the two angles that satisfy sinθ = -√2/2 are 5π/4 and 7π/4.
Why it is?
sinθ = -√2/2 is equivalent to saying that the sine of angle θ is negative and equal to √2/2.
We know that the sine function is positive in the first and second quadrants, and negative in the third and fourth quadrants. Therefore, we can limit our search for angles θ to the third and fourth quadrants where the sine function is negative.
In the third quadrant, the reference angle that satisfies sinθ = √2/2 is π/4, since the sine function is negative in this quadrant. Therefore, the angle θ in the third quadrant that satisfies sinθ = -√2/2 is:
θ = π + π/4 = 5π/4
In the fourth quadrant, the reference angle that satisfies sinθ = √2/2 is also π/4, since the sine function is negative in this quadrant. Therefore, the angle θ in the fourth quadrant that satisfies sinθ = -√2/2 is:
θ = 2π - π/4 = 7π/4
So the two angles that satisfy sinθ = -√2/2 are 5π/4 and 7π/4.
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The sum of two integers with different signs is 8. Give two possible integers that fit this discretion
Answer:
Step-by-step explanation:
16 - 8 which will give 8. The 16 is plus, the 8 is minus. They do have different signs.
15 - 7 which gives 8. Same explanation.
108 - 100 = 8 Same method.
Suppose that 72% of UCF students plan to vote in the presidential election. In a random sample of 1250 UCF students, let represent the proportion who plan to vote in the presidential election. What is the mean of the sampling distribution of What is the mean of the sampling distribution of
The average of the sampling distribution for the percentage of students at UCF who intend to cast a ballot in the upcoming presidential election is 0.72.
To solve this problemWe need to multiply the population proportion (p) by the sample size (n).
Given that 72% of UCF students plan to vote, we have p = 0.72.
The sample size is given as 1250, so n = 1250.
Let's denote the proportion of UCF students who plan to vote in the presidential election as p. According to the given information, p = 0.72.
So, The average of the sampling distribution for the percentage of students at UCF who intend to cast a ballot in the upcoming presidential election is 0.72.
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
13) The best prediction is that the college will need about 480 cookies.
14) The correct answer is Bus 47, with a median of 16.
Solution to the aforementioned questionFor Question 13:
The total number of students surveyed is 225. Out of these, 27 students prefer cookies. So, we can estimate that approximately (27/225) * 4000 = 480 students will prefer cookies.
Therefore, the best prediction is that the college will need about 480 cookies.
For Question 14:
The correct graph for displaying the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.
For Question 15:
We can see that the median for Bus 18 is (10+12)/2 = 11 and the median for Bus 47 is (16+16)/2 = 16. Therefore, Bus 47 typically has the faster travel time.
The correct answer is Bus 47, with a median of 16.
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what are some effects that can occur in a country if large numbers of people are out of work?
please don't answer to get points answer the question honestly and I'll mark you on brainless
it's not maths my bad it's social studies
Answer:
It increases national debt. This happens because the unemployed don't participate in doing taxes because they do not have a job. It also effects other businesses because people with less money won't buy as many things which leads to other companies losing money.
I need help ASAP please
Answer:
it should be 5
Step-by-step explanation:
-4 to 1 is 5, 1 to 6 is 5 so yea.
❊❊ HI ❊❊
THE SLOPE WILL BE 5
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⎟ > >⎟
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The perimeter of a rectangle is 20 cm. The length of the rectangle is 3 cm less than 2 1/4 times the width. Find the dimensions of the rectangle
Answer:
the dimension of the rectangle is 4 cm and 6 cm respectively
Step-by-step explanation:
The computation of the dimension of the rectangle is shown below:
Given that
The perimeter of the rectangle is 20 cm
The width be x
So, the length would be 2 1 ÷ 4 x - 3 i.e. 9 ÷ 4x - 3
Now as we know that
Perimeter of the rectangle = 2 (length + width)
20 = 2 (9 ÷ 4x - 3 + x)
20 = 9 ÷ 2x - 6 + 2x
20 = 4.5x - 6 + 2x
26 = 6.5x
x = 4 cm
Now the length would be
= 9 × 4 ÷ 4 - 3
= 6 cm
Hence, the dimension of the rectangle is 4 cm and 6 cm respectively
Solve for q. -9= q - 4.8=
Answer:
Step-by-step explanation:
-9+4.8=q-4.8+4.8
-4.2=q-4.8+4.8
-4.2=q
q=-4.2
5. The following table shows the number of students in a given class according to their age and sex. Age Sex Male Female 18 What percent of class are 13 years old? 13 15 Total 21 27
The percentage of the class that are 13 years old can be found to be
How to find the percentage ?First, we need to find the total number of students in the given class which would be:
= Number of 13 year olds + Number of 15 year olds
= 21 + 27
= 48 students
The percentage of students who are aged 13 would therefore be:
= Number of 13 year old students / Total number of students in class x 100 %
= 21 / 48 x 100 %
= 0. 4375 x 100 %
= 43. 75 %
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I need help asap please and thank you!!!!!
A sandwich shop has 60 stores and 80% of the stores are in California. The rest of the stores are in Nevada.
How many stores are in California and how many are in Nevada?
What is the x-intercept of 10x + 4y = -20
Answer:
(-2,0)
Step-by-step explanation:
When finding the x intercept, substitute 0 for Y. -20/10=-2.
I hope this helps
Answer:
The x-intercepts of that is (-2,0).
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
To solve problems, construct one-variable equations and inequalities.
How to use them to solve problems?As opposed to an inequality, which links two different values, an equation declares that two expressions are equal.
Create one-variable equations and inequalities, then utilize them to solve issues.
Include simple rational and exponential equations as well as those resulting from linear and quadratic functions.
In order to answer word problems, students should be able to decipher them and create equations and inequalities.
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f(x)=3x-4 and g(x) = x2 find the value of f(3)-g(2)
show all work
Answer: 1
f(x) = 3x - 4 => f(3) = 3.3 - 4 = 9 - 4 = 5
g(x) = x² => g(2) = 2² = 4
=> f(3) - g(2) = 5 - 4 = 1
Step-by-step explanation:
If sin(θ)=−4/7, and θ is in quadrant III, then find (a) cos(θ)= (b) tan(θ)= (c) sec(θ)= (d) csc(θ)= (e) cot(θ)=
In quadrant III, with sin(θ) = -4/7, we find that cos(θ) = -3/7, tan(θ) = 4/3, sec(θ) = -7/3, csc(θ) = -7/4, and cot(θ) = 3/4.
Given that sin(θ) = -4/7 and θ is in quadrant III, we can determine the values of various trigonometric functions using the information provided.
In quadrant III, sin(θ) is negative and cos(θ) is negative or positive. Since sin(θ) = -4/7, we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 to find cos(θ). Substituting the given value of sin(θ), we have (-4/7)^2 + cos^2(θ) = 1. Solving for cos(θ), we find that cos(θ) = -3/7.
Using the values of sin(θ) and cos(θ), we can find the remaining trigonometric functions. By definition, tan(θ) = sin(θ) / cos(θ). Substituting the given values, we have tan(θ) = (-4/7) / (-3/7) = 4/3.
The reciprocal functions can be found as follows: sec(θ) = 1 / cos(θ), csc(θ) = 1 / sin(θ), and cot(θ) = 1 / tan(θ). Substituting the values of cos(θ) and sin(θ), we find sec(θ) = -7/3, csc(θ) = -7/4, and cot(θ) = 3/4.
Therefore, in quadrant III, when sin(θ) = -4/7, the values of the trigonometric functions are: (a) cos(θ) = -3/7, (b) tan(θ) = 4/3, (c) sec(θ) = -7/3, (d) csc(θ) = -7/4, and (e) cot(θ) = 3/4 respectively.
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Five students, adriana, ben, chandra, diana, and ernesto, would each like one of the four spots at the regional science fair. Their names are placed in a hat, and four names are chosen at random to decide who attends the fair. What is the theoretical probability that chandra will be chosen as one of the science fair participants?.
The theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.
What is theoretical probability?Theoretical probability of an event is the ratio of number of favourable outcome to the total expected number of outcome of that event.
Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair.
Their names are placed in a hat, and four names are chosen at random to decide who attends the fair.
The total number of names are 5.The total number of names chosen are 4.The total number of ways 4 names can be taken out from 5 names is,
\(^5C_4\).
Here one spot needs to be fixed for Chandra. Now the total number of outcome remain 4 and favourable outcome remain 3.
Thus, the number of ways 4 names can be taken out such that it contains the name Chandra is
\(^4C_3\).
The theoretical probability that Chandra will be chosen as one of the science fair participants is,
\(P=\dfrac{^4C3}{^5C4}\\P=\dfrac{4}{5}\\P=0.8\\P=80\%\)
Thus, the theoretical probability that Chandra will be chosen as one of the science fair participants is 0.8 or 80%.
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On the windowsill is a plant that is 10 inches tall. It is growing 3 inches per
week. A second plant, which is 17 inches tall, is on the coffee table. It is
growing 2 inches per week. Eventually the two plants will be the same
height. How tall will the plants be? How many weeks will that take? *
Answer:18 days
Step-by-step explanation:
Here's a short table of heights:
day 0: height = 1
day 1: height = 1 + (1/2)(1) = 3/2
day 2: height = (3/2) + (1/3)(3/2) = 3/2 + 1/2 = 2
The pattern of heights is ...
(day, height) = (0, 1), (1, 1.5), (2, 2)
The plant is growing 1/2 its original height each day, so we can write the equation ...
h = 1 + d/2
We want to find the number of days (d) that result in a height of 10 (ten times the original height).
10 = 1 + d/2
9 = d/2 . . . . subtract 1
18 = d . . . . . multiply by 2
It took 18 days for the plant to grow to 10 times its original height.
Answer:
it would take 9 weeks for both of the plants to equally meet the same height which is 33 inches
Step-by-step explanation:
Can i please get branelist
10 mm
10 mm
The net of the right circular cylinder shown is made of
which set of shapes?
O1 circle and 1 square
1 circle and 1 rectangle that is not a square
O2 circles and 1 square
O2 circles and 1 rectangle that is not a square
The net of the right circular cylinder shown is made of:
2 circles and 1 rectangle that is not a square
The correct option is (D)
Net of a Cylinder:The net of a cylinder is a 2D structure made by unfolding it. It helps us to visualize the shape of a cylinder and its surface area. When we unfold a cylinder, we get a rectangle joined by two identical circles that form the top and the bottom bases of the cylinder shape.
Now, From the figure
We can easily see that, When we divide in three parts :
Top and bottom bases are two circles in shapes and middle one is become a rectangle in shape.
So, The right answer is :
2 circles and 1 rectangle that is not a square.
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For complete question, to see the attachment.
a professor pays 25 cents for each blackboard error made in lecture to the student who points out the error. in a career of n years filled with blackboard errors, the total amount in dollars paid can be approximated by a gaussian random variable yn with expected value 40n and variance 100n. what is the probability that y20 exceeds 1000? how many years n must the professor teach in order that p[yn > 1000] > 0.99?
(a) The probability that Y₂₀ exceeds 1000 is 3.91 × 10⁻⁶.
(b) The professor teach in order that the probability is n = 28.09 years.
The random variable Yₙ is defined as the total numbers of dollars paid in n years.
It is provided that Yₙ can be approximated by a Gaussian distribution, also known as Normal distribution.
The mean and standard deviation of Yₙ are:
μYₙ=40n
σYₙ =√100n
(a) For n = 20 the mean and standard deviation of Y₂₀ are:
μYₙ= 40n = 40×20 = 800
σYₙ = √100n = √100× 20 = 44.72
Compute the probability that Y₂₀ exceeds 1000 as follows:
P(Yₙ >100) = P( Yₙ - μYₙ/σYₙ > 1000 - 800/44.72)
= P(Z > 44.72)
= 1 - P(Z > 44.72)
= 0.00000391
By Using a z table for probability.
Thus, the probability that Y₂₀ exceeds 1000 is 3.91 × 10⁻⁶.
(b) It is provided that P (Yₙ > 1000) > 0.99.
P(Yₙ >1000) = 0.99
⇒ 1 - P(Yₙ < 1000) = 0.99
⇒ P(Yₙ <1000) = 0.01
⇒ P(Z < z) = 0.01
The value of z for which P (Z < z) = 0.01 is 2.33.
Compute the value of n as follows:
Z = Yₙ - μYₙ/σYₙ
⇒ 2.33 = 1000 - 40n/√100 n
⇒ 2.33 = 100/√n - 4√n
⇒ 5.4289 = (100 - 4n)²/n
⇒ 5.4289 = 10000 + 16n² - 800n/ n
⇒ 5.4289n = 10000 + 16n² -800n
⇒ 16n² - 805.4289n + 1000 = 0
The last equation is a quadratic equation.
The roots of a quadratic equation are:
n = -b ± √b-4ac/ 2a
a = 16
b = -805.4289
c = 10000
On solving the last equation the value of n = 28.09.
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Complete the following operations by filling in the value of the exponent for the result: 1041=10(103)(105)=1010−4105=10(104)4=10
The completed operations with the values of the exponents are:
1041 = 10^8
1010−4105 = 10^16
To complete the operations and fill in the value of the exponent for the result, let's break it down step by step:
1041 = 10(103)(105)
Here, we are multiplying 10 by 103 and then multiplying the result by 105. To find the exponent, we add the exponents when multiplying.
So, the exponent for the result is 3 + 5 = 8.
Therefore, the expression simplifies to 108.
1010−4105 = 10(104)4
In this case, we have 10 raised to the power of 104, and then we raise the result to the power of 4. When raising a power to another power, we multiply the exponents. So, the exponent for the result is 4 * 104 = 416. Hence, the expression simplifies to 1016.
Therefore, the completed operations with the values of the exponents are:
1041 = 10^8
1010−4105 = 10^16
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4. Which of the following differences could not give a distance between two points on a number line? Explain why. a. 19-7 c. -12-(-7) b. -3 - (-18) d. 14-(-6)
-12 -(-7) could not be a distance.
Distance:
Distance traveled is the total length of the path traveled between two positions. It can either be a 0 or a positive number that's mean it can never be a negative number.
So from the above-given statement we have
a) 19-7 = 12 (which is positive number)
b) -12 - (-7) = -12 + 7 = -5 ( which is a negative number)
c) -3-(-18) = -3 + 18 = 15 ( which is a positive number)
d) 14-(-6) = 14 + 6 = 20 ( which is a positive number)
Therefore option b i.e., -12 - (-7) cannot be a distance between two points on a number line.
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Fiona divided 3x2 5x-3 by 3x 2. the expression represents the remainder over the divisor. what is the value of a? -5 -1 1 5
The value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a polynomial:
3x² + 5x - 3
Which is divided by (3x + 2)
= (3x² + 5x - 3) ÷ (3x + 2)
\(\rm = \dfrac{\left(3x^2+5x-3\right)}{\left(3x+2\right)}\)
\(\rm =x+\dfrac{3x-3}{3x+2}\)
\(\rm =x+1+\dfrac{-5}{3x+2}\)
\(\rm =x+1-\dfrac{5}{3x+2}\)
By comparing with the given remainder.
a = -5
Thus, the value of a is -5 if the provided polynomial is divided by (3x + 2) option first -5 is correct.
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find the mass of the rectangular region 0≤x≤4, 0≤y≤3 with density function rho(x,y)=3−y
To find the mass of the rectangular region with the given density function rho(x, y) = 3 - y, where 0 ≤ x ≤ 4 and 0 ≤ y ≤ 3, we need to calculate the double integral of the density function over the region.
The mass of a region can be found by integrating the product of the density function and the area element over the region. In this case, the density function is rho(x, y) = 3 - y.
To calculate the mass, we need to set up the double integral over the rectangular region. The integral is given by:
M = ∬(0 to 4)(0 to 3) (3 - y) dA
To evaluate this integral, we integrate with respect to y first, and then with respect to x:
M = ∫(0 to 4) ∫(0 to 3) (3 - y) dy dx
Integrating with respect to y, we get:
M = ∫(0 to 4) [3y - (1/2)y^2] (0 to 3) dx
Simplifying the integral, we have:
M = ∫(0 to 4) (9/2) dx
Evaluating the integral, we get:
M = (9/2) * x | (0 to 4)
M = (9/2) * 4 - (9/2) * 0
M = 18
Therefore, the mass of the rectangular region is 18
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To calculate control limits, 20 subgroups of ______ must be saved. Definition.
A. five sets.
B. five subsets.
C. five samples.
Answer:
C. five samples.
Step-by-step explanation:
Here is a graph representing the relationship in question 3. Interpret the set of coordinates (30, 7).
children's tickets sold
60
55
50
45
40
30
25
20
5
(30, 7)
10 15 20 25 30 35 40
adult tickets sold
O 7 children's tickets and 30 adult tickets were sold
O 30 children's tickets and 7 adult tickets were sold
O When 7 tickets are sold, $30 is collected
O (30, 7) is not a possible solution
The correct option 2 that is 30 children's tickets and 7 adult tickets were sold.
Given : A graph which has adult tickets in the x - axis
and children tickets in the y - axis
The marked point is ( 30, 7 )
this means that the value of x axis 30 and y axis is 7
thus from the above information it is clear that there are 30 children's tickets and 7 adult tickets were sold.
So the correct option is Option 2
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I don't know how to "Simplify the expression of (3 ^1\4) * (3^2) " specifically to demonstrate the product of powers property (and show any steps I used too)
Answer:
11.85
Step-by-step explanation:
(3^1\4) = \(3^{\frac{1}{4} }\)
(3^2) = \((3)^{2}\)
Applying the law of indices,
\(a^{m}\) x \(a^{n}\) = \(a^{(m+n)}\)
\(3^{\frac{1}{4} }\) x \(3^{2}\) = \(3^{\frac{1}{4} + 2}\)
= \(3^{\frac{9}{4} }\)
= \(\sqrt[4]{3^{9} }\)
= \(\sqrt[4]{19683}\)
= 11.8445
≅ 11.84
the inequality 7-2/3x
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
The management of Asteria Inc. is studying the financial reports and statements of the company for the current accounting period. Which accounting head is a part of an off-balance-sheet item?
Answer:
What are the answers again??
Step-by-step explanation:
Questions 1. Let a = 1 and for n 21, define (a) Compute the first four members of the sequence (and conjecture a for mula for d (b) Prove your conjecture in part (a).
The sequence defined by a = 1 and d(n) = (n - 1)^2, for n ≥ 2, generates the first four members: 0, 1, 4, 9. The formula for d(n) can be conjectured as d(n) = (n - 1)^2. This conjecture can be proven by induction.
The sequence defined by a = 1 and d(n) = (n - 1)^2, for n ≥ 2, can be computed as follows:
For n = 1, a = 1 (given).
For n = 2, d(2) = (2 - 1)^2 = 1^2 = 1.
For n = 3, d(3) = (3 - 1)^2 = 2^2 = 4.
For n = 4, d(4) = (4 - 1)^2 = 3^2 = 9.
Based on these computations, we observe that the first four members of the sequence are 0, 1, 4, and 9. From this pattern, we can conjecture that the formula for d(n) is (n - 1)^2.
To prove this conjecture, we can use mathematical induction. The base case is n = 2, where d(2) = 1, and the formula (n - 1)^2 also yields 1. This confirms that the formula holds for the initial term.
Next, we assume that the formula holds for some arbitrary positive integer k, i.e., d(k) = (k - 1)^2.
Now we need to prove that it holds for k + 1.
Using the formula, we have d(k + 1) = ((k + 1) - 1)^2 = k^2.
On the other hand, we can directly compute d(k + 1) as (k + 1 - 1)^2 = k^2. Therefore, the formula holds for k + 1 as well.
By the principle of mathematical induction, we have proven that the formula d(n) = (n - 1)^2 holds for all positive integers n ≥ 2.
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a snack manufacturer finds that it must increase the salt content of its chips by 8 percent in order for a sample of consumers to notice that the chips are saltier than they were before (baseline). this example most nearly illustrates the concept of a( n ):
A threshold effect is when a small change in one variable results in a noticeable change in another variable. In this example, a small 8% increase in salt content of the chips is enough to produce a noticeable change in the saltiness of the chips to the sample of consumers.
The snack manufacturer can calculate the increase in salt content of their chips needed to produce the threshold effect by first determining the baseline salt content of the chips. Once this is known, they can then calculate what percentage increase to the salt content is needed by multiplying the baseline salt content by 8%. For example, if the baseline salt content of the chips is 10%, then the 8% increase in salt content would be calculated as 10% x 8% = 0.8%. This means that the snack manufacturer needs to increase the salt content of their chips by 0.8% to reach the threshold effect desired by the sample of consumers.
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19 3/5 × 20 2/5 secial product patterns to find the product
Answer: 19 3/5 x 20 2/5 = 9996/25 = 399 21/25