We can use the power rule to find the derivative of f(x) = x^n + x^(n-1). The power rule states that the derivative of x^n is nx^(n-1).
So, the derivative of x^n is nx^(n-1)
And the derivative of x^(n-1) is (n-1)x^(n-2)
So the derivative of f(x) = x^n + x^(n-1) is:
f'(x) = nx^(n-1) + (n-1)x^(n-2)
Now, if we combine the exponents we have :
f'(x) = nx^n-1 + nx^n-2
And we can factor out x^n-2 from the second term, we have:
f'(x) = nx^n-1 + (n-1)x^n-2*x^2
Now, we can simplify the expression by canceling the x^n-2 factor.
f'(x) = nx^n-1 + (n-1)x
And finally, by simplifying the exponent and factoring the constants, we have:
f'(x) = (nx + n - 1) / x^(2-n)
So the derivative of f(x) = x^n + x^(n-1) is f'(x) = (nx + n - 1) / x^(2-n)
a pepsi bottle is dropped from a height of 60m. how fast is it going when it still has 1.2s left in its fall
The speed of the Pepsi bottle would be 78.4 m/s.
To calculate the speed of the Pepsi bottle when it has 1.2 seconds left in its fall, we would need to know the acceleration due to gravity. Assuming a standard gravitational acceleration of 9.8 m/s^2, we can use the following equation to calculate the speed:
Speed = (2 * acceleration * distance)^(1/2)
where distance is the distance fallen (60m)
Speed = (2 * 9.8 * 60)^(1/2) = 78.4 m/s
It is important to know that this is the final velocity at time of impact and doesn't account for the time of fall and air resistance.
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Suppose a population consists of 850,000 people which of the following numbers of members of the population being surveyed could result in a parameter but not a sample statistic
The number of members of the population that could result in a parameter but not a statistic is given as follows:
A. 850
What is a parameter and what is a statistic?A parameter is used to describe the whole population, while a statistic is used to describe the sample.
For this problem, we have that:
The population size is of 850,000.The sample size is of 850.Meaning that 850,000 describes the population, and thus the correct option is option C.
Missing Information
The options are given as follows:
A. 850
B. Both 850 and 850,000
C. 850,000
D. Neither 850 nor 850,000
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What is angle CBD
A=60
D=80
C=25
Answer:
m∠CBD = 55°
Step-by-step explanation:
Angles BDA and BDC form a linear pair:
⇒ m∠BDA + m∠BDC = 180°
⇒ 80° + m∠BDC = 180°
⇒ m∠BDC = 100°
Interior angles of a triangle sum to 180°:
⇒ m∠CBD + m∠BDC + m∠DCB = 180°
⇒ m∠CBD + 100° + 25° = 180°
⇒ m∠CBD + 125° = 180°
⇒ m∠CBD = 55°
A snail travelled 48 cm in h.
Suppose the snail moved at a constant
speed and made no stops. How far
would the snail travel in 1 h?
A pool is being filled at the rate of 66 gallons per hour.
Fill in the table.
Answer:1/3=22, 1=66, 1.5=99
Step-by-step explanation:
The table represents a quadratic function f(x).
x f(x)
−10 24
−9 17
−8 12
−7 9
−6 8
−5 9
−4 12
If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
−7
6
12
36
For the given quadratic function, the coefficient b is equal to 12.
What is a Quadratic Function?
The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.
The question gives some points of the quadratic function, see below.
x f(x)
−10 24
−9 17
−8 12
−7 9
−6 8
−5 9
−4 12
From the given data you can find the coefficients by solving the system linear equation.
You can write a system linear equation using the points: (-10,24) ,(-9,17) and (-8,12) for example. Then, you have three equations:
100a-10b+c=24 (1)
81a-9b+c=17 (2)
64a-8b+c=12 (3)
Isolate the coefficient a, you have [tex]a=\frac{24+10b-c}{100}[/tex]. Replacing the variable a in equations 2 and 3, you have:
[tex]81* \frac{24+10b-c}{100}-9b+c=17 (2) \\\\ 64* \frac{24+10b-c}{100}-8b+c=12 (3)[/tex]
Simplifying, you can rewrite it as:
[tex]\frac{-90b+19c+1944}{100}=17 (2) \\ \frac{-40b+9c+384}{25}=12 (3)[/tex]
Next step, you should isolate the coefficient b from the previous equation 2. You have:
[tex]\frac{-90b+19c+1944}{100}=17\\ \\ -90b=1700-19c-1944\\ \\ -90b=-244-19c\\ \\ b=-\frac{-244-19c}{90} = \frac{244+19c}{90}[/tex]
[tex]b=\frac{(244+19c)}{90} (4)[/tex]
Replacing the variable b in the previous equation 3, you have:
[tex]\frac{-40*\frac{244+19c}{90}+9c+384 }{25} =12\\[/tex]. Multiplying both sides by 25, you find the coefficient c:
[tex]\frac{25*(-40(\frac{244+19c}{90})+9c+384)}{25}=12*25\\ \\ -40(\frac{244+19c}{90})+9c+384=300\\ \\ -4(\frac{244+19c}{9})+9c+384=300\\ \\ (\frac{-976-76c}{9})+9c+384=300\\ \\ -976-76c+81c+3456=2700\\ \\ -76c+81c=2700+976-3456\\ \\ 5c=220\\ \\ c=44[/tex]
From the previous equation 4, you finally find the coefficient b. See below.
[tex]b=\frac{244+19c}{90} \\ b=\frac{244+19*44}{90}\\ \\ b=\frac{244+836}{90}\\ \\ b=\frac{1080}{90}\\ \\ b=12[/tex]
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The following inequalities form a system.
y ≥ 3x + 1
x < −3
Which graph represents the system?
A) The graph shows a solid line, which passes through a point 0 comma 1 and a point 1 comma 4, with shading above the line. There is also a dashed line, which passes through a point 0 comma negative 3 and a point 1 comma negative 3, with shading below the line.
B) The graph shows a solid line, which passes through a point 0 comma 1 and a point 1 comma 4, with shading below the line. There is also a dashed line, which passes through a point 0 comma negative 3 and a point 1 comma negative 3, with shading below the line.
C) The graph shows a solid line, which passes through a point 0 comma 1 and a point 1 comma 4, with shading above the line. There is also a dashed line, which passes through a point negative 3 comma 0 and a point negative 3 comma 1, with shading to the right of the line.
D) The graph shows a solid line, which passes through a point 0 comma 1 and a point 1 comma 4, with shading above the line. There is also a dashed line, which passes through a point negative 3 comma 0 and a point negative 3 comma 1, with shading to the left of the line.
The graph that represents the system is option D.
The first inequality y ≥ 3x + 1 represents a line with a slope of 3 and a y-intercept of 1, and it is shaded above the line. This line is a solid line.
The second inequality x < -3 represents a vertical line with an x-intercept of -3, and it is shaded to the left of the line. This line is a dashed line.
The solution of the system is the intersection of the two regions, which is the area on the coordinate plane that is shaded above the solid line and to the left of the dashed line.
So the graph that represents the system is the one that shows a solid line with a slope of 3 and a y-intercept of 1, with shading above the line, and a dashed line with an x-intercept of -3, with shading to the left of the line. This is option D.
Answer:
D
Step-by-step explanation:
took the test xx
What is the measure?
Answer:
∠ U = 80°
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180° , that is
∠ U + 37° + 63° = 180°
∠ U + 100° = 180° ( subtract 100° from both sides )
∠ U = 80°
mathematical expression
When numbers and variables are properly combined using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions, a set of mathematical symbols known as an expression is produced.
What are Mathematical expressions?A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Therefore, when numbers and variables are properly combined using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions, a set of mathematical symbols known as an expression is produced.
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Complete question:
What is a mathematical expression?
Answer:
y=mx+b
Step-by-step explanation:
Cliff hanger leaps from a cliff. At first, the fall is modeled by
F(t)= -t2 + 2t + 305, where t is the time sense he jumped. After a certain amount of time , he opens his parachute, after which, his fall is modeled by
P(t) = -t + 295. At how many seconds did he open his chutes
He open his chutes at t = (3 ± √(-31)) / 2 seconds.
How to calculate the time?To find the time at which the person opened their parachute, we need to find the point of intersection between the two equations, F(t) and P(t).
The first equation is F(t) = -t^2 + 2t + 305, represents the fall before the parachute is open.
The second equation is P(t) = -t + 295, represents the fall after the parachute is open.
We can find the point of intersection by setting the two equations equal to each other and solving for t.
-t^2 + 2t + 305 = -t + 295
-t^2 + 3t = -10
t^2 - 3t + 10 = 0
using quadratic formula
t = (3 ± √(3^2 - 4110)) / 2*1
t = (3 ± √(9 - 40)) / 2
t = (3 ± √(-31)) / 2
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How many ordered pairs of positive integers $(x,y)$ are there such that $x \leq y \leq 1000$ and x+y is even?
There are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.
What is least common multiple (LCM)?The least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by lcm, is the smallest positive integer that is divisible by both a and b.
Given that, how many distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000,
1000 = 10³ = 2³×5³
Therefore, we get:
x = 2ᵃ×5ᵇ
y = [tex]2^c[/tex]×[tex]5^d[/tex]
where
0 ≤ a, b, c, d ≤ 3
a or c = 3
b or d = 3
To figure out the number of distinct ordered pairs (x, y), we need to find the distinct number of ordered quadruples (a, b, c, d)
there are.
Case 1 : Exactly 2 of a, b, c, d = 3
a = b = 3, c = 0, 1, 2, d = 0,1,2
a = d=3, b = 0, 1, 2, c = 0,1,2
c = b = 3, a = 0, 1, 2, d = 0, 1, 2
c = d = 3, a=0, 1, 2, b = 0, 1, 2
4(1×1×3×3) = 36
Case 2 : Exactly 3 of a, b, c, d = 3
a = b = c = 3, d = 0, 1, 2
a = b = d = 3, c = 0, 1, 2
a = c = d = 3, b = 0, 1, 2
b = c = d = 3, a = 0, 1, 2
4(1×1×1×3) = 12
Case 3 : Exactly 4 of a, b, c, d = 3
a = b = c = d = 3
1(1×1×1×1) = 1
Total =36+12+1=49
Hence. there are 49 distinct ordered pairs of positive integers (x, y) such that the least common multiple of x & y is 1,000.
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80) the referee awards a free kick. an opponent stands in front of the ball. play is restarted and the ball hits the opponent who is less than 10 yards from the ball. what decision should the referee make?
If an opponent stands less than 10 yards from the ball when a free kick is awarded, and the ball subsequently strikes that opponent, the referee should award an indirect free kick to the opposing team.
This is because the opponent is in violation of the laws of the game, specifically Law 13 - Free kicks which states that at a direct free kick, a player must be at least 10 yards (9.15m) from the ball until it is in play.
The indirect free kick should be taken from the spot where the opponent was when they were struck by the ball.
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as mars revolves around the sun, it travels at a rate of approximately 15 miles per second. convert this rate to miles per minute. at this rate, how many miles will mars travel in
The speed travelled by mars in miles per minutes is 900. As Given that the mars revolves around the sun at a rate of approximately 15 miles per second.
We know that , Speed = distance / time
Hence we have speed of the mars as 15 miles/sec.
To convert the rate from miles/sec to miles/ minute we have to multiply the given with minute i.e 60 sec.
miles x min = miles x 60 sec
sec x min sec x min
since , 1 minute = 60 sec
hence, new speed = 15 x 60 miles/ minute.
Therefore , the speed travelled by mars in miles per minutes is 900.
( a) In two minutes mars will travel 900 x 2 times with the same rate.
i.e 1800 miles per minute.
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The complete question is:
as mars revolves around the sun, it travels at a rate of approximately 15 miles per second. convert this rate to miles per minute. at this rate, how many miles will mars travel in 2 minutes ?
How do I solve this??????
Answer:
#13: 360; #14: 9 m^3
Step-by-step explanation:
x ^2 y z^3 = 9*5*8=360
81 m^4*n^3 = 9 m*n^3 * 9 m^3
A marble is going to be taken at random from a box of marbles.
The probability that the marble will be silver is 0.5
There must be an even number of marbles in the box.
(b) Explain why.
A probability is a number that reflects the chance or likelihood that a particular event will occur.
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails.
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chris decided to buy 102 feet of craft center material what is the cost
Answer: however much a foot of craft material is multiply it by 102
Step-by-step explanation:
58-s=g+4g
how could I solve this?
Answer:
Answer
Step-by-step explanation:
you can answer these NUTS!!!
A DJ charges an hourly fee and an equipment setup fee.
a. Write a formula for the cost, C, of hiring a DJ for n hours.
b. Find the inverse of the formula. What does the new formula represent?
c. If the DJ charged $550. for how many hours was she hired? Use the inverse formula.
a. C=
The formula for the cost, C, of hiring a DJ for n hours is C = hn + e
How to write a formula for the cost of hiring a DJ for n hours?a. The formula for the cost, C, of hiring a DJ for n hours is C = hn + e, where h is the hourly fee and e is the equipment setup fee.
b. To find the inverse of the formula, we can solve for n in terms of C and h:
n = (C - e) / h
The new formula represents the number of hours the DJ was hired for given the cost, C, and the hourly fee, h.
c. If the DJ charged $550, we can use the inverse formula to find the number of hours she was hired for.
n = (550 - e) / h
where e is equipment setup fee.
Since we are not given the equipment setup fee, we can't calculate the number of hours she was hired for.
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suppose you have ten dies with six faces each. if you randomly throw these dies, what the probability that the sum of all the top faces is divisible by 6?
The probability that the sum of all the top faces is divisible by 6 is 1/6.
1.This is because there are six possible outcomes when the dice are thrown, and only one of these outcomes (where the sum of the top faces is divisible by 6) has a probability of 1/6.
2.The other five outcomes have a probability of 0.
3.To explain this further, consider the following example: if we throw 10 dice, the possible outcomes are 6^10, or 6,561 outcomes. Of these 6,561 outcomes, only 1,089 will result in a sum of the top faces that is divisible by 6.
4.Therefore, the probability that the sum of all the top faces is divisible by 6 is 1,089/6,561, or 1/6.
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Which of the following exponential functions represents the graph below?
The function represent the given graph is f(x)= 1·(1/2)ˣ. Therefore, option B is the correct answer.
What is the exponential function?Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).
As, seen from the graph passes through (0,1) point.
Now, put x = 0, we get
y = 1 from equation B or D.
Now, as the value of x increases towards negative direction i.e. -5, -6, ....
Then, the value of y will be zero.
So, the function represent the graph is f(x)= 1·(1/2)ˣ
Therefore, option B is the correct answer.
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If Elayna bought 18 bags of topsoil and each bag contains 36 pounds, how many total bags did she buy?
648 pounds of topsoil in total.
( for this question it's asking how many bags she bought in total, which I dont understand cuz it already says she bought 18 bags.)
(It really should have asked, how much topsoil in total did she buy)
but what I did to find my ans is that I multiplied.
36×18, cuz it says each bag contains 36 pounds.
would a 7 inch long pen fit in a box with dimensions of 3 in x 4 in x 5 in? explain please
The 7 inches pen would not fit in the box with dimensions 3 in × 4 in × 5 in
How to answer the question on dimensionsThe 7 inches long pen would not fit in a box with dimensions of 3 inches x 4 inches x 5 inches because the dimensions of the box are not long enough to accommodate the length of the pen.
Specifically, the length dimension of the box (3 inches) is less than the length of the pen (7 inches), so the pen would not be able to fit inside the box.
Additionally, even if the length of the box was greater than 7 inches, the width and height dimensions of the box (4 inches and 5 inches, respectively) would likely be too small to accommodate the diameter of the pen.
In conclusion, the pen is too long for the box, and the box is not wide or tall enough to fit the pen.
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what is the base area of a pyramid with a volume of 72 m^3 and a height of 12 m 
Answer:
Thats the answer in the picture I designed and made it step by step so you can understand it
Hope it helps
The description below outline different payment options for working at a lawn mowing company. Use x to represent the number of lawns and y to represent the total payment.
For each equation and graph drag the situation that can be modeled by that relationship into the space in that row.
A mathematical rule that may have a value given to it is called a function.
What is a function?A mathematical rule that may have a value given to it is called a function.
A mathematical function is a rule that can have a value. We will now move on to determine which function may be categorised as displayed.
The equation for this quadratic function, y = 2x, is that Ashley pays $2 every day and provides $2 to her brother.
The total payment equals twice as many days as there are in a week. This is a linear function, and its equation is y= 2x - 2x = 2[tex]x^{2}[/tex]
The daily payouts begin at $2 and double with each passing day; this exponential function has the formula y = 2[tex]x^{2}[/tex]
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Which measure of central tendency lies at the 50th percentile for any distribution?
O percentile
O median
O mode
O mean
O It cannot be determined from the information given
The central tendency of the measure lies at the 50th percentile would be the median.
Option (B) is correct.
What is the measure of the central tendency?
The measure of central tendency is a statistical term that refers to a single value that summarizes or represents a set of data. There are several measures of central tendency, including the mean, median, mode, and percentile.
The measure of central tendency that lies at the 50th percentile for any distribution is the median. The median is the middle value of a set of data when it is arranged in order of magnitude. Half of the values in the set are above the median and half are below it. This means that the median splits the distribution into two equal parts, and it is not affected by outliers or extremely large or small values
Hence, the central tendency of the measure lies at the 50th percentile would be the median.
Option (B) is correct.
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Steve needs to earn a C in his Sociology class. His current test scores are 70, 77, 71, and 71. His final exam is worth 3 test scores. In order to earn a C, Steve's average must lie between 70 and 79 inclusive. What range of scores can Steve receive on the final exam to earn a C in the course
The range of scores that Steve needs to get an average of 70 to 79 is 66 to 87 Points.
To find the range of scores that Steve needs to have to stay in the 70 to 79 range we first need to define the variables that we need to find.
Let x = Score that Steve needs
Since the exam is worth 3 exams, we will then use 3x to denote the weight of the final exam.
Now we need to add all the other exams and divide it by the number of exams.
[tex]\frac{3x + 70+77+71+71}{7} = 70[/tex]
3x + 292 = 7 *70
3x = 490 -292
3x = 198
[tex]\frac{3x}{3} =\frac{198}{3}[/tex]
x = 66
Now let's look for the score that Steve needs to get to a 79 average.
[tex]\frac{3x + 70+77+71+71}{7} = 79[/tex]
3x + 292 = 7 * 79
3x + 292 = 553
3x = 553 - 292
3x = 261
x = 87
So the range of scores is 66 to 87 Points.
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Multiple choice question math!!
Marco is 1000 m due east of the centre of the park. His friend Ray is 1000 m due south of the centre of the park. Which is the correct expression for the exact distance between the two boys?
A. 500√ 2 m
B. 1000/√ 2 m
C. 500/√2 m
D. 1000√2 m
The correct expression for the exact distance between the two boys: 1000√2 m
The correct answer is an option (D)
Consider following diagram.
In right triangle ABC, AB represents the distance covered by the Marco and AC represents the distance covered by the Ray.
AB = 1000 m
AC = 1000 m
We need to find the correct expression for the exact distance between the two boys.
i.e., we need to find the length of hypotenuse BC.
Using Pythagoras theorem for right triangle ABC,
BC² = AB² + AC²
BC² = 1000² + 1000²
BC² = 1000000 + 1000000
BC² = 2 × 1000000
BC = [tex]\sqrt{2\times 1000000}[/tex]
BC = 1000√2 m
Therefore, the distance between the boys = 1000√2
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Each bucket holds 3 2/5 gallons of water. If it takes 6 buckets to fill a tank, how much water does the tank hold? A bucket.
What is the probability of rolling a one on the first die and a four on the second die?
Write your answer as a fraction or a whole number. With fractions, use a slash (/) to
separate the numerator and denominator.
Submit
Work it out
Not feeling ready yet? These can help:
The probability of rolling a one on the first die and a four on the second die is 1/36.
This is because there are six possible outcomes for each die (1, 2, 3, 4, 5, and 6) and the probability of rolling a specific number on one die is 1/6. To find the probability of rolling a specific number on two dice, you would multiply the individual probabilities of each die (1/6 x 1/6 = 1/36). Since there is only one combination of rolling a one on the first die and a four on the second die, the probability is 1/36.
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PLEASE HELP!! 100 POINTS!!
Answer:
Step-by-step explanation:
f(X) = 5X=25