Answer:
We can use inequality B to determine the number of sessions Sam needs to conduct. The reason is that he already has $50 and he wants to have enough money, so he needs to earn the remaining amount through tutoring. Thus, we can write the inequality as:
15s + 50 ≥ 125
where s is the number of tutoring sessions he needs to conduct. We can simplify and solve for s as follows:
15s ≥ 75
s ≥ 5
Therefore, Sam needs to conduct at least 5 tutoring sessions to have enough money to buy the video game.
The length of a rectangle is 3 cm longer than its width.
If the perimeter of the rectangle is 50 cm, find its length and width.
The length and width of the rectangle are 14 cm and 11 cm respectively
What is perimeter?Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.
The perimeter of a rectangle = l+l+w+w = 2(l+w)
represent the length by x and width by y
x = 3+y
p = 2(x+y)
represent 3+y for x
50 = 2( 3+y+y)
50 = 2( 3+2y)
50 = 6 +4y
4y = 50-6
4y = 44
divide both sides by 4
y = 44/4
y = 11 cm
x = 3+y
x = 3+11
x = 14
therefore the length and width in cm of the rectangle are 14 and 11 respectively
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For the following quadratic, identify the a,b, and c values:
2x²-3x - 5
a =
b=
C =
Answer:
The quadratic 2x² - 3x - 5 is in the standard form:
ax² + bx + c
Therefore, we can identify the values of a, b, and c from the coefficients of the quadratic:
a = 2
b = -3
c = -5
So, a = 2, b = -3, and c = -5 for the given quadratic equation.
Triangle QRS has vertices Q(-2, 2), R(-3, -4), and S(1, - 2).
Write the coordinate notation for a clockwise rotation of 180° about the origin.
(x, y) →(
The coordinate notation for a clockwise rotation of 180° about the origin include the following: (x, y) → (-x, -y).
What is a rotation?In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Generally speaking, the mapping rule for the rotation of a geometric figure about the origin by 180° is given by this mathematical expression:
(x, y) → (-x, -y)
Where:
x represents the coordinates on the x-axis of a graph.y represents the coordinates on the y-axis of a graph.In conclusion, the transformation rule (x, y) → (-x, -y) is used for the rotation of a geometric figure about the origin in a clockwise direction.
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Solve for x round to the nearest tenth
The value of x using trigonometric ratios, we get = 36.87°
How do trigonometric ratios work?Trigonometry uses the following six trigonometric ratios: sine, cosine, tangent, secant, and cotangent. Sin, cos, tan, sec, cosec, and cot are acronyms for these ratios.
Trigonometric ratios can be used to compare the relative angles of any two sides of a right-angled triangle, which has three sides altogether.
Here.
tan x° = 9/12
⇒ (tan x°) = (9/12)
⇒ x° = 36.86989765
⇒ x = 36.87°
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A business sets up a sinking fund so they will have a $61,000.00 to pay for a replacement piece of equipment in 9 years when the current equipment will be sold for scrap. If they make deposits at the end of every 2 months for 9 years in the investment that pays 5.9% compounded every 2 months, what size should each payment be?
The every 2 months payments are $
. (Round to 2 decimal place
Each payment should be $948.86, rounded to two decimal places
What is sinking fund?A sinking fund is a financial account or a reserve fund created by setting aside money periodically over a certain period of time to accumulate a sum of money needed to replace an asset or to repay a debt.
What is compounding?Compounding refers to the process of earning interest or investment returns on both the principal amount and the accumulated interest or returns from previous periods. In other words, compounding involves reinvesting the interest or returns earned on an investment, rather than withdrawing them, so that the investment grows at an increasing rate over time.
In the given question,
To determine the size of each payment that needs to be made at the end of every 2 months, we can use the formula for the future value of an annuity:
FV = Pmt x [(1 + r)^n - 1] / r
where FV is the future value, Pmt is the payment amount, r is the interest rate per period, and n is the total number of periods.
In this case, we know that the future value of the sinking fund should be $61,000, the interest rate per 2-month period is 5.9%/6 = 0.983%, and the total number of periods is 9 years x 12 months/year / 2 months/period = 54 periods.
Substituting these values into the formula, we get:
$61,000 = Pmt x [(1 + 0.00983)^54 - 1] / 0.00983
Solving for Pmt, we get:
Pmt = $61,000 x 0.00983 / [(1 + 0.00983)^54 - 1]
= $61,000 x 0.00983 / 0.6346
= $948.86
Therefore, each payment should be $948.86, rounded to two decimal places. .
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The equation p=144b represents the number of pencils p in b boxes graph the relationship on the coordinate plane
Step-by-step explanation:
To graph the relationship between the number of pencils and the number of boxes, we can plot some points that satisfy the equation p = 144b.
We can choose any values of b and calculate the corresponding values of p using the equation. For example:
When b = 0, p = 144(0) = 0. So one point on the graph is (0, 0).
When b = 1, p = 144(1) = 144. So another point on the graph is (1, 144).
When b = 2, p = 144(2) = 288. So another point on the graph is (2, 288).
We can continue this process to find more points, or we can notice that the equation p = 144b represents a linear relationship between p and b with a slope of 144. This means that every time we increase b by 1, we increase p by 144.
We can use this information to graph the equation by starting at the y-intercept (0, 0) and then moving up 144 units for each unit we move to the right. This gives us a straight line with a slope of 144 passing through the origin.
The graph of the equation p = 144b looks like this:
|
| .
| .
| .
| .
| .
| .
| .
----------------------------------
0 1 2 3 4 b
The horizontal axis represents the number of boxes (b), and the vertical axis represents the number of pencils (p). Each dot on the graph represents a point that satisfies the equation p = 144b.
Adolfo LaRosa obtained an installment loan of $6.800 to help pay his college tuition. Student loans do not
require a down payment. He obtained the loan from a local bank and agreed to repay the loan in 24 monthly
payments at an 18% APR.
Answer:
To calculate the monthly payment for an installment loan, we can use the formula:
M = P * r * (1 + r)^n / [(1 + r)^n - 1]
where:
M = monthly payment
P = principal (amount borrowed)
r = monthly interest rate (annual interest rate divided by 12)
n = total number of payments
In this case, Adolfo borrowed $6,800, and the loan is to be repaid in 24 monthly payments at an 18% APR. First, we need to calculate the monthly interest rate:
r = 18% / 12 = 0.015
Next, we can substitute the given values into the formula:
M = 6,800 * 0.015 * (1 + 0.015)^24 / [(1 + 0.015)^24 - 1]
M ≈ $342.03
Therefore, the monthly payment for Adolfo's installment loan is approximately $342.03.
Step-by-step explanation:
Answer:$342.03.
Step-by-step explanation:
A survey of 520 adults aged 18-24 year olds was conducted in which they were asked what they did last Friday night. It found:
172 watched TV
156 ate pizza
38 watched TV and ate pizza, but did not hang out with friends
36 watched TV and hung out with friends, but did not eat pizza
40 hung out with friends and ate pizza, but did not watch TV
38 watched TV, hung out with friends, and ate pizza
63 did not do any of these three activities
How may 18-24 year olds (of these three activities) only hung out with friends last Friday night?
Your Answer:
To find out how many 18-24 year olds only hung out with friends last Friday night, we need to subtract the number of people who engaged in other combinations of activities from the total number of people surveyed:
Total surveyed = 520
Watched TV only = 172 - 38 - 36 - 38 = 60
Ate pizza only = 156 - 38 - 36 - 40 = 42
Watched TV and ate pizza = 38
Did not do any of these three activities = 63
Therefore, the number of 18-24 year olds who only hung out with friends last Friday night can be calculated as follows:
Only hung out with friends = Total surveyed - (Watched TV only + Ate pizza only + Watched TV and ate pizza + Did not do any of these three activities)
Only hung out with friends = 520 - (60 + 42 + 38 + 63)
Only hung out with friends = 217
Therefore, 217 out of the 520 18-24 year olds surveyed only hung out with friends last Friday night.What is the period of the graph of y= 1/2 sin(pi x) + 3?
A. Pi
B. 2
C. 3
D. 1/2
Answer:
B. 2
Step-by-step explanation:
The standard form of a sine function is given by:
y = A sin(Bx - C) + D
where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.
In the given function y = 1/2 sin(pi x) + 3, we can see that the amplitude is 1/2, the frequency is pi, the phase shift is 0, and the vertical shift is 3.
The period of a sine function is given by:
Period = 2π/B
In this case, B = pi, so the period is:
Period = 2π/pi = 2
Therefore, the period of the graph of y = 1/2 sin(pi x) + 3 is 2, which is option B.
Answer:
Step-by-step explanation:
The period is 2.
Normally the period of sin(x) is 2pi, but the pi inside the sin(pix) is a horizontal compression by a factor of 1/pi. So 2pi·1/pi = 2
The "1/2" and "+3" do not impact the period. Those just impact the amplitude (vertical aspect) of the graph.
What is the circumference of the circle? Use 3.14 for π.
circle with a segment drawn from the center of the circle to a point on the circle labeled 3 inches
9.42 inches
18.84 inches
28.26 inches
88.74 inches
An angle measures 1 what fraction of a circle does the angle turn through
Answer:
1/360
Step-by-step explanation:
A full circle corresponds to a central angle of 360°.
A 1° angle corresponds to 1/360 of a full circle.
Answer:
1/360
Step-by-step explanation:
1° angle corresponds to 1/360 of a whole circle
HELP ME!!!!!!! Simplify 6⁸ x 6¹⁰ = 6[?]
Enter the missing superscript!!!!!
Answer:
Step-by-step explanation:
6^8 x 6^10 = 6^(8+10) = 6^18
Answer:
18
Step-by-step explanation:
a^x times a^y = a^x+y
Therefore, 6⁸×6¹⁰ -----> 8+10 = 6¹⁸
A state lotto has a prize that pays $1,600 each week for 25 years.
Find the total value of the prize: $
If the state can earn 9% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?
$
Answer:
Step-by-step explanation:
how many times does 0,002 go into 0,008
Answer:4 times
Step-by-step explanation: 2 4 6 8
What is the answer to question d ?PLEASE HELP
How does the graph change between point A and point B?
The graph increases.
The graph decreases.
The graph remains constant.
Mark this and return
78
tentViewers/AssessmentViewer/Activit
Save and Exit
Nex
Submit
Step-by-step explanation:
nothimg there to solve...
The correct answer for the graph change between point A and point B is,
⇒ The graph increases.
What is a graph?A diagram showing relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Now it is given that there are two points on the graph,
Point A and point B.
Now, in the first case the graph increases from (0,0) to Point A.
Here graph of a function will be increasing i..e the curve has a positive slope or positive rate of change at each point between them.
In the second case the graph continues to increases through Point B.
Here also, graph of a function will be increasing i..e the curve has a positive slope or positive rate of change at each point between them.
Hence, the graph is increases from (0,0) → Point A →Point B.
Therefore, the correct answer is- The graph increases.
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Complete question is,How does the graph change between point A and point B? On a coordinate plane, a graph increases from (0, 0) to point A and then continues to increase through B. The graph increases. The graph decreases. The graph remains constant. The graph increases, then decreases.
Find the area of a regular 8 sides polygon with radius 4 units long.
The area of a regular 8 sides polygon with radius 4 units long is 309 unit²
What is an area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The space enclosed by the boundary of a plane figure is called its area.
The area of a figure is the number of unit squares that cover the surface of a closed figure.
Given is a regular 8 sides polygon with radius 4 units long, we need to find its area,
We know that the regular 8-sided polygon is called an Octagon.
Area of an octagon =
A = 2(1+√2)a²
a = side
A = 2(1+√2)8²
A = 2(2.41)64
A = 309
Hence, the area of a regular 8 sides polygon with radius 4 units long is 309 unit²
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Given matrices
�
=
[
−
1
0
]
X=[
−1
0
] and
�
=
[
−
2
−
1
]
Y=[
−2
−1
] , which of the following matrices is
�
�
XY ?
From the given scenario, AB = [17 + 28, 47 + 58] = [23, 64]
How to calculate the product of matrices XY,To calculate the product of matrices XY, the number of columns in X must match the number of rows in Y. In this case, X has 1 column and Y has 2 rows, so the product XY is undefined.
A general example of this with matrices is:
Let A be a 2x3 matrix:
A = [1 2 3; 4 5 6]
Let B be a 1x2 matrix:
B = [7 8]
To calculate the product AB, we need the number of columns in A to match the number of rows in B.
In this case, A has 3 columns and B has 1 row, so the product AB is:
AB = [17 + 28, 47 + 58] = [23, 64]
P.S Your question is incomplete, so I showed how to calculate the product of matrices XY,
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A ferris wheel has a center that is 38 feet above the ground and a
radius of 28 feet. Use the diagram below to find the height at point A.
Round your answer to the nearest hundreth.
P
28 Feet
38
Feet
The height at the point A is 10 ft.
What is subtraction?In math, subtraction is when you take one number away from another number.
In other words, the subtraction of two from five gives you an answer of three.
Subtraction is typically the second operation in arithmetic, after addition.
Given that, a ferris wheel has a center that is 38 feet above the ground and a radius of 28 feet, there is A point on the wheel, we need to find the distance of this point from the ground,
To find the same, we will simply subtract the radius of the wheel from the distance of the center of the wheel,
Therefore,
The distance of the point A from the ground = 38 - 28 = 10 ft
Hence, the height at the point A is 10 ft.
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Suppose you take out a 45-year $150,000 mortgage with an APR of 6%. You make payments for 3 years (36 monthly payments) and then consider refinancing the original loan. The new loan would
have a term of 15 years, have an APR of 5.1%, and be in the amount of the unpaid balance on the original loan. (The amount you borrow on the new loan would be used to pay off the balance on the
original loan.) The administrative cost of taking out the second loan would be $1900. Use the information to complete parts (a) through (e) below.
a. What are the monthly payments on the original loan?
(Bound to the nearest cent as needed.)
The monthly payments on the original loan are $899.33.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the monthly payments on the original loan, we can use the formula for the monthly payment of an amortized loan:
M = P (r/12)(1 + r/12)ⁿ/ ((1 + r/12)ⁿ - 1)
where M is monthly payment, P is principal, r is monthly interest rate, n is total number of payments
For the original loan, P = $150,000, r = 0.06/12 = 0.005, and n = 45 years x 12 months/year = 540 months.
Substituting these values into the formula, we get:
M = 150,000(0.005)(1 + 0.005)⁵⁴⁰ / ((1 + 0.005)⁵⁴⁰- 1)
= 899.33
Therefore, the monthly payments on the original loan are $899.33.
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In the figure below, S is between Q and T, and R is the midpoint of QS. If RS=6 and QT=15, find ST.
ST=1
s
7
X
3
ST is having a length of 3 units.
What is Midpoint?A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway.
As per the given data:
R is the midpoint of QS:
QR = RS
RS = 6
QT = 15
S is between Q and T
QT = 15
QS + ST = 15
QR + RS + ST = 15
6 + 6 + ST = 15
ST = 3
The length of ST = 3.
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I really need help dispersing these fruits
From the Venn diagram, the sum of the numbers in all the circles and overlapping areas should add up to the total number of students surveyed, which is 85.
What is the Venn diagramIn the Venn diagram:
M represents the set of students who like mango.B represents the set of students who like banana.K represents the set of students who like kiwi fruit.The overlapping areas represent students who like two or three flavors.The "X" in the center represents the 2 students who like all three flavors.Using the information given:
35 students liked mango, so the circle representing mango should contain 35.37 students liked banana, so the circle representing banana should contain 37.26 students liked kiwi fruit, so the circle representing kiwi fruit should contain 26.2 students liked all three flavors, so the overlapping area of all three circles should contain 2.20 liked both mango and banana, so the overlapping area of mango and banana should contain 20.14 liked mango and kiwi fruit, so the overlapping area of mango and kiwi fruit should contain 14.3 liked banana and kiwi fruit, so the overlapping area of banana and kiwi fruit should contain 3.Note that the sum of the numbers in all the circles and overlapping areas should add up to the total number of students surveyed, which is 85.
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complete the number pattern 9;27;81?
Answer:
243
Step-by-step explanation:
Going in times 3 so 81 x 3 = 243
what is the surface area of the cone?
The surface area of the cone is 96π square centimeters (or approximately 301.59 square centimeters if we use a decimal approximation for π).
Calculating a cone's surface area is as follows:
SA = πr² + πrℓ
where l is the cone's slant height and r is the base's radius.
The radius and slant height in this instance are 6 cm and 10 cm, respectively. Therefore:
SA = π(6²) + π(6)(10)
= 36π + 60π
= 96π
The cone's surface area is 96 square centimetres, or roughly 301.59 square centimetres if we round to the nearest decimal.
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What does "things" refer to? Choose the word that completes the sentence.
The store was crammed with racks of used clothes. "How
pretty!" Mama said with a sigh as she stopped to examine
some silky scarves and beaded necklaces. "But we're here to
find things for you girls, not me."
"But we're here to find
for you girls, not me."
necklaces
clothes
racks
scarves
P
Answer: Clothes
Step-by-step explanation:
They are in a clothing store for the girls.
Hope this helped
There are 5 positive integers with the mean +5, the median = 5, and the mode = 8. What is the range of this data?
In response to the query, we have that So, depending on the precise equation choice of five positive numbers, the data range might be 5, 6, or 7.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. A mathematical assertion used in algebraic equations establishes the equivalence of two mathematical statements. For instance, in the equation 3x + 5 = 14, the equal sign creates a space between the values 3x + 5 and 14. To comprehend the relationship between the two sentences written on opposing sides of a letter, utilise a mathematical formula. The logo and the specific programme typically correspond. An illustration would be 2x - 4 = 2.
The five positive integers will be denoted as a, b, c, d, and e.
We know that c must equal 5, since the median is 5.
The three integers we now have add up to 15 (a + b + c = 15).
We may write the equation as follows since the mean is 5:
(a + b + c + d + e)/5 = 5
a + b + 18 = 25
a + b = 7
a = 1, b = 6, c = 5, d = 8, e = 8
a = 2, b = 5, c = 5, d = 8, e = 8
a = 3, b = 4, c = 5, d = 8, e = 8
Range = 8 - 1 = 7
Range = 8 - 2 = 6
Range = 8 - 3 = 5
So, depending on the precise choice of five positive numbers, the data range might be 5, 6, or 7.
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Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?
a cylinder with the diameter labeled 2.6 centimeters and the height labeled 3.8 centimeters
SA = 2π(1.3)2 + 1.3π(3.8)
SA = 2π(2.6)2 + 2.6π(3.8)
SA = 2π(2.6)2 + 1.3π(3.8)
SA = 2π(1.3)2 + 2.6π(3.8)
SA = 2π(1.3)² + 1.3π(3.8) is the equation that calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown.
How to find the correct formula?The correct equation to calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder is:
SA = 2πr(h + r)
where r is the radius of the cylinder (which is half of the diameter), and h is the height of the cylinder.
In this case, the radius is 1.3 centimeters (half of the diameter of 2.6 centimeters), and the height is 3.8 centimeters. Therefore, the correct equation to calculate the surface area (amount of wrapping paper needed) is:
SA = 2π(1.3)(3.8 + 1.3)
SA = 2π(1.3)(5.1)
SA ≈ 41.82 square centimeters
So, the amount of wrapping paper needed to completely cover the cylinder is approximately 41.82 square centimeters.
Identify the relevant measurements of the cylinder: In this case, the problem states that the cylinder has a diameter of 2.6 centimeters and a height of 3.8 centimeters.
Calculate the radius of the cylinder: The radius of the cylinder is half of its diameter. So, divide the diameter by 2: 2.6/2 = 1.3 centimeters. Therefore, the radius of the cylinder is 1.3 centimeters.
Use the formula for the surface area of a cylinder: The formula for the surface area of a cylinder is SA = 2πr(h + r), where r is the radius of the cylinder and h is its height. Plug in the values for r and h: SA = 2π(1.3)² + 1.3π(3.8).
Thus, SA = 2π(1.3)² + 1.3π(3.8) is the equation that alculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown.
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1. The proportion, p, of consumers who shop with coupons
is the ratio of the number, C, of consumers who use coupons
to the number, N, of consumers asked. Write an equation
for the proportion of consumers who shop with coupons.
The equation for the proportion, p, of consumers who shop with coupons is: p = C/N where C is the number of consumers who use coupons and N is the total number of consumers asked.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It consists of two expressions separated by an equal sign (=). The expression on the left side of the equal sign is equivalent to the expression on the right side. Equations can have one or more variables, which are usually represented by letters such as x, y, or z. The goal in solving an equation is to determine the value(s) of the variable(s) that make the equation true. This involves manipulating the expressions on both sides of the equal sign using algebraic operations such as addition, subtraction, multiplication, and division, to isolate the variable on one side of the equation. Equations are used in many areas of mathematics and science to represent relationships between variables and to solve problems. They are also used in various fields such as engineering, physics, and economics to model real-world situations and make predictions based on mathematical analysis.
Here,
This equation represents the ratio of the number of consumers who use coupons to the total number of consumers. It is commonly used in statistics and market research to measure the prevalence of a certain behavior or preference among a population. By calculating the proportion of consumers who use coupons, businesses can make informed decisions about their pricing strategies, promotions, and advertising campaigns.
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What is 8 and 5/8 minus 4 and 1/4
Answer:
2 3/8
Step-by-step explanation:
8 [tex]\frac{5}{8}[/tex]
- 4 [tex]\frac{1}{4}[/tex]
First you got to get the fractions to have the same denominator (or bottom number)
In this case it would be 8. You would multiply the 4 in 1/4 to get 8, and what you do to the bottom you have to do to the top, so the 1 would multiply by 2 as well to get to.
So the new equation would be,
8 [tex]\frac{5}{8}[/tex]
- 4 [tex]\frac{2}{8}[/tex]
5-2= 3
And the denominator stays the same so the fraction would be 3/8.
8-4=4 so the whole number would be 4
Making the full answer 4 3/8
ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST FOR ANSWERS
The explicit formula of the function s(n) is s(n) = 2n
The pattern of the infinite sequenceThe domain and the range of h(n)
Given that
h(n) is the number of houses
The possible values of n and h(n) are whole numbers
So, we have
Domain: All set of whole numbersRange: All set of whole numbersThe values of h(5) and h(11)
Based on the patterns in the sequence, we have
h(n) = n
So, we have
h(5) = 5
h(11) = 11
The explicit function of h(n)
In (b), we have
h(n) = n
The values of s(4) and s(7)
Given that
s(n) is the number of segments
Based on the patterns in the sequence, we have
s(n) = 2n
So, we have
s(4) = 8
s(7) = 14
The growth pattern of s(n)
Above, we have
s(n) = 2n
The above equation is a proportional equation
This means that
The growth pattern of s(n) is linear, with a constant rate of change
The explicit function of s(n)
Above, we have
s(n) = 2n
Hence, the explicit of s(n) is s(n) = 2n
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