modulus is prime x^2 = 123 mod 4-1 this implies 123 mode 3 and hence we get x^2 = 2 prime
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
therefore , modulus is prime x^2 = 123 mod 4-1 this implies 123 mode 3 and hence we get x^2 = 2
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How do you decide where
to start filling in a two-way frequency table
when some of the data are already there?
Two values of frequency can be used to calculate the final value in a particular row or column.
What is Statistic?The statistic is the study of mathematics which deal with relations between comprehensive data.
Here,
If a table already includes some data and we need to add more, we simply search for a row or column that holds the additional data. These two values can be used to calculate the final value in a particular row or column.
Thus, two values of frequency can be used to calculate the final value in a particular row or column.
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A frequency table of grade ha five clae (A, B, C, D, F) with frequencie of 3,12,14, 5,and 3 repectively. Uing percentage, what are the relative frequencie of the five clae?
The relative frequencies in percentage are:
A: (3 / 37) * 100 = 8.1%
B: (12 / 37) * 100 = 32.4%
C: (14 / 37) * 100 = 37.8%
D: (5 / 37) * 100 = 13.5%
F: (3 / 37) * 100 = 8.1%
Relative Frequency of GradesTo determine the relative frequencies in percentage, we first find the total number of data points. In this case, it is the sum of the frequencies of each grade: 3 + 12 + 14 + 5 + 3 = 37.
Next, we divide each frequency by the total number of data points and multiply by 100. This gives us the relative frequency of each grade as a percentage.
For example, the relative frequency of grade A is (3 / 37) * 100 = 8.1%, which means that 8.1% of the data points belong to grade A. Similarly, we can find the relative frequency of each of the other grades.
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Breyelle is planning on purchasing a new sports utility vehicle.
Answer:
Please type or attach a question to be answered. Currently, all you have is as a question is the statement "Breyelle is planning on purchasing a new sports utility vehicle."
24:56 basic ratio help help help
A nutritionist wanted to determine which of two behaviors would give people the most energy. She selected a sample of 50 adult participants.
For one month, the participants were asked to exercise for 30 minutes per day. For another month, they drank an energy drink every day. The order of the treatments were assigned to the participants at random.
The participants were asked to record each day when they completed their treatment and to rate their energy level that day on a scale of 1–10.
After the two months of treatments, the nutritionist collected the data and calculated and compared the mean change (exercise – energy drink) in energy level for all 50 participants.
Which statement about the randomization for the matched pairs design is correct?
A) For each participant, the nutritionist should flip a coin. If the coin lands on heads, the participant will be assigned to exercise during the first month and drink energy drinks during the second month. If the coin lands on tails, the participant will be assigned to drink energy drinks during the first month and exercise during the second month.
B) The nutritionist should place the names of the 50 participants on slips of paper and put them in a hat. She should then draw out 25 of the slips. Those participants will exercise for both months. The remaining 25 participants will drink energy drinks for both months.
C) The nutritionist should let the participants decide which treatment they would like to do first. That way, if they are too busy to exercise 30 minutes each day during the current month, they can save that treatment for the second month.
D) Because there are two treatments, exercise and drinking energy drinks, the nutritionist should divide the participants into 4 groups: 2 months of exercise, 2 months of energy drinks, 1 month of exercise followed by 1 month of energy drinks, and 1 month of energy drinks followed by 1 month of exercise. She can draw names from a hat to assign the participants to these 4 groups.
The statement which is correct for randomization for the matched pairs design is option (A).
What is meant by randomization?
Making something random is the process of randomization. Randomization is not haphazard; rather, a random process is a series of random variables representing a process whose results follow an evolution specified by probability distributions rather than a deterministic pattern.
A) In this option there are only two results, heads or tails. So the assigning is based on luck and is random
Also since both behaviours are covered by the people involved in both months, everyone is subjected to the test equally.
This statement about the randomization for the matched pairs design is correct.
B) Here all the participants are not treated fairly because only half people are subjected to exercising while the other half are assigned to have drinks for 2 months.
This statement is not correct.
C) This is not random as the participants are deciding for themselves.
This statement is also not correct.
D) In this also 2 groups has to participate in either of the challenges not both which does not make it fair.
This statement is also not correct.
Therefore the statement which is correct for randomization for the matched pairs design is option (A).
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Hudson is blocking off several rooms in a hotel for guests coming to his wedding. The
hotel can reserve small rooms that can hold 3 people, and large rooms that can hold 4
people. Hudson reserved twice as many large rooms as small rooms, which altogether
can accommodate 66 guests. Write a system of equations that could be used to
determine the number of small rooms reserved and the number of large rooms
reserved. Define the variables that you use to write the system.
Check picture for full question.
Let the number of small rooms = x. Let the number of large rooms = y. and the system of equation is y = 2x and 3x + 4y = 66.
What is system of equation?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations solved by an identical set of variables is called a scheme of linear equations."
Let the number of small rooms = x.
The number of large rooms = y.
The people that can be accommodated in small room = 3x.
The people that can be accommodated in large room = 4y.
Hudson reserved twice as many large rooms as small rooms, this is represented as:
y = 2x
The total accommodated guests are 66, this is represented as:
3x + 4y = 66
Hence, Let the number of small rooms = x. Let the number of large rooms = y. and the system of equation is y = 2x and 3x + 4y = 66.
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Determine the limits of each of the following sequences, if they exist, or explain why the sequence diverges. You must indicate if you use any standard limits, continuity or l'Hopital's rule. an = (n + 2)^2n/(n^2 - n - 6)^n bn = cosh(3/n) - 1/sinh(2/n) Verify your answers for both limits >>using MATLAB
The limit of this sequence is equal to the value of the function evaluated at n = ∞.
The limits of a sequence tell us the value that the sequence tends to approach as the number of terms in the sequence increases.
We'll begin with the first sequence,
=> an = (n + 2)²ⁿ/(n² - n - 6)ⁿ.
To determine the limit of this sequence, we must first determine if it is a continuous function.
In this case, we can see that the function is continuous for all values of n, so the limit is equal to the function evaluated at n = ∞.
Next, we'll examine the second sequence,
=> bn = cosh(3/n) - 1/sinh(2/n).
Again, we'll use the standard limit to determine if the sequence is continuous, and we can see that it is.
Therefore, the limit of this sequence is equal to the value of the function evaluated at n = ∞.
To verify our answers, we can use MATLAB to evaluate each function at n = ∞ and compare the results with our limits.
We can also use MATLAB to plot each sequence, which can help us to visualize the behavior of the sequences and confirm our answers.
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Alan gets on a moving walkway. This diagram shows Alan's position every 2
2
seconds.
The table below contains graphs that represent different things about his motion.
Drag a label for the y
-axis for each graph.
An acceleration is said positive when an object speeds up and the acceleration is negative when object slows down.
How to determine the acceleration?Point A to B object is not moving.
Point B to C object is positive acceleration.
Point C to D object is at constant velocity.
Point D to E object is not moving.
Point E to F object is negative acceleration.
Acceleration:
It is defined as the rate or direction of change in the velocity.
An acceleration is said positive when an object speeds up and the acceleration is negative when object slows down.
In the given a position vs time graph,
From point B to C, object is increasing its velocity thus the acceleration will be positive.
From point E to F, the object is slowing down thus the acceleration will be negative.
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Correct question:
Drag each label to the correct location on the image. Each label can be used more than once.
The position-time graph describes the motion of a moving object. Describe the motion represented by each segment of the graph.
not moving
constant velocity
positive acceleration
negative acceleration
a man is 6’4 tall and weighs 226 lbs. if the max weight for a person at this height is 204lbs, what % overweight is he?
The man is approximately 10.78% overweight for his height.
To calculate the percentage overweight, you can use the following formula:
Percentage overweight =(Actual Weight−Max Weight)/max weight × 100
Given the information you provided:
Actual Weight = 226 lbs
Max Weight = 204 lbs
Substitute these values into the formula:
Percentage over weight = (226-204)/204 ×100
=22/204×100
=10.78%
Hence, the man is approximately 10.78% overweight.
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express the following limit as a definite integral: limn→[infinity]∑i=1ni8n9=∫baf(x)dx
The limit of the definite integral will be limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx = ∫abxdx = [x^2/2]ab = (b^2/2 - a^2/2).
We can use the Riemann Sums method to find the definite integral representation of the given limit.
Given: limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx
Step 1: Define the function f(x) = x.
Step 2: Divide the interval [a, b] into n equal subintervals with the width of (b-a)/n. Let xi = a + i(b-a)/n be the right endpoint of the i-th subinterval.
Step 3: Evaluate the value of the sum for n subintervals, ∑i=1ni8n9. This is the Riemann Sum for the function f(x) = x over the interval [a, b].
Step 4: Let n tend to infinity. The limit of the Riemann Sums as n approaches infinity is the definite integral of the function f(x) = x over the interval [a, b].
Thus, limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx = ∫abxdx = [x^2/2]ab = (b^2/2 - a^2/2).
Note: To make the calculation more precise, we need to choose the values of a and b such that the limit of the Riemann Sums will be a definite value. However, in this case, we have not been given any specific values of a and b, so we have used general values for the purpose of demonstration.
Therefore, the limit of the definite integral will be limn→[infinity]∑i=1ni8n9 = ∫baf(x)dx = ∫abxdx = [x^2/2]ab = (b^2/2 - a^2/2).
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r packages include sample datasets. they also include reusable r functions and documentation about how to use the functions. 1 point true false
It is true that r packages include sample datasets. They also include reusable r functions and documentation about how to use the functions.
The r packages do contain reusable r functions and documentation about how to use the functions. Not only that but they also include the sample data sets and provide tests for checking the code that we have generated.
The r packages are distributed with fifteen base packages that include grid, method, compilers, base, datasets, tools, splines, graphics, stats, stats4, translations, utils, grDevices, parallel, and tcltk.
These r packages introduce simpler ways of the r code distribution and documentation.
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An engineer and his helper can do a certain job in 5 hrs. On a given day, they work together for 2 hrs then the helper left and the engineer finishes the rest of the work in 4 more hours. How long will it take for the engineer to do the job alone? 6.7 hrs 15 hrs
The engineer would take 8.5 hours to do the job alone, which is 3.5 hours more than when the helper was there. This is because the engineer is doing the same amount of work.
The engineer and his helper can do the job in 5 hours with amount of both working together. However, if the helper leaves, the engineer will have to work alone to finish the job. The engineer worked with the helper for 2 hours and then finished the job in 4 more hours, so the total time taken was 6 hours. To calculate how long it would take the engineer to do the job alone, we subtract the 2 hours the helper was there from the 6 hours total that it took to finish the job. This leaves 4 hours that the engineer would have to work alone, so the engineer would take 8.5 hours to do the job alone. This is 3.5 hours more than when the helper was there.
The complete question: An engineer and his helper can do a certain job in 5 hrs. On a given day, they work together for 2 hrs then the helper left and the engineer finishes the rest of the work in 4 more hours. How long will it take for the engineer to do the job alone?
A)6.7 hrs
B) 15 hrs
C) 12 Hrs
D) 8.5 hrs
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Determine whether the statements are true or false.
if a system of m linear equations in n variables is equivalent to a system of p linear equations in q variables, then m = p.
True, equivalent systems of linear equations always have the same number of variables (you can never reduce the number of variables and keep an equivalent system).
If a system of m linear equations in n variables is equivalent to a system of p linear equations in q variables, then m = p is true then.
Number of variables = number of columns in the matrix.
Cramer's rule is one of the important methods applied to solve a system of equations. In this method, the values of the variables in the system are to be calculated using the determinants of matrices. Thus, Cramer's rule is also known as the determinant method.
Cramer's rule can only be applies if
1.the number of equations in the linear system equals the number of variables i.e m = n.
2.the determinant of the coefficient matrix is non zero.
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11. Write an expression with all fractional
terms that applies four properties of
multiplication to simplify the expression to
one term, Include at least one term being
divided. Show your work and explain how
your expression simplifies.
The statement claims that the phrase may be reduced to the single fractional term 8/5.
What is fundamental expression?Expressions serve as the fundamental construction blocks of Statements since every BASIC word is composed of both expressions and keywords (such as GOTO, TO, and STEP). Therefore, in addition to basic mathematical operations and boolean expressions (such as 1 + 2,) expressions can also include functions, constants, and lvalues (scalar constants or arrays).
Let's use the expression: (2/3) x (4/5) ÷ (1/6)
Using the four properties of multiplication:
Associativity: (2/3) x (4/5) ÷ (1/6) = (2/3) x (4/5) ÷ (1/6)
Commutativity: (2/3) x (4/5) ÷ (1/6) = (4/5) x (2/3) ÷ (1/6)
Distributivity: (4/5) x (2/3) ÷ (1/6) = 4/5 x (2/3 ÷ 1/6) = 4/5 x (12/6) = 4/5 x 2
Identity: 4/5 x 2 = 4/5 x 2 = 8/5
As a result, the equation is reduced to the fraction 8/5.Each fractional term in the equation is streamlined using the characteristics of multiplication until only a fractional term is left.
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Select all the points in the solution set of the graph below.
Step-by-step explanation:
It's a the second one pick the second one
A linear relationship is given in the table.
x y
4 11
2 7
0 3
−2 −1
What is the slope of the relationship?
(A)−3
(B)−2
(C)2
(D)3
Answer:
C
Step-by-step explanation:
slope = diff in Y / diff in X
-4/-2 = 2
Answer: The answer is C
Step-by-step explanation:
First you need to calculate the difference between the data for x and the data for y. Lets start with the x axis.
X axis:
4 - 2 = 2
This means the the difference between each x point is -2.
Now for the y axis.
Y axis:
11 - 7 = 4
7 - 3 = 4
This means the the difference between the y axis points is -4
Now use rise over run to find the slope.
The rise is always the y coordinates and the run is always the x coordinates
So divide the difference of y by the difference of x.
-4/-2 = 2
The answer is C.
the number t of tickets sold at a concert is a function of the ticket cost c. which is the independent and dependant variable? is the domain discrete or continuous?
The independent variable is the ticket cost (c), and the dependent variable is the number of tickets sold (t).
The domain of the function could be either discrete or continuous, depending on the specific function and the way the ticket prices are set. For example, if the ticket prices are set in increments of $5, the domain would be discrete, and if the ticket prices can take on any value in a certain range, the domain would be continuous.
Domain TypeThe independent variable is considered to be the variable that is manipulated or controlled, while the dependent variable is the outcome or result that is affected by the manipulation of the independent variable.
In this case, the ticket cost (c) is the independent variable, because it is the factor that is being controlled or changed, and the number of tickets sold (t) is the dependent variable because it is the outcome that depends on the cost of the tickets.
To determine if the domain is discrete or continuous, you would need to examine the specific function and the way the ticket prices are set. For example, if the ticket prices are set in increments of $5, the domain would be discrete, meaning that it consists of separate, distinct values.
On the other hand, if the ticket prices can take on any value in a certain range, the domain would be continuous, meaning that it consists of all the values in a range without any gaps or interruptions.
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A construction company can purchase nails for $5 per pound and screws for $7 per dozen. How many pounds of nails and how many dozen screws can the company buy if their budget is at most $200?
a) Let x be the pounds of nails and let y be the dozens of screws. Write an inequality that would model this
situation.
The inequality for the model of the situation is 200 ≤ 5x + 7y.
What is system of inequality?At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the answer of a linear inequality is the ordered pair that resolves all inequalities in the system.
Given that, let x be the pounds of nails and let y be the dozens of screws.
The equation for, nails for $5 per pound is given as:
5x
The equation for, screws for $7 per dozen is given as:
7y
If their budget is at most $200, then the inequality representing the nails and the screws is:
200 ≤ 5x + 7y
Hence, the inequality for the model of the situation is 200 ≤ 5x + 7y.
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Which of the following T-tables would NOT be an appropriate model for the function shown here?
The second table has the points:
f(2) = 0
f(2) = 1
So it isn't even a function, that is the correct option.
Which of the given tables is not an appropiate model of the function?Here we have the graph of function x = f(x), where the values of x are shown on the horizontal axis and the values of f(x) ares hown on the vertical axis.
Something that you can see, is that when x = 0 (leftmost value) we have:
f(0) = 2.
So every table should have that, but if we look tat the second option we can see that:
f(2) = 0
f(2) = 1
So that table has tw different values for x = 2 (so it does not even represent a function). So that is the correct option.
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Write the equation for the product of 12 and eight
Answer:
to find product of 12 and 8
u need to multply 12x8=96
i think u study in class 1
Select the correct answer from each drop-down menu. Bob uses two sizes of square tiles, tile A and tile B, to tile his bathroom. The area of tile A is 20 square inches, and the area of tile B is 24 square inches. The length of tile is greater than the length of tile by approximately inches.
Area of the square figure is equal to the square of one of its sides. The difference in the length of the two tiles is 0.4 meters.
What is the area of the square?The area of the square figure is equal to the square of one of its sides.
Area of the square Tiles = (length of one side)²
We know that the area of a square is the square of one of its lengths, therefore, the length of each of the square tiles can be written as,
Area of the square Tiles = (length of one side)²
Length of the Tile A
Area of the square Tiles = (length of one side)²
√(Area of the square Tiles) = length of one side
Since, Area of the square tiles A is 20
Thus,
Length of tile A = √20 = 4.5 inches Approx.
Length of Tile B
Area of the square Tiles = (length of one side)²
√(Area of the square Tiles) = length of one side
Since, Area of the square tiles B is 20
Thus,
Length of tile B = √24 = 4.9 inches Approx.
Thus, the difference between the length of the two tiles can be written as,
Difference = 4.9 - 4.5
Difference = 0.4 inches
Hence, the difference in the length of the two tiles is 0.4 meters.
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Use the line on the graph to write an equation that represents the function.
y = x+
Answer:
y = -3x - 1
Step-by-step explanation:
We can represent the given line using an equation in slope-intercept form
[tex]y = mx+b[/tex]
In this form, [tex]m[/tex] is the line's slope, and [tex]b[/tex] is the y-coordinate of the point on the line when it touches the y-axis (its y-intercept).
First, we can solve for the line's slope using two points on the line and the formula m = rise / run. We can use the points (0, -1) and (1, -4), whose coordinates correspond to (x₁, y₁) and (x₂, y₂).
[tex]m = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \dfrac{-4 - (-1)}{1 - 0}[/tex]
[tex]m = \dfrac{-4 + 1}{1}[/tex]
[tex]m = -3[/tex]
So, the slope (m) of this line is -3.
We can plug that value into the model for slope-intercept form.
y = -3x + ▢
Now, we have to identify the line's y-intercept (the point on the line when it touches the y-axis). It is (0, -1). Finally, we can put the y-coordinate of that point into slope-intercept form equation.
y = -3x - 1
A bank credit card charge interet at the rate of 25% per year,compounded monthly. If a enior in college charge 1100 to pay for college expene, and intend to pay it in one year, what will he have to pay?
The amount the college senior will have to pay in one year, given the interest charge and the amount paid, is $ 1, 408. 80
How to find the amount?To find the amount, you need to use the future value formula. This would show the amount the college senior would pay in a year given what they spent on the credit card.
The monthly rate is:
= 25 % / 12
= 25 / 12 %
The amount the college senior will pay is:
= 1, 100 x ( 1 + 25 / 12 % ) ¹²
= $ 1, 408. 80
Note : The brackets are raised to the power of 12 because of the number of months in a year which is the amount of time till the college senior pays back.
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(12 pts.) a. p(-1.45 < z < .98) = ? b. p(z > -.68) = ? c. the area left of z is .0427. what is z ?
Probability (p) of a) Φ(.98) - Φ(-1.45), b) 1 - Φ(-.68) and c) standard normal variable (z) is Φ^(-1)(.0427).
In these questions, z refers to a standard normal variable with mean 0 and standard deviation 1. The cumulative distribution function (CDF) of a standard normal variable can be used to find probabilities for given intervals.
a) To find the probability that -1.45 < z < .98, we can use the CDF to find the area under the standard normal curve between these two values:
p(-1.45 < z < .98) = P(z < .98) - P(z < -1.45) = Φ(.98) - Φ(-1.45)
b) To find the probability that z > -.68, we can use the CDF to find the area under the standard normal curve to the right of this value:
p(z > -.68) = 1 - P(z < -.68) = 1 - Φ(-.68)
c) To find the value of z for a given area to the left of z, we can use the inverse CDF (also called the quantile function) of a standard normal variable, denoted as Φ^(-1)(p). This gives us the value of z such that the area to the left of z is equal to p.
p = .0427, so z = Φ^(-1)(.0427).
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On Thursday, he drinks 15 cups of water.
On Friday, he drinks 12 cups of water.
What is the percent change in his water intake?
What is the original amount of water in this problem?
What is the change in David's water intake in this problem?
What is the percent change?
Is it increasing or decreasing?
Answer:
The original amount of water in this problem is 15 cups. The change in David's water intake in this problem is a decrease of 3 cups. The percent change is a decrease of 20%.
Step-by-step explanation:
pls mark brainliest
A triangle has an area of 4 3/4 square units. the base is 3 units, what is the height?
.
The required height of the triangle for 3 units base is 3.16 units.
How to find are of right angled triangle?If a right triangle's height and hypotenuse are all that are known, we must first determine the base using the Pythagoras theorem before determining the triangle's area. After that, we may calculate its area using the formula 1/2 base height.
According to question:We have,
Area of triangle = 4(3/4)square units., Base = 3 units.
= 19/4 square units.
We know that
Area = bh/2
19/4 = (3)h/2
h = 19/6
h = 3.16 units
Thus, required height is 3.16 units.
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after the pool was full helens little brotherand his friend splashed g gallon of water out of the pool. there are 7 7/ gallons still left in the pool. write and solve an euation to find how much water was splashed out of the pool.
The equation for the splash is given by y=1(7/8) x
How much water was splashed out of the pool?Where y is the amount of water is the pool and x is the number of trips Helen has made.
To fill the pool, Helen must make 6 trips.
The amount of water is the pool y is given by
y=1 (7/8)x
Where x is the number of trips Helen has made. If we wish to find out how many trips she needs to make to fill 10 1/2 gallons in the pool, we solve for x:
y = 10 1/2 = 1(7/8) x
10 1/2 = 10.5 and 1 *7/8) = 1.875.
Thus, 10.5 = 1.875 x
x = 10.5/1.875
= 5.6
Since 5.6 trips makes no sense, we must round up to 6.
Thus, the answer is 6 trips.
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7t+10(5t+5)–10
can you help me with this question
Given the question:
7t+10(5t+5)-10
First, distribute:
7t+50t+50-10
Next, combine like terms (7t+50t and 50-10)
57t+40
This cannot be simplified further.
What is the best approximation of the solution to the system to the nearest integer values? Responses (−2, 6) begin ordered pair negative 2 comma 6 end ordered pair (6, −2) begin ordered pair 6 comma negative 2 end ordered pair (7, −2) begin ordered pair 7 comma negative 2 end ordered pair (−2, 7) begin ordered pair negative 2 comma 7 end ordered pair Graph of a system of linear equations. Equation 1 is 3 x minus 4 y equals negative 32. Equation 2 is 3 x plus 5 y equals 24.
The best approximation of the solution to the system is (-2, 7).
How did we get the values?Here's how I arrived at the solution using substitution method:
Given the system of linear equations:
3x - 4y = -32
3x + 5y = 24
We'll solve for x in equation 1 and substitute the result into equation 2:
3x - 4y = -32
x = (-32 + 4y) / 3
Substituting this expression of x into equation 2:
3((-32 + 4y) / 3) + 5y = 24
-32 + 4y + 15y = 24 * 3
13y = 24 * 3 + 32
13y = 96
y = 7.38
Rounding the value of y to the nearest integer, we get y = 7.
Substituting y = 7 back into the expression for x:
x = (-32 + 4 * 7) / 3
x = (-32 + 28) / 3
x = -4 / 3
Rounding the value of x to the nearest integer, we get x = -2.
Therefore, the best approximation of the solution to the system of linear equations is (-2, 7).
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Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts? (1 point) f(x) = −2x − 1 x g(x) 2 2 4 6 6 10 Group of answer choices:
A.The function f(x) has a higher y-intercept.
B.The function g(x) has a higher y-intercept.
C.They both have the same y-intercept.
D.The relationship between y-intercepts cannot be determined.
The answer is the function f(x) has a higher y-intercept, the correct option is A.
What is the slope of a straight line?A straight line of the form
y = mx + c
has its slope as 'm'
It is constant for a line. The more the slope is, the steeper the line is.
Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.
Given;
f(x) = −2x − 1 x
g(x) 2 2 4 6 6 10
Now by comparing the function to the slope-intercept form of a line we get;
The y-intercept of function f(x) is; -1
Also, the table for the function g(x) is given by;
x g(x)
2 2
4 6
6 10
The function g(x) satisfies the equation;
g(x)= 2x-2
The y-intercept of the function g(x) is; -2
We know that:
-1 > -2
Therefore, the slope answer will be f(x) is higher than the y-intercept of the function g(x).
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