The general antiderivative is; (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C
Given,
f (x) = x/8 + 1/8x + (1/8)ˣ
We have to find the antiderivative;
Antiderivative;-
In calculus, a differentiable perform F whose spinoff is sufficient to the initial perform f could be an antiderivative, inverse derivative, primitive perform, primitive integral, or integral of a perform f. Symbolically, this could be expressed as F' = f.
Here,
To find antiderivative, we have to integrate the function first;
Then,
∫ f(x) + g(x) dx = ∫ f(x) dx + g(x) dx
∫ f(x/8) dx = x² / 16
∫ f(1/8 x) dx = 1/8 ln |x|
∫ f(1/8ˣ) dx = -1/ (3 ln × 2 × 8ˣ)
That is,
∫ x/8 + 1/8x + 1/8ˣ dx = (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C
Therefore,
(x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C will be the antiderivative.
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a right triangle's height is 5 times the length of its base. if the area of the triangle is 160, what is its height?
If a right triangle's height is 5 times the length of its base and the area of the triangle is 160, then the height of the triangle is 40 units
A right triangle's height is 5 times the length of its base
Consider the length of the base as b and the height as h
h = 5b
The area of the triangle = 160 square units
The area of the triangle = 1/2 × b × h
Where b is the base of the triangle
h is the height of the triangle
Substitute the values in the equation
1/2 × b × h = 160
1/2 × b × 5b = 160
1/2 ×5b^2 = 160
5b^2 = 320
b^2 = 320/5
b^2 = 64
b = [tex]\sqrt{64}[/tex]
b = 8 units
Then the height of the triangle h = 5b
= 5 × 8
= 40 units
Therefore, the height of the triangle is 40 units
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louisa walks from her school 40 feet south and then walks 100 feet east. what is the shortest distsnce louisa is from her school? round to the nearest tenth
The shortest distance Louisa is from her school is 107.7 feet
How to determine the shortest distance from her school?From the question, we have the following parameters that can be used in our computation:
East = 100 feet
South = 40 feet
The shortest distance from her school is calculated using the following theorem
Shortest distance = √(East² + South²)
Substitute the known values
Shortest distance = √(100² + 40²)
Evaluate
Shortest distance = 107.7
Hence, the shortest distance = 107.7 feet
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The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 59.1. O b. 7.688. O C. 7.018. O d. 49.25.
The point estimate of the population standard deviation is Select one is 5.4558.
Given data
9,13,15,15,21,24
We have to find first mean
Here n=6
[tex]$\begin{aligned} \text { mean } \bar{x} & =\frac{\sum x_i}{n} \\ & =\frac{9+13+15+15+21+24}{6} \\ & =\frac{97}{6} \\ & =16.166\end{aligned}$[/tex]
[tex]$\therefore$[/tex] Standard deviation
[tex]S=\sqrt{\frac{\sum\left(x_i-x\right)^2}{n-1}}$$[/tex]
S= root (9-16.(66)^2+(13-16.166)^2+(15-16.166)^2+(15-16.166)^2+(21-16.166)^2+(25- 16.166)^2/(6-1)
[tex]\begin{aligned}& =\sqrt{\frac{148.833336}{5}} \\& =\sqrt{29.7666} \\& =5.4558\end{aligned}[/tex]
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Answer:
Step-by-step explanation:
b) 7.688 The point estimate of the population standard deviation is 7.688. The point estimate of a population parameter is the estimate of the population parameter based on a single sample. In this case, the point estimate of the population standard deviation is the sample standard deviation, which is a measure of the spread or variability of the sample data. To calculate the sample standard deviation, we need to first calculate the sample mean, which is the average of the values in the sample. In this case, the sample mean is (9 + 13 + 15 + 15 + 21 + 24)/6 = 14.5. We can then use this value to calculate the sample standard deviation, which is √(((9-14.5)² + (13-14.5)² + (15-14.5)² + (15-14.5)² + (21-14.5)² + (24-14.5)²)/6) = 7.688. This is the point estimate of the population standard deviation. The other answer choices are not the sample standard deviation.
An arithmetic sequence has a 2nd term of -2 and a 7th term of 18.
1. What is the 10th term in the sequence? 2. Write an explicit formula for the sequence.
3. Write a recursive formula for the sequence.
4. What is the sum of the first 10 terms?
Answer:
Step-by-step explanation:
The figure is made up of a cone and a cylinder.
To the nearest whole number, what is the volume of this figure?
Use 3.14 to approximate π . Round only your final answer to the nearest whole number.
Enter your answer in the box.
The volume of the composite shape is 38mm³(nearest whole number)
What is a composite solid?A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.
The volume of a the composite solid above = volume of cone + volume of cylinder
volume of cone = 1/3πr²h
=1/3×3.14×2²×3
= 12.56mm³
volume of the cylinder = πr²h
= 3.14×2²×2
= 25.12mm³
therefore the volume of the shape = 12.56+25.12
= 37.68mm³
= 38mm³( nearest whole number)
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Is 700% of 6 less than 10,greater than 10 but less than 100,or greater than 100?
Greater than 100. 700% of 6 is 42.
What is the correct way to do 2x+24+x=150
Answer:
Step-by-step explanation:
for this one you need to solve for x and x=42
Answer:
Step-by-step explanation:
Divide both sides by 2. Divide 24 by 2 to get 12.
There are three methods used to solve systems of equations: graphing, substitution, and elimination.
Use the elimination method to get rid of one of the variables.
Find the value of one variable.
Find the value of the remaining variables using substitution.
Clearly state the final answer.
Check your answer by substituting both values into either of the original equations.
Without graphing or plugging in any values, enter a point that lies on y – 5 = 2(x + 9).
For the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that, the equation of the line is
y – 5 = 2(x + 9)
Compare the equation with the standard equation as
y-y₁=m(x-x₁)
y – 5 = 2(x + 9).
y-5=2(x-(-9)
Where x₁ and y₁ are the points on which the line lies.
Thus, for the given equation, y – 5 = 2(x + 9) the line passes through (5,-9).
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PLS ACTUALLY ANSWER BOTH REASONS !!!!! 100 PTS CHOICES ARE THE SAME FOR BOTH
The blanks in this two-column proof should be completed (filled) as follows:
Statements Reasons_______________
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
What is the Right Triangles Similarity Theorem?In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.
What is CPCTC?In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.
Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.
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Answer:
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
Step-by-step explanation:
or what the guy said on top :D
In triangle def, m∠d = (2x 19)°, m∠e = (3x 24)°, and m∠f = 87°. determine the degree measure of the exterior angle to ∠d. 54° 39° 141° 126°
Each corner of a triangle can form an exterior angle of the triangle by extending one side of the triangle. As we can see in above picture, where 'w' is exterior angle of angle 'z'.
The measure of the exterior angle to ∠d is 126°. So, the correct option is option (D).
We have given that,
A ∆DEF such that m∠d = (2x + 19)°,
m∠e = (3x + 24)°, and m∠f = 87°.
we have to find out the degree measure of the exterior angle to ∠d.
As we know that sum of angles of triangle is equal to 180° .
so, m∠d + m∠e + m∠f = 180°
=> (3x + 24)° + (2x + 19)° + 87° = 180°
=> (5x + 24 + 19 + 87)° = 180°
=> 5x + 130° = 180°
=> 5x = 50°
=> x = 10°
plug this value in angle d , angle e we get ,
m∠d = (3 ×10 + 24 )° = 54°
We can see that adding the angle measurement d and the exterior angle measurement gives d = 180 degrees. This is because they are a pair of adjacent angles and both lie on a straight line.
measure of Exterior angle of ∠d + measure of ∠d = 180°
Measure of exterior angle of ∠d
= 180° - m∠d
= 180° - 54° = 126°
Hence, the measure of exterior angle of d is 126°.
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A CBS News/New York Times poll found that 329 out of 763 randomly selected adults said they would travel to outer space in their lifetime, given the chance. Estimate the true proportion of adults who would like to travel to outer space with 88% accuracy. Round your answers to at least three decimal places.
The true proportion of adults is in the interval 0.4026< P< 0.4594.
Here we have to estimate the true population of adults who would like to travel to outer space with 88% accuracy.
Data provided:
selected (x) = 329
Total(n) = 763
Sample proportion (p') = x/n
= 329/ 763
= 0.431
Critical z-value = 1.59
margin of error(E) = z[tex]\sqrt{p'( 1-p')/n}[/tex]
= 1.59 [tex]\sqrt{0.431(1-0.431) / 763}[/tex]
= 1.59 × 0.0179
= 0.0284
88% confidence interval is:
(p' ± E) = ( 0.431 ± 0.0284)
= 0.4594 and 0.4026
Therefore the estimate is 0.4026< P< 0.4594.
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Write an equation for the nth term of the arithmetic seqeuence. Then find a10. 12,1,112,2,.
An equation for the nth term of the arithmetic sequence: an = n - 6.
ad 10th term a10 = 4.
Define the term arithmetic sequence?A sequence of a form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.A common difference of the sequence is d, and the number an is the first term.The formula for the nth term of the
an = a + (n -1)d
In which,
a = initial termd = common differencen = total number of termsThe arithmetic sequence is given as-
−5,−4,−3,−2, ...
Then, the equation will be
d = a2 - a1
d = -4 - (-5) = 1
an = a + (n -1)d
an = -5 + n - 1
Put n = 10 in the equation.
a10 = 10 - 6
a10 = 4
Thus, the 10th term of the sequence is 4.
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The correct question is-
Write an equation for the nth term of the arithmetic sequence. Then find a10.
−5,−4,−3,−2, ...
a business major needs 3 humanities courses to graduate. they can be selected from 29 courses offered. how many ways can the 3 courses be selected?
The number of ways 3 courses can be selected is 3654.
How to calculate combination?
The sequence of the results is irrelevant when calculating the overall outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n denotes the total number of items and r denotes the number of things being chosen at a time.The sum of all positive integers that are greater than zero and less than your number is known as a factorial. An exclamation point is written after the number to represent a factorial.Total no. of courses available = 29
Courses needed to graduate = 3
No of ways these courses can be selected:
= ²⁹C₃
= 29!/ [(29-3)! - 3!]
= 29! / 26! 3!
= 29 * 28 * 27 * 26!/ 26! 3*2
= 29* 14* 9
=3654
So, the number of ways 3 courses can be selected is 3654.
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I am a number with 3 tens and 23 ones. What number am I
Answer:
Is it 53?
Step-by-step explanation:
3 tens means 30, and adding 23 ones would be 53
12 is 30% of what number?
Answer: 3.6
Step-by-step explanation:
Step 1: 30/100 = x/12
Step 2: Multiply 12x30 and then divide it by 100
Factor each polynomial
Answer:
(x + 7)(x² - 8)
Step-by-step explanation:
x³ + 7x² - 8x - 56 =
let's put the total multiplier x² out of brackets
x²(x + 7) - 8x - 56 =
let's put the total multiplier -8 out of brackets
x²(x + 7) - 8(x + 7) =
let's put the total multiplier (x + 7) out of brackets
(x + 7)(x² - 8)
PLS HELP!!! I really need help!
Use substitution to solve the system.
5x + 4y = 9
-2x + y = -14
Answer:
x=9/5 − 4y/5
x = 7 + y/2
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
21 out of 300 equals what percent
Answer:
7%
Step-by-step explanation:
When trying to figure out percentages, we can try to use a proportional relationship. Percent means out of a hundred, and since we don't know the percentage on top, we can mark it as ?.
21/300 = ?/100
To figure this out quickly, we can try figuring out how many times we need to multiply or divide to get to the next number. Between 21 and ?, we can't do anything because we are unsure of what ? is.
Between 300 and 100, we can notice that to get to 100, we must divide by 3. 300/3 = 100
This means that the first ratio is three times the amount of the second ratio, which means that the second ratio is 1/3 of the first.
We can multiply 21 by 1/3 (or divide by 3), which will get us to 7.
7/100 = 0.07 = 7%
help w this, dont guess
please
help I will give brainly
The distance AC to be covered for the given triangle will be 429.94 meters.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given triangle,
By cosine law,
Cos∠ABC = (220² + 430² - AC²)/(2 × 220 × 430)
Cos∠ABC = (233300 - AC²)/189200
Cos(180° - 75°) = (233300 - AC²)/189200
(233300 - AC²) = -48968.56
AC² = 184331.4367
AC = 429.94 meter
Hence "The distance AC to be covered for the given triangle will be 429.94 meters".
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Calculate the social security and Medicare deductions for the following employee assume a tax rate of 6.2% on $128,400 for social security and 1.45% for Medicare. Logan has a cumulative earnings before this pay period was $128,300 , and pay amount this period was$3,000. What is the social security and what was the medicare
The social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
What is arithmetic?
Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots
Main body:
Cumulative Earnings before this pay period = $128,300
pay amount this period = $3000
tax rate of 6.2% on social security = 6.2%
effective earning = 128300 = 3000
= 125300
social security deduction = 6.2 % of 125300
⇒ 6.2 *125300 /100
⇒$7768
Medicare deductions = 1.45%
⇒ 1.45*125300/100
⇒$1816
Hence , the social security and Medicare deductions for the following employee are $7768 and $1816 respectively.
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mary lee's natural food store sells a combination of teas. the most popular is a mixture of a tea that sells for per pound with one that sells for per pound. if she needs of tea that will sell for per pound, how many pounds of each tea should she use?
She may thus combine 21 pounds of tea priced at $3 and 14 pounds of tea priced at $2 to create tea that costs $2.6 per pound.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
Let 3x be the pounds of tea for $3 and 2x be the pounds of tea for $2.
Total required pounds=35
3x+2x=35
x=35/5
x=7
So, She can add 21 pounds of tea for $3 and 14 pounds of tea for $2 to make the tea that is $2.6 per pound.
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The hypotenuse of a right triangle measures 15 cm and one of its legs measures 1 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
The value of the other leg of the right angled triangle is found as 4√14 cm.
Explain the term Pythagorean theorem?In a right-angled triangle, every square of a hypotenuse side is equal to total sum of the squares of the remaining two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.For the given question, the values for the right angled triangle are-
Hypotenuse (H) - 15 cm
Side (B) = 1 cm
Let the other side be (P).
Then,
H² = P² + B²
P² = H² - B²
Put the values-
P² = 15² - 1²
P² = 225 - 1
P² = 224
P = 4√14
Thus, the value of the other leg of the right angled triangle is found as 4√14 cm.
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urgent help needed the question is written in the image below plss
#1= 36
#2=81
#3= 32
#4=125
The diameter, d, of the circle below is 77 cm.
What is the circumference of the circle?
Give your answer to 1 d.p.
77 cm
circumference = nd
Answer:
C ≈ 241.9 cm
Step-by-step explanation:
the circumference (C) of the circle is calculated as
C = πd ( d is the diameter )
here d = 77 , then
C = π × 77 ≈ 241.9 cm ( to 1 dec. point )
in order to calculate the correlation between two variables related to the same sample what do you need to calculate first?
In order to calculate the correlation between two variables related to the same sample you need to calculate first the mean of each variable.
Before determining the correlation, the covariance of the two variables in the issue must always be computed. The standard deviation of each variable is then needed. The correlation analysis is calculated by dividing the covariance even by combination of a standard deviations of two or more variables.
A correlation is a statistical measurement of the two-variable connection. The measure works best with parameters that have a linear connection with one another.
The degree of the relationship between two variables is examined using correlation. To get the correlation between two variables, divided the covariance value by the standard deviation of both variables. Correlation analysis for two variables in the same sample should be performed. If you run a survey with two factors, a responder should be able to answer both variables at a glance. Furthermore, other participants' replies to the parameter might be evaluated for a correlation test.
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A researcher is interested in whether using your finger to follow the words you are reading changes reading speed. He has students complete a reading speed test, first without using their fingers to follow the words and then again while using their fingers to follow the words. The researcher randomly selects a sample of 56 students who, at the beginning of the study, scored an average of 256 words per minute on the reading speed test. In the trial where they used their fingers while they read, the students scored an average of 6 words per minute higher. The standard deviation of the difference scores was 29. Since the sample size is larger than 30, the researcher can assume that the sampling distribution of MD is normal. He uses a repeated-measures t test to test that the mean difference is zero, and he describes the results as follows: In the trial where they used their fingers while they read, the reading speed among students is not significantly different than when they do not use their fingers while they read, t(55) = 1.55, p = 0.127. If the researcher had used a repeated-measures ANOVA to test that the mean reading speed is the same before and after using their fingers while they read, he would describe the results as follows (fill in all missing values): In the trial where they used their fingers while they read, the reading speed among students is different than when they do not use their fingers while they read, F()=, p = 0.127.
The confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
On Subtracting 1 from your sample size, we get
150 – 1 = 149.
On Subtracting confidence level from 1, and then divide by two.
(1 – .95) / 2 = 0.025
Now, df = 149 and α = 0.025
from the table at df = 149 we got 2.262.
Divide your sample standard deviation by the square root of your sample size.
28 / √(150) = 2.28
Now, 2.262 × 2.28 = 5.17
So, the confidence interval be,
(150 - 5.17 , 150 + 5.17) = (144.83 , 155.17)
Hence, the confidence interval for the given ANOVA test to calculate the average typing speed be, (144.83 , 155.17) and the margin of error of the poll be, ±5.17
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what
Expand 2 ( c − 2 )
Answer:
[tex]\boxed{\tt 2c-4}[/tex]
Step-by-step explanation:
[tex]\tt 2\left(c-2\right)[/tex]
Apply the distributive property:-
[tex]\tt 2\left(c-2\right)=2c-2\times \:2[/tex]
[tex]\bf 2\times\:2=4[/tex]
[tex]\tt 2c-4[/tex]
___________________
Hope this helps!
Have a great day!
does someone mind helping me with this question? Thank you!
Answer:
50,000
Step-by-step explanation:
1,750 x 2 = 3,500
25,000 x 2 = 50,000
Drag the tiles to the correct boxes to complete the pairs.
The correct boxes to the complete pairs are,
12 - 1/2r → (-8 - r) + (2r - 4)
r - 13/6 → (7r - 3/2) - (2/3 + 6r)
13r + 20 → (6r + 7) + (13 + 7r)
-12 + r → (-8 - r) + (2r - 4)
What is simplified expression?
Writing a similar expression devoid of similar terms is what is meant by the expression "simplify." In other words, we will rewrite the expression using the fewest number of terms.
Consider, the given expressions
(1) (6r + 7) + (13 + 7r)
Simplifying this,
6r + 7 + 13 + 7r
13r + 20
(2) (13 - 3/2r) - (1 - r)
Simplifying this,
13 - 3/2r - 1 + r
12 - 1/2r
(3) (-8 - r) + (2r - 4)
Simplifying this,
-8 - r + 2r - 4
-12 + r
(4) (7r - 3/2) - (2/3 + 6r)
Simplifying this,
7r - 3/2 - 2/3 - 6r
r - 13/6
Hence, the correct boxes to the complete pairs are,
12 - 1/2r → (-8 - r) + (2r - 4)
r - 13/6 → (7r - 3/2) - (2/3 + 6r)
13r + 20 → (6r + 7) + (13 + 7r)
-12 + r → (-8 - r) + (2r - 4)
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Complete question:
Complete question is attached below,