Basically in this question we will apply product rule of diffrentiation .
f(t) = 3t (t-6)
f'(t) = (3t)'.(t-6) +(t-6)'.(3t)
f'(t) = 3(1). (t-6) + (1).3t
f'(t) = 3t-18 +3t
Final Answer - f'(t) = 6t -18
Differentiating the given function. f(t) = 3 t (t − 6) gives f'(t) = 6t - 18 using the product rule of differentiation.
Given that, f(t) = 3t.(t-6)
To differentiate the given function we use product rule in order to simplify the differentiation.
Divide the function into two different products and then differentiate :
f(t) = 3t (t-6)
f'(t) = (3t)'.(t-6) +(t-6)'.(3t)
f'(t) = 3(1). (t-6) + (1).3t
f'(t) = 3t-18 +3t (or)
expand the given f(t) = 3t.(t-6)
= 3t^2 - 18 t
we have , f'(x) = n.x^(n-1) if f(x) = x^n
differentiating f(t) = f'(t) = 2(3t) - 18
= 6t - 18
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There are 120 students in the 6th grade 56% of them failed. How many failed, Round to the nearest whole number.
120 multiplied by 56% equals 67.2 students.
The number 67 becomes the result of rounding to the nearest whole number, which is 67.2.
Describe an example of a whole number.A collection of positive integers and zero, whole numbers are numbers without fractions. The set of integers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,... and it is denoted by the sign "W". Whole Numbers: W = 0 through 10 (inclusive).
How does math define a whole number?Absolute numbers those figures that contain zero and natural integers. neither a fraction nor a decimal. {0, 2, 3, 4, 5 6, 7, 8, 9,10, 11 …} Integer. A counting number, zero, or the negative.
The number of students who failed can be calculated by multiplying the total number of students by the percentage that failed:
120 students * 56% = 67.2 students
Rounding to the nearest whole number, 67.2 students becomes 67 students.
So, 67 students failed in the 6th grade.
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write a scenario for this linear function: f(x)=30x+45
write a story for this exponential function: f(x)=4(3)^x
Answer:
scenario: GCF =15
15(30x+45 15+15)
15(2x+3) answers
Which choice shows the coordinates of C’ if the trapezoid is reflected across the y-axis? On a coordinate plane, trapezoid A B C D has points (2, 1), (3, 5), (5, 3) and (3, 1). (–5, 3) (3, –5) (5, –3) (–3, 5)
The coordinates of C’ if the trapezoid is reflected across the y-axis is
(- 5, 3).
What is Transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given:
A reflection through the axis and is given by the following transformation rule:
(x, y) -------> (-x, y)
We have the following point:
C = (5, 3)
Now, Applying the transformation rule we have:
(5, 3) -------> (-5, 3)
So, C' is given by:
C '= (- 5, 3)
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Help pleasee asap 15 points!!
Answer:
They are supplementary angles
Pls help me with showing work i’ll give brainliest
Answer:
50/11
Step-by-step explanation:
because 50/11=4.54
[tex]\sqrt[3]{100} =4.64[/tex]
so 4.54<4.64
Answer:
hyy can you my friend,,,,
if ln(x) = 3.23 , what is the value of x
If ln(x) = 3.23 , the value of x is 25.28.
Therefore the answer is 25.28.
If ln(x) = 3.23, then x can be found by using the exponential function.
The natural logarithm function, represented by ln(x), gives the power to which e (approximately equal to 2.71828) must be raised to equal x. So, if ln(x) = 3.23, it means that e^3.23 = x.
The exponential function is the inverse of the natural logarithm, so if ln(x) = 3.23, then
x = e^(ln(x))
= e^(3.23).
Using a calculator, we can find that e^(3.23) ≈ 25.28.
So, the value of x is approximately 25.28.
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Solve for the given variable. 9(4 + c) = 99
The composite figure above is made from an isosceles triangle and a rectangle. What is the area of the composite figure?
Answer:
Area of the composite figure is 516
Step-by-step explanation:
picture above
Seema read 511 of the book during weekday and the ret of the
book he planned to read during the weekend. What part of the book
i left for reading during the weekend?
Seema left 6/11 of the book for reading over the weekend.
To calculate the part of the book left for reading during the weekend, we need to subtract the part of the book Seema read during the weekday from the total book.
If Seema reads 5/11 of the book during the weekday, then:
11 - 5 = 6This means 6/11 of the book is left for reading during the weekend. It is important to note that the fraction of the book read during the weekday and the fraction left for reading during the weekend add up to the total book. This means that 11/11 of the book will be read by Seema in total.
This question should be written as:
Seema reads 5/11 of the book during weekday and the rest of the book she planned to reads during the weekend. What part of the book is left for reading during the weekend?Learn more about Mike has read 2/4 book here: brainly.com/question/23514329
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which of the following statements shows a relationship that is correlated but not causal, a, b, c, or d? the amount of rainfall received and level of water in the lake. the number of lights left on each day and the amount of the electric bill. the increase of warm, sunny days and the number of ice cream vendors visible. the number of hours worked and how much money is made.
a. The amount of rainfall received and level of water in the lake have casual and correlation relation.
b. The number of lights left on each day and the amount of the electric bill have casual and correlation relation.
c. The increase of warm, sunny days and the number of ice cream vendors visible have not casual but correlation relationship.
d. The number of hours worked and how much money is made, have casual and correlation relation.
We have to shows a relationship that is correlated but not causal, a, b, c, or d.
a. The amount of rainfall received and level of water in the lake.
There have two events:
Event 1: The amount of rainfall
Event 2: The level of water
The both event are related to each other because when the rainfall heavily then the level of water increase
So the relation in the statement is casual and correlation.
b. The number of lights left on each day and the amount of the electric bill.
Event 1: The number of lights left on each day
Event 2: The amount of the electric bill
The both event are related because when the light left then the bill of electricity increases.
So the relation in the statement is casual and correlation.
c. The increase of warm, sunny days and the number of ice cream vendors visible.
Event 1: The increase of warm, sunny days.
Event 2: The number of ice cream vendors visible.
The both events are related to each other because it is possible that in one place have many vendors in other hand some place have no vendors.
So this statement is not casual but there have correlation between them.
d. The number of hours worked and how much money is made.
Event 1: The number of hours worked.
Event 2: How much money is made.
Both event are related to each other because if a person worked extra hours he/she will be paid according to this.
So the relation in the statement is casual and correlation.
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An electronics company finds that 5 out of 25 capacitors produced are damaged. How many damaged items can they expect if the company produces 1,535 capacitors?
Answer:
Welcome to Brainly! I saw that this was your very first question. I will gladly assist you with your problem. (see explanation).
Step-by-step explanation:
The calculation of the estimated damaged items in the situation where 23,025 capacitors were produced is displayed below:
(5 times 23,025 capacitors) / (1,535 capacitors)
= 75
Therefore, when 23,025 capacitors are produced, 75 damaged products are expected.
Hope this helped!)
1 (calculator)
Mr Houston bought a new car for £18500 in July 2010.
Its value depreciated by 15% in the first year, 18% in the
second year and 25% in the third year.
By how much had its initial price fallen by July 2013?
The percentage decrease from first to third year is; 47.725%
How to calculate percentage decrease?To find the percentage decrease, work out the difference (decrease) between the two numbers you are comparing. Thereafter, divide the decrease by the original number and then multiply the answer by 100.
Amount of car in 2010 = £18500
It depreciated by 15% in the first year. Thus;
Amount after first year = (100% - 15%) * 18500
= £15725
It depreciated by 18% in the second year. Thus;
Amount after second year = (100% - 18%) * 15725
= £12,894.5
It depreciated by 25% in the third year. Thus;
Amount after third year = (100% - 25%) * 12,894.5
= £9,670.875
Thus;
Decrease from first to third year = (18500 - 9670.875)/18500 * 100%
= 47.725%
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Can you solve this please?
Answer:
Step-by-step explanation:
I dont understand the question?
how many different ways can you arrange these 10 people in a circle? (two arrangements are considered the same, if one arrangement could be rotated to get the other arrangement.)
You can arrange 10 people in a circle in 362880 different ways if two arrangements are considered the same
What is a combination?In mathematics, a combination or combinations are all the possible groupings that can be made of a given number of elements, without repeating them and regardless of the order in which they are found.
Information about the problem:
As the table is round, the first person can take any seat, then the seat on the right can be taken by 1 of 9 people, then the next seat by 1 of 8 and so on until the 10th person has no choice of seats.
This is expressed by:
9*8*7*6*5*4*3*2
9!
362,880
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How do you find the cov of X and Y?
Step-by-step explanation:
The covariance of two variables X and Y is a measure of the relationship between their changes. It is calculated as:
cov(X, Y) = (1/n) * sum((x_i - mean(X)) * (y_i - mean(Y)))
where n is the number of observations, x_i and y_i are the values of X and Y respectively for the i-th observation, mean(X) and mean(Y) are the means of X and Y respectively.
In Python, you can use the numpy library to calculate the covariance as follows:
import numpy as np
X = [x_1, x_2, ..., x_n]
Y = [y_1, y_2, ..., y_n]
cov = np.cov(X, Y)[0][1]
A measurement of the intensity and direction of the linear relationship between two random variables, X and Y, is called covariance. A definition of covariance is:
Cov(X, Y) is equal to E[(X - E(X))(Y - E(Y))].
where E[...] is the anticipated value operator and E(X) and E(Y) is the expected values of X and Y, respectively.
If Cov(X, Y) is positive, X and Y have the propensity to rise or fall together. Cov(X, Y) is a measure of the tendency for two variables to move in opposite directions. When Cov(X, Y) equals 0, X and Y are said to be uncorrelated.
You must be aware of the expected values as well as the joint probability distribution of X and Y in order to compute the covariance of X and Y.
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use order of operations to evaluate the numerical expression 4²+(10×2)
Answer:
36Step-by-step explanation:
[tex] {4}^{2} + (10 \times 2) \\ 16 + (10 \times 2) \\ 16 + 20 \: \: \: \: \: \: \: \: \: \: \: \\ 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]4^2+(10\times2)[/tex]
[tex]4^2+20[/tex]
[tex]16+20[/tex]
[tex]=\boxed{36}[/tex]
Which describes the number and type of roots of the equation x^3 + 121x = 0
Answer:
x=0
Step-by-step explanation:
xx(x^2+121)=0
x=0
x^2+121=0
x=0
if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx=
The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).
Given that:
∫3−5f(x)dx=6
∫3−5g(x)dx=3
We need to find: ∫3−5[2f(x) 6g(x)]dx
To solve this problem, we will use the properties of integration:
Property 1:
If c is a constant, then
∫cf(x)dx=c∫f(x)dx
Property 2:
If f(x) and g(x) are two functions, then
∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx
Using Property 1, we can rewrite the given equation as:
∫3−5[2f(x) 6g(x)]dx = ∫3−5[12f(x)g(x)]dx
Using Property 2, we can further simplify the equation as:
∫3−5[12f(x)g(x)]dx = ∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx
Now we can substitute the given values:
∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx = 12∫3−5f(x)dx + 12∫3−5g(x)dx
Substituting the given values for the integrals of f(x) and g(x), we get:
12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3)
Simplifying, we get:
12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3) = 12(9) = 108
Therefore, the answer is
∫3−5[2f(x) 6g(x)]dx = 108
The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).
the complete question is :
if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx will be equal to ?
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During the basketball game on Thursday, Robert and Adian scored 37 points. Adian
scored 5 less than twice the amount Robert had. How many points did Adian score
on Thursday?
If you could also show the steps that would be great no required though.
Step-by-step explanation:
So here we need to make two equations, as follows:
[tex]r + a = 37 \\ a = 2r - 5[/tex]
R being Robert and A being Aiden
Since we have A alone in the second equation, we can plug that into the first equation
R + (2R - 5) = 37
Let's add 5 to each side
R + 2R = 42
3R = 42
And lastly we will divide by 3 to get R alone
R = 14
Now that we know Robert scored 14 points, we can plug that into the first equation.
R + A = 37
14 + A = 37
Subtracting 14 from both sides
A = 23
la quema de gasolina en un automóvil libera aproximadamente 3x104 kcal/gal. si un automóvil promedia 38 km/gal cuando se conduce a 95 km/h, lo que req
The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.
We have,
If a car averages 38 km/gal when driven at 95 km/h, we can calculate the fuel consumption in gallons per kilometer (gal/km).
Fuel consumption (gal/km) = 1 / (average fuel efficiency in km/gal)
Fuel consumption (gal/km) = 1 / 38
Now, to determine the energy requirement in kcal per kilometer (kcal/km), we multiply the fuel consumption by the energy released per gallon of gasoline:
Energy requirement (kcal/km) = Fuel consumption (gal/km) * Energy released per gallon (kcal/gal)
Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)
Now,
Fuel consumption (gal/km) = 1 / 38
Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)
Energy requirement (kcal/km) = (1 / 38) * (3 x 10^4 kcal/gal)
≈ 789.47 kcal/km
Therefore,
The approximate energy requirement for the car when driven at 95 km/h is 789.47 kcal/km.
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The complete question:
"Burning gasoline in a car releases approximately 3 x 10^4 kcal/gal. If a car averages 38 km/gal when driven at 95 km/h, what is the energy requirement in kcal per kilometer (kcal/km) for the car?"
use the figure to find the ration in simplest form . AB/BC.
Answer: 3:2
Step-by-step explanation:
AB / BC = AB:BC
therefore, 6:4
6:4 simplified -> 3:2
Ue the given condition to write an equation for the line in point-lope form and in lope-intercept form. Slope = 1/2, paing through the origin
The equation of the line in point-slope form and in slope-intercept form are both y = 1/2x.
There are three common forms of the equation of a line:1. Point-Slope Form: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.
2. Slope-Intercept Form: y = mx + b, where m is the slope of the line and b is the y-intercept.
3. Standard Form: Ax + By = C, where A and B are coefficients that define the slope and y-intercept of the line.
If a line has a slope of 1/2 and passing through the origin, then:
m = 1/2
(x1, y1) = (0,0)
Plug in the values in the point-slope form and in slope-intercept form.
point-slope form
y - y1 = m(x - x1)
y - 0 = 1/2(x - 0)
y = 1/2x
slope-intercept form
y = mx + b
y = 1/2x + b
Substitute the values of x and y and solve for the y-intercept, b.
0 = 1/2(0) + b
b = 0
y = 1/2x + 0
y = 1/2x
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If x is a real number, find the minimum value of 3^{x²-4x+8}
The minimum value of 3^{x²-4x+8} is 81. The solution has been obtained by using maxima-minima.
What is maxima-minima?
The extrema of a function are known as its maximum and minimum. The maximum and smallest values of a function within the predetermined set of ranges are known as maxima and minima. The function's maximum value and minimum value are referred to as the absolute maxima and absolute minima, respectively, for the function across the whole range.
We are given f(x) = 3^{x²-4x+8}
The function is minimum when {x²-4x+8} is minimum.
When the form of the equation is ax^2 + bx + c, then minimum is at -b/2a
Here, a = 1 and b = -4
So,
x = 4/2 = 2
So, {x²-4x+8} at x = 2 is
⇒(2)^2 - 4(2) + 8
⇒4 - 8 + 8
⇒4
So, the minimum value of f(x) is
3^4 = 81
Hence, the minimum value of 3^{x²-4x+8} is 81.
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if angie books one more catering job for the month, requiring 350 labor hours, how much additional overhead should she expect to incur?
Overhead Rate * Labor Hours , additional overhead should she expect to incur.
What is additional overhead ?
Overhead refers to the ongoing costs to operate a business but excludes the direct costs associated with creating a product or service. Overhead costs can be fixed, variable, or a hybrid of both.
To determine the additional overhead that Angie should expect to incur if she books one more catering job requiring 350 labor hours, The overhead rate is the amount of overhead costs per labor hour.
If we have the overhead rate, we can calculate the additional overhead as follows:
Additional Overhead = Overhead Rate * Labor Hours
Overhead Rate * Labor Hours , additional overhead should she expect to incur.
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Use a ratio box to solve this problem. a. The 1/12 scale model of the rocket stood 48 inches high. What was the height of the actual rocket?
The actual height of the rocket is 576 inches.
What is cross multiply?Cross multiply is to multiply the numerator of each side of a proportion by the denominator of the other side.
A ratio box is a visual tool that can be used to solve proportion problems. To use a ratio box to solve this problem, we can set up the following ratio:
1/12 : 48 inches : : x : actual height
where x is the unknown value that we want to find.
To solve for x, we can cross-multiply and simplify the equation:
1/12 * actual height = 48 inches
actual height = 48 inches * 12/1
actual height = 576 inches
So the actual height of the rocket is 576 inches.
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If the two lines below are perpendicular and the slope of the red line is -7.
what is the slope of the green line?
OA
B. 7
O C.
C. -
D. -7
HEFF
5
10
Answer:
Step-by-step explanation:
10
How much of a 60% solution is needed to make 50ml of a 15% solution ? A 750 ml B 15 ml C 75 ml D 12.5 ml
12.5ml of a 60% solution is required to create 50ml of a 15% amount solution. You can compute this using a proportion.
50% x 15% = 7.5 ml, and 7.5 ml x 60% = 12.5 ml
12.5ml of a 60% solution is required to create 50ml of a 15% solution. You can compute this using a proportion. To begin with, we must ascertain how much of the 15% solution is required to make 50ml. To accomplish this, multiply 50 ml by 15%, which yields the answer of 7.5 ml. This means that to make 50ml, 7.5ml of the 15% solution is required. The next step is to calculate how much of the 60% solution is needed to create 7.5ml. To do this, divide 7.5 ml by 60%, which yields the result 12.5 ml. This indicates that in order to create 50ml of the 60% solution, 12.5ml of the 60% solution
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Given the recursive formula shown, what are the first 4 terms of the sequence?
The first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.
Explain about the recursive formula?A straightforward illustration of either a recursive function is the factorial, which multiplies a number by itself while lowering it slowly. Recursive functions can refer to a wide variety of self-referential looping functions, such as those whereby n = n + 1 assuming an operational range.For the stated question:
f(n) :
f(1) = 6
f(n) = f(n - 1) + 7, if n > 1.
Thus,
First term, n = 1: f(1) = 6
Second term, n = 2:
f(2) = f(2 - 1) + 7
f(2) = f(1) + 7
f(2) = 6 + 7
f(2) = 13
Third term: n = 3.
f(3) = f(3 - 1) + 7
f(3) = f(2) + 7
f(3) = 13 + 7
f(3) = 20
Fourth term: n = 4.
f(4) = f(4 - 1) + 7
f(4) = f(3) + 7
f(4) = 20 + 7
f(4) = 27
Thus, the first 4 terms of the sequence by the given recursive formula is found as: 6 , 13, 20, 27.
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The set of integers in set Builder form
Answer:
The symbol W denotes the whole number. The symbol Z denotes integers. The symbol N denotes all natural numbers or all positive integers. The symbol R denotes real numbers or any numbers that are not imaginary
i think you mean this , i hope is help
Alicia invests £2130 into an account that pays 0.5%. Alicia invests £2130 into an account that pays
Alicia will have £2,238.93 in her account after 10 years if she invests £2130 in a 0.5% account.
What is percent?A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
principal=£2,130.00
rate=0.5%
time=10 years
Compound interest earned=£108.93
Total amount=£2,238.93
Alicia will have £2,238.93 in the account after 10 years when she invests £2130 into an account that pays 0.5%.
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Complete question:
Alicia invests £2815 into an account that pays 1% compound interest per year. Work out how much Alicia will have in the account after 10 years.
