Number of integers 'p' for which there exist a triangle with the given side length 3p -1 , 3p , p² + 1 is equal to five that is 1, 2, 3, 4, 5.
Using triangular inequality of triangle :
sum of two sides > third side
a. 3p - 1 + p² + 1 > 3p
⇒p² > 0
True result.
b. 3p + p² + 1 > 3p - 1
⇒ p² > -2
True result.
c. 3p - 1 + 3p > p² + 1
⇒ p² -6p + 2 < 0
Roots are : p = [ -(-6) ± √(-6)² -4(1)(2) ] /2(1)
= ( 6 ± √28 ) 2
= 5.6 or 0.35
Integer value of p are in between 0.35 to 5.6 are :
1, 2, 3, 4, 5
Therefore, the integer value of 'p' for the given side length of the triangle is equal to five that is 1, 2, 3, 4, 5.
For how many positive integers 'p' does there exist a triangle with sides of length 3p-1 , 3p , and p² + 1 ?
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Which graph shows the new position of the rectangle after a translation?
The graph that shows the new position of the rectangle after a translation is; Option C
How to interpret Translation in Transformation?When it comes to transformation in mathematics, there are different types such as reflection, dilation, rotation, translation.
Now, we are dealing with translation which is defined as a transformation of a shape in a plane that preserves the length, which tells us that the object is transformed without getting its dimensions affected.
In this case, we see the rectangle in the graph and we can conclude that the translation of the rectangle shows the correct translation would be the second option because it shows that the length is preserved without getting its dimensions or shape altered.
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Bookwork code: N39
The diagram below shows a sketch of the curve
y = x² + 10x - 12.
P is the turning point of the curve.
Work out the coordinates of P.
Answer:
(-5,-37)
Step-by-step explanation:
Complete the square
(x+5)^2-37
The number of flaws per square yard in a type of carpet material varies with mean flaws per square yard and standard deviation flaws per square yard.
a. Without doing any calculations, explain which event is more likely:
randomly selecting a
square yard of material and finding 2 or more flaws
randomly selecting square yards of material and finding an average of or more flaws
b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).
c. Calculate the probability of the second event in part (a)
a. It is more likely to randomly select square yards of material and finding an average of or more flaws.
b. Normal distribution assumes that the data is continuous and symmetric, but in this case, the number of flaws per square yard is a count data, and it is not symmetric. Therefore, a normal distribution cannot be used to calculate the probability of the first event in part (a).
c. To calculate the probability of the second event in part (a), we would need the mean and standard deviation of the number of flaws per square yard, as well as the specific threshold of "or more flaws" to calculate the area under the curve that is greater than or equal to that threshold. Without that information, I cannot provide an accurate probability calculation.
Carpet Flaw Probability CalculationI determined that it was not possible to calculate the probability of the second event in part (a) without the specific mean and standard deviation of the number of flaws per square yard and the specific threshold of "or more flaws." This is because in order to calculate the probability of an event, you need to know the underlying distribution of the data and the specific cut-off point for the event in question.
In the other part of the question, I stated that it is more likely to randomly select square yards of material and finding an average of or more flaws than it is to randomly select a square yard of material and finding 2 or more flaws.
I came to this conclusion without any calculations because in general, when you are looking for a specific number of flaws (in this case, 2 or more flaws) in a single square yard, it is typically less likely than finding an average of that number of flaws when you look at multiple square yards. This is because the number of flaws per square yard can vary, so even if the average is 2 or more flaws per square yard, it is still possible to find square yards with fewer than 2 flaws.
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evaluate the expression when x=20 and y=4.
Answer: where is the expression
Step-by-step explanation:
given a and b in exercises 11 and 12, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. A= |1 2 4| | -2 |
|0 1 4| b= | 2 |
|-2 -4 -3| | 9 |
|1 2 1| | 0 |
A= |-3 -1 2| b= | 1 |
|0 5 3| | -1 |
The augmented matrix for the linear system corresponding to the matrix equation Ax = b is |1 2 4 0| |-2 2 9| |0 1 4 1| |2 -1| |-2 -4 -3 -1| |9 -1|. Solving the system yields the solution vector (x, y, z) = (5, -1, 4).
The augmented matrix for the linear system Ax = b is a way of combining the two matrices into one matrix. In this case, it is the combination of the coefficient matrix A and the constant matrix b. This new matrix contains all of the information needed to solve the linear system, as it contains both the coefficients of the variables and the solutions of the equations. We can solve the linear system by performing row operations to the augmented matrix, which is equivalent to solving the equations in the original matrix equation. After performing the row operations, we will be left with the solution vector (x, y, z) = (5, -1, 4). This solution vector represents the values of the variables that satisfy the original equation.
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Which of the following is a counterexample for the hypothesis " If a team plays at home, then they win the game?"
a. The team plays at home and wins the game.
b. The team plays away and wins the game.
c. The team plays at home and loses the game.
d. The team plays away and loses the game.
Look at the problem in example. Rolando also adds money to his subway fare card.
How much does Rolando pay for 20 rides? Show your work.
Answer:
Rolando pays $63 for 20 rides
Step-by-step explanation:
this was the question right???
Marisol spent 34.5 hours on her science project. She worked 1.5 hours each day on her project. How many days did Marisol work on her science project?
Answer:
23
Step-by-step explanation:
just divide 34.5 and 1.5 that gives you the ammount of days she worked on her project
question 7 fill in the blank: while cleaning data, a data analyst can use a changelog to keep a chronological list of changes they make. they can refer to it during the___period if there are errors or questions.
A changelog is a record of changes made to a dataset during the data cleaning process.
It can serve as a helpful reference for data analysts and other stakeholders to understand the changes that were made and the reasons why they were made. It is important for data analysts to keep a detailed changelog in order to learn from their mistakes and to provide a detailed audit trail for any future questions about the data.
The formula for calculating the value of a changelog is as follows:
changelog= Number of Changes Made + Complexity of Changes + Accuracy of Changes
The number of changes made to the data set is an important factor in calculating the changelog value. The more changes that are made, the more valuable the changelog will be. The complexity of the changes is also important. If the changes are complex and require a lot of effort to make, the changelog will be more valuable. Finally, the accuracy of the changes is also a factor. If the changes are accurate and correct, then the changelog will be more valuable.
Overall, a changelog is a valuable tool for data analysts to keep a detailed record of the changes they make to a dataset. This record can be used to ensure accuracy and to provide a detailed audit trail for any questions that may arise in the future.
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The graph above shows the cost of parking at the airport. Jay left on a business trip and had to leave his car at the airport for 5 days. Based on the graph, what is the total cost that he paid for the parking?
A.
$33.50
B.
$31.00
C.
$26.00
D.
$20.00
The total cost that he paid for the parking for 5 days is $26.00.
What is a linear equation?When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
There are both one-variable and two-variable linear equations.
The graph above shows the cost of parking at the airport,
since the graph is a straight line so it is the condition for a linear equation,
from the graph, the y-axis shows the price in dollars and the x-axis shows the number of days,
line of the graph passes from coordinates (0, 6) and (6, 30)
equation of line is y = mx + c
where c is initial cost when x is 0, y is 6
c = 6
and m = (y₂- y₁)/(x₂ - x₁)
m = (30 - 6)/(6 - 0)
m = 4
equation of line is,
y = 4x + 6
cost for 5 days,
x = 5
y = 4(5) + 6
y = 26
cost is $26.00
Hence cost for 5 days is $26.00, option C is correct.
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10) in the game of scrabble, each player begins by drawing 7 tiles from a bag containing 100 tiles. there are 42 vowels, 56 consonants, and 2 blank tiles in the bag. emma chooses her 7 tiles and is surprised to discover that all of them are vowels. we can use a simulation to see if this result is likely to happen by chance. Part A: State the question of interest using the language of probability. (2 points)
Part B: How would you use random digits to imitate one repetition of the process? What variable would you measure? (3 points)
Part C: Use digits from a table of random digits or use a calculator to perform one repetition. Submit the list of random digits and indicate those that represent vowels. (3 points)
Part D: In 500 repetitions of the simulation, there was one time when all seven tiles were vowels. What conclusion can you draw from this result? (2 points) (10 points
The probability of randomly drawing seven vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles is low. One time throughout the simulation's 500 iterations, all seven tiles were vowels.
Part A: What is the probability of randomly drawing 7 vowels from a bag of 100 tiles consisting of 42 vowels, 56 consonants and 2 blank tiles?
Part B: To imitate one repetition of the process, you would use a table of random digits or a calculator to randomly generate seven digits, each between 0 and 9. The variable you would measure is the number of vowels drawn.
Part C:
Random Digits: 4, 2, 5, 7, 8, 8, 4
Vowels: 2, 8, 8, 4
Part D: This result suggests that it is possible to randomly draw all vowels in one draw, although it is unlikely.
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fill in the blank. let where is an integer greater than___. compute the number of values of for which the sum of the squares of the digits of is at most .
Let where is an integer greater than 9. compute the number of values of for which the sum of the squares of the digits of is at most 25.
The question asks us to count the number of values of for which the sum of the squares of the digits of is at most 25. To solve this problem, we can use a loop to iterate through all possible values of starting from 9 and up. For each value of , we can then calculate the sum of the squares of the digits of by using modulo and division operations to extract each digit and square it. If the sum of the squares of the digits of is at most 25, we can add 1 to the count of values. After the loop completes, we will have the total number of values of for which the sum of the squares of the digits of is at most 25.
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
Three polynomials are factored below, but some coefficients and constants are missing. All of the missing values of a, b, c, and
d are integers.
1. x² - 8x + 15 = (ax + b)(cx + d)
2. 2x³ - 8x² - 24x = 2x(ax + b)(cx + d)
3.6x² + 14x + 4 = (ax + b)(cx + d)
Fill in the table with the missing values of a, b, c, and d.
b
a
1. 1
2. 1
3.
Submit
Pass
-5
1
C
1
2
d
Question ID: 504360
-6
Save an
150
The factorization of three polynomials (x2 - 8x + 15) = (ax + b)(cx + d) is (x-5) (x-3)
Explain about the equation?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 by the symbol "equal."
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
The general equation of a straight line is given by the expression y = mx + c, where m is the gradient and y = c is the point at which the line intersects the y-axis.
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the lengths of the legs of a right triangle are 7 in. and 2 in. what is the length of the hypotenuse? enter your answer rounded to the nearest tenth in the box.
3/4÷3/8 write a sentence to describe your answer
Answer:
We multiply 3/4 with the reciprocal of 3/8 which is 8/3. This leaves us with 3/4x8/3 which equals 24/12. This can be simplified into 2.
Please help me
Use the converse of the Pythagorean theorem to decide whether ΔABC is a right triangle by answering the questions.
1. Use the Pythagorean theorem to find AD. Show your work. (3 points)
2. Find AC. Show your work. (3 points)
3. Is ΔABC a right triangle? Explain. (4 points)
Using Pythagorean theorem, AD = 9 units and AC = 25 units.
ΔABC is a right triangle.
How to use the Pythagorean theorem to find AD?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Using Pythagorean theorem:
AB² = AD² + BD²
AD = √(AB² - BD²)
AD = √(15² - 12²)
AD = 9 units
AC = AD + CD
AC = 9 + 16 = 25 units
For ΔABC:
The hypotenuse is AC = 25.
Using Pythagorean theorem to confirm if ΔABC a right triangle. That is:
AC² = BC² + AB²
25² = 20² + 15²
625 = 625
Since the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, ΔABC is a right triangle.
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Is this correct???????
When Boris bought his house, he got his mortgage through a bank. The mortgage was a personal, amortized loan for 91500, at an interest rate of 3.3% , with monthly payments for a term of 40 years.
Answer: As the loan is amortized, Boris will make a series of equal payments each month for the duration of the loan, with each payment comprising of both interest and principal. The amount of interest in each payment will decrease over time, while the amount of principal in each payment will increase.
To calculate the monthly payments, we can use the formula:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
Where:
M = monthly payment
P = the principal or the loan amount = 91500
i = interest rate as a decimal = 3.3%/12 = 0.00275
n = total number of payments = 40 years x 12 months/year = 480
By substituting the values in the formula:
M = 91500 [ 0.00275 (1 + 0.00275)^480 ] / [ (1 + 0.00275)^480 - 1]
M = $439.65
So the monthly payment that Boris will make is $439.65. This amount will stay the same throughout the loan term, but the proportion of interest to principal in each payment will change as the loan is amortized.
Step-by-step explanation:
Mr. Abad's class is composed of 28 boys and 35 girls. If he is going to make groups of boys and groups of girls for the activities, what is the biggest number of children in the group if they are of the same number?
what is asked?
what is given?
word clue?
complete answers?
The biggest number of children in the group would be 14 boys and 14 girls.
What is mean by basic division?Basic division is an arithmetic operation that involves two numbers. It is used to find out how many times one number can be divided into another. It is sometimes referred to as division or division by a divisor.
Division is the inverse operation of multiplication. This means that division is the opposite of multiplication. When a number is multiplied by another number, the result is the product of the two numbers. When a number is divided by another number, the result is the quotient of the two numbers.
The process of division involves finding the number of times that one number can be divided into another. Division is performed by dividing the dividend (the number being divided) by the divisor (the number that divides the dividend). The result of the division is the quotient.
Division can be done using a variety of methods. Long division is a traditional method of division, often taught to students in elementary school. It involves breaking down each number into individual digits and then dividing them one at a time.
Another type of division is short division, which is a simpler and faster method of division that can be done in one step. Short division can be used when the divisor is a single-digit number.
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Which answer is it bc I’m in direee need
Correct option is C, The height of triangular prism is not 6 units, it is 15 units.
What number of sides does a triangle have?A triangle base, a translated copy, and three faces that join the appropriate sides make up a triangular prism, a three-sided prism. There are no rectangular sides in an oblique right triangle; it is only a right triangle. A right triangle is a uniform triangular prism, which has square sides and equilateral bases.
In essence, it is a polyhedron with three parallel sides, three surface normals in the same plane, and three surface normals (which is not necessarily parallel to the base planes). These three faces make it a parallelogram. Every cross-section that follows the base faces yields the same triangle.
For the given triangular prism,
The perimeter of base = Side + Side + Side = 13+11+8 = 32 units
The area of base = 1/2 × Base × Height = 1/2 × 11 × 6 = 33 units²
The height of prism = 15 units
The lateral surface area = (side + side + side) × height = 15 × (13 + 11 + 8) = 480 units²
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PART C Why might you want to represent the triangle's perimeter with one of the
expressions you wrote in Part B, rather than with 6x - 6.3?
In order yo calculate the perimeter of a triangle, one should add the length of its sides. For example, if the triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c
What is the perimeter?Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.
The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangle, sum of the three sides equals the perimeter.
Units are always a part of the final response. The final answer should be given in centimeters if the triangle's sides are in that unit.
An overview was given as your information is incomplete and couldn't be found.
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The table below shows some values of a function g(x)
Which function represents the relationship shown in the table?
Answer:
g(x) = 4x - (1/2)
Second choice
Step-by-step explanation:
Using points: (-2, -8.5) and (-1, -4.5)
y2 - y1 -4.5 - (-8.5) -4.5 + 8.5 4
slope = ----------- = --------------- = --------------- = --- = 4
x2 - x1 -1 - (-2) -1 + 2 1
Answer:
the answer should be g(x) = 4x - (1/2)
Step-by-step explanation:
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Let x be the number of $1 bills and y be the number of $10 bills.
We know that:
x + y = 59 (the total number of bills)
x + 10y = 239 (the total monetary value of the bills)
We can use the first equation to solve for one of the variables in terms of the other. For example:
x = 59 - y
We can substitute this expression for x into the second equation:
(59 - y) + 10y = 239
59 + 9y = 239
9y = 180
y = 20 (the number of $10 bills)
We can use this value of y to find the number of $1 bills by substituting it back into the first equation:
x + y = 59
x + 20 = 59
x = 39 (the number of $1 bills)
Therefore, the motel clerk has 39 $1 bills and 20 $10 bills.
In this diagram, circle A has radius = 5.8 and DC = 8.1. BC is tangent line, calculate the distance of BC.
The measure of tangent BC from the given figure is 12.6 units.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
Given that, Circle A has radius =5.8 and DC=8.1. BC is tangent line.
Here, AB=AD= 5.8 units and AC=AD+DC =5.8+8.1
= 13.9
Using Pythagoras theorem, we have
AC²=AB²+BC²
13.9²=5.8²+BC²
BC²= 193.21-33.64
BC²= 159.57
BC=12.6 units
Therefore, the measure of tangent BC is 12.6 units.
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At the movie theatre, child admission is $6.00 and adult admission is $9.50. On Tuesday, 143 tickets were sold for a total sales of $1089.00. How many adult
tickets were sold that day?
Answer:
Step-by-step explanation:
Let x=child number
Let y=adult number
so, x+y=143
and 6x+9.5y=1089
Form x+y=143, we got x=143-y
so, 6x+9.5y=1089
will be 6(143-y) +9.5y=1089
then we got y=66
We are looking for adult ticket were sold, so it is 66 tickets.
Kareem makes muffins using a ratio of 3.5 cups of flour for every 1.75 cups of sugar.
If he has 3.5 cups of sugar, how much flour does he need to make the muffins?
Answer:
3.5 cups of sugar / 1.75 cups of sugar = 2
3.5 x 2 = 7 cups of flour
Kareem needs 7 cups of flour to make muffins.
Word problem example but want to see step by step.
A thief steals a number of rare plants from a nursery. On the way out, the thief meets three security guards, one after another. To each security guard, the thief is forced to give one-half the plants that he still has, plus 3 more. Finally, the thief leaves the nursery with 4 plants. How many plants were originally stolen?
There were originally 36 plants in the nursery.
What is the number of plants?From the question, we have that we can be able to show the total number of the plants as x.
Hence;
When he passes the 1st guard:
x - (0.5x+2)
x -0.5x - 2
0.5x-2 plants left
When he passes the 2nd guard
(0.5x-2) - (0.5(.5x-2)+2)
0.5x - 2 - (0.25x-1+2)
0.5x - 2 - (0.25x+1)
0.5x - 2 - 0.25x - 1
When he passes the 3rd guard
(0.25x-3) - (0.5(0.25x-3)+2) = 1
0.25x - 3 - (0.125x-1.5+2) = 1
0.25x - 3 -(0.125x+.5) = 1
0.25x - 3 - 0.125x - 0.5 = 1
0.125x - 3.5 = 1
0.125x = 1 + 3.5
Then;
x = 4.5/0.125
x = 36 plants
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The scatter plot below shows the population of a village (P) over time (t). Describe the relationship between the population of the village and time.
A. The population is decreasing over time.
B. The population is increasing over time.
C. The population remains roughly the same.
D. None of these
The correct option regarding the relationship between the population of the village and time is given as follows:
A. The population is decreasing over time.
How to describe the relationship?The variables of the scatter plot are given as follows:
Input variable: time t.Output variable: Population p.From the points on the scatter plot, we have that when the value of t increases, the value of P decreases.
This means that the scatter plot shows a decreasing relationship, and thus the correct option is given by option A.
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give an example of a nonempty subset u of r2 such that u is closed under scalar multiplication, but u is not a subspace of r2.
One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.
This set is closed under scalar multiplication as if a and (x,y) are in u, a*(x,y) will also be in u because rational numbers are closed under multiplication.
A subset can be described with different properties, one of them is closure, a subset U is closed under an operation if the operation is applied to any two elements of U, and the result is also an element of U.
In mathematics, a subset is a set that is completely contained within another set. It is defined as a set U that is a part of a set S, such that every element of U is also an element of S. The notation used to indicate that U is a subset of S is U ⊆ S.
However, this set u is not a subspace of R^2 because it doesn't contain the zero vector (0,0) and it doesn't close under addition, as the sum of two rational numbers may not be a rational number.
Therefore, One example of a nonempty subset u of R^2 such that u is closed under scalar multiplication, but u is not a subspace of R^2, is the set u = {(x, y) | x, y are rational numbers}.
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please help me asap!!!
The inequality equation for the given graph is option B: y ≤ 1/3x - 4.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality equations are -
y ≥ 1/3x - 4
y ≤ 1/3x - 4
y ≤ 1/3x + 4
y ≥ 1/3x + 4
In a graph of an inequality, the symbols (<,>) are represented using a dotted line and the symbols (≤,≥) are represented using a straight line.
Now, write the inequality in equation form -
y = 1/3x - 4
y = 1/3x + 4
Substituting the values of x and y with origin (0,0) -
0 = 1/3(0) - 4
0 = -4
0 = 1/3(0) + 4
0 = 4
Putting the inequality symbol back -
y ≥ -4
This statement is false as seen in the graph.
y ≤ -4
This statement is true as seen in the graph.
y ≤ 4
This statement is false as seen in the graph.
y ≥ 4
This statement is false as seen in the graph.
Therefore, the equation for the graph is y ≤ 1/3x - 4.
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