The statements
(a) If x and y are integers such that 3xy then 3x.
(b) For any integers x, y, and z, if x y and xz, then x(y - z).
(c) If x and y are integers such that x > 1 and if x divides y, then the solution is x(y - 1)
are proved.
The term integers in math is defined as are the collection of whole numbers and negative numbers.
Here we know that x and y are the integers,
Then it takes both positive and negative numbers.
Then we take y=1, then we apply it on the expression then we get,
=> 3x(1) = 3x.
Similarly here we have take that xy|z means xy is a factor of z,
Here we can say xym = z for some integer m.
=> x × ym = z, and ym is an integer by closure hence x is a factor of z such that x|z.
Similarly here we can also y * xm = z, and consider xm is an integer, hence y is a factor of z, i.e. y|z.
Where in the third one, we can take x|y means there exists a constant is written as y = kx
Where as y|x means there exists a constant written as x = cy
When we compare these, then we get,
=> y = kx = kcy
Here we have to true if kc = 1 and since k and c are integers, then we have k = c = 1
Therefore y = kx becomes y = 1*x or y = x
Similarly x = cy becomes x = 1*y or x = y
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A farmer is tilling his rectangular field. The length of the field is 54 meters and distance
between opposite corners is 90 meters. How wide is the farmer's field?
As per the Pythagoras theorem, the width of the farmer's field is 74.83 meters.
In math the term Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
The general form of the Pythagoras theorem is written as,
=> hypotenuse² = opposite side² + adjacent side²
Here we have know that a farmer is tilling his rectangular field.
Where the known length of the field is 54 meters and distance between opposite corners is 90 meters.
As we all know that here we have here is a triangle.
And then here we need to use Pythagorean Theorem is calculated as,
=> 50² + w² = 90²
When we simplify this one then we get,
=> 2500 + w² = 8100
=> w² = 5600
=> w = 74.83
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Enter the resulting inequality.
11 > −2; Subtract 11 from both sides.
The resulting inequality is
If 11 is Subtracted from both sides, the resulting inequality is 9 > -4
How find the resulting inequality?
An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4
Initially, you have 11 > −2
If you subtract 11 from both sides, you will have:
11 -2 > −2-2
9 > -4
Thus, the resulting inequality will be 9 > -4
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Somebody help me please with this question!!
What is the expanded form for 72 cubed?
Answer:373248
Step-by-step explanation:
72^3 = 373248
Solve by substitution.
x - 2y = 3
2x + 4y = 6
([?], [ ]
Enter
[tex]\begin{cases} x-2y=3\\ 2x+4y=6 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{x-2y=3}\implies x=2y+3 \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{2(\underset{x}{2y+3})+4y=6}\implies 4y+6+4y=6\implies 8y+6=6 \\\\\\ 8y=0\implies y=\cfrac{0}{8}\implies \boxed{y=0}\hspace{5em}\stackrel{2(0)+3}{\boxed{x=3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (3~~,~~0)~\hfill[/tex]
heellllpp guys i will give brainlist
and number is doubled and the result is increased by 8 if the final result is 36
Answer:
14
Step-by-step explanation:
36 - 8 = 28
28 / 2 = 14
The equation y =7400x represents the number of miles, y, that the satellite Space Explorer flies in x hours. Find the rate of change.
If the equation "y = 7400x" represents the number of miles(y) , that satellite space explorer files in x hours , then the rate of change is 7400 miles per hour.
The Rate Of Change is also known as "Slope" ,
The rate of change can be found by taking the derivative of the equation ⇒ y = 7400x with respect to x.
The derivative of the equation "y = 7400x" with respect to x is ;
⇒ dy/dx = d/dx(7400x) = 7400 .
Therefore , rate of change of the equation "y = 7400x" is 7400 miles per hour , that means the satellite explorer files will cover 7400 miles in 1 hour .
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Mrs.Henderson has 16 boys in her class of 24 students. Mr.Gregory has 18 boys in his class of 30. Which class has the greater ratio of boys to student s? Explain
The greater ratio of boys to students in the class of Mrs. Henderson's class is, 0.67
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Given that,
Mrs. Henderson has 16 boys in her class of 24 students
Mr. Gregory has 18 boys in his class of 30
Greater ratio = ?
Ratio in Mrs. Henderson = number of boys/total students
= 16/24
= 2/3
= 0.67
Ratio in Mrs. Gregory = number of boys/total students
= 18/30
= 3/5
= 0.6
Hence, the ratio is greater in Mrs. Henderson's class 0.67
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a family eats at a restaurant. the bill is $38.00. the family leaves a tip and spends $44.27. how much was the tip as a percentage of the bill?
Answer:
14.16%
Step-by-step explanation:
[tex]=(\frac{44.27-38}{44.27} )(100)=(\frac{6.27}{44.27} )(100)=\frac{627}{44.27} =14.16[/tex]
Hope this helps
find the rate of change between the points (-1,30) and (-6,10)
Answer:
Step-by-step explanation:
The rate of change, also known as the slope, between two points can be found using the formula:slope = (y2 - y1) / (x2 - x1)where (x1, y1) and (x2, y2) are the coordinates of the two points.To find the slope between the points (-1, 30) and (-6, 10), we can plug in the coordinates into the formula:slope = (10 - 30) / (-6 - (-1)) = -20/-5 = 4So the rate of change or the slope between the points (-1,30) and (-6,10) is 4.This means that the y-value of the second point is 4 units lower than the y-value of the first point for every unit you move to the left on the x-axis.
In the figure, ABCD is a square, E is the midpoint of side AD, and F is the midpoint of side BC. The area of the shaded region is
what fraction of the area of square region ABCD?
Answer:
option (D) is the correct one ...
MARK ME AS BRAINLIEST ...At Lake clay, marine biologist catch, tag, and release 50 small mouth bass. over the next few days, they catch 175 smallmouth bass, of which 7 have the original tags. what is the estimated population of smallmouth bass in lake clay?
Answer: The estimated population of smallmouth bass in lake clay can be calculated using the Lincoln-Petersen index.
This method is based on the idea that the proportion of tagged fish among all the fish caught will be proportional to the proportion of the total population that was tagged.
Formula: N = (C1 * N1) / (C2 - 1)
where N is the estimated population, C1 is the total number of fish caught, N1 is the number of tagged fish caught, and C2 is the number of tagged fish caught among all fish caught.
In this case:
C1 = 175 (total number of smallmouth bass caught)
N1 = 50 (number of smallmouth bass initially tagged)
C2 = 7 (number of tagged smallmouth bass caught among all fish caught)
So, the estimated population of smallmouth bass in Lake clay is:
N = (C1 * N1) / (C2 - 1) = (175 * 50) / (7-1) = 8750
Therefore, the estimated population of smallmouth bass in Lake clay is 8750.
Step-by-step explanation:
D. Ray saved $4 on a shirt that was was originally
$32. What percent was the discount?
Answer: The percent was 12.5%
Selina had been renting for 13 months when there was a flood. The total cost to replace her damaged belongings was $1,960.00. What percent would Selina have saved if she had a renters' insurance policy at a monthly cost of $21.00? Round to the nearest tenth of a percent.
Answer:
13 × 21=293
10/100×293=$29.3
In parallelogram ABCD, AB = 6x-4, CD = 5x + 1, and BC = 2x.
What is the perimeter of ABCD?
D
Perimeter =
A
units
C
B
Answer:
15x-3
Step-by-step explanation:
Recall that parallelograms, as the name implies, have two pairs of parallel sides. In this case, line segments AB and CD are parallel to each other, and then BC and DA are parallel to each other:
Perimeter = AB + BC + CD + DA = (6x-4) + (2x) + (5x+1) + (2x) = 15x - 3
Find the volume of a cone, to the nearest cubic inch, with a height of 24 in. And diameter of 40 in. Use 3. 14 for pi
The volume of the cone with mentioned dimensions of height and diameter are 10,048 cubic inches.
The volume of come can be calculated by the formula -
V = πr²h/3, where V represents volume of the cone, r represents radius of the cone and h represents height of the cone. Furthermore, radius is half of the diameter. Hence, calculating radius first.
Radius = 40/2
Performing division on Right Hand Side of the equation
Radius = 20 inches
Keep the values in formula of cone to find the volume of the cone
Volume of the cone = (3.14 × 20² × 24)/3
Performing division on Right Hand Side of the equation
Volume of the cone = 3.14 × 20² × 8
Performing multiplication on Right Hand Side of the equation
Volume of the cone = 10,048 inch³
Thus, the volume of cube is 10,048 cubic inches.
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Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
When y = 5x the possible outcome of table is 2.8 when x = 4 , 3.88 when x= 7 and 3.33 when x= 4 .
Function range :A function's range can refer to one of two closely related ideas: The function's image is its codomain. Given two sets, X and Y, a function is a binary relation between X and Y if, for every x in X, there is exactly one y in Y that corresponds to f. Take a look at the function y = f(x). The range of the function is the spread of all the y values from the lowest to the highest. Substitute all of x's values into the given expression for y to determine whether it is positive, negative, or equal to other values.
if y=5 x
y= 7 and X = 4 , then
7= 5(4)
7 = 20
= 20/7
= 2.8
when Y =9 and X = 7 then,
9 = 5(7)
9 = 35
35/9
= 3.88
when Y = 6 and X = 4 then,
6= 5(4)
6= 20
20/6
= 3. 33
Missing function of table are 2.88 , 3.88,3.33
What is the range of the function?
The range is (0;+∞). The values are all positive (if a positive number is raised to a power, the result cannot be negative), and the value cannot be zero, so the range is (0;+∞).
Incomplete question :
Create a table from y=5x. You can just do numbers like
Y 7. 9. 6
X 4. 7. 4 or sum I just need the table
Complete the table for the given rule.
Rule:y=5x
x, y
5,4,2
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find the measures of <X <Y.
The missing interior angles of the hexagon is as follows:
∠X = 135 degrees
∠Y = 135 degrees
How to find the angles in a polygon?The polygon above has 6 sides. Therefore, the polygon is a hexagon. The sum of interior angles of a polygon is ( n − 2 ) × 180°.
where
n = number of sidesThe sum of interior angles in an hexagon is calculated as follows:
180(6 - 2) = 180(4) = 720 degrees
Therefore, the angles of x and y are congruent.
Hence,
let
∠x = ∠y = a
Therefore,
2a + 91 + 149 + 100 + 110 = 720
2a = 720 - 450
2a = 270
a = 270 / 2
a = 135 degrees
Therefore,
∠x = ∠y = 135 degrees.
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Tom Sullivan's charge account statement shows an unpaid balance of $1,392. 8. The periodic rate is 2. 5% of
the unpaid balance. If he also has new purchases of $152. 87, what is his new balance?
Tom Sullivan's new account balance after all the transactions that has occurred as per the information provided will be $1,580.49.
Unpaid balance = $1,392. 8
Periodic rate = 2.5%
New purchase = $152.87
New Balance = $1,392. 8 + 2.5% + $152.87
A financial institution's account balance is the sum of money it has on hand during the current accounting period. It is the balance carried forward from the previous month plus the net difference between the credits and debits posted in any given accounting cycle.
An account balance offers current and convenient information about how much money you currently have on hand. An account balance offers a convenient way to manage the money coming in and going out while keeping track of all transactions.
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while logistic regression and classification and regression trees (cart) have the same end goal, each model approaches the goal in a different way. discuss the differences in the two models. provide a specific example of a situation where employing a cart model would be preferable to a logistic regression model. explain what makes the cart model superior in your example.
Logistic regression models the probability of a binary outcome, while CART models segment data into categories. For example, CART is preferable when data has complex interactions, as it can partition data into multiple categories.
Logistic regression and classification and regression trees (CART) are two different machine learning models used for binary classification problems. Logistic regression models the probability of one class or the other based on a linear combination of input variables. This makes it useful for predicting a binary outcome, such as whether a customer will purchase a product or not. On the other hand, CART is a decision tree model that divides data into categories. It uses a tree-like structure to split the data into segments based on the input features. This makes it useful for dealing with data with complex interactions, as it can partition data into multiple categories. For example, a CART model would be preferable to a logistic regression model if there are multiple underlying factors that affect the binary outcome. In this case, a CART model could more accurately identify the categories that are associated with a particular outcome. Overall, CART models are superior for dealing with data with complex interactions, whereas logistic regression is better for simpler data.
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a credit card company looking for unusual activity examines the number of transactions on a credit card in each of the last 10 months. these numbers are given below. 10 8 7 9 10 6 8 7 9 9 use a calculator to create a frequency distribution. in how many months have 10 transactions occurred?
10 transactions have occurred in 2 months.
In frequency tables or charts, frequency distributions are displayed. The actual number of observations that fall into each range can be seen in frequency distributions, as well as the proportion of observations that do.
To create a frequency distribution:
Count the number of occurrences for each value (in this case, transactions).
Group the values into ranges (if applicable).
Tabulate the frequency (number of occurrences) for each value or range.
For this set of numbers, the frequency distribution is:
Transactions | Frequency
6 | 1
7 | 2
8 | 2
9 | 3
10 | 2
So, in 10 months, 10 transactions have occurred in 2 months.
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What is the equation of the following graph? Use equation y = mx + b (picture included)
solutions to y<-x and 2x+y>2
The solution to the inequality is (2, -2)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y<-x and 2x+y>2
Express them as equations
So, we have
y = -x and 2x + y = 2
This gives
2x - x = 2
Evaluate
x = 2
Recall that
y = -x
So, we have
y = -2
Hence, the solution is (2, -2)
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What is the length of CD when;
C: (-3 , -4)
D: (1 , -2)
CD is about 2.83 in length when C: (-3 , -4) D: (1 , -2) in coordinate geometry.
How is this determined?In coordinate geometry, the distance formula, which is the square root of (x2 - x1)2 + (y2 - y1)2, can be used to determine the length of CD.
In this instance, point C's coordinates are (-3, -4) and point D's coordinates are (1, -2). Using the distance formula with these values as input, we obtain:
√((1 - (-3))^2 + ((-2) - (-4))^2) = √(4 + 4) = √8 = 2.8284271247461903
In simpler terms, you can use the distance formula, which is the square root of the sum of the differences of their x- and y-coordinates squared, to determine the separation between two points in a coordinate plane.
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an automobile manufacturer claims that their van has a 57.2 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this van. after testing 91 vans they found a mean mpg of 56.9 with a standard deviation of 1.8 mpg. is there sufficient evidence at the 0.025 level that the vans underperform the manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.
The null and alternative hypotheses for the above scenario are
H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon
Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon
Given that,
One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level
To find: state the null and alternative hypotheses for the above scenario.
The null and alternative hypotheses for the above scenario are
H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon
Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon
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hi help pls n thanks
The required domain is x ≥ -4.So option(4) is correct.
What is domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
According to question:From the graph, we can see that curve is starting from -4 to infinity in x direction.
By baby curve method
x ≥ -4
Thus, required domain is x ≥ -4.So option(4) is correct.
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with an average, you add everything up and then divide the total by the number of items you are adding. this gives every number equal weight in the average. but what if you want to weight one item more than others? you will use a weighted average. this can be used, for example, to determine your grade in a class. follow these steps to find the weighted average in the problem below. first, convert each percentage to a decimal. then, multiply each percentage in decimal form by its respective grade. and lastly, add everything up to find the weighted average. for example, emily received a 67 on her first economics exam, which counts for 20% of her grade; an 84 on her second exam, which counts for 30% of her grade; and a 78 on her third exam, which counts for 50% of her grade. what is her weighted average in the class?
Answer:
Based on the weights assigned to these grades, Emily's weighted average in the class would be 77.6 marks.
Please Help. I'll give Brainliest
Answer: Number 2
Step-by-step explanation:
Angle 1 + Angle 2 + Angle 3 = 180 degrees because its a straight line, so we immediately eliminate number 1 and 4 (Because it says the angles add up to 270). Next, we look at 2 and 3. 3 is incorrect because with just 1 right angle, QRST might be a rectangle. Therefore, number 2 is correct. :>
X
y
1
17
2
24
3
31
ept of the line represented by the table.
4
38
The slope is of m = 7 and the y-intercept is of b = 10.
How to define the linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the table, when x increases by one, y increases by 7, hence the slope m is given as follows:
m = 7.
Hence:
y = 7x + b.
When x = 1, y = 17, hence the intercept b is given as follows:
7 + b = 17
b = 10.
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