The nth derivative of each function is n!.
Taking the nth derivative of a function is the process of calculating successive derivatives and observing the patterns that occur.
In your example, the function given is f(x) = xⁿ. To find the nth derivative, you need to calculate the first few derivatives and observe the pattern that occurs.
The first derivative of the function f(x) = xⁿ is f'(x) = [tex]nx^{n-1}[/tex]
The second derivative is f''(x) = [tex]n(n-1)x^{n-2}[/tex]
From here, you can see that the pattern is that the exponent of x decreases by 1 each time, and the coefficient of x increases by n-1 each time.
Therefore, the nth derivative of
f(x) = xⁿ => f^(n)(x) = [tex]n(n-1)(n-2)...(n-(n-1))x^{n-n}[/tex] = n!x⁰ = n!.
This result is true for any value of n, so the nth derivative of f(x) = xⁿ is always equal to n.
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A loading dock at a warehouse has a ramp that is 16 feet in length. The length from the edge of the loading dock to the end of the ramp is 14 feet. What is the height of the loading dock to the nearest tenth of a foot?
The required height of the loading dock is approximately 7.746 feet (to the nearest tenth of a foot).
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. Let's call the height of the loading dock "h". The ramp, the distance from the edge of the loading dock to the end of the ramp, and the height of the loading dock form a right triangle. The Pythagorean theorem states that for any right triangle, the square of the length of the hypotenuse (the ramp in this case) is equal to the sum of the squares of the other two sides (the height and the distance from the edge of the loading dock to the end of the ramp).
In this case, we can write:
16² = h² + 14²
256 = h² + 196
60 = h²
Taking the square root of both sides, we get:
h = √60
h ≈ 7.746
Therefore, the height of the loading dock is approximately 7.746 feet (to the nearest tenth of a foot).
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36. suppose a system of linear equations has a 3 5 augmented matrix whose fifth column is a pivot column. is the system consistent? why (or why not)?
A 3 5 augmented matrix whose fifth column is a pivot column. that is [0, 0, 0, 0, c] where c is not equal to 0. This implies that the system is inconsistent.
What is pivot column in matrix?The goal of pivoting is to turn a leading one into a zero for an element that is above or below it.
A matrix's left-hand side element is referred to as the "pivot" or "pivot element" when you wish the components above and below it to be 0.
This element usually has a value of 1.
If and only if the echlon form of the augmented matrix designating the linear system of equations contains no row of the type, then the linear system is said to be consistent.
Given that, a 3 5 augmented matrix whose fifth column is a pivot column. that is [0, 0, 0, 0, c] where c is not equal to 0.
This implies that the system is inconsistent.
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what is the null hypothesis two tailed test?
The null hypothesis in a two-tailed test states that there is no significant difference or relationship between two variables being compared.
In hypothesis, the invalid speculation is an assertion about the populace that expects there is no massive distinction or connection between two factors. In a two-followed test, the invalid speculation expresses that there is no distinction or connection between the two gatherings being looked at. The two-followed test is utilized when we are keen on testing whether the mean of an example is essentially not the same as the mean of a populace, without determining a course. For instance, a two-followed test might be utilized to test whether another drug affects pulse, without determining whether it will increment or lessening circulatory strain. The elective speculation in a two-followed test is that there is a huge contrast or connection between the two gatherings.
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Table 2
Distance (km) Money (S)
0
10
20
30
40
1,2001
0
1
23
4
?
Unit rate:
Equation:
Answer:
Unit Rate: $10/km
Equation: x=y/10 or y=10x
Choose the correct option
The sides that cannont be the sides of a triangle are the ones in option B.
2cm, 6cm, 4cm
Which of the follwing cannot be the sides of a triangle?If A, B, and C are the sides of a triangle, then the triangular inequality says that:
A + B > C
A + C > B
C + B > A
So, any set of 3 sides where the sum of two of the sides is smaller than the other side cannot be the sides of a triangle.
Then the correct option will be b:
2cm, 4cm, 6cm
If we add the two shorter ones we will get:
2cm + 4cm = 6cm
And that is not larger than the other side, so it isthe correct option.
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Question 11 help ! Urgently
Answer:
Can u pls type the question in??
help 25 point as soon as possible
Answer:
8x8 > 9x7 (64 > 63)
Step-by-step explanation:
Please Answer by looking at the screenshot. Will be giving 10 points.
The complete expression that gives equivalent values is:
x⁻⁸ . x⁹ = x⁻⁶ . x⁷ = x⁻⁴ . x⁵ = x¹ = x⁻² . x³
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
x⁻ . x = x⁻ . x = x⁻ . x = x = x⁻ . x
Where the exponents are blank
There is no general answer to this, and one of the possible solutions is as follows:
To start with, we create an expression of the following format:
x⁻ⁿ . xⁿ⁺¹ = x¹
Using the above as a guide, we have the following:
x⁻⁸ . x⁹ = x¹
x⁻⁶ . x⁷ = x¹
x⁻⁴ . x⁵ = x¹
x⁻² . x³ = x¹
So, the equivalent expression is x⁻⁸ . x⁹ = x⁻⁶ . x⁷ = x⁻⁴ . x⁵ = x¹ = x⁻² . x³
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PQRST is a solid regular pyramid on a square base QRST
where QR = 20 cm and edge PQ = 30 cm.
Find
a the height of P above the base QRST
b the angle that PS makes with the base QRST
c the total surface area of the pyramid including
the base.
Answer: a) To find the height of the pyramid, we can use the Pythagorean theorem. Let H be the height of the pyramid, and let M be the midpoint of QR. Then, PM is half of PQ, which is 15 cm. We can use the Pythagorean theorem to find H:
H^2 = PQ^2 - PM^2
H^2 = 30^2 - 15^2
H^2 = 675
H = sqrt(675) = 5 sqrt(3) cm
b) To find the angle that PS makes with the base QRST, we can use trigonometry. Let A be the foot of the perpendicular from P to the base QRST, and let B be the midpoint of PS. Then, we have:
tan(angle PSB) = AB / PB
Since triangle PAB is a right triangle, we can use the Pythagorean theorem to find AB:
AB^2 = AP^2 - PB^2
AB^2 = H^2 + (PQ/2)^2 - PB^2
AB^2 = (5 sqrt(3))^2 + (15/2)^2 - PB^2
AB^2 = 225/4 + 75 - PB^2
AB^2 = 375/4 - PB^2
Since triangle PBS is also a right triangle, we can use the Pythagorean theorem to find PB:
PB^2 = PS^2 - BS^2
PB^2 = (2 H)^2 - (PQ/2)^2
PB^2 = 4 (5 sqrt(3))^2 - (15/2)^2
PB^2 = 500 - 56.25
PB^2 = 443.75
Substituting these values into the equation for tan(angle PSB), we get:
tan(angle PSB) = sqrt(375/4 - 443.75) / sqrt(443.75)
tan(angle PSB) = -0.4385
Since angle PSB is in the second quadrant, we have:
angle PSB = 180 degrees + arctan(-0.4385) = 152.4 degrees (rounded to one decimal place)
c) To find the total surface area of the pyramid, including the base, we can divide the pyramid into four triangular faces and a square base. The area of each triangular face can be found using the formula:
area = (1/2) base * height
where the base is the length of one edge of the square base, and the height is the height of the pyramid. The area of the base is simply the area of the square QRST, which is (20 cm)^2 = 400 cm^2. Therefore, we have:
area of each triangular face = (1/2) (20 cm) (5 sqrt(3) cm) = 50 sqrt(3) cm^2
total surface area = 4 (50 sqrt(3) cm^2) + 400 cm^2 = 200 sqrt(3) cm^2 + 400 cm^2
total surface area = (200 + 200 sqrt(3)) cm^2 ≈ 532.4 cm^2 (rounded to one decimal place)
Step-by-step explanation:
-4x=3(x+7) solve this please
Please help me solve this problem ASAP
Answer:
In the triangle we are given Angle A,B andC
a) To find the value of x we will say
angle A + angle B + angle C = 180(sum of angles in triangle add up to 180)
35 + 52 + 3(x+2) = 180
87 + 3x + 6 = 180
3x + 93 = 180
3x = 180 - 93
3x = 87
x = 29
b) To find the measure for angle C we need to substitute the value of x
angle c = 3(x+2)
= 3(29+2)
= 3(31)
= 93
2. A table of values is given below. Write the equation of the line.
tody
0 2
-8-8
y
-7
-8
-4
<-8
10
-8
Answer:-7
Step-by-step explanation:
suppose you have 100 dollars in your bank account and you earn 2.25% interest per year. let mn be the amount of money in your account after n years. determine the amount of money you have in your account after years 1, 2, 3, and 4 to 2 decimal places:
The amount of money you have in your account after years 1, 2, 3, and 4 are $102.25, $204.5, $306.75 and $409 respectively.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan.
Given that, you have 100 dollars in your bank account, and you earn 2.25% interest per year.
We need to find the amount of money you have in your account after years 1, 2, 3, and 4 years
Find for Simple interset :-
Simple interset = PRT / 100
P = Principal amount, r = rate and t = year
For 1 year, put t = 1
A = 100×1×2.25 / 100 + 100
= $102.25
To find the amount for 2nd, 3rd and 4th year, just multiply these numbers to the interset earned in 1st year,
For 2 year,
A = $102.25×2
A = $204.5
For 3 year,
A = $102.25×3
A = $306.75
For 4 year,
A = $102.25×4
A = $409
Hence, the amount of money you have in your account after years 1, 2, 3, and 4 are $102.25, $204.5, $306.75 and $409 respectively.
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2. A certain TV can be purchased from the manufacturer for $220. A certain online retailer has a standard markup of 25%, and a certain superstore has a standard markup of 45%.
(a) What is the price of the TV when purchased online? What is the price of the TV when purchased at the superstore?
(b) What is the difference between the prices in Part (a)? How does this relate to the difference in the markup?
Answer:
(1) As a result, the Monitor costs $275 to buy online. (2) There is a 20% price disparity between the two retailers.
What is a good illustration of purchased?10,000 pairs of shoes are ordered by Shoes Unlimited from an overseas vendor. This entails the business issuing a purchase requisition, which serves as a formal promise to buy the specified kind and number of shoes.
(a) To find the price of the TV when purchased online, we can add 25% markup to the manufacturer's price of $220:
Price online = $220 + (0.25 * $220)
Price online = $220 + $55
Price online = $275
So the price of the TV when purchased online is $275.
To find the price of the TV when purchased at the superstore, we can add 45% markup to the manufacturer's price of $220:
Price at superstore = $220 + (0.45 * $220)
Price at superstore = $220 + $99
Price at superstore = $319
So the price of the TV when purchased at the superstore is $319.
(b) The difference between the prices in part (a) is:
Price at superstore - Price online = $319 - $275 = $44
The difference in markup between the two stores is:
Markup at superstore - Markup online = 45% - 25% = 20%
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When can a correlation coefficient based on an observational study be used to support a claim of cause and effect?
A. When the correlation coefficient is close to −1 or +1.
B. When the scatterplot of the data has little vertical variation.
C. When the correlation coefficient is equal to −1 or +1.
D. Never
A correlation coefficient based on the observational study cannot be used to support a claim of cause and effect. The correct answer is D: never.
Correlation does not imply causation, and while a strong correlation between two variables may suggest that there is a relationship between them, it does not prove that one variable causes the other. Observational studies are particularly susceptible to confounding variables, which can make it difficult or impossible to determine whether a relationship between two variables is causal or not.
To establish causality between two variables, a randomized controlled experiment is required. In a randomized controlled experiment, the experimenter can manipulate the independent variable and observe the effect on the dependent variable, while controlling for other variables that might affect the outcome. By randomly assigning subjects to different treatment groups, the experimenter can ensure that any differences in the outcome between groups are due to the treatment, rather than some other factor.
Therefore, while a correlation coefficient can be a useful tool for describing the relationship between two variables, it cannot be used to establish causality.
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If 580 books were sold at the book fair,__of the book were fiction
The number of fiction books is given as follows:
58 fiction books.
How to obtain the number of fiction books?The number of fiction books is obtained applying the proportions in the context of the problem.
The total number of books is of 580, while the percentage of fiction books is of 10%. Hence the number of fiction books is obtained as follows:
0.1 x 580 = 58 fiction books.
Missing InformationThe percentage of fiction books is of 10%.
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Mrs.Mathers science class is growing sunflowers. Georges sunflower grew a total of 2.218 inches this week. Brians grew a total of 2.21 inches. Whose sunflower grew the most?
Georges sunflower grew the most.
How to compare two decimal numbers ?
Write the decimal numbers in a place value chart.Compare the digits starting with the greatest place value.If the digits are the same, compare the digits in the next place value to the right. Keep comparing digits with the same place value until you find digits that are different.Given :
Georges sunflower grew : 2.218 inches
Brians grew : 2.21 inches
Since , two decimal number is compared using Compare the digits starting with the greatest place value and If the digits are the same, compare the digits in the next place value to the right. Keep comparing digits with the same place value until you find digits that are different.
Therefore , we can see that
2.218 inches > 2.21 inches
Hence , georges sunflower grew the most.
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Y=2/3x+8
Y=1/2x+10
What is x?
Answer:
May you please give me the brainliest answer:
To find the value of x, we can set the two given equations equal to each other, since they both represent the same value of y:
2/3x + 8 = 1/2x + 10
We can simplify this equation by first getting rid of the fractions. To do this, we can multiply both sides of the equation by the least common multiple of the denominators, which is 6:
6(2/3x + 8) = 6(1/2x + 10)
4x + 48 = 3x + 60
Next, we can isolate the x term on one side of the equation by subtracting 3x from both sides:
4x - 3x + 48 = 60
Simplifying this gives:
x + 48 = 60
Finally, we can isolate x by subtracting 48 from both sides:
x = 60 - 48 = 12
Therefore, x = 12.
1- What is the connection between exponential function and geometric sequence.
Exponential functions and geometric sequences are closely related, as the terms in a geometric sequence can be expressed using an exponential function.
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant called the common ratio. For example, a geometric sequence starting with 2 and with a common ratio of 3 would be: 2, 6, 18, 54, 162, ...
The general formula for a geometric sequence is:
a_n = a_1 * r^(n-1)Where:
a_n is the nth term of the sequence.a_1 is the first term of the sequence.r is the common ratio.n is the number of terms.Exponential functions have the general form:
f(x) = a * b^xWhere:
a is a constant.b is the base.x is the exponent.If we take the formula for a geometric sequence and rewrite it as an exponential function, we get:
a_n = a_1 * r^(n-1) = a_1 * (1 + (r-1))^(n-1)Using the binomial expansion formula, we can simplify this to:
a_n = a_1 * (1 + (r-1))^(n-1) = a_1 * (1 + (r-1)*(n-1))This is an exponential function with base (1 + (r-1)) and exponent (n-1). Therefore, the terms of a geometric sequence can be expressed using an exponential function.
Conversely, if we have an exponential function of the form f(x) = a * b^x, then we can find a geometric sequence by evaluating the function for a range of values of x. For example, if we take f(x) = 2 * 3^x and evaluate it for x = 1, 2, 3, 4, we get the geometric sequence 6, 18, 54, 162.
~ Zeph
please help thank you very much people
Answer:
The exponential model that represents the population y of the city t years after 2014 is y = 471,000 * 1.04^t.
The estimated population in 2020 is about 591,000.
A park is in the shape of a right triangle with an area of 294 yd². The shortest side of the park (one of the legs) is 21 yds. The city council would like to add a path along the longest side of the park (the hypotenuse). How long would the path be?
So the length of the path along the longest side of the park would be 35 yds.
Why a triangle exists.The three sides of a triangle, a three-sided polygon in geometry, are made up of three edges and three vertices. A triangle's most important property is that its internal angles can all be added up to 180 degrees.
The area of a right triangle is given by the formula A = (1/2) * b * h, where b and h are the lengths of the legs of the triangle. Since one of the legs of the park is 21 yds and the area is 294 yd², we can solve for the length of the other leg:
A = (1/2) * b * h
294 = (1/2) * 21 * h
h = (2 * 294) / 21
h = 28
So the length of the other leg of the triangle is 28 yds.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that the sum of the squares of the legs of a right triangle is equal to the square of the length of the hypotenuse:
c² = a² + b²
Plugging in the values we have, we get:
c² = 21² + 28²
c² = 441 + 784
c² = 1225
c = 35
So the length of the path along the longest side of the park would be 35 yds.
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A bicycle store costs $4200 per month to operate. The store pays an average of $55 per bike. The average selling price of each bicycle is $195. How many bicycles must the store sell each month to break even?
The store must sell 30 bicycles each month to break even.
To break even, the total revenue from selling bicycles must be equal to the total cost of operating the store. Let's calculate the revenue and cost of the store for selling x bicycles in a month.
Revenue from selling x bicycles = selling price per bike × number of bikes sold
= $195x
Cost of operating the store = fixed cost + variable cost
= $4200 + (cost per bike × number of bikes sold)
= $4200 + ($55x)
To break even, the revenue must equal the cost. So we can set up the linear equation equation:
$195x = $4200 + $55x
Solving for x, we get:
$140x = $4200
x = $4200 / $140
x = 30
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STUVWXYZ is a cuboid. M and N are the mid-points of
ST and WZ respectively.
Find angle
a SYW
b TNX
c ZMY
MN= 17.09 cm
NMV =16.31°
What is a Cuboid?A cuboid is a six-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube." A cuboid is similar to a cube in that a cuboid can become a cube by varying the lengths of the edges or the angles between the faces.
From the given image,
MV = 1/2 VS = 6cm (midpoint)
NV = 1/2YV = 5cm (midpoint)
MV = [tex]\sqrt{MV^2 + UV^2} = \sqrt{6^2 + 16^2}[/tex] = 17.09 cm
MN= [tex]\sqrt{MV^2 + MU^2} = \sqrt{6^2 + 16^2 + 5^2}[/tex] = 17.80cm
TanNMV = NU/MV = 5/17.09
= 16.31°
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A rectangular garden measures by 21ft by 39ft . Surrounding (and bordering) the garden is a path 2ft wide. Find the area of this path.
The area of the path is 256 square feet.
What is the area of rectangle?
The area of a rectangle is given by the formula:
Area = length x width
where "length" and "width" are the dimensions of the rectangle. To find the area of a rectangle, simply multiply the length by the width.
To find the area of the path surrounding the rectangular garden, we need to subtract the area of the garden from the area of the larger rectangle that includes the path. The larger rectangle measures 25 feet by 43 feet.
Area of the larger rectangle = 25 ft * 43 ft = 1075 sq ft
Area of the garden = 21 ft * 39 ft = 819 sq ft
So, the area of the path surrounding the garden is:
Area of the larger rectangle - Area of the garden = 1075 sq ft - 819 sq ft = 256 sq ft
Hence, the area of the path is 256 square feet.
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How do you calculate simple savings
The simple savings can be calculated using the interest formula. This is given as Interest = P (principal)× R (interest rate)×T (period).
An interest-bearing savings account without the usual minimum balance requirements is used by clients in a simple savings account. The formula used to calculate simple savings is given,
[tex]\text{Interest on savings account} = \text{daily balance} \times \text{rate of interest}\times\frac{\text{no. of days}}{365}[/tex]. And the simple interest is calculated by the following formula,
[tex]\text{Interest} = \mathrm{P (principal)\times R (interest\;rate)\times T (time\;period)}[/tex].
Imagine that you had a savings account with $20,000 and 3% interest paid annually. The interest rate is 0.03, so the formula would be as follows: Interest = $20,000 x 0.03 x 1 = $600. So the value is $600.
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find the measure of the missing angles
Answer:
b = 50°
c = 130°
Step-by-step explanation:
B
Vertical angles are congruent (have the same measurement)
C
Adjacent angles ae supplemental (add to 180°)
Answer:
b = 50°
c = 130°
Step-by-step explanation:
1. Sketch the solid of rotation formed by rotating the given two-dimensional figure
using the horizontal line shown as an axis of rotation.
The image of the transformation is added as an attachment
How to determine the image of the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we can see that
The horizontal line is the axis of rotation
Using the above as a guide, we have the following:
The image of the transformation would be a reflection of the original figure on the other axis
See attachment for the image of the transformation
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There are 9 chocolate bars in a bag of Halloween candy. The bag is dropped and 5 of the chocolate bars break. You take one random chocolate bar out, eat it and take another out. What is the probability that neither of these were broken?
Answer:
Below
Step-by-step explanation:
4 out of 9 are not broken first bar not broken chance is then 4/9
now there are 8 bars left and 3 are not broken so for the second bar thee is a 3/8 chance of not being broken
4/9 * 3/8 = 12/72 = 1/6
Answer:
it's below because
Step-by-step explanation:
1/6 !!!!!!!!!!!!!!
An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.P(High- quality oil) = 0.3P(medium - quality oil)=0.4P (no oil)= 0.3What is the probability of finding oil (to 1 decimal)?
The probability of finding oil (to 1 decimal) is 0.7.
How are probabilities defined?Probability is a statistic that is used to show the possibility or chance that a certain event will occur. Probabilities can be expressed as fractions from 0 to 1, in contrast to percentages from 0% to 100%. The four main types of probability that mathematicians study are axiomatic, classic, empirical, and subjective. Given that the terms potential and probability are interchangeable, you could define probability as the probability that a particular event will take place.
To determine probability the Preliminary geologic , we obtain,
P(oil)=0.3+0.4
P(oil)=0.7.
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What is the measure of arc a d b? 107° 146° 253° 287°
The measure of the arc ADB is 253 degrees. This means that the correct option is option C.
In the given diagram, we can clearly see that -
Using the rules of symmetry, we can conclude that,
∠AOD = ∠BOC
and similarly,
∠AOB = ∠DOC
Also since we know that -
∠AOD+∠DOC=180°
We can write - 2∠AOD+2∠DOC=360°
In the question here, it is given that the angle ∠AOD=73°
So, using the value of the angle AOD, we can calculate that -
= 2(73°) + 2∠DOC=360°
= 146° + 2∠DOC=360°
= 2∠DOC=360°-146°
= 2∠DOC=214°
= ∠DOC=107°
And
∠ADB=2∠A0D+∠DOC
=∠ADB=146°+107°
=∠ADB=253°
Hence, option C is the correct option.
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Answer: the answer is C 253°
Step-by-step explanation: see below.