The derivative of e²ˣ is 2e²ˣ.
A derivative of any function is the rate of change that will be made on the function if its independent variable changes by a small amount.
Now a function can also have another function in it. Then if we need to find the derivative of that function we need to use the chain rule. This states that for any variable x, if there is a function
f(g(x)) then derivative of f(g(x) will be f'(g(x))⋅g'(x)
this means that we need to first hold the function in it constant and then multiply the function's derivative with respect to x.
Here f(g(x)) = e²ˣ where g(x) is 2x
Now we will first hold 2x as one variable. We know that d/x of eˣ is eˣ
Hence we get
e²ˣ
Now we will differentiate 2x. The derivative of 2x is 2
Hence we get the derivative as
2e²ˣ
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Sally goes out for breakfast once per week and gets the same thing each time, for a total of $4.52 per trip. She has already spent $31.64 this year on her breakfast. What is the first term of the sequence? To get to the next term, you would. This means that the common difference is There are 20 weeks left in this school year for Sally. If she continues getting breakfast at this rate how much money will she have spent on breakfast by the end of the year?
The requried first term of the sequence is $6.32.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values
Here,
The amount of money Sally spends on breakfast each week forms an arithmetic sequence.
Let's use the formula for the sum of an arithmetic sequence to find the first term of the sequence. We know that Sally has already spent $31.64, which means that she has made 31.64/4.52 = 7 visits to the breakfast place. So the sum of the first 7 terms of the sequence is:
S₇ = 7/2 * (a₁ + a₇)
We know that a₇ = $4.52, so we can plug this into the formula and simplify
S₇ = 7/2 * (a₁ + 4.52)
a₁ = $6.32
Similarly, all the outcomes can be evaluated,
By the end of the year, Sally will have spent $891.36 on breakfast.
Therefore, the first term of the sequence is $6.32.
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……helpppppppppppppppppp
Answer:
to show how much rainfall there is between months in different regions
. Molly travels 90km to get home after work. She leaves at 6pm and arrives home at 7:30pm.
Calculate her average speed in km per hour
Answer:
60 Kilometers per hour
Step-by-step explanation:
To solve for how long it took Molly to get home, we can use this equation:
7:30 - 6 = 1:30So, Molly took an hour and 30 minutes, or 90 minutes to travel 90km.
To get the number of km she traveled every hour, we can use this equation:
90 × [tex]\frac{2}{3}[/tex] = 60Why do we multiply by 2/3?
We multiply by [tex]\frac{2}{3}[/tex] because if we need to figure out the average speed for every hour (60) we need to convert 90 to 60, and to do that we multiply the 90 by [tex]\frac{2}{3}[/tex].
Therefore, Molly travels 60km every hour.
what is the estimate of 5/8 - 1/10? A. 0 B. 1/2 C. 1 D. 1 1/2 which one is it??
The estimate of 5/8 - 1/10 is 0.5, which is option B.
What is division in mathematics?
In mathematics, division is an arithmetic operation that is used to split a quantity into equal parts or to find the number of times one quantity is contained within another quantity. It is the inverse operation of multiplication, and is represented by the symbol "÷" or "/".
To estimate 5/8 - 1/10, we can round 5/8 to the nearest tenth, which is 0.6, and round 1/10 to the nearest tenth, which is 0.1. Then we can subtract them to get an estimate of the difference:
5/8 - 1/10 ≈ 0.6 - 0.1 = 0.5
Hence, the estimate of 5/8 - 1/10 is 0.5, which is option B.
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If triangle XYZ is dilated from center C by a scale factor of 0.5 to form triangle X’Y’Z’, where is the center of the dilation, point c, located?
The center of the dilation, point C, is located at the same point as it was before the dilation. This is because the center of dilation is the point from which the dilation occurs, and it does not change during the dilation process.
To find the coordinates of point C, we can use the properties of dilations. The coordinates of the vertices of the dilated triangle are found by multiplying the coordinates of the original triangle by the scale factor.
So, if the coordinates of point X are (x1, y1), the coordinates of point X' will be (0.5x1, 0.5y1). Similarly, the coordinates of point Y' will be (0.5x2, 0.5y2) and the coordinates of point Z' will be (0.5x3, 0.5y3), where (x2, y2) and (x3, y3) are the coordinates of points Y and Z, respectively.
Since point C is the center of dilation, the coordinates of point C will be the same as the coordinates of the midpoint of the line segment connecting points X and X', points Y and Y', and points Z and Z'. The midpoint of a line segment is found by averaging the coordinates of the endpoints. So, the coordinates of point C will be:
C = ((x1 + 0.5x1)/2, (y1 + 0.5y1)/2) = (0.75x1, 0.75y1)
Therefore, the center of the dilation, point C, is located at (0.75x1, 0.75y1).
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what is 1040 schedule 2?
Schedule 2 is an important part of the 1040 tax form that can help taxpayers report additional taxes or adjustments to income that aren't directly entered on the main form.
The 1040 form has several schedules that taxpayers may need to fill out depending on their financial situation. One of these schedules is the Schedule 2.
Schedule 2 is used to report additional taxes or adjustments to income that can't be entered directly on the main 1040 form. It's essentially an addendum to the main tax form. This schedule is often used when taxpayers have income from sources that aren't subject to withholding, such as self-employment income or rental income, or when they have certain deductions or credits that require additional reporting.
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What is the conversion of 720 hours to days?
720 hours is equal to 30 days.
One hour contains 60 minutes or 3,600 seconds.
In one day there are 24 hours.
Earth requires 24 hours to complete one rotation.
It is defined as exactly 86,400 seconds.
1 Hour equal to 0.041666667 Days
We have to convert 720 hours to days,
We have to divide the number of given hours by the number of hours in one day.
There are 24 hours in a day,
so we can write it as:
720 hours / 24 hours/day = 30 days
Hence, After conversion we get 720 hours is exactly equal to 30 days.
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Question 9(Multiple Choice Worth 4 points)
(05.05 MC)
Which of the following is a solution to this inequality?
y>3/5x-2
O (5,0)
0 (0, -2)
O (1, 1)
O(-5, -6)
Answer:
Hi! In order to determine which answer is correct, remember that if an ordered pair is a solution of the inequality, then the ordered pair will satisfy the inequality. Let's plug each of these ordered pairs into the inequality.
A. 5, 0
Substitute 5 and 0 for x and y.
[tex]0 > \frac{3}{5} (5) - 2[/tex]
0 > 1 is not true. Therefore, A is NOT correct.
B. 0, -2
Substitute 0 and -2 for x and y.
[tex]-2 > \frac{3}{5} (0) -2[/tex]
-2 > -2 is not true. Therefore, B is NOT correct.
C. 1, 1
Substitute 1 and 1 for x and y.
[tex]1 > \frac{3}{5} (1) - 2[/tex]
1 > [tex]-\frac{7}{5}[/tex] is true. Therefore, C. 1, 1 is CORRECT.
D. -5, -6
Substitute -5 and -6 for x and y.
[tex]-6 > \frac{3}{5} (-5) - 2[/tex]
-6 > -5 is not true. Therefore, D is NOT correct.
Hope this helps!
Can someone help me on this?
The correct linear equation for the table is,
⇒ y = - 5x - 2
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The table is shown in figure.
Now, Let two points from the table are (4, - 22) and (3, - 17).
Hence, Equation of linear function is,
⇒ y - (- 22) = (- 17 - (-22)) / (3 - 4) (x - 4)
⇒ y + 22 = (5/- 1) (x - 4)
⇒ y + 22 = - 5 (x - 4)
⇒ y + 22 = - 5x + 20
⇒ y = - 5x + 20 - 22
⇒ y = - 5x - 2
Thus, The correct linear equation for the table is,
⇒ y = - 5x - 2
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A series of isosceles triangles are drawn between two red line segments.
a
= 22°.
The value of x found using the properties of the isosceles triangle is 92°.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Although this triangle's two sides are equal, the base of the triangle is the side that is not equal.
Given a = 22°
Since it is an isosceles triangle, a = 1 = 22°
One of the properties of a triangle is that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.
Here ∠2 is the exterior angle of the first isosceles triangle.
So ∠2 = ∠1 + a = 22 + 22 = 44°
Now∠ 3 = ∠2 = 44°
∠x = 180 - (∠2+∠3) = 180 - (44+44) = 92°
∠4 = 180 - (x+∠1) = 180 - (92+22) = 66°
∠5 = ∠4 = 66°
∠y = 180 - 66 -66 = 48°
∠6 = 180 - ∠y - ∠3 = 180 - 48 - 44 = 88°
∠7 = ∠6 = 88°
∠x = 180 - ∠7 = 180- 88 = 92°
Therefore the value of x found using the properties of the isosceles triangle is 92°.
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Explain how to solve the equation. c/6 equals 9
Answer: c = 54
Step-by-step explanation:
c/6 = 9
c/6*(6) = 9*6
c = 54
Answer: c = 54
Step-by-step explanation:
c/6 = 9
you then multiply c/6 by it's denominator, which in this case 6. What you do on one side, you have to do to the other.
6 · c/6 = 9 · 6
Then you multiply everything, 6 cancels out denominator 6 which leaves C and 9 turns into 54. Meaning c equals 54.
c = 54
To check, you can replace c with 54 in your original equation.
54/6
54÷6 = 9
Assertion (A) : "The collection of all natural numbers less than 100" is a set.
Reason (R) : A set is a well-defined collection of the distinct objects.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Based on the assertion and the reason regarding the weight of an object and upthrust experienced by the body in a fluid; Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). The correct option is A.
What is the principle of floatation?The principle of floatation states that an object will float in a fluid if the upthrust that is experienced by the object is equal to or greater than the weight of the object.
The upthrust experienced by a body is the upward force that a liquid or gas exerts on a body floating in it.
Upthrust on a body depends on the acceleration due to gravity, the density of the liquid, and the volume of the body immersed in the liquid.
The weight of a body is the force of gravity acting on the body. The weight of a body acts downward.
Thus in a fluid, the weight of an object acts downward while the upthrust on the object acts in an upward direction.
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Given f(x)=x^2+9 and g(x) =-x-7, find (f+g)(x).
Answer:
x^2 - x + 2.
Step-by-step explanation:
Answer:
x² - x + 2
Explanation
Work out using the given functions to set up and simplify (f + g) (x)
what is 1.86 m in feet?
The value of given 1.86 meters after converting it into feet is equal to 6.1024 feet.
Meter is the unit which is used to measure length.Feet is the unit which is also used to measure length.Both are used to measure length we can convert meter to feet.1 meter is equal to 3.28084 feet
⇒ 1.86 meters = ( 1.86 ) × ( 3.28084 ) feet
⇒ 1.86 meters = 6.1023624 feet
Round off the value upto four decimal places we get,
⇒ 1.86 meters = 6.1024 feet
Therefore, the unit of 1.77 meters after converted to feet the value is equal to 6.1024 feet ( approximately ) .
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Mr. Pratt bought a block of fudge that weighed 8 2/3 pounds. He cut the fudge into 4 equal pieces. What was the weight of each piece of fudge? (IXl)
(please help quickly!!)Emma had to finish her 399-page novel by Friday. She had already read 266 pages. Write and solve an equation to show how many pages Emma had left to read by Friday.
p − 266 = 399; p = 665 pages
p over 266 equals 2; p = 532 pages
p + 266 = 399; p = 133 pages
133p = 266; p = 2 pages
C is the correct answer. If there is a total of 399 pages, adding the pages she has left to the pages she has already read (266 pages) it would equal the total, that she has to read 133 pages still.
The value of 4 less than the product of 0.25 and x is greater than 6.
What are all the possible values of x?
Answer: x = {41,42,43...}
Step-by-step explanation:
0.25x - 4 > 6
0.25x > 6 + 4
0.25x > 10
x > 10/0.25
x > 40
The possible values of x are {41,42,43...}
Which set of ordered pairs (x,y)(x,y) could represent a linear function? \mathbf{A}= A= \,\,\left\{(-4, 2),\,\,(-2, 3),\,\,(2, 5),\,\,(4, 6)\right\} {(−4,2),(−2,3),(2,5),(4,6)} \mathbf{B}= B= \,\,\left\{(1, 2),\,\,(3, 4),\,\,(5, 6),\,\,(6, 8)\right\} {(1,2),(3,4),(5,6),(6,8)} \mathbf{C}= C= \,\,\left\{(-1, -1),\,\,(0, 2),\,\,(1, 4),\,\,(2, 6)\right\} {(−1,−1),(0,2),(1,4),(2,6)} \mathbf{D}= D= \,\,\left\{(2, 9),\,\,(4, 6),\,\,(5, 3),\,\,(6, 0)\right\} {(2,9),(4,6),(5,3),(6,0)}
The sets of ordered pairs that could represent a linear function are A and D.
What is linear function ?
A linear function is a mathematical function that can be graphically represented as a straight line. It has a constant rate of change between any two points, which means that the slope (i.e., the steepness of the line) is constant.
To determine if a set of ordered pairs can represent a linear function, we need to check if there is a constant rate of change (i.e., a constant slope) between any two pairs of points. If there is a constant rate of change, then the set of ordered pairs could represent a linear function.
Let's check each set of ordered pairs:
A = {(-4, 2), (-2, 3), (2, 5), (4, 6)}
The rate of change between (-4, 2) and (-2, 3) is 1/2.
The rate of change between (-2, 3) and (2, 5) is 1/2.
The rate of change between (2, 5) and (4, 6) is 1/2.
Therefore, the set A could represent a linear function.
B = {(1, 2), (3, 4), (5, 6), (6, 8)}
The rate of change between (1, 2) and (3, 4) is 1.
The rate of change between (3, 4) and (5, 6) is 1.
The rate of change between (5, 6) and (6, 8) is 2.
Therefore, the set B could not represent a linear function.
C = {(-1, -1), (0, 2), (1, 4), (2, 6)}
The rate of change between (-1, -1) and (0, 2) is 3.
The rate of change between (0, 2) and (1, 4) is 2.
The rate of change between (1, 4) and (2, 6) is 2.
Therefore, the set C could not represent a linear function.
D = {(2, 9), (4, 6), (5, 3), (6, 0)}
The rate of change between (2, 9) and (4, 6) is -1.5.
The rate of change between (4, 6) and (5, 3) is -3.
The rate of change between (5, 3) and (6, 0) is -3.
Therefore, the set D could represent a linear function.
Therefore, the sets of ordered pairs that could represent a linear function are A and D.
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What is the conversion of 20 ml to tsp ?
There will be approx four teaspoons of US measurement system in 20 ml. That is the unit conversion of 20 mililitre is equals to four teaspoons.
A milliliter is a unit of volume equal to 1/1000 of a liter. It is the same as a cubic centimeter. A US teaspoon is a unit of volume in the cooking system that is equal to 1/3 of a tablespoon or 1/48 of a US cup. To calculate the value in milliliters to the corresponding value in teaspoons [US], multiply the amount in milliliters by 0.2028841362 (conversion factor). Here is the formula: Value in teaspoons [US]
= value in milliliters × 0.2028841362
Now we need to convert 20 ml to teaspoons. So using the above formula we can write the number of teaspoons in 20 ml is Value in teaspoons [US]
= value in milliliters × 0.2028841362
= 20 ml × 0.2028841362
= 4.057682724 ~ 4
Hence required value is 4 teaspoons.
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Two families, one of three and one of five, hire a bach for $196 per night. If the cost is shared equally among the eight people, how much will it cost the family of three per night?
Answer:
$73.5
Step-by-step explanation:
$196/8 = $24.5 ---> $196 shared equally with 8 people
24.5*3 = $73.5 ---> The cost for the family of three
What sum of money lent out at 6 1/4 p. A to get 75 rupees as intrest in 8 months
The sum of money lent out at 6 1/4 p.a. to get 75 rupees as interest in 8 months is 1800 rupees.
To find the sum of money lent out at 6 1/4 p.a. to get 75 rupees as interest in 8 months, we can use the formula for simple interest:
I = P × R × T
Where:
- I is the interest
- P is the principal (the sum of money lent out)
- R is the annual interest rate
- T is the time in years
In this case, we know that I = 75, R = 6.25% (6 1/4 p.a.), and T = 8/12 (8 months is 8/12 of a year). We can plug these values into the formula and solve for P:
75 = P × 6.25% × 8/12
75 = P × 0.0625 × 0.6666666666666666
75 = P × 0.041666666666666664
P = 75 ÷ 0.041666666666666664
P = 1800
Therefore, the sum of money lent out at 6 1/4 p.a. to get 75 rupees as interest in 8 months is 1800 rupees.
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2.13(m + 2) = 8.52
what is the answer
Answer:
2
Step-by-step explanation:
2.13 (m + 2) = 8.52
m + 2 = 8.52/2.13
m + 2 = 4
m = 4 - 2
m = 2
Conan fills 5 tubes. 2 tennis balls are left. How many tubes does Conan need to put away all the tennis balls?
Conan needs 16 tubes to store all 17 tennis balls because each tube can carry three balls.
what is unitary method ?The unit technique is a way of challenge where you first assess the value of a specific unit, than multiply that value to get the answer. Simply defined, a minimum unit value is extracted from a specified multitude using the unit method. For contrast, 40 pens will set you back 400 rupees, or $1.01. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal remain equivalent. (Hyper Algebra, Statistical Analysis, Mathematics of Matrix or Players)
given
conan fills 5 tubes with 3 balls each
2 tennis balls are left
Conan needs 16 tubes to store all 17 tennis balls because each tube can carry three balls.
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Write a possible sum for 6/8 use 1/4 of one of the add in’s
explain how you found your answer
The sum of fractions [tex]\frac{1}{4}[/tex] and [tex]\frac{6}{8}[/tex] is equal to one.
Fraction addition teaches us how to combine two or more fractions with the same or different denominators. The addition of fractions is determined by two major factors:
1.Identical denominators
2.Various denominators
If the denominators of two fractions are the same (such fractions are said to be like fractions), they can be added directly. If the denominators are different (such fractions are known as unlike fractions), we must change the denominators and then add the fractions.
If the denominators of two or more fractions are the same, we can simply add the numerators while keeping the denominator constant.
To add fractions with the same denominators, follow the steps below:
1. Add the numerators while keeping the denominator constant.
2.Summarize the fraction.
When two or more fractions with different denominators are added together, we cannot directly calculate the numerators.
To add fractions with different denominators, follow the steps below:
1. Examine the fractions' denominators.
2.Make the fraction denominators the same by finding the LCM of the denominators and rationalising them.
3. Add the fraction numerators while keeping the denominator constant.
4.Simplify the fraction to obtain the final total.
As we have fractions with different denominator first of all we take LCM which is equal to 8.
[tex]\frac{1}{4} + \frac{6}{8} = \frac{2+6}{8} = \frac{8}{8} = 1.[/tex]
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What is 22 1/4 in fraction and divided by 890
The fraction 22 1/4 divided by 890 gives 1/40 or 0.025.
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
Given is a mixed fraction 22 1/4.
This has to be first converted to improper fraction.
22 1/4 = (22 × 4 + 1) / 4 = 89/4
Now we have to divide the fraction 89/4 by 890.
89/4 ÷ 890 = 89/4 × 1/890
(since in the division of fractions, the second term becomes the reciprocal and the operation changes to multiplication).
89/4 ÷ 890 = 89/4 × 1/890
= 1/40
= 0.025
Hence the quotient when 22 1/4 divided by 890 is 0.025.
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$25 hourly is how much per year?
$25 hourly is $52,000 per year.
To convert an hourly rate to an annual salary, we need to multiply the hourly rate by the number of hours worked per week, then by the number of weeks worked per year.
Assuming a standard work week of 40 hours and 52 weeks in a year, we can calculate the annual salary for an hourly rate of $25 as:
Annual salary = Hourly rate x Hours per week x Weeks per year
Annual salary = $25/hour x 40 hours/week x 52 weeks/year
Annual salary = $52,000
Therefore, an hourly rate of $25 is equivalent to an annual salary of $52,000.
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what is the result of 6022 x 1023 ?
The value of (6022*1023) will be = 61,60,506
As per question,
We need to find the value of (6022*1023)
For finding the value of given expression, we will use the identity of multiplication.
So, applying the multiplication identity:
We can write the above as:
6022*1023 = (6000+22) * (1000+23)
As we know,
(a+b)*(c+d) = ac+ad+bc+bd
So, applying the identity in above expression,
We will get,
6022*1023 = (6000+22) * (1000+23)
=(6000*1000)+(6000*23)+(22*1000)+(22*23)
=(6000000+138000+22000+506)
=61,60,506
Multiplication is a way of calculating the product of two or more integers in mathematics. It is one of the most fundamental mathematical operations that we utilise every day.
Multiplication is the process of taking one integer and multiplying it by a certain number of times. 5 multiplied by 4 is 5 + 5 + 5 + 5 = 20. We took the number 5 and multiplied it by four. This is why multiplication is often known as "times".
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what is the mean absolute error?
Answer:
Step-by-step explanation: Mean Absolute Error is a model evaluation metric used with regression models. The mean absolute error of a model with respect to a test set is the mean of the absolute values of the individual prediction errors over all instances in the test set.
how to find point of inflection
To find a point of inflection, take the second derivative of the function, set it equal to zero and solve for x, and verify the point by checking the sign of the second derivative on either side of the point.
Follow these steps to locate a point of inflection:
Take the function's second derivative. The derivative of the first derivative is the second derivative. This will give you the concavity of the function.Put the second derivative to zero and find x. This will show you where the concavity changes.At this stage, check to see if the sign of the second derivative changes. The point is a point of inflection if the second derivative is positive to the left of the point and negative to the right of the point. The point is not an inflection point if the sign of the second derivative does not change.Check the concavity of the curve on each side of the point to verify it.It is a point of inflection if the curve shifts from concave up to concave down at the point. It is also a point of inflection if it transitions from concave down to concave up.
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what is 5 foot 8 inches in cm?
As per the conversion factor, 5 foot 8 inches is equal to 172.72 centimeters
In this case, we're talking about converting from feet and inches to centimeters.
To convert 5 feet 8 inches to centimeters, we need to first convert the feet to inches, and then add the total number of inches. Since one foot is equal to 12 inches, we can multiply 5 feet by 12 to get 60 inches. Then, we add the remaining 8 inches to get a total of 68 inches.
Now, we need to use a conversion factor to convert inches to centimeters. One inch is equal to 2.54 centimeters, so we can multiply 68 inches by 2.54 to get the answer in centimeters.
To summarize, the conversion factors we used are:
1 foot = 12 inches
1 inch = 2.54 centimeters
=> (68 inches x 2.54 cm/inch) = 172.72 centimeters
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