Answer:
1/256
Step-by-step explanation:
4^-4 is the same thing as 1/4*1/4*1/4*1/4 which is 1/256
Answer:
1/256
Step-by-step explanation:
4⁻⁴ = 1/(4⁴) = 1/256
f(x) = sin(x² + 2x - 1)²
f'(x) = ?
Need Best Answer? Give the explanation!
ok thx.
It depends if you mean
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin^2(x^2+2x-1)[/tex]
i.e. the sine part is getting squared, or
[tex]f(x) = \sin(x^2+2x-1)^2 = \sin\left((x^2+2x-1)^2\right)[/tex]
i.e. the argument to sine is getting squared. I'll assume the first case, since it's fairly common convention to write [tex]g(x)^2 = \bigg(g(x)\bigg)^2[/tex].
Now if
[tex]f(x) = \sin^2(x^2+2x-1)[/tex]
• by the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2 + 2x - 1) \left(\sin(x^2+2x-1)\right)'[/tex]
• using the derivative of sine and the chain rule again we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) \left(x^2+2x-1\right)'[/tex]
• with the power and chain rules we have
[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) (2x+2)[/tex]
Recalling the double angle identity for sine,
[tex]\sin(2x) = \sin(x) \cos(x)[/tex]
we can rewrite the derivative among several other ways as
[tex]\boxed{f'(x) = (2x+2) \sin(2x^2+4x-2)}[/tex]
When you are determining the probability of an event, why must the probablilty be between 0 and 1? explain your answer.
Probability is the ratio of the desired outcomes to all possible outcomes.
If there are no desired outcomes, the ratio is 0 over all possible outcomes, thus 0.
If the event is all possible outcomes, the ratio is all possible outcomes over all possible outcomes, thus 1.
Probability can never be below zero or negative because desired outcomes can never be negative. If an event is impossible that means there are no desired outcomes meaning that probability is zero, thus couldn't fall below
Probability can never exceed 1 as desired outcomes can never be greater than total outcomes.
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The mean output of a certain type of amplifier is 498 watts with a standard deviation of 12 watts. If 86 amplifiers are sampled, what is the probability that the mean of the sample would be less than 494.7 watts
Mean (m) = 498
Standard deviation (σ) = 12
Sample size (n) = 86
The probability that the sample mean would differ from Population mean by less than 494.7 watts
P(m - s < Z < m + s)
P(498-494.7 < Z < 498+ 494.7)
Using the Z formula :
Zscore = (x - m) / (σ/√n)
x = 498 - 494.7 = 3.3 , x = 498 + 494.7 = 992.7
Z = (3.3 - 498) / (12/√86) = -383.48
P(Z < -383.48)
Z = (992.7 - 498 ) / (12/√86) = 383.48
P(Z<383.48)
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The number f of miles a ship is from its destination x hours after starting a voyage is given by f(x) = 80-20x. The number f of miles a submarine is from its destination x hours after leaving port is shown in the graph below. State the distance and length of time if each voyage. The ship traveled ___ miles in __ hours. The submarine traveled __ miles in __ hours.
The ship traveled 80 miles in 4 hours while the submarine traveled 75 miles in 5 hours.
How to determine the distance and time traveled?Based on the information provided, we can logically deduce that the ship is initially 80 miles away from its destination. Thus, f(x) would be equal to 0, if it traveled 80 miles and 0 miles away from its destination:
f(x) = 80 - 20x
0 = 80 - 20x
20x = 80
x = 80/20
x = 4 hours.
By critically observing the graph (see attachment) for the submarine's voyage, we can logically deduce the following:
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Identify which functions have complex roots by selecting the function names on the provided coordinate plane.
The functions that have complex roots are b and d.
What is complex root?Complex roots are the imaginary root of polynomial functions. The complex roots are represented as α = a + ib, and β = c + id.
When the quadratic equation has a discriminant value less than zero will have imaginary roots.
Out of the given functions, a ,b, c, and d, the function with complex roots are b and d.
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Answer:
b &d is correct. i just took the test. :)
Step-by-step explanation:
hello i need help on these question if u can
Answer:
The third one of the first question.
use the distrubutive property to simply -8(6x+3)
can someone help with this please
Use the information provided to create a polynomial function described below.
Degree of 3
Zeros are -3, 4, 6
End behavior is as x increases in the positive direction y increases in the positive direction.
Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial is x³- 7x² - 6x + 72.
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
The polynomial using the given information can be made as shown below.
Given the zeros of the polynomial are -3, 4, and 6.
P(x) = (x+3)(x-4)(x-6) = x³- 7x² - 6x + 72
To check the end behaviour of the function, the graph of the function can be plotted as shown in the below image.
Hence, the polynomial is x³- 7x² - 6x + 72.
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A given line passes through the points (2,3) and (2,−3). Determine the equation of the line that is perpendicular to the given line and passes through the point (−1,5).
could someone break this down for me? multiple choice in attachment
The required equation of the line is y = 5
Equation of a lineThe equation of a perpendicular line to a line in point-slope form is expressed as:
y-y1 = -1/m(x-x1)
m is the slope
(x1, y1) is any point on the line
Determine the slope
Slope = -3-3/2-2
y = ∞
Since there is no slope, hence the equation of the line will be in the form y = b
where b is the y-coordinate of the point. Hence the required equation of the line is y = 5
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Someone help please!?!
Answer: a≈6,1.
Step-by-step explanation:
The sine theorem states:
[tex]\boxed {\frac{a}{sinA^0} =\frac{b}{sinB^0}= \frac{c}{sinC^0} }[/tex], ⇒
[tex]a=\frac{c*sinA^0}{sinC^0}[/tex]
m∡A=180°-(m∡B°+m∡C°)
=180°-(68°+76°)
=180°-144°
=36°. ⇒
[tex]a=\frac{c*sin36^0}{sin76^0}\\ =\frac{10*sin36^0}{sin76^0} \\\approx6,1.[/tex]
Good luck an' have a nice day!
Can 10 people be divided into two groups with a ratio of 1 : 2? Explain.
Answer:
noStep-by-step explanation:
Can 10 people be divided into two groups with a ratio of 1 : 2?
Explain.
10 : 3 = 3.33
or 10 : 3 = 9 remaining 1
since it is not possible to divide a person into three parts, your answer is no
the measures of the sides of a triangle are 2x+3, 8x-4 and x^2. Write an expression that describes the perimeter of the triangle
Answer:
[tex]\textsf{Perimeter}=x^2+10x-1[/tex]
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
Given sides of a triangle:
[tex]2x + 3[/tex][tex]8x - 4[/tex][tex]x^2[/tex]Therefore, to find the perimeter of the triangle, sum the given sides:
[tex]\begin{aligned}\sf Perimeter & = (2x+3)+(8x-4)+x^2\\& = 2x+3+8x-4+x^2\\& = x^2 + 2x+8x+3-4\\& = x^2+10x-1\end{aligned}[/tex]
Perimeter=
Sum of sidesx²+2x+3+8x-4x²+2x+8x+3-4x²+10x-1The names of the months are each written on a slip of paper. if a slip of paper is randomly drawn, which scenario depicts mutually exclusive events? begins with a j and contains a u ends with an r and has five or fewer letters has thirty-one days and ends with a y contains an e and has thirty or fewer days
Answer:
Ends with r and has five or fewer letters
Step-by-step explanation:
Answer:
The answer is : B
Step-by-step explanation:
trust me I did it on edge 2022
Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
557. 0.00000103
Answer:
Hence, 0.00000103 can be expressed as [tex]$1.03 \times 10^{-6}$[/tex].
Step-by-step explanation:
- Given 0.00000103
- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .
- Then count n and write no. as a product with a power of 10 .
Step 1 of 1
Consider 0.00000103,
1.03
Decimal has moved 6 places to right.
The power will be negative as the original no. is less than 1 .
[tex]$$\begin{array}{r}1.03 \times 10^{-6} \\0.00000103=1.03 \times 10^{-6}\end{array}$$[/tex]
In the interval 0 to the power 0360 find x in which the sin is 0.6691. give your answer to the nearest degree
The angle for which the sine value is 0.6691 is found to be 42°.
What is the sine value?
A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of physics, sound and light waves are represented by the sine function.
When the angle between a right-angled triangle's base and hypotenuse changes, the sine's value changes.
[tex]sin^{-1}(0.6691)[/tex]=41.99°≈42°
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Use the given graph to determine the limit, if it exists. (4 points)
A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3.
Find limit as x approaches three from the right of f of x. .
Explanation:
Refer to the graph below. It should be similar to what your teacher gave you, based off the description.
Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.
As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.
In terms of notation, we can write [tex]\displaystyle \lim_{x\to3^{+}}f(x) = 3[/tex]
The portion [tex]x \to 3^{+}[/tex] means we're approaching 3 from the positive side, aka the right hand side on the number line.
A principal amount of $3000 is invested for 3 years at 4% compounded semi-annually. Use the compound interest formula to determine how much interest was earned on the investment.
The $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
Here,
P = $3000
r = 4% = 0.04
n = 2
t = 3 years
After plugging all the values in the formula:
[tex]\rm A = 3000(1+\dfrac{0.04}{2})^{2\times 3}[/tex]
After solving:
A = $3,378.49
I = A - P = 3,378.49 - 3000 = $378.49
Thus, the $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.
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Find two digit number that is one less than a square number,and when doubled is one less than a square number.
Which of the following appear in the diagram below?
Check all that apply.
z
A. YX
B. ZXYZ
C. ZYXZ
D. YW
Answer:
A , B, D
Step-by-step explanation:
YX is the segment joining points Y and X and is defined (A)
∠ XYZ is the angle between XY and YZ and is defined (B)
∠ YXZ is the angle between YX and XZ
However there is no segment joining XZ ← not defined
YW is the segment joining points Y and W and is defined (D)
A population of squirrels is growing in a Louisiana forest with a monthly growth constant of 55 percent. If the initial count is 100100 squirrels, how many are there in a year? Round any intermediate calculations, if needed, to no less than six decimal places, and round your final answer to the nearest whole number.
The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.
The final value of any quantity growing constantly at a particular rate is given as [tex]V = V_{0}e^{rt}[/tex] ,
where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.
The current population of squirrels (V₀) = 100.
The growth rate (r) = 5% per month.
The time period (t) = 1 year = 12 months.
Hence, the final population of squirrels (V), is given as:
[tex]V = V_{0}e^{rt}[/tex] ,
or, [tex]V = 100e^{(0.05*12)}[/tex] ,
or, [tex]V = 100e^{0.60}[/tex] ,
or, V = 100*1.822119,
or, V = 182.2119 ≈ 182.
Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.
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A plane has a maximum fuel capacity of 5,300 gallons. The airline requires that the pilot fly no more than 400 minutes before refueling. A one-way flight to a certain destination requires 2,000 gallons of fuel and 190 minutes of flight time. How many round trips can the pilot make before having to refuel?
A) 1
B) 2
C) 3
D) 4
Answer:
it is B
Step-by-step explanation:
that is because j3jejejdudduiwjsj
The requried pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1
To determine how many round trips the pilot can make before having to refuel, we need to consider both the fuel capacity and the flight time limit.
Given:
Maximum fuel capacity = 5,300 gallons
Flight time limit before refueling = 400 minutes
Fuel required for one-way flight = 2,000 gallons
Flight time for one-way flight = 190 minutes
First, let's calculate the maximum number of one-way trips the pilot can make based on the fuel capacity:
Max one-way trips based on fuel capacity = Maximum fuel capacity / Fuel required for one-way trip
Max one-way trips = 5,300 gallons / 2,000 gallons = 2.65 trips
Since we cannot have a fraction of a trip, we need to consider the flight time limit.
The total flight time for a round trip is twice the one-way flight time: 2 * 190 minutes = 380 minutes.
The pilot can fly a round trip as long as the flight time for the round trip is within the flight time limit. In this case, the round-trip flight time of 380 minutes is less than the flight time limit of 400 minutes.
Therefore, the pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1
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9 burgers and 1 doughnut cost $31.30. 3 doughnuts and 6 burgers cost $26.70. Find the cost of 2 burgers.
Answer:
$6.40
Step-by-step explanation:
let d be the cost of 1 doughnut and b the cost of 1 burger.
set up 2 equations and solve for b
9b + d = 31.3 → (1)
6b + 3d = 26.7 → (2)
multiplying (1) by - 3 and adding to (2) will eliminate d
- 27b - 3d = - 93.9 → (3)
add (2) and (3) term by term to eliminate d
- 21b + 0 = - 67.2
- 21b = - 67.2 ( divide both sides by - 21 )
b = 3.2
then
cost of 2 burgers = 2 × $3.20 = $6.40
a student
multiplied 4552 by 175 instead of multiplying by 157 how much was his product greater than the correct product
The student product is 81936 greater than the correct product
How to multiply numbers?The student was suppose to multiply 4552 by 157 but instead he multiplied 4552 by 175.
Therefore, let's find how much his product is greater than the correct product.
incorrect product = 4552 × 175 = 796600
Correct product = 4552 × 157 = 714664
Therefore,
difference = 796600 - 714664 = 81936
Therefore, his product is 81936 greater than the correct product.
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Use natural logarithms to solve the equation. Round to the nearest thousandth.
7e^2x + 10 = 29
Answer:
x ≈ 0.499
Step-by-step explanation:
The value of x can be found by undoing the operations done to it.
SolutionThe operations done to the variable are ...
multiply it by 2use that as the exponent with a base of emultiply the result by 7add 10We undo these operations in reverse order:
7e^(2x) + 10 = 29 . . . . given
7e^(2x) = 19 . . . . . . . . . subtract 10
e^(2x) = 19/7 . . . . . . . . . divide by 7
2x = ln(19/7) . . . . . . . . take the natural logarithm
x = (ln(19/7))/2 . . . . . . divide by 2
The rounded result is ...
x ≈ 0.499
What is 72,910 / 10^2
a customer buys 3 cappuccinos that costs $2.54 each and a bottle of water that costs $0.76 she gives the shop assistant $20 how much change should she receive
Answer:
$11.62
Step-by-step explanation:
2.54×3=$7.62
0.76+7.62=8.38
20-8.38=$11.62
Answer:
Step-by-step explanation:
Discussion
3 cappuccinos at 2.54 each 2.54 * 3 = 7.62
1 bottle of water at 0.76 0.76*1 = .76 Add
Total 8.38
Change = 20 - 8.38 = 11.62
Answer
She should receive 11.62 in change.
1. Try It #1
If f(x) is a linear function, and (2,3) and (0,4) are points on the line, find the slope. Is this function increasing or decreasing?
Answer:
The slope of the line representing the linear function f(x) is determined as [tex]$-\frac{1}{2}$[/tex]. The function f(x) is decreasing because the slope is less than zero, i.e., m<0.
Step-by-step explanation:
A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).
It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.
Step 1 of 1
Determine the slope of the line.
The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
So, substitute [tex]$4 \& 3$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$0 \& 2$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,[tex]$m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$[/tex]
The slope of the line is obtained as [tex]$-\frac{1}{2}$[/tex]. Now, as [tex]$-\frac{1}{2} < 0$[/tex], so the function f(x) is decreasing.
Can someone help me out on this
Answer:
Step-by-step explanation:
i have no clue what to do
Answer:
4x + 3y = 12
Step-by-step explanation:
Answer:
4x + 3y = 12
Step-by-step explanation:
At x-intercept, y = 0.
∴ When we substitute y = 0 into the equation, x should equal 3.
• 1st equation: 3x + 4(0) = 12 ⇒ x = 4 ❌
• 2nd equation: 4x + 3(0) = 7 ⇒ x = 7/4 ❌
• 3rd equation: 3x + 4(0) = 7 ⇒ x = 7/3 ❌
• 4th equation: 4x + 3(0) = 12 ⇒ x = 3 ✅
This means the 4th option is the correct one.
To check, we can replace x = 0 into the 4th equation to see if the y-intercept value comes out to be 4:
4(0) + 3y = 12 ⇒ y = 4 ✅
Solve for X if possible:
5x -4y = 24
x =_
The possible values of x be 4.8, 5.6 and 6.4.
What is equation?The statement of equality between two expressions consisting of variables and/or numbers.
Given:
5x -4y = 24
when y=0
5x = 24
x = 4.8
when y=1,
5x= 28
x= 5.6
when y=2,
5x= 32
x= 6.4
Hence, the possible values of x is 4.8, 5.6 and 6.4.
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