if the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square. the area of this square will be 40cm^2 greater than the area of the rectangle. Find the area of the rectangle.
Answers
Answer: 30 cm^2.
Step-by-step explanation:
Let the original length of the rectangle be l and its width be w. Then, according to the problem:
(l - 4) = (w + 5) (equation 1)
Also, the area of the square is 40 cm^2 more than the area of the rectangle. Mathematically, we can represent this as:
(l - 4 + 5)^2 = lw + 40
Simplifying the left-hand side and substituting equation 1, we get:
l^2 - 2lw + w^2 = lw + 40
l^2 - 3lw + w^2 - 40 = 0
(l - 8)(l - 5) = 0
Therefore, l = 8 or l = 5. If we substitute l = 8 into equation 1, we get:
w = (l - 4) - 5 = -1
This is not a valid solution since the width cannot be negative. Therefore, the only valid solution is l = 5, which gives:
w = (l - 4) + 5 = 6
So the area of the rectangle is:
A = lw = 5 x 6 = 30 cm^2.
Answer:
steps explanations: x - 4 = y + 5 (sides of a square)
(x - 4)(y + 5) = 40
Which gives;
(y + 5) (y + 5) = 40
y² + 10y + 25 = 40
y² + 10y + 25 - 40 = 0
y² + 10y - 15 = 0
a=1 b=10 and c=-15
Related Questions
You ride your bike 1 3/4 miles to your friend's apartment and then another
1 3/10 miles to school. How many miles do you ride your bike in all?
Answers
Answer:3 1 /20
Step-by-step explanation:= 1+3/4+1+3/10
Solve for x and y.
8
7
X
y
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By answering the presented question, we may conclude that Therefore, the solution to the system of equations is: x = 36/31 and y = 57/31.
What is equation?In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation "x2 + 2x - 3 = 0," for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.
From the given system of equations, we have:
[tex]8x + 7y = 17 ...(1)\\x - 3y = -5 ...(2)\\x = 3y - 5 ...(3)\\8(3y - 5) + 7y = 17\\24y - 40 + 7y = 17\\31y = 57\\y = 57/31\\x = 3(57/31) - 5\\x = 36/31[/tex]
Therefore, the solution to the system of equations is:
x = 36/31 and y = 57/31.
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The solution to the system of equations is: x = 36/31 and y = 57/31.
What is equation?In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,[/tex]" for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.
From the given system of equations, we have:
[tex]$\begin{aligned} & 8 x+7 y=17 \ldots(1) \\ & x-3 y=-5 \ldots(2) \\ & x=3 y-5 \ldots(3) \\ & 8(3 y-5)+7 y=17 \\ & 24 y-40+7 y=17 \\ & 31 y=57 \\ & y=57 / 31 \\ & x=3(57 / 31)-5 \\ & x=36 / 31\end{aligned}$[/tex]
Therefore, the solution to the system of equations is:
x = 36/31 and y = 57/31.
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Question 2 Which is NOT the method that can be used to show congruency of two triangles? a) SSS b) ASA c) SAS d) SSA 0) None of the above Review Question3 ASATABFE by the HL method mZ AST 48 and m FEB 3x Find x.
Answers
Answer:
NO.2- SSA is not the method to show the congruency of two triangles.
a) Explain the concept of a greedy algorithm. b) Provide an example of a greedy algorithm that produces an optimal solution and explain why it produces an optimal solution. c) Provide an example of a greedy algorithm that does not always produce an optimal solution and explain why it fails to do so.
Answers
a) A greedy algorithm is an approach to problem-solving that makes the locally optimal choice at each step with the hope of finding a globally optimal solution.
This means that at each step, the algorithm chooses the best available option without considering the future consequences of that decision.
(b) An example of a greedy algorithm that produces an optimal solution is the activity selection problem.
Given a set of activities with their start and end times, the goal is to select the maximum number of non-overlapping activities. The greedy algorithm sorts the activities by their end times and selects the first non-overlapping activity.
It then repeats this process with the remaining non-overlapping activities until all activities have been selected. This algorithm produces an optimal solution because selecting the activity with the earliest end time leaves the maximum amount of time available for the remaining activities.
(c) An example of a greedy algorithm that does not always produce an optimal solution is the knapsack problem.
Given a set of items with their weights and values, the goal is to maximize the value of items that can be carried in a knapsack of a given weight capacity. The greedy algorithm selects items based on their value-to-weight ratio until the knapsack is full.
However, this algorithm can fail to produce an optimal solution if there are items with high value but large weight, which cannot fit in the knapsack after the algorithm selects several low-value items with small weight. In such cases, a more sophisticated algorithm is required to find the optimal solution.
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What is the measure of angle C? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠C= ° Right triangle A B C, with right angle C B A. Side A B is three centimeters, side B C is four centimeters, and side C A is five centimeters.
Answers
The measure of angle C is 53.13 degrees.
What are trigonometric functions?
Trigonometric functions are a set of mathematical functions used to relate the angles of a right triangle to the lengths of its sides. There are six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Each function represents a ratio of two sides of a right triangle.The tangent function, denoted as tan(x), is a trigonometric function that represents the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Calculating the value of angle C :
The three sides of the given right triangle are 3 cm, 4 cm, and 5 cm.
To find the measure of angle C, we can use the trigonometric function called inverse tangent, or arctan, which gives the ratio of the length of the opposite side to the length of the adjacent side.
Using the Pythagorean Theorem, we can verify that the given triangle is a right triangle:
[tex]5^2 = 3^2 + 4^2[/tex]
[tex]25 = 9 + 16[/tex]
[tex]25 = 25[/tex]
So, the triangle is a right triangle.
To find the measure of angle C, we can use the arctan function:
[tex]tan(C) =opposite/adjacent = 3/4[/tex]
[tex]C = arctan(3/4) \approx 53.13[/tex] degrees
Therefore, the measure of angle C is 53.13 degrees (rounded to the nearest hundredth).
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Answer needed ASAP!!
:)
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The answer of the given question based on the finding the m∠QTS from a circle with the measure of minor arc the answer is the measure of angle ∠QTS is 60° degrees.
What is Arc?In geometry, arc is portion of a curve or circle. It is defined as the part of the curve that is contained between two points, called endpoints, on curve. The length of arc is fraction of the circumference of circle, determined by the measure of central angle that subtends it.
An arc is typically denoted by two endpoints, with small arc or arc symbol above the two letters. For example, an arc with endpoints A and B would be denoted as "⌒AB" or "AB".Arcs can be classified based on their measure or position of their endpoints.
An arc with measure less than 180 degrees is called minor arc, while an arc with measure greater than 180 degrees is called major arc. An arc with measure equal to 180 degrees is called semicircle.
Since arc QS is a minor arc, we know that angle ∠QTS is half the measure of arc QS. Therefore, we have:
m∠QTS = (1/2) m arc QS
m∠QTS = (1/2) (120°) [Substituting the given value of m arc QS]
m∠QTS = 60°
Therefore, the measure of angle ∠QTS is 60° degrees.
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a confidence interval for a population mean was reported to be to . if , what sample size was used in this study? (round your answer up to the next whole number.)
Answers
The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.
What is deviation?Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.
Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.
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The sample size cannot be determined from this information alone. A confidence interval for a population mean is calculated based on the mean of a sample, the sample size, and the standard deviation.
What is deviation?Deviation is the difference between the expected value or average of a set of data and the actual value. For example, if the average of a set of numbers is 10 and one of the numbers is 15, the deviation of that number is 5. Deviation is a measure of how much variation exists in a set of data. It is an important tool used to measure the accuracy of a data set and identify outliers within that data set. Deviation is also used to measure the volatility of a stock or other investment, which is a measure of how much its price changes over time.
Therefore, to determine the sample size, the mean, standard deviation, and confidence interval of the sample must all be known.
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Complete Question:
A 95% confidence interval for a population mean was reported to be 152 to 160. If s 15, what sample size was used in this study?
Which of the following algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order? A Heap Sort B Quick Sort Merge Sort (D Radix Sort
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B) Quick Sort is algorithms sorts data by recursively splitting the array into smaller sub-arrays, until eventually reaching single-element sections, and then joins the sub-arrays back together in sorted order
What is Merge Sort Algorithm?Merge Sort is an effective algorithm for sorting the data items of a list or an array. This algorithm's fundamental idea is to break the unsorted list into many sub-lists until every sub-list contains only one item.
The merging procedure then recombines all of the sublists, resulting in a sorted list. Divide-and-conquer is the name given to this merging process. Merge Sort divides the original list into N sublists, each of which contains one element.
The Merge Sort algorithm is faster than other sorting algorithms when it comes to time complexity. The time complexity of Merge Sort is O (n log n), which is better than Bubble Sort and Insertion Sort.
It is a more efficient sorting algorithm than other algorithms, such as bubble sort, which has a higher time complexity of O (n²).
Therefore, we can say that Merge Sort is the most efficient algorithm to sort an array in ascending or descending order.
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the starting salaries of individuals with a certain degree are normally distributed with a mean of $30,000 and a standard deviation of $2,500. what is the probability that a randomly selected individual with the degree will get a starting salary of at least $34,375?
Answers
The value we obtain from the table will be subtracted from 1 to obtain the probability that we are looking for.P(z < 1.75) = 0.9599 (from the standard normal distribution table)Therefore, P(z ≥ 1.75) = 1 - P(z < 1.75) = 1 - 0.9599 = 0.0401.The probability that a randomly selected individual with the degree will get a starting salary of at least $34,375 is 0.0401, or 4.01%.
We have been given that the starting salaries of individuals with a certain degree are normally distributed with a mean of $30,000 and a standard deviation of $2,500.We are required to determine the probability that a randomly selected individual with the degree will get a starting salary of at least $34,375.
We know that the Z-score formula is given as:$$z=\frac{x-\mu}{\sigma}$$Where:x = Value for which we need to find the probability.μ = Mean of the distribution.σ = Standard deviation of the distribution.Using this formula, we can find the Z-score for the given data as follows:$$z=\frac{x-\mu}{\sigma}$$$$\frac{34,375-30,000}{2,500}=1.75$$Now, we can use the normal distribution table to find the probability of a Z-score being less than or equal to 1.75.
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What is the next term of 24,30,36,42,48
Answers
Answer:
54
Step-by-step explanation:
Add six each time -> 24 + 6 = 30 + 6 = 36 etc
All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
* 24% of the students purchased their lunch
* 190 students brought their lunch from home.
How many students are in the sixth grade?
Answers
24% of the students bought their lunch on Monday. Therefore, the number of students in the 6th grade is 190
Step-by-step explanation:
if x < y < z and all three are consecutive non-zero integers, then which of the following must be a positive odd integer?
Answers
Option (A) x+1 is a positive odd integer.
Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.
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PLSS HELP IVE TRIED EVERYTHING
Answers
Answer:
Step-by-step explanation: To obtain the function g(x) that represents the indicated transformations of the graph of f(x) = 2, which are a translation 1 unit up followed by a horizontal stretch by a factor of 2, we can follow these steps:
To translate f(x) = 2 one unit up, we can add 1 to the function: f(x) + 1.
To horizontally stretch f(x) + 1 by a factor of 2, we can multiply the input (x) by 1/2: f(1/2 x) + 1.
Therefore, the function g(x) that represents the indicated transformations of f(x) is:
g(x) = f(1/2 x) + 1
g(x) = 2(1/2 x) + 1
g(x) = x + 1
Urgent Help! 100 points to whoever is willing ^-^
Noise-canceling headphones have microphones to detect the ambient, or background, noise. They interpret those noises as sinusoidal functions. To cancel out that noise, the headphones create their own sinusoidal functions that mimic the incoming noise, but it changes them in one of two ways.
1. The mimic function is the negative of the noise's function.
2. The mimic function is the noise function shifted one-half period.
The headphones then play the noise function together with the mimic function, which cancels the noise.
Instructions
• Find the frequency of any musical note in hertz (Hz).
• Use the frequency to write f(x), the sine function for the note. For example, [tex]A_4[/tex] has a frequency of 440 Hz. In radians, we describe this note as y = sin(440(2πx)) or y − sin(880πx)
• Graph the sine function for the chosen note.
• Use one of the two methods listed above to write g(x), the mimic function that cancels that note's sound. Graph that function.
• Write a third function, h(x), that is the sum of f(x) and g(x). Graph it.
• Use your three graphs to explain why g(x) cancels out f(x).
Answers
f(x) = sin(2πfx)
To cancel out this note, we need to create a mimic function g(x) that is either the negative of f(x) or shifted one-half period. Let's consider the two cases separately:
1. Mimic function is the negative of f(x):
In this case, the mimic function g(x) is simply the negative of f(x):
g(x) = - sin(2πfx)
We can graph f(x) and g(x) together to see how they cancel each other out:
Graph of f(x) and g(x) when g(x) is the negative of f(x):
The blue graph represents f(x), while the red graph represents g(x). As we can see, the two functions are equal in magnitude but opposite in sign. When we add them together, we get:
h(x) = f(x) + g(x) = sin(2πfx) - sin(2πfx) = 0
This means that the sound of the musical note is cancelled out completely.
2. Mimic function is the noise function shifted one-half period:
In this case, the mimic function g(x) is the sine function with the same frequency as f(x), but shifted one-half period:
g(x) = sin(2πfx + π)
We can graph f(x) and g(x) together to see how they cancel each other out:
Graph of f(x) and g(x) when g(x) is the noise function shifted one-half period:
The blue graph represents f(x), while the red graph represents g(x). As we can see, the two functions are equal in magnitude but out of phase by one-half period. When we add them together, we get:
h(x) = f(x) + g(x) = sin(2πfx) + sin(2πfx + π)
Using trigonometric identities, we can simplify this expression to:
h(x) = 2cos(π/2)sin(2πfx + π/2)
h(x) = 2cos(π/2)cos(2πfx) (since sin(2πfx + π/2) = cos(2πfx))
h(x) = 2sin(2πfx)
This means that the sound of the musical note is cancelled out completely.
In summary, the mimic function g(x) cancels out the sound of the musical note by either being the negative of the noise function or being the noise function shifted one-half period. In both cases, the mimic function has the same frequency as the noise function, but is equal in magnitude and opposite in sign or out of phase by one-half period. When we add the noise function and the mimic function together, they cancel each other out and we are left with no sound.
Emily needs enough fabric for 3½ hats, since she has half done already. If each hat requires1 2/7 feet of fabric how much will she need to make the 3½ hats
Answers
Using simple mathematical operations we know that 4.5 ft of fabric is needed.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, to find the fabric needed:
1 2/7 feet of fabric
Then, 3 1/2 hands will need:
= 9/7 * 7/2
= 9/2
= 4.5 ft of cloth
Therefore, using simple mathematical operations we know that 4.5 ft of fabric is needed.
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Correct question:
Emily needs enough fabric for 3 1/2 hat's since she has half a hat done already. if each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hat's?
20. Assertion(A): The sides of a triangle are 5cm, 12cm and 13cm and its area is 30 cm². Reason(R): Area of a triangle is base x height. (a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion, (b) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion. (c) Assertion is true but the Reason is false. (d) Assertion is false but the Reason is true.
Answers
An equilateral triangle as a side of 35 cm what is the distance around the triangle
Answers
Answer:
Step-by-step explanation:
To find the perimeter of an equilateral triangle is equalled to 3s.
35 x 3
105
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane. x + 3y + 4z = 9_______.
Answers
The largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9 has dimensions x = 1.5, y = 1, and z = 2.25, with a maximum volume of 3.375 cubic units.
To find the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 3y + 4z = 9, we can use the method of Lagrange multipliers.
Let the sides of the rectangular box be represented by the variables x, y, and z. We want to maximize the volume V = xyz subject to the constraint x + 3y + 4z = 9.
The Lagrangian function is then given by L = xyz + λ(x + 3y + 4z - 9).
Taking the partial derivatives of L with respect to x, y, z, and λ, and setting them equal to zero, we get:
yz + λ = 0
xz + 3λ = 0
x*y + 4λ = 0
x + 3y + 4z - 9 = 0
Solving these equations simultaneously, we get:
x = 1.5, y = 1, z = 2.25, and λ = -0.5625
Therefore, the maximum volume of the rectangular box is V = 1.512.25 = 3.375 cubic units.
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Please help it’s for tmr, I only have 18 minutes left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Answers
Leo might therefore have 36 or 48 toy soldiers, which is a choice between the two numbers.
What is the greatest number that is possible?The attempt to demonstrate that your integer is larger than anyone else's integer has persisted through the ages, despite their being more numbers than there are atoms in the universe. The largest number that is frequently used is a googolplex (10googol), which equals 101¹⁰⁰.
We'll name Leo's collection of toy soldiers "x" the amount. We are aware of:
We can infer x to be one of the following figures from the first condition: 28, 32, 36, 40, 44, 48, or 52.
To find out which of these integers meets the other two requirements, we can try each one individually:
x + 6 = 34 and x + 3 = 31, neither of which is a multiple of five, if x = 28.
X + 6 = 38 and X + 3 = 35, none of which is a multiple of 5, follow if x = 32.
When x = 36, x + 6 = 42, a multiple of 7, and x + 3 = 39, a multiple of 5, follow. This might be the answer.
x + 6 = 46 and x + 3 = 43, neither of which is a multiple of five, if x = 40.
x + 6 = 50 and x + 3 = 47, neither of which is a multiple of five, if x = 44.
When x = 48, x + 6 = 54, a multiple of 7, and x + 3 = 51, a multiple of 5, follow.
x + 6 = 58 and x + 3 = 55, neither of which is a multiple of five, if x = 52.
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Suppose we select one 2015 Spotify user at random
and record his or her age and whether his or her favorite music genre is pop.
(a) Draw a tree diagram to model this chance process.
(b) Find the probability that the person identifies his or her favorite music genre as pop.
(c) Suppose the chosen person identifies his or her favorite music genre as pop. What’s the probability
that he or she is aged 13–24?
Answers
Answer:11
Step-by-step explanation:
if the measure of and acute angle is represented by x, then the measure of the angle that it is complementary which is represented by 90-x
Answers
The measure of the angle that it is complementary which is represented by 90-x is always true. Option A
What is an acute angle?An acute angle is simply defined as an angle that measures from 90° and 0°. This means that it is smaller than a right angle.
It is formed in the space between two intersecting lines or planes, or from the intersection of two shapes.
What is a complementary angle?A complementary angle can be defined as a pair of angles whose sum is equal or equivalent to 90 degrees.
From the information given, we have that;
x is the acute angle
The complementary angle is 90 - x
We can see that the angle x must be complementary to be subtracted from 90 degrees.
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The complete question:
If the measure of an acute angle is represented by x, then the measure of its complement is represented by 90 – X.
always true
sometimes true
never true
17. The sum of the interior angles of a pentagon is6x + 6y. Find y in term of x
Answers
Answer:
We know that, the sum of interior angles of an n-sided polygon is (n−2)×180⁰
For a pentagon, n=5
so,
[tex] \implies \rm \: 6x + 6y = (n - 2)180[/tex]
[tex] \implies \rm \: 6(x + y) = (5 - 2)180[/tex]
[tex] \implies \rm \: 6(x + y )= 3 \times 180[/tex]
[tex] \implies \rm \: (x + y) = \dfrac{3 \times 180}{6} [/tex]
[tex] \implies \rm \: (x + y) = \dfrac{ 3 \times \cancel{180} \: \:30}{ \cancel6} [/tex]
[tex] \rm \implies \: x + y = 90[/tex]
[tex] \underline{\boxed{\implies \rm \: y= 90 - x}}[/tex]
Pentagon FormulasThere are many formulas related to a pentagon. A few basic ones are given below.
Diagonals of a pentagon: = n × (n − 3) ÷ 2 = 5 × (5 − 3) ÷ 2 = 5Sum of interior angles of a pentagon: = 180° × (n − 2) = 180° × (5 − 2) = 540°Each exterior angle of a regular pentagon: = 360° ÷ n = 360° ÷ 5 = 72°Each interior angle of regular pentagon: = 540° ÷ n = 540° ÷ 5 = 108°Area of a regular Pentagon = 1/2 × Perimeter × ApothemPerimeter of Pentagon = (side 1 + side 2 +side 3 + side 4 + side 5)Write an explicit formula for an, the nth term of the sequence 16,19,22
Answers
The explicit formula for the nth term of the sequence 16, 19, 22 is:
[tex]a_n = 16 + 3(n-1)[/tex]
What is an sequence ?
A sequence is an ordered list of numbers or other mathematical objects that follow a particular pattern. Each individual number or object in the sequence is called a term. The pattern that governs the sequence is usually defined by a rule or formula that determines how each term is related to the previous terms. Sequences can be finite or infinite, depending on whether there is a last term or not. They can also be arithmetic, geometric, or have more complicated patterns. The formula for the nth term of a sequence is typically derived from observing patterns or relationships among the given terms.
Finding the explicit formula for the given sequence :
To find the explicit formula for the given sequence 16, 19, 22, we can first observe that each term in the sequence is obtained by adding 3 to the previous term. That is, 19 = 16 + 3 and 22 = 19 + 3. This suggests that the sequence follows an arithmetic pattern, where each term is the sum of the first term and a multiple of a common difference d (in this case, d = 3) multiplied by the position of the term minus 1 (n-1).
Using this pattern, we can write the explicit formula as follows:
[tex]a_n = a_1 + d(n-1)[/tex], where [tex]a_1[/tex] is the first term and d is the common difference.
Plugging in the values for the first term and common difference in the given sequence, we get:
[tex]a_n = 16 + 3(n-1)[/tex]
Therefore, the explicit formula for the nth term of the sequence 16, 19, 22 is:
[tex]a_n = 16 + 3(n-1)[/tex]
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The zero product property, says that if a product of two real numbers is 0, then one of the numbers must be 0.
a. Write this property formally using quantifiers and variables.
b. Write the contrapositive of your answer to part (a).
c. Write an informal version (without quantifier symbols or variables) for your answer to part (b).
Answers
The contrapositive of the zero product property is that if neither of the two real numbers is 0, then the product of the two numbers will not be 0. In plain language, this means that if neither of the two numbers are 0, then the product of the two numbers cannot be 0.
In an informal version, this can be stated as "if neither number is 0, then their product cannot be 0". This can be understood as "if neither number is 0, the result of multiplying them together cannot be 0". In other words, the product of two real numbers will not be 0 if neither of them is 0.
please help me !!!!!!
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The equation representing total fraction strip is ³/₃ + ¹/₃ = ⁴/₃.
option B.
What is a fraction?
A fraction is a mathematical representation of a part of a whole or a ratio between two numbers. It consists of a numerator, which represents the number of parts being considered, and a denominator, which represents the total number of parts in the whole.
For this case, 1 is divided into, and 1 divide into 3.
To obtain the total fractions, we will add the individual fractions as shown below;
For this first fraction = ¹/₃ + ¹/₃ + ¹/₃
For the second fraction = ¹/₃
Total fraction = 3(¹/₃ + ¹/₃ + ¹/₃) + ¹/₃
Total fraction = ³/₃ + ¹/₃ = ⁴/₃
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A retailer can buy waterproof jackets that last for five years at a cost of $150 for 50 jackets. The other option is buying jackets that last for two years at a cost of $80 for 50 jackets. Which option offers the biggest savings? Show your work.
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The waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.
What is a cost function?The cost curve, which in economics expresses production costs as a function of output. The loss function is a function that has to be minimised in mathematical optimization. A cost function evaluates how inaccurate the model is in estimating the connection between X and y.
Given that, cost of waterproof jackets that last for 5 years = $150 for 50 jackets.
Thus, cost of one jacket = 150/50 = $3.
The jacket lasts 5 years thus for 1 year the equivalent cost is:
3/5 = $0.60.
Now, for the other jacket:
Cost per year is = (80/50) / 2 = $0.80 per jacket per year.
Hence, the waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.
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phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. she takes a simple random sample of 80 sophomores and finds that 52 of them bring a bag lunch. a simple random sample of 104 seniors reveals that 78 of them bring a bag lunch.Do these data give convincing evidence to support Phoebe’s hunch?
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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.
What is p-value?The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.
The ratio of seniors bringing a bag lunch= 78/104 or 0.75,
while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.
This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.
Further, the difference between the proportions is
0.75-0.65 = 0.1,
which is a large enough difference to be considered significant.
The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.
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What is the value of v i need help
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Therefore , the solution of the given problem of unitary method comes out to be V has a value of -13/3.
What is a unitary method?By using preexisting variables, this common convenience, or all essential components from the initial Bishop malleable study that adhered to a specific methodology, the objective may be accomplished. If the term affirmation result does not occur, both essential components will event miss the statement; however, if it does, it then becomes possible to reach the entity once more.
Here,
TU = 4v and QR = 5v plus 17 allow us to write:
=> QR = TU + UP + PS + SR + RQ
Inputting the numbers provided yields:
=> 5v + 17 = 4v + UP + v + 26 + SR + 5v plus
When we simplify the solution, we obtain:
=> UP + SR + 6v + 26 = 0
Because UP and SR are opposite and equivalent, we can write:
=> UP = -SR
By replacing this in the preceding solution, we obtain:
=> UP - UP + 6v + 26 = 0
When we simplify the solution, we obtain:
=> 6v + 26 = 0
26 is subtracted from both parts to yield:
=> 6v = -26
When we multiply both parts by 6, we get:
=> v = -26/6
If we simplify, we get:
=> v = -13/3
V therefore has a value of -13/3.
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Does anybody know the answer to the question below?
A cuboid box has dimensions 40 cm by 30 cm by 20 cm. The box is to hold knitting needles. What is the size of the biggest knitting needle the box can hold?
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Answer:
The largest knitting needle that the box can hold would have to fit inside the box diagonally from corner to corner.
Using the Pythagorean theorem, we can find the diagonal of the box:
d = sqrt(40^2 + 30^2 + 20^2)
d = sqrt(1600 + 900 + 400)
d = sqrt(2900)
d = 53.85 cm (rounded to two decimal places)
Therefore, the largest knitting needle that the box can hold would have a length of 53.85 cm or less.
what is the target domain for a poisson distribution?
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The target domain for a Poisson distribution is given the term (0, inf) which can be seen correct in option B.
A Poisson distribution's target domain is (0, inf). This means that the Poisson distribution can only be specified for non-negative integer values of the random variable it is modelling.
The Poisson distribution is a discrete probability function, which indicates that the variable may only take particular values from a finite list of integers. A Poisson distribution estimates how many times an event will occur in "x" amount of time. In other words, it is the probability distribution resulting from the Poisson experiment.
A Poisson experiment is a statistical experiment that categorises the experiment as either successful or unsuccessful. A limiting process of the binomial distribution is the Poisson distribution.
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Complete question:
What is the target domain for a Poisson distribution?
1) (-inf, inf)
2) (0, inf)
3) (-inf, 0]
4) [0, inf)
