The amounts of goo after each hour are given as follows:
1 hour: 20 grams.2 hours: 40 grams.3 hours: 80 grams.n hours: 10(2)^n.The time that it takes for the goo to return to original size is given as follows:
n hours, for which:
[tex](2)^n(0.25)^n = 1[/tex]
How to model the situation?An increasing exponential function is defined as follows:
y = a(1 + r)^x.
For which the parameters are given as follows:
a is the initial value.r is the growth rate, as a decimal.Her sample is of 10 grams, and the amopunt of goo increases by 100%, hence the parameter values' are given as follows:
a = 10, r = 1.
Thus the exponential function is defined as follows:
y = 10(2)^n.
Then the amounts are given as follows:
One hour: y = 10 x 2 = 20 grams.Two hours: y = 10 x 2² = 40 grams.Three hours: y = 10 x 2³ = 80 grams.A decreasing exponential function is given as follows:
y = a(1 - r)^x.
The goo shrinks by 75% every hour, hence:
r = 0.75.
The amount after n hours is of 10(2)^n, hence the shrinking function is given as follows:
[tex]y = 10(2)^n(0.25)^n[/tex]
It returns to the original amount when:
y = 10.
Hence:
[tex]10 = 10(2)^n(0.25)^n[/tex]
[tex](2)^n(0.25)^n = 1[/tex]
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The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -5 < x < -4?
Under the < is a _ thing
Answer: “Rate of change” just means “slope”. All of calculus is just ways to find the slope for curves. Find y at -5 and at -4 and calculate the slope.
Step-by-step explanation:
Need help finding missing answers
Check the picture below.
so let's start with 34, well a centroid is the point where all "medians" meet, well a median is half of the segment, the heck does that mean? well, it means that CG = GD, and since CD is 34, that means that GD = 17.
let's keep in mind that a centroid cuts all medians in a 2 : 1 ratio, meaning one cut-side is twice as along as the other, that said
[tex]\stackrel{\textit{keeping in mind that BG=57}}{\cfrac{BH}{HG}=\cfrac{2}{1}\implies \cfrac{BH}{HG}=\cfrac{2\cdot \frac{57}{2+1}}{1\cdot \frac{57}{2+1}}}\hspace{10em} \cfrac{BH=38}{HG=19} \\\\\\ \cfrac{HD}{EH}=\cfrac{2}{1}\implies \cfrac{HD}{15}=\cfrac{2}{1}\implies HD=30\hspace{5em}\stackrel{15~~ + ~~30}{ED=45} \\\\\\ \stackrel{\textit{keeping in mind that CF=39}}{\cfrac{CH}{HF}=\cfrac{2}{1}\implies \cfrac{CH}{HF}=\cfrac{2\cdot \frac{39}{2+1}}{1\cdot \frac{39}{2+1}}}\hspace{10em}\cfrac{CH=26}{HF=13}[/tex]
-2(x+5)=4 math homework help
Answer:
-7
Step-by-step explanation:
-2(x+5)=4
First, distributive property,
-2x-10=4
Add 10 to both sides,
-2x=14
Divide both sides by -2
-7
how do you get 3/8 from 13/8
You can get 3/8 from 13/8 by subtraction. The solution is 10 / 8
How to get 3/8 from 13/8In order to get 3/8 from 13/8 we would have to carry out a subtraction of fractions.
That is we would have: 13/8 - 3/8
take the lcm of the denominator
[tex]\frac{13 - 3}{8}[/tex]
= 10 / 8
Hence when we take 3 / 8 from 13 / 8, the solution that we would have would be from subtraction. This is 10 / 8
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factorisé x2 + 14x +49
The expression is factorized to give (x + 7) and (x + 7)
What is factorization?Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.
Given the quadratic equation;
x² + 14x +49
Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7
Now, substitute the numbers in the expression
x² + 7x + 7x + 49
Make into two expressions, we have;
(x² + 7x) + (7x + 49)
factor out the common terms, we get;
x(x + 7)+ 7(x + 7)
Then, we have;
(x + 7)
(x + 7)
Hence, the factorized form is (x + 7) and (x + 7)
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Simplify the following expression: -16 -8/2 + 25 ÷ 5 + 1
A. -18
B. 6
C. 10
D. -6
please, if you write an absurd anwser i will report it
a) The function is continuous in it's entire domain.
b) The increasing and decreasing intervals for the function are given as follows:
Increasing: (0,2).Decreasing: (2,10).What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.
The lateral limits for the function in this problem are defined as follows:
[tex]\lim_{x \rightarrow 2^-} A(x) = \lim_{x \rightarrow 2} x^2 + 2 = 2^2 + 2 = 6[/tex][tex]\lim_{x \rightarrow 2^+} A(x) = \lim_{x \rightarrow 2} \frac{-3x + 30}{4} = 0.25(-3(2) + 30) = 6[/tex]The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.
The intervals of increase and decrease are given as follows:
Increasing: (0,2). -> y = x² increases for x > 0, the 2 changes just the range.Decreasing: (2,10). -> decreasing line, due to the negative slope.TranslationThe function for this problem is the piece-wise function A(x).
Item a asks if the function is continuous.
Item b asks when the function is increasing and when it is decreasing.
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15 minutes for 5 songs = minutes per song
Answer:
The average minutes per song would be 3.
F(x)=2 sin (1/2x)+1
What is the midline of the functionless
Answer: 4
Step-by-step explanation:
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Suppose a young couple deposits $1000 at the end of each quarter in an account that earns 7.6%, compounded quarterly, for a period of 8 years. After the 8 years, they start a family and find they can contribute only $200 per quarter. If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, how much will they have in the account (to help with their child’s college expenses)?
If they leave the money from the first 8 years in the account and continue to contribute $200 at the end of each quarter for the next 19 years, the future value in the account to help with their child's college is $215,293.42.
How the future value is computed?The future value for this investment is computed in two separate solutions.
We have used an online finance calculator to facilitate the process.
The future value denotes the present deposits compounded at an interest rate.
Initial Deposits:
N (# of periods) = 32 quarters (8 years x 4)
I/Y (Interest per year) = 7.6%
PV (Present Value) = $0
PMT (Periodic Deposit) = $1,000
Results:
FV = $43,489.87
Sum of all periodic payments = $32,000.00
Total Interest = $11,489.87
Subsequent Deposits:
N (# of periods) = 76 quarters (19 years x 4)
I/Y (Interest per year) = 7.6%
PV (Present Value) = $43,489.87
PMT (Periodic Payment) = $200
Results:
Future Value (FV) = $215,293.42
Sum of all periodic payments = $15,200 ($200 x 76 quarters)
Total Interest = $156,603.55
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13.A rectangle and a square have the same perimeter 120 cm. Find the side of the square. If the rectangle has a breadth 5cm less than that of the square. Find the breadth, length and area of the rectangle.
Answer:
Step-by-step explanation:
A square board is attached to a wall. The board is divided into four squares and each square is painted either black or white. In how many ways can the board be painted if we can rotate the given board about its center? The answer is not 14 or 16.
The board can be rotated in 4 different ways (0, 90, 180, 270 degrees) and each of the four squares can be painted in 2 different ways (black or white). Since we can rotate the board, the order in which the squares are painted does not matter, so we must divide by the number of ways to rearrange the squares. So, there are (2^4) / 4 = 6 ways the board can be painted when we take rotations into account.
How to calculate the Rotation rate?To calculate turnover, it is necessary to consider the departures and additions of people to the company in the period. Calculating turnover is quite simple: you need to add the number of admissions and the number of dismissals, then just divide by 2 and then divide by the total number of employees within your company.
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Does anunify know this ?Simplify and round the answer to the nearest hundreths place
The simplified form of the expression [tex]\sqrt[5]{1215}[/tex] is [tex]3\sqrt[5]{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, A radical [tex]\sqrt[5]{1215}[/tex].
Now we'll prime factor 1215.
= [tex]\sqrt[5]{5\times243}[/tex]
= [tex]\sqrt[5]{5\times3\times81}[/tex].
= [tex]\sqrt[5]{5\times3\times3\times3\times3\times3}[/tex].
= [tex]3\sqrt[5]{5}[/tex].
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Given the following table, find the domain and range of the function.
A) domain: {2, 4, 5, 9}
B) range: {2, 4, 5, 9}
C) range: {-3, 1, 5, 7}
D) domain: {-3, 1, 5, 7}
The domain and range of the function on the table are the ones in options B and C.
Domain: {-3, 1, 5, 7}
Range: {2, 4, 5, 9}
How to find the domain and range of the function?For a function y = f(x), we define the domain as the set of the inputs, this is, the set of the possible values of x.
On the other hand, the range is the set of the outputs, this is, the set of the possible values of y.
Then the domain is just the set of the values of x on the table:
Domain: {-3, 1, 5, 7}
And the range is the set of the values of y on the table:
Range: {2, 4, 5, 9}
Then the correct options are C and B.
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Which scale of measurement most reasonably applies to Confidence in Science?
The scale of measurement most reasonably applies to Confidence in Science is ordinal.
What are scales of measurement?The basic four scales used in measurements are continuous, discreet, ordinal and nominal. The continuous measurement scale is used to take the values in between a permitted range. For example weight, height, sales, rate etc.
In discreet measurements only take the whole numbers within a permitted range. For example, count of people, number of objects etc. Ordinary, logically ordered categorical values. For example, the size of clothes,
Nominal measurements include not logically ordered categorical values. For example, nationality, language etc. The scale of measurements most reasonably applies to Confidence in Science is ordinal.
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Audrey mowed 12 lawns in 9 hours. What was her rate of mowing in hours per lawn?
On solving the provided question, we got to know that - arbitrary number So the money she earns is equal to 10 times w plus 15, which can be expressed as: 10w + 15
what is arbitrary number?A number is considered arbitrary if its only unique characteristic is that it has a high value. You can think of them informally as the numbers that your opponent picked. Any number appears to be worthless intuitively.
Since the question allows us to use any number, we decide to make the money she makes from washing the car equal $10. We'll also assume that she gets paid $15 to wax the car.
So the money she earns is equal to 10 times w plus 15, which can be expressed as:
10w + 15
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Four student government officers want to go to the state convention. It will cost them $100 for registration, $375 for transportation and food, and $41 per person for the hotel. There is $425 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip?
cars___?
Answer:
$100 + $375 + $41(4) = $516
$516 - $425 = $91
$91 / $5 = 18.2 cars
Therefore, the four student government officers must wash 18 cars in order to have enough money to pay for the trip.
The temperature at a mountain cabin on
Saturday morning measured -12 degrees
Fahrenheit. The temperature decreased
another 8 degrees Saturday night. In
degrees Fahrenheit, what was the
temperature at the cabin Saturday night?
G-12 H 12
F -20
J -4
On Saturday night, the temperature at the mountain cabin decreased another 8 degrees from -12 degrees Fahrenheit, so the temperature at the cabin on Saturday night was -12 degrees - 8 degrees = -20 degrees Fahrenheit.
10. Matt has twice as many stickers as David. If David has d stickers, and Matt gives David 10 stickers, how many stickers does each have in terms of d?
Therefore, the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.
Define term.A term is a phrase or statement that is used to convey a certain meaning. Rap, punk, grunge, and heavy metal are examples of words used to characterize certain musical genres. To the majority of people, at least, "sweetie" is a word of affection.
What are phrases and statements?A phrase is a collection of words with significance but which is not usually a complete sentence. A set of words that form a sentence must have a topic.
We know that Matt has twice as many stickers as David, so if David has d stickers, then Matt has 2d stickers.
When Matt gives David 10 stickers, David has d+10 stickers and Matt has 2d-10 stickers.
So the number of stickers David has in terms of d is d+10 and the number of stickers Matt has in terms of d is 2d-10.
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-50 POINTS- if you guess you’ll be reported.
If P=(4,7) Find D2 (P)
You will be reported if you guess. The result is -1 if P=(4,7)on D2 (P). Consequently, P=(4,7) in D2 reports -1. (P).
What is the value of D2 (P)?Given p= (4,7)
The answer to 4 p+7 is 4(-2)+7=-8+7=-1
The value of the denominator (d2), a weighting factor, is depends on the control chart's subgroup size, n. Based on a subgroup size of 5, the value of d2 in the case is 2.326. Following is a brief list of the d2 values for other subgroup sizes.
The table of constants below contains the d2 value, which is determined by the subgroup size. The average moving range, or MR-bar, will be used if your subgroup size is one. Model No. The average range is 0.220, and the mean is 0.8057 (X-bar). The D2 function gives the sample range of n independent, normally distributed random variables with the same mean and a standard deviation of 1 the anticipated value.
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The volume of a cylinder is 1,200 yd^3 if it’s height is multiplied by 1/4, what will be the new volume of the cylinder?
Therefore , the solution of the given problem of volume comes out to be
you would then possess 1/9 of the volume.
What is volume used for?The term "volume" refers to how much general space an object occupies. Unlike mass, volume changes depending on the surroundings. The mass of a substance in a given volume is referred to as its "density." It describes the relationship between mass and volume.
Here,
A cylinder has a volume of V = r2h.
As a result, V = r2[(1/3)]h is obtained by multiplying h by 1/3.
The (1/3) can be moved to the front to obtain V = [(1/3)]r2h because you are free to multiplied in any ratio you choose.
Thus, you would receive one-third of the initial mass.
What would occur if you increased the radius by 1/3 in contrast to this?
Next, you would have
=> V = π[(1/3)r]2h
=> V = π(1/9)r2h
=> V = (1/9)πr2h
You would then possess 1/9 of the volume.
Therefore , the solution of the given problem of volume comes out to be
you would then possess 1/9 of the volume.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answer: To solve a quadratic equation of the form ax^2 + bx + c = 0, there are several steps that Inga could use. Here are three options:
She could complete the square to rewrite the equation in the form (x + p)^2 = q.
She could use the quadratic formula: x = (-b +/- √(b^2 - 4ac)) / (2a).
She could factor the equation to rewrite it in the form (x + r)(x + s) = 0.
Option 1: Completing the square
To complete the square, Inga could add and subtract (b/2)^2 to the equation to get:
a(x^2 + bx + (b/2)^2) - (b/2)^2 = 0
Then, she could rewrite the equation in the form:
a(x + (b/2))^2 = (b/2)^2
Option 2: Using the quadratic formula
To use the quadratic formula, Inga could substitute the values of a, b, and c into the formula to get:
x = (-12 +/- √(12^2 - 4 * 2 * -3)) / (2 * 2)
= (-12 +/- √(144 + 24)) / 4
= (-
Step-by-step explanation:
carmela translates f (x) = x2 to create p (x). If p 9 (x) = f (x+3) -10 sketch the graph
The function p(x) = (x + 3)² is transformed 3 units left along the x-axis.
What are some rules of function transformations?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over the x-axis, (x, -y).
Given, A function f(x) = x².
Now, p(x) = f(x + 3).
p(x) = (x + 3)² and it is a transformed function to the parent function f(x).
Now, The function p(x) = (x + 3)² is transformed 3 units to the left along the x-axis.
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18.
M is the midpoint of WX and
YZ. Is YW = ZX? Why?
W
M
Which graph represents a function?
P
12 cups to 2 pints ratio
"what is the median of the following values 9,9,2,8,11,6,4"
Answer: 8
Step-by-step explanation:
Arrange the data in ascending order, and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
Rearrange 9, 9, 2, 8, 11, 6, 4 in ascending order:
2, 4, 6, 8, 9, 9, 11
The number eight appears to be in the very middle, therefore it is the median.
Find the sum of all the natural numbers from 1 to 400, inclusive, that are not divisible by 11. The answer is not 35840.
Answer: The sum of the numbers from 1 to 400 that are divisible by 11 is equal to $11 \cdot 666 = 7326$.
Step-by-step explanation:
To find the sum of all the natural numbers from 1 to 400 that are not divisible by 11, we can first find the sum of all the natural numbers from 1 to 400, and then subtract the sum of all the natural numbers from 1 to 400 that are divisible by 11.
The sum of the natural numbers from 1 to 400 is equal to $\frac{400 \cdot 401}{2} = 80150$.
There are 400/11 = 36 numbers that are divisible by 11 between 1 and 400, inclusive. The sum of these numbers is equal to $11 + 22 + 33 + \dots + 396 = 11(1 + 2 + 3 + \dots + 36)$. The sum of the first 36 natural numbers is equal to $\frac{36 \cdot 37}{2} = 666$. Therefore, the sum of the numbers from 1 to 400 that are divisible by 11 is equal to $11 \cdot 666 = 7326$.
Subtracting the sum of the numbers that are divisible by 11 from the sum of all the numbers from 1 to 400 gives us a final answer of $80150 - 7326 = 72824$. This is not equal to 35840, as stated in the problem.
Answer:
The sum is 72874--------------------------------
Use the sum of the first n terms formula for an AP:
[tex]S_n=n(t_1+t_n)/2[/tex]The sum of all natural numbers from 1 to 400:
[tex]S_{400}=400(1+400)/2=200*401=80200[/tex]The greatest natural number less than 400 but divisible by 11:
400/11 ≈ 36Sum of the numbers divisible by 11:
1*11 + 2*11 + ... + 36*11 = 11(1 + 2 + ... + 36) = 11*36*(1 + 36)/2 = 11*18*37 = 7326Sum of the numbers not divisible by 11:
80200 - 7326 = 72874a crowded bus makes several stops along a city street,with no passengers boarding the bus at any stop.At the 1st stop 1/3 of the passengers exit.At the 2nd stop 3/7 of the remaining passengers exit the bus.What fraction of the original passengers remain on the bus?
The fraction of the original passengers remaining on the bus is 11/21.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
Given, A crowded bus makes several stops along a city street, with no passengers boarding the bus at any stop.
.At the 1st stop 1/3 of the passengers exit.
At the 2nd stop, 3/7 of the remaining passengers exit the bus.
Therefore, The fraction of the original passengers who remain on the bus is,
= [(1 - (1×1/3) - (1)×(1/3)×(3/7)].
= [ 1 - (1/3) - (3/21)].
= [ (2/3) - (3/21)].
= [(14 - 3)/21].
= 11/21.
So, 11/21 remains on the bus.
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Math Kangaroo Brazil 2020 Grade 7-8 Question. Please Solve both question 25 and 26
According to the information, Jonas realized that the four-digit sequence showing the distance traveled was the same sequence showing the time at 22h10min (question 25). Also, Lady Josephine removed 1/2 of impurities of the package of beans (question 26).
How to calculate at what time Jonas realized the sequences of distance, and time were the same (Question 25)?To calculate at what time Jonas realized the sequences of distance and time were the same we have to perform the following mathematics operation:
21h00min - 22h10min = 1h10min = 70 min1 min = 0.016h70 min = 1.16h1.16h + 21h = 22.1h = 22h10minHow to calculate what fraction of the total amount of impurities was removed from the package (question 26)?To calculate what fraction of the total amount of impurities was removed from package we have to perform the following mathematical operation:
Total impurities in package: 8%Impurities removed from the package: 4%8 / 2 = 4According to the above, we can infer that 4% of impurities equals 50% or 1/2 of the total impurities in the package.
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