Total time for whole journey can be calculated by adding the three parts of the journey which would give answer as 2.5 hours.
What is a fraction?
The components of an entire or group of items are represented by fractions. A fraction consists of two components. The numerator is that the figure at the top of the line. It details the amount of equal portions that were taken from the total or collection. The denominator is that the figure that appears below the line.
Main Body:
total time = 20 minutes + 40 minutes + 1 hour 30 minutes
= 2.5 hours or 5/2 hours.
Hence total time for journey is 2.5 hours.
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A bicycle wheel with radius 30cm made 1000 revolutions. What distance did it cover?
The distance covered by bicycle is 1.885 km.
What is distnace?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
Given: A bicycle wheel with radius 30cm made 1000 revolutions.
We have to find the total distance covered by bicycle.
First to find the circumference of the bicycle wheel.
Circumference = 2πr
where, r is the radius.
Here r = 30.
So,
Circumference = 2 x π x 30 = 60π
Now to find the total distance,
D = circumference x number of revolutions.
D = 60π x 1000
D = 188,495.5592 cm
D = 188,495.5592 /1000 km
D = 1.88 km
Therefore, the distance covered by bicycle is, 1.885 km.
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HELP MEEE I NEED THIS DONE NOW PLS
Answer:
A: $7.50 per cap
Step-by-step explanation:
IM BACCCCKKKKK XD
we use the slope formula of y2-y1/x2-x1
37.5-22.5/5-3
15/2
7.5
So he gets $7.50 per cap
Hopes this helps please mark brainliest
Answer: He gets $7.50 per cap.
Step-by-step explanation:
If at 3 caps he got $22.50, we'll need to divide $22.50 by 3 to get the cost for a single cap.
$22.50/3 = $7.50
This means that he gets $7.50 per cap.
amber bought a used car valued at $16,000. when this car was new, it was sold for $28,000. if the car depreciates exponentially at a rate of 9% per year, approximately how old is the car? round your answer to the nearest tenth of a year.
The car is about a year old if it depreciates exponentially at a rate of 9% per year 0.62
In order to know how old the car is, we will use the depreciation formula expressed below:
[tex]P_{t}=P_{0}e^{rt}[/tex]
[tex]P_t[/tex] is the final price = 16000
[tex]P_0[/tex] is the initial price = 28000
Given the rate of 0.09
Substitute the given parameters into the formula to get the time "t"
[tex]16000 = 28000e^{0.09t}[/tex]
[tex]\frac{16000}{28000} = e^{0.09t}[/tex]
t=0.5714/0.9139
This shows that the car is about a year old if it depreciates exponentially at a rate of 9% per year
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Write a program to calculate the total price for car wash services. A base car wash is $10. A dictionary with each additional service and the corresponding cost has been provided. Two additional services can be selected. A '-' signifies an additional service was not selected. Output all selected services, according to the input order, along with the corresponding costs and then the total price for all car wash services.
to calculate the total price for car wash services. A base car wash is $10. A dictionary with each additional service and the corresponding cost has been provided. Two additional services can be selected. A '-' signifies an additional service was not selected. Output all selected services, according to the input order, along with the corresponding costs and then the total price for all car wash services.
"""
Python version: 3.6
Python program to calculate the total price for car wash services
"""
# dictionary containing the services as keys and their price as values
services = {'Air freshener' : 1, 'Rain repellent' : 2, 'Tire shine' : 2, 'Wax' : 3, 'Vacuum' : 5}
# variable to store the base car wash price
base_wash = 10
# variable to store the total price
total = 0
# read the 2 services
service_choice1 = input()
service_choice2 = input()
print("ZyCar Wash")
# display the base wash price
print("Base car wash -- ${}".format(base_wash))
total += base_wash # add base_wash to total
# first service read is in services dictionary
if service_choice1 in services:
total += services[service_choice1] # add the price for the service to total
# display the service and its price from dictionary
print("{} -- ${}".format(service_choice1, services[service_choice1]))
# second service read is in services dictionary
if service_choice2 in services:
total += services[service_choice2] # add the price for the service to total
# display the service and its price from dictionary
print("{} -- ${}".format(service_choice2, services[service_choice2]))
# display the total price
print("----")
print("Total price: ${}".format(total))
# end of program
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Based on the triangle shown, what is the approximate value of Cos(20)?
Use exact fractions. To receive credit for this question, you must show your work.
3
5
e
The value of cos 2θ will be;
⇒ cos 2θ = 7/25
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The sides of triangle are 3 , 5, 4
Now,
Since, In a triangle;
cos 2θ = 2cos²θ - 1 .....(i)
And, cos θ = Base / Hypotenuse
Substitute all the values, we get;
cos θ = Base / Hypotenuse
cos θ = 4 / 5
Substitute above value in equation (i), we get;
cos 2θ = 2cos²θ - 1
cos 2θ = 2(4/5)² - 1
cos 2θ = 32/25 - 1
cos 2θ = 7/25
Thus, The value of cos 2θ will be;
⇒ cos 2θ = 7/25
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Jordan and her grandmother are making a quilt. They will cut square pieces from
fabric to make their quilt. They have already purchased three lengths of fabric. The
lengths are 30 inches 48 inches and 60 inches what is the largest length each
square can be in order to have the least amount of waste from the fabric
The largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.
What is a square?It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.
It is given that, Jordan and her grandma are creating a quilt as a result. To make their quilt, they will cut square pieces of cloth. They have already bought three fabric lengths. 30 inches, 48 inches, and 60 inches are the lengths.
The total length of the fabric is,
=30+48+60
=138 inches
The perimeter of a square is,
P = 4a
138 = 4a
a=138/4
a=34.5 inches
Thus, the largest length each square can be in order to have the least amount of waste from the fabric will be 34.5.
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How many gallons of a 35% solution should be mixed with 7 gallons of a 60% solution to create a 50% solution?
From the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.
As given in the question,
Quantity of 60% solution in making 50% solution is = 7 gallons
Let us consider y gallons be the quantity of 35% solution to make 50% solution.
Quantity used to make 50% solution is (7 + y)
Required equation is:
(y × 35%) + (7× 60%) = (7+y) 50%
⇒(35y/100) + (420/100) = (350 + 50y)/100
⇒35y + 420 = 350 + 50y
⇒50y - 35y = 420 -350
⇒15y = 70
⇒y = 4.666..
⇒y = 4.7 gallons ( approximately)
Therefore, from the given gallons of solution to make 50% solution approximately 4.7 gallons of 35% solution need to be mixed.
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so lets say you have to do 257+102+51+41 which is 451 right?
so what would it be if someone took 30% of that 451 like tax what would you be left with? first person to answer CORRECTLY ill give u thanks
First we are supposed to find 30% of 451
30/100×451 = 135.3
So, 451 - 136= 315.7
Therefore I would be left with 315.7
Answer:
$315.70
Step-by-step explanation:
the sum of these is 451 so to find 30 percent we multiply 451 by 30 percent
First turn 30 percent into a decimal by moving the decimal point to places to the left
0.30 and now we multiply
0.3x451
135.30 is 30% of 451 and since someone is taking it we subtract it by 451
451-135.30
315.70 is what you are left with
But if it was tax you would add this to the total amount you are spending
Hopes this helps please mark brainliest
which one of the following is not statistical sampling? simple random sample. stratified random sampling. cluster sampling. convenience sampling.
Convenience sampling is not a type of statistical sampling.
What is statistical sampling?
Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study.
If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.
Main body:
Simple random sample:
Each individual and group of individuals have the same chance of being selected for the sample. To obtain a basic random sample, one needs technology, random number generators, or some other type of chance mechanism.
stratified Random sample :
The population is first divided into sections. There are some people from each group in the overall sample. Each group's participants are chosen at random.
Cluster sampling:
Grouping the population first, a cluster random sample is taken. Every member of some of the groups makes up the overall sample. The selection of the groups is random.
Hence Convenience sampling is not a type of statistical sampling.
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A survey of 225 students showed the mean number of hours spent studying per week was 20. 6 and the standard deviation was 2. 7. Assuming a 90% confidence level, the margin of error is approximately.
The margin of error is approximately 0.3
To answer the question, we must figure out what margin of error corresponds to a 90% confidence level. The definition of the margin of error used to create confidence intervals for the population mean is as follows;
Mean = μ = 20.6
Standard deviation = σ = 2.7
Number of students = n = 225
the result of the sample mean's standard error and the accompanying z-score. The formula used to compute the sample mean's standard error is;
⇒ σ / √n
The z-score associated with a 90% confidence level:
From the given table z-score is 1.645
Therefore, the margin of error;
σ / √n * 1.645 = 2.7/√225 * 1.645
= 0.296
Hence, the margin of error is approximately 0.3
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Answer:
Approximately 0.3 of an error is allowed.
Given data in question
Confidentialevel=90%
Mean = μ = 20.6
2.7 as the standard deviation
N = 225 students are enrolled.
the outcome of the standard error of the sample mean and the corresponding z-score. The formula used to determine the standard error of the sample mean is;
⇒ σ / √n
The z-score for a 90% degree of confidence is:
Z-score for the provided table is 1.645.
Consequently, the error margin;
σ / √n * 1.645 = 2.7/√225 * 1.645
= 0.296
Consequently, the margin of error is roughly 0.3.
Uncle Saul's car goes 42 3/10 miles on a gallon of gas. There are 2 1/2 gallons of gas remaining in his gas tank.
3. How many miles can he drive before running out of gas?
4. Saul drives a total of 19 9/10 miles each day during his 5-day workweek. Will he need to buy more gas for the upcoming week? explain your answer.
please help asap tysm <33
Answer:
Step-by-step explanation:
quit
Please help me do these two!! I don’t understand what to do with the arc(sin,cos,tan) in these problems. I’ll mark branliest!!
Answer:
See below=====================
Use identities:
sin (x + y) = sin x cos y + cos x sin ytan (x - y) = (tan x - tan y)/(1 + tan x tan y)sin (sin⁻¹ x) = xcos (cos ⁻¹ x) = xtan (tan⁻¹ x) = xsin (cos⁻¹ x) = √ (1 - x²)cos (sin⁻¹ x) = √ (1 - x²)Question 11sin (sin⁻¹ 4x + cos⁻¹ x) = sin (sin⁻¹ 4x) cos (cos⁻¹ x) + cos (sin⁻¹ 4x) sin(cos⁻¹ x) = 4x*x + √ (1 - (4x)²) * √ (1 - x²) = 4x² + √(1 - x²)(1 - 16x²)Question 12tan (tan ⁻¹ 1 - tan ⁻¹ √x) = [tan (tan ⁻¹ 1) - tan (tan ⁻¹ √x)] / [1 + tan (tan ⁻¹ 1) tan (tan ⁻¹ √x)] =(1 - √x) / (1 + 1*√x) = (1 - √x) / (1 + √x)Answer:
[tex]\textsf{11.} \quad 4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}[/tex]
[tex]\textsf{12.} \quad \dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}[/tex]
Step-by-step explanation:
Question 11[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Double Angle Identity}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Inverse Trigonometric Identities}\\\\$\sin(\cos^{-1}x)=\sqrt{1-x^2}$\\\\$\cos(\sin^{-1}x)=\sqrt{1-x^2}$\\\end{minipage}}[/tex]
Given trigonometric expression:
[tex]\sin ( \sin^{-1} 4x + \cos^{-1} x)[/tex]
Using the Sine Double Angle Identity:
[tex]\textsf{Let $A=\sin^{-1}4x$}[/tex][tex]\textsf{Let $B=\cos^{-1}x$}[/tex]Therefore:
[tex]\begin{aligned}\sin ( \sin^{-1} 4x + \cos^{-1} x)&=\sin(\sin^{-1}4x) \cos (\cos^{-1}x)+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x \cdot x+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \cos(\sin^{-1}4x) \sin(\cos^{-1}x)\\&=4x^2+ \sqrt{1-(4x)^2}\sqrt{1-x^2}\\&=4x^2+ \sqrt{1-16x^2}\sqrt{1-x^2}\end{aligned}[/tex]
Question 12[tex]\boxed{\begin{minipage}{5 cm}\underline{Tan Double Angle Identity}\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
Given trigonometric expression:
[tex]\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})[/tex]
Using the Tan Double Angle Identity:
[tex]\textsf{Let $A=\tan^{-1}1$}[/tex][tex]\textsf{Let $B=\tan^{-1}\sqrt{x}$}[/tex]Therefore:
[tex]\begin{aligned}\tan(\tan^{-1}1-\tan^{-1}\sqrt{x})&=\dfrac{\tan (\tan^{-1}1) - \tan (\tan^{-1}\sqrt{x})}{1 + \tan (\tan^{-1}1) \tan (\tan^{-1}\sqrt{x})}\\\\&=\dfrac{1 - \sqrt{x}}{1 + 1 \sqrt{x}}\\\\&=\dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}\\\\\end{aligned}[/tex]
Allie and Roman attempted to graph the blue line.
Allie's equation was y = 2x - 8
Roman's equation was y = − 2x + 8
Who had the correct equation and why? Explain your an-
swer in 1 to 2 complete sentences.
Roman's equation is correct.
What is an equation?
An equation is composed of two expressions joined by an equals sign. The phrases on each side of the equals sign are referred to as the equation's "bottom left" and "top part." The right hemisphere of an equation is frequently considered to be zero. Assuming that this does not limit the generality, it is possible to implement this by subtracting the right-hand side from both sides. The most frequent sort of equation is a polynomial equation, which has two polynomial sides. A scale into which weights are inserted is akin to an equation. When equal weights of material (for example, grain) are placed in the two pans, the scale is balanced and the weights are said to be equal.
given equations,
Allie's equation is y = 2x - 8
Roman's equation is y = -2x + 8
Roman's equation matches the given graph, so his equation is correct.
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suppose braking distance for the new system is normally distributed with s 5 10. let x denote the sample average braking distance for a random sample of 36 observations. which values of x are more contradictory to h0 than 117.2, what is the p-value in this case, and what conclusion is appropriate if a 5 .10?
The x value that more contradictory to h0 than 117.2 is the value less than 117.2 and p-value is 0.0465 and the conclusion is we reject h0.
How to calculate p-value?μ = mean = 120
x = 117.2
σ = standard deviation = 10
n = random sample = 36
Lets take the z test,
z = [tex]\frac{x-\mu }{\sigma / \sqrt{n}}[/tex]
= [tex]\frac{117.2 - 120}{10/\sqrt{36}}[/tex]
= [tex]\frac{-2.8}{1.667}[/tex]
= -1.68
From the test, we know test is left tailed and the rejection area is negative. So, the less x than 117.2 the more contradictory to h0.
For p-value use z-score table and we get 0.0465. Because the p-value is less than the appropriate α, which is 0.1, it can be concluded that h0 is rejected.
Thus, the less x value than 117.2 the more contradictory to h0 and we rejected h0 because p-value is lower than appropriate α.
Your question is incomplete, but most probably your full question was (image attached)
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Subtract (3x-4x+2) from (7x-10x-8x) then divide the difference by -2x
Answer: -6
Step-by-step explanation:
Answer:
5 + (1/x)
Step-by-step explanation:
(3x - 4x + 2) - (7x - 10x - 8x)
3x - 4x + 2 - 7x + 10x + 8x
(3x - 4x - 7x + 10x + 8x) = 10x
10x + 2
10x + 2 10x 2 1
---------- = ------- + ------- = 5 + ------
2x 2x 2x x
I hope this helps!
Subtract 8x10 from x² - 2x.
Answer:(4 x 103) x (2 x 107) = ( 4 x 2 ) x ( 103 + 7 ) = 8 x 10 10.
Step-by-step explanation:
The obtained expression after subtracting 8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
Is given expression is, Subtract 8x¹⁰ from x² - 2x.
In mathematics, subtraction is defined as the difference between two quantities. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.
=8x¹⁰-x²+2x
=8(x²)⁵-x²+2x
=x²(8x⁴-1)+2x
Thus, the obtained expression after subtracting 8x¹⁰ from x² - 2x will be x²(8x⁴-1)+2x.
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Rewrite in vertex form by completing the square:
x^2+4x+3x
The required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.
What is the parabola in vertex form?The equation of a parabola expressed in vertex form is
y = a(x - h)² + k
Where a is a multiplier and (h, k) are the coordinates of the vertex
The expression is given in the question as
f(x) = x² + 4x + 3
To complete the perfect square:
We have to add/subtract ( half the coefficient of the x- term )² to x² - 4x
f(x) = x² + 2(2)x + 4 - 4 + 3
f(x) = (x + 2)² - 1
Thus, the required equation of a parabola expressed in vertex form is f(x) = (x + 2)² - 1.
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How do I factor this expression completely?
The factors of the given expression are [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex] .
What are the factors?In mathematics, a factor is a divisor of a given integer that divides it exactly, leaving no leftovers. We may employ a variety of techniques, including the division method and the multiplication method, to determine the factors of a given integer. When we need to split anything into equal rows and columns, compare prices, exchange money, and other real-world scenarios, we employ factors.
The given expression is [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{1}{2} }[/tex]
Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex], so we can write
= [tex]x^{\frac{-3}{2}} -2x^{\frac{-1}{2} }+ x^{\frac{-1}{2}}(x^{2\times\frac{1}{2}})[/tex]
Factor out the common term [tex]x^{\frac{-1}{2} }[/tex]
= [tex]x^{\frac{-3}{2}} + x^{\frac{-1}{2}}(-2+x^{2\times\frac{1}{2}})[/tex]
Apply the exponential rule [tex]a^{b+c}= a^{b}a^{c}[/tex],
= [tex]x^{\frac{-3}{2}}-2 x^{1}x^{\frac{-3}{2} }+ x^{2}x^{\frac{-3}{2}}[/tex]
Factor out the common term [tex]x^{\frac{-3}{2} }[/tex]
= [tex]x^{\frac{-3}{2} }(1-2x+x^{2})[/tex]
= [tex]x^{\frac{-3}{2} }(x-1)^{2}[/tex]
= [tex]\frac{(x-1)^{2}}{x^{\frac{3}{2} }}[/tex]
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participants should be selected by chance for an experimental or control group so each has equal probability of being assigned to any of the groups. this is done by
The instance in question was chosen at random assignment.
Given statement;
Participants should be selected by chance for an experimental or control group so each has an equal probability of being assigned to any of the groups.
The given case is done by Random assignment.
In Mathematical experiments, random assignment refers to the use of chance processes to ensure that each participant has an equal chance of being assigned to any particular group. Participants in studies are divided into several groups at random, such as the experimental group or the treatment group.
It is known as random assignment.
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determine the compression work if the final state is 500 kpa. (round the final answer to two decimal places.)
The compression work if the final state is 500 kpa will be 44.32KJ
Step-by-step explanation:
The stated circumstance is;
P₁= 1.0 MPa
T₁ = 250°C
M=0.6 Kg
v₂=0.4v₁
v₁=0.30661 m/sec
P₂=1 Mpa
T₂=250°C
repairs made to the piston;
W= mP(V2-V1),
W= 0.6*1,000(0.232-0.30661)
W= -44.32\J
illustrates the compression work using (- ve)
Since there is pressure in the final condition, the compression work is 44.32. (KJ)
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Find X and Y so that the Quadrilateral is a Parallelogram. Answer below and show work.
The values of x and y are given by 8 and 9 respectively.
Since the quadrilateral is a parallelogram. So the opposite sides should be equal and parallel.
So,
4x-17 = 2x-1
4x-2x = 17-1
2x = 16
x = 8
Again the angles (3y+5) and (5y-13) are alternating angles with respect to parallel opposite sides of parallelogram and diagonal as transversal. So they are equal.
3y+5 = 5y-13
5y-3y = 13+5
2y = 18
y = 18/2
y = 9
So the values are, x=8 and y=9.
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Sue is thinking of buying some 2-liters sodas which are on sale for $1.25 each . The total cost C, of all the 2- liter sodas will be proportional to the number of 2- liter sodas, S, that she buys . Which equation represents the relationship between C and S
The total cost of all the 2- liter sodas will be proportional to the number of 2- liter sodas that Sue buys is c = 1.25s
How to explain the equation that represents the relationship between the cost and soda?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, Sue is thinking of buying some 2-liters sodas which are on sale for $1.25 each.
Let the number of soda be s.
The total cost will be:
c = 1.25 × s
c = 1.25s
The cost is 1.25s.
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Whatis the length of the hypotenuse of a right triangle with legs 6 meters and 8 meters?.
Answer:
10 meters
Step-by-step explanation:
Use the pythagorean theorem. 'c' represents the length of the hypotenuse of a right triangle.
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]6^{2} +8^{2} = 100\\[/tex]
[tex]c^{2} =100\\c=10[/tex]
Take the sq rt of 100 which is 10
Answer:
10 meters
Step-by-step explanation:
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
hypotenuse = √(6² + 8²)
hypotenuse = √(36 + 64)
hypotenuse = √100
hypotenuse = 10 m
What is the end behavior of the function f(x) = 5/4x²,
As x→ ∞o. f(x) → -∞
O As x-00. f(x) → ∞0
As X→ ∞o, f(x) → -∞
O As x-00, f(x) → -∞0
As x→
O As x →
∞o. f(x) → ∞0
∞0. f(x) → -∞
The end behavior of function is positive non decreasing.
What is meant by function ?A function is a relationship between a set of inputs and a set of allowable outputs in mathematics. The feature of functions is that each input corresponds to exactly one output. For example, in the function f(x)=x², any x input will result in only one output.
A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions are everywhere, and they are crucial for constructing physical relationships in the sciences.
How to solve?Given function f(x) = 5/4x²
as the function is square of x hence we can clearly see function is positive
Hence end behavior of function is positive non decreasing.
The complete question is : What is the end behavior of the function f(x)=5/4x2?
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1/2(x+2) = -1/3 (x+3)
Answer:
[tex]X=-2\frac{2}{5}[/tex]
Step-by-step explanation:
1/2(x+2)=-1/3(x+3)
1/2x+1=-1/3x-1
+1/3x
5/6x+1=-1
-1. -1
5/6x=-2
/5/6. /5/6
x=-2*6/5
x=-12/5
x= -2 2/5
Hopes this helps please mark brainliest
Over which interval is this function continually decreasing?
The given function is continuously decreasing for x = (-∝, 1).
Given function,
f(x) = | 4(x - 1) | + 2
⇒ f(x) = |4||x-1| + 2
⇒ f(x) = 4|x - 1| + 2
If x ≥ 1, |x - 1| = x - 1
⇒ f(x) = 4(x - 1) + 2 = 4x - 4 + 2
⇒ f(x) = 4x - 2
On differentiating on both sides:
f'(x) = 4 > 0
⇒ Function is continuously increasing for x ≥ 1.
If x < 1, |x - 1| = -(x - 1) = 1 - x
⇒ f(x) = 4(1 - x) + 2 = 4 - 4x + 2
⇒ f(x) = 6 - 4x
On differentiating on both sides:
f'(x) = -4 > 0
⇒ Function is continuously decreasing for x < 1.
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GCF of 21 and -24x PLS I NEED HELP IN THESE THERES SO MANY
Answer: 3
Step-by-step explanation:
Element X is a radioactive isotope such that every 30 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 1400 grams, how long would it be until the mass of the sample reached 800 grams, to the nearest tenth of a year? please help
It would take approximately 14.1 years (to the nearest tenth of a year) for the mass of the sample of Element X to reach 800 grams.
To determine how long it would take for the mass of the sample of Element X to reach 800 grams, we can use the information provided about its rate of decay.
Given:
Initial mass (M₀) = 1400 grams
Decay rate: The mass decreases by half every 30 years.
To solve this problem, we need to find the time it takes for the mass to decrease from 1400 grams to 800 grams.
Let's set up an equation to represent the decay of the mass:
M(t) = [tex]M\circ * (1/2)^(t/30)[/tex]
Here, M(t) represents the mass at time t in years, M₀ is the initial mass, and t is the time in years.
We need to find the value of t when M(t) = 800 grams:
800 = [tex]1400 * (1/2)^(t/30)[/tex]
To solve for t, we can take the logarithm of both sides of the equation (base 1/2) to isolate t:
[tex]log\base1/2(800/1400) = t/30[/tex]
Using logarithmic properties, we can simplify further:
[tex]log\base1/2(4/7) = t/30[/tex]
Now, we can solve for t by multiplying both sides of the equation by 30:
[tex]t = 30 * log\base1/2(4/7)[/tex]
Using a calculator or logarithmic tables, we find:
t ≈ 14.1 years
Therefore, it would take approximately 14.1 years (to the nearest tenth of a year) for the mass of the sample of Element X to reach 800 grams.
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Work out the trapezium below
Answer:
A = 40 cm^2
Step-by-step explanation:
A = (3+13)/2 * 5
A = 16/2 * 5
A = 8 * 5
A = 40 cm^2
1- Suppose Alice's actual height was 120.5 cm. If she shrank to 1/10 of her height, how small did she become?
2- Suppose Alice grew to 10 times her normal size. How tall did she become?
1. When Alice shrank, the height will be 12.05cm.
2. When she grew 10 times, the height will be 1205cm.
How to calculate the value?1. Since Alice's actual height was 120.5 cm and she shrank to 1/10 of her height, the height will be:
= 1/10 × 120.5
= 12.05 cm
2. If Alice grew to 10 times her normal size, the height will be:
= 120.5 × 10
= 1205cm
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