Given f(x) = 4* and its inverse f-¹ (z) = log4z. If f (6) = 4096, then f-¹ (4096) = |
-L
(Just type answer, no spaces)
help please
The numeric value of the inverse function at x = 4096 is given as follows:
f-¹ (4096) = 6.
How to find the inverse function?To find the inverse function, we exchange x and y in the original function, then isolate y.
The transformation rule for each point on the inverse function, compared to the original function, is given as follows:
(x,y) -> (y,x).
f(6) = 4096, hence the point on the function is:
(6, 4096).
Then the point on the inverse will be of:
(4096, 6).
Meaning that:
f-¹ (4096) = 6.
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A motorboat can maintain a constant speed of 23 miles
per hour relative to the water. The boat makes a trip
upstream to a certain point in 52 minutes; the return trip
takes 40 minutes. What is the speed of the current?
The speed of the current is
mile(s) per hour.
25 POINTS. HELP W THE EQUATION TYSM
Step-by-step explanation:
cubing on both sides,
(-4)³= ³√(9x-1)³
-64=9x-1
-64+1=9x
-63=9x
-63/9=x
x=-7
Guys please help
Find the intersection of y = 2(x+2) and y = 4(x-4).
Answer:
(10, 24)
Step-by-step explanation:
First equate both the equations,
2(x+2) = 4(x-4)
Then expand the brackets,
2x + 4 = 4x - 16
Collect like terms in each sides,
4 + 16 = 4x - 2x
Simplify and solve,
20 = 2x
20 ÷ 2 = x
x = 10
Then substitute 10 for x in one of the equations,
y = 2(x + 2)
y = 2(10 + 2)
y = 24
Therefore, the point of interssection is (10, 24).
you can solve this using the simultaneous equation
so y = y
4(x-4) = 2( x + 2)
4x - 16 = 2x +4
4x - 2x = 4+16
2x/2=20/2
therefore x=10
y=2 (x+2)
y=2(10+2)
y=2(12)
y=24
for each positive integer n, what is the largest value of p such that zero is the most likely number of successes in n independent trials with success probability p?
The largest value of success probability p with zero as most likely number of success with n independent trials is equal to 1 / ( n + 1 ).
Probability of success is equal to p
Probability of failure is equal to ( 1 - p)
Number of trials is positive integer n
Condition for 'n' independent trials :
Zero is most likely number of success
⇒ P(0) ≥ P(1)
⇒ ⁿC₀ p⁰ ( 1 - p )ⁿ⁻⁰ ≥ ⁿC₁ p¹ ( 1 - p )ⁿ⁻¹
⇒ ( 1 - p )ⁿ ≥ np ( 1 - p )ⁿ⁻¹
⇒( 1 - p ) ≥ np
⇒ np + p ≤ 1
⇒ p ≤ 1 / ( n + 1 )
Largest value of p is equal to 1 / ( n + 1 ).
Therefore, the largest value of success probability p with n independent trials is equal to 1 / ( n + 1 ).
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Find the solution to the linear system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3:
The solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:
[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]
Let x(t) and y(t) be the solution of the linear system of differential equations:
[tex]$\frac{dx}{dt} = ax + by$[/tex]
[tex]$\frac{dy}{dt} = cx + dy$[/tex]
with initial conditions x(0)=5 and y(0)=3.
The general solution of the system of differential equations can be written as:
[tex]$x(t) = e^{at} (X0 \cos(bt) + Y0 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (X0 \sin(bt) - Y0 \cos(bt))$[/tex]
where X0 = 5 and Y0 = 3.
Therefore, the solution of the system of differential equations satisfying the initial conditions x(0)=5 and y(0)=3 is given by:
[tex]$x(t) = e^{at} (5 \cos(bt) + 3 \sin(bt))$[/tex]
[tex]$y(t) = e^{ct} (5 \sin(bt) - 3 \cos(bt))$[/tex]
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which expression is equivalent to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a
The equivalent expression of 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a is 136/120a + 107/120b.
One common way to simplify an expression is to use the unitary method, which involves finding a common denominator and then canceling out like terms.
In this case, we'll use the unitary method to find an equivalent expression to 4/5a + 2/3b + 1/8 - 7/6b - 3/4 - 2/5a.
To start, we'll find a common denominator for all the terms in the expression.
The least common multiple of 5, 3, 8, 6, and 5 is 120. Now, we can convert all the fractions to have a denominator of 120.
Next, we'll simplify each term by dividing the numerator and denominator by their greatest common factor.
96/120a can be simplified to 8/10a by dividing both the numerator and denominator by 8. 80/120b can be simplified to 2/3b by dividing both the numerator and denominator by 40. And so on.
Finally, we'll rearrange the terms and simplify them using the unitary method. We'll start by canceling out like terms, which have the same variable and the same sign.
So, 8/10a and 96/120a are both positive and have the variable a, so we can simplify them to 104/120a.
Similarly, we can simplify 2/3b and 105/120b to 107/120b. We'll then add up all the positive terms and subtract all the negative terms.
The final equivalent expression is
=> 104/120a + 107/120b + 15/120 - 90/120
=> (104 + 107 + 15 - 90)/120a + (107/120)b
=> 136/120a + 107/120b.
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The ratio of a rectangle's length to the rectangle's width is 6:11. If
the perimeter of the rectangle is 510 units, then what is the length of
the rectangle?
Answer:
Step-by-step explanation:
90
By solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.
What are equations?
It primarily consists of a variable, sometimes with a numerical constant in addition.
Take the following illustration into consideration to quickly grasp this idea. 3x – 4 = 5. It is a simple equation of class 7.
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
So, we know that the ration is 6:11 and the perimeter is 510 units.
Then, form and solve the equation as follows:
510 = 2(6x + 11x)
510 = 12x + 22x
510 = 34x
x = 510/34
x = 15
Then, the length will be:
6x
6(15)
90 units
Therefore, by solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.
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help, need answer asap
The area of the triangle is 1 square foot.
Waht is the area of the triangle?Remember that the area of a triangle of base B and height H is:
A =B*H/2
Here we can see that:
B = 3ft
H = (2/3) ft
Replacing that in the area formula we will get:
A = (3ft)*(2/3)ft/2 = 1 ft²
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pls help meeeeeee with this problem
Answer:
9
Step-by-step explanation:
this is the explanation 6×3=18 18÷2=9
Do u know what this is
Answer:
248
Step-by-step explanation:
Find the volume of each box, then add them up.
Volume = l x w x h
Top: 5 x 2 x 5 = 50
Middle: 6 x 4 x 3 = 72
Bottom: 9 x 7 x 2 =126
Total = 50 + 72 + 126 = 248 cubic feet
In the xy-plane, a line with equation 2y = 4.5 intersects a parabola at exactly one point. If the parabola has equation y = −4x2 + bx, where b is a positive constant, what is the value of b ?
Answer: b=6
Step-by-step explanation:
a large Ghirardelli bar is 30cm long and 12cm wide. a smaller Ghirardelli bar is 10cm long. If the bars are similar, what is the width of the smaller Ghirardelli's bar?
Answer:
Step-by-step explanation:
if the bars are similar, they are proportional.
make a proportion: length = 30 = 10
width 12 x
cross multiply: 12 times 10 = 120
divide by the number that ids left - 120 ÷ 30 = 4 cm
The width of the smaller bar is 4 cm.
Find the slope and y-intercept of the graph of the equation.
Answer:
The slope: 4
Y-intercept: 9
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
In this case y = 4x + 9
m = 4
b = 9
So,
The slope: 4
Y-intercept: 9
Answer:
Slope: 4/1 or 4
Y-Intercept: 9
Step-by-step explanation:
y = mx + b is the Slope Intercept Formula. 'm' in the formula stands for rate of change in y/x, which is practically slope. 'b' in the formula is where the line crossed the y line. It's where it intercepts with y.
explain in your own words why it takes more to prove that quadrilaterals are similar
Proving that quadrilaterals are congruent takes more because all quadrilaterals are polygons of four sides and they all have a sum angle of 360°
Explaining quadrilaterals?
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals' internal angles add up to a constant 360 degrees.
What is quadrilateral formula?
When the diagonal and the sum of the lengths of the perpendiculars drawn from the remaining two vertices are known, the area of the quadrilateral can be determined as follows Area of quadrilateral = (12) diagonal length sum of the lengths of the perpendiculars drawn from the remaining two vertices.
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The complete question is -
Explain in your own words why it takes more to prove quadrilaterals congruent. Include examples demonstrating how ""just angles"" or ""just sides"" is not enough.
Naomi is using pairs of numbers from the set below to find sums, differences, products, and quotients
-6 2.7 -2/3 4 1/5 -5.1
Determine whether each statement about Naomi's calculations is true.
Select True or False for each statement.
The greatest possible sum of two numbers is 6.9.
The least possible difference of two numbers is -11.1. 0
The greatest possible product of two numbers is 11.34
The least possible quotient of two numbers is -6.3
The greatest possible sum of two number is 6.7. Naomi's statement is false.
The least possible difference between two number is -10 Naomi's statement is false
The greatest product of two number in the set is 30.6. Naomi's statement is false
The least possible quotient of two numbers from the set is -6. Naomi statement is false
What are mathematical operations?In mathematics, an operation is a function which takes zero or more input values to a well-defined output value. The number of operands is the arity of the operation.
The greatest possible sum = 4+2.7 = 6.7
The least possible difference = -6-4 = -10
The greatest possible product = -6×-5.1 = 30.6
The least possible quotient = 4÷ -2/3 = -12/2 = -6
Therefore all Naomi's statement are false.
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While visiting your friend in the city, you see two roads that intersect as shown. Your friend tells you that the angle between the roads on the north side is 69° and the angle between the roads on the south side is (3x)°. Find the value of x.
Answer and Step-by-step explanation:
Let's call the angle between the roads on the south side "y" for simplicity. Since the two roads intersect, the sum of the two adjacent angles on one side must add up to 180 degrees. Therefore, we can set up an equation:
y + 69 = 180
Solving for y, we get:
y = 180 - 69 = 111
We also know that y is equal to 3x, so we can set up another equation:
3x = 111
Solving for x, we get:
x = 37
Therefore, the value of x is 37.
Hope it helps! : )Mrs Ananaya is buying pencils in packs of 12, notebooks in packs of 16, and red pens in packs of 20. She needs to buy the same number of pencils, notebooks, and red pens. What is the least number of packs of each item that she can buy?
Answer:
Below
Step-by-step explanation:
You need to find the LCD of 12 16 and 20
Using Prime Factorization:
12 = 2 * 2 * 3
16 = 2 * 2 * 2 * 2
20 = 2 * 2 * 5
2 2 2 2 3 5 so LCD will be 2 * 2 * 2 * 2 * 3 * 5= 240
so she will need 240 / 12 = 20 packs of pencils
240 / 16 = 15 packs of notebooks
240 / 20 = 12 packs of pens
(5x + 14)°
(8x-10)
Pls help me
I am stoopid
What is the midpoint of the segment shown below O A (-7/2, 3/2) O B. (-7,3) O c. (-7/2, 3) O D. (-7,3/2)
Answer:
B.
Step-by-step explanation:
The midpoint of a line segment is found by taking the average of the x-coordinates and the y-coordinates of the endpoints of the segment.
The midpoint of segment AB can be found as follows:
Midpoint of AB = ((-7/2 + -7)/2, (3/2 + 3)/2) = (-7, 3)
Since the midpoint of AB is the same as point B, we can conclude that the midpoint of segment AB is (-7, 3).
The maximum weight, w, that a stepladder can hold is 250 pounds. Which inequality represents this situation?
O w ≥ 250
w > 250
O w ≤ 250
w < 250
Answer: C
Step-by-step explanation:
Just look for the less than or equal to sign
Find three consecutive positive integers such that
twice the product of the first and third is 2 less
than twenty times the second.
The three consecutive positive integers satisfying the statement are
9, 10, and 11.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Let, The three numbers be n, (n + 1), and (n + 2).
Therefore, the numerical expression of the given statement is,
2(n)(n + 2) + 2 = 20(n + 1)
2n² + 4n + 2 = 20n + 20.
2n² - 16n - 18 = 0.
n² - 8n - 9 = 0.
n² - 9n + n - 9 = 0.
n(n - 9) + 1 (n - 9) = 0.
(n - 9)(n + 1) = 0.
n = 9 is the positive integer.
So, The numbers are 9, 10, and 11.
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80% of 25$
…………………….
$20
there is two ways to solve this.
ratio form:
80% / 100% = X / $25
---> 2000 / 100 = X
---> X = 20
Decimal form:
80% --- move decimal two places to the left.
80% = 0.8 --- now multiply decimal by total value
0.8 x 25 = 20
$20.
Marcus bought a plant that originally cost $40. All plants were discounted 35%. What did Marcus pay for the plant after the discount
Pleeeeeeeeeeeease answer this for me I’ll give brainly pls pls pls pls
Answer: S=V cubed
Step-by-step explanation:
Answer: A. S = cube of V
Step-by-step explanation:
Cube both sides of the equation to single s out
A group of volunteers tagged and released 29 owls as part of a research project. Later, the researchers counted 902 owls, 11 of which had tags. To the nearest whole number, what is the best estimate for the owl population?
The best estimate for the owl population is 2,378.
The population of the owl can be estimated using the concept of proportion. Proportion refers to a mathematical comparison between two numbers. According to the concept, if two sets of given numbers are increasing or decreasing in the same ratio, hence the ratios are said to be directly proportional to each other.
Based on the provided information, 29 owls are tagged and released as part of a research project. Assume that the total number of owl populations is x. At the later time, researchers counted 902 owls and found the 11 were tag. Hence, there are 18 tagged owls which are not accounted for. Assuming that the proportional of tagged owls to number of owls counted applies to the remaining population, the total number of owls can be best estimated as:
x = (902/11)*29 = 2,378
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HELP PLS AND FAST!!!
Answer:
The correct equation you're looking for is the first choice: [tex]\frac{240 miles}{5 hours}[/tex] = 48 miles per hour.
Step-by-step explanation:
The formula to show the relationship between rate, time, and distance is [tex]rt=d[/tex], where [tex]r[/tex] represents the rate of change, [tex]t[/tex] represents time, and [tex]d[/tex] represents the total distance. Since you are given the distance and time, and are looking for the rate of change, then you need to divide the total distance traveled by the time it took to travel that distance, so the correct equation is [tex]\frac{240miles}{5hours}[/tex] = 48 miles per hour.
Have a great day! Feel free to let me know if you have any more questions :)
Can someone please explain how to solve this step by step so I could learn how to do this, if I don’t figure this out I’m literally gonna shoot myself
[tex]2x+2y=-8 \implies x+y=-4 \implies y=-4-x[/tex]
We can substitufe this result into the second equation.
[tex]-10x-5(-4-x)=-5 \\ \\ -10x+20+5x=5 \\ \\ -5x+20=5 \\ \\ -5x=-15 \\ \\ x=3 \implies y=-4-3=-7[/tex]
[tex]\therefore[/tex] The solution is [tex](3,-7)[/tex].
which number completes the sequence
Answer:
6
Step-by-step explanation:
The number completes the sequence is 6
20% of all the children in a class are left-handed. 4 children are left handed. How many children are there in a class altogether?
Answer: 20 children in total.
Step-by-step explanation: If you do 20% of 20 you get 4.
20
let the total children be x
therefore 20/100 × x =4
x = 400/10
x =20