Answer:
The answer is "[tex]\int e^{ax}\ dx=\frac{e^{ax}}{a}+c[/tex]".
Step-by-step explanation:
Please find the complete question in the attached file.
[tex]\int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\f(x)=ke^{-kx}, \ [0, \infty]\\\\[/tex]
let m is the median
[tex]so,\\\\ \int^{m}_{a}\ f(x)\ dx=\frac{1}{2}\\\\\to \int^m_0 k\cdot e^{-kx}=\frac{1}{2}\\\\\to [\frac{k\cdot e^{-kx}}{-k}]^m_0=\frac{1}{2}\\\\\to [- e^{-kx}]^m_0=\frac{1}{2}\\\\\to - e^{-km} +1=\frac{1}{2}\\\\\to e^{-km} =\frac{1}{2}\\\\\to e^{km} =2\\\\\to \ln(e^{km}) =\ln 2\\\\\to km= \ln \ 2\\\\\to m=\frac{\ln \ 2}{k}\\\\ \text{the answer is: } \\\\ \to \int e^{ax}\ dx=\frac{e^{ax}}{a}+c[/tex]
What is the volume of the cube below?
Answer:
D. 9h
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cuboid Formula: V = a²h
a is the sides of the cubeh is the heightStep-by-step explanation:
Step 1: Define
Identify variables
a = 3
h = h
Step 2: Find Volume
Substitute in variables [Volume of a Cuboid Formula]: V = 3²hEvaluate exponents: V = 9hAnswer:
D. 9h
Step-by-step explanation:
Volume of a cube = Length × Width× Height
= 3×3×h
= 9h
Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?
41 years ago, when Sally was 13 and her mother was 39.
Step-by-step explanation: I've heard this question b4
х
3
3(x+4) represents the area of the rectangle above. Which expression below is equivalent by the Distributive Property?
O 3x+12
O (3 + x) +4
O (x + 4) - 3
O 3x + 4
Answer:
O 3x+12
Step-by-step explanation:
3(x + 4) = (3 · x) + (3 · 4)
= 3x + 12
Write the equation of a line passing through (4,1) and parallel to y = 3/2x + 3.
Answer:
y = 3/2x - 5
Step-by-step explanation:
y = 3/2x + b
1 = 3/2(4) + b
1 = 6 + b
-5 = b
A college had a tuition of $35,000, then increased it by 10%, then decreased it by 5%. What is the new tuition of the college after this increase and decrease?
Answer:
$36,575 is the new tuition
Please help ASAP. Differentiating polynomials
Answer:
Step-by-step explanation:
If the function is
[tex]y=x^2-4x[/tex], then its derivative is
y' = 2x - 4. This is equal to 0 where
2x - 4 = 0 and
2x = 4 so
x = 2. When x = 2 in the original equation:
[tex]y =2^2-4(2)[/tex] so
y = -4. So the coordinate is (2, -4). On to the next one:
If the function is
[tex]y=25x +\frac{1}{x}[/tex] then its derivative is
[tex]y'=25-\frac{1}{x^2}[/tex]. This is equal to 0 where
[tex]25-\frac{1}{x^2}=0[/tex] and
[tex]-\frac{1}{x^2}=-25[/tex] or, in simpler terms:
[tex]\frac{1}{x^2}=\frac{25}{1}[/tex] so
[tex]25x^2=1[/tex] and
[tex]x^2=\frac{1}{25}[/tex] so
x = ±[tex]\sqrt{\frac{1}{25} }[/tex] so
x = [tex]\frac{1}{5},- \frac{1}{5}[/tex]. When you plug those into the original equation, you get the coordinates
[tex](\frac{1}{5},10)[/tex] and [tex](-\frac{1}{5},-10)[/tex]
1, 3, 2, 2, 1, 3, 3, 1
Part A: What is the mean of the data? Show your work. (4 points)
Part B: Use your answer from Part A to calculate the mean absolute deviation for the data. Show your work. (6 points)
Answer:
(I only know part A. sorry) The mean is 2.
Step-by-step explanation:
To find the mean of data you have to add all of the numbers and then divide by the total number of numbers being added. (I hope that made sense)
So you have to do- 1+3+2+2+1+3+3+1=16 -and then- 16÷8=2 -so you're answer is 2.
The area of a rectangular painting is 5049 cm. If the width of the painting is 51 cm, what is its
length?
Answer:
The length is 99 centimeters.
Step-by-step explanation:
The area of a rectangle is found by multiplying:
A = Length • width
We also know that the area of the rectangular painting is 5,049 cm^2
An equation to represent this is:
51w = 5049
To find w, divide:
5049/51 = 99
CHECK YOUR ANSWER:
Formula tor area of a rectangle:
Length x width
Use formula with the measurements:
99 x 52 = 5049
So the length is 99 centimeters.
HOPE THIS HELPS!
A factory makes orange paint by mixing red paint and yellow paint in the ratio 7:2. The factory makes 2700 litres of orange paint every day. How many litres of yellow paint does the factory use every day?
Answer:
2700÷9=300
300×2=600liters yellow paint
Please help I’ve been struggling for ages!
Answer:
"D" only 1 & 2
Step-by-step explanation:
−5x+2y=9
y=7x
solve the system of equation
The amount of fence a farmer needs to create a garden with width w and length 1 is F = 5w + 21.
Which formula represents l in terms of F and w?
what is the equation of the red graph? g(x)=? A. g(x)=-x^2 B. g(x)=x^2 C. g(x)=(4-x)^2 D. g(x)=(8-x)^2
the answer of course is bobbies
Answer
the answer if b in the above
which segments are congruent?
Answer:
LN and NK
Step-by-step explanation:
line LK was bisected (cut in half) by JM
the segment created by the bisector will be congruent
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
Ir = 4cm
2.5 cm
3 cm
3 cm
[?]%
Round to the nearest tenth of a percent.
Answer:
38.8%
Step-by-step explanation:
Area of the triange:
6*6.5*.5= 19.5
Area of the circle:
π*16= 16π
19.5/16π= .387940174
38.8%
Answer:
38.8%
Step-by-step explanation:
The ratio of pennies: nickels is proportional to the ratio of nickels: dimes, and to the ratio of dimes: quarters. If you have one penny and two nickels, how much money do you have?
Answer:
11 cents
Step-by-step explanation:
1 penny = 1 cent
1 nickel = 5 cents
2×1 nickel = 10 cents
1 penny + two nickels
= 1 cent + 10 cents
= 11 cents
Hiiioo! Can someone please help me out! :)❤️
Answer:
-2/3
3/2
Step-by-step explanation:
slope is m in the equation y = m*x+b.
3y=-2x-3
y=-2/3x-1
parallel lines have the same slope, so slope of parallel lines is -2/3
perpendicular lines have negative the inverse
so -(-3/2)=3/2
In order for the parallelogram to be a
rhombus, x = [?].
(x + 15)
(2x - 40)
Help pleaseeee
Answer:
Step-by-step explanation:
x+15 = 2x-40
Move x to the right side and you get 15 = x-40
Move -40 to the left side and you get x = 55
In order for the parallelogram to be a rhombus, x must equal 55.
What is a rhombus?A rhombus is a quadrilateral that has four equal sides.
Some of the properties we need to know are:
- The opposite sides are parallel to each other.
- The opposite angles are equal.
- The adjacent angles add up to 180 degrees.
We have,
If a parallelogram is a rhombus, it means that all four sides of the parallelogram have equal length.
We can set the expressions for the opposite sides of the parallelogram equal to each other and solve for x.
x + 15 = 2x - 40
First, we can simplify by adding 40 to both sides and getting:
x + 55 = 2x
Next, we can subtract x from both sides and get:
55 = x
Therefore,
In order for the parallelogram to be a rhombus, x must equal 55.
To verify this, we can substitute x = 55 back into the expressions for the sides:
x + 15 = 55 + 15 = 70
2x - 40 = 2(55) - 40 = 70
Both opposite sides have an equal length of 70, so the parallelogram is a rhombus.
Thus,
In order for the parallelogram to be a rhombus, x must equal 55.
Learn more about Rhombus here:
https://brainly.com/question/27870968
#SPJ2
what is the nth term of 1/3 4/7 7/11 2/3
Answer:
[tex]\frac{1+3(n-1)}{3+4(n-1)}[/tex]
Step-by-step explanation:
First find the pattern.
1/3 gets 5/21 added to it but doing that to 4/7 does not get 7/11, so it's nto normal adding.
if you multiply 1/3 gets 12/7, but if you multiply that by 4/7 you don't get 7/11 so it's not normal multiplcation.
I would next try only adding to the numerator and denominator separately.
so 1/3 gets 3 added to the 1 and 4 added to the 3. Doing that again gets us (4+3)/(7+4) = 7/11 and doing it again gets us 10/15 = 2/3. So that is the right answer.
So we know what is happening. if you start with 1/3 and increasingthe numerator by 3 and denominator by 4 then we know it's going to look like (1+3(n-1))/(3+4(n-1)) because the first term is when n=1 and we want that to cancel out. You can also simplify it and get (3n-2)/(4n-1)
Let me know if it doesn't make sense.
What is the value of x?
OA 73°
OB. 71°
OC. 70°
OD. 68°
Answer:
OB.71
Step-by-step explanation:
correct me if I'm wrong
Answer:C.70
Step-by-step explanation:
Which statement is NOT true concerning the graphing of a linear system?
------------------------------------------------------------------------------------------------------------------------------
Systems of linear equations that contain coordinates with fractions or decimals can be challenging.
You need to be careful and plot straight lines.
You can only graph a system of linear equations with a graphing calculator.
The point of intersection of lines that intersect at a shallow angle is difficult to determine.
You can only graph a system of linear equations.
If f(x) = x^2 + 1 find f (a+1)
Answer:
f(a + 1) = a² + 2a + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationExpand by FOILStep-by-step explanation:
Step 1: Define
Identify
f(x) = x² + 1
Step 2: Evaluate
Substitute in x [Function f(x)]: f(a + 1) = (a + 1)² + 1Expand [FOIL]: f(a + 1) = a² + 2a + 1 + 1Combine like terms: f(a + 1) = a² + 2a + 2Answer:
[tex]{ \tt{f(x) = {x}^{2} + 1 }} \\ { \tt{f(a + 1) = {(a + 1)}^{2} + 1 }} \\ { \tt{f(a + 1) = ( {a}^{2} + 2a + 1) + 1 }} \\ { \tt{f(a + 1) = {a}^{2} + 2a + 2}}[/tex]
A watch that originally cost $110 has been marked down to $88. What was the percent of the markdown ?
12%
10%
25%
20%
Answer:
20%
Step-by-step explanation:
When calculating percents, it is important to divide by the initial value, not the end value. The formula for calculating percents is
[tex]\frac{finalvalue - inititalvalue}{initialvalue} * 100[/tex]
Plugging our values into this formula, we get
[tex]\frac{88-110}{110} * 100 = 20[/tex] as our answer.
please please help!! limited time! i don’t understand!
Answer:
option b ) 18
Step-by-step explanation:
The questions states 3 different values for f(x)
f(x) = 3x + 12, if x ≤ -2
f(x) = 4 , if -2 < x < 3
f(x) = 2x² if x ≥ 3
Evaluate f(3)
x = 3, that is x ≥ 3
So we will have to choose f( x ) = 2x²
f( 3 ) = 2 (3)²
= 2 x 9
= 18
No files just ty0e it in please and thank you
sorry im answering late..
Answer:
27
Step-by-step explanation:
9x0=0 9x1=9 9x2=18
[9x3=27] 9x4=36 9x5=45
9x6=54 9x7=63 9x8=72
9x9=81 9x10=90 9x11=99
9x12=108
What is the area, in square inches, of the shape below?
Answer:
27.44 in²
Step-by-step explanation:
The formula for area of a triangle is a=[tex]\frac{bh}{2}[/tex], where a is area, b is base length, and h is height.
We can sub in the base and height lengths we know to work out the area. This gives a=[tex]\frac{5.6*9.8}{2}[/tex] or [tex]\frac{54.88}{2}[/tex].
This solves to 27.44 in².
**This content involves area of triangles, which you may wish to revise. If you are required to do this by hand, you may also like to review multiplying and dividing decimals. I'm always happy to help!
HELP PLEASEEEE !!!!!
Answer:
5%
Step-by-step explanation:
5 customers ordered large cold drinks so the probability would be 5/100
To convert 5/100 to percent, just do 5/100 x 100%
9
Find the area of the triangle.
Please help
Answer:
[tex]6ft^2[/tex]
Step-by-step explanation:
The formula to find the area of a triangle: [tex]A=\frac{1}{2} bh[/tex]
The base is 4 because 2 + 2 = 4
[tex]A=\frac{1}{2}( 4)(3)[/tex]
[tex]A=\frac{1}{2} (12)[/tex]
[tex]A=6[/tex]
Hope this helps
Answer:
A) The first one for whole triangle = 6ft^2
or
B) The second one for blue = 3ft^2
Step-by-step explanation:
T1 Area = 1/2 x 3 x 4 = 6ft^2
T2 Area = 1/2 x 3 x 2 = 3ft^2
T3 Blue Area = 6-3 = 3ft^2
What portion of shared $7500 security costs should be apportioned to store A?
Answer:
3,750
Step-by-step explanation:
2500+1250+625+625=5000
2500/5000=.50 or 50%
7500X.50=3750
Sam had $42 to spend on 12 raffle tickets. After buying them he had $6 left. How much did each raffle ticket cost?
Answer:
Each raffle ticket cost $3.