Wayne's mistake is that he omitted the parentheses around the two factors of 2x² and 8.
What is parentheses?Parentheses, also known as round brackets, are punctuation marks that are used to contain related information within a sentence. They are most commonly used to set off additional information, such as a clarification or an example. Parentheses can also be used to indicate a digression from the main point of a sentence, or to indicate that something is not essential to the foundation of a statement. In addition, they can be used to indicate an interruption in a sentence, or to separate items in a list. Parentheses are also used to indicate a pause or an aside in dialogue.
The step should have been written as: 4x (2x² + (8)(2x+3)). This properly shows that 8 is being multiplied by the expression 2x+3, rather than being added to it.
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Please Help ASAP - 100 pts + Brainliest if the answer is correct!
The sum of the infinite geometric series is: ²/₅
How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;
[tex]S_{\infty} = \frac{a}{1 - r}[/tex]
where;
a is first term
r is common ratio
The first term is; a = ⁴/₁₅
Common ratio; r = ⁴/₉ ÷ ⁴/₁₅ = ⁵/₃
r = ²⁰/₂₇ ÷ ⁴/₉ = ⁵/₃
Thus;
[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ (⁵/₃ - 1)
[tex]S_{\infty}[/tex] = ⁴/₁₅ ÷ ²/₃
= ²/₅
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Answer:
How to find the sum of the infinite geometric series?The formula for the sum of an infinite geometric series is;S_∞ = a/(1 - r)where;a is first termr is common ratioThe first term is; a = 4/15Common ratio; r = (4/9)/(4/15) = 5/3r = (20/27)/(4/9) = 5/3Thus;S_∞ = (4/15)/((5/3) - 1)S_∞ = (4/15)/(2/3) = 2/5
A block of wood with dimensions 10 in. by 10 in. by 6 in. has a 2 in. by 2 in. square hole cut through the square face, as shown.
A top view of a square block shows the square face with sides 10 inches long. A square hole near the right side has sides 2 inches long. A side view shows that the square cut goes through the block, from the top face to the bottom.
Top View Side View
What is the volume of the resulting block of wood?
Responses
24 in3
24 in3
576 in3
576 in3
600 in3
600 in3
624 in3
624 in3
The volume of the resulting block of wood is 576 in³. The correct option is the second option 576 in³
Calculating the volume of the resulting block of woodFrom the question, we are to determine the volume of the resulting block of wood.
From the given information,
The dimensions of the block of wood is 10 in. by 10 in. by 6 in.
First, we will calculate the original volume of the block of wood.
The original block of wood has a volume of
V = 10 x 10 x 6
V = 600 in³
Now, we will determine the volume og the hole that was cut through
The dimensions of the hole is 2 in. by 2 in. by 6 in.
Volume of the hole = 2 x 2 x 6
Volume of the hole = 24 in³
The resulting block would have a volume of
Volume of resulting block = 600 - 24
Volume of resulting block = 576 in³
Hence, the volume is 576 in³.
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Solve for x. Round to the nearest tenth, if necessary.
x=
Step-by-step explanation:
For RIGHT triangles the cos of an angle = adjacent LEG / hypotenuse
so for THIS triangle cos 55° = x / 9.3
re-arrange to 9.3 * cos 55° = x
use calculator to find x = ~ 5.3 units (rounded)
Answer:
x = 5.3
Step-by-step explanation:
As triangle XYZ is a right triangle, and we have been given angle X, the side adjacent the angle, and the hypotenuse, we can use the cosine trigonometric ratio to solve for x.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
Given:
θ = 55°A = xH = 9.3Substitute the given values into the formula and solve for x:
[tex]\implies \cos 55^{\circ}=\dfrac{x}{9.3}[/tex]
[tex]\implies x=9.3 \cos 55^{\circ}[/tex]
[tex]\implies x=5.3342608...[/tex]
[tex]\implies x=5.3\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x is 5.3 to the nearest tenth.
Type the correct answer in each box. Use numerals instead of words. Consider function g. g ( x ) = { 6 , - 8 ≤ x < - 2 0 , - 2 ≤ x < 4 - 4 , 4 ≤ x < 10 What are the values of the function when x = - 2 and when x = 4 ? g ( - 2 ) = g ( 4 ) =
After addressing the issue at hand, we can state that Therefore, function g(-2) = 0 and g(4) = -4.
what is function?Mathematicians investigate numbers and their varieties, equations and adjacent tissues, shapes but instead their locations, and potential locations for these things. The term "function" refers to the relationship here between set of inputs, each with its own output. A function is a relationship of both inputs and outputs in which each input results in a single, distinct production. Each function has its own domain, codomain, or scope. The letter f is commonly used to denote functions (x). An x represents entry. On functions, each capabilities, so several capabilities, in capabilities, and on operations are the four major types of accessible functions.
When x = -2, g(x) = 0.
When x = 4, g(x) = -4.
Therefore, g(-2) = 0 and g(4) = -4.
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What is the greatest number of unit cubes that would fit in a rectangular prism that is 12 units tall, 5 units long, and 7 units wide?
A 420
B 84
C 60
D 7
Answer:
A or 420
Step-by-step explanation:
Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.
Question Content Area
At the beginning of the period, the Cutting Department budgeted direct labor of $37,260 and supervisor salaries of $43,370 for 4,140 hours of production. The department actually completed 4,500 hours of production.
Determine the budget for the department assuming that it uses flexible budgeting.
Answer:
To determine the flexible budget for the Cutting Department, we need to use the information provided to adjust the original budget for the actual level of production.
First, we need to calculate the variable cost per hour of production:
Variable cost per hour = Direct labor / Hours of production
Variable cost per hour = $37,260 / 4,140 hours
Variable cost per hour = $9
Next, we can use this variable cost per hour to calculate the flexible budget for the actual level of production:
Flexible budget = (Variable cost per hour x Actual hours of production) + Fixed costs
Flexible budget = ($9 x 4,500 hours) + $43,370
Flexible budget = $40,500 + $43,370
Flexible budget = $83,870
Therefore, the flexible budget for the Cutting Department, based on the actual level of production of 4,500 hours, is $83,870.
As time, t, passes the value of an investment is modeled by 푉(푡) = 50(0.9)푡. Which of the following statements is supported by the behavior of V(t)?
The value of the investment modeled by the function V(t) = 50(0.9)^t Decreases at a decreasing rate, starting with an initial value of 50.
We are given the investment value function V(t) = 50(0.9)^t. This function describes the value of an investment over time, t. Let's analyze the behavior of V(t) and find a statement that is supported by this function.
1. The initial value of the investment is V(0) = 50(0.9)^0 = 50(1) = 50. So, the investment starts with a value of 50.
2. The function V(t) contains a term (0.9)^t, which indicates that as time passes, the investment value decreases. This is because 0.9 is between 0 and 1, so raising it to a power of t (as t increases) results in a smaller value.
3. The rate of decrease is not constant, as the function is exponential, not linear. This means the value of the investment decreases at a decreasing rate over time.
Based on the behavior of V(t), the following statement is supported:
As time passes, the value of the investment modeled by the function V(t) = 50(0.9)^t decreases at a decreasing rate, starting with an initial value of 50.
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Assume that the data has a normal distribution and the number of observations is
greater than fifty. Find the critical z value used to test a null hypothesis.
a = 0.05 for a two-tailed test.
O±2.575
O±1.764
O±1.645
O±1.96
-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.
A null hypothesis is what?A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.
Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).
The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.
Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.
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Which statement describes the relationships between x and y in these two equations?
y = 25x
y = x + 25
Responses
In y = 25x, the value of y is 25 more than the value of x, and in y = x + 25, the value of y is 25 times the value of x.
In y = 25x and y = x + 25, the value of y is 25 more than the value of x.
In y = 25x and y = x + 25, the value of y is 25 times more than the value of x.
In , y, = 25, x, and , y, = , x , + 25, the value of , y, is 25 times more than the value of , x, .
In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.
That statement that best describes the relationship between x and y in the given equations is: d. In y = 25x, the value of y is 25 times the value of x, and in y = x + 25, the value of y is 25 more than the value of x.
How to Interpret the Linear Relationship Equation?In the equation y = 25x, the value of y is directly proportional to x and is 25 times greater than x. This means that as x increases, y increases by a multiple of 25. For example, if x = 2, then y = 50 (25 x 2), and if x = 4, then y = 100 (25 x 4).
In the equation y = x + 25, the value of y is equal to the value of x plus 25. This means that y is always 25 greater than x, regardless of the value of x. For example, if x = 2, then y = 27 (2 + 25), and if x = 4, then y = 29 (4 + 25).
The answer is option d.
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Write the equation of the line that has a slope of 4 / 3 and passes through the point ( 0, - 3 ).
Answer: y = 4/3x -3
Step-by-step explanation:
What is the perimeter and area of a right triangle, which has the measures of its sides, the horizontal 4m, the vertical 3m, and the diagonal 5m?
a) 12m and 6m²
b) 12m and 10m²
c) 21m and 21m²
d) 6m and 12m²
e) 6m and 7.5m²
Answer:
the answer is c because every side of a triangle sides are he same so c is your answer
will give thanks
trig
The data in the triangle is not sufficient to find the asked values in the question.
Explain about the sine rule:The relationship in between sides and angles for non-right (oblique) triangles is known as the Law of Sines. It simply asserts that for all sides and angles of a given triangle, the ratio of the length of a side to the sine angle opposite this side is the same.
You must know between two angles but one side of the triangle (AAS or ASA) either two sides and an angle opposing one of them in order to employ the Law of Sines (SSA).
g/sinG = h/sinH = f/sinF
Where G, H and F are the angles and g, h and f are the angles' opposing sides.
Put the values:
g/sin136 = 13/sinH = 7/sinF
The three pairs of expression are-
HF/sin136 = 13/sinH ; 13/sinH = 7/sinF and g/sin136 = 7/sinF.
HF = 13*sin136/sinH
HF = 10.97/SinH
From the found 3 expression, each has two missing value.
Thus, the angles F and H is not possible to find.
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The average height of a boy in the United States, from birth through 60 months, can be modeled by y = 2.9square root of (x) + 20.1 where y is the average height, in inches, of boys who are x months of age. What would be the expected difference in height between a child 49 months of age and a child 16 months of age?
Answer:
Step-by-step explanation:
To find the expected difference in height between a child 49 months of age and a child 16 months of age, we need to first find the average height of each child and then find the difference between them.
For a child who is 49 months old, the average height can be found by substituting x = 49 in the given equation:
y1 = 2.9sqrt(49) + 20.1 = 42.7 inches
For a child who is 16 months old, the average height can be found by substituting x = 16 in the given equation:
y2 = 2.9sqrt(16) + 20.1 = 28.9 inches
Therefore, the expected difference in height between the two children would be:
y1 - y2 = 42.7 - 28.9 = 13.8 inches
So we can expect the child who is 49 months old to be, on average, 13.8 inches taller than the child who is 16 months old.
PLS HURRY I AM GIVING BRAINLIEST!!!
the question is in the photo!!
1) The system of inequalities that models this scenario will be:
6x + 3y ≤ 24
6x + 3y ≥ 4
2)
i) the solution for y is y ≤ 5 - 2x.
ii) the solution for y is y ≥ 3 - x.
3) The graph is attached accordingly.
a)
Let's use the variables x and y to represent the number of Mickey pretzels and Mickey bars, respectively, that Mrs. Tobie can buy. We want to ensure that at least four children get one snack each, so the inequality for the total number of snacks should be greater than or equal to 4.
Also, Mrs. Tobie has a budget of S24, so the cost of the snacks should be less than or equal to S24. Putting these together, we get:
6x + 3y ≤ 24 (budget constraint)
6x + 3y ≥ 4 (at least four snacks)
So the system of inequalities that models this scenario is:
6x + 3y ≤ 24
6x + 3y ≥ 4
b)
To solve for y in each inequality, we need to isolate y on one side of the inequality sign.
For the first inequality, we have:
x + y ≥ 3
Subtracting x from both sides, we get:
y ≥ 3 - x
So the solution for y is y ≥ 3 - x.
For the second inequality, we have:
6x + 3y ≤ 15
Dividing both sides by 3, we get:
2x + y ≤ 5
Subtracting 2x from both sides, we get:
y ≤ 5 - 2x
So the solution for y is y ≤ 5 - 2x.
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Find the values of x and y. Write your answers in simplest form.
Answer:
y = 4
x = 4√2 or 5.66
Step-by-step explanation:
If the △ is a right △ with 1 angle 45o, then the other angle is also 45o. This △ will be isosceles right triangle with y = 4
Pythagorean theorem: c^2 = a^2 + b^2
x^2 = y^2 + 4^2
x^2 = 4^2 + 4^2
x^2 = 32
x = √32 = 4√2 = 5.66
Examples 1 and 2 1 HOTELS The function y = 100(1.05) represents the cost per night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opened.
a. Graph the function.
Answer:
The graph of the function y = 100(1.05) is shown below.
b. Calculate the cost of the hotel per night after six years.
The cost of the hotel per night after six years is $130.25. This is calculated by plugging in t = 6 into the equation y = 100(1.05)^t and solving for y.
c. What is the overall cost of 7 nights at the hotel in its sixth year of operation?
The overall cost of 7 nights at the hotel in its sixth year of operation is $910.75. This is calculated by multiplying the cost per night after six years ($130.25) by 7 nights.
2 LEARNING RESOURCES
Discuss the advantages of using online learning resources for students.
One of the main advantages of using online learning resources for students is convenience. Online learning resources can be accessed from virtually any location with an internet connection, allowing students to learn from the comfort of their own homes or from mobile devices when they are on the go. Furthermore, online learning resources reduce the need for students to commute to and from a physical school, meaning that students have more time for their studies, hobbies, and other activities.
Another advantage of online learning resources is adaptability. Online learning resources may be tailored to the needs of each individual student and can easily be adjusted should a student’s needs
In a grocery store, a $12 case of soda is discounted 20%. How much will you save?
Answer: 9.60
Step-by-step explanation:
Labeled price = $ 12
Discount = 20% of labeled price = 12 x 20%
= 12 x 2 / 10 = 24 / 10 = $ 2.4
Sale price = Labeled price - Discount.
Sale price = $ 12 - $ 2.40 = $ 9.60
Thus the sale price of the case of soda is 9.60 $
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $11.50. The drama club must make at least $980 from ticket sales to cover the show's costs. Write an inequality that could represent the possible values for the number of student tickets sold, � s, and the number of adult tickets sold, � a, that would satisfy the constraint.
Using inequality, x < 63.33, Student take 62 and adult take 68.
By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.
A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.
The student's ticket sells fοr $5,
adult ticket sells fοr $950,
Tοtal auditοrium = 130,
If x represents the number οf student, then adult = 130 - x,
∴ 5x + 9.5y > 950
insert y = 130 - x5x + 9.5(130 - x) > 950,
5x + 1235 - 9.5 x > 950
x < 63.33
∴ Student take 62 and adult take 68.
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quick Math Answer ok
Answer:
See below.
Step-by-step explanation:
For this problem, we are asked to find x, the hypotenuse.
There are a few ways to find the hypotenuse, but an easy way is to use the Pythagorean Theorem.
Represented as;
[tex]a^2 + b^2 = c^2\\(Short \ Leg)^2 + (Long \ Leg)^2 = (Hypotenuse)^2.[/tex]
We have 2 given values, the short leg and the long leg. We can begin solving for the hypotenuse.
Substitute:
[tex]40^2+42^2=c^2[/tex]
[tex]3364 = c^2[/tex]
Square Root the Equation:
[tex]\sqrt{3364} = \sqrt{c^2}[/tex]
[tex]c = 58.[/tex]
The Hypotenuse is 58. Our final answer is Letter D.
Anjali borrow 19000 rupees at 6% interest for 2 years at the end of 2 years she pays 15000 rupees and a gold ring to the money lender. What is the value of the gold ring
Answer:
Gold ring = 6180
Step-by-step explanation:
Gold ring = ?
I = prt
= 19000 x 6% x 2
= 2180
Amount to be paid= 19000 + 2180
= 21180
gold ring = 21180 - 15000
= 6180
Help with math problems
Answer:
in absolute value you consider both the positive and negative side of the expression in the absolute bar.
How to multiply polynomials
Answer:
To multiply polynomials, you can follow these steps:
Distribute each term of the first polynomial to each term of the second polynomial.
Combine like terms.
Simplify the resulting expression.
Here is an example:
(2x + 3)(x - 4)
Distribute:
2x(x - 4) + 3(x - 4)
Combine like terms:
2x^2 - 8x + 3x - 12
Simplify:
2x^2 - 5x - 12
So, (2x + 3)(x - 4) = 2x^2 - 5x - 12.
Step-by-step explanation:
You deposit $1,000 into a bank account. The account pays 3.75% annual interest compounded monthly. Find the balance after 6 years.
Your answer:
O $14,162.62
O 1,471.92
O $1,251.88
O $1,018.90
The answer of the given question based on the compound interest is the balance after 6 years is $14,162.62 (option a).
What is Amount?Amount refers to total value of something, usually in terms of a money. It can also be used in context of a quantity of something, such as an amount of the time or an amount of the material.
formula for the compound interest is :
A = P(1 + r/n)^(nt)
Where,
A = final amount
P = principal amount
r = annual interest rate
n = the number of times interest is to be compounded per year
t = time in years
In this case, we have:
P = $1,000
r = 3.75% = 0.0375 (annual interest rate as a decimal)
n = 12 (monthly compounding)
t = 6 years
Substituting the values into formula, we will get:
A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾
A = $1,4162.62
Therefore, the balance after 6 years is $14,162.62 (option a).
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The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.
What is probability?The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).
This can be calculated using the formula P(A|B) = P(A∩B) / P(B)
P(positive | disease) = P(positive ∩ disease) / P(disease)
= 141 / (141+16)
= 0.898
Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.
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Find the Area of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
The area of the figure is obtained to be approximately 74.1 units².
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
The rectangle has the length of 6 units.
The rectangle has the breadth of 10 units.
The semicircle has a diameter of 6 units.
The semicircle has the radius of 3 units.
The formula for area of rectangle is -
Area (r) = l × b
Substitute the values into the equation -
Area (r) = 6 × 10
Area (r) = 60 units²
The formula for area of semicircle is -
Area (r) = πr² / 2
Substitute the values into the equation -
Area (s) = [3.14 × (3)²] / 2
Area (s) = 28.26 / 2
Area (s) = 14.13 units²
The total area of the diagram is -
Total Area = Area (r) + Area (s)
Substitute the values into the equation -
Total Area = 60 + 14.13
Total Area = 74.13 units²
Therefore, the area of the figure is 74.1 units².
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What is the length of TR?
Answer:
2x + 30
Step-by-step explanation:
assuming there is no other data
4x + 6 + 24 - 2x =
2x + 30
Jenelle bought a home for $470,000, paying 18% as a down payment, and financing the rest at 5.4% interest
for 30 years. Round your answers to the nearest cent.
How much money did Jenelle pay as a down payment? $
What was the original amount financed? $
What is her monthly payment? $
If Jenelle makes these payments every month for thirty years, determine the total amount of money she
will spend on this home. Include the down payment in your answer. $
Video
Using percentage, we can find:
1- 84600
2- 385400
3- 20811.6
4- 7576776
What do you mean by percentage?A percentage's denominator, often referred to as a ratio's or a fraction's, is always 100. Sam, for instance, would have gotten 30 out of a potential 100 points if his math test score had been 30%. It is written as 30:100 in ratio form and 30/100 in fraction form. In this context, "%" is read as "percent" or "percentage" to represent a percentage. This percent symbol can always be converted to a fraction or decimal equivalent by "dividing by 100".
Now in the question,
Downpayment = 18% of 470000
= 84600
original amount financed =
470000-84600
= 385400
Monthly payment = 5.4% of 385400
= 20811.6
Total payment in 30 years = 7576776
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If the quotient of 3/8 and 1/4 is subtracted from the product of 2 1/4 and 1 1/7 what is the difference
Answer:
Step-by-step explanation:
(9/4 * 8/7) - (3/8*4/1) =
(72/28) - (12/8)
18/7 - 3/2
36/14 - 21/14
15/14 = 1 1/14
number that multiplys into -144 ans adds into -10
Answer:
-12 and 2
Step-by-step explanation:
1. Notice that both numbers have to be negative. This means that one number has to be negative, and the number with the largest value has to be negative.
2. Think of numbers that multiply to -144
3. Check and see if they add to -10
4. The only numbers that satisfy this are -12 and 2
Consider the function
f(t)=1−2t+4t2.
Give the largest value of t such that the percentage rate of change equals 100. Give your answer to one decimal place.
Answer:
The percentage rate of change of a function f(t) is given by:
(Δf / f) x 100
where Δf is the change in f and f is the original value of the function.
To find the largest value of t such that the percentage rate of change equals 100, we need to find the value of t for which:
(Δf / f) x 100 = 100
Simplifying, we get:
Δf / f = 1
This means that the change in f is equal to the original value of f.
So, we need to solve the equation:
f(t + Δt) - f(t) = f(t)
where Δt is the change in t.
Substituting the given function, we get:
[1 - 2(t + Δt) + 4(t + Δt)^2] - [1 - 2t + 4t^2] = 1 - 2t + 4t^2
Simplifying, we get:
-8tΔt + 8Δt^2 = 1
Since we are interested in the largest value of t, we can assume that Δt is a small positive number, such that Δt << t.
Ignoring the term Δt^2, we get:
-8tΔt = 1
Solving for Δt, we get:
Δt = -1 / (8t)
Substituting this value of Δt back into the equation -8tΔt + 8Δt^2 = 1, we get:
-8t(-1 / (8t)) + 8(-1 / (8t))^2 = 1
Simplifying, we get:
1 / t^2 = 1
Solving for t, we get:
t = 1
Therefore, the largest value of t such that the percentage rate of change equals 100 is t = 1.