Step-by-step explanation:
The indefinite integral of the polynomial function (x^4 + 2x^3 + 3x^2 + 4x + 5) is:
∫(x^4 + 2x^3 + 3x^2 + 4x + 5)dx = (x^5)/5 + x^4 + (3/2)x^2 + (2/3)x^3 + 5x + C
where C is an arbitrary constant of integration.
Answer:
Step-by-step explanation:
exponents and powers
find n
(2²n)4x(2^n)2=2^16-1
The value of "n" is approximately 2.6666667.
What is exponent ?Exponent is a mathematical operation that represents repeated multiplication of the same number.
We can start by simplifying the left side of the equation:
(2^(2n))^4 * (2^n)^2 = 2^16 - 1
Using the exponent rules:
a^m * a^n = a^(m + n)
We can simplify the left side of the equation further:
2^(4n + 2n) = 2^16 - 1
Combining the exponents:
2^(6n) = 2^16 - 1
Now we can use the fact that if a^m = a^n, then m = n to solve for "n":
6n = 16
Dividing both sides by 6:
n = 16/6 = 8/3
Therefore, The value of "n" is approximately 2.6666667.
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Lesley's fruit salad contains 40% grapes. Which figure represents 40%?
A. A hundred grid with five columns of ten squares shaded
B. A hundred grid with four columns of seven squares shaded
C. A hundred grid with three columns of ten squares shaded
D. A hundred grid with four columns of ten squares shaded
Answer:
The answer is D
Step-by-step explanation:
Percentages can be represented in Hundred Grid. It is a 10*10 grid that helps solves problems like yours.
In your case, it says 'Which figure represents 40% ?'
This means that you must shade 4 whole columns.
Because number 1, Each row or column contains 10 squares which can also represent 10%. And if you were to shade 2 rows or columns that would mean it is 20%.
So to sum it up:4 whole columns = 40% out of 100
So a hundred grid with 4 columns of ten square shaded should be your answer.
I'm always happy to help!
If −8x+6y=4 is a true equation, what would be the value of −8x+6y+6?
the value of the algebraic equation −8x+6y+6 will be 10.
What is algebraic Expression?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 +.
Given, −8x+6y=4 is a true equation
To find the value of the equation −8x+6y+6
=> −8x+6y+6
Since −8x+6y = 4 given
Thus,
=> 4 + 6
=> 10
Therefore, the value of the algebraic equation −8x+6y+6 will be 10.
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Caleb is comparing the growth of plants using two different fertilizers Use the measurement of the center from the box plots to make an inference about the data
Part A:
Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.
Part B:
The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.
What is the box-and-whisker plot?A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.
Given:
Caleb is comparing the growth of plants using two different fertilizers.
The box-and-whisker plot is given.
From the diagram, we can clearly see that the median of A is less than the median of B.
Part A:
Based on the medians, the plants in Group A grew less on average, as compared to the plants in Group B.
Part B:
The range and IQR are greater in Group B as compared to Group A, so there is less variability in the growth of plants in Group B.
Therefore, the blanked words are given above.
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In a group of 50 students, 20 like only Maths and 15 like only Science. If the number of students who do not like any of the two subjects is double of the number of students who like both subjects, find the number of students who like at most one subject by using a Venn-diagram.
To solve this problem using a Venn diagram, we need to start by drawing a rectangle to represent the group of 50 students, and then draw two overlapping circles to represent the subjects of Math and Science. Let's label the regions of the Venn diagram as follows:
M: Students who like MathS: Students who like ScienceMS: Students who like both Math and ScienceNeither: Students who like neither Math nor ScienceWe know that 20 students like only Math, 15 students like only Science, and the number of students who like both subjects is unknown. We also know that the number of students who like neither subject is double the number of students who like both subjects. Let's use this information to fill in the Venn diagram:
The number of students who like at least one subject is the sum of the students who like only Math, the students who like only Science, and the students who like both subjects: 20 + 15 + MS.The number of students who like neither subject is double the number of students who like both subjects: 2MS.We can set up an equation using this information:
20 + 15 + MS + 2MS = 50
Simplifying this equation, we get:
3MS = 15
MS = 5
Now we can fill in the Venn diagram:
M MS
\ /
\/
/ \
S----MS
We know that MS = 5, so the number of students who like at most one subject is:
20 (like only Math) + 15 (like only Science) + MS (like both subjects) = 20 + 15 + 5 = 40.
Therefore, 40 students in the group of 50 like at most one subject.
Trevor pet goat weighed 6 3/8 pounds when it was born. By age 3, the goat weighed 8 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Trevor goat at age 3. 8 3/8 8 3 6 3/8 + x are the symbols
The weight of Trevor's goat will be 51 pounds at age 3.
We can use the following equation to calculate the weight of Trevor's goat at age 3,
Weight at age 3 = 6 3/8 × 8
First, we require to convert 6 3/8 to an improper fraction, so we multiply 6 by 8 to get 48 and then add the numerator 3 to get 51. So, 6 3/8 can be composed as 51/8.
Next, we multiply 51/8 by 8 to calculate the weight at age 3,
51/8 × 8 = 408/8 = 51
Therefore, the weight of Trevor's goat will be 51 pounds at age 3.
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--The given question is incomplete; the complete question is
"Trevor's pet goat weighed 6 3/8 pounds when it was born. By age 3, the goat weighed 8 times as much. Fill each box with a number or symbol from the list to show how to find the weight of Trevor's goat at age 3."--
geometry, please help.
Answer:
MN ≈ 92.1
Step-by-step explanation:
given the figures are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{MN}{IJ}[/tex] = [tex]\frac{KL}{GH}[/tex] ( substitute values )
[tex]\frac{MN}{21}[/tex] = [tex]\frac{57}{13}[/tex] ( cross- multiply )
13 MN = 21 × 57 = 1197 ( divide both sides by 13 )
MN ≈ 92.1 ( to the nearest tenth )
Please solve both questions 6 and 7
Answer:
6. 4x + 28 + x + 19 + 3x + 13
x = 15
7. x + 123 + 113 + 97 + 90 = 540
x = 117
Step-by-step explanation:
6. 4x + 28 + x + 19 + 3x + 13 = 180
8x + 60 = 180
8x = 120
x = 15
7. x + 123 + 113 + 97 + 90 = 540
x + 423 = 540
x = 117
Consider APQR in the figure below.
The perpendicular bisectors of its sides are SV, TV, and UV. They meet at a single point V.
(In other words, V is the circumcenter of APQR.)
Suppose UV=30, PS= 64, and RV=78.
Find PU, PR, and QV.
Note that the figure is not drawn to scale.
The given values are below:
PU = 72PR = 128QV = 78How to get the valuesNote that point V is the intersection of the three perpendicular bisectors of a triangle which is also the center of the subtriangle circumference
So QV = RV = PV = 78
Point S is the midpoint of PR
So PR = 2,
PS = 2 x 64 = 128.
Because triangle QUV is a right triangle,
QV = 78.
UV= 30
QV^2 + UV^2 = QV^2
Therefore, PU = 72
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a woman making $2500 per month has her salary reduced by 10% because of sluggish sales. one year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. find her salary after the raise. g
After the raise, the salary of woman becomes $2700.
Salary Reduction and RaiseThe answer was determined through simple arithmetic calculations.
First, the initial salary of $2500 was reduced by 10%, which is calculated as $2500 * 0.1 = $250.So the new salary after the reduction was $2500 - $250 = $2250.Next, a 20% raise was given over the reduced salary of $2250, which is calculated as $2250 * 0.2 = $450.Finally, the raise was added to the reduced salary, resulting in $2250 + $450 = $2700.So, the woman's salary after the raise is $2700.This method of calculation can be applied to any similar scenario where an initial salary is reduced by a certain percentage and then increased by another percentage. The formula used can be generalized as:
Final Salary = (Initial Salary - Initial Salary * Reduction Percentage) * (1 + Raise Percentage)
It's a simple and straightforward method that can be easily applied to find the final salary in similar cases.
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Can someone help me with this and find the amount budgeted
Answer:
Step-by-step explanation:
ok so it is 100 amount budgeted i calculated all of them dont be mad if i did it wrong i am really bad at math and here is a calmng photo to calm you and elp you think
[tex]\sqrt{x}[/tex]largest possible of x and smallest possible value of x
Answer:
A.) 16
B.) 18
Step-by-step explanation:
Mode is the number that shows up the most. For A.) they are saying the mode is 1. We see that for 1, the corresponding number is 17. Since no number can go larger than 17, that means x must be 16.
For B.) they are saying the mode is 2. the corresponding number is X. they want the smallest value possible, so what we do if find the largest number, which is 17, and simply add one
the high level of airline ticket sales that travel agencies experience during summer is an example of what component of a time series? a. long-term trend b. cyclical variation in. seasonal variation d. random variation
The high level of airline ticket sales that travel agencies experience during summer is an example of (option C.)Seasonal component of a time series.
A time series is a set of observations collected over a period of time, and it can be decomposed into various components, including trend, cyclical, seasonal, and random variation.
The trend component represents the overall pattern of the time series, such as an upward or downward trend. The cyclical component represents the repeating patterns that are not related to the regular seasons or calendar years. The seasonal component represents the regular variations that occur at specific times of the year, such as the summer months in this example. The random variation represents the unpredictable fluctuations in the time series.
Since the high level of airline ticket sales during summer is a regular variation that occurs every year at the same time, it is an example of the Seasonal component of a time series.
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Complete question:
The high level of airline ticket sales that travel agencies experience during summer is an example ofwhich component of a time series?
A.Trend.
B.Cyclical.
C.Seasonal.
D.Random variation
how many lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed? choose all that apply.
The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.
What is combination?In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.
here, we have,
Given data:
{1 ,2, 3 ,4, 5}
Formula for combinations is used since the order does not matter and repetition is allowed.
nCr = (n + r -1) /(r! * (n-1)!)
where n is the total number of items and r is the items to be picked
now, we get,
5C3 = (5 + 3 - 1)! /(3! * (5 -1)!
5C3 = 7!/(3! *4!) Simplifying the factorials)
5C3 = 5040/(6*24)
5C3 =5040/144
5C3 = 35
Hence, The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.
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what is 60/40 simplified
Answer:
3/2
Step-by-step explanation:
You can divide the numerator and denominator by its GCF(Greatest common factor) which in this case is 20.
60/ 20 = 3
40/20 = 2
3/2
An ancient Chinese problem: "A pool of water is 10 feet across, and in the middle of it stood a reed which
projected one foot above the water. When the wind blows the reed over, the top just reached to the edge of
the pool. How deep is the water?" Illustrate and solve. Show all work!
According to the question, the depth of the water is 11 feet.
What is the depth ?The depth of something refers to how deep or far down it goes. It can refer to physical measurements such as the depth of a lake or ocean or the depth of a hole, or to metaphorical measurements such as the depth of knowledge or the depth of emotions. In terms of physical measurements, depth is usually referred to in terms of length or distance.
Let x be the depth of the water
The reed is 11 feet tall (10 feet in the water + 1 foot above the water)
The circumference of the pool is 10π feet
The volume of water in the pool = (circumference x depth) = 10πx
The volume of the reed = (area of base x height) = π(5²) x 11 = 275π
The total volume of the pool and reed = 10πx + 275π
10πx + 275π = 10π(11)
10πx = 110π
x = 11
Therefore, the depth of the water is 11 feet.
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PLEASE HELP ME PLEASE THANK YOU
PART A
Craig went bowling with $35.50 to spend. He rented the shoes for $6.50 and paid $7.25 for each game.WRITE AN EQUATION TO DETERMINE X,THE GREATEST NUMBER OF GAME CRAIG COULD HAVE PLAYED. ONLY WRITE EQUATION HERE
Equation:__________
PART B
Determine what the greatest number of games he can play is. SHOW YOUR WORK
Answer:_________Games
Answer:
A. $6.50 + $7.25x ≤ $35.50
B. 4 games
Step-by-step explanation:
x = number of games played
$6.50 + $7.25x ≤ $35.50
7.25x ≤ 35.5 - 6.50
7.25x ≤ 29
x ≤ 29/7.25
x ≤ 4
Please helpppp
graph 0.2 and its opposite
graph 9 and its opposite
Answer:
I need the answer tooo
The function f(x) = 500(1 − 0.19 )x2 models the price of a share of stock over time. Part A The price of the stock models exponential Choose... . What is the rate of exponential growth or exponential decay? % Part B Which expression is equivalent to the function f(x) = 500(1 − 0.19 )x2 ? A. f(x) = 202.5x B. f(x) = 20.1246x C. f(x) = 500(0.9)x D. f(x) = 500(1.0909)x
The function f(x) = 500(1 - 0.19)^x² is an exponentially decaying function.
The rate of decay is 0.19 or 19% and an equivalent expression to it is
f(x) = 500(0.9)^x.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f(x) = 500(1 - 0.19)^x² for the price of a share of stock.
This would be an exponentially decaying function because (1 - 0.19) is less than 1.
The rate of exponential decay is 0.19 or 19%.
An equivalent expression to the function f(x) = 500(1 - 0.19)^x² is,
f(x) = 500(0.9)^x.
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At the Hula Factory, the assembly line produces 212 leis in a batch. The leis are packaged in boxes with 30 each. If 14 batches are made in one day, how many leis will be leftover at the end of it?
Answer:
-2 leis.
Step-by-step explanation:
212 * 14 = 2,968 leis
2,968/30 = 99 boxes
99*30=2970
2968-2970=-2
There is a problem with the wording of this question. There isn't a total so it's really confusing...
Lin ran 2 3/4 miles in 2/5 of an hour.
2
Noah ran 8 2/3 miles in 4/3
of an hour.
c) How far would Noah run in 1 hour?
Answer:The distance cover by Noah in 1 hour to cover distance is 6.5 miles
Step-by-step explanation:
A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts
that are more than 2 standard deviations from the mean. The quality-control engineer
knows that the bolts coming off the assembly line have mean length of 12 cm with a
standard deviation of 0.10 cm. For what lengths will a bolt be destroyed?
The lengths that the bolt will be destroyed are given as follows:
Less than 11.8 cm.More than 12.2 cm.How to obtain the lengths?The lengths are obtained applying the proportions in the context of this problem.
Considering the mean length of 12 cm, and the standard deviation of 0.1 cm, the length that is 2 standard deviations below the mean is given as follows:
12 - 2 x 0.1 = 11.8 cm.
The length that is 2 standard deviations above the mean is given as follows:
12 + 2 x 0.1 = 12.2 cm.
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Sales of the smart phone continued to grow exponentially beyond 2011.
In 2010, approximately 39.99 million smartphones of this brand were sold worldwide.
In 2011, approximately 72.9 million smartphones of this brand were sold worldwide.
In which year did the number of smartphones the brand sold exceed 200 million?
Answer: This question can be solved using exponential growth formula:
N = N0 * e^(rt)
Where N is the number of smartphones, N0 is the initial number, r is the growth rate, t is the number of years and e is the base of the natural logarithm (approximately equal to 2.718).
First, we need to find the growth rate:
r = (ln(N/N0)) / t
Using the data from 2010 and 2011:
r = (ln(72.9/39.99)) / 1
Next, we can find the year when the number of smartphones sold exceed 200 million:
N = 200 million
N0 = 39.99 million
t = (ln(N/N0)) / r
t = (ln(200/39.99)) / r
To find the year, we need to add t to the initial year 2010.
The number of smartphones the brand sold exceeded 200 million in the year 2023.
Step-by-step explanation:
if 3x-9=6 whats the value of x
Answer:
the value of x is 5
Step-by-step explanation:
3x=6+9
3x=15
x=5
Need help please thank you
The numeric values of the graphed function at x = 1 and x = 3 are given as follows:
f(1) = 0.7.f(3) = 0.4.How to obtain the numeric values?Tracing a vertical line through the coordinate x = 1, we have that the line would cross the graph at approximately y = 0.7, hence the numeric value is estimated as follows:
f(1) = 0.7.
Following the same procedure through x = 3, the line would cross the graph at approximately y = 0.4, hence the numeric value is estimated as follows:
f(3) = 0.4.
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To evaluate 8^2/3 find
To evaluate [tex]8^{\frac{2}{3} }[/tex] first find the square of 8 and then take the cube root.
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Depending on the powers they possess, many rules of exponents are given.
Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.
The given value can be written as:
[tex]8^{\frac{2}{3} } = \sqrt[3]{8^{2} }[/tex]
Hence, to evaluate [tex]8^{\frac{2}{3} }[/tex] first find the square of 8 and then take the cube root.
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Please help thank you
Answer:
∠ A = 138° , ∠ C = 75°
Step-by-step explanation:
ABCD has parallel bases and is a trapezium
each lower base angle is supplementary to the upper base angle on the same side.
∠ A + 42° = 180° ( subtract 42° from both sides )
∠ A = 138°
∠ B + ∠ C = 180 , that is
12x - 3 + 9x - 6 = 180
21x - 9 = 180 ( add 9 to both sides )
21x = 189 ( divide both sides by 21 )
x = 9
Then
∠ C = 9x - 6 = 9(9) - 6 = 81 - 6 = 75°
Which of the following is equal to the rational expression when x ≠ -2 or 3?
The simplification of the given rational expression when x is not equal to 2 or negative 3 is determined as (x + 1)/(x + 3).
What is Simplification of expression?Expressions can be made simpler by expanding any brackets, multiplying or dividing any terms, using the laws of indices if necessary, grouping like terms together by adding or subtracting, and finally rewriting the expression. The BODMAS rule states that when an expression has brackets ((),, []), we must first solve or simplify the bracket before moving on to "order" (which refers to powers and roots, etc.), followed by division, multiplication, addition, and subtraction from left to right.
The simplification of the given expression when x is not equal to 2 or negative 3 is determined as follows;
[tex]$=\frac{(x+1)(x-2)}{(x-2)(x+3)}$[/tex]
cancel "[tex]$\mathrm{x}$-2[/tex]" since it is common to numerator and denominator
[tex]$$=\frac{(x+1)}{(x+3)}$$[/tex]
Thus, the simplification of the given rational expression when [tex]$\mathrm{x}$[/tex]is not equal to 2 or negative 3 is determined as [tex]$(x+1) /(x+3)$[/tex].
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Meena owns a small business selling bagels. She knows that in the last week 35
customers paid cash, 12 customers used a debit card, and 17 customers used a credit
card.
If next week, she is expecting 700 customers, about how many would you expect to
pay with a debit card? Round your answer to the nearest whole number.
131 customers would expect to pay with a debit card out of 700 Customers.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
customers paid by cash=35
customers used a debit card = 12
customers used a credit card = 17
If she is expecting 700 customers then number of customers used Debit card will be
= 700 x 12/ (35+12+17)
= 700 x 12/64
= 131.25
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A composite figure is shown.
Which of the following represents the total area of the figure?
Answer:
16.425 in²
Step-by-step explanation:
Surface area of composite figure:Area of upper triangle:
b = 2.5 in ; h = 2.3 in
[tex]\sf \boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex]
[tex]\sf =\dfrac{1}{2}*2.5 * 2.3\\\\ =\dfrac{5.75}{2}\\\\=2.875 \ in^2[/tex]
Area of bottom triangle:
h = 5.2 - 2.3
= 2.9 in
[tex]\sf Area \ of \ bottom \ triangle = \dfrac{1}{2}*3*2.9[/tex]
= 4.35 in²
Area of rectangle:
Area of rectangle = l * w
= 4 * 2.3
= 9.2 in²
Area of composite figure = area of upper triangle + area of bottom triangle + area of rectangle
= 2.875 + 4.35 + 9.2
= 16.425 in²