A histogram analysis usually gives an adequate display, but a box and whisker plot can add more detail while enabling the display of different sets of data on the same graph.
Given Data: 42, 44, 50, 54, and 56
The median can be referred to as the second quartile (Q2) or 50th percentile of the data set.
The median value shows that 50% of the data set is above it while 50% is below it also.
So, 50 is the median, and this means that 50% of the data lie above 50.
Learn more about the median of a box plot here:
brainly.com/question/14277132
#SPJ1
Create a rational function that has the
given lines as asymptotes.
1. y = 0, x = −3, x = 0, and x = 2
2. y = 3/2, x = -1, and x= 1/2
The rational functions with the given asymptotes are presented as follows:
1. y = 1/(x³ + x² - 6x).
2. y = 1.5x²/(x² + 0.5x - 0.5).
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
For item 1, due to the vertical asymptotes, the denominator is given as follows:
x(x + 3)(x - 2) = x(x² + x - 6) = x³ + x² - 6x.
As the horizontal asymptote is of zero, the numerator has a lower degree than the denominator, hence it can be constant, and the function is given as follows:
y = 1/(x³ + x² - 6x).
For item 2, the denominator is given as follows:
(x + 1)(x - 0.5) = x² + 0.5x - 0.5.
Due to the horizontal asymptote of 3/2, the degree of the numerator must be the same as the denomiator, with a coefficient 3/2 that of the denominator, hence the numerator is given as follows:
3x²/2 = 1.5x².
Meaning that the function is:
y = 1.5x²/(x² + 0.5x - 0.5).
More can be learned about the asymptotes of a function at https://brainly.com/question/4138300
#SPJ1
PROBLEM SOLVING
The area of a door is given by the expression 7x- 14. The door's length is 7 feet.
7. Write an expression to represent the 8. Evaluate your expression for for x = 6,
width of the door.
to find the door's actual width.
9. Find the area of the door.
10. Find the perimeter of the door.
Answer:
see below
Step-by-step explanation:
area of a door = length * width = 7* width = 7x-14
so width = ( 7x-14 ) / 7 = x-2
when x=6 width = 4
area = 4*7 = 28
perimeter = (4+7)*2 = 22
help ill give brainless
Answer: c
Step-by-step explanation:
quite easy because y=mx+b (y=3x-1)
the -1 is the y-intercept. (Where the line meets the y line. c is the only one where the y-intercept is -1
Find the period of this function:
A. 2
B. 4
C. 6
D. 8
Answer:
is 2
because it's below for and two is the closest answer to the function variable answer to this question that you have here
If a pair of linear equation in two variable have no solution then the pair of lines are
If a pair of linear equations in two variables have no solution then the pair of lines are inconsistent or parallel lines.
Solutions of a pair of linear equations:
Depending on the number of variables and type of equations there are 3 types of solutions to an equation.
1. Unique Solution (One solution):
When there is only one variable then the linear equation will have a Unique Solution or One solution. In the case of pair of linear equations, the linear equation will have a unique solution when the straight lines are intersected at a single point.
2. No solution:
When the given pair of linear equations is inconsistent equations the linear equation will have no solutions in common or we can say that the given lines are non-intersected lines. Usually, a pair of parallel lines will have no solutions.
3. Infinite Solutions (Many solutions):
When the given lines are overlapped on each other or coincident with each other the given lines will have Infinite Solutions. These intersected lines.
Therefore,
If a pair of linear equations in two variables have no solution then the pair of lines are inconsistent or parallel lines.
Learn more about Linear equations at
https://brainly.com/question/18751934
#SPJ1
Write a division problem with 1/4
as the dividend and 3 as the divisor. Then, find the quotient.
(GIVING 20 POINTS)
When 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.
What is meant by dividend?The amount that needs to be split up into a specific number of equal pieces in a division problem is known as the dividend. Similar to the example given above, the dividend is the number 20 and the divisor is the number 5 when we divide a group of 5 individuals into a group of 20 apples.A number is divided by any other number in division to get a new number. Thus, the dividend is the number that is divided in this context. The divisor is the quantity that divides the provided quantity. The resultant number is what is known as the quotient. When a number is divided partially by a divisor, the result is known as the remainder.Dividend/Divisor is the quotient.
Divide the dividend by the divisor to obtain the quotient.
Here, Dividend = 1/4
Divisor = 3
Divisor/Dividend =(1/4)/3 = 1/12
So, when 1/3 is the dividend and 3 is the divisor, the quotient is 1/12.
To learn more about dividend, refer to:
https://brainly.com/question/30278644
#SPJ4
Suppose that ????(1)=8, ????(4)=7, ???? '(1)=9, ???? '(4)=−3, and ???? '' is continuous. Find the value of the definite integral ∫x????″(x) ????x on the interval [1,4].
The value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [tex][1,4][/tex] is -5.
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. Definite integration involves finding the exact area between a curve and the x-axis over a specified interval. Indefinite integration involves finding the general antiderivative of a function, which is a function that, when differentiated, will yield the original function.
The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
Given that ????(1) = 8, ????(4) = 7, ???? '(1) = 9, and ???? '(4) = -3, we can use the method of integrating by parts to evaluate the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4].
Let u = ????(x) and dv = x dx. Then du = ???? '(x) dx and v = x^2/2.
Using the method of integrating by parts, we have:
∫[tex]x????"(x)????(x) dx= x????(x)[/tex] ×[tex]\frac{x}{2} -[/tex]∫[tex](\frac{x^{2} }{2} )????'(x) dx[/tex]
We can use the same method of integrating by parts to evaluate the second integral on the right-hand side. Let [tex]u=\frac{x^{2} }{2}[/tex] and [tex]dv=????'(x) dx[/tex]. Then [tex]du=x dx[/tex] and [tex]v=????(x)[/tex].
So we have:
∫[tex]x????"(x)????(x) dx = x????(x)[/tex]× [tex]\frac{x}{2} - \frac{x}{2} ^{2}????(x) + c[/tex]
Where C is an arbitrary constant of integration.
We can use the given values of ????(1) and ????(4) to evaluate the definite integral:
∫[tex]x????"(x)????(x) dx[/tex] = 4????(4) * 4/2 - (4^2/2)????(4) + 4????(1) * 1/2 - (1^2/2)????(1)
= 28 - 14 * 7/2 + 4 * 8/2 = 28 - 49 + 16 = -5.
Therefore, the value of the definite integral ∫[tex]x????"(x)????(x) dx[/tex] on the interval [1, 4] is -5.
To know more about integration visit:
https://brainly.com/question/18125359
#SPJ4
PLEASE HELP
Which of the following functions has the same horizontal asymptote as the function graphed below
A function which has the same horizontal asymptote as the function graphed above include the following: A. f(x) = 4^{x + 2} - 3.
What is a horizontal asymptote?In Mathematics, a horizontal asymptote simply refers to a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).
In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential growth function represents a horizontal asymptote and it has an equation of y = 3, as shown in the image attached below.
Read more on horizontal asymptote here: https://brainly.com/question/14492751
#SPJ1
Macy's starting balance in her checking account was $654.98. She wrote one check in the amount of $321.45 and made a
deposit that she forgot to write into her check register. At the end of the month, Macy's ending balance was $452.78. Find the
amount of the deposit.
$119.25
$114.38
$121.56
$116.74
Answer:
$119.25.
Step-by-step explanation:
Let's call the deposit amount "D".
Starting balance: $654.98
Check amount: -$321.45
Deposit: +D
Ending balance: $452.78
So, we can set up an equation:
$654.98 - $321.45 + D = $452.78
Solving for D:
$654.98 - $321.45 + D = $452.78
$333.53 + D = $452.78
D = $119.25
So the deposit amount was $119.25.
how much time fo students at your school spend on the internet? you collect sata from the 32 members of your ap statistics class and calculate the mean amount of time that these students spent on the internet yesterday
Calculating the mean amount of time that these students spent on the internet yesterday it is not appropriate because sample is a convenience sample to determine condition for population mean.
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, median, and mode.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in ascending order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.
Learn more about Mean:
https://brainly.com/question/1136789
#SPJ4
consider the function f(x,y) = x 2y, defined on d, i.e., the region bounded by the parabolas y= 2x2 and y= 1 x2. a. sketch the region din the x−yplane. b. evaluate the integral ∫∫ df(x,y)dxdy.
the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get: ∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is illustrated in the figure below.
b. ∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
a. The region D in the x-y plane is the area bounded by the two parabolas y= 2x2 and y= 1 x2. This can be seen in the sketch below.
b. To evaluate the integral ∫∫ df(x,y)dxdy, we need to evaluate the integral of the function f(x,y) = x2y over the region D. We can do this by setting up the integral as follows:
∫∫ df(x,y)dxdy = ∫-2 to 2 ∫2x2 to 1x2 x2(y)dxdy
Next, we can evaluate the integral by substituting the limits of integration for x and y and integrating with respect to x first. We get:
∫∫ df(x,y)dxdy = ∫-2 to 2 x2(1x2-2x2)dx = ∫-2 to 2 x2(-x2)dx = ∫-2 to 2 -x4dx = [-x5/5]from -2 to 2 = -2^5/5 + 2^5/5 = 0
Learn more about integral here
https://brainly.com/question/18125359
#SPJ4
we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this? a.6 b.10 c.30 d.60
The number of unique committees is 240 / 4 = 60. So the answer is d. 60.
What is the combination?
The permutation is to select an object and then arrange it and it cares about the orders while Combination is about only selecting an object without caring about the orders.
To form a committee with 2 women and 2 men, we have 4 choices for the first woman, 3 choices for the second woman, 5 choices for the first man, and 4 choices for the second man.
Therefore, the number of ways to form a committee is 4 * 3 * 5 * 4 = 240. This is the total number of combinations, and to find the number of unique committees,
we need to divide by the number of ways to arrange the members within each committee.
As the members are distinguishable, the number of arrangements is simply 2! * 2! = 4.
Therefore, the number of unique committees is 240 / 4 = 60. So the answer is d. 60.
To learn more about the combination visit,
https://brainly.com/question/26852614
#SPJ4
.A polling organization announces that the proportion of American voters who favor congressional term limits is 64%, with a 95%
confidence margin of error of 3%. Which of the following statements is a correct interpretation of 95% confidence?
A. If the poll were conducted again in the same way, there is a 95% chance that the fraction of voters favoring term limits in the
second poll would be between 61% and 67%.
B. There is a 95% probability that the true percent of voters favoring term limits is between 61% and 67%.
C. If the poll were conducted again the same way, there is a 95% probability that the percent of voters favoring term limits in the
second poll would be within 3% of the percent favoring term limits in the first poll.
D. Among 95% of the voters, between 61% and 67% favor term limits.
E. None of the above.
Why do we use a pooled estimate of the population?
By merging information from several sources, a pooled estimate of the population is utilised to gain a better picture of the population mean as a whole.
When a person or organisation needs to combine data from several sources to better understand a population, they utilise a pooled estimate of the population. This can be accomplished in a number of ways, such as by integrating data from several surveys, data from various time periods, or data from various geographical regions .A more complete and accurate view of the population can be acquired by combining the data from several sources. Because it enables a more precise assessment of a population's needs and traits, this is particularly helpful for making judgements about policy or resource distribution. The comparison of several populations or the analysis of changes across time can both be done using pooled estimates. This is necessary to comprehend population change and determine the most effective resource allocation.
Learn more about population mean here
https://brainly.com/question/19538277
#SPJ4
A diagonal of a square mirror is 10 inches long. What is the length, in inches, of each side of the mirror?.
An equation is shown below.
√−x=x+6 Which of these statements are true? Choose all that are correct. A.x=−9 satisfies the equation.
в. This equation has exactly one solution. c. This equation has the same solution set as−x=x2+12x+36. D. This equation has the same solution set as−x=x2+36. E.x=−4
Given quadratic equation has same solution set as -x=x²+12x+36 i.e. C.
Quadratic equations: what are they?A second-degree algebraic equation in x is a quadratic equation. Ax2 + bx + c = 0 is the quadratic equation in its standard form, with a and b acting as coefficients, x acting as the variable, and c acting as the constant term.
The coefficient of x2 must not be zero (a 0) for an equation to qualify as a quadratic equation. The x2 term comes first, followed by the x term, and finally the constant term when stating a quadratic equation in standard form. Instead of being written as fractions or decimals, the numerical values a, b, and c are frequently expressed as integral values.
Now,
Given equation is √-x=x+6
-x = (x+6)²
-x = x² +36+12x
x² + 11x + 36 = 0
As it is same quadratic equation as given in option C.
Hence,
Given quadratic equation has same solution set as
-x = x² + 12x + 36.
To know more about quadratic equations visit the link
brainly.com/question/30098550?referrer=searchResults
#SPJ4
Long division method square root of 5508409
Answer:
2347
2347 * 2347 = 5508409
Step-by-step explanation:
Hope it helps! =D
Given the following probabilities, compute all joint probabilities.
P(A) = .9
P(B | A) = .4
P(AC) = .1
P(B | AC) = .7
The joint probabilities are: P(A and B) = 0.36, P(A and C) = 0.1, P(AC and B) = 0.07.
What do you mean by Probability?Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1. An event with probability 0 cannot occur, and an event with probability 1 is certain to occur. The probability of an event A is usually written as P(A) and is calculated as the number of favorable outcomes divided by the total number of possible outcomes in the sample space. For example, if a fair six-sided die is rolled, the sample space is the set of all possible outcomes (1, 2, 3, 4, 5, 6), and the probability of rolling a 4 is 1/6. Probability is used in many fields to make predictions, draw inferences, and make decisions under uncertainty.
We can use the formula for conditional probability to calculate the joint probabilities:
P(A and B) = P(B | A) * P(A) = .4 * .9 = .36
P(A and C) = P(A) * P(C | A) = .9 * P(C) / P(A) = .9 * .1 / .9 = .1
P(AC and B) = P(B | AC) * P(AC) = .7 * .1 = .07
So, the joint probabilities are:
P(A and B) = .36
P(A and C) = .1
P(AC and B) = .07
To know more about outcomes visit:
https://brainly.com/question/19916581
#SPJ4
30 points! Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Slope of the line: ___
Answer:
m = 5/4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (0, -3) (4,2)
We see the y increase by 5 and the x increase by 4, so the slope is
m = 5/4
Bob bought 2 t-shirts at 249. 95 pesos each and a pair of pants for 675. 95. How much change did he get from his 1 000 peso bill?
1. What is asked?
2. What are given?
3. What is/are the hidden question?
4. What operations will you use to solve the problem?
5. What is number sentence?
6. What is the answer?
pasagot po tnx
I will mark you as brainliest if your answer is good :3
The solution is :
1. How much change did he get from 1500-pesos bill.
2. 2 t-shirt 249.95 pesos pants for 675.95 pesos .
3. 2 t-shirt and pair of pants.
4. 249.95 pesos + 675.95 pesos and subtraction 1500-pesos bill.
5. Seventy-four and twenty cents.
6. 74.20 pesos.
Arithmetic is one of the oldest and elementary branches of mathematics, originating from the Greek word ‘Arithmos’, which means ‘number’. Arithmetic involves the study of numbers, especially the properties of traditional operations, such as: Addition, Subtraction, Multiplication, Division.
The arithmetic operators based on these operations are ‘+’, ‘-’, ‘×’ and ‘÷’.
as given, Bobby bought:
2 shirts bought at 249.95 each
Pair of pants for 675.95
So,
How much change did he get from his 1500 peso bill ? (correction : 1500 peso)
2 shirts for 249.95 each.
249.95 * 2 = 499.9
Total spent on the shirts : 499.9
A pair of pants bought for: 675.95
Total money spent = 675.95 + 499.9 = 1175.85
In order to determine the final solution we have to subtract the total amount from 1500.
1500 - 1175.85 =324.15
He will getting a change of 324. 15 pesos .
Therefore, The solution is :
1. How much change did he get from 1500-pesos bill.
2. 2 t-shirt 249.95 pesos pants for 675.95 pesos .
3. 2 t-shirt and pair of pants.
4. 249.95 pesos + 675.95 pesos and subtraction 1500-pesos bill.
5. Seventy-four and twenty cents.
6. 74.20 pesos.
To learn more about arithmetic visit : brainly.com/question/29116011
#SPJ4
Bob received 824.15 pesos as change from his 1 000-peso bill.
What is asked?
The question asks for the change Bob received from his 1 000-peso bill.
What are given?
The given information is that Bob bought 2 t-shirts at 249.95 pesos each and a pair of pants for 675.95.
What is/are the hidden question?
The hidden question is: How much did Bob spend in total?
What operations will you use to solve the problem?
To solve the problem, you need to find the total amount that Bob spent, and then subtract it from his 1 000-peso bill to get his change.
What is the number sentence?
The number sentence would be: change = 1 000 pesos - (2 * 249.95 pesos + 675.95 pesos)
What is the answer?
To find the answer, you can calculate the expression in the number sentence:
change = 1 000 pesos - (2 * 249.95 pesos + 675.95 pesos)
change = 1 000 pesos - (499.90 pesos + 675.95 pesos)
change = 1 000 pesos - 1175.85 pesos
change = 824.15 pesos
To learn more about pesos please click on below link.
https://brainly.com/question/8007129
#SPJ4
suppose that one customer who participated in the study is chosen at random. what is the probability that the customer had a high level of satisfaction and used the company more than five times per month?
The probability of an event is given by the number of favorable outcomes divided by the total number of possible outcomes.
In this case, the favorable outcome is that the customer had a high level of satisfaction and used the company more than five times per month. The total number of possible outcomes is the total number of customers in the study, which is 700.
Therefore, the desired probability can be calculated as:
P(High satisfaction and more than 5 times per month) = 70 / 700
And the answer is P(High satisfaction and more than 5 times per month) = 70 / 700 = 1/10.
To know more about probability
brainly.com/question/11234923
#SPJ4
how to develop the shape of the hole in the cone when it intersects with a cylinder
The generatrix of a cylinder is intersected by a plane parallel to its axis to determine the shape of the hole in the cylinder, while the generatrix of a cone is intersected by a plane via its vertex.
We select cutting planes that intersect both surfaces along their generatrixes in order to construct the intersection points of a cone and a cylinder. A cylinder's generatrix is intersected by a plane parallel to its axis, and a cone's generatrix is intersected by a plane via its vertex.
Since the line passing through the cone's vertex is parallel to the axis of the cylinder, the system of planes that intersect both surfaces in their generatrixes is a pencil-shaped arrangement of planes.
The cone and the cylinder are both intersected by every plane of that pencil in two different generatrixes.
In contrast to the vertices of the surfaces, the junction curve has four points that are intersections of these four lines.
To learn more about intersection of cylinder and cone link is here
brainly.com/question/9465455
#SPJ4
If the side ratio is 9:16, the perimeter ratio is
The perimeter ratio of the figures is given as follows:
9:16.
How to obtain the perimeter ratio?Considering the side length ratio of a:b, the perimeter ratio has the proportion given as follows:
a:b.
This is because both the side lengths and the perimeter are measured in units, hence the perimeter ratio is the same as the side length ratio.
Considering that the area is measured in square units and the volume in cubic units, their ratios would be given as follows:
Area: a² : b².Volume: a³ : b³.More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1